The T-shaped OH–C2H2 complex is formed in helium droplets via the sequential pick-up and solvation of the monomer fragments. Rovibrational spectra of the a-type OH stretch and b-type antisymmetric CH stretch vibrations contain resolved parity splitting that reveals the extent to which electronic angular momentum of the OH moiety is quenched upon complex formation. The energy difference between the spin-orbit coupled 2B1 (A″) and 2B2 (A′) electronic states is determined spectroscopically to be 216 cm−1 in helium droplets, which is 13 cm−1 larger than in the gas phase [Marshall et al., J. Chem. Phys. 121, 5845 (2004)]. The effect of the helium is rationalized as a difference in the solvation free energies of the two electronic states. This interpretation is motivated by the separation between the Q(3/2) and R(3/2) transitions in the infrared spectrum of the helium-solvated 2Π3/2 OH radical. Despite the expectation of a reduced rotational constant, the observed Q(3/2) to R(3/2) splitting is larger than in the gas phase by ≈0.3 cm−1. This observation can be accounted for quantitatively by assuming the energetic separation between 2Π3/2 and 2Π1/2 manifolds is increased by ≈40 cm−1 upon helium solvation.

Electrophilic addition of the hydroxyl radical to the π bond of acetylene produces, as an intermediate, the carbon-centered 2-hydroxy vinyl radical (Γe = A′; HC=CHOH).1–3 Along the entrance channel to this reaction, a dipole-quadrupole interaction stabilizes a T-shaped, hydrogen bonded complex (OH–C2H2), whose zero-point level lies ≈2.7 kcal mol−1 below the separated reactants.4 Moreover, this entrance channel complex is located behind a barrier ≈1 kcal mol−1 above the reactant asymptote.4–6 The orbital degeneracy of the OH moiety is lifted upon complex formation, and the orbital angular momentum is quenched upon C–O bond formation. Nuclear motion carrying the system from reactants to products, therefore, occurs on two coupled potential surfaces (A′ and A″), which are degenerate at long range and distinguished by the orientation of the OH singly occupied pπ orbital. Electronic structure theory predicts, in the absence of spin-orbit coupling, an A′ − A″ energetic separation of ≈140 cm−1 at the T-shaped equilibrium configuration of the entrance channel complex.4 

The spectroscopy of T-shaped OH–C2H2 probes the extent to which electronic angular momentum is quenched as the system evolves from separated reactants towards the 2-hydroxy vinyl intermediate.7,8 The spectrum is complicated by the coupling of this partially quenched electronic angular momentum to the end-over-end rotation of the complex, which manifests as a dramatic change in the rotational fine structure expected for a near-prolate asymmetric top in either the unquenched or fully quenched limits.7 Marshall and Lester have reported a rigid-T spectroscopic model that accounts for this angular momentum coupling and quenching,7 and simulations of the antisymmetric CH stretch fundamental, when compared to gas-phase infrared (IR) photodissociation spectroscopy measurements, reveal the A′–A″ (B2B1) energetic separation to be ≈203 cm−1.8 In the present study, the OH–C2H2 complex is stabilized in helium nanodroplets and probed with IR laser spectroscopy. The OH and CH stretch spectra are sufficiently resolved to reveal the extent to which the solvent affects this electronic angular momentum quenching upon complexation.

The rigid-T model of Marshall and Lester accounts for spin-orbit coupling and Coriolis interactions in the complex that together lift the four-fold Ω-degeneracy associated with the OH electronic angular momentum.7 In the limit of weak intermolecular interaction, the projections of both spin and orbital angular momenta remain separately quantized along the OH bond-axis. As the intermolecular interaction increases, the orbital angular momentum becomes partially quenched, leading to an uncoupling of the spin angular momentum from the molecular framework. In the strong-interaction limit, the orbital angular momentum of the OH moiety is fully quenched, and the alignment of the singly occupied pπ orbital results in two distinct electronic states having 2B1 and 2B2 symmetries, which correlate, respectively, to the (2Π3/2 + 1Σ+) and (2Π1/2 + 1Σ+) asymptotes (Figure 1). The rigid-T model treats this anisotropy for orbital motion about the C2 axis in analogy to the Renner-Teller interaction,9,10 that is, via an electronic angular momentum quenching term in the Hamiltonian that allows for a smooth transition from the unquenched, weak-interaction limit (analogous to Hund’s case (a) coupling) to the fully quenched, strong-interaction limit (analogous to Hund’s case (b) coupling).11,12

FIG. 1.

Correlation diagram for the electronic states of OH–C2H2 included in the rigid-T spectroscopic model. As the spectroscopic fitting parameter ρ evolves from 0 to −3000 cm−1, the energy level separation changes from ASO = − 139 cm−1 in the unquenched limit (the orbital angular momentum has quantized projections onto the a-axis equal to ±ħ) to ρ in the fully quenched limit (the projection of orbital angular momentum onto the a-axis is ill-defined). From left to right, the (2Π3/2 + 1Σ+) and (2Π1/2 + 1Σ+) asymptotes evolve into electronic states having 2B1 and 2B2 symmetries, respectively.

FIG. 1.

Correlation diagram for the electronic states of OH–C2H2 included in the rigid-T spectroscopic model. As the spectroscopic fitting parameter ρ evolves from 0 to −3000 cm−1, the energy level separation changes from ASO = − 139 cm−1 in the unquenched limit (the orbital angular momentum has quantized projections onto the a-axis equal to ±ħ) to ρ in the fully quenched limit (the projection of orbital angular momentum onto the a-axis is ill-defined). From left to right, the (2Π3/2 + 1Σ+) and (2Π1/2 + 1Σ+) asymptotes evolve into electronic states having 2B1 and 2B2 symmetries, respectively.

