Sequential capture of OH and CO by superfluid helium droplets leads exclusively to the formation of the linear, entrance-channel complex, OH–CO. This species is characterized by infrared laser Stark and Zeeman spectroscopy via measurements of the fundamental OH stretching vibration. Experimental dipole moments are in disagreement with *ab initio* calculations at the equilibrium geometry, indicating large-amplitude motion on the ground state potential energy surface. Vibrational averaging along the hydroxyl bending coordinate recovers 80% of the observed deviation from the equilibrium dipole moment. Inhomogeneous line broadening in the zero-field spectrum is modeled with an effective Hamiltonian approach that aims to account for the anisotropic molecule-helium interaction potential that arises as the OH–CO complex is displaced from the center of the droplet.

## I. INTRODUCTION

The exothermic exchange reaction between OH and CO to give H and CO_{2} is one of the most important reactions in atmospheric and combustion chemistry.^{1} In both the terrestrial atmosphere^{2} and high temperature combustion environments,^{3} it is largely responsible for the oxidation of CO in addition to being an important sink for the OH radical. It is a prototypical example of a tetratomic “complex-forming” reaction,^{4} where the “complex” corresponds to the chemically bound hydroxycarbonyl intermediate (HOCO).^{5,6} At energies well below the exit channel barrier, HOCO dissociates to give H and CO_{2} via a deep-tunneling mechanism, which was revealed by dissociative photodetachment studies of the anion (HOCO^{−}).^{1,7–9} These measurements have spurred several recent theoretical investigations of the tunneling mechanism and its mode specificity,^{9–12} including full-dimensional quantum dynamics calculations.^{13,14} Here we investigate the outcome of the sequential capture of OH (or OD) and CO by superfluid helium droplets and the ensuing solvent-mediated reaction using infrared (IR) laser spectroscopy.

The *trans* isomer of HOCO has been characterized at high resolution by microwave,^{15,16} far-IR,^{17,18} and mid-IR spectroscopies.^{19–22} While the *trans*-HOCO isomer represents the global minimum on the reactive potential energy surface,^{8,10,23,24} other minima include the *cis*-HOCO isomer and two weakly bound linear complexes (OH–CO and OH–OC), both of which lie in the entrance valley to the reaction. Vibrational frequencies for both *trans*- and *cis*-HOCO have been obtained via anion photoelectron spectroscopy^{25} and matrix isolation spectroscopy.^{26–28} A rotational spectrum of *cis*-HOCO has been reported by Endo and co-workers.^{16} The OH–CO complex is bound by ∼320 cm^{−1} and the interconversion barrier leading to *trans*-HOCO lies ∼330 cm^{−1} above the asymptotic OH + CO energy.^{8,10,23} The OH stretch overtone spectroscopy and photodissociation dynamics of OH–CO have been extensively studied by Lester and co-workers in a series of seminal papers.^{29–35} The other predicted entrance channel complex, OH–OC, has never been observed experimentally.

Helium droplets provide a cold (0.4 K)^{36} liquid environment that very weakly interacts with foreign species.^{37–39} The highly dissipative nature of the liquid with respect to heat means that foreign species very quickly thermalize to the droplet temperature, such that it is possible to trap molecular systems in local minima. For example, different conformers of molecules are readily “frozen out” in helium droplets with a relative abundance that is unchanged with respect to the gas phase.^{40–43} Other examples of kinetic trapping in helium droplets include the formation of the high energy cyclic isomer of (H_{2}O)_{6},^{44} non-equilibrium clusters of HF,^{45} and pre-reactive complexes such as Cl–HCN^{46} and Ga–HCN.^{47} The dissipative nature of helium droplets is ideally suited for trapping entrance channel complexes along bimolecular reaction paths, such as for the OH + CO reaction.

The HOCO complex is not expected to be produced following the association reaction between OH and CO in helium droplets, because the zero-point corrected barrier in going from OH + CO to *trans*-HOCO is above the asymptotic reaction energy.^{10} The internal energy of the molecular fragments is expected to be dissipated on a time scale that is fast in comparison to the time scale for complex formation in helium droplets; therefore, the *in situ* bimolecular reaction is expected to occur between monomers lacking internal energy. In the absence of tunneling, any positive barrier in the entrance channel will thereby serve to trap the system in one of the pre-reactive OHCO wells. Nevertheless, we searched for spectroscopic signals corresponding to both *trans*- and *cis*-HOCO. The search resulted in no evidence for either of these species, indicating that barriers are sufficiently high such that the reaction does not proceed in helium droplets on the time scale of the experiment (∼2 ms). Instead, we find that the helium-mediated OH + CO association reaction leads exclusively to the OH–CO entrance channel complex. We report a detailed spectroscopic analysis of this species by employing high-resolution Stark and Zeeman measurements in the vicinity of the fundamental OH stretching vibration.

