The near-ultraviolet π*π absorption system of weakly bound complexes formed between tropolone (TrOH) and formic acid (FA) under cryogenic free-jet expansion conditions has been interrogated by exploiting a variety of fluorescence-based laser-spectroscopic probes, with synergistic quantum-chemical calculations built upon diverse model chemistries being enlisted to unravel the structural and dynamical properties of the pertinent ground [X̃1A] and excited [Ã1Aπ*π] electronic states. For binary TrOH ⋅ FA adducts, the presence of dual hydrogen-bond linkages gives rise to three low-lying isomers designated (in relative energy order) as INT, EXT1, and EXT2 depending on whether docking of the FA ligand to the TrOH substrate takes place internal or external to the five-membered reaction cleft of tropolone. While the symmetric double-minimum topography predicted for the INT potential surface mediates an intermolecular double proton-transfer event, the EXT1 and EXT2 structures are interconverted by an asymmetric single proton-transfer process that is TrOH-centric in nature. The ÃX̃ origin of TrOH ⋅ FA at ν̃00=27484.45cm1 is displaced by δν̃00=+466.76cm1 with respect to the analogous feature for bare tropolone and displays a hybrid type − a/b rotational contour that reflects the configuration of binding. A comprehensive analysis of vibrational landscapes supported by the optically connected X̃1A and Ã1Aπ*π manifolds, including the characteristic isotopic shifts incurred by partial deuteration of the labile TrOH and FA protons, has been performed leading to the uniform assignment of numerous intermolecular (viz., modulating hydrogen-bond linkages) and intramolecular (viz., localized on monomer subunits) degrees of freedom. The holistic interpretation of all experimental and computational findings affords compelling evidence that an external-binding motif (attributed to EXT1), rather than the thermodynamically more stable cleft-bound (INT) form, was the carrier of fluorescence signals observed during the present work.

The binding motifs engendered by hydrogen bonding and the reactive channels governed by proton transduction are ubiquitous in chemistry and kindred fields of molecular science.1 A large body of work has examined fundamental aspects of these interactions from a solitary (single-proton) perspective; however, processes mediated by the cooperative action of several hydrogen bonds play pivotal roles in diverse phenomena of importance, including the structural integrity of supermolecular complexes2 (e.g., the DNA double helix)3 as well as the recognition events responsible for their formation4 (e.g., Watson-Crick DNA base paring)3,5 and the degradation pathways leading to their destruction (e.g., DNA mutation by tautomeric shifts).6 Because the distinct hydrons engaged in multiple proton-transfer reactions couple with the restricted heavy atom motions of the nuclear framework and the large-amplitude displacements of each other, their dynamics are expected to be more intricate and varied than those of their single-proton counterparts, as highlighted by theoretical predictions of “plateau-like” potential-surface topographies that support “structureless” transition-state geometries.7 The ensuing analyses have focused on weakly bound adducts formed between formic acid (FA) and tropolone (TrOH), where the latter species is known to undergo rapid intramolecular single-proton transfer via a tunneling mechanism.8 In particular, the amphoteric (proton donating and accepting) nature of the FA ligand can produce unusual (dual) hydrogen-bonding motifs upon complexation with the dynamically active TrOH substrate, at least one of which offers the tantalizing possibility of an intermolecular double proton-transfer (DPT) channel.9 

The tropolone monomer utilized in the present work long has served as a model compound for quantitative investigation of coherent (intramolecular) single proton-transfer processes.8 Both the ground10 (X̃1A1) and the lowest-lying singlet excited11 (Ã1B2) states of this molecule support symmetric double-minimum potential surfaces in which two stable and equivalent enolic tautomers (Cs) are isolated by a barrier of finite height that defines the transition-state configuration (C2v). Although classically hindered, rapid interconversion between these degenerate species can occur by way of quantum-mechanical proton tunneling, thereby leading to a characteristic bifurcation of each rovibronic feature that reflects the attendant distribution of electron-charge density and displacement of atomic centers within the molecular framework. In particular, the tunneling-induced splitting for the vibrationless (zero-point or υ = 0) levels of the X̃1A1 and Ã1B2 manifolds has been determined to be12–14Δ0X̃=29193.7969(11)MHz (∼0.9738 cm−1) and Δ0Ã=17.869(18)cm1 – a twenty fold change in keeping with the nature of the π*π electron promotion.10,11 A variety of spectroscopic probes have documented the pronounced vibrational specificity15 and isotopic dependencies13,16 that accompany this unimolecular transformation in both the ground and excited electronic potential surfaces, thereby highlighting the multidimensional nature of the underlying reaction coordinate.

The presence of aromatic and enolic functionalities has enabled a variety of weakly bound tropolone complexes, TrOH ⋅ M, to be synthesized in situ under cryogenic molecular-beam conditions.17 Most studies have focused on the structural and dynamical consequences of such incipient “solvation” as revealed commonly by observed differences in the location, δν̃00=ν̃00TrOHMν̃00TrOH, and the splitting, Δ0=Δ0ÃΔ0X̃, of the ÃX̃ origin band. Van der Waals addends dominated by dispersion forces have been shown to produce additive red-shifts (δν̃00<0) that scale in proportion to their polarizability and are believed to bind preferentially above the seven-membered aromatic ring.17 Rare-gas atoms (M ≡ Ar,  Kr,  Xe)18,19 typically cause a modest drop in Δ0; however, ligands having anisotropic polarizabilities (M ≡ N2,19,20 CO20,21) can reduce the efficiency of hydron migration markedly, a result attributed to an increase in effective barrier opacity induced by the coupling of intramolecular and intermolecular degrees of freedom. In contrast, adducts capable of donating or accepting hydrogen bonds (M ≡ H2O,22–24 CH3OH,24 CO225,26) have been found to generate pronounced blue shifts (δν̃00>0), the extent of which can be correlated to their binding energy and proton affinity.25 Although the precise nature of these entities remains controversial even for the prototypical TrOH ⋅ H2O system,23,24 the absence of discernable tunneling-induced bifurcation (Δ0 ≈ 0) suggests quasi-planar interactions with the enolic C—OH/C=O moieties in a manner that introduces sizable asymmetries into the potential-surface topography and essentially quenches coherent reaction pathways. The ensuing analyses build upon recent theoretical predictions27 of unusual double hydrogen-bonding and proton-transfer motifs engendered by the docking of amphoteric ligands into the five-membered C—O—H⋯O = C reaction cleft, as might be envisioned for the binary complexes formed between tropolone and formic acid, TrOH ⋅ FA.

During the preparation of this manuscript, Pejlovas and coworkers28 published a brief report on the microwave spectrum recorded for binary TrOH ⋅ FA complexes. The rotational constants deduced by these authors from 25 assigned transitions suggested an internal binding motif (vide infra) commensurate with that required for DPT events; however, no evidence for dynamical (tunneling-induced) bifurcation of the vibrationless ground electronic state was observed. Pertinent details of this work have been incorporated into the ensuing discussion so as to contrast the distinct experimental and theoretical results emerging from the present study.

The experimental configuration exploited for the present work is depicted schematically in Fig. 1, with specific details for each vibronically resolved laser-induced fluorescence (LIF), dispersed-fluorescence (DF), stimulated emission pumping (SEP), and fluorescence hole-burning (FHB) measurement being included in the captions of figures. In brief, tunable visible light was generated by utilizing the second harmonic of a pulsed Nd:YAG system (20 pps repetition rate, ∼10 ns pulse duration; Spectra-Physics PRO-270-20, PRO-250-20, or GCR-4-20 where the former two were injection seeded) to pump a tunable dye laser (Lamda Physik FL3002E or ScanMate 2E, or Sirah PSCAN-D-30).29 The resulting 720–740 nm output was frequency doubled by means of a servo-locked BBO crystal (Inrad Autotracker II/III or Sirah FCU-AT) with portions of the residual fundamental being directed to a heated iodine absorption cell and a solid monitor etalon to afford absolute30 and relative wavelength metrics. After passing through a variable attenuator (Newport), the isolated ultraviolet radiation was filtered spatially and recollimated to a diameter of 3-4 mm through use of a Keplerian telescope that had a diamond pinhole mounted at its focus point. Prior to entering the sample chamber, the resulting ultraviolet beam was sampled to measure the relative shot-to-shot power for active signal normalization.

FIG. 1.

Experimental configuration. A tunable dye laser excited by the second harmonic of a pulsed Nd:YAG system was employed for laser-induced fluorescence (LIF) and dispersed-fluorescence (DF) measurements, the latter based on a 0.75 m scanning monochromator. Scattered light in the vacuum chamber was mitigated by directing the spatially filtered ultraviolet radiation through Brewster-angle windows and conical-baffle assemblies prior to intersecting the pulsed free-jet expansion of molecules 1-2 cm downstream from the nozzle orifice. A second dye/Nd:YAG apparatus was deployed for double-resonance studies built upon fluorescence hole burning (FHB) and stimulated emission pumping (SEP) techniques, with the counter-propagating beam being aligned to maximize spatial overlap in the interaction region without retracing of optical paths. Synchronous triggering of the pulsed-valve actuator and Nd:YAG lamps/Q-switches by an external delay generator ensured temporal coincidence of jet-cooled molecular complexes and interrogating ultraviolet pulses.

FIG. 1.

Experimental configuration. A tunable dye laser excited by the second harmonic of a pulsed Nd:YAG system was employed for laser-induced fluorescence (LIF) and dispersed-fluorescence (DF) measurements, the latter based on a 0.75 m scanning monochromator. Scattered light in the vacuum chamber was mitigated by directing the spatially filtered ultraviolet radiation through Brewster-angle windows and conical-baffle assemblies prior to intersecting the pulsed free-jet expansion of molecules 1-2 cm downstream from the nozzle orifice. A second dye/Nd:YAG apparatus was deployed for double-resonance studies built upon fluorescence hole burning (FHB) and stimulated emission pumping (SEP) techniques, with the counter-propagating beam being aligned to maximize spatial overlap in the interaction region without retracing of optical paths. Synchronous triggering of the pulsed-valve actuator and Nd:YAG lamps/Q-switches by an external delay generator ensured temporal coincidence of jet-cooled molecular complexes and interrogating ultraviolet pulses.

Close modal

All experiments took place in a stainless-steel vacuum vessel that was evacuated to a base pressure of <10−7 Torr through use of a liquid nitrogen-baffled diffusion pump (Varian VHS-6 with 362-6 cold trap) backed by a rotary mechanical pump (Leybold D65B). Weakly bound complexes between tropolone (TrOH) and formic acid (FA) were synthesized in situ by means of a supersonic free-jet expansion based on a current-loop-actuated pulsed valve (R. M. Jordan C-211SS) that had been modified for 20 pps operation. Requisite samples of TrOH and FA were obtained commercially (Aldrich) and used without further purification, as was the deuterium oxide (Cambridge Isotope Laboratories, 99.9 at.%) employed for isotopic studies. Each reagent was maintained in a thermally regulated high-pressure glass vessel and entrained in a separate flow of helium carrier gas so as to control their relative ratios. The resulting effluents were transported by independent runs of inert tubing and coalesced only in the flow-through chamber directly behind the nozzle orifice, thus allowing for the rapid mixing of adducts and minimizing the possibility of undesired reaction such as those leading to salt formation.

Ultraviolet radiation entered and exited the vacuum apparatus through invaginated arms of ∼0.8 m length, each of which incorporated a fused-silica window mounted at Brewster’s angle and a series of three electroformed conical baffles designed to minimize scattered light in the centermost portion of the chamber. Identical sets of f/1.0 imaging optics situated on both sides of the plane defined by intersecting molecular and laser beams were used to monitor spontaneous emission from the interaction region (1-2 cm downstream from the nozzle orifice). For LIF, FHB, and SEP experiments, the fluorescence collected by one of these lens assemblies was imaged through a rectangular aperture before impinging on the photocathode of an ambient-temperature photomultiplier tube (Hamamatsu R331). In the case of DF measurements, photons collected by the remaining optical train were relayed (by enhanced-aluminum mirrors) and focused (by fused-silica lenses) onto the entrance slit of a 0.75 m f/6.0 monochromator (Jobin-Yvon 750M with Hamamatsu R331 detector) where they were dispersed by a 2400 lines/mm diffraction grating blazed for λ = 330 nm. Typical DF scans were performed with a slit width of 100 μm yielding an effective resolution of ∼5 cm−1. Resulting photocurrents were amplified (LeCroy VV100B) and directed to a CAMAC time-gated integrator (LeCroy 2249SG with Stanford Research Systems DG535 gate generators) that allowed for the digitization and averaging of fluorescence signals, as well as the simultaneous recording of frequency and power metrics. All data-acquisition and laser-/monochromator-scanning tasks were performed by a dedicated personal computer running a custom LabView™ software package. The pump-probe delay times employed for FHB studies were adjusted to maximize isomer-labeling signals and to minimize detector-saturation effects (from pump scattering), usually leading to values of 150-300 ns. The limited lifetime of the TrOH ⋅ FA excited state demanded short (<10 ns) pump-dump delays for SEP measurements, with the discrimination of desired fluorescence-depletion patterns being facilitated by use of the monochromator as a broadband spectral filter.

Theoretical predictions of potential-surface topographies, molecular-complex geometries, and relative isomer energies relied on methods implemented in the public31 (G09 rev. D.01) and developmental32 (GDV rev. H27) versions of the Gaussian quantum-chemical suite. This included approaches built upon the Hatree-Fock (HF), density functional theory33 (DFT, with B3LYP,34 CAM-B3LYP,35 and M06-2X36 hybrid correlation-exchange models), and coupled-cluster37 (CCSD, with singles and doubles excitation) frameworks, as well as their excited-state analogs of configuration-interaction singles (CIS),38 time-dependent DFT39 (TD-DFT), and equation of motion CCSD40 (EOM-CCSD). The ensuing analyses have selected Dunning’s double-ζ (cc-pVDZ ≡ pVDZ) and triple-ζ (cc-pVTZ ≡ pVTZ) correlation-consistent basis sets41 as a reasonable compromise between computational accuracy and expense, with augmentation by diffuse functions (aug-cc-pVDZ ≡ apVDZ and aug-cc-pVTZ ≡ apVTZ) allowing for reliable description of electronically excited manifolds. All computations utilized pruned numerical integration grids of ultrafine quality (99 radial shells each containing 590 angular points) and structural refinements employed very-tight convergence criteria that led to residual root-mean-square (rms) forces of <10−6 hartree/bohr. Counterpoise-corrected (cp) calculations were performed on the ground state to account for basis-set superposition error (BSSE);42,43 however, such effects became negligible in the saturated limit of large bases. The PyVib2 (v2.0DEV)44 program was used to project vibrational force fields between isomeric forms and electronic states, and the visualization of quantum-chemical results exploited the GaussView (V5.0.9),45 Avogadro (v1.10),46 and CYLview (v1.0b561)47 packages.