Close modal

Here, we expand upon this two-state model to include the effect of centrifugal distortion, which becomes important at the higher-resolution observed for the He droplet spectra, in comparison to the gas-phase photodissociation spectra. Centrifugal distortion terms appended to the asymmetric top Hamiltonian are often essential for modeling rovibrational spectra of small molecules in He droplets, and we find this to be the case here. Indeed, distortion constants derived from spectra of He-solvated molecules and complexes are often substantially larger than the associated gas-phase values,13–15 an effect which has been discussed in detail.16,17

The Hamiltonian used to model the rotational energy level pattern of He-solvated OH–C2H2 is given below

H ˆ = H ˆ rot + H ˆ SO + H ˆ CD + H ˆ q .
(1)

The terms in the effective Hamiltonian account for asymmetric top rigid rotation, spin-orbit coupling, centrifugal distortion, and angular momentum quenching, respectively. The Hamiltonian is represented in a parity conserving Hund’s case (a) basis, given in Eq. (2), which is an appropriate zeroth-order description for the unquenched limit in field-free space,7 

J , P , λ , σ , ϵ = 1 2 J , P , λ , σ + ϵ ( 1 ) ( J 1 / 2 ) J , P , λ , σ .
(2)

The total angular momentum (less nuclear spin), J, is half integral, and the projections of the total, orbital, and spin angular momenta onto the a-axis of the T-shaped complex are p, λ, and σ, respectively, where P = p 1 2 , λ = ± 1 and σ = ± 1 2 . Under zero-field conditions, the total angular momentum and parity, ϵ 1 P + σ , are conserved, where ϵ = ± 1.

Here, we briefly summarize the salient features of the Hamiltonian in the absence of rotation. For this two-state model, off-diagonal spin-orbit coupling, which connects states differing in λ , is ignored. The spin orbit term in the Hamiltonian ( H ˆ S O ), therefore, consists simply of a diagonal term, which is given in Eq. (3), with matrix elements given in Eq. (4),

H ˆ SO = A SO l z s z ,
(3)
λ , σ , ϵ | H ˆ SO | λ , σ , ϵ = A SO λ σ .
(4)

The quenching term in the Hamiltonian ( H ˆ q ), composed of Hougen’s operators,18 is given in Eq. (5) and has matrix elements given in Eq. (6),

H ˆ q = ρ 2 l ¯ + 2 + l ¯ 2 ,
(5)
λ , σ , ϵ | H ˆ q | λ , σ , ϵ = ρ 2 .
(6)

H ˆ q connects states differing by two in λ, thereby coupling states belonging to different spin-orbit manifolds in the unquenched limit. Collecting these matrix elements and defining ω = λ + σ, we have the Hamiltonian matrix in the absence of rotation (Eq. (7)). The matrix in the absence of rotation is actually 8 × 8 because of the ±ϵ degeneracy; however, we have omitted this degeneracy in Eq. (7) for clarity,

ω = + 3 / 2 ω = 1 / 2 ω = + 1 / 2 ω = 3 / 2
H SO + H q = A SO / 2 ρ / 2 0 0 ρ / 2 A SO / 2 0 0 0 0 A SO / 2 ρ / 2 0 0 ρ / 2 A SO / 2 .
(7)

The eigenvalues of each 2 × 2 block (Eq. (8)) reveal the definition of the spectroscopic fitting parameter ρ. In the strong-interaction limit, in which the interaction energy is much larger than the 2Π OH spin orbit coupling (−139 cm−1), ρ is the energy difference between 2B1 (A″) and 2B2 (A′) electronic states in the C2v, T-shaped configuration,

Δ E B 2 B 1 = A SO 2 + ρ 2 .
(8)

Therefore, the magnitude of ρ can be varied in the model to span the unquenched to fully quenched limits, in which the energy difference between the two doubly degenerate electronic states begins as ASO in the weak-interaction limit and becomes ρ in the strong-interaction limit. Following established conventions,7,12 a positive value for ρ corresponds to the 2B1 (A″) state being higher in energy than the 2B2 (A′) state.

The rotational Hamiltonian ( H ˆ rot ) and its matrix elements are given elsewhere.7 The 8 × 8, J = 1 2 block of the full Hamiltonian matrix is given in Eq. (9) to illustrate two effects present in the rotating molecule. (The ∓ signs in the matrix correspond to ϵ = ± 1 blocks, and centrifugal distortion terms are omitted for clarity.) The first effect is a Coriolis interaction of the form 2 J ˆ a ( l ˆ a + s ˆ a ) , which lifts the ±ω degeneracy. For example, in the unquenched limit, states with P = 1 2 and ω = ± 3 2 are split by ≈3A, which is about 3.5 cm−1. Therefore, at the low temperature of He droplets, states with ω + 3 2 have negligible population. The second effect, revealed in the He droplet spectra, is parity splitting,

P = 1 / 2 , ω = + 3 / 2 P = 1 / 2 , ω = 1 / 2 P = 1 / 2 , ω = + 1 / 2 P = 1 / 2 , ω = 3 / 2
H = A + ( B + C ) / 4 + A SO / 2 ρ / 2 ( B + C ) / 2 0 0 ρ / 2 ( B + C ) / 2 A + ( B + C ) / 4 A SO / 2 0 0 0 0 ( B + C ) / 4 A SO / 2 ρ / 2 ( B C ) / 2 0 0 ρ / 2 ( B C ) / 2 4 A + ( B + C ) 4 + A SO / 2 .
(9)

The ±ϵ degeneracy is lifted, in part, by spin-uncoupling terms in the Hamiltonian (JS), which couple the different spin-orbit manifolds and result in the off-diagonal elements proportional to ∓(B ± C)/2. For example, in the unquenched limit (ρ ≲ 1 cm−1), the ∓(B + C)/2 terms lead to a splitting of the P = 1 2 and ω = 3 2 level on the order of 0.001 cm−1. However, once ρ becomes similar in magnitude to ASO, the difference between ±ϵ blocks is sufficient to parity split this level by ≈0.15 cm−1. Therefore, parity splitting is a sensitive spectroscopic probe of the extent to which electronic angular momentum is quenched in the complex. Figure 2 shows the evolution of parity splitting in the P = 1 2 , ω = 3 2 and P = 3 2 , ω = 3 2 levels with increasing ρ . As discussed previously,7 parity splitting is especially large in the P = 1 2 , ω = 3 2 manifold of levels, and, as shown below, it is fully resolved in the He droplet spectra. Figure 3 shows the states of the two separate nuclear spin species Γ n s = 3 A 1 B 2 that are populated at the temperature of He droplets (0.35 K) and the expected increase in parity splitting with increasing J quantum number (ρ = − 165 cm−1).

