Efficient calculation of highly excited vibrational energy levels of floppy molecules: The band origins of H+3up to 35 000 cm−1

Resource Optimization for Quantum Dynamics with Tensor Networks: Quantum and Classical Algorithms

The exponential scaling of the quantum degrees of freedom with the size of the system is one of the biggest challenges in computational chemistry and particularly in quantum dynamics. We present a tensor network approach for the time-evolution of the nuclear degrees of freedom of multiconfigurational chemical systems at a reduced storage and computational complexity. We also present quantum algorithms for the resultant dynamics. To preserve the compression advantage achieved via tensor network decompositions, we present an adaptive algorithm for the regularization of nonphysical bond dimensions, preventing the potentially exponential growth of these with time. While applicable to any quantum dynamical problem, our method is particularly valuable for dynamical simulations of nuclear chemical systems. Our algorithm is demonstrated using ab initio potentials obtained for a symmetric hydrogen-bonded system, namely, the protonated 2,2'-bipyridine, and compared to exact diagonalization numerical results.

A nearly complete treatment of the effect of non-adiabaticity on rovibrational energies of H3+ (Part III)

In this article, significant contributions of non-adiabaticity for the rovibrational bound states up to 25 000 cm-1 and total angular momentum J = 0-20 of H3+ are investigated. A coupled-perturbed full configuration interaction (CP-FCI) treatment is applied to calculate all couplings between electronic states caused by the nuclear motion. These derivative couplings were evaluated up to the second order by means of a perturbation treatment and include all nuclear Cartesian first and second derivatives of the electronic wavefunctions. In particular, the coupling of special derivatives with respect to r and R in the Jacobi coordinate representation is more significant than thought. The perturbation approach is especially optimal for the treatment of weak non-adiabaticity in case of rovibrational energies in H3+ and had not been available before for H3+ or other triatomics. Using exclusively Gaussian basis functions for CP-FCI appears to be sufficient, because explicit correlated wavefunctions are already used for all other potential energy contributions. Our work is an extension of earlier non-adiabatic investigations based on first derivative couplings of electronic states that led to the concept of geometry-dependent effective nuclear masses and which needs only a single potential energy surface for the dynamics. The implementation allows us to include all non-adiabatic effects up to the order of O(μ-2), μ being the reduced nuclear mass. Our treatment works for any isotopologue and for the whole potential energy curve or surface. By this treatment, a further reduction in deviations to experimental data for most rovibrational levels to less than 0.1 cm-1 is possible. For the related transition frequencies, 1366 of 1720 known rovibrational transitions in H3+ have deviations less than 0.1 cm-1 without using any empirically adjustable parameters or optimizing the nuclear mass for a specific transition. For many questionable assignments (deviations >0.3 cm-1) of observed transitions in H3+, a new labeling is proposed.

A New Ab Initio Potential Energy Surface and Rovibrational Spectra for the CO-N2O Complex

We constructed a new ab initio potential energy surface (PES) for CO-N2O which includes the intramolecular Q3 normal coordinate for the N2O ν3 antisymmetric stretching vibration. The intermolecular potential was evaluated employing the supermolecular method at the [CCSD(T)]-F12a level, with the aug-cc-pVTZ basis set plus bond functions. By integral over the intramolecular Q3 coordinate, we obtained the vibrationally averaged PESs for the CO-N2O system in the ground and ν3 excited states of N2O. Each PES features one nearly T-shaped global minimum and one skewed T-shaped local minimum. Based on these obtained PESs of CO-N2O, the radial discrete variable representation/angle finite base representation method and the Lanczos algorithm were applied for the calculations of bound states and rovibrational energy levels. The calculated ν3 vibrational band origin shift of the N2O monomer in CO-N2O is 2.7570 cm-1, matching well with the observed value of 2.9048 cm-1. The computed microwave and infrared transition frequencies, as well as the rotational parameters, are consistent with the experimental observations.

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.

