Dual hydrogen-bonding motifs in complexes formed between tropolone and formic acid

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 (C_s) are isolated by a barrier of finite height that defines the transition-state configuration (C_2v). 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 be^12–14 $Δ0X̃=29 193.7969(11)MHz$ (∼0.9738 cm⁻¹) and $Δ0Ã=17.869(18)cm−1$ – 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 dependencies^13,16 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, $δν̃00=ν̃00TrOH⋅M−ν̃00TrOH$⁠, and the splitting, $Δ0=Δ0Ã−Δ0X̃$⁠, of the $Ã−X̃$ 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 CO^20,21) 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 CO₂^25,26) 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.

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) C_s 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 

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 (⁠$ΔrO1⋯O2X̃≈0.1Å$⁠) and a significant elongation of the intramolecular hydrogen bond (⁠$ΔrO1⋯H3X̃≈0.25Å$⁠), as well as strong angular distortions of the five-membered ring (⁠$ΔθC1–O2–H3X̃=+7.4°$ and $ΔθO2–H3⋯O1X̃=−11.5°$⁠). 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, $ΔE′X̃=ΔEX̃+ΔεX̃$⁠, 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 (⁠$ΔEpt′X̃$⁠) 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 $ΔEpt′X̃$ 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 (C_s) transition-state geometry having $ν̃rxX̃≈i 1340cm−1$⁠. The highly asymmetric potential topography and sizable reaction impediment (⁠$ΔEptX̃≈3552.4cm−1$ and $ΔEpt′X̃≈2666.5cm−1$⁠) 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 

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, $ΔEbindX̃TrOH⋅FA$⁠, stem from counterpoise-corrected estimates for interaction energy of the ground state, $ΔEint,cpX̃TrOH⋅FA$⁠, as adjusted for monomer-deformation effects,^42,54

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

Table II presents a summary of energy metrics and structural parameters calculated for the lowest-lying singlet excited state, $à 1A′π*π$⁠,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 $Ã−X̃$ transitions build on the intense $Ã1B2−X̃1A1$ 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), $ΔEveeÃ−X̃η$ 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), $ΔEaeeÃ−X̃η$⁠, as well as their vibrational zero-point corrected counterparts, $ΔEaee′Ã−X̃η=ΔEaeeÃ−X̃η+ΔεÃ−X̃η$ where $ΔεÃ−X̃η=εÃη−εX̃η$⁠, relies on the properties of fully relaxed structures determined independently for the optically connected manifolds.

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

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 $δν̃00,aee′η$ values, which afford the most direct comparison to spectroscopic measurements of the $Ã−X̃$ 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 (⁠$δ′ν̃00>0$⁠) 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 $Ã1A′π*π$ 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 $ΔEinvÃ=EPLÃ−EAPLÃ$ magnitude, which have been compiled in Table II along with their zero-point corrected counterparts, $ΔEinv′Ã$⁠. 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 $Ã1A′π*π$ 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 (⁠$ΔEinvÃ=494cm−1$⁠) and proton-transfer (⁠$ΔEptÃ=4765cm−1$⁠) 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)¹¹ $Ã1B2−X̃1A1$ (π^*←π) absorption system of bare tropolone located at $ν̃00=27 017.69cm−1$⁠.¹⁴ Laser-induced fluorescence (LIF) spectra acquired for the initial portion of the analogous $Ã−X̃$ 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 $ν̃00=27 484.45cm−1$⁠, leading to a spectral offset of $δν̃00=+466.76cm−1$ 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.

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 $TrOH⋅FA2$ 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 $Δν̃=ν̃−ν̃00≈300cm−1$⁠, 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 $Ã1A′π*π$ 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 $ν̃00+750cm−1$ 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 $à 1A′ π∗π$ 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 μ_eg listed for a given complex reflecting $Ã−X̃$ resonances originating from either the ground-state or excited-state equilibrium configuration. The calculated asymmetry parameters, $κ=2B−A−C/A−C$⁠, show all species to be near-prolate asymmetric tops and the vanishing inertial defects, Δ I = I_c − I_a − I_b where I_ξ (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 $X̃ 1A′$ permanent electric dipole moments (⁠$μgg≡μgg$⁠) 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 $à 1A′$ quantity (⁠$μee=μee$⁠) for EXT1 to dominate over those of INT and EXT2 by 18% and 30%, respectively.

As shown in Fig. 2, the inertial coordinate system for each binary TrOH ⋅ FA adduct has the molecular framework residing in the a − b 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 $Ã−X̃$ resonance should be indicative of the isomer being interrogated, with the μ_eg 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 μ_eg (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 μ_b/μ_a 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 μ_b/μ_a = − 0.811 falls 23.5% in magnitude upon electronic excitation (increasing the a − axis projection) and, although the INT μ_b/μ_a = 2.988 ratio remains essentially unaltered, the non-planarity that distinguishes the corresponding excited state is expected to yield a minute type − c contribution, μ_c/μ_b = 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 $Ã1B2−X̃1A1$ 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, E_pulse ≤ 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 

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 $Hˆυ″X̃$ and $Hˆυ′Ã$ (for vibronic manifolds υ″ and υ′) were adapted from those employed for prior rotational-tunneling studies of the $Ã1B2−X̃1A1$ 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, $Δυ″X̃$ and $Δυ″Ã$⁠, were fixed to zero, as were quantities governing interactions between members of a tunneling doublet (viz., F,  F_J, and F_K). For this isomer, rotational levels of the symmetric (antisymmetric) υ″ = 0 manifold having near-prolate quantum number K_a 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 $b−polarized0±±$ and $a−polarized0±∓$ 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 $ν̃00=27 484.45cm−1$⁠, 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 Γ_G = 0.075 cm⁻¹ and Γ_L = 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 μ_eg 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 $Ã−X̃$ 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, T_eff,⁵⁸ 

where $EυJτMX̃$ is the energy of an $X̃1A′$ eigenstate characterized by vibrational and rotational quantum numbers υ and J, with τ = K_a − K_c 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,

where k_B is the Boltzmann constant and the partition function $qTeff=∑υJτMe−EυJτMX̃/kBTeff$ 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 $T̃0=27 484.510(11)cm−1$ differs slightly from the measured center of the vibronic profile at $ν̃00=27 484.45cm−1$⁠, 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, Γ_G = 0.104(13) cm⁻¹ and Γ_L = 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 $Ã−X̃$ transition electric dipole moment to vary during the TrOH ⋅ FA band-contour regression led to μ_b/μ_a = 0.763(55), which suggests μ_eg 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 μ_eg 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 $Ã−X̃$ 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 $Ã 1B2π*π$ 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 $Ã−X̃$ resonances, with the abscissa, which specifies the displacement of observed emission features (at $ν̃$⁠) from the excitation source, $Δν̃=ν̃−ν̃pump$⁠, 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 $0≤Δν̃≤2000cm−1$ 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 $Δν̃≈2500cm−1$⁠, 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 $Δν̃≤500cm−1$ region where the intermolecular and out-of-plane bending motions of weakly bound TrOH ⋅ FA complexes should reside.