FIG. 2.

Energy level diagram for the ground vibrational state of OH–C2H2, in which the spectroscopic fitting parameter ρ is changed from 0 to −500 cm−1. The rotational constants are the ground state values determined for the He-solvated complex, as listed in Table I. The parity splitting in the P , ω = ( 1 2 , 3 2 ) manifold of levels (red) rapidly evolves with increasing ρ , whereas the splitting of levels in the P , ω = ( 3 2 , 3 2 ) manifold (black) is too small to be visible in the figure. The dashed line indicates the value of ρ extracted from the He droplet spectra.

FIG. 2.

Energy level diagram for the ground vibrational state of OH–C2H2, in which the spectroscopic fitting parameter ρ is changed from 0 to −500 cm−1. The rotational constants are the ground state values determined for the He-solvated complex, as listed in Table I. The parity splitting in the P , ω = ( 1 2 , 3 2 ) manifold of levels (red) rapidly evolves with increasing ρ , whereas the splitting of levels in the P , ω = ( 3 2 , 3 2 ) manifold (black) is too small to be visible in the figure. The dashed line indicates the value of ρ extracted from the He droplet spectra.

Close modal
FIG. 3.

Energy level diagram for the ground vibrational state of OH–C2H2, in which the spectroscopic fitting parameter ρ is set equal to −165 cm−1. The rotational constants are the ground state values determined for the He-solvated complex, as listed in Table I. The + and − signs indicate the parity of the level (i.e., the sign of ϵ). The quantum number labels are those associated with the fully unquenched limit (ρ = 0), except for J, which remains a good quantum number for all values of ρ. The P , ω = ( 1 2 , 3 2 ) manifold is shifted down in energy by 1 cm−1 for clarity. The nuclear spin weight ratio (A1 : B2) is 3:1. At 0.35 K, >99% of the OH–C2H2 ensemble resides in the energy levels shown here.

FIG. 3.

Energy level diagram for the ground vibrational state of OH–C2H2, in which the spectroscopic fitting parameter ρ is set equal to −165 cm−1. The rotational constants are the ground state values determined for the He-solvated complex, as listed in Table I. The + and − signs indicate the parity of the level (i.e., the sign of ϵ). The quantum number labels are those associated with the fully unquenched limit (ρ = 0), except for J, which remains a good quantum number for all values of ρ. The P , ω = ( 1 2 , 3 2 ) manifold is shifted down in energy by 1 cm−1 for clarity. The nuclear spin weight ratio (A1 : B2) is 3:1. At 0.35 K, >99% of the OH–C2H2 ensemble resides in the energy levels shown here.

Close modal

Electric dipole transition intensities are computed as described in Ref. 7, and spectra are simulated for both rovibrational a-type (OH stretch) and b-type (antisymmetric CH stretch) bands for the values of ρ between 0 and −3000 cm−1, as shown in Figures 4 and 5. Both a- and b-type spectral simulations were described in detail previously,7 although in the context of lower resolution spectra with a rotational temperature equal to 6 K. We discuss here those features that become evident at the higher resolution afforded by the He droplet spectra. The line widths, rotational constants, and rotational temperature adopted for the simulations reported here are those extracted from the He droplet spectra (Table I).

FIG. 4.

Evolution of the a-type band (OH stretch) with increasing |ρ| (top to bottom). The parity doubling of the qQ1/2(1/2) and qQ1/2(3/2) transitions is shown with increasing |ρ| as the solid black lines. The red simulation corresponds to the value of ρ found for the He-solvated complex.

FIG. 4.

Evolution of the a-type band (OH stretch) with increasing |ρ| (top to bottom). The parity doubling of the qQ1/2(1/2) and qQ1/2(3/2) transitions is shown with increasing |ρ| as the solid black lines. The red simulation corresponds to the value of ρ found for the He-solvated complex.

Close modal
FIG. 5.

Evolution of the b-type band (antisymmetric CH stretch) with increasing |ρ| (top to bottom). The red simulation corresponds to the value of ρ found for the He-solvated complex.

FIG. 5.

Evolution of the b-type band (antisymmetric CH stretch) with increasing |ρ| (top to bottom). The red simulation corresponds to the value of ρ found for the He-solvated complex.

Close modal
TABLE I.

Spectroscopic parameters (in cm−1) determined from the simulations of the a- and b-type spectra of OH–C2H2.a

Helium (a-type) Helium (b-type) Gas (b-type)b
ν0  3525.265 (1)  3278.800 (1)  3278.64 (1) 
A″  1.186  1.186  1.217 (8) 
ΔAc  −0.008  −0.254  −0.015 (12) 
(B + C)/2″  0.060 5  0.060 5  0.1399d 
Δ(B + C)/2c  −0.000 7  −0.000 7  0d 
(BC)/2″  0.000 1  0.000 1  0.01d 
Δ(BC)/2c  0d 
DJe  0.000 29  0.000 29  0d 
DKe  0.007 8  0.007 8  0d 
ρ″  −165  −165  −148.1 (7) 
Δρc  0.0  0.0  0d 
Γ  0.008  0.05  0.30d 
Trot (K)  0.35  0.35  6d 
Helium (a-type) Helium (b-type) Gas (b-type)b
ν0  3525.265 (1)  3278.800 (1)  3278.64 (1) 
A″  1.186  1.186  1.217 (8) 
ΔAc  −0.008  −0.254  −0.015 (12) 
(B + C)/2″  0.060 5  0.060 5  0.1399d 
Δ(B + C)/2c  −0.000 7  −0.000 7  0d 
(BC)/2″  0.000 1  0.000 1  0.01d 
Δ(BC)/2c  0d 
DJe  0.000 29  0.000 29  0d 
DKe  0.007 8  0.007 8  0d 
ρ″  −165  −165  −148.1 (7) 
Δρc  0.0  0.0  0d 
Γ  0.008  0.05  0.30d 
Trot (K)  0.35  0.35  6d 
a

Numbers in parentheses are 2σ uncertainties in the last digit. The spin-orbit coupling constant was fixed at −139.0508 cm−1 in the simulations.

b

From Ref. 8.

c

The change is taken as the excited state minus the ground state constant.

d

Parameter fixed in contour fit.

e

The ground and excited state constants are the same.

