Vibration Rotation Tunneling Research Articles

The He-H3 + complex. I. Vibration-rotation-tunneling states and transition probabilities.

With a He-H3 + interaction potential obtained from advanced electronic structure calculations, we computed the vibration-rotation-tunneling (VRT) states of this complex for total angular momenta J from 0 to 9, both for the vibrational ground state and for the twofold degenerate v2 = 1 excited state of H3 +. The potential has three equivalent global minima with depth De = 455.3 cm-1 for He in the plane of H3 +, three equatorial saddle points that separate these minima with barriers of 159.5 cm-1, and two axial saddle points with energies of 243.1 cm-1 above the minima. The dissociation energies calculated for the complexes of He with ortho-H3 + (oH3 +) and para-H3 + (pH3 +) are D0 = 234.5 and 236.3 cm-1, respectively. Wave function plots of the VRT states show that they may be characterized as weakly hindered internal rotor states, delocalized over the three minima in the potential and with considerable amplitude at the barriers. Most of them are dominated by the jk = 10 and 11 rotational ground states of oH3 + and pH3 +, with the intermolecular stretching mode excited up to v = 4 inclusive. However, we also found excited internal rotor states: 33 in He-oH3 +, and 22 and 21 in He-pH3 +. The VRT levels and wave functions were used to calculate the frequencies and line strengths of all allowed v2 = 0 → 1 rovibrational transitions in the complex. Theoretical spectra generated with these results are compared with the experimental spectra in Paper II [Salomon et al., J. Chem. Phys. 156, 144308 (2022)] and are extremely helpful in assigning these spectra. This comparison shows that the theoretical energy levels and spectra agree very well with the measured ones, which confirms the high accuracy of our ab initio He-H3 + interaction potential and of the ensuing calculations of the VRT states.

Ammonia dimer: extremely fluxional but still hydrogen bonded

In the 1980s, Nelson, Fraser, and Klemperer (NFK) published an experimentally derived structure of the ammonia dimer dramatically different from the structure determined computationally, which led these authors to the question “Does ammonia hydrogen bond?". This question has not yet been answered satisfactorily. To answer it, we have developed an ab initio potential energy surface (PES) for this dimer at the limits of the current computational capabilities and performed essentially exact six-dimensional calculations of the vibration-rotation-tunneling (VRT) spectra of NH3-NH3 and ND3-ND3, obtaining an unprecedented agreement with experimental spectra. In agreement with other recent electronic structure calculations, the global minimum on the PES is in a substantially bent hydrogen-bonded configuration. Since the bottom of the PES is exceptionally flat, the dimer is extremely fluxional and the probability of finding it in configurations that are not hydrogen bonded is high. Nevertheless, the probability of hydrogen-bonded configurations is large enough to consider the ammonia dimer to be hydrogen bonded. We also show that NFK’s inference that the ammonia dimer is nearly rigid actually results from unusual cancellations between quantum effects that generate differences in spectra of different isotopologues.

Rovibrational jet-cooled spectroscopy of the Kr–H2O van der Waals complex in the [formula omitted] bending mode region of H2O

Five rovibrational bands of the Kr–H2O complex have been recorded in the ν2 bending region of H2O using a quantum cascade laser coupled to a pulsed slit supersonic jet. Four of them have been unambiguously assigned to the Σ and Π states in v2=1,111,110, and 212 rotational levels of the monomer based on ground state combination differences and similarities with the vibration–rotation tunneling states of Ar–H2O. One of the bands is tentatively assigned to a combination band with two quanta of intermolecular van der Waals stretching mode (νs). Due to the efficient rovibrational cooling in our pulsed supersonic expansion, all observed bands originate from the lowest lying states. Four of them are from the lowest ortho ground state Σe(101) and one of them is from the lowest para ground state Σe(000). The jet-cooled spectra have been analyzed in terms of a nearly free internal rotor model taking into account Coriolis couplings between close lying Σ and Π levels. Molecular parameters for the five upper vibrational states, band origin, rotational and centrifugal distortion constants have been accurately determined. The β parameter describing the Coriolis coupling between the Σ and Π states originating from the (212) state has also been obtained.

