Calculating vibrational energies and wave functions of vinylidene using a contracted basis with a locally reorthogonalized coupled two-term Lanczos eigensolver

Using nested tensor train contracted basis functions with group theoretical techniques to compute (ro)-vibrational spectra of molecules with non-Abelian groups

In this paper, we use nested tensor-train contractions to compute vibrational and ro-vibrational energy levels of molecules with five and six atoms. At each step, we fully exploit symmetry by using symmetry adapted basis functions obtained from an irreducible tensor method. Contracted basis functions are determined by diagonalizing reduced dimensional Hamiltonian matrices. The size of matrices of eigenvectors, used to account for coupling between groups of coordinates, is reduced by discarding rows and columns. The size of the matrices that must be diagonalized is thus substantially reduced, making it possible to use direct eigensolvers, even for molecules with five and six atoms. The symmetry-adapted contracted vibrational basis functions have been used to compute J = 0 energy levels of the CH3CN (C3v) and J > 0 levels of CH4.

HCl trimer: HCl-stretch excited intramolecular and intermolecular vibrational states from 12D fully coupled quantum calculations employing contracted intra- and inter-molecular bases

We present fully coupled, full-dimensional quantum calculations of the inter- and intra-molecular vibrational states of HCl trimer, a paradigmatic hydrogen-bonded molecular trimer. They are performed utilizing the recently developed methodology for the rigorous 12D quantum treatment of the vibrations of the noncovalently bound trimers of flexible diatomic molecules [Felker and Bačić, J. Chem. Phys. 158, 234109 (2023)], which was previously applied to the HF trimer by us. In this work, the many-body 12D potential energy surface (PES) of (HCl)3 [Mancini and Bowman, J. Phys. Chem. A 118, 7367 (2014)] is employed. The calculations extend to the intramolecular HCl-stretch excited vibrational states of the trimer with one- and two-quanta, together with the low-energy intermolecular vibrational states in the two excited v = 1 intramolecular vibrational manifolds. They reveal significant coupling between the intra- and inter-molecular vibrational modes. The 12D calculations also show that the frequencies of the v = 1 HCl stretching states of the HCl trimer are significantly redshifted relative to those of the isolated HCl monomer. Detailed comparison is made between the results of the 12D calculations on the two-body PES, obtained by removing the three-body term from the original 2 + 3-body PES, and those computed on the 2 + 3-body PES. It demonstrates that the three-body interactions have a strong effect on the trimer binding energy as well as on its intra- and inter-molecular vibrational energy levels. Comparison with the available spectroscopic data shows that good agreement with the experiment is achieved only if the three-body interactions are included. Some low-energy vibrational states localized in a secondary minimum of the PES are characterized as well.

Theoretical modeling of molecules in weakly interacting environments: trifluoride anions in argon

The properties of molecules can be affected by the presence of a host environment. Even in inert rare gas matrices such effects are observable, as for instance in matrix isolation spectroscopy. In this work we study the trifluoride anion in cryogenic argon environments. To investigate the structure and vibrational properties of the guest-host systems, a potential energy surface of compound F-3-argon structures is determined from ab initio calculations with the CCSD(T)-F12b approach. Argon environments are probed with minima hopping optimizations of extended trifluoride-argon clusters. The vibrations of F-3 within the optimized environments are examined with anharmonic vibrational analyses. Among the three identified structural surroundings for the trifluoride, two are characterized by relatively favorable guest-host and host-host interactions as well as vibrational zero-point energies. A striking dependence of the trifluoride properties on the particular argon environment reveals the delicate influence of the host atoms on the guest molecule. Very good agreement with measured data suggests that in experiment F-3 occupies a double-vacancy site.

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.

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.

The Peculiar Interaction of Trifluoride Anions with Cryogenic Rare Gas Matrices

In this contribution, we present theoretical modeling of the interaction between rare gas matrices and a trifluoride guest anion, as well as its quantitative effect on measured vibrational spectra. Using a combination of coupled-cluster electronic structure calculations and a many-body potential expansion coupled with permutation invariant polynomial fitting and anharmonic vibrational spectrum simulations, we shed light on the origin of the trifluoride matrix effects observed experimentally. The theoretical spectra are found to reproduce accurately the measured data while providing deeper insights into the effects of the guest-host interaction. The investigations reveal that neon can only stabilize trifluoride in hexagonal cavities formed by double vacancies, while argon can host the anion in a variety of cavities ranging from zero to two defects in the matrix. The origin of this structural variability can be traced back to the disparate strengths of the host-host interactions in neon and argon. The present work demonstrates the importance of theoretical modeling to complement matrix isolation experiments, which alone do not provide direct information about the structure of the matrices or about the physical origin of their interaction and of their spectroscopic signature.

A pair potential modeling study of F3− in neon matrices

First-principles investigations of the trifluoride anion in a neon environment reveal a small blue-shift of the fundamental vibrational excitations.