## II. EXPERIMENTAL METHODS

The apparatus used for measuring helium droplet depletion spectra has been described in detail earlier,^{37,48–50} and we only include some important aspects here. Helium nanodroplets consisting of several thousand atoms are generated by expanding high pressure, low temperature helium gas through a 5 *μ*m pinhole nozzle. The expansion is skimmed and the droplet beam passes into a pick-up chamber, which houses a pyrolysis source and pick-up cell. The pyrolysis source consists of a water cooled, resistively heated quartz tube that is used to produce the OH and OD radicals via thermal decomposition of tert-butyl hydroperoxide^{51} or tert-butyl deuteroperoxide,^{52} respectively (Eq. (1)). The flow rate of precursor through the tube is adjusted to maximize the number of OH(D) doped helium droplets. The droplet beam subsequently passes through the pick-up cell, which contains a CO pressure optimized for the pick-up of one CO molecule per droplet (except for the OD–CO survey scan, for which the pressure was higher). Further downstream, the doped droplets are overlapped with the idler output from a continuous wave optical parametric oscillator (OPO).^{50} Subsequently, the droplet beam is detected with a quadrupole mass spectrometer (QMS),

For the zero-field spectra, the IR output from the OPO system was aligned collinearly with the droplet beam, and for the Stark and Zeeman spectra, the output crossed (nearly perpendicularly) the droplet beam ∼30 times in a multipass cell.^{51,53} The polarization of the laser beam can be aligned either parallel or perpendicular to the electric (or magnetic) static field axis. The Stark field is calibrated via measurements of the field induced splitting of the HCN *R*(0) line into its two Δ*M _{J}* components.

^{54}The separation between the Stark electrodes is found to be 3.10 ± 0.03 mm. Details of the Zeeman cell, which previously have not been reported, are contained in the supporting information (see Fig. S1 of the supplementary material). The static magnetic field (0.425(2) T) is calibrated with a high-precision, hand-held Hall probe.

When the IR radiation is absorbed by the species in the helium droplet, energy transfer to the solvent occurs on a time scale that is fast in comparison to the flight time of droplets to the detector, which results in the evaporation of several hundred helium atoms. Thus, when on resonance, the ionization cross section of the droplet is smaller than when off resonance, and this photo-induced cross section reduction for ionization is detected by the QMS. The output from the QMS is processed with a lock-in amplifier (laser is amplitude modulated at ∼80 Hz) and plotted against the output from a high-precision wavemeter (repeatability ±20 MHz) to give the depletion spectra. For the species investigated here, we tuned the quadrupole to pass either ions with mass 17 (OH^{+}), 29 (COH^{+}), or 44 u (CO_{2}^{+}), which all result from the ionization induced fragmentation of OH–CO. Except for the OH–CO survey spectrum, the spectra have been normalized to laser power.

## III. THEORETICAL METHODS

Electronic structure computations were all carried out using the CFOUR software package.^{55} Geometries, harmonic frequencies, potential energy surfaces, and dipole moment surfaces were all computed at the CCSD(T)/Def2-TZVPD level of theory. The convergence of dipole moments was tested by single point energy computations employing Dunning’s aug-cc-pVXZ basis sets.^{56} Dipole moments computed using the Def2-TZVPD basis are essentially the same as those computed with the aug-cc-pVQZ basis.

To obtain the vibrationally averaged dipole moment for OH–CO, we calculate the ground state vibrational wave function in a two-dimensional representation consisting of the center of mass separation between the OH and CO fragments (*R*) and the angle (θ_{1}) between the OH bond and a vector along *R*. In this picture, the CO bending motion is assumed to be negligible, and the angle (θ_{2}) between the CO bond and the vector along *R* is fixed at 0° (θ_{1} = 180° and θ_{2} = 0° corresponds to the OH–CO equilibrium geometry). The calculation is carried out in two steps based on the Jacobi coordinate Hamiltonian, expressed in terms of *R* and θ_{1}, their conjugate momenta and the reduced mass associated with the complex *μ _{R}*,

First the vibrational energies and wave functions are obtained for the one-dimensional cuts through the potential in *R* at θ_{1} = 160° and in θ_{1} with *R* = 3.9856 Å using a discrete variable representation (DVR).^{57,58} These values are chosen to be close to the maximum in the probability amplitude. A direct product basis is generated from these wave functions, and the two-dimensional Schrödinger equation is solved in this basis. The procedure closely follows the approach we used to obtain the vibrational wave functions for ICN^{−}.^{59} In the present work, the stretch wave function is based on 500 DVR points ranging from 3.2 to 4.8 Å, while 500 DVR points based on Legendre polynomials are used to describe the bend wave function. The lowest 100 and 60 solutions to stretch and bend Hamiltonians, respectively, are used to generate the basis for the two-dimensional calculation.