Quantum-chemical analyses performed on the ground electronic state (X̃1A) of binary complexes formed between TrOH and FA have identified three low-lying isomers, all of which have equilibrium (EQ) configurations of planar (PL) Cs symmetry. Pertinent energy metrics and structural parameters have been compiled in Table I for both wavefunction-based (HF/apVTZ and CCSD/apVDZ) and DFT-based (B3LYP/apVTZ and M06-2X/apVTZ) methods, with findings obtained from smaller basis sets, other functionals (viz., CAM-B3LYP which gave results between those of B3LYP and M06-2X), and counterpoise-corrected calculations being relegated to the supplementary material. As shown in Fig. 2, each TrOH ⋅ FA species is dominated by dual hydrogen-bonding interactions involving the ketonic oxygen (O3) and hydroxylic proton (H2) of the FA ligand; however, the precise nature of coupling to the TrOH framework differs markedly. The internal (INT) conformation has FA docked directly into the TrOH reaction cleft by enlisting its ketonic oxygen (O1) as a hydrogen-bond acceptor (HBA) and its phenolic proton (H3) as a hydrogen-bond donor (HBD).48 In contrast, the forms designated as external-1 (EXT1) and external-2 (EXT2) rely on neighboring hydrogen atoms of the aromatic ring (H1 or H4) as proton donors, with either the ketonic (O1) or phenolic (O2) oxygen center serving as a proton acceptor. Differential (external) binding motifs of similar character have been reported by Thut et al.49 for the binary adducts created between amphoteric FA and 7-hydroxyquinoline, where the quinolic nitrogen atom was found to act as a HBA (N⋯H—O—C) while two proximate C—H moieties competed as distinct HBD sites (C—H⋯O=C). The competitive formation of cyclic substrate-ligand structures with dual hydrogen-bond linkages (rather than concatenated species) also has been implicated in the binary and higher-order complexes of FA with phenol.50 

TABLE I.

Ab Initio predictions for the ground electronic states of TrOH ⋅ FA complexes. Model chemistries based upon wavefunction and density functional methods were exploited to predict ground-state [X̃1A] relative energies (ΔEX̃) and their zero-point corrected counterparts (ΔEX̃) for the binary adducts of TrOH and FA, with optimized structural parameters for hydrogen-bond linkages (viz., donor/acceptor bond distances and intra-/inter-molecular bond angles) being tabulated.48 Also reported are the barrier heights (ΔEptX̃ and ΔEptX̃) and imaginary normal-mode frequencies (νrxX̃) for the intermolecular DPT reaction in the INT isomer, as well as for the intramolecular single proton-transfer process that interconverts EXT1 and EXT2. Counterpoise-corrected binding energies, ΔEbindX̃TrOHFA, were calculated by accounting for the deformation energy, ΔEdefX̃η, where η = TrOH or FA, sustained by each monomer subunit.

HF/apVTZB3LYP/apVTZM06-2X/apVTZCCSD/apVDZ
INTEXT1EXT2INTEXT1EXT2INTEXT1EXT2INTEXTEXT2
Energy metrics (cm−1ΔEX̃ 161.8 1075.7 77.3 1499.7 491.4 1813.7 52.8 1009.2 
 ΔEX̃ 201.7 1080.7 151.7 1484.7 502.4 1796.2 110.7 1005.2 
 ΔEptX̃ 7707.1 5708.6 3073.8 2587.7 2945.6 2726.2 4951.6 3552.4 
 ΔEptX̃ 6280.9 4687.8 1524.3 1724.9 1413.0 1890.6 3389.3 2666.5 
 ν̃rxX̃ 545.4i 1859.2i 1079.2i 1247.0i 1131.5i 1343.6i 1156.7i 1147.9i 
 ΔEbindX̃TrOHFA 2899.3 2758.0 1852.1 3602.9 3546.8 2133.4 4422.6 3949.8 2634.4 3291.3 3314.6 2402.3 
 ΔEdefX̃TrOH 392.5 73.2 57.6 1087.0 105.7 82.7 770.8 120.5 87.4 482.2 78.2 58.4 
 ΔEdefX̃FA 107.8 126.7 53.2 277.8 302.0 95.0 229.5 277.3 91.7 114.5 159.9 68.0 
Structural metrics (Å or deg) rHBDX̃ 2.043 2.478 2.499 1.835 2.289 2.355 1.832 2.230 2.273 1.912 2.251 2.283 
 rHBAX̃ 1.826 1.848 1.983 1.655 1.699 1.854 1.679 1.692 1.842 1.743 1.754 1.863 
 rO1H3X̃ 2.125 1.951 1.913 2.166 1.823 1.745 2.119 1.862 1.794 2.129 1.887 1.838 
 rO1O2X̃ 2.591 2.523 2.509 2.630 2.490 2.458 2.599 2.500 2.473 2.635 2.534 2.514 
 θC1O2H3X̃ 113.4 108.0 107.0 114.1 104.2 102.5 113.5 105.4 103.9 111.6 104.7 103.7 
 θO2H3O1X̃ 108.6 116.6 118.3 107.0 122.0 125.2 108.1 120.1 122.9 110.3 120.9 123.0 
 θHBDX̃ 151.0 162.3 165.7 148.8 165.7 165.2 149.3 165.0 166.6 146.6 167.3 166.2 
 θHBAX̃ 171.4 172.4 172.7 166.2 170.1 172.5 171.5 170.8 172.9 168.3 171.5 169.3 
HF/apVTZB3LYP/apVTZM06-2X/apVTZCCSD/apVDZ
INTEXT1EXT2INTEXT1EXT2INTEXT1EXT2INTEXTEXT2
Energy metrics (cm−1ΔEX̃ 161.8 1075.7 77.3 1499.7 491.4 1813.7 52.8 1009.2 
 ΔEX̃ 201.7 1080.7 151.7 1484.7 502.4 1796.2 110.7 1005.2 
 ΔEptX̃ 7707.1 5708.6 3073.8 2587.7 2945.6 2726.2 4951.6 3552.4 
 ΔEptX̃ 6280.9 4687.8 1524.3 1724.9 1413.0 1890.6 3389.3 2666.5 
 ν̃rxX̃ 545.4i 1859.2i 1079.2i 1247.0i 1131.5i 1343.6i 1156.7i 1147.9i 
 ΔEbindX̃TrOHFA 2899.3 2758.0 1852.1 3602.9 3546.8 2133.4 4422.6 3949.8 2634.4 3291.3 3314.6 2402.3 
 ΔEdefX̃TrOH 392.5 73.2 57.6 1087.0 105.7 82.7 770.8 120.5 87.4 482.2 78.2 58.4 
 ΔEdefX̃FA 107.8 126.7 53.2 277.8 302.0 95.0 229.5 277.3 91.7 114.5 159.9 68.0 
Structural metrics (Å or deg) rHBDX̃ 2.043 2.478 2.499 1.835 2.289 2.355 1.832 2.230 2.273 1.912 2.251 2.283 
 rHBAX̃ 1.826 1.848 1.983 1.655 1.699 1.854 1.679 1.692 1.842 1.743 1.754 1.863 
 rO1H3X̃ 2.125 1.951 1.913 2.166 1.823 1.745 2.119 1.862 1.794 2.129 1.887 1.838 
 rO1O2X̃ 2.591 2.523 2.509 2.630 2.490 2.458 2.599 2.500 2.473 2.635 2.534 2.514 
 θC1O2H3X̃ 113.4 108.0 107.0 114.1 104.2 102.5 113.5 105.4 103.9 111.6 104.7 103.7 
 θO2H3O1X̃ 108.6 116.6 118.3 107.0 122.0 125.2 108.1 120.1 122.9 110.3 120.9 123.0 
 θHBDX̃ 151.0 162.3 165.7 148.8 165.7 165.2 149.3 165.0 166.6 146.6 167.3 166.2 
 θHBAX̃ 171.4 172.4 172.7 166.2 170.1 172.5 171.5 170.8 172.9 168.3 171.5 169.3 
FIG. 2.

Binding motifs for binary TrOH ⋅ FA adducts. The planar (Cs) ground-state geometries predicted by coupled-cluster theory for the low-lying binary adducts of tropolone and formic acid are shown, with the inertial axis system and π*π transition electric dipole-moment vector superimposed on each structure. The formation of dual hydrogen bonds leads to three distinct binding motifs where the FA ligand either docks into the reaction cleft of TrOH (INT) or adjoins it through ring-mediated interactions involving ketonic (EXT1) or hydroxylic (EXT2) oxygen atoms. The labels used to distinguish atomic centers are displayed along with the hydrogen-bond donor (HBD) and acceptor (HBA) linkages.48 

FIG. 2.

Binding motifs for binary TrOH ⋅ FA adducts. The planar (Cs) ground-state geometries predicted by coupled-cluster theory for the low-lying binary adducts of tropolone and formic acid are shown, with the inertial axis system and π*π transition electric dipole-moment vector superimposed on each structure. The formation of dual hydrogen bonds leads to three distinct binding motifs where the FA ligand either docks into the reaction cleft of TrOH (INT) or adjoins it through ring-mediated interactions involving ketonic (EXT1) or hydroxylic (EXT2) oxygen atoms. The labels used to distinguish atomic centers are displayed along with the hydrogen-bond donor (HBD) and acceptor (HBA) linkages.48 

Close modal

The disparate consequences of TrOH ⋅ FA complexation are embodied in the tropolone-centric distances and angles listed in Table I, which must be compared to analogous quantities computed for the bare TrOH substrate (cf. the supplementary material). While exterior binding alters the reaction site only slightly, interior binding causes a notable increase in the O⋯O donor-acceptor separation (ΔrO1O2X̃0.1Å) and a significant elongation of the intramolecular hydrogen bond (ΔrO1H3X̃0.25Å), as well as strong angular distortions of the five-membered ring (ΔθC1–O2–H3X̃=+7.4° and ΔθO2–H3O1X̃=11.5°). Such geometry changes are consistent with the suppression of solitary (intramolecular) proton-transfer dynamics in favor of newly formed (intermolecular) DPT channels. The intermolecular hydrogen-bond donor (θHBDX̃) and acceptor (θHBAX̃) angles resulting from complex formation also are reported in Table I. In general, these quantities tend to approach values of 180° with increasing strength of interaction, as shown by the heterodimers and homodimers of carboxylic acids51 where donating and accepting moieties are found to adopt nearly collinear configurations.

All of the model chemistries in Table I concur in predicting the INT isomer to be the global minimum-energy configuration for the ground electronic state of TrOH ⋅ FA, ΔEX̃=0 (by definition), with full geometry optimizations performed at the potent CCSD/apVDZ level of theory suggesting EXT1 and EXT2 to be less stable by 52.8 cm−1 and 1009.2 cm−1, respectively. Corrections applied for the vibrational zero-point-energy (ZPE ≡ ε) computed from harmonic force fields, ΔEX̃=ΔEX̃+ΔεX̃, retain this energy ordering and increase the gap between the lowest-lying INT and EXT1 species by as much as a factor of two. Estimates of relative free energies, ΔGX̃, computed by the composite G3,52 G4,52 and CBS-APNO53 schemes at both cryogenic (0 K) and ambient (300 K) temperatures (cf. supplementary material) parallel the trends obtained from coupled-cluster analyses. These results collectively afford strong theoretical evidence that INT is the thermodynamically preferred conformation of the binary TrOH ⋅ FA adduct and cast doubt on existence of the EXT2 structure under cold molecular-beam conditions.

The INT complex is of particular interest owing to the presence of an intermolecular DPT coordinate that takes the form of a symmetric double-minimum potential surface as shown in Fig. 3(a). The transition state (TS) for this process uniformly is predicted to be of aplanar (APL) C2 symmetry and to support a lone imaginary frequency (ν̃rxX̃) of 1156.7 cm−1 magnitude. Computed barrier heights (ΔEptX̃) and their ZPE-corrected counterparts (ΔEptX̃) are substantially higher than those reported for the single-proton-transfer pathway of bare TrOH,10 with CCSD/apVDZ analyses suggesting complexation to increase ΔEptX̃ and ΔEptX̃ by 48.9% and 38.3%, respectively. Given the significant heavy atom motion required to pass between the TS and EQ configurations, such energy metrics would imply tunneling within the ground electronic manifold of INT to be inefficient and the attendant bifurcation of rovibrational features (e.g., Δ0X̃) to be vanishingly small. As highlighted in Fig. 3(b), the EXT1 and EXT2 adducts are linked by an intramolecular (TrOH-centric) single-proton-transfer event whereby atom H3 shuttles between oxygen centers O1 and O2 via a planar (Cs) transition-state geometry having ν̃rxX̃i1340cm1. The highly asymmetric potential topography and sizable reaction impediment (ΔEptX̃3552.4cm1 and ΔEptX̃2666.5cm1) that mediate this transformation preclude coherent quantum-mechanical tunneling processes while the “cold” molecular-beam conditions employed for the present studies would tend to discount classical “above-the-barrier” dynamics.

Although quantum-chemical analyses uniformly predict the INT isomer to be the most stable form of the binary TrOH ⋅ FA adduct, the considerable structural rearrangement of TrOH and FA that must transpire upon complexation might impose kinetic impediments that dominate over purely thermodynamic considerations. Such issues can be addressed quantitatively in terms of ground-state monomer deformation energies,42 

ΔEdefX̃η=ECPLXX̃ηEEQX̃η,
(1)

which represent energy increase caused by the distortion of species η (η = TrOH or FA) from its isolated equilibrium geometry, EEQX̃η, to the equilibrium configuration of the complex, ECPLXX̃η. All of the model chemistries in Table I suggest EdefX̃TrOH values for the INT isomer to be substantially higher (by factors of 5-10) than those for EXT1 and EXT2, with the corresponding EdefX̃FA parameters showing much less variation. These results are in keeping with the pronounced distortion of the intramolecular reaction site (vide supra) incurred by docking of the FA ligand into the enolic cleft of the TrOH substrate. On the other hand, the energy penalties sustained from rearrangement of monomers in the INT configuration are offset, in part, by the formation of two strong hydrogen bonds, which display donor (HBD) and acceptor (HBA) distances of rHBDX̃=1.912Å and rHBAX̃=1.743Å that are considerably shorter than those predicted for the competing external complexes. The TrOH ⋅ FA binding energies in Table I, ΔEbindX̃TrOHFA, stem from counterpoise-corrected estimates for interaction energy of the ground state, ΔEint,cpX̃TrOHFA, as adjusted for monomer-deformation effects,42,54

ΔEbindX̃TrOHFA=ΔEint,cpX̃TrOHFA+ΔEdefX̃TrOH+ΔEdefX̃FA,
(2)

thus referencing this quantity to fully relaxed monomers at infinite separation. The resulting CCSD/apVDZ values of ΔEbindX̃TrOHFA reveal INT and EXT1 to have comparable binding energies of ∼3300 cm−1, while EXT2 is less strongly bound by roughly 30%.

