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.

Using a pruned basis and a sparse collocation grid with more points than basis functions to do efficient and accurate MCTDH calculations with general potential energy surfaces.

We propose a new collocation multi-configuration time-dependent Hartree (MCTDH) method. It reduces point-set error by using more points than basis functions. Collocation makes it possible to use MCTDH with a general potential energy surface without computing any integrals.

A two-step quadrature-based variational calculation of ro-vibrational levels and wavefunctions of CO using a bisector- 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 CO. A two-step method [J. Tennyson and B.

Theory cracks old data: Rovibrational energy levels of H-CO derived from experiment.

Measurements of rovibrational spectra of clusters provide physical insight only if spectral lines can be assigned to pairs of quantum states, and further insight is obtained if one can deduce the quantitative energy-level pattern. Both steps can be so difficult that some measured spectra remain unassigned, one example is H-CO. To extend the scope of spectroscopic insights, we propose to use theoretical information in interpretation of spectra.

Computing vibrational energy levels using a canonical polyadic tensor method with a fixed rank and a contraction tree.

In this paper, we use the previously introduced Canonical Polyadic (CP)-Multiple Shift Block Inverse Iteration (MSBII) eigensolver [S. D. Kallullathil and T.

Computing vibrational spectra using a new collocation method with a pruned basis and more points than basis functions: Avoiding quadrature.

We present a new collocation method for computing the vibrational spectrum of a polyatomic molecule. Some form of quadrature or collocation is necessary when the potential energy surface does not have a simple form that simplifies the calculation of the potential matrix elements required to do a variational calculation. With quadrature, better accuracy is obtained by using more points than basis functions.

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.

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.

Computing vibrational energy levels by solving linear equations using a tensor method with an imposed rank.

Present day computers do not have enough memory to store the high-dimensional tensors required when using a direct product basis to compute vibrational energy levels of a polyatomic molecule with more than about five atoms. One way to deal with this problem is to represent tensors using a tensor format. In this paper, we use the canonical polyadic (CP) format.

A rectangular collocation multi-configuration time-dependent Hartree (MCTDH) approach with time-independent points for calculations on general potential energy surfaces.

We introduce a collocation-based multi-configuration time-dependent Hartree (MCTDH) method that uses more collocation points than basis functions. We call it the rectangular collocation MCTDH (RC-MCTDH) method. It does not require that the potential be a sum of products.

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.

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.

Computational study of the rovibrational spectrum of CO-N.

The CO2-N2 complex is formed from two key components of Earth's atmosphere, and as such, has received some attention from both experimental and theoretical studies. On the theory side, a potential energy surface (PES) based on high level ab initio data was reported [Nasri et al., J.

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.

A collocation-based multi-configuration time-dependent Hartree method using mode combination and improved relaxation.

Although very useful, the original multi-configuration time-dependent Hartree (MCTDH) method has two weaknesses: (1) its cost scales exponentially with the number of atoms in the system; (2) the standard MCTDH implementation requires that the potential energy surface (PES) be in the sum-of-product (SOP) form in order to reduce the cost of computing integrals in the MCTDH basis. One way to deal with (1) is to lump coordinates into groups. This is mode combination (MC).

Machine Learning Optimization of the Collocation Point Set for Solving the Kohn-Sham Equation.

The rectangular collocation approach makes it possible to solve the Schrödinger equation with basis functions that do not have amplitude in all regions in which wave functions have significant amplitude. Collocation points can be restricted to a small region of space. As no integrals are computed, there are no problems due to discontinuities in the potential, and there is no need to use integrable basis functions.

Computational Study of the Rovibrational Spectra of CHD and CHD.

In this paper, we present rovibrational energy levels of CHD and CHD. They are computed with a large basis and the Lanczos algorithm. CHD and CHD are believed to play an important role in interstellar space, but so far, there are no definitive observations.

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

An accurate ab initio ground-state intermolecular potential energy surface (PES) was determined for the CO-CO 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.

Using collocation and a hierarchical basis to solve the vibrational Schrödinger equation.

We show that it is possible to compute vibrational energy levels of polyatomic molecules with a collocation method and a basis of products of one-dimensional harmonic oscillator functions pruned so that it does not include functions for which the indices of many of the one-dimensional functions are nonzero. Functions with many nonzero indices are coupled only by terms that depend simultaneously on many coordinates, and they are typically small. The collocation equation is derived without invoking differences of interpolation operators, which simplifies implementation of the method.

A pruned collocation-based multiconfiguration time-dependent Hartree approach using a Smolyak grid for solving the Schrödinger equation with a general potential energy surface.

Standard multiconfiguration time-dependent Hartree (MCTDH) calculations use a direct product basis and rely on the potential being a sum of products (SOPs). The size of the direct product MCTDH basis scales exponentially with the number of atoms. Accurate potentials may not be SOPs.

Using rectangular collocation with finite difference derivatives to solve electronic Schrödinger equation.

We show that a rectangular collocation method, equivalent to evaluating all matrix elements with a quadrature-like scheme and using more points than basis functions, is an effective approach for solving the electronic Schrödinger equation (ESE). We test the ideas by computing several solutions of the ESE for the H atom and the H cation and several solutions of the Kohn-Sham equation for CO and HO. In all cases, we achieve millihartree accuracy.

Computing vibration-rotation-tunnelling levels of HOD dimer.

Using an accurate 6D water dimer potential energy surface, we compute vibration-rotation-tunnelling levels of HOD dimer, by assuming that the two monomers are rigid. HOD dimer has two isomers, a D-bonded isomer and an H-bonded isomer, and the wavefunctions of both isomers have amplitude in four wells. HOD dimer is important because, unlike the case of H2O dimer or D2O dimer, it is possible to measure the largest tunnelling splitting.

Using an iterative eigensolver and intertwined rank reduction to compute vibrational spectra of molecules with more than a dozen atoms: Uracil and naphthalene.

We use a direct product basis, basis vectors computed by evaluating matrix-vector products, and rank reduction to calculate vibrational energy levels of uracil and naphthalene, with 12 and 18 atoms, respectively. A matrix representing the Hamiltonian in the direct product basis and vectors with as many components as there are direct product basis functions are neither calculated nor stored. We also introduce an improvement of the Hierarchical Intertwined Reduced-Rank Block Power Method (HI-RRBPM), proposed previously in Thomas and Carrington, Jr.

Neural networks vs Gaussian process regression for representing potential energy surfaces: A comparative study of fit quality and vibrational spectrum accuracy.

For molecules with more than three atoms, it is difficult to fit or interpolate a potential energy surface (PES) from a small number of (usually ab initio) energies at points. Many methods have been proposed in recent decades, each claiming a set of advantages. Unfortunately, there are few comparative studies.