As the system evolves between the unquenched and fully quenched limits, the a-type spectral feature that stands out is the separation between the intense central Q-branch and the P and R branch lines adjacent to it. In the unquenched limit, the spectrum resembles that of a symmetric top in a degenerate vibronic state, having half-integer J quantum numbers (with half-integer projections p) and qQ to qR(J″) spacing equal to odd multiples of (B + C)/2. In the fully quenched limit, the spectrum instead resembles an asymmetric top in a non-degenerate electronic state, having integer N quantum numbers (with integer projections Ka) and qQ to qR(J″) spacing equal to even multiples of (B + C)/2. Between these two limits, with the resolution achieved in this experiment, parity splitting is clearly observed. The parity splitting associated with the qQ1/2(1/2) and qQ1/2(3/2) transitions and its evolution with ρ are shown as black lines in Figure 4. The evolution of rotational fine-structure is even more pronounced for the b-type band (Figure 5), for which the ΔP = ± 1 selection rule reveals the dramatic ρ dependent change in the origins of (ΔP, ω) rotational sub-bands.7 In Figure 5, individual sub-bands are labeled in the unquenched limit with the convention, ΔPQP. Again, as the magnitude of ρ increases from top to bottom in the figure, the spacing between sub-bands evolves from the expected pattern for a symmetric top in a degenerate electronic state, having half-integer quantum numbers, to a pattern resembling an asymmetric top with integer quantum numbers.

Helium droplets13–15,19 consisting of ≈4000 atoms20,21 are produced by expanding He at 17 K and 30 bar through a 5 μm diameter nozzle. The expansion is skimmed, and the resulting droplet beam passes into a “pick-up” chamber that contains differentially pumped sources of OH and C2H2. The OH radicals are formed from the pyrolytic decomposition of tert-butyl hydroperoxide in a low pressure (≈10−4 Torr), effusive pyrolysis source, which has been described in detail elsewhere.22 The droplet beam passes within 1 cm of the pyrolysis source exit, and OH radicals are picked up by the He droplets and cooled to ≈0.4 K. Several hundred microseconds downstream, the droplet beam passes through a pick-up cell containing C2H2. Upon droplet pick-up, the C2H2 thermal energy and the condensation energy associated with OH–C2H2 cluster formation are dissipated via He atom evaporation, returning the system to ≈0.4 K. The doped droplets are probed with the output of an IR-optical parametric oscillator (OPO) laser system, the tuning and calibration of which has been described elsewhere.23 Vibrational excitation of the He-solvated OH–C2H2 complex results in the evaporation of ≈700 He atoms, which leads to a reduction in the average droplet geometric cross section and a concomitant decrease in the ion signal associated with the electron impact ionization of the beam. The mass spectrum of the ionized droplet ensemble reveals peaks associated with the charge-transfer ionization and subsequent fragmentation of the dopants.14 For the spectroscopy of the OH–C2H2 complex, the ion signal is monitored with a quadrupole mass spectrometer on mass channel m/z = 14 u, (CH2)+, which allows for the discrimination against IR depletion signals related to the acetylene monomer. The IR beam from the OPO is amplitude modulated at 80 Hz, and the ion signal is processed with a lock-in amplifier as the OPO wavelength is tuned continuously with ≈10 MHz resolution. The resulting depletion spectra are normalized to laser power, which is kept at a level so as to mitigate saturation effects in the spectra.

The structure of the 2B1 OH–C2H2 complex was optimized at the coupled-cluster singles and doubles with perturbative triples corrections (CCSD(T))/aug-cc-pVTZ level of theory using the program package CFOUR.24 Here, the restricted open-shell Hartree–Fock wave function was used for the correlation energy calculation, and the core orbitals were kept frozen. At this optimized geometry (inset Fig. 1), the electronic energy separation (ρ) between 2B1 and 2B2 states was computed at the coupled-cluster singles, doubles and triples with perturbative quadruples corrections (CCSDT(Q))25–32 level of theory with a focal point analysis (FPA) approach.33–37 The functional forms employed for the extrapolation to the complete basis set (CBS) limit are38,39

E HF X = E H F + a e b X ( X = 3 , 4 , 5 )

and

E corr X = E corr + a X 3 ( X = 4 , 5 ) .

Here, X stands for the cardinal number of a correlation consistent aug-cc-pVXZ basis set.40 

The energy points for FPA at ROHF, MP2, CCSD, and CCSD(T) levels of theory were computed using the program package MOLPRO.41 The CCSDT and CCSDT(Q) increments were computed as additive corrections, using the program package CFOUR along with the MRCC program of Kállay.42 The core correction, Δ(core), is the difference between all-electron (AE) and frozen-core (FC) CCSD(T)/aug-cc-pCVTZ single point energies. The diagonal Born-Oppenheimer correction (DBOC)43 was computed at the HF/aug-cc-pVTZ level with a unrestricted Hartree-Fock (UHF) reference wave function. The first-order relativistic correction44 from the one-electron mass-velocity and Darwin terms was computed at the CCSD(T)/aug-cc-pVTZ level of theory. The results of the FPA computations are given in Table II.

TABLE II.