## IV. RESULTS

### A. Survey spectrum

A survey spectrum covering the 3500–3660 cm^{−1} region is shown in Fig. 1, which was recorded with conditions optimized for sequential capture of OH and CO. Positive spectroscopic signal corresponds to ion current depletion in mass channel 17 u (OH^{+}). Other than the *Q*(3/2) and *R*(3/2) transitions of OH and weak features due to H_{2}O_{2},^{51,60} one strong band is observed near 3551 cm^{−1}. The dashed lines in Fig. 1 labeled as “OH–CO” and “OH–OC” represent harmonic band origin shifts from the OH monomer, which were computed at the CCSD(T)/Def2-TZVP level of theory. For the OH–CO complex, the computed 19 cm^{−1} red shift is in rather good agreement with the 3551 cm^{−1} band (17 cm^{−1} red shift from OH monomer), whereas a 10 cm^{−1} blue shift is predicted for the OH–OC complex. The dashed line labeled as “*trans*-HOCO” represents the experimental gas-phase band origin for the OH stretch.^{22} Similar survey spectra were recorded in mass channels 29 u (HCO^{+}) and 44 u (OCO^{+}), and both contained the band at 3551 cm^{−1}. None of the survey spectra contain evidence for either the higher energy OH–OC linear complex or the covalently bound HOCO radical. Sequential capture of OH and CO by helium droplets apparently leads to the exclusive formation of the linear OH–CO entrance channel complex. The analysis of high resolution spectra in the vicinity of the 3551 cm^{−1} band confirms this assignment.

### B. OH–CO zero-field spectrum

Figure 2 contains several high resolution scans (black traces) in the vicinity of the 3551 cm^{−1} band with different electric fields applied to the Stark electrodes. The bottom spectrum corresponds to the zero-field condition. Cursory examination of the zero-field spectrum reveals *P*, *Q*, and *R* branches. The separation between the *Q* branch and the first *P* and *R* branch transitions is approximately equal to 5*B* (∼0.24 cm^{−1}), which is consistent with the half-integer *J* quantum numbers and the ^{2}Π_{3/2} electronic ground state expected for a linear complex containing the hydroxyl radical and a closed shell partner. Individual transitions are labeled in the figure with the standard convention Δ*J*(*J*″).

The effective Hamiltonian used to model the zero-field spectrum is given in Eq. (3), which contains terms for rigid rotation and spin-orbit coupling.^{61} The tensor operators $T1J$, $T1L$, and $T1S$ correspond to the total (less nuclear spin), orbital, and spin angular momenta, respectively. The parameters *A*_{SO} and *B* are the spin-orbit coupling constant and the rotational constant for the OH–CO complex, respectively,

Equation (4) is obtained upon expanding the dot products. The *p* and *q* indices span { − 1, 0, and + 1} and are associated with laboratory-fixed and molecule-fixed components of the angular momenta, respectively,

We chose to omit the last group of terms falling under the *q* = ± 1 summation, because they contribute to, respectively, off-diagonal spin-orbit coupling that shifts the electronic energy independent of *J*, a constant contribution to the electronic energy that can be absorbed into the vibronic band origin, and an *L*-uncoupling interaction that mixes Π and Σ states leading to Λ-doubling. The estimated Λ-doubling is several orders smaller than the experimental line widths (∼250 MHz).

The Hamiltonian matrix is represented in a Hund’s case (a) primitive basis (Eq. (5)),

The quantum numbers Λ, Σ, and Ω correspond to projections of the orbital $\eta =1$, spin $S=1/2$, and total angular momenta of OH–CO onto the molecular frame z-axis (*q* = 0), respectively. *M _{J}* is the projection of the total angular momentum onto the laboratory frame Z-axis (

*p*= 0), which is defined as the axis of the static electric or magnetic field applied to the laser interaction region.