FIG. 3.

Proton-transfer dynamics in ground-state TrOH ⋅ FA. Reaction pathways within the X̃1A1 ground state of the binary TrOH ⋅ FA adduct are depicted schematically based on the relative CCSD/apVDZ energies for stationary points. The symmetric double-minimum well of the INT isomer in panel (a) mediates an intermolecular DPT process where two degenerate tautomers of Cs symmetry are interconverted by way of an aplanar (C2) transition-state configuration, with the substantial barrier height calling for a tunneling-induced mechanism. The EXT1 and EXT2 forms in panel (b) are linked by an intramolecular single proton-transfer event localized in the TrOH substrate that retains planarity throughout; however, the asymmetry of the potential-surface topography severely limits the probability of tunneling.

FIG. 3.

Proton-transfer dynamics in ground-state TrOH ⋅ FA. Reaction pathways within the X̃1A1 ground state of the binary TrOH ⋅ FA adduct are depicted schematically based on the relative CCSD/apVDZ energies for stationary points. The symmetric double-minimum well of the INT isomer in panel (a) mediates an intermolecular DPT process where two degenerate tautomers of Cs symmetry are interconverted by way of an aplanar (C2) transition-state configuration, with the substantial barrier height calling for a tunneling-induced mechanism. The EXT1 and EXT2 forms in panel (b) are linked by an intramolecular single proton-transfer event localized in the TrOH substrate that retains planarity throughout; however, the asymmetry of the potential-surface topography severely limits the probability of tunneling.

Close modal

Table II presents a summary of energy metrics and structural parameters calculated for the lowest-lying singlet excited state, Ã1Aπ*π,55 of the binary TrOH ⋅ FA complex. The equilibrium geometry optimized for each isomer parallels that found for the ground state and displays ≤10% deviations (in distances and angles) for kindred hydrogen-bond linkages. The accompanying ÃX̃ transitions build on the intense Ã1B2X̃1A1 resonance of bare tropolone11 and entail π*π electron-promotion processes that are centered primarily about the seven-membered aromatic ring. The tabulated values of vertical excitation energy (vee), ΔEveeÃX̃η where η = INT, EXT1, or EXT2, follow directly from the minimum-energy configuration predicted for corresponding X̃1A species. In contrast, the evaluation of adiabatic excitation energies (aee), ΔEaeeÃX̃η, as well as their vibrational zero-point corrected counterparts, ΔEaeeÃX̃η=ΔEaeeÃX̃η+ΔεÃX̃η where ΔεÃX̃η=εÃηεX̃η, relies on the properties of fully relaxed structures determined independently for the optically connected manifolds.

TABLE II.

Ab Initio predictions for the excited electronic states of TrOH ⋅ FA complexes. Model chemistries based upon wavefunction and density functional methods were exploited to characterize the lowest-lying singlet excited state [Ã1Aπ*π] for the binary adducts of TrOH and FA. While vertical excitation energies (ΔEveeÃX̃) were evaluated at optimized ground-state geometries, their adiabatic counterparts excluding and including zero-point corrections (ΔEaeeÃX̃ and ΔEaeeÃX̃) entailed energy differences between the equilibrium configurations of the optically connected manifolds. Comparison with bare TrOH predictions allowed values of spectral shift for the ÃX̃ resonance, δν̃00,vee, δν̃00,aee, and δν̃00,aee to be estimated. Excited-state barriers to proton-transfer (ΔEptà and ΔEptÃ) and skeletal inversion (ΔEinvà and ΔEinvÃ) also are reported, as are various structural parameters for each species.48 

CIS/apVTZTD-B3LYP/apVTZTD-M06-2X/apVTZEOM-CCSD/apVDZ
INTEXT1EXT2INTEXT1EXT2INTEXT1EXT2INTEXT1EXT2
Energy and spectral metrics (cm−1ΔEveeÃX̃ 37 750.3 38 389.0 38 478.4 30 924.1 31 554.0 31 031.0 32 175.3 32 887.3 32 794.6 31 255.2 31 753.8 32 854.0 
 ΔEaeeÃX̃ 35 194.0 35 725.0 35 465.3 28 685.2 29 597.2 28 651.1 30 271.8 31 159.6 30 672.0 28 606.7 29 603.2 29 941.7 
 ΔEaeeÃX̃ 34 390.1 34 746.6 34 462.1 27 823.9 28 563.1 27 699.2 29 245.9 30 176.9 29 660.3 27 707.0 28 695.2 28 946.8 
 δν̃00,vee −277.1 361.6 451.0 146.9 776.8 253.8 −119.1 593.0 500.3 −926.5 −427.7 672.4 
 δν̃00,aee 25.4 556.4 296.7 149.5 1 061.4 115.4 −106.2 781.7 294.1 −809.7 186.8 525.3 
 δν̃00,aee 187.2 543.6 259.2 407.8 1 147.0 283.1 −127.3 803.7 287.2 −801.2 187.0 438.7 
 ΔEptà6066.1 4649.31 3604.7 989.2 1684.1 … 4765.3 1935.8 
 ΔEptà4601.2 4036.8 1674.6 890.9 243.2 … … 1084.4 
 ν̃rxà935.2ia 1775.8i 1107.4ia 1369.5i 1077.5i … … 1119.2i 
 ΔEinvà20.6 PL PL 356.3 PL PL 354.1 56.4 15.5 493.5 PL PL 
 ΔEinvà−149.7 176.9 326.3 −40.0 −37.7 … 
Structural metrics (Å & deg) rHBDà1.949 2.540 2.501 1.816 2.346 2.353 1.690 2.281 2.281 1.708 2.299 2.282 
 rHBAà1.853 1.904 2.031 1.711 1.789 1.854 1.643 1.760 1.872 1.654 1.763 1.942 
 rO1H3à2.170 1.949 1.936 2.322 1.980 1.926 2.302 1.886 1.865 2.342 1.738 1.656 
 rO1O2à2.609 2.520 2.516 2.732 2.571 2.547 2.678 2.517 2.505 2.711 2.466 2.431 
 θC1O2H3à114.4 108.2 107.4 113.4 106.3 105.1 114.2 105.6 104.9 112.4 102.6 100.7 
 θO2H3O1à106.5 116.3 117.0 104.4 116.8 118.9 101.0 119.4 120.0 100.8 126.2 129.4 
 θHBDà153.1 161.0 166.6 165.3 167.5 168.1 159.6 162.7 166.2 159.2 162.5 166.3 
 θHBAà168.8 171.3 173.2 160.2 168.4 171.4 170.2 170.4 173.0 171.7 168.7 173.0 
CIS/apVTZTD-B3LYP/apVTZTD-M06-2X/apVTZEOM-CCSD/apVDZ
INTEXT1EXT2INTEXT1EXT2INTEXT1EXT2INTEXT1EXT2
Energy and spectral metrics (cm−1ΔEveeÃX̃ 37 750.3 38 389.0 38 478.4 30 924.1 31 554.0 31 031.0 32 175.3 32 887.3 32 794.6 31 255.2 31 753.8 32 854.0 
 ΔEaeeÃX̃ 35 194.0 35 725.0 35 465.3 28 685.2 29 597.2 28 651.1 30 271.8 31 159.6 30 672.0 28 606.7 29 603.2 29 941.7 
 ΔEaeeÃX̃ 34 390.1 34 746.6 34 462.1 27 823.9 28 563.1 27 699.2 29 245.9 30 176.9 29 660.3 27 707.0 28 695.2 28 946.8 
 δν̃00,vee −277.1 361.6 451.0 146.9 776.8 253.8 −119.1 593.0 500.3 −926.5 −427.7 672.4 
 δν̃00,aee 25.4 556.4 296.7 149.5 1 061.4 115.4 −106.2 781.7 294.1 −809.7 186.8 525.3 
 δν̃00,aee 187.2 543.6 259.2 407.8 1 147.0 283.1 −127.3 803.7 287.2 −801.2 187.0 438.7 
 ΔEptà6066.1 4649.31 3604.7 989.2 1684.1 … 4765.3 1935.8 
 ΔEptà4601.2 4036.8 1674.6 890.9 243.2 … … 1084.4 
 ν̃rxà935.2ia 1775.8i 1107.4ia 1369.5i 1077.5i … … 1119.2i 
 ΔEinvà20.6 PL PL 356.3 PL PL 354.1 56.4 15.5 493.5 PL PL 
 ΔEinvà−149.7 176.9 326.3 −40.0 −37.7 … 
Structural metrics (Å & deg) rHBDà1.949 2.540 2.501 1.816 2.346 2.353 1.690 2.281 2.281 1.708 2.299 2.282 
 rHBAà1.853 1.904 2.031 1.711 1.789 1.854 1.643 1.760 1.872 1.654 1.763 1.942 
 rO1H3à2.170 1.949 1.936 2.322 1.980 1.926 2.302 1.886 1.865 2.342 1.738 1.656 
 rO1O2à2.609 2.520 2.516 2.732 2.571 2.547 2.678 2.517 2.505 2.711 2.466 2.431 
 θC1O2H3à114.4 108.2 107.4 113.4 106.3 105.1 114.2 105.6 104.9 112.4 102.6 100.7 
 θO2H3O1à106.5 116.3 117.0 104.4 116.8 118.9 101.0 119.4 120.0 100.8 126.2 129.4 
 θHBDà153.1 161.0 166.6 165.3 167.5 168.1 159.6 162.7 166.2 159.2 162.5 166.3 
 θHBAà168.8 171.3 173.2 160.2 168.4 171.4 170.2 170.4 173.0 171.7 168.7 173.0 
a

Multiple imaginary frequencies present for this transition-state configuration.

When combined with analogous quantities predicted for the bare tropolone substrate at equivalent levels of theory,11 the ÃX̃ transition parameters compiled in Table II allow the spectral shift accompanying formation of complex η to be estimated as:

δν̃00,ξη=ΔEξÃX̃ηΔEξÃX̃TrOH,
(3)

where ξ = vee or aee with the inclusion of primes in the latter case signifying correction for vibrational zero-point effects. Several trends can be gleaned from the resulting δν̃00,aeeη and δν̃00,aeeη values, which afford the most direct comparison to spectroscopic measurements of the ÃX̃ origin band. More specifically, CIS, TD-B3LYP, and TD-M06-2X analyses concur in asserting EXT1 to display a substantially larger blue shift than that of EXT2 while the INT form has either a small blue shift (δν̃00>0) or a red shift (δν̃00<0 for TD-M06-2X). In contrast, the potent EOM-CCSD level of theory predicts a substantial (∼800 cm−1) red shift for INT as well as modest (<200 cm−1) and significant (∼500 cm−1) blue shifts for EXT1 and EXT2.

Although binary TrOH ⋅ FA complexes are not expected to undergo dramatic structural rearrangements upon electronic excitation, there is a clear propensity for calculations performed on the lowest-lying singlet excited state to yield aplanar (APL) stationary points. Such assertions must be tempered by the known shortcomings inherent to each quantum-chemical scheme, with TD-DFT treatments of bare tropolone producing non-planar Ã1B2π*π equilibrium geometries that contradict experimental findings.11 As shown in Table II, the present analyses uniformly suggest an aplanar minimum-energy structure for the Ã1Aπ*π state of INT while EXT1 and EXT2 are predicted to retain planarity by all methods except TD-M06-2X (where the computed barrier to planarity is minute and readily surmounted by vibrational zero-point effects).

The excited-state aplanarity of TrOH ⋅ FA adducts can be partitioned into two categories depending on whether or not structural distortion affects the TrOH substrate. More specifically, the INT equilibrium configurations predicted by CIS, TD-M06-2X, and EOM-CCSD all entail non-planarity of the tropolone framework, as evinced by twisting of the O1—C2—C1=O2 dihedral angle (cf. Fig. 2). In contrast, the analogous stationary point obtained at the TD-B3LYP level of theory essentially retains planarity of the monomer subunits but hinges them into an out-of-plane motif of C1 symmetry. The attendant inversion coordinates take the form of symmetric double-minimum potential wells that present barriers to planarity of ΔEinvÃ=EPLÃEAPLÃ magnitude, which have been compiled in Table II along with their zero-point corrected counterparts, ΔEinvÃ. One important structural implication for this aplanarity is a rearrangement of hydrogen-bond donating and accepting centers that results in intermolecular angles (θHBDÃ and θHBAÃ) closer to those observed for the EXT1 and EXT2 isomers. The emerging landscape for the Ã1Aπ*π potential surface suggests the INT form of TrOH ⋅ FA to be quasi-rigid in nature, with hindered large-amplitude degrees of freedom for coupled inversion (ΔEinvÃ=494cm1) and proton-transfer (ΔEptÃ=4765cm1) pathways possibly leading to unique spectral signatures for the associated dynamics. Unfortunately, the significant heavy atom motion accompanying these intermolecular transformations, combined with the substantial reaction impediments imposed by high-lying transition states of differential symmetry (e.g., planar for hydron migration), would tend to discount the clear manifestation of such effects in spectroscopic experiments.

As suggested by quantum-chemical calculations, the lowest-lying fully allowed electronic transitions for small TrOH-centric complexes are expected to build upon the intense (f ≈ 0.1)11Ã1B2X̃1A1 (π*π) absorption system of bare tropolone located at ν̃00=27017.69cm1.14 Laser-induced fluorescence (LIF) spectra acquired for the initial portion of the analogous ÃX̃ resonance in jet-cooled adducts formed between TrOH and FA are depicted in Fig. 4, where the optically unsaturated profile is compared to a high-field trace that permits weaker features to be discriminated. The origin for the TrOH ⋅ FA species has been assigned to the prominent peak at ν̃00=27484.45cm1, leading to a spectral offset of δν̃00=+466.76cm1 that is the largest yet reported for a binary complex based upon the tropolone substrate. Focusing on the EOM-CCSD results in Table II, the blue direction of this complexation shift is in keeping with those estimated from adiabatic excitation energies for EXT1 and EXT2, but opposite to that predicted for INT. Although the origin band does not show evidence of dynamical bifurcation, it does exhibit an intriguing rotational contour as well as minute isotopic structures (vide infra). The strength of observed LIF signals tends to diminish progressively as the vibronic energy within the excited electronic manifold increases, essentially vanishing for displacements (from the origin) in excess of ∼750 cm−1. Franck-Condon arguments would interpret this observation as being indicative of a modest geometry change upon π*π electron promotion; however, such assertions must be tempered by possible variations in spontaneous-emission quantum yields. Indeed, the strongest LIF features of TrOH ⋅ FA dominate over those of residual tropolone, reflecting either a high efficiency of complex formation or a reduced propensity to undergo radiationless relaxation.56 Unfortunately, attempts to extract quantitative fluorescence lifetimes from temporal waveforms did not give meaningfully different values for TrOH and TrOH ⋅ FA, both of which were limited by the finite duration of the incident laser excitation pulse.

FIG. 4.