Focal point analysis of the OH–C2H22B12B2 relative energy.a

Unit: cm−1 ΔEe(ROHF) +δ[MP2] +δ[CCSD] +δ[CCSD(T)] +δ[CCSDT] +δ[CCSDT(Q)] NET
AVDZb  +153.61  +10.10  +0.75  +4.96  +1.05  −0.80  +169.67 
AVTZ  +151.37  +2.59  +1.54  +2.74  [+1.05]  [−0.80]  [+158.49] 
AVQZ  +149.53  +0.22  +0.04  +2.74  [+1.05]  [−0.80]  [+152.78] 
AV5Z  +148.98  −1.21  −0.26  +2.68  [+1.05]  [−0.80]  [+150.44] 
CBS LIMIT  [+148.78]  [−2.74]  [−0.55]  [+2.61]  [+1.05]  [−0.80]  [+148.35] 
Function  a + becX  a + bX−3  a + bX−3  a + bX−3  Addition  Addition   
X (fit points)=  (3,4,5)  (4,5)  (4,5)  (4,5)       
FC-CCSD(T)/aug-cc-pVTZ reference geometry 
Δ(core) = − 0.74; Δ(DBOC) = + 0.37; Δ(rel) = − 0.23. 
ΔEe(FPA) = + 148.35 − 0.74 + 0.37 − 0.23 = + 147.75 cm1 
Unit: cm−1 ΔEe(ROHF) +δ[MP2] +δ[CCSD] +δ[CCSD(T)] +δ[CCSDT] +δ[CCSDT(Q)] NET
AVDZb  +153.61  +10.10  +0.75  +4.96  +1.05  −0.80  +169.67 
AVTZ  +151.37  +2.59  +1.54  +2.74  [+1.05]  [−0.80]  [+158.49] 
AVQZ  +149.53  +0.22  +0.04  +2.74  [+1.05]  [−0.80]  [+152.78] 
AV5Z  +148.98  −1.21  −0.26  +2.68  [+1.05]  [−0.80]  [+150.44] 
CBS LIMIT  [+148.78]  [−2.74]  [−0.55]  [+2.61]  [+1.05]  [−0.80]  [+148.35] 
Function  a + becX  a + bX−3  a + bX−3  a + bX−3  Addition  Addition   
X (fit points)=  (3,4,5)  (4,5)  (4,5)  (4,5)       
FC-CCSD(T)/aug-cc-pVTZ reference geometry 
Δ(core) = − 0.74; Δ(DBOC) = + 0.37; Δ(rel) = − 0.23. 
ΔEe(FPA) = + 148.35 − 0.74 + 0.37 − 0.23 = + 147.75 cm1 
a

The symbol δ denotes the increment in the energy difference (ΔEe) with respect to the previous level of theory in the order of ROHF → MP2 → CCSD → CCSD(T) → CCSDT → CCSDT(Q). The numbers in brackets result from basis set extrapolations (using the specified functions and fit points below the energies) or additivity approximations, while the numbers without brackets are computed explicitly.

b

AVXZ is defined as aug-cc-pVXZ.

The spin-orbit coupling term (ASO) that arises from the coupling between 2B1 and 2B2 states of OH–C2H2 was computed using complete active space self-consistent field (CASSCF) and multireference configuration interaction (MRCI) methods. The 2B1 equilibrium structure at the CCSD(T)/aug-cc-pVTZ level was used as the reference geometry. The active spaces were gradually increased to the full valence active space (17 electrons in 15 orbitals) to investigate the convergence of the calculated ASO. The spin-orbit coupling constant of the free hydroxyl radical (OH) using full valence active space (7 electrons in 5 orbitals) was also computed for comparison. All spin-orbit coupling computations were performed using the program package MOLPRO,41 and the results are summarized in Table III.

TABLE III.

Spin-orbit coupling constant (−ASO) between 2B1 and 2B2 states of OH–C2H2 complex at CASSCF and MRCI levels of theory using various active spaces.

OH-C2H2 (elecs,orbs) Aso(CASSCF)/cm−1 Aso(MRCI)/cm−1
(9,7)  134.96  132.49 
(9,8)  134.96  132.46 
(9,9)  134.97  132.42 
(11,10)  134.97  132.42 
(17,13)  134.96  132.42 
(17,15)a  134.97  ... 
OH(7,5)b  136.32  132.18 
OH-C2H2 (elecs,orbs) Aso(CASSCF)/cm−1 Aso(MRCI)/cm−1
(9,7)  134.96  132.49 
(9,8)  134.96  132.46 
(9,9)  134.97  132.42 
(11,10)  134.97  132.42 
(17,13)  134.96  132.42 
(17,15)a  134.97  ... 
OH(7,5)b  136.32  132.18 
a

Full valence active space.

b

Full valence active space for OH.

The FPA approach was also employed to compute D0, and the results are shown in Table IV. The computed 634 cm−1 dissociation energy is lower than the 956 cm−1 upper limit determined from the analysis of the OH product state distributions associated with the photodissociation of the gas-phase complex.4 

TABLE IV.

Focal point analysis of the dissociation energy: OH–C2H2(2B1) → OH(2Π) + C2H2(1Σ).a

Unit: cm−1 ΔEe(ROHF) +δ[MP2] +δ[CCSD] +δ[CCSD(T)] +δ[CCSDT] +δ[CCSDT(Q)] NET
AVDZ  +545.97  +632.15  −116.17  +110.51  +0.31  +4.51  +1177.28 
AVTZ  +538.39  +659.61  −139.87  +101.53  [+0.31]  [+4.51]  [+1164.48] 
AVQZ  +514.51  +632.33  −152.16  +102.45  [+0.31]  [+4.51]  [+1101.95] 
AV5Z  +506.70  +612.66  −151.17  +101.81  [+0.31]  [+4.51]  [+1074.82] 
CBS LIMIT  [+503.41]  [+592.03]  [−150.14]  [+101.18]  [+0.31]  [+4.51]  [+1051.30] 
Function  a + becX  a + bX−3  a + bX−3  a + bX−3  Addition  Addition   
X (fit points)=  (3,4,5)  (4,5)  (4,5)  (4,5)       
FC-CCSD(T)/aug-cc-pVTZ reference geometry 
Δ(core) = + 2.57; Δ(DBOC) = + 0.19; Δ(rel) = − 5.51; Δ(ZPV E) = − 412.57. 
D0(FPA) = + 1051.30 + 2.57 + 0.19 − 5.51 − 412.57 = + 635.98 cm−1 
Unit: cm−1 ΔEe(ROHF) +δ[MP2] +δ[CCSD] +δ[CCSD(T)] +δ[CCSDT] +δ[CCSDT(Q)] NET
AVDZ  +545.97  +632.15  −116.17  +110.51  +0.31  +4.51  +1177.28 
AVTZ  +538.39  +659.61  −139.87  +101.53  [+0.31]  [+4.51]  [+1164.48] 
AVQZ  +514.51  +632.33  −152.16  +102.45  [+0.31]  [+4.51]  [+1101.95] 
AV5Z  +506.70  +612.66  −151.17  +101.81  [+0.31]  [+4.51]  [+1074.82] 
CBS LIMIT  [+503.41]  [+592.03]  [−150.14]  [+101.18]  [+0.31]  [+4.51]  [+1051.30] 
Function  a + becX  a + bX−3  a + bX−3  a + bX−3  Addition  Addition   
X (fit points)=  (3,4,5)  (4,5)  (4,5)  (4,5)       
FC-CCSD(T)/aug-cc-pVTZ reference geometry 
Δ(core) = + 2.57; Δ(DBOC) = + 0.19; Δ(rel) = − 5.51; Δ(ZPV E) = − 412.57. 
D0(FPA) = + 1051.30 + 2.57 + 0.19 − 5.51 − 412.57 = + 635.98 cm−1 
a