Matrix elements in the primitive case (a) representation are derived by applying the Wigner-Eckart theorem and standard angular momentum algebraic manipulations (Eq. (6)),^{61}

The matrix elements given in Eq. (6) are almost completely diagonal, except for the term that falls under the *q* = ± 1 summation. This term corresponds to an off-diagonal spin-rotation contribution to the energy that is expected to be small for *J* levels populated at 0.35 K, for example, it has a selection rule equal to ΔΩ = ΔΣ = ± 1, and therefore couples different spin-orbit manifolds that are separated by ∼140 cm^{−1}.

In an *ad hoc* manner, we include in the Hamiltonian matrix a single quadratic centrifugal distortion term that is diagonal in all quantum numbers, i.e., $\u2212DJJ2J+12$. We find this to be the simplest way to model the *J*-dependence of the molecule-helium interaction potential, which is expected to become more anisotropic with increasing *J*.^{62} Unlike the typical definition that applies to gas-phase molecules, the centrifugal distortion term used here models the increase in the solvent-solute *effective* moment of inertia as *J* increases. The Hamiltonian matrices are diagonalized for both the ground and excited vibrational states. The spin-orbit coupling constant, *A _{SO}*, is set equal to the OH monomer value (−139.05 cm

^{−1}), and the

*B*and

*D*constants are allowed to differ in the ground and excited vibrational manifolds.

_{J}The transition dipole moment operator projected onto the laser polarization axis and its matrix elements in the primitive case (a) basis are given in Eqs. (7) and (8), respectively,

The summation over the *p* index in Eq. (8) allows for the prediction of spectra obtained with either parallel, perpendicular, or random laser electric field polarizations relative to the lab-frame Z-axis. The ** M** matrix is transformed via the matrix operation, $Ue\u2020MUg=I$, where

*U*_{g}and

*U*_{e}are the eigenvector matrices for the ground and excited vibrational levels, respectively. The elements of the intensity matrix,

**, correspond to $Iij/w$, where**

*I**I*is the intensity of the transition from the

_{ij}*j*th ground-state level to the

*i*th excited-state level, and

*w*is a Boltzmann weight with

*T*= 0.35 K.

_{rot}The simulation of the zero-field spectrum is shown as the red trace along the bottom of Fig. 2, and the best fit band origin along with the rotational and centrifugal distortion constants are given in Table I. We note again that the simulations assume a ^{2}Π_{3/2} electronic ground state for the spectral carrier, which is consistent with computations and previous OH stretch overtone spectroscopy of the OH–CO complex.^{29,30}

Helium . | ν_{0}
. | B″
. | B′
. | D″
. | D′
. | μ″ (D)
. | μ′ (D)
. |
---|---|---|---|---|---|---|---|

OH–CO | 3551.233(1) | 0.0480(5) | 0.0478(3) | 0.000 09(1) | 0.000 08(2) | 1.852(5) | 1.885(6) |

OD–CO | 2616.478(2) | 0.0490(7) | 0.0481(7) | 0.000 14(6) | 0.000 10(4) | 1.88(8) | 1.94(5) |

Gas^{b} | B″ | ||||||

OH–CO | 0.0972(1) | ||||||

OD–CO | 0.0961(5) |

Helium . | ν_{0}
. | B″
. | B′
. | D″
. | D′
. | μ″ (D)
. | μ′ (D)
. |
---|---|---|---|---|---|---|---|

OH–CO | 3551.233(1) | 0.0480(5) | 0.0478(3) | 0.000 09(1) | 0.000 08(2) | 1.852(5) | 1.885(6) |

OD–CO | 2616.478(2) | 0.0490(7) | 0.0481(7) | 0.000 14(6) | 0.000 10(4) | 1.88(8) | 1.94(5) |

Gas^{b} | B″ | ||||||

OH–CO | 0.0972(1) | ||||||

OD–CO | 0.0961(5) |

^{a}

The spin-orbit coupling constant was fixed at −139.0508 cm^{−1} in the simulations.

We measured similar spectra for OD + CO. The survey scan (with higher CO pressure than for OH + CO) reveals bands that correspond to OD–CO and most likely OD–(CO)_{2} (see Fig. S2 of the supplementary material), while there is no evidence for OD–OC. The high resolution scan of the OD–CO band reveals a similar structure to that of OH–CO (see Fig. S3 of the supplementary material).