A new six-dimensional ab initio potential energy surface and rovibrational spectra for the N2-CO2 complex

New six-dimensional ab initio potential energy surfaces (PESs) for the N2-CO2 complex, which involve the stretching vibration of N2 and the Q3 normal mode for the ν3 asymmetric stretching vibration of CO2, were constructed using the CCSD(T)-F12/AVTZ method with midpoint bond functions. Two vibrational averaged 4D interaction potentials were obtained by integrating over the two intramolecular coordinates. It was found that both PESs possess two equivalent T-shaped global minima as well as two in-plane and one out-of-plane saddle points. Based on these PESs, rovibrational bound states and energy levels were calculated applying the radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm. The splitting of the energy levels between oN2-CO2 and pN2-CO2 for the intermolecular vibrational ground state is determined to be only 0.000 09 cm-1 due to the higher barriers. The obtained band origin shift is about +0.471 74 cm-1 in the N2-CO2 infrared spectra with CO2 at the ν3 zone, which coincides with the experimental data of +0.483 74 cm-1. The frequencies of the in-plane geared-bending for N2-CO2 at the ν3 = 0 and 1 states of CO2 turn out to be 21.6152 and 21.4522 cm-1, the latter reproduces the available experimental 21.3793 cm-1 value with CO2 at the ν3 zone. The spectral parameters fitted from the rovibrational energy levels show that this dimer is a near prolate asymmetric rotor. The computed microwave transitions as well as the infrared fundamental and combination bands for the complex agree well with the observed data.

Using Collocation to Solve the Schrödinger Equation

We review the collocation approach to the solution of the Schrödinger equation and its uses in applications. Interrelations between collocation and other methods are highlighted. We also stress advantages and disadvantages of the rectangular collocation formulation. Using collocation makes it possible to use any, e.g. optimized, coordinates and basis functions, including nonintegrable basis functions, and provides a straightforward way of dealing with singularities in the potential. In addition, we stress that using collocation facilitates tuning the shape of basis functions and the placement of points, both of which can be done with machine-learning methods. Applications to electronic and vibrational problems are reviewed focusing on calculations for molecules on surfaces for which there are few variational calculations. Collocation has advantages when potential energy surfaces are unavailable, in particular, for molecule-surface systems, and for systems for which standard direct product quadrature grids, often used with variational methods, are costly.

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.

A new potential energy surface and rovibrational spectra of the CO-CO2 complex: Dependence on the antisymmetric stretching vibration of CO2

We present a new ab initio five-dimensional potential energy surface for the CO-CO2 complex containing the Q3 normal mode for the ν3 asymmetric stretching vibration of the CO2 unit. The potential was calculated by supermolecular approach at the CCSD(T)-F12 level with aug-cc-pVTZ basis set plus midpoint bond functions. Two vibrationally averaged four-dimensional potentials for CO-CO2 with CO2 in the ground and ν3 excited states were generated by the integration of the five-dimensional potential over the Q3 intramolecular coordinate. Each potential displays a T-shaped global minimum with the C end in the CO unit pointing toward the C atom in the CO2 unit and a T-shaped local minimum but with the CO monomer rotated by 180º. The rovibrational bound states and energy levels for the CO-CO2 dimer were obtained employing the radial discrete variable representation (DVR)/angular finite basis representation (FBR) method in conjunction with the Lanczos algorithm. The vibrational ground and some lower excited states for CO-CO2 are localized around the global minimum because of the higher potential barriers. The band origin is blueshifted by 0.2089 cm-1 for CO-CO2 in the CO2 ν3 range, which is consistent with the experimental result of 0.211 cm-1. The geared bending vibrational frequencies for CO-CO2 are 24.7101 and 24.5549 cm-1 at the ground and ν3 excited states of CO2, respectively. The predicted rovibrational frequencies as well as spectral constants coincide with the available observations, and these parameters show the CO-CO2 complex is a nearly prolate asymmetric rotor.

Algebraic DVR Approaches Applied to Piecewise Potentials: Symmetry and Degeneracy

Algebraic discrete variable representation (DVR) methods that have been recently proposed are applied to describe 1D and 2D piecewise potentials. First, it is shown that it is possible to use a DVR approach to describe 1D square well potentials testing the wave functions with exact results. Thereafter, Morse and Pöschl-Teller (PT) potentials are described with multistep piecewise potentials in order to explore the sensibility of the potential to reproduce the transition from a pure square well energy pattern to an anharmonic energy spectrum. Once the properties of the different algebraic DVR approaches are identified, the 2D square potential as a function of the potential depth is studied. We show that this system displays natural degeneracy, accidental degeneracy and systematic accidental degeneracy. The latter appears only for a confined potential, where the symmetry group is identified and irreducible representations are constructed. One particle confined in a rectangular well potential with commensurate sides is also analyzed. It is proved that the systematic accidental degeneracy appearing in this system is removed for finite potential depth.