See Table II for footnote.

The aforementioned spectral trends for a 6 K ensemble were previously compared to gas-phase photodissociation spectra of both a- and b-type bands of the T-shaped complex.7,8 Parity splitting indicative of ρ was not resolved in the a-type OH stretch overtone, although the spectrum could be clearly identified as being due to a complex near the unquenched limit. This assignment was based on the separation of partially resolved P and R branches from an intense central Q branch. Indeed, the partially resolved a-type band could be satisfactorily simulated with a ρ value set equal to the ab initio value determined by the same authors, namely, −140 cm−1.4,7 However, in a subsequent report, the sub-bands of the b-type CH stretch fundamental could be contour fitted, further constraining the gas-phase value of ρ to −148.1(7) cm−1.8 There is excellent agreement between this gas-phase experimental value and the energy difference computed with the focal point approach, which places the 2B1 level 147.75 cm−1below the energy of the 2B2 level (Table II), in the absence of spin-orbit coupling. Using Eq. (8), the energetic difference between the two spin-orbit coupled levels in the gas phase is found to be 203 cm−1.

Figures 6 and 7 show the a-type OH and OD stretch fundamentals, respectively, for the He-solvated OH(D)–C2H2 complex. Line widths less than 0.01 cm−1 are observed, and this resolution is sufficient to resolve parity splitting in the P = 1 2 , ω = 3 2 manifold of levels. Figure 8 shows the b-type CH stretch spectrum of He-solvated OH–C2H2, which also contains sufficiently narrow lines to reveal parity splitting within some of the (ΔP, ω) rotational sub-bands. Assignments of individual rovibrational transitions are given in Figure 9, where the labeling scheme, ΔPΔJP(J″), is based on quantum numbers in the unquenched limit. Transitions derived from parity split levels in the P = 1 2 , ω = 3 2 manifold are explicitly labeled below the a-type simulation. Parity splitting is not resolved for transitions derived from levels in the P = 3 2 , ω = 3 2 manifold.

FIG. 6.

Experimental a-type band (OH stretch) and simulation (red) based on the constants listed in Table I.

FIG. 6.

Experimental a-type band (OH stretch) and simulation (red) based on the constants listed in Table I.

Close modal
FIG. 7.

Experimental a-type band (OD stretch) and simulation (red) based on the constants listed in Table I. The constants that have been modified for this OD–C2H2 simulation are (B + C)/2″ = 0.0600, DJ = 0.000 35, and ν0 = 2597.492. All other constants are the same as those for the OH–C2H2a-type band.

FIG. 7.

Experimental a-type band (OD stretch) and simulation (red) based on the constants listed in Table I. The constants that have been modified for this OD–C2H2 simulation are (B + C)/2″ = 0.0600, DJ = 0.000 35, and ν0 = 2597.492. All other constants are the same as those for the OH–C2H2a-type band.

Close modal
FIG. 8.

Experimental b-type band (antisymmetric CH stretch) and simulation (red) based on the constants listed in Table I.

FIG. 8.

Experimental b-type band (antisymmetric CH stretch) and simulation (red) based on the constants listed in Table I.

Close modal
FIG. 9.

Assignments of transitions observed in the a-type (bottom) and b-type (top) bands, using the notation ΔPΔJP(J″). Here, the quantum number P is only “good” in the ρ → 0 limit. The parity doubling associated with the a-type transitions from P″ = 1/2 levels is shown at the bottom of the spectrum. Transitions (a-type) from P″ = 3/2 levels are observed as single, undoubled peaks. Peaks labelled as PΔJ1/2 in the b-type spectrum arise from P, ω = 1/2, +3/2 → P, ω = 1/2, −3/2 transitions, which can be represented alternatively as P, ω = + 1/2, 3/2 → P, ω = − 1/2, 3/2 transitions.

FIG. 9.

Assignments of transitions observed in the a-type (bottom) and b-type (top) bands, using the notation ΔPΔJP(J″). Here, the quantum number P is only “good” in the ρ → 0 limit. The parity doubling associated with the a-type transitions from P″ = 1/2 levels is shown at the bottom of the spectrum. Transitions (a-type) from P″ = 3/2 levels are observed as single, undoubled peaks. Peaks labelled as PΔJ1/2 in the b-type spectrum arise from P, ω = 1/2, +3/2 → P, ω = 1/2, −3/2 transitions, which can be represented alternatively as P, ω = + 1/2, 3/2 → P, ω = − 1/2, 3/2 transitions.