The ground state rotational constants for OX–CO complexes are reduced to ∼50% of their gas phase values, which is relatively similar to other helium-solvated rotors with rotational constants of similar magnitude.^{37} The solvent contribution to the effective moment of inertia arises from the anisotropy in the He–(OX–CO) interaction potential, resulting in a renormalization of the rotational constant in going from the gas phase to liquid helium.^{63} The vibrational red shift from OX monomer is 17.27 cm^{−1} for OH–CO, 14.82 cm^{−1} for OD–CO, and 19.4 cm^{−1} for OD–(CO)_{2}. For comparison, the gas phase overtone (v = 2-0) red shifts divided by two are 14.8 cm^{−1} for OH–CO and 13.0 cm^{−1} for OD–CO, which are less than those observed here for the fundamental bands due to vibrational anharmonicity. Although the gas-phase fundamental OX stretching bands have not been observed, on the basis of an empirically observed dependence of the solvent shift on the complexation induced red shift of OX stretches,^{37} we estimate the solvent shifts for OX–CO complexes to be ∼2 cm^{−1} to the red.

### C. OH–CO Stark spectra

The Stark effect is accounted for by appending the Stark operator^{61} (Eq. (9)) to the zero-field effective Hamiltonian. Here, the tensor operators, $T1\mu $ and $T1E$ correspond to the molecular dipole moment and the external static Stark field, respectively,

Matrix elements of the Stark operator in the primitive case (a) basis are given in the following equation, where the magnitude of the vibrationally averaged dipole moment and the applied electric field are $\mu $ and $E$, respectively,

Stark spectra acquired at three separate field strengths are shown in Fig. 2 along with simulations, from which the magnitude of the permanent electric dipole moments in the ground and excited vibrational states are extracted. The Stark spectra were recorded with a perpendicular laser polarization configuration relative to the applied electric field. The agreement between experiment and simulation is generally excellent when the zero-field rotational constants are retained and the dipole moments are set equal to *μ*″ = 1.852(5) and *μ*′ = 1.885(6) D. The error bars are largely due to the uncertainty in the applied field strength. The vibrationally averaged induced dipole moment upon OH + CO complexation is ∼0.1 D.

### D. OH–CO Zeeman spectra

The Zeeman effect is accounted for by appending a truncated form of the Zeeman operator^{61} (Eq. (11)) to the zero-field effective Hamiltonian. Here, the tensor operator $T1B$ corresponds to the external static Zeeman field,

Here we aim to account for the interaction between the orbital and spin angular momenta and the magnetic field. Because hyperfine splitting is not resolved at zero-field, as a first approximation we omit terms in the effective Hamiltonian that model the interaction between nuclear spin angular momenta and the field. The matrix elements of the Zeeman operator in the primitive case (a) representation are given in the following equation, where the *g*-factors, *g _{L}* and

*g*, are set equal to 1.0 and 2.0032, respectively,

_{S}^{61}

Like the Stark effect, application of the Zeeman field mixes zero-field *J* levels; however, additionally, the Zeeman effect mixes different spin orbit manifolds via the terms parameterized by the magnitude of *μ _{B}B_{Z}g_{S}*. Experimental Zeeman spectra recorded with

*B*= 0.425(2) T are shown in Fig. 3. Both the magnitude of the calibrated magnetic field and the zero-field rotational constants are fixed in the simulations. Excellent agreement is obtained between simulation and experiment for both parallel and perpendicular polarization configurations, despite there being zero adjustable parameters. We take this as an indication that the form chosen for the effective Zeeman Hamiltonian is appropriate at this level of resolution (line widths typically ∼250 MHz).

_{Z}We note here that the Zeeman measurement provides unequivocal evidence for the ^{2}Π_{3/2} description of the electronic ground state of the OH–CO complex. Moreover, because of the anisotropic solvation environment about the molecular axis (e.g., the helium density in *A*′ and *A*″ planes should differ, in principle), one might posit a small solvent-induced quenching of the orbital angular momentum, and this effect would be revealed in the Zeeman spectrum. We find the Zeeman spectrum to be quite sensitive to the value of *g _{L}*. Within the error of the experiment, we judge that the simulation and experiment begin to disagree upon reducing the

*g*factor below about 0.98 (a 2% change), indicating that solvent-induced angular momentum quenching is, at most, a minor effect.