Survey of excited-state experiments. The initial portion of the ÃX̃ (π*π) absorption system is depicted for weakly bound complexes formed between tropolone and formic acid in a free-jet expansion. Laser-induced fluorescence (LIF) spectra acquired under optically unsaturated (∼3 μJ/pulse) and saturated (∼35 mJ/pulse) conditions are compared with the fluorescence hole-burning (FHB) profile obtained by tagging the origin (000) of the binary TrOH ⋅ FA adduct at ν̃00=27484.45cm1 with a temporally advanced (∼300 ns) high-power (∼35 mJ/pulse) beam while scanning a weak (∼3 μJ/pulse) probe laser to higher energies. The effective spectral resolution of ∼0.15 cm−1 allowed several excited-state vibronic progressions built upon low-frequency intermolecular and intramolecular modes to be assigned, with the subset of these features selected for dispersed fluorescence (DF) studies being identified. The prominent LIF peak at 27 779.78 cm−1 (missing from FHB trace) has been attributed to a tertiary TrOHFA2 species.

FIG. 4.

Survey of excited-state experiments. The initial portion of the ÃX̃ (π*π) absorption system is depicted for weakly bound complexes formed between tropolone and formic acid in a free-jet expansion. Laser-induced fluorescence (LIF) spectra acquired under optically unsaturated (∼3 μJ/pulse) and saturated (∼35 mJ/pulse) conditions are compared with the fluorescence hole-burning (FHB) profile obtained by tagging the origin (000) of the binary TrOH ⋅ FA adduct at ν̃00=27484.45cm1 with a temporally advanced (∼300 ns) high-power (∼35 mJ/pulse) beam while scanning a weak (∼3 μJ/pulse) probe laser to higher energies. The effective spectral resolution of ∼0.15 cm−1 allowed several excited-state vibronic progressions built upon low-frequency intermolecular and intramolecular modes to be assigned, with the subset of these features selected for dispersed fluorescence (DF) studies being identified. The prominent LIF peak at 27 779.78 cm−1 (missing from FHB trace) has been attributed to a tertiary TrOHFA2 species.

Close modal

The topmost trace in Fig. 4 highlights fluorescence hole-burning (FHB) data acquired by selectively labeling the putative TrOH ⋅ FA origin band at 27 484.45 cm−1 while scanning a much more intense and temporally advanced depletion laser over the depicted wavenumber range. As expected for a single contributing species, a one-to-one correspondence between LIF and FHB features is found throughout the low-energy region; however, the prominent LIF peak at 27 779.78 cm−1 clearly is absent from the FHB profile, as are several higher-lying resonances extending beyond a relative shift of 295 cm−1. Given the reported tendency for successive TrOH-centric adducts to produce additive spectral shifts,17,19,24,26 this interloper has been attributed to a tertiary TrOHFA2 species, an assertion corroborated by concentration-dependence studies that monitored the strength of LIF signals as the proportion of FA ligand entrained in helium carrier gas was varied systematically by changing the temperature of the liquid sample.

The ensuing analyses of electronically excited TrOH ⋅ FA will focus on LIF features that are blue-shifted from the origin band by less than Δν̃=ν̃ν̃00300cm1, all of which can be attributed (by FHB) to a single species that nominally represents a lone isomer of the binary adduct. The vibronic patterns observed throughout this region should arise primarily from low-frequency intermolecular modes of the Ã1Aπ*π potential surface, with Fig. 4 illustrating several notable progressions that have been assigned (vide infra). Extensive fluorescence-based survey scans performed over both higher (>500 cm−1 beyond the ν̃00+750cm1 LIF cutoff) and lower (≥1400 cm−1 below ν̃00) energy ranges failed to uncover other signals depending on the simultaneous entrainment of TrOH and FA in the supersonic free-jet expansion. On the other hand, population labeling of the putative TrOH ⋅ FA origin led to discernable FHB peaks that extended more than 2000 cm−1 to the blue, reflecting the ability of this double-resonance technique to detect weak resonances that are subject to rapid non-radiative relaxation processes.

Detailed analyses of rotationally resolved band contours can prove indispensible for unraveling the structural characteristics of participating ground (g) and excited (e) rovibronic levels while simultaneously elucidating properties of the optical processes that couple them. Table III contains a summary of rotational constants (A,  B,  C) estimated for the X̃1A and Ã1Aππ potential surfaces of the three low-lying binary TrOH ⋅ FA adducts, as well as associated amplitudes and components for the permanent, μgg=gμˆg and μee=eμˆe, and transition, μeg=eμˆg, electric dipole-moment vectors. These results follow from coupled-cluster levels of theory applied to the rigid minimum-energy geometries optimized for each electronic manifold, with the two values of μeg listed for a given complex reflecting ÃX̃ resonances originating from either the ground-state or excited-state equilibrium configuration. The calculated asymmetry parameters, κ=2BAC/AC, show all species to be near-prolate asymmetric tops and the vanishing inertial defects, Δ I = IcIaIb where Iξ (ξ = a,  b, or c) signifies a diagonal moment of inertia, reinforce the planar nature of predicted structures apart from that of the electronically excited INT form. The magnitudes of the X̃1A permanent electric dipole moments (μggμgg) computed for the EXT1 and EXT2 binding motifs are 5.3% and 26% smaller than that of the INT structure; however, π*π electron promotion is expected to cause the analogous Ã1A quantity (μee=μee) for EXT1 to dominate over those of INT and EXT2 by 18% and 30%, respectively.

TABLE III.

Spectroscopic parameters predicted for binary TrOH ⋅ FA complexes. Equilibrium geometries predicted by coupled-cluster theory for the ground [X̃1A] and excited [Ã1A] states of binary TrOH ⋅ FA adducts were used to estimate the rotational constants (A,  B,  and C), asymmetry parameters (κ), and inertial defects (Δ I) for the INT, EXT1, and EXT2 isomers. The inertial components (μa,  μb,  μc) and magnitude (μμ) of the permanent and transition electric dipole moments also are tabulated, where each quantity has been evaluated at the minimum-energy configuration of the pertinent electronic manifold.

X̃stateCCSD/apVDZÃ(π*π) state EOM–CCSD/apVDZ
ParameterINTEXT1EXT2INTEXT1EXT2
Inertial constants Acm1×102 7.166 5.121 5.180 6.329 5.174 5.167 
 Bcm1×102 1.537 1.693 1.644 1.747 1.658 1.620 
 Ccm1×102 1.265 1.272 1.248 1.481 1.256 1.233 
 κ −0.908 −0.781 −0.799 −0.890 −0.794 −0.803 
 ΔIamuÅ2 −92.64 
Permanent electric dipole moment μaD −4.137 −3.542 −1.645 −3.538 −4.214 −1.344 
 μbD 1.036 1.938 −2.693 0.719 1.924 −3.289 
 μcD 1.523 
 μD 4.265 4.037 3.156 3.919 4.633 3.553 
Transition electric dipole moment μaD 0.767 2.666 −1.932 0.910 2.971 −2.667 
 μbD 2.291 0.351 1.566 2.923 1.119 1.653 
 μcD −0.072 
 μD 2.416 2.666 2.487 3.062 3.175 3.138 
X̃stateCCSD/apVDZÃ(π*π) state EOM–CCSD/apVDZ
ParameterINTEXT1EXT2INTEXT1EXT2
Inertial constants Acm1×102 7.166 5.121 5.180 6.329 5.174 5.167 
 Bcm1×102 1.537 1.693 1.644 1.747 1.658 1.620 
 Ccm1×102 1.265 1.272 1.248 1.481 1.256 1.233 
 κ −0.908 −0.781 −0.799 −0.890 −0.794 −0.803 
 ΔIamuÅ2 −92.64 
Permanent electric dipole moment μaD −4.137 −3.542 −1.645 −3.538 −4.214 −1.344 
 μbD 1.036 1.938 −2.693 0.719 1.924 −3.289 
 μcD 1.523 
 μD 4.265 4.037 3.156 3.919 4.633 3.553 
Transition electric dipole moment μaD 0.767 2.666 −1.932 0.910 2.971 −2.667 
 μbD 2.291 0.351 1.566 2.923 1.119 1.653 
 μcD −0.072 
 μD 2.416 2.666 2.487 3.062 3.175 3.138 

As shown in Fig. 2, the inertial coordinate system for each binary TrOH ⋅ FA adduct has the molecular framework residing in the ab plane with the direction of the a − axis, which nominally points toward the carbon atom of the FA ligand, changing markedly. Owing to their structural similarities, EXT1 and EXT2 are predicted to support comparable rotational constants within the X̃1A and Ã1A potential surfaces (cf. Table III), while the analogous parameters for INT differ significantly. Likewise, the transition properties for the ÃX̃ resonance should be indicative of the isomer being interrogated, with the μeg vectors superimposed on Fig. 2 describing vertical excitation processes evaluated for ground-state equilibrium geometries. In keeping with the ring-centered nature of this π*π electron promotion, the INT complex is anticipated to display primarily type − b bands that would be reminiscent of those observed in the absorption system of bare TrOH. The substantial reorientation of μeg (with respect to inertial frames) for the EXT1 and EXT2 species should lead to vibronic features having a − polarized and hybrid − a/b contours, respectively. However, the μb/μa ratio of 0.132 obtained for the minimum-energy configuration of the EXT1 ground state is found to be nearly tripled when the optimized structure of the Ã1A manifold is considered, suggesting adiabatic transitions to possess a greater type − b character. In contrast, the EXT2 value of μb/μa = − 0.811 falls 23.5% in magnitude upon electronic excitation (increasing the a − axis projection) and, although the INT μb/μa = 2.988 ratio remains essentially unaltered, the non-planarity that distinguishes the corresponding excited state is expected to yield a minute type − c contribution, μc/μb = 0.025.

To facilitate TrOH ⋅ FA rotational analyses, high-quality LIF scans of the 000 band at 27 484.45 cm−1 were acquired by attenuating incident laser powers to levels that minimized perturbative broadening effects yet still provided satisfactory signal-to-noise ratios. The resulting spectrum is depicted in Fig. 5 along with various simulated profiles designed to elucidate the nature of the complex being interrogated. Tandem datasets recorded for the symmetric tunneling component of the Ã1B2X̃1A1 origin (00+0+) in bare tropolone confirmed the optically unsaturated conditions employed for these studies. Indeed, the pulse energies applied for the present TrOH ⋅ FA measurements, Epulse ≤ 6 μJ (in a collimated beam of 3-4 mm dia.), were several orders of magnitude lower than those reported for similar investigations of jet-cooled TrOH.57 

FIG. 5.

Rotational-contour analysis of TrOH ⋅ FA origin band. The optically unsaturated LIF profile acquired for the origin (000) band of jet-cooled TrOH ⋅ FA complexes (∼0.12 cm−1 laser bandwidth) is compared with simulations exploiting coupled-cluster predictions of ÃX̃ rotational constants and transition properties for the INT, EXT1, and EXT2 isomers (displaced above discrete data points), as well as with the results of a least-squares regression based upon the EXT1 structure (superimposed on discrete data points). The inset highlights features attributed to the 000 resonances of 13C isotopologs at natural abundance.

FIG. 5.

Rotational-contour analysis of TrOH ⋅ FA origin band. The optically unsaturated LIF profile acquired for the origin (000) band of jet-cooled TrOH ⋅ FA complexes (∼0.12 cm−1 laser bandwidth) is compared with simulations exploiting coupled-cluster predictions of ÃX̃ rotational constants and transition properties for the INT, EXT1, and EXT2 isomers (displaced above discrete data points), as well as with the results of a least-squares regression based upon the EXT1 structure (superimposed on discrete data points). The inset highlights features attributed to the 000 resonances of 13C isotopologs at natural abundance.

Close modal

Ensuing band-contour analyses of TrOH ⋅ FA entailed direct simulation of LIF profiles (transition frequencies and intensities) based on the energy levels and linestrengths obtained from numerical diagonalization of model Hamiltonians, Hˆ, describing the independent rovibronic structure supported by the ground and excited states. The requisite expressions for HˆυX̃ and Hˆυà (for vibronic manifolds υ″ and υ′) were adapted from those employed for prior rotational-tunneling studies of the Ã1B2X̃1A1 absorption system in tropolone14 and its monodeuterated isotopolog (TrOD).16 To account for the strongly encumbered DPT dynamics of the INT complex, parameters for tunneling-induced bifurcation, ΔυX̃ and ΔυÃ, were fixed to zero, as were quantities governing interactions between members of a tunneling doublet (viz., F,  FJ, and FK). For this isomer, rotational levels of the symmetric (antisymmetric) υ″ = 0 manifold having near-prolate quantum number Ka even:odd were given statistical weights of 36:28 (28:36), with the vanishing of Δ0X̃ and the imposed equivalence of symmetric/antisymmetric inertial constants producing spectral patterns tantamount to those of a rigid (non-tunneling) molecular framework (characterized by bpolarized0±± and apolarized0± transitions). In the case of EXT1 and EXT2, uniform (1:1) nuclear-spin statistics were presumed and tunneling processes were excluded from the calculations of eigenvalues and eigenvectors.

The three curves placed above the discrete TrOH ⋅ FA data points in Fig. 5 represent the results of spectral simulations performed for the INT, EXT1, and EXT2 binary adducts, with rotational constants and transition properties set equal to those estimated from coupled-cluster theory (cf. Table III). For this analysis, the origin was fixed at the experimental value of ν̃00=27484.45cm1, the ground-state population in the free-jet expansion was modeled by a Boltzmann distribution of temperature T = 3 K, and the Voigt lineshape applied to each calculated rovibronic line (for 0 ≤ J ≤ 60) was characterized by Gaussian and Lorentzian (half-width) parameters of ΓG = 0.075 cm−1 and ΓL = 0.001 cm−1 (in keeping with the effective experimental resolution). Even a cursory inspection of Fig. 5 shows the contours generated for the two external-binding motifs to be in much better agreement with spectroscopic findings than that obtained for their cleft-bound counterpart. The inability of the latter to reproduce the detailed structure and overall shape of the LIF profile would tend to discount INT as the complex being interrogated by the present study and perforce implicate the EXT1 or EXT2 form. The rotational patterns computed for EXT2 appear to mimic experimental results more uniformly than those of EXT1, despite the considerably lower energy predicted for the latter (cf. Table I); however, the subtle band-contour differences between these species stem primarily from a modest change in the direction of the transition dipole moment. Although quantum-chemical calculations suggest the ground-state orientations of μeg for EXT1 and EXT2 to yield a − polarized and hybrid − a/b features, respectively, these attributes are expected to become more equitable when the electronically excited Ã1A manifold is considered.