Close modal

For the OH containing complexes, a consistent set of rotational constants (except for ΔA) is used to generate simulations for a- and b-type vibrational bands. Typical reductions in rotational constants from gas-phase values are observed, which are derived from the He solvent’s contribution to the rotor’s effective moment of inertia.13–15 For example, the (B + C)/2 constant is 2.3 times smaller in He droplets, whereas the faster rotational motion about the a inertial axis leads to an effective A constant much closer to the gas-phase value. These effects are consistent with several previous studies of closed-shell systems in He droplets,14 including the analogous T-shaped HF–C2H2 complex.45 The change in the A rotational constant upon vibrational excitation is significantly larger for the perpendicular CH stretch, in comparison to the OH stretch band. Again, this effect was also observed for HF–C2H2 and has been discussed previously.45 Table V compares rotational constants extracted from b-type rovibrational spectra of the T-shaped OH– and HF–C2H2 complexes in the gas-phase and in He droplets.

TABLE V.

Comparison of gas phase and He droplet constants determined from b-type bands.a

(b-type)  OH–C2H2  HF–C2H2b 
Δν0(He-gas)  +0.26 (1) cm−1  +0.078 (2) cm−1 
Agas/AHe  1.03  1.23 (1) 
ΔAgasAHe  0.06  0.13 (2)c 
(B + C)gas/(B + C)He  2.31  2.15 (2) 
ρgas/ρHe  0.897 (27)  ... 
(b-type)  OH–C2H2  HF–C2H2b 
Δν0(He-gas)  +0.26 (1) cm−1  +0.078 (2) cm−1 
Agas/AHe  1.03  1.23 (1) 
ΔAgasAHe  0.06  0.13 (2)c 
(B + C)gas/(B + C)He  2.31  2.15 (2) 
ρgas/ρHe  0.897 (27)  ... 
a

Numbers in parentheses are 2σ uncertainties in the last digit.

b

From Refs. 45 and 52.

c

The ΔA constant associated with the b-type HF–C2H2 band in the He droplet spectrum has been refit, assuming all the constants in Ref. 45, except DK is set to 0.0078 cm−1, as is done here for OH–C2H2.

Excellent agreement between the experiment and the two-state model is obtained when the spin-orbit coupling constant of OH is fixed to the gas-phase value (−139 cm−1) and ρ is set equal to −165 cm−1. This effectiveρ value is constrained on the basis of combination differences of parity split lines in the qQ1/2 branch of the a-type spectrum and is largely independent of small changes made to the values chosen for rotational and distortion constants, leading to an estimated experimental error bar of ±1 cm−1. However, because combination differences give the sum, ρ″ + ρ′, the −165(1) cm−1 value extracted from the a-type spectrum is necessarily the average value in the ground and excited vibrational states. The remarkable agreement between experimental and simulated line positions for both a- and b-type spectra, using this common value of ρ, provides strong confidence in its value.

As described above, the spectroscopic fitting parameter ρ is defined in the rigid-T model as the energy difference between 2B1 and 2B2 electronic states in the strong-interaction limit, in which orbital angular momentum is fully quenched. In the intermediate regime, however, the energy difference between spin-orbit coupled states is determined from Eq. (8). Given the IR spectra here, which probe transitions within the lowest electronic level, it is not possible to separately determine ρ and ASO. For example, combination differences involving transitions from the parity doubled JP,ω = 1/21/2,3/2 level reveal only the ratio, ρ A SO = 1 . 19 ( 1 ) . For the gas-phase species, computations targeting full-valence active space MRCI reveal a rather small difference (on the order of 0.1 cm−1) between the ASO constants of OH and its complex with acetylene (Table IV), a result that is expected for a system closer to the weak-interaction limit. It is altogether a different question how much the solvent may affect the spin-orbit coupling in OH monomer, which is a far more difficult theoretical problem. Nevertheless, the two-state model is explicitly defined and parameterized using the ASO constant of gas-phase OH. The value for ρ extracted from the He droplet spectra (−165(1) cm−1) is therefore obtained under the assumption that the spin-orbit coupling constant for the He-solvated complex is equivalent to that of the gas-phase OH monomer. This provides the most direct connection to the gas-phase two-state model, allowing for a single adjustable parameter, ρ, to describe the solvent effect on the energetic separation between the two electronic states.

With this model, the energy difference (Eq. (8)) between coupled electronic states in the complex is determined spectroscopically (from the value of ρ A SO ) to be 216 cm−1 in He droplets, which is 13 cm−1 larger than the value measured for the gas-phase complex. The sign of this energy difference implies that the reduction in free energy upon solvation is larger for the 2B1 electronic state, in comparison to the 2B2 state.

In our previous report on the IR spectrum of the OH monomer in He droplets,22 we noted that the separation between Q(3/2) and R(3/2) transitions implies an energetic separation between 2Π3/2 and 2Π1/2 levels that is greater than in the gas-phase; otherwise, an unphysical rotational constant larger than the gas-phase value is necessary to account for the energy difference between the two rovibrational transitions. This anomalous spitting in the droplet spectrum can be rationalized if we assume a small differential solvation energy with respect to the two lowest energy electronic states of OH. Specifically, the 2Π3/2 electronic state is expected to have associated with it a more negative free energy of solvation than does 2Π1/2. This difference derives from the differing electron density distributions about the bond axis. The density is cylindrically symmetric in the 2Π1/2 ground rotational state (J = 1/2), but it is already partially aligned in the lowest rotational state (J = 3/2) within the 2Π3/2 manifold of levels.46 This partial alignment should result in a larger attractive interaction between the OH dopant and the He density localized in the first few solvent shells, driving the 2Π3/2 ground state lower in energy upon solvation, in comparison to 2Π1/2.

