In this paper, we report a new intermolecular potential energy surface and rovibrational transition frequencies and line strengths computed for the OCS dimer. The potential is made by fitting energies obtained from explicitly correlated coupled-cluster calculations and fit using an interpolating moving least squares method. The rovibrational Schroedinger equation is solved with a symmetry-adapted Lanczos algorithm and an uncoupled product basis set. All four intermolecular coordinates are included in the calculation. On the potential energy surface we find, previously unknown, cross-shaped isomers and also polar and non-polar isomers. The associated wavefunctions and energy levels are presented. To identify polar and cross states we use both calculations of line strengths and vibrational parent analysis. Calculated rotational constants differ from their experimental counterparts by less than 0.001 cm(-1).

We demonstrate that it is possible to use a variational method to compute 50 vibrational levels of ethylene oxide (a seven-atom molecule) with convergence errors less than 0.01 cm. This is done by beginning with a small basis and expanding it to include product basis functions that are deemed to be important. For ethylene oxide a basis with fewer than 3 × 10 functions is large enough. Because the resulting basis has no exploitable structure we use a mapping to evaluate the matrix-vector products required to use an iterative eigensolver. The expanded basis is compared to bases obtained from pre-determined pruning condition. Similar calculations are presented for molecules with 3, 4, 5, and 6 atoms. For the 6-atom molecule, CHCH, the required expanded basis has about 106 000 functions and is about an order of magnitude smaller than bases made with a pre-determined pruning condition.

In this paper we show that it is possible to use an iterative eigensolver in conjunction with Halverson and Poirier's symmetrized Gaussian (SG) basis [T. Halverson and B. Poirier, J. Chem. Phys. 137, 224101 (2012)] to compute accurate vibrational energy levels of molecules with as many as five atoms. This is done, without storing and manipulating large matrices, by solving a regular eigenvalue problem that makes it possible to exploit direct-product structure. These ideas are combined with a new procedure for selecting which basis functions to use. The SG basis we work with is orders of magnitude smaller than the basis made by using a classical energy criterion. We find significant convergence errors in previous calculations with SG bases. For sum-of-product Hamiltonians, SG bases large enough to compute accurate levels are orders of magnitude larger than even simple pruned bases composed of products of harmonic oscillator functions.

Although phase-space localized Gaussians are themselves poor basis functions, they can be used to effectively contract a discrete variable representation basis [A. Shimshovitz and D. J. Tannor, Phys. Rev. Lett. 109, 070402 (2012)]. This works despite the fact that elements of the Hamiltonian and overlap matrices labelled by discarded Gaussians are not small. By formulating the matrix problem as a regular (i.e., not a generalized) matrix eigenvalue problem, we show that it is possible to use an iterative eigensolver to compute vibrational energy levels in the Gaussian basis.

Recent significant improvements of the numerical solutions of the time-dependent Schrödinger equation beg the question as to whether these recent methods are comparable in efficacy (in terms of accuracy and computational time) to the current "method of choice," i.e., the Chebyshev expansion of the time-evolution operator and the fast-Fourier-transform method of determining the kinetic energy. In this paper we review the methods in question and, by studying the time development of a coherent wave packet in an oscillator well, we are able to assess the effectiveness of the various methods. It turns out that the new generalizations come close (to within an order of magnitude) to being able to generate solutions as precisely and efficiently as the Chebyshev-fast-Fourier-transform method. The strict unitarity of the generalized methods may be an advantage. We also show that the fast-Fourier-transform approach to calculating the kinetic energy can be replaced by straightforward numerical differentiation to obtain the same precision.