Functional Tensor-Train Chebyshev Method for Multidimensional Quantum Dynamics Simulations

Methods for efficient simulations of multidimensional quantum dynamics are essential for theoretical studies of chemical systems where quantum effects are important, such as those involving rearrangements of protons or electronic configurations. Here, we introduce the functional tensor-train Chebyshev (FTTC) method for rigorous nuclear quantum dynamics simulations. FTTC is essentially the Chebyshev propagation scheme applied to the initial state represented in a continuous analogue tensor-train format. We demonstrate the capabilities of FTTC as applied to simulations of proton quantum dynamics in a 50-dimensional model of hydrogen-bonded DNA base pairs.

A full-dimensional ab initio intermolecular potential energy surface and rovibrational spectra for OC-HF and OC-DF

We present a full-dimensional ab initio intermolecular potential energy surface (IPES) for the OC-HF van der Waals complex. 3167 ab initio points were computed at the frozen-core (FC) explicitly correlated coupled cluster [FC-CCSD(T)-F12b] level, with the augmented correlation-consistent polarized valence quadruple-zeta basis set plus bond functions. Basis set superposition error correction was also considered by the full counterpoise procedure. Gaussian process regression (GPR) was used to map out the potential energy surface, while a multipole expansion method was employed to smooth the ab initio noise of intermolecular potential in the long range. The global minimum of -1248.364 cm^-1 was located at the linear configuration with the C atom pointing toward the H atom of the HF molecule. In addition, a local minimum of -602.026 cm^-1 was found at another linear configuration with the O atom pointing toward the H atom of the HF molecule. The eigenstates were calculated on the vibrational averaged four-dimensional IPESs with the mixed radial discrete variable representation/angular finite basis representation method and Lanczos propagation algorithm. The dissociation energy D₀ was calculated to be 701.827 cm^-1, well reproducing the experimental value of 732 ± 2 cm^-1. The dipole moment surfaces were also fitted by GPR from 3132 ab initio points calculated using the coupled cluster method [CCSD(T)] with AVTZ basis set plus bond functions. The frequencies and relative line intensities of rovibrational transitions in the HF (DF) and CO stretching bands were further calculated and compared well with the experimental results. These results indicate the high fidelity of the new IPES.

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.

Direct product-type grid representations for angular coordinates in extended space and their application in the MCTDH approach

Multi-configurational time-dependent Hartree (MCTDH) calculations using time-dependent grid representations can be used to accurately simulate high-dimensional quantum dynamics on general ab initio potential energy surfaces. Employing the correlation discrete variable representation, sets of direct product type grids are employed in the calculation of the required potential energy matrix elements. This direct product structure can be a problem if the coordinate system includes polar and azimuthal angles that result in singularities in the kinetic energy operator. In the present work, a new direct product-type discrete variable representation (DVR) for arbitrary sets of polar and azimuthal angles is introduced. It employs an extended coordinate space where the range of the polar angles is taken to be [-π, π]. The resulting extended space DVR resolves problems caused by the singularities in the kinetic energy operator without generating a very large spectral width. MCTDH calculations studying the F·CH₄ complex are used to investigate important properties of the new scheme. The scheme is found to allow for more efficient integration of the equations of motion compared to the previously employed cot-DVR approach [G. Schiffel and U. Manthe, Chem. Phys. 374, 118 (2010)] and decreases the required central processing unit times by about an order of magnitude.