To test for the magnitude of this differential solvation effect, we revisit the spectrum of He-solvated OH in Figure 10. While the Q(3/2) rovibrational transition is split due to lambda doubling, this splitting is not resolved for the R(3/2) transition due to a homogeneous broadening mechanism.22 The simulations below the experimental spectrum are generated using a three-state model22 that assumes the B0,1 constants are reduced to 98.5% of their gas-phase values, which is similar to the reduction observed for He-solvated hydrogen fluoride.47 We note, however, that the Q(3/2) to R(3/2) spacing is larger than that in the gas phase (by ≈0.3 cm−1) even if we assume rotational constants that are 100% their gas-phase values. The three-state model from Ref. 22 is modified to include a diagonal term that increases the energetic separation between 2Π3/2 and 2Π1/2 levels in the absence of rotation. As shown in the figure, the spacing between Q(3/2) and R(3/2) transitions is best reproduced when the 2Π3/2 and 2Π1/2 levels are split by an additional ≈50 cm−1 beyond the gas-phase energetic difference. Larger (smaller) reductions of the B0,1 constants require larger (smaller) values of this splitting parameter in the model for a satisfactory reproduction of the experimental spectrum. In the limit of gas-phase rotational constants (i.e., the He contributes nothing to the rotor’s effective moment of inertia), the droplet spectrum can be accounted for by assuming a 10 cm−1 differential solvation energy between 2Π3/2 and 2Π1/2 levels. The physical origin of the increased splitting between Q(3/2) and R(3/2) transitions can be traced to a detuning of the spin-uncoupling interaction that couples 2Π3/2 and 2Π1/2 levels in the rotating molecule, which is expected if these levels are indeed driven further away from each other upon helium solvation.

FIG. 10.

Experimental Q(3/2) and R(3/2) transitions of the He-solvated OH monomer (top panel) compared to simulations (bottom panel) that assume a 1.5% reduction in the B0,1 rotational constants and a spin-orbit coupling constant equal to the gas-phase value (−139.0508 cm−1). The simulated spectra have been translated such that the Q(3/2) fe transitions are at the same frequency (vertical dashed line). The experimental spacing between the Q(3/2) and R(3/2) transitions is most closely reproduced by the three-state model when the energy difference between 2Π3/2 and 2Π1/2 levels is increased by ≈50 cm−1 beyond the gas-phase value.

FIG. 10.

Experimental Q(3/2) and R(3/2) transitions of the He-solvated OH monomer (top panel) compared to simulations (bottom panel) that assume a 1.5% reduction in the B0,1 rotational constants and a spin-orbit coupling constant equal to the gas-phase value (−139.0508 cm−1). The simulated spectra have been translated such that the Q(3/2) fe transitions are at the same frequency (vertical dashed line). The experimental spacing between the Q(3/2) and R(3/2) transitions is most closely reproduced by the three-state model when the energy difference between 2Π3/2 and 2Π1/2 levels is increased by ≈50 cm−1 beyond the gas-phase value.

Close modal

This differential solvation effect is apparently transferred to the OH–C2H2 complex, and it is revealed in the rigid-T model as an increase in ρ . Indeed, the electronic state with the more negative free energy of solvation, 2B1, is the one that correlates to the partially aligned 2Π3/2 ground state of OH monomer. Although a challenging problem, the theoretical machinery necessary to compute such solvation energy differences of electronic states in He-solvated molecules exists,48–51 and we hope this report motivates future theoretical efforts that employ OH–C2H2 as a benchmark.

The OH–C2H2 complex,4,7,8 having a T-shaped equilibrium structure analogous to HF–C2H2,45,52 is formed in helium droplets following the sequential addition of the OH and C2H2 monomers. Dissipation of translational, internal, and complexation energies via He atom evaporation leads to a 0.35 K ensemble, which is probed with high-resolution IR laser spectroscopy in the high frequency X–H stretch region. Although limited by inhomogeneous broadening effects due to the matrix environment, spectral line widths are sufficiently narrow to reveal the spectral signatures associated with the coupling of partially quenched electronic angular momentum to molecular rotation. Parity doubling in both a- and b-type rovibrational bands is modeled with a modified version of Marshall and Lester’s rigid-T model,7 which accounts for the quenching of orbital angular momentum upon complex formation. Combination differences in the a-type band constrain the energetic difference between 2B2 (A′) and 2B1 (A″) spin-orbit coupled electronic states to be 216 (1) cm−1. This energy difference in He droplets is 13 cm−1 larger than the value obtained from a contour fit of the C–H antisymmetric stretch b-type band of the gas-phase species. This difference is attributed solely to a He solvent effect, rather than a problem with the contour fitting of the gas-phase spectrum. This conclusion is justified by high level electronic structure theory computations targeting the CCSDT(Q)/CBS level via a focal-point approach, which predict the 2B22B1 energy difference for the isolated system to be within 1 cm−1 of the experimental gas-phase value.

The deviation of the (2B22B1) energetic difference in He-solvated OH–C2H2 from its value in the gas-phase is rationalized in terms of a differing free energy of solvation associated with the two electronic states. Specifically, the 2B1 electronic state is driven lower in energy upon solvation, in comparison to the 2B2 electronic state. The more strongly affected 2B1 state correlates to the 2Π3/2 + 1Σ+ reaction asymptote and nominally corresponds to the singly occupied pπ electron pointing out of the molecular plane.

Spectroscopy of the OH monomer in He reveals a similar effect consistent with the solvation energy difference discovered for the complex. The lowest energy spin-orbit coupled 2Π3/2 manifold of levels, in which the electron density distribution about the bond axis is already partially aligned in the lowest J = 3/2 rotational level, is apparently driven lower in energy upon solvation in comparison to the 2Π1/2 manifold, which has a cylindrically symmetric electron density in the lowest rotational state. This differential solvation effect leads to an effective splitting between the 2Π3/2 and 2Π1/2 levels that is at least 10 cm−1 larger than that in the gas phase. However, this value is based on the assumption that the He solvent contributes nothing to the OH rotor’s effective moment of inertia. With a physically reasonable estimate of the rotational constant of He-solvated OH, the model predicts a splitting between 2Π3/2 and 2Π1/2 levels that is ≈50 cm−1 larger than the gas-phase energetic difference.

G.E.D. acknowledges support from the National Science Foundation (CHE-1054742) and partial support from the donors of the American Chemical Society Petroleum Research Fund (50223-DNI6). The original development of the rigid-T model was supported by The H. Axel Schupf ’57 Fund for Intellectual Life. The authors are very grateful to Marsha I. Lester (University of Pennsylvania) for her encouragement of this work and for bringing this collaboration together.

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