On the variational computation of a large number of vibrational energy levels and wave functions for medium-sized molecules

Abstract

In a recent publication [J. Chem. Phys. 127, 084102 (2007)], the nearly variational DEWE approach (DEWE denotes Discrete variable representation of the Watson Hamiltonian using the Eckart frame and an Exact inclusion of a potential energy surface expressed in arbitrarily chosen coordinates) was developed to compute a large number of (ro)vibrational eigenpairs for medium-sized semirigid molecules having a single well-defined minimum. In this publication, memory, CPU, and hard disk usage requirements of DEWE, and thus of any DEWE-type approach, are carefully considered, analyzed, and optimized. Particular attention is paid to the sparse matrix-vector multiplication, the most expensive part of the computation, and to rate-determining steps in the iterative Lanczos eigensolver, including spectral transformation, reorthogonalization, and restart of the iteration. Algorithmic improvements are discussed in considerable detail. Numerical results are presented for the vibrational band origins of the (12)CH(4) and (12)CH(2)D(2) isotopologues of the methane molecule. The largest matrix handled on a personal computer during these computations is of the size of (4x10(8))x(4x10(8)). The best strategy for determining vibrational eigenpairs depends largely on the actual details of the required computation. Nevertheless, for a usual scenario requiring a large number of the lowest eigenpairs of the Hamiltonian matrix the combination of the thick-restart Lanczos method, shift-fold filtering, and periodic reorthogonalization appears to result in the computationally most feasible approach.

MARVEL analysis of the measured high-resolution spectra of 14NH3

“…The height of the effective barrier is 2021720 cm À 1 , when relativistic effects (about þ 20 cm À 1 ), BornOppenheimer diagonal corrections (about À10 cm À 1 ), and zero-point vibrations (about þ244 cm À 1 ) are all considered [20,100,150,151]. Treating the inversion motion is challenging for perturbative approaches and calls for fourth-age quantum chemical [152] nuclear motion treatments [131,[153][154][155][156]. (4) The parent isotopologue of ammonia, 14 NH 3 , exists in two nuclear-spin isomer forms (Table 1), ortho (proton quartet) and para (proton doublet), which correspond to different values of the total nuclear spin (I) of the three H atoms [157].…”

Ab initio calculation of the rotational spectrum of methane vibrational ground state

“…16 The vibrational and/or rotational spectra of methane has been the topics of many theoretical studies, see Refs. [17][18][19][20][21][22][23][24][25][26][27][28][29][30] to quote a few. However, as far as we are aware, only Signorel et al 31 have investigated its effective rotational dipole moment coefficients.…”

Systematically expanding nondirect product bases within the pruned multi-configuration time-dependent Hartree (MCTDH) method: A comparison with multi-layer MCTDH

“…[1][2][3][4][5][6][7] When D, the number of dimensions, is less than about ten, it is possible to use a direct (or tensor) product basis. [8][9][10][11][12] Direct product bases (DPBs) are conceptually simple and, more importantly, they make it possible to efficiently evaluate matrix-vector products (MVPs) when iterative methods are used to solve the Schrödinger equation. The CPU cost scales as N D+1 and the memory cost scales as N D , where N is a representative number of 1D functions.…”