Using collocation to study the vibrational dynamics of molecules

In this paper, I review collocation methods for solving the time-independent and the time-dependent Schroedinger equation. Unlike traditional variational methods, collocation methods do not require integrals and quadrature. Either collocation or quadrature is necessary if the potential does not have a special form. If the basis is a direct product of univariate bases and the quadrature grid is also a direct product, there exist variational methods that do not require quadrature approximations for potential energy matrix elements. These methods, however, do require storing, in computer memory, vectors with as many components as there are quadrature points. For this reason direct-product variational methods are poor for problems with more than five atoms. There are well established ideas for reducing the size of the basis in a variational calculation. Three such ideas are: 1) prune the direct product basis; 2) use basis functions that are products of multivariate functions; 3) optimise the basis functions (e.g. Multiconfiguration time-dependent Hartree). Reducing the basis size, however, is not enough to the make variational methods tractable because, for all three of these ideas, quadrature rears its ugly head. Collocation is an attractive alternative to variational methods.

Vibrational heat-bath configuration interaction

We introduce vibrational heat-bath configuration interaction (VHCI) as an accurate and efficient method for calculating vibrational eigenstates of anharmonic systems. Inspired by its origin in electronic structure theory, VHCI is a selected CI approach that uses a simple criterion to identify important basis states with a pre-sorted list of anharmonic force constants. Screened second-order perturbation theory and simple extrapolation techniques provide significant improvements to variational energy estimates. We benchmark VHCI on four molecules with 12-48 degrees of freedom and use anharmonic potential energy surfaces truncated at fourth and sixth orders. When compared to other methods using the same truncated potentials, VHCI produces vibrational spectra of tens or hundreds of states with sub-wavenumber accuracy at low computational cost.

A variational calculation of vibrational levels of vinyl radical

We report the vibrational energy levels of vinyl radical (VR) that are computed with a Lanczos eigensolver and a contracted basis. Many of the levels of the two previous VR variational calculations differ significantly and differ also from those reported in this paper. We identify the source of and correct symmetry errors on the potential energy surfaces used in the previous calculations. VR has two equivalent equilibrium structures. By plotting wavefunction cuts, we show that two tunneling paths play an important role. Using the computed wavefunctions, it is possible to assign many states and thereby to determine tunneling splittings that are compared with their experimental counterparts. Our computed red shift of the hot band at 2897.23 cm^-1, observed by Dong et al. [J Chem. Phys. 128, 044305 (2008)], is 4.47 cm^-1, which is close to the experimental value of 4.63 cm^-1.

Analysis of QED and non-adiabaticity effects on the rovibrational spectrum of H3 + using geometry-dependent effective nuclear masses

The influence of QED effects (including one- and two-electron Lamb-shift, Araki-Sucher term, one-loop self-energy, and finite nuclear size correction) together with non-adiabatic effects on the rovibrational bound states of H₃ ⁺ has been investigated. Non-adiabaticity is modeled by using geometry-dependent effective nuclear masses together with only one single potential energy surface. In conclusion, for rovibrational states below 20 000 cm^-1, QED and relativistic effects do nearly compensate, and a potential energy surface based on Born-Oppenheimer energies and diagonal adiabatic corrections has nearly the same quality as the one including relativity with QED; the deviations between the two approaches for individual rovibrational states are mostly below 0.02 cm^-1. The inclusion of non-adiabatic effects is important, and it reduces deviations from experiments mostly below 0.1 cm^-1.

Computational Study of the Rovibrational Spectra of CH2D+ and CHD2. J Phys Chem A 2019;123:10281-10289. [PMID: 31657568 DOI: 10.1021/acs.jpca.9b09045] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

In this paper, we present rovibrational energy levels of CH₂D⁺ and CHD₂⁺. They are computed with a large basis and the Lanczos algorithm. CH₂D⁺ and CHD₂⁺ are believed to play an important role in interstellar space, but so far, there are no definitive observations. The predictions of this paper should facilitate detection. For CH₂D⁺, two CH stretch bands have been studied at high resolution. Compared to our calculated energies, the root-mean-square error is 0.08 cm^-1. For CHD₂⁺, one CH stretch band has been studied at high resolution. Compared to our calculated energies, the root-mean-square error is 0.5 cm^-1. Errors are larger, for both isotopologues, for bend states. We attribute these errors to the potential energy surface. Wave function and probability distribution plots are used to make assignments. The ν₁ band of CHD₂⁺ is significantly perturbed, and according to our calculations, the 3ν₃ state is closest and might be the most important perturber.