The solid curve superimposed on the LIF data in Fig. 5 highlights the results of a nonlinear least-squares regression performed on the ÃX̃ origin band of the binary TrOH ⋅ FA adduct under the assumption of an external-binding motif. For this analysis, the rotational constants of the vibrationless (υ″ = 0) manifold in the X̃1A potential surface were set equal to those generated by CCSD/apVDZ calculations of the EXT1 isomer, while their excited-state (υ′ = 0) counterparts were refined iteratively, as was the location of ν̃00, the direction of the transition dipole moment, and the Lorentzian/Gaussian contributions to the Voigt lineshape. Attempts to incorporate quartic centrifugal-distortion effects or to vary ground-state parameters simultaneously did not lead to meaningful convergence of the fitting procedure. Rather than assuming the jet-cooled population of TrOH ⋅ FA rovibrational levels to be equilibrated thermally according to temperature T, the present work exploited a pseudothermal distribution characterized by an energy dependent effective temperature, Teff,58 

Teff=T0+T1EυJτMX̃,
(4)

where EυJτMX̃ is the energy of an X̃1A eigenstate characterized by vibrational and rotational quantum numbers υ and J, with τ = KaKc and M specifying the body-fixed and space-fixed projections of (rotational) angular momentum. This ansatz follows from the energy-gap model of rotational relaxation59 and leads to fractional populations given by an extended Boltzmann form,

fυJτMX̃=eEυJτMX̃/kBTeffqTeff,
(5)

where kB is the Boltzmann constant and the partition function qTeff=υJτMeEυJτMX̃/kBTeff affords a measure of thermally accessible quantum states. While T0 can be related to the conventional temperature of a thermal distribution, a positive (negative) value of T1 delineates the population excess (deficit) that exists in the free-jet expansion for levels of high rovibrational energy.

The quality of agreement achieved between the experimental and simulated TrOH ⋅ FA band contours in Fig. 5 is deemed to be quite good, reinforcing the assertion of an external-binding motif for the interrogated species. The rotational constants extracted for the vibrationless excited state, A = 5.099(18) × 10−2, B = 1.635(27) × 10−2, and C = 1.260(14) × 10−2 cm−1 (one standard deviation uncertainty in parentheses), deviate from EOM-CCSD predictions for the EXT1 isomer by −1.44%, −1.40%, and −0.34%, respectively. The corresponding term energy of T̃0=27484.510(11)cm1 differs slightly from the measured center of the vibronic profile at ν̃00=27484.45cm1, with the latter value preferred (for consistency) in subsequent discussions of vibrational landscapes. The effective rotational temperature of the free-jet expansion, as embodied in the T0 = 3.092(76) K and T1 = 4.09(77) × 10−2 K/cm−1 parameters, is in keeping with previous studies performed in this laboratory60 and elsewhere.58 The Gaussian and Lorentzian contributions to the Voigt lineshape, ΓG = 0.104(13) cm−1 and ΓL = 0.0 cm−1 (held fixed), yield an instrumental resolution larger than the bandwidth of the excitation source, reflecting, in part, the geometry (finite acceptance angle) of fluorescence detection.

Allowing orientation of the ÃX̃ transition electric dipole moment to vary during the TrOH ⋅ FA band-contour regression led to μb/μa = 0.763(55), which suggests μeg to make an angle of 37.3° ± 2.0° with respect to the a − axis. This ratio has a magnitude commensurate with those predicted for the ground (−0.811) and excited (−0.620) states of EXT2 (cf. Table III), but deviates somewhat (by factors of 5.8 and 2.0) from the analogous metrics estimated for EXT1. While this would seem to implicate EXT2 as the carrier of fluorescence, such assertions must be tempered by the sizable energy penalties associated with its formation (956.4 and 894.5 cm−1 relative to EXT1, without and with ZPE corrections), as well as the accompanying reduction in monomer binding strength (912 cm−1 relative to EXT1). Least-squares analyses based upon an EXT2 (rather than EXT1) ansatz led to a nearly indistinguishable simulation profile that gave very similar spectroscopic parameters. In contrast, attempts to model the LIF data quantitatively by assuming the INT structure demanded significant contributions from c − polarized features that only could be realized by directing μeg normal to the planar molecular framework. Similar unphysical consequences were obtained by trying to incorporate the effects of axis switching.60 

The weak structure appearing on the blue wing of the prominent TrOH ⋅ FA origin band in Fig. 5 (cf. expanded view in inset) has been attributed to the analogous 000 resonances of monosubstituted 13C − isotopologs at natural abundance. These features were included in least-squares simulations by inserting “cloned” copies of the rotational contour for the parent (all 12C) species with adjustable heights and positions (band origins), thus assuming rovibrational energies and transition properties to be affected negligibly by modification of carbon centers. Although substitution can take place at eight sites, only five distinct isotopic peaks could be identified under present instrumental resolution. Extracted amplitudes and displacements (scaled relative to those of the parent species) have been compiled in the supplementary material, where they are compared with quantum-chemical estimates of 13C shifts for the ÃX̃ origins of the INT, EXT1, and EXT2 isomers. Even after taking into consideration the possible overlap of adjacent lines, quantitative agreement between experiment and theory is not realized for any of the binary adducts; however, the observed pattern and extent of isotopic structure seem to be reproduced best by the EXT1 or EXT2 complex.

While the TrOH ⋅ FA band contours provide strong evidence for an external-binding (nominally EXT1) motif rather than the thermodynamically more-stable INT species, the veracity of this claim must be accessed critically against other discordant factors. In particular, the recent jet-cooled microwave studies of Pejlovas et al.28 have reported a binary adduct that supports A,  B, and C constants of 2180.7186(98), 470.873 90(25), and 387.689 84(22) MHz, which deviate from the predicted INT (ground-state) parameters of Table III by −1.48%, −2.15%, and −2.14%, respectively. Nevertheless, measured rotational spectra were noted to contain numerous unidentified transitions of considerable intensity (μgg2) that could not be assigned to excited vibrational levels of the proposed structure. It is conceivable that these “interloping” features herald the presence of other TrOH ⋅ FA entities (EXT1 or EXT2) ignored by the targeted search for a DPT system undertaken by these authors. Possible reasons for the lack of discernable INT fluorescence signatures in the current study will be addressed below.

A comprehensive understanding of vibrational landscapes for the electronic manifolds participating in the TrOH ⋅ FAπ*π absorption system requires the synergistic interpretation of all available spectroscopic measurements. This task was facilitated by the results of quantum-chemical calculations, including harmonic (vibrational) force fields predicted with high levels of electron correlation, as well as by the abundance experimental and theoretical information that exists for the analogous X̃1A1 and Ã1B2π*π states of bare tropolone. Dispersed fluorescence (DF) acquired by selectively exciting isolated vibronic bands of TrOH ⋅ FA under cryogenic free-jet conditions proved to be a key ingredient for interpreting the LIF patterns encoded in Fig. 4, enabling assignments of excited-state vibrational degrees of freedom to be “bootstrapped” from their more reliable ground-state counterparts. Figure 6 displays a subset of data obtained by independently pumping (at ν̃pump) six distinct ÃX̃ resonances, with the abscissa, which specifies the displacement of observed emission features (at ν̃) from the excitation source, Δν̃=ν̃ν̃pump, reflecting the absolute vibrational term energy within the X̃1A potential surface (i.e., assuming complexes are created in their vibrationless ground state). Typical DF profiles spanned the 0Δν̃2000cm1 range and showed the progressive reduction in fluorescence intensity with increasing Δν̃ that would be expected (by Franck-Condon arguments) for a modest geometry change between the optically connected manifolds. The ability to discern monochromator signals from baseline fluctuations vanished in the vicinity of Δν̃2500cm1, thus making the spectral window containing informative O—H and C—H stretching modes inaccessible to the present studies. Consequently, the ensuing analyses will focus primarily on the Δν̃500cm1 region where the intermolecular and out-of-plane bending motions of weakly bound TrOH ⋅ FA complexes should reside.

FIG. 6.

Dispersed fluorescence spectra for binary TrOH ⋅ FA complexes. The dispersed fluorescence (DF) spectra resulting from selective excitation of seven isolated vibronic transitions in the ÃX̃ (π*π) absorption system of jet-cooled binary TrOH ⋅ FA adducts are shown on a common abscissa scale that reflects term energy in the ground potential surface. These data were acquired by tuning a modestly intense (∼1-2 mJ/pulse, ∼0.15 cm−1 bandwidth) pump beam successively to the indicated resonances (specified by displacement from the 000 band) and scanning a 0.75 m (f/6.0) grating monochromator while normalizing the spectrally resolved signal by total (undispersed) fluorescence intensity. The 100 μm slit width employed for these studies gave an effective bandwidth of ∼5 cm−1 with at least three independent scans, obtained by averaging the response evoked by 32 incident laser pulses for each 0.5 cm−1 increment in grating position, being co-added to enhance signal-to-noise ratios. In addition to the ground-state vibrational assignments appearing on each trace, the inset of panel (a) contrasts the DF profile measured for bare TrOH by exciting the symmetric origin (00+0+) of the analogous π*π electronic system under free-jet expansion conditions.

FIG. 6.

Dispersed fluorescence spectra for binary TrOH ⋅ FA complexes. The dispersed fluorescence (DF) spectra resulting from selective excitation of seven isolated vibronic transitions in the ÃX̃ (π*π) absorption system of jet-cooled binary TrOH ⋅ FA adducts are shown on a common abscissa scale that reflects term energy in the ground potential surface. These data were acquired by tuning a modestly intense (∼1-2 mJ/pulse, ∼0.15 cm−1 bandwidth) pump beam successively to the indicated resonances (specified by displacement from the 000 band) and scanning a 0.75 m (f/6.0) grating monochromator while normalizing the spectrally resolved signal by total (undispersed) fluorescence intensity. The 100 μm slit width employed for these studies gave an effective bandwidth of ∼5 cm−1 with at least three independent scans, obtained by averaging the response evoked by 32 incident laser pulses for each 0.5 cm−1 increment in grating position, being co-added to enhance signal-to-noise ratios. In addition to the ground-state vibrational assignments appearing on each trace, the inset of panel (a) contrasts the DF profile measured for bare TrOH by exciting the symmetric origin (00+0+) of the analogous π*π electronic system under free-jet expansion conditions.

Close modal

A compilation of low-frequency fundamentals measured and predicted for the ground electronic state of TrOH ⋅ FA is presented in Table IV. The listed quantum-chemical results follow from unscaled harmonic force fields computed by the CCSD/apVDZ model chemistry for the three most stable binary adducts, with the attendant normal-mode displacement coordinates illustrated in Fig. 7 accentuating the remarkable similarities in low-frequency nuclear motions among these isomers. The Cs symmetry of the X̃1A equilibrium geometries for the presumed rigid external-binding motifs leads to modes having either a′ in-plane (IP) or a″ out-of-plane (OOP) character; however, the non-rigidity conferred by active proton-transfer channels in the INT framework would permit more refined classification under the feasible (G4) subset of the encompassing complete nuclear permutation-inversion group.61 The essentially planar nature of the transition electric dipole moment responsible for the π*π electron promotion (vide supra) suggests a propensity for vibronic transitions originating from the totally symmetric (a′) vibrationless level of the ground state, as well as subsequent emission processes from the pumped electronically excited state, to involve only even quanta of a″ vibrations in combination with even or odd quanta of their a′ counterparts. As such, the a″ vibrational frequencies in Table IV stem from the corresponding overtone bands found in the DF profiles.

TABLE IV.

Ground-state vibrational modes for binary TrOH ⋅ FA complexes. Experimentally determined frequencies for low-lying fundamentals supported by the X̃1A ground state of the binary TrOH ⋅ FA adduct are compared with unscaled CCSD/apVDZ predictions of harmonic force fields for the INT, EXT1, and EXT2 isomers. Intermolecular degrees of freedom are labeled in order of increasing energy by consecutive Greek letters while tropolone-centric vibrations employ a previous numerical nomenclature,10 with the distinction being based on the projection of normal-mode displacement vectors for the complex onto those for the TrOH and FA monomers.44 The generalized descriptions of nuclear motion and accompanying symmetry designations apply to all isomeric forms.

Predicted frequency (cm−1)
Description of vibrational motionMode label (symmetry)Experimental frequency (cm−1)INTEXT1EXT2
Donor-hinge torsion αa 29.93 28.54 31.76 16.59 
Acceptor-hinge torsion βa 30.55 43.80 41.60 40.32 
TrOH/FA sheering γa 69.03 91.89 72.93 68.02 
TrOH HBD stretching δa 111.30 134.17 118.76 106.55 
TrOH ring torsion ν39a 115.29 93.59 112.73 103.26 
TrOH HBA stretching εa 166.48 178.72 166.56 144.38 
TrOH ring folding ν38a 176.87 173.85 183.14 186.08 
FA OOP wagging ζa 185.53 187.64 189.93 156.00 
OH—O breathing/ring deformation ν36a … 375.14 361.94 359.49 
Ring deformation/OH—O distortion ν35a … 336.96 373.54 380.29 
OH—O breathing/ring deformation ν33a … 445.13 442.58 445.53 
 Root-mean-square (rms) deviation 43.10 16.17 43.44 
Predicted frequency (cm−1)
Description of vibrational motionMode label (symmetry)Experimental frequency (cm−1)INTEXT1EXT2
Donor-hinge torsion αa 29.93 28.54 31.76 16.59 
Acceptor-hinge torsion βa 30.55 43.80 41.60 40.32 
TrOH/FA sheering γa 69.03 91.89 72.93 68.02 
TrOH HBD stretching δa 111.30 134.17 118.76 106.55 
TrOH ring torsion ν39a 115.29 93.59 112.73 103.26 
TrOH HBA stretching εa 166.48 178.72 166.56 144.38 
TrOH ring folding ν38a 176.87 173.85 183.14 186.08 
FA OOP wagging ζa 185.53 187.64 189.93 156.00 
OH—O breathing/ring deformation ν36a … 375.14 361.94 359.49 
Ring deformation/OH—O distortion ν35a … 336.96 373.54 380.29 
OH—O breathing/ring deformation ν33a … 445.13 442.58 445.53 
 Root-mean-square (rms) deviation 43.10 16.17 43.44 
FIG. 7.

Ground-state vibrations of binary TrOH ⋅ FA complexes. Building on CCSD/apVDZ harmonic force fields predicted for the X̃1A ground state of the binary TrOH  ⋅  FA adducts, normal-mode displacement vectors are shown for the lowest-energy vibrations of the INT, EXT1, and EXT2 isomers. The TrOH-centric modes have been designated by prior numerical-labeling conventions,10,11 while their intermolecular counterparts have been denoted in order of increasing observed (ground-state) energy by consecutive Greek letters.

FIG. 7.

Ground-state vibrations of binary TrOH ⋅ FA complexes. Building on CCSD/apVDZ harmonic force fields predicted for the X̃1A ground state of the binary TrOH  ⋅  FA adducts, normal-mode displacement vectors are shown for the lowest-energy vibrations of the INT, EXT1, and EXT2 isomers. The TrOH-centric modes have been designated by prior numerical-labeling conventions,10,11 while their intermolecular counterparts have been denoted in order of increasing observed (ground-state) energy by consecutive Greek letters.