Neural Network Potential Energy Surfaces for Small Molecules and Reactions

We review progress in neural network (NN)-based methods for the construction of interatomic potentials from discrete samples (such as ab initio energies) for applications in classical and quantum dynamics including reaction dynamics and computational spectroscopy. The main focus is on methods for building molecular potential energy surfaces (PES) in internal coordinates that explicitly include all many-body contributions, even though some of the methods we review limit the degree of coupling, due either to a desire to limit computational cost or to limited data. Explicit and direct treatment of all many-body contributions is only practical for sufficiently small molecules, which are therefore our primary focus. This includes small molecules on surfaces. We consider direct, single NN PES fitting as well as more complex methods that impose structure (such as a multibody representation) on the PES function, either through the architecture of one NN or by using multiple NNs. We show how NNs are effective in building representations with low-dimensional functions including dimensionality reduction. We consider NN-based approaches to build PESs in the sums-of-product form important for quantum dynamics, ways to treat symmetry, and issues related to sampling data distributions and the relation between PES errors and errors in observables. We highlight combinations of NNs with other ideas such as permutationally invariant polynomials or sums of environment-dependent atomic contributions, which have recently emerged as powerful tools for building highly accurate PESs for relatively large molecular and reactive systems.

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.

Mode-Specific Tunneling Splittings for a Sequential Double-Hydrogen Transfer Case: An Accurate Quantum Mechanical Scheme

We present the first accurate quantum dynamics calculations of mode-specific tunneling splittings in a sequential double-hydrogen transfer process. This is achieved in the vinylidene-acetylene system, the simplest molecular system of this kind, and by large-scale parallel computations with an efficient theoretical scheme developed by us. In our scheme, basis functions are customized for the hydrogen transfer process; a 4-dimensional basis contraction strategy is combined with the preconditioned inexact spectral transform method; efficient parallel implementation is achieved. Mode-specific permutation tunneling splittings of vinylidene states are reported and tremendous mode-specific promotion effects are revealed; in particular, the CH2 rock mode enhances the ground-state splitting by a factor of 10(3). We find that the ground-state vinylidene has a reversible-isomerization time of 622 ps, much longer than all previous estimates. Our calculations also shed light on the importance of the deep intermediate well and vibrational excitation in the double-hydrogen transfer processes.

Manipulating interfacial hydrogens at palladium via STM

In this contribution, we provide a quantum dynamical analysis of the interfacial hydrogen migration mediated by scanning tunneling microscopy (STM). It is observed that the hydrogen impurity favors resurfacing over occupation of the bulk and subsurface sites whenever possible. The present simulations give strong indication that the experimentally observed protuberances after STM-excitation are due to H accumulating in the vicinity of the surface.

Approximate first-principles anharmonic calculations of polyatomic spectra using MP2 and B3LYP potentials: comparisons with experiment

Anharmonic vibrational spectroscopy calculations using MP2 and B3LYP computed potential surfaces are carried out for a series of molecules, and frequencies and intensities are compared with those from experiment. The vibrational self-consistent field with second-order perturbation correction (VSCF-PT2) is used in computing the spectra. The test calculations have been performed for the molecules HNO3, C2H4, C2H4O, H2SO4, CH3COOH, glycine, and alanine. Both MP2 and B3LYP give results in good accord with experimental frequencies, though, on the whole, MP2 gives very slightly better agreement. A statistical analysis of deviations in frequencies from experiment is carried out that gives interesting insights. The most probable percentage deviation from experimental frequencies is about -2% (to the red of the experiment) for B3LYP and +2% (to the blue of the experiment) for MP2. There is a higher probability for relatively large percentage deviations when B3LYP is used. The calculated intensities are also found to be in good accord with experiment, but the percentage deviations are much larger than those for frequencies. The results show that both MP2 and B3LYP potentials, used in VSCF-PT2 calculations, account well for anharmonic effects in the spectroscopy of molecules of the types considered.

Vibrational energy levels of difluorodioxirane computed with variational and perturbative methods from a hybrid force field

We have computed vibrational energy levels of difluorodioxirane (CF2O2). For the potential, a Taylor expansion in normal coordinates is used. The CCSD(T) and MP2 methods and correlation consistent basis sets of quadruple-zeta quality are used to determine the force constants. The vibrational Schrödinger equation was solved using both a variational method and second order perturbation theory. The Watson kinetic energy operator and a discrete variable representation were used with the DEWE (E. Mátyus, G. Czakó, B.T. Sutcliffe and A.G. Császár, J. Chem. Phys. 127 (2007) 084102) computer program to do the variational calculations. For the variational calculations, the average absolute deviation of fundamentals, with respect to experimental values, is less than 3 cm(-1). Perturbative results are almost as good. About 300 vibrational levels were computed. (16)O→(18)O isotopic shifts have also been calculated variationally for the lowest 75 vibrational energy levels and are compared to experimental results.

The vibrational bound states of isomerising disilyne

Full-dimensional variational calculations are reported for the isomerising disilyne molecule, Si2H2. Large-scale calculations using coordinates based on orthogonal satellite vectors permitted the computation of excited vibrational state energies and wavefunctions for all four isomeric forms: dibridged Si(H2)Si, monobridged Si(H)SiH, disilavinylidene H2SiSi, and trans-bent HSiSiH. Energies and wavefunctions have been determined for the lowest 2400 totally symmetric vibrational states; this set includes highly excited states above all three chemically relevant isomerisation barriers--up to about 8300 cm(-1) above the (dibridged) ground state. States strongly localised in the dibridged, monobridged, and disilavinylidene regions of the potential energy surface have been found as well as many partially or fully delocalised states. For the trans-bent form, only partially localised states have been identified. Comparisons are made with similar literature calculations on the isovalent acetylene-vinylidene system HCCH/H2CC.