Intermolecular dynamics of NH3-rare gas complexes in the ν2 umbrella region of NH3 investigated by rovibrational laser jet-cooled spectroscopy and ab initio calculations.

High resolution jet-cooled spectroscopy experiments have been realized to investigate the intermolecular dynamics of van der Waals (vdW) heterodimers between NH3 and rare gas (Rg) atoms in the ν2 umbrella mode region of NH3. With respect to a previous study dedicated to NH3-Ar [Asselin et al. Mol. Phys. 116, 3642 (2018)], the sensitivity and spectral resolution of our laser spectrometer coupled to a pulsed supersonic jet have been significantly improved to derive more accurate excited state spectroscopic parameters from rovibrational analyses. In addition, we calculated the ground and ν2 excited vibration-rotation-tunneling (VRT) states of these complexes on the four-dimensional ab initio potential energy surfaces from Loreau et al. [J. Chem. Phys. 141, 224303 (2014), ibid. 143, 184303 (2015).] Transition frequencies and intensities of the allowed ν2 = 1 ← 0 transitions obtained from the calculated energy levels and wave functions agree well with the experimental data and are helpful in their analysis. By means of a pseudodiatomic model with the assumption of weak Coriolis coupling, the rovibrational analysis of both the Πe/f(j = 1,k = 0) ←Σf(j = 0,k = 0) and Σf(j = 1,k = 0) ←Σf(j = 0,k = 0) transitions in ortho NH3-Rg (Rg = Ne, Ar, Kr, Xe) complexes enabled us to determine reliable excited state parameters and derive accurate values of the effective vdW bond length Reff, force constant ks, and vdW stretching frequency νs. Comparison between the experimental structural parameters and those from the ab initio calculated VRT levels shows good agreement for NH3-Ne, NH3-Ar and NH3-Kr, and a similar variation of Reff, ks, and νs with the polarizability of Rg in the ground and ν2 excited states. Anomalously small values of νs and ks derived for NH3-Xe in the Πe/f(j = 1,k = 0) state suggest that the applied model is not valid in this case, due to the presence of another state coupling to the perturbed Πf state. Such a state could not be found, however.

Gas-phase water: Features of hydrogen bonding deduced from far-infrared VRT spectra proving the cluster formation in vacuum

Far-infrared vibration–rotation-tunneling (VRT) spectra of gas-phase water reported previously have been interpreted in terms of polaronic exciton coupled model. An increase of the energy gap (Δν) between the neighboring absorption lines, which is observed in the spectrum within a pattern responsible for water cluster absorption, correlates with spin–orbit coupling parameter (β). Namely, experimental ratio (Δνi+1/Δνi) = 1.188996 ± 0.051361 has been found in fair agreement with β= 1.19100654 that implies the accumulation of difference between the absorption and emission energies. This correlation means the electrons coupled with protons establishing hydrogen bonds accumulate the energy difference. Relation deduced earlier for Boson peak frequency admitted to estimate fast Debye relaxation time for water that is found to be 0.183704 ps.

Structure and torsional dynamics of the water octamer from THz laser spectroscopy near 215 μm.

Clusters of eight water molecules play an important role in theoretical analysis of aqueous structure and dynamics but have proven to be challenging experimental targets. Here we report the high-resolution spectroscopic characterization of the water octamer. Terahertz (THz) vibration-rotation-tunneling (VRT) spectroscopy resolved 99 transitions with 1 part per million precision in a narrow range near 46.5 wave numbers, which were assigned to the h16 octamer via detailed isotope dilution experiments. Fitting to a semi-rigid symmetric top model supports predictions of two coexisting cuboidal structures and provides precise values for the changes in their rotational constants. Comparison with theory and previous spectroscopic data provides a characterization of the two structures and the observed torsional vibration and supports the prediction that the D2d symmetry structure is lower in energy than the S4 isomer.

The Water Dimer Investigated in the 2OH Spectral Range Using Cavity Ring-Down Spectroscopy.