_{L}## V. DISCUSSION

### A. Outcome of the OH + CO reaction in helium droplets

Sequential capture and solvation of OH and CO by helium droplets leads to the exclusive formation of the OH–CO linear complex, as confirmed by IR spectroscopy in the fundamental OH stretching region. We find no evidence for the formation of either *cis*- or *trans*-HOCO. This observation is consistent with estimates of the OH–CO → *trans*-HOCO entrance channel barrier from kinetics studies, namely, 140–315 cm^{−1}.^{64,65} In agreement with these experimental estimates, zero-point energy corrected *ab initio* calculations predict the barrier to be 330 cm^{−1} above the asymptotic OH + CO energy.^{8,10,23,24} Furthermore, and perhaps surprisingly, we find no evidence for the OH–OC complex, which is predicted by *ab initio* theory to be bound by ∼160 cm^{−1} and separated from the OH–CO complex by a barrier of similar size.^{10,29}

It seems possible that as OH and CO approach within a helium droplet, long-range forces along the potential valley pre-orient the complex into the more electrostatically favorable OH–CO configuration and funnel the system into the OH–CO minimum, precluding the formation of OH–OC. An electrostatic pre-orientation mechanism was similarly invoked to rationalize the helium-assisted trapping of linear (HCN)_{n} clusters upon sequential addition of HCN to droplets containing the (HCN)_{n−1} species.^{66} To test the feasibility of this mechanism, we have computed barrier heights along the OH–OC↔OH–CO interconversion pathway as a function of the intermolecular separation, *R* (Fig. S4 of the supplementary material). As is evident from the potential slice shown in Fig. 4 (*R* = 4 Å), interconversion between linear complexes largely involves motion along the θ_{2} coordinate, i.e., the internal rotation of the CO moiety. Computations find the OH–CO → OH–OC interconversion barrier to be ∼3 *kT* at *R* = 20 Å, whereas the barrier in the reverse direction is ∼0.7 *kT*. This theoretical result implies that the long-range reorientation of the complex into the more electrostatically favorable OH–CO configuration will have the effect of biasing the outcome of cluster formation events, which is consistent with the experimental observation.

### B. Comparison of experimental and computed dipole moments

The OH–CO experimental dipole moment for the ground vibrational state is 1.852(5) D. Computations at the CCSD(T)/aug-cc-pVQZ level of theory predict an equilibrium dipole moment equal to 2.185 D, which differs from the experimental value by 0.333 D. An error of this magnitude is not expected at this level of electronic structure theory, as the dipole moment operator is a sum of one-electron operators and is easily converged with increasing level of theory and basis set size. We have confirmed the convergence of the computed dipole moment at the equilibrium geometry (e.g., at the CCSD(T)/aug-cc-pVTZ level, *μ* = 2.186 D), and we therefore take the observed difference as a relatively good measure of the deviation between the experimental dipole moment and the gas-phase equilibrium value. The experimental measurement necessarily probes the expectation value of the permanent dipole moment, and vibrational averaging must be taken into account. Moreover, it is necessary to assess the extent by which the helium solvent contributes to the measured dipole.

Miller and co-workers reported an electrostatic elliptical cavity model to estimate the dipole induced polarization of the helium solvent, which leads to a modification of the measured dipole moment: *μ _{He}* =

*μ*+

_{gas}*μ*.

_{ind}^{54}The model was found to quantitatively reproduce the observed dipole change for both HCN and HCCCN in going from the gas phase to helium droplets. Using the elliptical cavity model, we estimate the magnitude of the induced moment to be $\mu ind\u22720.01D$ (the sign of the induced moment is negative). Therefore, on its own, the solvent polarization effect cannot account for the 0.333 D discrepancy between the experimentally measured and computed (equilibrium) dipoles.

The most likely source of vibrational averaging is large-amplitude intermolecular motion about the two in-plane angles (θ_{1} and θ_{2}), as shown in Fig. 4. The black contours (50 cm^{−1}) represent a slice of the CCSD(T)/Def2-TZVPD potential energy surface for $R\u2192=4.0\xc5$. This combination of basis set and level of theory similarly gave a 2.185 D dipole moment at the equilibrium OH–CO geometry (θ_{1}, θ_{2} = 180°, 0°). The projection of the dipole vector onto $R\u2192$ is shown as the red contours (0.1 D). The largest variation in the dipole occurs for motion along θ_{1}, which is expected because this internal coordinate corresponds to the large-amplitude bending motion of the lighter and more polar hydroxyl moiety (1.62 D dipole moment; *B*_{0} = 18.55 cm^{−1}).

We chose both one-dimensional (Fig. 5; θ_{1} scanned, *R* = *R _{mp}* = 3.9856 Å) and two-dimensional (scanning both θ

_{1}and

*R*) vibrational averaging schemes, which are carried out according to the procedures described in the theoretical methods section (more information can be found in the supplementary material; Figs. S5–S9). Upon vibrational averaging about the θ

_{1}in-plane angle (

*R*is fixed at its most probable value), we obtain a 0.2638 D reduction for the dipole projected onto $R\u2192$. A relatively small additional reduction (0.007 D) is obtained via the 2D averaging scheme. About 80% of the difference between the experimental $\mu R\u2192$ and

*ab initio*

*μ*can already be accounted for by simply averaging over the large-amplitude bending motion of the hydroxyl moiety, which is clearly the leading effect. We estimate that the majority of the remaining difference is likely due to a combination of vibrational averaging due to OH stretching and bending motion of the heavier and less polar CO moiety.

