Using monomer vibrational wavefunctions as contracted basis functions to compute rovibrational levels of an H2O-atom complex in full dimensionality

Full quantum calculations of the line shape for H2O perturbed by Ar at temperatures from 20 to 300 K

This work theoretically studied the spectral line shape of H2O perturbed by Ar in the temperature range of 20-300 K for the pure rotational lines below 360 cm-1, as well as three lines (31, 2 ← 44, 1, 54, 2 ← 41, 3, and 73, 5 ← 60, 6) in the v2 band. In order to perform precise dynamical calculations at low collision energies, a full-dimensional long-range potential energy surface was constructed for the H2O-Ar system for the first time to correct the long range of our newly developed intermolecular potential energy surface. Subsequently, the six line-shape parameters (pressure-broadening and -shifting parameters, their speed dependencies, and the complex Dicke parameters) were determined from the generalized spectroscopic cross section by the full quantum time-independent close-coupling approach on this new potential energy surface. Our theoretical results are in good agreement with the available experimental observations. Furthermore, the influence of the speed-dependence and Dicke narrowing effects on the line contour was revealed by comparing the differences among the Hartmann-Tran, quadratic-speed-dependent Voigt, and Voigt profiles. The temperature dependence of each line-shape parameter was further parameterized using the triplet-power-law for three pure rotational 61, 6 ← 52, 3, 41, 4 ← 32, 1, and 31, 3 ← 22, 0 lines. These line-shape parameters will provide a comprehensive set of theoretical references for subsequent experimental measurements.

A two-step quadrature-based variational calculation of ro-vibrational levels and wavefunctions of CO2 using a bisector-x molecule-fixed frame

In this paper, we propose a new two-step strategy for computing ro-vibrational energy levels and wavefunctions of a triatomic molecule and apply it to CO2. A two-step method [J. Tennyson and B. T. Sutcliffe, Mol. Phys., 1986, 58, 1067] uses a basis whose functions are products of K-dependent "vibrational" functions and symmetric top functions. K is the quantum number for the molecule-fixed z component of the angular momentum. For a linear molecule, a two-step method is efficient because the Hamiltonian used to compute the basis functions includes the largest coupling term. The most important distinguishing feature of the two-step method we propose is that it uses an associated Legendre basis and quadrature rather than a K-dependent discrete variable representation. This reduces the cost of the calculation and simplifies the method. We have computed ro-vibrational energy levels with J up to 100 for CO2, on an accurate available potential energy surface which is known as the AMES-2 PES and present a subset of those levels. We have converged most levels up to 20 000 cm-1 to 0.0001 cm-1.

Bending Relaxation of H2 O by Collision with Para- and Ortho-H2

We extend our recent theoretical work on the bending relaxation of H2 O in collisions with H2 by including the three water modes of vibration coupled with rotation, as well as the rotation of H2 . Our full quantum close-coupling method (excluding the H2 vibration) is combined with a high-accuracy nine-dimensional potential energy surface. The collisions of para-H2 O and ortho-H2 O with the two spin modifications of H2 are considered and compared for several initial states of H2 O. The convergence of the results as a function of the size of the rotational basis set of the two colliders is discussed. In particular, near-resonant energy transfer between H2 O and H2 is found to control the vibrational relaxation process, with a dominant contribution of transitions withΔ j 2 = j 2 f - j 2 i ${{\rm{\Delta }}j_2 = j_2^f - j_2^i }$ =+ 2 , + 4 ${ + 2, + 4}$ ,j 2 i ${j_2^i }$ andj 2 f ${j_2^f }$ being respectively the H2 initial and final rotational quantum numbers. Finally, the calculated value of the H2 O bending relaxation rate coefficient at 295 K is found to be in excellent agreement with its experimental estimate.