Two setups based on CW cavity ring-down spectroscopy were used at Bruxelles and Rennes to record jet-cooled water dimer absorption between 7188 and 7285, and between 7357 and 7386 cm(-1). Some 19 absorption features are reported, significantly more than in the literature. Limited high-resolution information is available due to strong overlap between neighboring vibration-rotation-tunneling (VRT) structures and to spectral broadening induced by short upper state vibrational predissociation lifetimes, likely to range between 100 and 20 ps. Rotational band contours analyses are performed to assign the partly resolved VRT structures to the v1v2v3,vfvb = 000,11; 200,00; 000,20; and 101,00 zero-order vibrational states. Their wavenumbers are found to be 7192.34, 7225.86, 7240.57, and 7256.99 cm(-1), respectively. Both so-called acceptor-switching tunneling components are involved in the assignments whose tentative character is discussed.

Development of a "First-Principles" Water Potential with Flexible Monomers. III. Liquid Phase Properties.

The MB-pol full-dimensional water potential introduced in the first two papers of this series [J. Chem. Theory Comput. 2013, 9, 5395 and J. Chem. Theory Comput. 2014, 10, 1599] is employed here in classical and quantum simulations of liquid water under ambient conditions. Comparisons with the available experimental data for several structural, thermodynamic, and dynamical properties indicate that MB-pol provides a highly accurate description of the liquid phase. Combined with previous analyses of the dimer vibration-rotation tunneling spectrum, second and third virial coefficients, and cluster structures and energies, the present results demonstrate that MB-pol represents a major step toward the long-sought "universal model" capable of describing the properties of water from the gas to the condensed phases.

Development of a "First Principles" Water Potential with Flexible Monomers: Dimer Potential Energy Surface, VRT Spectrum, and Second Virial Coefficient.

The development of a "first principles" water potential with flexible monomers (MB-pol) for molecular simulations of water systems from gas to condensed phases is described. MB-pol is built upon the many-body expansion of the intermolecular interactions, and the specific focus of this study is on the two-body term (V2B) representing the full-dimensional intermolecular part of the water dimer potential energy surface. V2B is constructed by fitting 40,000 dimer energies calculated at the CCSD(T)/CBS level of theory and imposing the correct asymptotic behavior at long-range as predicted from "first principles". The comparison of the calculated vibration-rotation tunneling (VRT) spectrum and second virial coefficient with the corresponding experimental results demonstrates the accuracy of the MB-pol dimer potential energy surface.

An adiabatic model for calculating overtone spectra of dimers such as (H 2 O) 2

The near-infrared and visible wavelength spectrum of the water dimer is considered to be the major contributor to the so-called water continuum at these wavelengths. However, theoretical models of this spectrum require the simultaneous treatment of both monomer and dimer excitations. A model for treating this problem is proposed which is based upon a Franck-Condon-like separation between the monomer and dimer vibrational motions. In this model, one of the monomers is treated as the chromophore and its absorption is assumed to be given by its, possibly perturbed, vibrational band intensity. The main computational issue is the treatment of separate monomer and dimer motions. Various approaches for obtaining dimer vibration-rotation tunnelling spectra that allow for monomer motion are explored. These approaches include ways of treating the adiabatic separation of dimer vibrational modes from monomer vibrational modes. We classify the adiabatic separation methods under four main approaches: namely fixed-geometry, free-monomer, perturbed-monomer and coupled-monomer methods. The latter being the most computationally expensive as the monomer wave functions are dependent on the dimer coordinates. For each of these approaches, expectation values over the full potential are calculated for the given monomer vibrational wave functions. Various full (named VAP 2pD in the text) and partial (VAP (+p)D) averaging techniques are outlined to calculate the vibrationally averaged, monomer state-dependent, dimer interaction potentials. The computational costs associated with application of these techniques to the water dimer are estimated and the prospects for full calculations based on this approach are assessed.

Water dimer vibration–rotation tunnelling levels from vibrationally averaged monomer wavefunctions

The vibration–rotation tunnelling (VRT) spectra for the water dimer obtained by vibrationally averaging the dimer potential over accurate water monomer wavefunctions is reported. The vibrational averaging requires evaluation of the 12D dimer potential energy surface at more than 10 12 distinct geometries. The resulting vibrational spectra of the low-lying dimer states are presented and compared with both less computationally expensive methods based on fixed nuclei approximations and the recent (6+6) d adiabatic calculations of Leforestier et al. [38] (2009). The procedure gives some modest improvement in the agreement with experimental values for the vibration–rotation tunnelling (VRT) states of (H 2O) 2 and (D 2O) 2. This approach can be extended to treat dimer states involving monomer overtone excitations, which is important in obtaining water dimer spectra at infrared and visible wavelengths at atmospheric temperatures, and in characterizing the dimer contribution to the so-called water continuum absorption at these wavelengths.