_{e}### C. Origin of zero-field splitting: orientational anisotropy of the (OH–CO)–(He)_{N} potential

The zero-field spectrum is shown in greater detail in Fig. 6 (black trace), which reveals substantial broadening of the *P*(5/2) and *R*(3/2) transitions (∼1.2 GHz). The other *P*- and *R*-branch transitions exhibit slightly asymmetric line shapes shaded towards the vibrational band origin. Moreover, the base around the *Q*-branch is broadened. These broadening effects are not reproduced in simulations of the zero-field spectrum (red trace), which assume a transition-independent Lorentzian line shape of 250 MHz. We analyze this broadening in terms of the anisotropic solvent-solute interaction potential, which leads to *J*-dependent inhomogeneous broadening.

Several authors have discussed potential sources of inhomogeneous broadening due to finite droplet size effects and the distribution of droplet sizes in the beam.^{67–74} Experimental evidence for some of the proposed inhomogeneous broadening mechanisms has been reported,^{68,70,72,73,75} such as the observation of the simultaneous excitation of translational motion (3D harmonic oscillator type states) and tunneling inversion in helium-solvated ammonia.^{75} An early and relevant example of finite size effects in rovibrational spectra was reported by Nauta and Miller, who observed a zero-field splitting of the HCN *R*(0) transition into (at least what appeared to be) its Δ*M _{J}* components.

^{68}They discussed the mechanism of this solvent-induced splitting in analogy to the Stark effect, for which a field strength of 4.5 kV/cm (

*μ*⋅

*E*= 0.23 cm

^{−1}) leads to a similar splitting (∼200 MHz) for the isolated species. The origin of this effect was posited as being due to the anisotropic nature of the molecule-helium interaction potential when the molecule is displaced from the center of the droplet.

In a seminal paper by Lehmann,^{67} a comprehensive overview of various inhomogeneous broadening mechanisms was reported along with rigorous calculations of the magnitude and expected importance of each. In this work, Lehmann computed the molecule-helium interaction potential, translational states, and radial distribution function for an HCN solute in a 3 nm diameter helium droplet. The long-range dispersion and induction interactions between the solute and the helium were found to lead to an anisotropic interaction potential. For example, as the HCN impurity approaches the surface of the droplet, the alignment of the molecular dipole parallel to the surface results in a larger dipole-induced polarization of the solvent, in comparison to a perpendicular alignment. The interaction potential can be expanded in Legendre polynomials (Eq. (13)), where *θ* is defined as the angle between the symmetry axis of the solute and the displacement vector connecting the solute’s center of mass to the center of the droplet, which has a normalized magnitude equal to *r*,

For HCN at its most probable normalized displacement (0.4), the first four coefficients in the expansion are 0.43, 0.0036, 0.0098, and 0.000 17 cm^{−1} for *n* = 0–3, respectively.^{67} The $P0cos\theta $ term acts as a confining potential that keeps the HCN solute near the center of the droplet, whereas the anisotropic $P1,2,3cos\theta $ terms couple the rotational and translational motions of the solute and therefore provide a mechanism for *J*-dependent inhomogeneous line broadening.^{67}

We have attempted to model the effect of the aforementioned broadening source by appending a single additional term to our effective zero-field Hamiltonian. However, for simplicity, we have neglected the coupling of OH–CO rotational angular momentum to its (translational) orbital angular momentum within the droplet, although the machinery necessary to do so for closed-shell linear molecules has been reported by Lehmann.^{67} We instead model the problem approximately by treating the coupling of radial motion within the droplet to molecular rotational motion. The anisotropic part of the interaction potential is written simply as $V\u2032=c1rD001*+c2rD002*$, where the higher-order terms in the potential expansion are assumed to be negligible. Matrix elements of the anisotropic potential are derived for the primitive case (a) representation (Eq. (14)),

The *M* quantum number is now defined as the projection of the total angular momentum (less nuclear spin and translational orbital angular momenta) onto the displacement vector connecting the center of the droplet and the OH–CO center of mass.