A New Full-Dimensional Ab Initio Intermolecular Potential Energy Surface and Rovibrational Energies of the H2O-H2 Complex

H2O-H2 is a prototypical five-atom van der Waals system, and the interaction between H2O and H2 plays an important role in many physical and chemical environments. However, previous full-dimensional intermolecular potential energy surfaces (IPESs) cannot accurately describe the H2O-H2 interaction in the repulsive or van der Waals minimum region. In this work, we constructed a full-dimensional IPES for the title system with a small root-mean-square error of 0.252 cm-1 by using the permutation invariant polynomial neural network method. The ab initio calculations were performed by employing the explicitly corrected coupled cluster [CCSD(T)-F12a] method with the augmented correlation-consistent polarized valence quintuple-ζ basis set. Based on the newly developed IPES, the bound states of the H2O-H2 complex were calculated within the rigid-rotor approximation. The transition frequencies and band origins agreed well with the experimental values [Weida, M. J.; Nesbitt, D. J. J. Chem. Phys. 1999, 110, 156-167] with errors less than 0.1 cm-1 for most transitions. Those results demonstrate the high accuracy of our new IPES, which would build a solid foundation for the collisional dynamics of H2O-H2 at low temperatures.

Computing excited OH stretch states of water dimer in 12D using contracted intermolecular and intramolecular basis functions

Due to the ubiquity and importance of water, water dimer has been intensively studied. Computing the (ro-)vibrational spectrum of water dimer is challenging. The potential has eight wells separated by low barriers, which makes harmonic approximations of limited utility. A variational approach is imperative, but difficult because there are 12 coupled vibrational coordinates. In this paper, we use a product contracted basis whose functions are products of intramolecular and intermolecular functions computed using an iterative eigensolver. An intermediate matrix F facilitates calculating matrix elements. Using F, it is possible to do calculations on a general potential without storing the potential on the full quadrature grid. We find that surprisingly many intermolecular functions are required. This is due to the importance of coupling between inter- and intra-molecular coordinates. The full G₁₆ symmetry of water dimer is exploited. We calculate, for the first time, monomer excited stretch states and compare P(1) transition frequencies with their experimental counterparts. We also compare with experimental vibrational shifts and tunneling splittings. Surprisingly, we find that the largest tunneling splitting, which does not involve the interchange of the two monomers, is smaller in the asymmetric stretch excited state than in the ground state. Differences between levels we compute and those obtained with a [6+6]D adiabatic approximation [Leforestier et al. J. Chem. Phys. 137 014305 (2012)] are ∼0.6 cm^-1 for states without monomer excitation, ∼4 cm^-1 for monomer excited bend states, and as large as ∼10 cm^-1 for monomer excited stretch states.

ABC+D: A time-independent coupled-channel quantum dynamics program for elastic and ro-vibrational inelastic scattering between atoms and triatomic molecules in full dimensionality

We discuss the details of a time-independent quantum mechanical method and its implementation for full-dimensional non-reactive scattering between a closed-shell triatomic molecule and a closed-shell atom. By solving the time-independent Schrödinger equation within the coupled-channel framework using a log-derivative method, the state-to-state scattering matrix (S-matrix) can be determined for inelastic scattering involving both the rotational and vibrational modes of the molecule. Various approximations are also implemented. The ABC+D code provides an important platform for understanding an array of physical phenomena involving collisions between atoms and molecules.

Recent advances in quantum theory on ro-vibrationally inelastic scattering

Molecular collisions are of fundamental importance in understanding intermolecular interaction and dynamics. Its importance is accentuated in cold and ultra-cold collisions because of the dominant quantum mechanical nature of the scattering. We review recent advances in the time-independent approach to quantum mechanical characterization of non-reactive scattering in tetratomic systems, which is ideally suited for large collisional de Broglie wavelengths characteristic in cold and ultracold conditions. We discuss quantum scattering algorithms between two diatoms and between a triatom and an atom and their implementation, as well as various approximate schemes. They not only enable the characterization of collision dynamics in realistic systems but also serve as benchmarks for developing more approximate methods.