Vibration–rotation-tunneling states of the benzene dimer: an ab initio study

An improved intermolecular potential surface for the benzene dimer is constructed from interaction energies computed by symmetry-adapted perturbation theory, SAPT(DFT), with the inclusion of third-order contributions. Twelve characteristic points on the surface have been investigated also using the coupled-cluster method with single, double, and perturbative triple excitations, CCSD(T), and triple-zeta quality basis sets with midbond functions. The SAPT and CCSD(T) results are in close agreement and provide the best representation of these points to date. The potential was used in calculations of vibration-rotation-tunneling (VRT) levels of the dimer by a method appropriate for large amplitude intermolecular motions and tunneling between multiple equivalent minima in the potential. The resulting VRT levels were analyzed with the use of the permutation-inversion full cluster tunneling (FCT) group G(576) and a chain of subgroups that starts from the molecular symmetry group C(s)(M) of the rigid dimer at its equilibrium C(s) geometry and leads to G(576) if all possible intermolecular tunneling mechanisms are feasible. Further information was extracted from the calculated wave functions. It was found, in agreement with the experimental data, that for all of the 54 G(576) symmetry species (with different nuclear spin statistical weights) the lower VRT states have a tilted T-shape (TT) structure; states with the parallel-displaced structure are higher in energy than the ground state of A symmetry by at least 30 cm(-1). The dissociation energy D(0) equals 870 cm(-1), while the depth D(e) of the TT minimum in the potential is 975 cm(-1). Hindered rotation of the cap in the TT structure and tilt tunneling lead to level splittings on the order of 1 cm(-1). Also intermolecular vibrations with excitation energies starting at a few cm(-1) were identified. A further small, but probably significant, level splitting was assigned to cap turnover, although in scans of the potential surface we could not find a plausible 'reaction path' for this process. Rotational constants were extracted from energy levels calculated for total angular momentum J = 0 and 1, and from expectation values of the inertia tensor. Although the end-over-end rotational constant B + C agrees well with the measured microwave spectra, there is disagreement with the measurements concerning the (a)symmetric rotor character of the benzene dimer. It is concluded from calculations for the 54 nuclear spin species that the microwave spectrum should show overlapping contributions from many different species. Another interesting conclusion regards the role of the quantum number K, for a prolate near-symmetric rotor the projection of the total angular momentum on the prolate axis. For the benzene dimer, K has a substantial effect on the energy levels associated with the intermolecular motions of the complex.

Vibration−Rotation−Tunneling Levels of the Water Dimer from an ab Initio Potential Surface with Flexible Monomers