Computational study of the ro-vibrational spectrum of CO-CO2

An accurate ab initio ground-state intermolecular potential energy surface (PES) was determined for the CO-CO₂ van der Waals dimer. The Lanczos algorithm was used to compute rovibrational energies on this PES. For both the C-in and O-in T-shaped isomers, the fundamental transition frequencies agree well with previous experimental results. We confirm that the in-plane states previously observed are geared states. In addition, we have computed and assigned many other vibrational states. The rotational constants we determine from J = 1 energy levels agree well with their experimental counterparts. Planar and out-of-plane cuts of some of the wavefunctions we compute are quite different, indicating strong coupling between the bend and torsional modes. Because the stable isomers are T-shaped, vibration along the out-of-plane coordinates is very floppy. In CO-CO₂, when the molecule is out-of-plane, interconversion of the isomers is possible, but the barrier height is higher than the in-plane geared barrier height.

Low-temperature chemistry using the R-matrix method

Techniques for producing cold and ultracold molecules are enabling the study of chemical reactions and scattering at the quantum scattering limit, with only a few partial waves contributing to the incident channel, leading to the observation and even full control of state-to-state collisions in this regime. A new R-matrix formalism is presented for tackling problems involving low- and ultra-low energy collisions. This general formalism is particularly appropriate for slow collisions occurring on potential energy surfaces with deep wells. The many resonance states make such systems hard to treat theoretically but offer the best prospects for novel physics: resonances are already being widely used to control diatomic systems and should provide the route to steering ultracold reactions. Our R-matrix-based formalism builds on the progress made in variational calculations of molecular spectra by using these methods to provide wavefunctions for the whole system at short internuclear distances, (a regime known as the inner region). These wavefunctions are used to construct collision energy-dependent R-matrices which can then be propagated to give cross sections at each collision energy. The method is formulated for ultracold collision systems with differing numbers of atoms.

The kinetic energy operator for distance-dependent effective nuclear masses: Derivation for a triatomic molecule

The kinetic energy operator for triatomic molecules with coordinate or distance-dependent nuclear masses has been derived. By combination of the chain rule method and the analysis of infinitesimal variations of molecular coordinates, a simple and general technique for the construction of the kinetic energy operator has been proposed. The asymptotic properties of the Hamiltonian have been investigated with respect to the ratio of the electron and proton mass. We have demonstrated that an ad hoc introduction of distance (and direction) dependent nuclear masses in Cartesian coordinates preserves the total rotational invariance of the problem. With the help of Wigner rotation functions, an effective Hamiltonian for nuclear motion can be derived. In the derivation, we have focused on the effective trinuclear Hamiltonian. All necessary matrix elements are given in closed analytical form. Preliminary results for the influence of non-adiabaticity on vibrational band origins are presented for H₃⁺.

A-VCI: A flexible method to efficiently compute vibrational spectra

The adaptive vibrational configuration interaction algorithm has been introduced as a new method to efficiently reduce the dimension of the set of basis functions used in a vibrational configuration interaction process. It is based on the construction of nested bases for the discretization of the Hamiltonian operator according to a theoretical criterion that ensures the convergence of the method. In the present work, the Hamiltonian is written as a sum of products of operators. The purpose of this paper is to study the properties and outline the performance details of the main steps of the algorithm. New parameters have been incorporated to increase flexibility, and their influence has been thoroughly investigated. The robustness and reliability of the method are demonstrated for the computation of the vibrational spectrum up to 3000 cm^-1 of a widely studied 6-atom molecule (acetonitrile). Our results are compared to the most accurate up to date computation; we also give a new reference calculation for future work on this system. The algorithm has also been applied to a more challenging 7-atom molecule (ethylene oxide). The computed spectrum up to 3200 cm^-1 is the most accurate computation that exists today on such systems.

Investigation of Nonadiabatic Effects for the Vibrational Spectrum of a Triatomic Molecule: The Use of a Single Potential Energy Surface with Distance-Dependent Masses for H3. J Phys Chem A 2017;121:7016-7030. [PMID: 28820589 DOI: 10.1021/acs.jpca.7b04703]

On the basis of first-principles, the influence of nonadiabatic effects on the vibrational bound states of H₃⁺ has been investigated using distance-dependent reduced masses and only one single potential energy surface. For these new vibrational calculations, potentials based on explicitly correlated wave functions are used where, in addition, adiabatic corrections and relativistic contributions are taken into account. For the first time, several different fully distance-dependent reduced mass surfaces in three dimensions have been incorporated in the vibrational calculations.