Close modal

The vibrations of TrOH ⋅ FA can be partitioned broadly into those dominated by the intramolecular motion of a single monomer unit (TrOH or FA) and those governed mainly by intermolecular displacement of the addends. The TrOH-centric modes, which have been designated by adopting prior numerical-labeling conventions,10,11 are found in close proximity to those of bare tropolone, in keeping with the modest red or blue shifts predicted by ab initio calculations. The six (6) total intermolecular degrees of freedom for the binary adduct span the 0Δν̃500cm1 range and have been denoted in order of increasing observed (ground-state) energy by consecutive Greek letters α through ζ. The lowest-lying feature that could be attributed primarily to the FA ligand should reside outside the spectral region depicted in Fig. 6, with the reported bulk-gas value62 of 626.2 cm−1 for this O=C—O deformation expected to increase (per CCSD/apVDZ calculations) to 666.4, 678.5, and 665.9 cm−1 for INT, EXT1, and EXT2, respectively. While the ensuing discussion will highlight strategies deployed to assign the prominent fundamentals of TrOH ⋅ FA, complete tabulations of identified ground-state and excited-state levels have been included in the supplementary material along with the results of detailed frequency analyses based on quadratic Dunham-like expressions.

An overview of the ground-state vibrational landscape for TrOH ⋅ FA can be gleaned from the emission spectrum in Fig. 6(a), which was obtained by pumping the ÃX̃ origin band at ν̃00=27484.45cm1. By comparing analogous DF data acquired for bare tropolone (inset in Fig. 6(a)), the peak at Δν̃=230.58cm1 can be attributed to 2ν39, the symmetry allowed first overtone of an out-of-plane (OOP) skeletal deformation, ν̃39a, localized on the TrOH framework (cf. Fig. 7). This lowest-energy, TrOH-centric vibration exhibits a blue shift of 12.26 cm−1 (relative to tropolone) and permits all features at smaller values of Δν̃ to be attributed to intermolecular degrees of freedom, many of which are found to appear in combination with one or more quanta of ν39. Two in-plane (IP) modes that modulate the linkage of TrOH and FA adducts have been labeled as δ and γ in Fig. 6, with the bottom panel highlighting the γ10 and γ20 vibronic transitions that terminate on the fundamental and first-overtone levels of the latter displacement.

Pumping the resonance 64.46 cm−1 to the blue of the ÃX̃ origin, 000+64.46cm1, channels emission into the γ mode such that numerous ground-state overtone and combination bands in the DF trace of Fig. 6(b) embody this IP sheering motion (cf. Fig. 7). This trend is continued by excitation of 000+128.03cm1 (cf. Fig. 6(g)), where the intensity alterations exhibited by successive members of the γ progression reflect attendant variations in Franck-Condon factors. Such observations correlate the 000+64.46cm1 and 000+128.03cm1 LIF peaks to the γa degree of freedom in the Ã1A manifold, enabling them to be assigned respectively as γ01 and γ02. As shown in Tables IV and V, the extracted γ vibrational frequencies in the ground and excited states, as well as the corresponding −4.57 cm−1 shift following π*π electron promotion, are reproduced best by force fields computed for the external-binding motifs of TrOH ⋅ FA, with analogous predictions made for the INT species deviating markedly from experimental findings. Figure 6(d) demonstrates ground-state features built upon the δa intermolecular displacement to be enhanced strongly by pumping of the 000+103.53cm1 LIF band. This rocking motion between TrOH and FA subunits (cf. Fig. 7) undergoes a 7.77 cm−1 drop in fundamental frequency (from 111.30 to 103.53 cm−1) following electronic excitation, in keeping with quantum-chemical results obtained for the EXT1 and EXT2 isomers.

TABLE V.

Excited-state vibrational modes for binary TrOH ⋅ FA complexes. Experimentally determined frequencies for low-lying fundamentals supported by the Ã1A excited state of the binary TrOH ⋅ FA adduct are compared with unscaled EOM-CCSD/apVDZ predictions of harmonic force fields for the INT, EXT1, and EXT2 isomers. Values in parentheses represent changes in vibrational energy following π*π electron promotion, with assignment of intermolecular and tropolone-centric modes facilitated by projection of excited-state normal coordinates onto their ground-state counterparts.44 The generalized descriptions of nuclear motion hold true for all isomeric forms; however, the Cs symmetry designations apply only to the EXT1 and EXT2 forms since the INT framework adopts an aplanar equilibrium geometry upon electronic excitation.

Predicted frequency (cm−1)
Description of vibrational motionMode label (symmetry)Experimental frequency (cm−1)INTEXT1EXT2
Donor-hinge torsion αa 23.09 (−6.84) 28.17 (−0.37) 24.83 (−6.93) 21.48 (+4.89) 
Acceptor-hinge torsion βa 29.90 (−0.65) 40.20 (−3.60) 39.45 (−2.15) 36.59 (−3.73) 
TrOH ring torsion ν39a 47.50 (−67.79) 85.32 (−8.27) 45.99 (−66.74) 52.76 (−50.50) 
TrOH/FA sheering γa 64.46 (−4.57) 114.39 (+22.50) 70.24 (−2.69) 64.95 (−3.07) 
TrOH HBD stretching δa 103.53 (−7.77) 188.38 (+54.21) 113.23 (−5.53) 101.90 (−4.65) 
TrOH HBA stretching εa 158.43 (−8.05) 215.49 (+36.77) 166.40 (−0.16) 126.24 (−18.14) 
 Root-mean-square (rms) deviation 120.46 (100.88) 16.96 (8.61) 33.38 (23.66) 
Predicted frequency (cm−1)
Description of vibrational motionMode label (symmetry)Experimental frequency (cm−1)INTEXT1EXT2
Donor-hinge torsion αa 23.09 (−6.84) 28.17 (−0.37) 24.83 (−6.93) 21.48 (+4.89) 
Acceptor-hinge torsion βa 29.90 (−0.65) 40.20 (−3.60) 39.45 (−2.15) 36.59 (−3.73) 
TrOH ring torsion ν39a 47.50 (−67.79) 85.32 (−8.27) 45.99 (−66.74) 52.76 (−50.50) 
TrOH/FA sheering γa 64.46 (−4.57) 114.39 (+22.50) 70.24 (−2.69) 64.95 (−3.07) 
TrOH HBD stretching δa 103.53 (−7.77) 188.38 (+54.21) 113.23 (−5.53) 101.90 (−4.65) 
TrOH HBA stretching εa 158.43 (−8.05) 215.49 (+36.77) 166.40 (−0.16) 126.24 (−18.14) 
 Root-mean-square (rms) deviation 120.46 (100.88) 16.96 (8.61) 33.38 (23.66) 

Panel (e) of Fig. 6 shows DF features attributed to the aforementioned 2ν39 TrOH-centric vibration to be enhanced strongly by pumping of the LIF resonance at 000+94.99cm1. The inference that 2ν39 drops precipitously in energy from 230.58 cm−1 in the ground state to 94.99 cm−1 in the excited state parallels the behavior reported for this OOP displacement in prior studies of bare tropolone11 and reflects the floppy nature of this 1ππ manifold. Quantum-chemical calculations based on the EXT1 geometry (cf. Tables IV and V) are in near-quantitative agreement with the observed −67.79 cm−1 change in ν39a following π*π electron promotion, while kindred predictions for INT and EXT2 yield less satisfactory results of −8.27 cm−1 and −50.50 cm−1, respectively.

The remaining DF traces in Fig. 6, panels (c) and (d), stem from the excitation of two closely spaced LIF peaks that are displaced from the ÃX̃ origin by 70.49 and 77.47 cm−1. These pump lines have been assigned as 3901α01 and 3901β01 where the excited vibronic state has ν39a in combination with one quantum of an intermolecular mode, αa or βa, that describes a hinged OOP displacement of the TrOH ⋅ FA framework (cf. Fig. 7). The resulting emission spectra display nearly identical patterns that favor transitions terminating on ground-state levels involving the corresponding vibrational degree of freedom (α or β), many of which are separated from one another by ≤2 cm−1 and barely are discernable under monochromator-limited resolution (vide infra). Tables IV and V show αa to undergo a −6.84 cm−1 (−21.0%) shift upon π*π electron promotion while βa changes by only −0.65 cm−1 (−2.13%), with both observations being reproduced best by calculations based on the EXT1 structure. Careful inspection of the saturated LIF profile in Fig. 4 reveals minute features at 27 484.54 (000+23.09) and 27 514.35 cm−1 (000+29.90cm1) that have been attributed to the nominally forbidden α01 and β01 resonances – an assertion that must reflect the breakdown of canonical selection rules by higher-order interactions (e.g., vibronic coupling). Although it did not prove feasible to disperse the fluorescence generated by these weak bands, supporting evidence for this assignment can be found in their distinct rotational contours, which seem to be dominated by intense Q–branches commensurate with those expected for type–c transitions.

The double-resonance techniques of stimulated emission pumping63 (SEP) afford a viable means of interrogating closely spaced levels within the ground electronic potential surface while simultaneously mitigating restrictions imposed by small Franck-Condon factors. Unfortunately, the ability to discern SEP signatures by the venerable fluorescence-dip detection scheme64 (which relies on the competition between spontaneous and stimulated emission processes) can be compromised by short excited-state lifetimes, such as those encountered in tropolone and its weakly bound adducts. Nevertheless, Fig. 8 contrasts DF and SEP datasets acquired in tandem by selectively pumping the TrOHFAÃX̃ origin band at 27 484.45 cm−1. As expected, the DF profile is reproduced well by its SEP counterpart; however, the enhanced resolution of the latter enables the 3910α10 and 3910β10 transitions to be distinguished readily, thereby affirming the slightly different energies of 144.5 cm−1 and 146.5 cm−1 for the αν39 and βν39 vibrations of the X̃1A potential surface that were inferred from the monochromator-limited experiments of Fig. 6. An additional intermolecular mode, labeled as εa and attributed to an in-plane stretch of the TrOH hydrogen-bond acceptor linkage (cf. Fig. 7), can be seen in the SEP spectrum at 166.48 cm−1. Although the Ã1A analog of ε was not targeted by DF studies, this assignment is confirmed, in part, by isotopic-shift patterns (vide infra). Several higher-lying TrOH-centric vibrations built upon the ν̃33a/ν̃36aOH—O breathing/ring-deformation and ν̃38a ring-folding motions can be identified, as well as various combinations with the ζa OOP wagging displacement of the FA subunit; however, these designations are supported by little more than quantum-chemical calculations and must be viewed as being tentative, at best.

FIG. 8.

Stimulated emission pumping of binary TrOH ⋅ FA adducts. The stimulated emission pumping (SEP; top trace) spectrum obtained by pumping the ÃX̃ origin band (000) of jet-cooled binary TrOH ⋅ FA adducts is compared to the analogous dispersed fluorescence (DF; bottom trace) profile by using a common abscissa scale that reflects X̃1A1 vibrational term energy. To discriminate against intense LIF signals generated as the dump laser scanned over interloping TrOH vibronic resonances, desired fluorescence-depletion signatures were monitored through a “bandpass filter” implemented by tuning the 0.75 m monochromator to the vicinity of ν̃00=27484.45cm1 and increasing the entrance/exit slit widths to ∼600 μm. The light trace depicts the raw SEP data acquired by averaging the response evoked by 32 laser pulses for each 0.06 cm−1 increment of the dump frequency while the superimposed dark curve represents the results of a quadratic LOESS locally weighted regression smoothing procedure.81 The enhanced spectral resolution of SEP experiments (∼0.15 cm−1) relative to their DF counterparts (∼5 cm−1) enabled transitions terminating on closely spaced X̃1A levels to be distinguished, leading to assignment of the highlighted ground-state vibrational features.

FIG. 8.

Stimulated emission pumping of binary TrOH ⋅ FA adducts. The stimulated emission pumping (SEP; top trace) spectrum obtained by pumping the ÃX̃ origin band (000) of jet-cooled binary TrOH ⋅ FA adducts is compared to the analogous dispersed fluorescence (DF; bottom trace) profile by using a common abscissa scale that reflects X̃1A1 vibrational term energy. To discriminate against intense LIF signals generated as the dump laser scanned over interloping TrOH vibronic resonances, desired fluorescence-depletion signatures were monitored through a “bandpass filter” implemented by tuning the 0.75 m monochromator to the vicinity of ν̃00=27484.45cm1 and increasing the entrance/exit slit widths to ∼600 μm. The light trace depicts the raw SEP data acquired by averaging the response evoked by 32 laser pulses for each 0.06 cm−1 increment of the dump frequency while the superimposed dark curve represents the results of a quadratic LOESS locally weighted regression smoothing procedure.81 The enhanced spectral resolution of SEP experiments (∼0.15 cm−1) relative to their DF counterparts (∼5 cm−1) enabled transitions terminating on closely spaced X̃1A levels to be distinguished, leading to assignment of the highlighted ground-state vibrational features.

Close modal

The low-energy modes identified for the X̃1A and Ã1Aππ potential surfaces of TrOH ⋅ FA have been summarized in Tables IV and V where they are compared systematically with the predictions of harmonic force fields deduced for various equilibrium configurations. The root-mean-square (rms) deviations between experimental and theoretical frequencies for the ground (excited) states of the INT, EXT1, and EXT2 isomers are found to be 43.10 (120.46), 16.17 (16.96), and 43.44 cm−1 (33.38 cm−1), respectively, with the corresponding metrics for the shifts incurred by ππ electron promotion being 100.88, 8.61, and 23.66 cm−1. In keeping with the conclusions inferred from rotational band-contour analyses, these results show the external-binding motifs to afford a much better description for spectroscopic findings than their INT counterpart, despite the greater thermodynamic stability expected for the latter species. More specifically, the vibrational landscapes supported by the binary TrOH ⋅ FA complex appear to be reproduced most uniformly by calculations based upon the EXT1 structure.

Introduction of deuterated-water (D2O) vapor to the stagnation mixture of the free-jet expansion allows the labile protons of TrOH and FA (viz., H2 and H3) to be replaced by more massive deuterons and leads to the formation of four discrete isotopologs: the parent TrOH ⋅ FA species, the monodeuterated TrOD ⋅ FA and TrOH ⋅ FA-d analogs, and the doubly deuterated TrOD ⋅ FA-d complex. Although the Born-Oppenheimer approximation demands the electronic potential surface governing nuclear dynamics to remain unaltered upon isotopic substitution, vibrational energies and displacements will be affected by such atomic-mass changes. Indeed, microwave spectroscopy performed on tropolone13 has reported proton-transfer channels to be quenched by the exchange of 12C for 13C at specific carbon centers of the aromatic ring, a result explained by the slight lifting of degeneracy for the interconverting (vibrationless) tautomers. Similar effects can be anticipated for the binary adducts of TrOH and FA, with the implicit loss of double-minimum symmetry for TrOD ⋅ FA and TrOH ⋅ FA-d tending to preclude isotopic scrambling by any tunneling-mediated mechanism of hydron migration. As such, every ÃX̃ vibronic transition associated with the INT, EXT1, or EXT2 isomers of TrOH ⋅ FA should be fractionated into four distinct isotopically labeled features.