Noncovalently bound molecular complexes beyond diatom–diatom systems: full-dimensional, fully coupled quantum calculations of rovibrational states

The methodological advances made in recent years have significantly extended the range and dimensionality of noncovalently bound molecular complexes for which full-dimensional quantum calculations of their rovibrational states are feasible.

A Time-Independent Quantum Approach to Ro-vibrationally Inelastic Scattering between Atoms and Triatomic Molecules

A full-dimensional time-independent quantum mechanical theory for ro-vibrationally inelastic scattering of triatomic molecules with atoms is formulated. The Jacobi-Radau coordinate system used in the calculation allows not only a near perfect description of the vibrational problem but also the adaptation of the exchange symmetry for A₂B type triatoms. The S-matrix elements are obtained by solving the close-coupling equations with contracted basis using the log-derivative method. This method is applied to the inelastic scattering of the water molecule by a chlorine atom, which sheds light on the energy gap law in energy transfer in atom-triatom collisions.

DCl-H2O, HCl-D2O, and DCl-D2O Dimers: Inter- and Intramolecular Vibrational States and Frequency Shifts from Fully Coupled Quantum Calculations on a Full-Dimensional Neural Network Potential Energy Surface

We report full-dimensional and fully coupled quantum calculations of the inter- and intramolecular vibrational states of three isotopologues of the hydrogen chloride-water dimer: DCl-H₂O (DH), HCl-D₂O (HD), and DCl-D₂O (DD). The present study extends our recent theoretical investigation of the nine-dimensional (9D) vibrational level structure of the HCl-H₂O (HH) dimer [Liu, Y.; Li, J.; Felker, P. M.; Bačić, Z. Phys. Chem. Chem. Phys. 2021, 23, 7101-7114]. It employs the same accurate 9D permutation invariant polynomial-neural network potential energy surface and the highly efficient bound-state methodology. The objective of this work is to elucidate the isotopologue variations of a range of bound-state properties of the hydrogen chloride-water dimer and compare them to those of the HH dimer. In order to achieve this, for the isotopologues considered, the rigorous 9D quantum calculations performed encompass all intramolecular vibrational fundamentals, and their frequency shifts relative to the isolated monomer values, together with the low-lying intermolecular vibrational states in each of the intramolecular vibrational manifolds of interest. Moreover, for the ground state of each isotopologue, several informative vibrationally averaged intermolecular geometric properties of the dimer are computed, as well as the three rotational constants. The energies of the intermolecular inversion and rock modes, which mainly involve the motions of the water moiety, differ greatly for H₂O and D₂O, but are much less sensitive to whether the hydrogen chloride isotopologue is HCl or DCl. On the other hand, the excitation of the HCl/DCl stretch changes significantly the energies of the water inversion and rock modes. The DCl stretch frequency shift computed in 9D for the DD dimer, -114.91 cm^-1, agrees extremely well with the corresponding experimental value of -115.20 cm^-1 measured by Saykally and co-workers.

Using nondirect product Wigner D basis functions and the symmetry-adapted Lanczos algorithm to compute the ro-vibrational spectrum of CH4-H2O

By doing calculations on the methane-water van der Waals complex, we demonstrate that highly converged energy levels and wavefunctions can be obtained using Wigner D basis functions and the Symmetry-Adapted Lanczos (SAL) method. The Wigner D basis is a nondirect product basis and, therefore, efficient when the kinetic energy operator has accessible singularities. The SAL method makes it possible to exploit symmetry to label energy levels and reduce the cost of the calculation, without explicitly using symmetry-adapted basis functions. Line strengths are computed, and new bands are identified. In particular, we find unusually strong transitions between states associated with the isomers of the global minimum and the secondary minimum.

HCl–H2O dimer: an accurate full-dimensional potential energy surface and fully coupled quantum calculations of intra- and intermolecular vibrational states and frequency shifts

The present work reports a new full-dimensional potential energy surface (PES) of the HCl–H₂O dimer, and the first fully coupled 9D quantum calculations of the intra- and intermolecular vibrational states of the complex, utilizing this PES.