In order to qualitatively reproduce the line broadening in the *P*(5/2), *R*(3/2), and *Q*-branch regions of the spectrum, the $c2(r)$ term must be approximately equal to the rotational constant (0.048 cm^{−1}). The blue spectrum in Fig. 5 is a simulation using $c2(r)=B$ and $c1(r)=c2(r)/3$. The simulation is carried out with a random laser polarization configuration relative to the quantization axis, which is randomly oriented in the laboratory frame of reference. The splitting observed in the *P*(5/2), *R*(3/2), and *Q*-branch transitions is strongly affected by the $c2rD002*$ anisotropy term, and with the aforementioned parameters, the model reproduces quite well the qualitative widths of these features. We find that upon reducing the value of $c2(r)$ to that computed for HCN (∼0.014 cm^{−1}),^{67} the splitting due to orientational anisotropy cannot account for the experimentally observed line widths and substructure (e.g., the simulated *R*(5/2) width is now only ∼500 MHz), suggesting a more anisotropic interaction between OH–CO and (He)_{N}, in comparison to HCN–(He)_{N}.

In the absence of an (OH–CO)–(He)_{N} interaction potential, we are only able to say that the simulation can be made to qualitatively reproduce the experimental zero-field broadening. We emphasize however, to assess whether or not the values of $c1(r)$ and $c2(r)$ used in the model are realistic, future calculations of the molecule-helium potential will be required, along with a complete treatment of angular momentum coupling that includes the orbital motion of the impurity about the center of the droplet. Other broadening sources, such as translational-rotational coupling due to hydrodynamic effects are also predicted to be *J*-dependent.^{67} These effects along with a realistic averaging over the spread of droplet sizes must also be accounted for to quantitatively model the broadening observed here for OH–CO. A future paper on this subject will address these issues along with a quantitative analysis of similar inhomogeneous broadening observed in the zero-field spectrum of HCCCN. We note in closing that like other systems studied in helium droplets,^{76–78} inhomogeneous line broadening of low *J* transitions appears to be largely quenched upon application of a Stark field that produces a *μ* ⋅ *E* interaction on the order of ∼*B*. This is also apparently true for the case of the Zeeman effect, as demonstrated here. These phenomena have yet to be explained.

## VI. SUMMARY

Sequential capture and solvation of OH and CO by helium droplets lead to the exclusive formation of the OH–CO linear complex, as confirmed by IR spectroscopy in the fundamental OH stretching region. A systematic spectroscopic study is reported for the OH–CO hydroxyl stretching band near 3551 cm^{−1}. The ground state rotational constant is observed to be reduced by about a factor of two in comparison to the gas-phase value. Stark spectra reveal the vibrationally averaged dipole moments in the ground and excited vibrational states to be 1.852(5) and 1.885(6) D, respectively. The computed equilibrium dipole moment at the CCSD(T)/aug-cc-pVQZ level of theory is 0.333 D larger than the experimental ground state value. Nearly 80% of this difference can be accounted for by averaging the dipole moment over the OH intermolecular bending coordinate on the *A*′ potential surface. Zeeman spectra reveal the magnitude of *g*-factors to be the same as those expected for the isolated OH system, thereby indicating that, within the experimental error, neither complexation with CO nor solvation in superfluid helium results in any quenching of the orbital angular momentum.

Strongly *J*-dependent inhomogeneous line broadening effects are observed in the zero-field rovibrational spectrum. We have attempted to simulate this broadening via the application of a model that partially accounts for the coupling of translational and rotational motions that arise from the anisotropic nature of the molecule-helium interaction potential as the impurity is displaced from the droplet’s center of mass. Qualitative broadening features are reproduced, although it is not yet clear if the parameters in the model are physically reasonable, the confirmation of which will require a calculation of the (OH–CO)–(He)_{N} interaction potential averaged over both low-lying electronic states (*A*′ and *A*″).

## SUPPLEMENTARY MATERIAL

See supplementary material for the discussion of the Zeeman cell (Figure S1 of the supplementary material), OD–(CO)n spectra (Figures S2 and S3 of the supplementary material), potential energy and dipole moment surfaces (Figures S4–S6 of the supplementary material), and the complete results from one- and two-dimensional vibrational averaging schemes (Figures S7–S9 of the supplementary material).

## Acknowledgments

G.E.D. acknowledges support from the Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences, Geosciences and Biosciences Division of the US Department of Energy (DOE) under Contract No. DE-FG02-12ER16298. G.E.D. also acknowledges the hospitality of Heather Lewandowski and JILA, where this manuscript was written. A.B.M. acknowledges support from the National Science Foundation (Grant No. CHE-1619660).