Semiclassical basis sets for the computation of molecular vibrational states

In this paper, we extend a method recently reported [F. Revuelta et al., Phys. Rev. E 87, 042921 (2013)] for the calculation of the eigenstates of classically highly chaotic systems to cases of mixed dynamics, i.e., those presenting regular and irregular motions at the same energy. The efficiency of the method, which is based on the use of a semiclassical basis set of localized wave functions, is demonstrated by applying it to the determination of the vibrational states of a realistic molecular system, namely, the LiCN molecule.

The vibration-rotation-tunneling levels of N2-H2O and N2-D2O

In this paper, we report vibration-rotation-tunneling levels of the van der Waals clusters N2-H2O and N2-D2O computed from an ab initio potential energy surface. The only dynamical approximation is that the monomers are rigid. We use a symmetry adapted Lanczos algorithm and an uncoupled product basis set. The pattern of the cluster's levels is complicated by splittings caused by H-H exchange tunneling (larger splitting) and N-N exchange tunneling (smaller splitting). An interesting result that emerges from our calculation is that whereas in N2-H2O, the symmetric H-H tunnelling state is below the anti-symmetric H-H tunnelling state for both K = 0 and K = 1, the order is reversed in N2-D2O for K = 1. The only experimental splitting measurements are the D-D exchange tunneling splittings reported by Zhu et al. [J. Chem. Phys. 139, 214309 (2013)] for N2-D2O in the v2 = 1 region of D2O. Due to the inverted order of the split levels, they measure the sum of the K = 0 and K = 1 tunneling splittings, which is in excellent agreement with our calculated result. Other splittings we predict, in particular those of N2-H2O, may guide future experiments.

Two new methods for computing vibrational energy levels

I review two new ideas for coping with the size of large product basis sets and large product grids when one computes vibrational energy levels. The first is based on a tensor reduction scheme. It exploits advantages of a sum-of-products potential. The key idea is to use a basis each of whose function is a sum of optimized products and to compress the number of terms in each basis function. When the potential does not have the sum-of-products form, it is usually necessary to use quadrature. The second idea uses a nondirect product grid that has structure and is therefore compatible with efficient matrix–vector products.

Theoretical prediction of the linear isomers for rare gas-carbon disulfide complexes: He-CS₂, Ne-CS₂, and Ar-CS₂

Theoretical studies of the potential energy surfaces (PESs) and bound states are performed for rare gas-carbon disulfide complexes, He-CS2, Ne-CS2, and Ar-CS2. Three two-dimensional intermolecular PESs are constructed from ab initio data points which are calculated at the CCSD(T) level with aug-cc-pVTZ basis set supplemented with bond functions. We find that the three PESs have very similar features and each PES can be characterized by a global T-shaped minimum, two equivalent local linear minima, and the saddle points between them. The T-shaped isomer is energetically more stable than the linear isomer for each complex. The linear isomers, which have not been observed in experiment so far, are predicted from our PESs and further identified by bound state calculations. Moreover, we assign several intermolecular vibrational states for both the T-shaped and linear isomers of the three complexes via the analysis of wavefunctions. The corresponding vibrational frequencies are calculated from the bound state energies for these assigned states. These frequencies could be helpful for further experimental studies, especially for the linear isomers. We also calculate the rovibrational transition frequencies for the three T-shaped isomers and the pure rotational transition frequencies for the linear isomers, respectively. The accuracy of the PESs is validated by the good agreement between theoretical and experimental results for the rovibrational transition frequencies and spectroscopic parameters.

Calculating and assigning rovibrational energy levels of (15N2O)2, (15N14NO)2, 14N2O-15N2O and 15N14NO-15N2O

In this paper we report transition frequencies and rotational constants computed for several isotopologues of the nitrous oxide dimer. A previously reported intermolecular potential, the symmetry adapted Lanczos algorithm and an uncoupled product basis set are used to do the calculations. Rotational transition frequencies and rotational constants are in good agreement with experiment. We calculate states localized in both polar and nonpolar wells on the potential surface. Two of the four isotopologues we study have inequivalent monomers. They have wavefunctions localized over a single polar well.