Exact quantum dynamics background of dispersion interactions: case study for CH4·Ar in full (12) dimensions

A full-dimensional ab initio potential energy surface of spectroscopic quality is developed for the van-der-Waals complex of a methane molecule and an argon atom. Variational vibrational states are computed on this surface including all twelve (12) vibrational degrees of freedom of the methane-argon complex using the GENIUSH computer program and the Smolyak sparse grid method. The full-dimensional computations make it possible to study the fine details of the interaction and distortion effects and to make a direct assessment of the reduced-dimensionality models often used in the quantum dynamics study of weakly-bound complexes. A 12-dimensional (12D) vibrational computation including only a single harmonic oscillator basis function (9D) to describe the methane fragment (for which we use the ground-state effective structure as the reference structure) has a 0.40 cm^-1 root-mean-square error (rms) with respect to the converged 12D bound-state excitation energies, which is less than half of the rms of the 3D model set up with the 〈r〉₀ methane structure. Allowing 10 basis functions for the methane fragment in a 12D computation performs much better than the 3D models by reducing the rms of the bound state vibrational energies to 0.07 cm^-1. The full-dimensional potential energy surface correctly describes the dissociation of the system, which together with further development of the variational (ro)vibrational methodology opens a route to the study of the role of dispersion forces in the excited methane vibrations and the energy transfer from the intra- to the intermolecular vibrational modes.

Full quantum calculation of the rovibrational states and intensities for a symmetric top-linear molecule dimer: Hamiltonian, basis set, and matrix elements

The rovibrational energy levels and intensities of the CH₃F-H₂ dimer have been obtained using our recent global intermolecular potential energy surface [X.-L. Zhang et al., J. Chem. Phys. 148, 124302 (2018)]. The Hamiltonian, basis set, and matrix elements are derived and given for a symmetric top-linear molecule complex. This approach to the generation of energy levels and wavefunctions can readily be utilized for studying the rovibrational spectra of other van der Waals complexes composed of a symmetric top molecule and a linear molecule, and may readily be extended to other complexes of nonlinear molecules and linear molecules. To confirm our method, the rovibrational levels of the H₂O-H₂ dimer have been computed and shown to be in good agreement with experiment and with previous theoretical results. The rovibrational Schrödinger equation has been solved using a Lanczos algorithm together with an uncoupled product basis set. As expected, dimers containing ortho-H₂ are more strongly bound than dimers containing para-H₂. Energies and wavefunctions of the discrete rovibrational levels of CH₃F-paraH₂ complexes obtained from the direct vibrationally averaged 5-dimensional potentials are in good agreement with the results of the reduced 3-dimensional adiabatic-hindered-rotor (AHR) approximation. Accurate calculations of the transition line strengths for the orthoCH₃F-paraH₂ complex are also carried out, and are consistent with results obtained using the AHR approximation. The microwave spectrum associated with the orthoCH₃F-orthoH₂ dimer has been predicted for the first time.

Toward breaking the curse of dimensionality in (ro)vibrational computations of molecular systems with multiple large-amplitude motions

Methodological progress is reported in the challenging direction of a black-box-type variational solution of the (ro)vibrational Schrödinger equation applicable to floppy, polyatomic systems with multiple large-amplitude motions. This progress is achieved through the combination of (i) the numerical kinetic-energy operator (KEO) approach of Mátyus et al. [J. Chem. Phys. 130, 134112 (2009)] and (ii) the Smolyak nonproduct grid method of Avila and Carrington, Jr. [J. Chem. Phys. 131, 174103 (2009)]. The numerical representation of the KEO makes it possible to choose internal coordinates and a body-fixed frame best suited for the molecular system. The Smolyak scheme reduces the size of the direct-product grid representation by orders of magnitude, while retaining some of the useful features of it. As a result, multidimensional (ro)vibrational states are computed with system-adapted coordinates, a compact basis- and grid-representation, and an iterative eigensolver. Details of the methodological developments and the first numerical applications are presented for the CH₄·Ar complex treated in full (12D) vibrational dimensionality.