Upon spiking free-jet expansions of tropolone and formic acid with D2O vapor, LIF scans performed over the region of Fig. 4 (cf. supplementary material) revealed a prominent doublet of doublets pattern embracing the TrOH ⋅ FA origin at 27 484.45 cm−1. Assignment of these features was facilitated by their intensities (which should reflect the efficiency and extent of deuterium incorporation) and by the sizeable blue shift of 47.182(16) cm−1 reported for the Ã1B2X̃1A1 absorption system of TrOD.38 For the parent TrOH ⋅ FA species, Table VI contains the absolute location of the 000 resonance and the relative displacements of other cold vibronic bands (vide infra) terminating on low-lying fundamentals of the Ã1A manifold, ν01. These quantities afford a reference point for tabulating the transition shift induced by isotopic substitution, δν̃aη=ν̃aην̃aTrOHFA, where a=000orν01 and η denotes the isotopolog of interest. The largest displacement of the 000 peak stems from deuteration of TrOH to form TrOD ⋅ FA, with the resulting value of δν̃000TrODFA=+29.92cm1 being of the same sign and of similar magnitude to that observed for bare tropolone. Replacing the labile FA proton by a deuteron leads to a modest red shift of δν̃000TrOHFA -d=1.79cm1 while the weakest LIF signal is attributed to TrOD ⋅ FA-d and gives rise to δν̃000TrODFA-d=+28.21cm1. As such, the measured separation between the proximate origin bands for TrOH ⋅ FA-d and TrOH ⋅ FA (−1.79 cm−1) nearly matches that found for the analogous TrOD ⋅ FA-d and TrOD ⋅ FA features (−1.71 cm−1), in keeping with the aforementioned paired-doublet spectral profile.

TABLE VI.

Isotopic shifts for TrOH ⋅ FA vibronic transitions. Observed spectral shifts measured relative to the ÃX̃ origin (000) of the parent TrOH ⋅ FA species are tabulated for cold vibronic transitions terminating on Ã1Aπ*π fundamentals. Analogous quantities (referenced to their TrOH ⋅ FA counterparts) are reported for the deuterated TrOD ⋅ FA, TrOH ⋅ FA-d, and TrOD ⋅ FA-d isotopologs. These findings are compared with coupled-cluster predictions made for the INT, EXT1, and EXT2 isomers, with the accompany values of rms deviation (based on isotopic shifts) revealing the quality of agreement attained between theory and experiment. Since the nominally forbidden α01, β01, and 3901 resonances are not seen directly in FHB studies of isotopically substituted complexes, their positions have been inferred from the allowed α02, β02, and 3902 bands by assuming harmonic behavior.

Isotopically substituted species
BandSourceTrOH ⋅ FATrOH ⋅ FA-dTrOD ⋅ FA-dTrOD ⋅ FARMS deviation of isotopic shifts
001 Experiment 27 484.45 −1.79 28.21 29.92  
INT 27 707.00 16.14 29.33 13.20 24.54 
EXT1 28 695.20 1.28 22.49 21.21 10.86 
EXT2 28 946.81 2.49 43.75 41.25 16.68 
α01 Experiment 23.09 0.07 −0.24 −0.25  
INT 28.17 −0.04 −0.12 −0.08 0.24 
EXT1 24.83 −0.05 −0.16 −0.11 0.20 
EXT2 21.48 −0.04 −0.11 −0.07 0.25 
β01 Experiment 29.90 −0.24 −0.16 −0.12  
INT 40.20 −0.25 −0.33 −0.08 0.17 
EXT1 39.45 −0.07 −0.08 −0.01 0.22 
EXT2 36.59 −0.17 −0.26 −0.10 0.13 
3901 Experiment 47.50 0.00 −1.27 −1.27  
INT 85.32 −0.21 −0.62 −0.41 1.10 
EXT1 45.99 −0.09 −0.18 −0.09 1.61 
EXT2 52.76 0.00 −0.10 −0.10 1.66 
γ01 Experiment 64.46 −0.04 −0.34 −0.27  
INT 114.39 −0.31 −0.84 −0.53 0.62 
EXT1 70.24 −0.03 −0.33 −0.29 0.02 
EXT2 64.95 −0.06 −0.34 −0.28 0.02 
δ01 Experiment 103.53 −0.26 −0.48 −0.28  
INT 188.38 −2.43 −2.77 −0.32 3.16 
EXT1 113.23 −0.47 −0.78 −0.31 0.37 
EXT2 101.90 −0.39 −0.46 −0.08 0.24 
ε01 Experiment 158.43 −3.60 −3.10 0.41  
INT 215.49 −5.24 −5.29 −0.16 2.79 
EXT1 166.40 −3.92 −4.12 −0.19 1.23 
EXT2 126.24 −3.18 −3.19 −0.01 0.60 
Isotopically substituted species
BandSourceTrOH ⋅ FATrOH ⋅ FA-dTrOD ⋅ FA-dTrOD ⋅ FARMS deviation of isotopic shifts
001 Experiment 27 484.45 −1.79 28.21 29.92  
INT 27 707.00 16.14 29.33 13.20 24.54 
EXT1 28 695.20 1.28 22.49 21.21 10.86 
EXT2 28 946.81 2.49 43.75 41.25 16.68 
α01 Experiment 23.09 0.07 −0.24 −0.25  
INT 28.17 −0.04 −0.12 −0.08 0.24 
EXT1 24.83 −0.05 −0.16 −0.11 0.20 
EXT2 21.48 −0.04 −0.11 −0.07 0.25 
β01 Experiment 29.90 −0.24 −0.16 −0.12  
INT 40.20 −0.25 −0.33 −0.08 0.17 
EXT1 39.45 −0.07 −0.08 −0.01 0.22 
EXT2 36.59 −0.17 −0.26 −0.10 0.13 
3901 Experiment 47.50 0.00 −1.27 −1.27  
INT 85.32 −0.21 −0.62 −0.41 1.10 
EXT1 45.99 −0.09 −0.18 −0.09 1.61 
EXT2 52.76 0.00 −0.10 −0.10 1.66 
γ01 Experiment 64.46 −0.04 −0.34 −0.27  
INT 114.39 −0.31 −0.84 −0.53 0.62 
EXT1 70.24 −0.03 −0.33 −0.29 0.02 
EXT2 64.95 −0.06 −0.34 −0.28 0.02 
δ01 Experiment 103.53 −0.26 −0.48 −0.28  
INT 188.38 −2.43 −2.77 −0.32 3.16 
EXT1 113.23 −0.47 −0.78 −0.31 0.37 
EXT2 101.90 −0.39 −0.46 −0.08 0.24 
ε01 Experiment 158.43 −3.60 −3.10 0.41  
INT 215.49 −5.24 −5.29 −0.16 2.79 
EXT1 166.40 −3.92 −4.12 −0.19 1.23 
EXT2 126.24 −3.18 −3.19 −0.01 0.60 

The observed isotopic shifts of the ÃX̃ origin band can be attributed to differential changes of vibrational zero-point energies within the ground and excited electronic states. Table VI includes estimates of δν̃000η parameters for the INT, EXT1, and EXT2 isomers of TrOH ⋅ FA as deduced from the unscaled harmonic force fields predicted by CCSD/apVDZ and EOM-CCSD/apVDZ model chemistries. Although producing incorrect signs for the small isotopic shifts accompanying deuteration of FA, calculations based on the EXT1 structure tend to reproduce the measured energy ordering and spectral profile much better than their INT and EXT2 counterparts, an assertion reinforced by complied rms deviations between experiment and theory. The nearly 1:2:1 clustering pattern suggested for the 000 resonances of INT departs from the doublet of doublets (2:2) found in LIF traces; however, this chemically intuitive result is consistent with the coalescence of TrOD ⋅ FA and TrOH ⋅ FA-d origin bands that would take place in the presence of rapid intermolecular proton transfer. Likewise, the displacements predicted by substituting TrOD for TrOH in EXT2 disagree with spectroscopic findings by nearly a factor of two.

The utility of jet-cooled LIF spectra measured with D2O spiking diminished rapidly as displacement from the ÃX̃ origin increased owing, in part, to the extensive overlap of multiple isotopically fractionated transitions (cf. supplementary material). To circumvent this difficulty, FHB experiments were performed by successively labeling the isolated 000 resonance for each partially deuterated complex and scanning a second probe laser to higher energies so as to acquire vibronic profiles that segregated their independent vibrational landscapes within the Ã1A potential surface. The four datasets of interest are plotted in Fig. 9 on a common abscissa scale that has been referenced to the distinct location of 000 for individual isotopologs, thus emphasizing the dependence of excited-state features on isotopic substitution. Assignments for the most prominent peaks are noted with lines connecting vibrations that undergo appreciable changes upon deuteration. The isotopic-shift parameters estimated for cold fundamental bands, δν̃ν01η, can be found in Table VI, where they are compared with analogous quantum-chemical predictions made for the INT, EXT1, and EXT2 isomers of the binary adduct.

FIG. 9.

Isotopically sorted fluorescence hole-burning spectra. Fluorescence hole-burning (FHB) spectra for the four partially deuterated isotopologs of jet-cooled TrOH ⋅ FA are plotted on a common abscissa scale that reflects excited-state term energy. These data were acquired by successively labeling the isolated ÃX̃ origin band (000) for each species with a weak probe laser while scanning a spatially overlapped and temporally advanced pump beam of much higher power over the initial 200 cm−1 portion of the π*π absorption system. The experimental resolution of ∼0.10 cm−1 clearly demonstrates the subtle changes in vibrational landscape caused by isotopic substitution and facilitates assignment of Ã1Aπ*π vibronic levels, including the subset of such features highlighted on the bottom trace.

FIG. 9.

Isotopically sorted fluorescence hole-burning spectra. Fluorescence hole-burning (FHB) spectra for the four partially deuterated isotopologs of jet-cooled TrOH ⋅ FA are plotted on a common abscissa scale that reflects excited-state term energy. These data were acquired by successively labeling the isolated ÃX̃ origin band (000) for each species with a weak probe laser while scanning a spatially overlapped and temporally advanced pump beam of much higher power over the initial 200 cm−1 portion of the π*π absorption system. The experimental resolution of ∼0.10 cm−1 clearly demonstrates the subtle changes in vibrational landscape caused by isotopic substitution and facilitates assignment of Ã1Aπ*π vibronic levels, including the subset of such features highlighted on the bottom trace.

Close modal

Aside from reflecting the nature of TrOH ⋅ FA species responsible for fluorescence signals, the information compiled in Table VI bolsters spectroscopic assignments already made for vibronic bands of the ÃX̃ absorption system. The modest isotopic shifts estimated for the α01 and β01 resonances, which are built upon OOP intermolecular fundamentals attributed to hinged motion of donor and acceptor linkages, display rms deviations between experiment and theory that slightly favor an external-binding motif. As demonstrated by the 3901 features of TrOD ⋅ FA and TrOD ⋅ FA-d, the lowest-energy tropolone-centric vibration of the excited state, ν39a, changes substantially when the labile proton of the TrOH substrate is replaced by a more massive deuteron, with the absence of a sizeable shift upon deuteration of the FA ligand (to yield TrOH ⋅ FA-d) corroborating the intramolecular character of this mode. Quantum-chemical predictions for all three isomers severely underestimate this behavior and give somewhat finer agreement for the INT ansatz; however, the absolute frequency of ν39 in the Ã1A manifold is reproduced much better for EXT1 (cf. Table V). Conversely, the in-plane intermolecular degrees of freedom accessed by γ01 and δ01 exhibit similar alterations upon isotopic substitution of either the TrOH or FA subunit, which combine in a nearly additive fashion to give the shifts for the doubly deuterated TrOD ⋅ FA-d complex. Such observations are modeled well by coupled-cluster analyses based upon the EXT1 and EXT2 molecular frameworks.

The isotopic shifts caused by deuteration can resolve overlapping ÃX̃ vibronic bands in the parent TrOH ⋅ FA species and foster a more complete description of the vibrational landscape. One example can be found in the ν̃00+158.4cm1 LIF peak of Fig. 4, where the distorted contour suggests two contributing features that have been attributed to 3902γ01 (based on known frequencies for the isolated modes) and ε01 (built on an a′ in-plane intermolecular stretching motion). In part, these assignments are supported by established isotopic-shift parameters for the 3901 (γ01) transition, which is displaced appreciably (modestly) towards lower energies in TrOD ⋅ FA and TrOD ⋅ FA-d, but barely moved in TrOH ⋅ FA-d. As shown in Fig. 9, one member of the ν̃00+158.4cm1 resonance in TrOH ⋅ FA shifts red upon deuteration of the TrOH substrate in keeping with the expectation for 3902γ01; however, a second participant shifts in the same direction only upon substitution of the FA ligand. This behavior has not been seen for any other low-lying Ã1A mode and strongly suggests a new vibrational degree of freedom to be involved. Because εa entails modulation of the hydrogen-bond linkage accepted by the ketonic moiety of TrOH (cf. Fig. 7), it is reasonable to expect isotopic exchange of the labile FA proton to produce a substantial alteration in the attendant normal coordinate and a commensurate change in δν̃ε01η (cf. Table VI). Indeed, the contrasting isotopic response of γ013902 and ε01 leads to the curious result that their relative energy ordering flips between the TrOH ⋅ FA-d and TrOD ⋅ FA complexes. Similar analyses can be applied to the blended LIF peak at ν̃00+190.2cm1, allowing it to be dissected into components arising from 3904 and γ03.

The holistic interpretation of experimental and computational findings outlined above has provided compelling evidence that the EXT1 configuration of the binary TrOH ⋅ FA adduct is the carrier of all observed fluorescence signals. While the lack of discernable spectral signatures for EXT2 can be justified in terms of the diminished propensity for this higher-energy species to form in a “cold” free-jet expansion, the absence of the thermodynamically most-stable INT isomer, which has been identified in recent microwave studies,28 demands further explanation. The substantial range of excitation energies probed by the present work (viz., ±1500 cm−1 from the ÃX̃ origin of bare TrOH), combined with the general expectation that hydrogen-bonding complexes should display ππ spectral shifts, δν̃00, on the order of hundreds of wavenumbers,17,65 argues for the action of other effects, such as rapid nonradiative relaxation by internal conversion (IC) and intersystem crossing (ISC) mechanisms akin to those implicated for the fluorescence quenching of vibronically excited tropolone.25,56,66 Indeed, ample literature precedence exists for the differential modulation of photophysical properties by site-selective “micro-solvation” of a chromophore-containing substrate,67–69 phenomena that ultimately must reflect complexation-induced changes in the locations and interactions of electronic manifolds.