The 12-dimensional ab initio potential for the water dimer with flexible monomers from Huang et al. (J. Chem. Phys. 2008, 128, 034312) was used in accurate calculations of the vibration-rotation-tunneling (VRT) levels of (H2O)2 and (D2O)2 involving the intermolecular rovibrational and tunneling states as well as the intramolecular vibrations. For the intermolecular VRT levels we used a 6 + 6d model in which the fast intramolecular vibrations are adiabatically separated from the much slower intermolecular vibrations, tunneling motions, and overall rotations. We also tested two six-dimensional (6d) rigid monomer models in which the monomers were frozen either at their equilibrium geometry or at their ground state vibrationally averaged geometry. All the results from the 6 + 6d model agree well with the large amount of detailed experimental data available from high-resolution spectroscopy. For most of the parameters characterizing the spectra the results of the two 6d rigid monomer models do not significantly differ from the 6 + 6d results. An exception is the relatively large acceptor tunneling splitting, which was the only quantity for which the 6d model with the monomers frozen at their equilibrium geometry was not in good agreement with the experimental data. The 6d model with monomers at their vibrationally averaged geometry performs considerably better, and the full 6 + 6d results agree with the measurements also for this quantity. For the excited intramolecular vibrations we tested two 6 + 6d models. In the first model the excitation was assumed to be either on the donor in the hydrogen bond or on the acceptor, and to hop from one monomer to the other upon donor-acceptor interchange. In the second model the monomer excitation remains localized on a given monomer for all dimer geometries. Almost the same frequencies of the intramolecular vibrations were found for the two models. The calculations show considerable variations in the frequencies of the intramolecular modes for transitions involving different tunneling levels and different values of the rotational quantum number K. For K = 0 --> 0 transitions these variations largely cancel, however. A comparison with experimental data is difficult, except for the acceptor asymmetric stretch mode observed in high-resolution spectra, because it is not clear how much the different transitions contribute to the (unresolved) peaks in most of the experimental spectra. The large red shift of the donor bound OH stretch mode is correctly predicted, but the value calculated for this red shift is too small by more than 20%. Also in the smaller shifts of the other modes we find relatively large errors. It is useful, however, that our detailed calculations including all ground and excited state tunneling levels provide an explanation for the splitting of the acceptor asymmetric stretch band observed in He nanodroplet spectra, as well as for the fact that the other bands in these spectra show much smaller or no splittings.

An accurate analytic representation of the water pair potential

The ab initio water dimer interaction energies obtained from coupled cluster calculations and used in the CC-pol water pair potential (Bukowski et al., Science, 2007, 315, 1249) have been refitted to a site-site form containing eight symmetry-independent sites in each monomer and denoted as CC-pol-8s. Initially, the site-site functions were assumed in a B-spline form, which allowed a precise optimization of the positions of the sites. Next, these functions were assumed in the standard exponential plus inverse powers form. The root mean square error of the CC-pol-8s fit with respect to the 2510 ab initio points is 0.10 kcal mol(-1), compared to 0.42 kcal mol(-1) of the CC-pol fit (0.010 kcal mol(-1) compared to 0.089 kcal mol(-1) for points with negative interaction energies). The energies of the stationary points in the CC-pol-8s potential are considerably more accurate than in the case of CC-pol. The water dimer vibration-rotation-tunneling spectrum predicted by the CC-pol-8s potential agrees substantially and systematically better with experiment than the already very accurate spectrum predicted by CC-pol, while specific features that could not be accurately predicted previously now agree very well with experiment. This shows that the uncertainties of the fit were the largest source of error in the previous predictions and that the present potential sets a new standard of accuracy in investigations of the water dimer.

Refinements in the description of excited VRT states of the water dimer

Extensive new spectroscopic measurements are combined with a global analysis of the ground state data in order to re-examine and to refine the description of the excited vibration rotation tunneling (VRT) states of the water dimer. Notably, six new ‘donor torsion’ subbands are analytically identified, current vibrational assignments of the K a = 1 stacks are reassessed, the previously reported (H2O)2 donor torsion overtone (DT)2 and hydrogen bond stretch (S) data sets are augmented, and four new (S) subbands have been measured. Unusually large Coriolis effects are predicted, excited state E2 ↔ E1 assignments are reinforced, and possibilities of experimentally determining ground state AS splitting in (H2O)2 from excited state data are discussed.

Terahertz Vibration−Rotation-Tunneling Spectroscopy of the Ammonia Dimer: Characterization of an out of Plane Vibration

The terahertz vibration-rotation-tunneling (VRT) spectrum of the ammonia dimer (NH(3))(2) has been measured between ca. 78.5 and 91.9 cm(-1). The dipole-allowed transitions are separated into three groups that correspond to the 3-fold internal rotation of the NH(3) subunits. Transitions have been assigned for VRT states of the A-A (ortho-ortho) combinations of NH(3) monomer states. The spectrum is further complicated by strong Coriolis interactions. K = 0 <-- 0, K = 1 <-- 0, K = 0 <-- 1, and K = 1 <-- 1 progressions have been assigned. The band origins, rotational constants, asymmetry doubling, centrifugal distortion, and Coriolis coupling constant have been determined from the fit to an effective Hamiltonian. These VRT transitions are tentatively assigned to an out of plane vibration with a K = 0 state at 89.141305(47) cm(-1), and a K = 1 state at 86.77785(9) cm(-1).

A ‘first principles’ potential energy surface for liquid water from VRT spectroscopy of water clusters

We present results of gas phase cluster and liquid water simulations from the recently determined VRT(ASP-W)III water dimer potential energy surface (the third fitting of the Anisotropic Site Potential with Woermer dispersion to vibration-rotation-tunnelling data). VRT(ASP-W)III is shown to not only be a model of high 'spectroscopic' accuracy for the water dimer, but also makes accurate predictions of vibrational ground-state properties for clusters up through the hexamer. Results of ambient liquid water simulations from VRT(ASP-W)III are compared with those from ab initio molecular dynamics, other potentials of 'spectroscopic' accuracy and with experiment. The results herein represent the first time to the authors' knowledge that a 'spectroscopic' potential surface is able to correctly model condensed phase properties of water.

Elucidating the role of many-body forces in liquid water. I. Simulations of water clusters on the VRT(ASP-W) potential surfaces.

We test two new potentials for water, fit to vibration-rotation tunneling (VRT) data by employing diffusion quantum Monte Carlo simulations to calculate the vibrational ground-state properties of water clusters. These potentials, VRT(ASP-W)II and VRT(ASP-W)III, are fits of the highly detailed ASP-W (anisotropic site potential with Woermer dispersion) ab initio potential to (D(2)O)(2) microwave and far-infrared data, and along with the SAPT5s (five-site symmetry adapted perturbation theory) potentials, are the most accurate water dimer potential surfaces in the literature. The results from VRT(ASP-W)II and III are compared to those from the original ASP-W potential, the SAPT5s family of potentials, and several bulk water potentials. Only VRT(ASP-W)III and the spectroscopically "tuned" SAPT5st (with N-body induction included) accurately reproduce the vibrational ground-state structures of water clusters up to the hexamer. Finally, the importance of many-body induction and three-body dispersion are examined, and it is shown that the latter can have significant effects on water cluster properties despite its small magnitude.

Water dimer hydrogen bond stretch, donor torsion overtone, and “in-plane bend” vibrations

We report the measurement and analysis of 64 new Ka=0←0,1 and Ka=1←0,1 transitions of (H2O)2 and 16 new Ka=0←0 transitions of (D2O)2 by terahertz laser vibration–rotation–tunneling spectroscopy of a planar supersonic expansion between 140.5 and 145.5 cm−1. The transitions in both isotopomers correspond to A′ vibrations assigned to the hydrogen bond stretch (translational) and donor torsion overtone vibrations. The interchange splitting is 56.3 GHz in Ka=0 of the excited state of (H2O)2, nearly 3 times the value of the ground state, and the bifurcation tunneling splitting is 1.8 GHz, over 2 times the value of the ground state. We compare the existing experimental spectra with calculations on state-of-the-art intermolecular potential energy surfaces and critically review the vibrational assignments reported in the literature. We show that the discrepancy between theory and experiment regarding the assignment of the feature near 103 cm−1 can be resolved by considering E2→E1 transitions, which had not been considered previously.

Bifurcation tunneling dynamics in the water trimer

Recent far-infrared vibration–rotation–tunneling experiments have probed intricate details of the hydrogen bond tunneling dynamics in the water trimer through excitation of intermolecular vibrational transitions to states of sequentially increasing energy. The experimentally observed bifurcation splitting in the water trimer evolves from an equally spaced quartet in the vibrational ground state to a slightly asymmetrical quartet for intermediate torsional vibrational states lying below 100 cm−1. Even more asymmetric bifurcation splittings have been observed in the out-of-plane librational band of (H2O)3 near 520 cm−1. These patterns may be caused by the bifurcation and flip rearrangements becoming comparable in magnitude. Alternatively, some of the data can be fitted by introducing tunneling matrix elements corresponding to multiple elementary rearrangements. Analysis of the observed bifurcation tunneling splittings of (D2O)3 confirms that the dominant bifurcation pathway includes the torsional flipping motion of the neighboring water molecules. Quantification of the bifurcation matrix elements of (D2O)3 furthermore reveals that these vary within each torsional manifold.