Figure 10 compares EOM-CCSD/apVDZ vertical excitation energies (vee) predicted for the singlet and triplet excited manifolds of TrOH to those computed for the INT, EXT1, and EXT2 isomers of TrOH ⋅ FA, where the pertinent ground-state (X̃1A1 or X̃1A) equilibrium configuration has been used for each species. The attendant G4 symmetry labels [A1,B2A and A2,B1A] and excited-from-ground transition designations (ππ or πn) stem from the correlation of tropolone molecular orbitals to those of the weakly bound complexes, with primes serving to distinguish different orbitals of similar character.70 The resulting numerical values of vee have been tabulated in the supplementary material, which also reveals two lower-lying triplet levels, classified as 3B2ππ and 3A1ππ, at 2.47 eV and 3.10 eV, respectively.

FIG. 10.

Vertical excitation energies for singlet and triplet manifolds. The EOM-CCSD/apVDZ vertical excitation energies (in eV) predicted for singlet (in blue) and triplet (in red) excited states of TrOH are compared to those computed for the INT, EXT1, and EXT2 isomers of the binary TrOH  ⋅  FA adduct. The labels for G4 permutation-inversion symmetry and for excited-from-ground transition designations, as well as the dashed (for singlet) and dotted (for triplet) lines interconnecting various manifolds, reflect the correlation of TrOH molecular orbitals to those of the individual complexes.

FIG. 10.

Vertical excitation energies for singlet and triplet manifolds. The EOM-CCSD/apVDZ vertical excitation energies (in eV) predicted for singlet (in blue) and triplet (in red) excited states of TrOH are compared to those computed for the INT, EXT1, and EXT2 isomers of the binary TrOH  ⋅  FA adduct. The labels for G4 permutation-inversion symmetry and for excited-from-ground transition designations, as well as the dashed (for singlet) and dotted (for triplet) lines interconnecting various manifolds, reflect the correlation of TrOH molecular orbitals to those of the individual complexes.

Close modal

In contrast to most other carbonyl compounds, the intense (fully allowed) singlet ππ transition in tropolone, Ã1B2X̃1A1, resides considerably lower in energy than the weak (nominally forbidden) singlet πn resonance, B̃1A2X̃1A1 (per Fig. 10), an occurrence that has been attributed to the presence of an intramolecular hydrogen bond.71 As first elaborated by Brealey and Kasha to explain the blue shifting of πn absorption bands in hydroxylic solvents,72 this phenomenon stems from hydrogen bonding to the lone-pair of the C=O group, with the resulting stabilization of the ground-state electronic configuration being offset in its excited-state counterpart by the promotion of non-bonding electron density to a π- type antibonding orbital. Corroboration for this assertion can be found in the vee predictions of Fig. 10, where the 1A2πn state of EXT1, which entails site-specific binding of FA to the TrOH carbonyl moiety combined with an πn excitation localized on the attendant oxygen atom, exhibits a striking destabilization (or blue shift) relative to those of INT and EXT2. This disparity has direct photophysical ramifications since vibronic coupling between neighboring πn and ππ singlet manifolds has been shown to serve as a potent mediator for S1S0 IC processes.73 Given that the strength of this “proximity effect” diminishes rapidly with increasing πnππ separation, the quantum-chemical results summarized in Fig. 10 would suggest such radiationless-relaxation channels to be least effective in the case of EXT1 and tend to support the conjecture that other TrOH ⋅ FA isomers might be more prone to systemic quenching of their ππ fluorescence.

The spin-orbit coupling (SOC) mechanisms that govern ISC are subject to various conditions and constraints,74 the most notable of which are embodied in the venerable El-Sayed rules75 and the familiar energy-gap law.76 While the latter (which holds true in the weak-coupling limit) imposes an inverse exponential dependence of radiationless-transition probability on the adiabatic energy difference between interacting levels, the former (which reflects fundamental symmetry properties of SOC) stipulates that the efficiency of such events will be enhanced strongly by a change of orbital type. When applied to the 1π*π excited states of interest, these assertions suggest that a nearby triplet manifold of 3πn (rather than 3ππ) parentage will dominate ISC taking place by first-order SOC under the usual Condon approximation. Arguments based on phenomenological Hamiltonians and the G4 symmetry of bare TrOH further restrict Ã1B2 interactions to proximate levels of 3A1MS=±1, 3A2MS=±1, and 3B1MS=0 characters,74,77 where parentheses denote magnetic quantum numbers for the triplet-spin wavefunction.

Given the SOC criteria elaborated above, ISC pathways mediated by the lowest-lying 3B2ππ and 3A1ππ levels (both outside the energy window of Fig. 10), as well as by other 3ππ manifolds, can be discounted for the Ã1B2ππ surface of interest. As shown in Fig. 10, the 3A2πn state of TrOH possesses the appropriate orbital parentage to allow for efficient ISC from the 1π*π configuration and has a predicted vee only 0.16 eV higher. More importantly, this singlet-triplet energy gap, ΔEST, is changed markedly and specifically by complexation, giving values of 0.36, 0.55, and 0.15 eV for the INT, EXT1, and EXT2 isomers of TrOH ⋅ FA. Although the greater proximity of 1B2ππ and 3A2πn in EXT2 and INT would tend to enhance nonradiative-relaxation probabilities for these species, such claims must be tempered by the differences that may exist between vertical and adiabatic energies, with the coupled-cluster analyses in Table II indicating that ΔEaeeÃX̃ΔEveeÃX̃ can be as much as −0.36 eV. Structural optimization of the 1B2ππ and 3A2πn states at the TD-M062X/apVTZ level of theory found vee estimates of ΔEST in INT, EXT1, and EXT2 (0.19, 0.36, and 0.09 eV) to drop to 0.08, 0.14, and −0.06 eV upon consideration of minimum-energy geometries. These results, which stretch the typical limits of quantum-chemical accuracy, reinforce the perception of more efficient 1B2ππISC3A2πn radiationless transitions in EXT2 and INT, thus affording another viable mechanism for the quenching of their spontaneous-emission channels.

The preceding discussion has provided some justification for IC and ISC events that depend strongly on the specific nature of binding in the TrOH ⋅ FA complex, thereby advancing the hypothesis that enhancement of radiationless relaxation for the EXT2 and INT isomers can lead to the effective suppression of competing spontaneous-emission phenomena. Even if one neglects the obvious modifications to Fig. 10 that will accompany full geometry optimizations and vibrational zero-point corrections, a myriad of other factors might conspire to alter this proposed scenario. For example, vibronic spin-orbit interactions and attendant non-Condon effects can markedly increase the efficacy of nominally discounted ISC processes,74 including nonradiative 1ππISC3ππ transitions that otherwise violate the El-Sayed rules. Likewise, dynamical reaction pathways mediated by conical intersections among ground and excited potential energy surfaces have been implicated in numerous photophysical and photochemical mechanisms,78 with “dark” manifolds of σn or σπ character often playing a pivotal role for the dissipation of electronic energy.79 Thus, further experimental and theoretical work clearly is needed to elaborate the nonradiative channels accessible to weakly- bound TrOH adducts.

The near-ultraviolet π*π absorption system of the dual hydrogen-bonding complexes formed between tropolone (TrOH) and formic acid (FA) has been interrogated under cryogenic free-jet expansion conditions by exploiting a quartet of laser-spectroscopic probes based on fluorescence detection. Complimentary quantum-chemical calculations built upon a variety of model chemistries have been enlisted to unravel the structural and dynamical properties of the optically coupled manifolds. Three low-lying isomers denoted as INT, EXT1, and EXT2 have been predicted to exist for the binary TrOH ⋅ FA adduct, with coupled-cluster analyses suggesting their relative energies without (with) corrections for vibrational zero-point effects, ΔEX̃ (ΔEX̃), to be 0.0 (0.0), 52.8 (110.7), and 1009.2 cm−1 (1005.2 cm−1), respectively. The X̃1A ground potential surface of the INT species supports a symmetric double-minimum topography where a sizeable barrier of ΔEptX̃=4951.6cm1 (ΔEptX̃=3389.3cm1) height mediates an intermolecular double proton-transfer (DPT) process that interconnects two degenerate tautomers. In contrast, the EXT1 and EXT2 forms are linked by an intramolecular (TrOH-centric) single proton-transfer pathway characterized by a highly asymmetrical reaction coordinate that would tend to discount tunneling-induced mechanisms. Similar consideration applies for the pertinent electronically excited Ã1Aπ*π state;55 however, stationary points optimized for the INT structure reveal a marked propensity for the molecular framework to lose planarity and, therefore, to further encumber hydron-migration dynamics. Indeed, although the internal-binding motif represents the global minimum-energy configuration of TrOH ⋅ FA, the dramatic reorganization of TrOH that must transpire to allow docking of FA into the five-membered reaction cleft results in a substantial monomer deformation energy, ΔEdefX̃(TrOH)=482.2cm1, which could serve as an effective impediment to complex formation.

Laser-induced fluorescence (LIF) measurements performed on jet-cooled TrOH ⋅ FA complexes revealed a richly structured ÃX̃ absorption system that displayed well resolved vibronic progressions extending nearly 750 cm−1 to the blue of the prominent origin (000) band at ν̃00=27484.45cm1. The displacement of the latter from the analogous Ã1B2X̃1A1 feature of bare tropolone gave a complexation-induced spectral shift of δν̃00=+466.76cm1, which is the largest ever reported for a binary TrOH adduct. Complementary fluorescence hole-burning (FHB) studies confirmed all low-lying transitions to stem from a single isomeric form, with some evidence being found for the creation of higher-order species [e.g., TrOHFA2] under certain experimental conditions. A detailed analysis of the 000 resonance showed quantum-chemical predictions for the external-binding motifs to afford a much better description for the observed rotational contour than those for the more-stable INT form. By assuming detected fluorescence to arise solely from the EXT1 isomer and exploiting CCSD/apVDZ estimates of rotational constants for the X̃1A ground state, least-squares simulations of the origin band enabled refined spectroscopic parameters to be extracted for the vibrationless Ã1A level, as well as for the nature of the transition that mediates the π*π electron-promotion process.

Dispersed fluorescence (DF) data obtained by pumping isolated ÃX̃ resonances that accessed a compendium of Ã1Aππ vibronic levels proved to be crucial for unraveling the vibrational landscapes supported by optically connected potential surfaces, allowing assignments of excited-state features to be built upon their ground-state counterparts. Comprehensive analysis of DF and LIF spectral patterns led to the identification of numerous intermolecular [e.g., αa, βa, γa, δa, and εa] and intramolecular [e.g., ν39a which is TrOH-centric in nature] degrees of freedom, with the higher resolution afforded by limited stimulated emission pumping (SEP) measurements facilitating the discrimination of closely spaced peaks. Unscaled harmonic force fields computed for the external-binding motifs at coupled-cluster levels of theory were deemed to reproduce the observed frequencies of fundamental vibrations much more uniformly than analogous predictions based upon the INT framework, thereby reinforcing the assertion that the EXT1 isomer is the carrier of observed fluorescence signals.

Spiking of the free-jet expansion source with D2O vapor allowed the labile protons of TrOH and FA to be exchanged by more massive deuterons, leading to the formation of four isotopically labeled binary complexes: TrOH ⋅ FA, TrOD ⋅ FA, TrOH ⋅ FA-d, and TrOD ⋅ FA-d. The LIF measurements performed on this mixture of isotopologs revealed the ÃX̃ origin band to be fractionated into a doublet of doublets pattern, which was well reproduced by quantum-chemical calculations based upon the EXT1 configuration. Complementary FHB experiments enabled overlapping π*π vibronic features to be isotopically sorted, with the deuterium frequency shifts sustained by low-lying fundamentals of the Ã1Aππ state being described best by the unscaled harmonic force fields predicted for external-binding structures.

The concerted fluorescence-based measurements and quantum-chemical calculations that form the crux of efforts discussed herein have provided a self-consistent body of evidence in support of an external-binding motif for the binary TrOH ⋅ FA adduct created under free-jet expansion conditions. In particular, the holistic interpretation of all available experimental (e.g., band contours and vibrational landscapes) and theoretical (e.g., relative energies and binding metrics) findings would tend to implicate the EXT1 geometry that has the FA ligand adjoining the carbonyl moiety of the TrOH substrate. Such conclusions must be contrasted with those reported in the recent microwave work of Pejlovas et al.,28 where a directed search for DPT-containing systems driven by density-functional predictions of inertial constants for a cleft-bound isomer identified at least 25 lines attributable to this entity. While the dominant size of the permanent electric dipole moment supported by the INT structure facilitates its discrimination by pure rotational spectroscopy, these authors also noted the existence of numerous unassigned transitions of appreciable strength that could be indicative of other isomeric constituents. Given similarities between the methods employed for the in situ synthesis of weakly bound complexes, it is probable that the INT species also exists in the molecular-beam environments examined during the current study, with the absence of discernable fluorescence signatures suggesting the corresponding π*π resonance to reside outside the substantial spectral range surveyed (viz., > ± 1500 cm−1 from the ππ origin of bare TrOH) or the quantum yield for spontaneous emission to be vanishingly small owing to efficient channels for nonradiative relaxation that depend on the specific site of substrate-ligand binding. Since computational analyses have afforded some validation for the latter, future experiments might enlist absorption-based probes like cavity ring-down spectroscopy80 to search the region proximate to the Ã1B2X̃1A1 origin band of tropolone for vestiges of non-fluorescing vibronic features.

See supplementary material for (1) full reference citations, (2) tables of optimized equilibrium and transition-state geometries for the ground and excited electronic surfaces of TrOH ⋅ FA, (3) a table of hydrogen-bonding metrics for TrOH, (4) tables of additional quantum-chemical results for TrOH ⋅ FA isomers (including other model chemistries, counterpoise corrections, free-energy estimates, and harmonic force fields), (5) a table of measured and computed 13C-isotopolog parameters for the ÃX̃ origin band of TrOH ⋅ FA, (6) tables of observed and predicted vibrational levels in the ground and excited electronic states of TrOH ⋅ FA along with optimized Dunham-expansion parameters, (7) a table of predicted vertical excitation energies for the singlet and triplet manifolds of TrOH ⋅ FA isomers, and (8) a figure of labeled/sorted fluorescence spectra recorded for partially deuterated isotopologs of TrOH ⋅ FA.

The work described in this paper was completed under the auspices of Grant Nos. CHE-1112239 and CHE-1464957 awarded by the Chemical Structures, Dynamics, and Mechanisms Program in the Directorate for Mathematical and Physical Sciences of the United States National Science Foundation, the continuing support of which is gratefully acknowledged. Computational efforts were supported in part by the Yale University Faculty of Arts and Sciences High Performance Computing Center and by the National Science Foundation under Grant No. CNS-0821132, which partially funded acquisition of requisite computer facilities.

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