Complete nuclear motion Hamiltonian in the irreducible normal mode tensor operator formalism for the methane molecule

Abstract

A rovibrational model based on the normal-mode complete nuclear Hamiltonian is applied to methane using our recent potential energy surface [A. V. Nikitin, M. Rey, and Vl. G. Tyuterev, Chem. Phys. Lett. 501, 179 (2011)]. The kinetic energy operator and the potential energy function are expanded in power series to which a new truncation-reduction technique is applied. The vibration-rotation Hamiltonian is transformed systematically to a full symmetrized form using irreducible tensor operators. Each term of the Hamiltonian expansion can be thus cast in the tensor form whatever the order of the development. This allows to take full advantage of the symmetry properties for doubly and triply degenerate vibrations and vibration-rotation states. We apply this model to variational computations of energy levels for (12)CH(4), (13)CH(4), and (12)CD(4).

First theoretical global line lists of ethylene (12C2H4) spectra for the temperature range 50−700 K in the far-infrared for quantification of absorption and emission in planetary atmospheres

“…Ab initio studies of small polyatomic molecules emerged in the past decades with drastically improved computational methods and hardware resources. A breakthrough in predicting rotationally resolved spectra of small molecules was made possible by accurate electronic structure calculations of the molecular PESs and DMSs (see, e.g., Partridge & Schwenke 1997;Cours et al 2002;Yurchenko et al 2009;Nikitin et al 2009;Lodi et al 2011;Császár et al 2010;Szalay et al 2011;Huang et al 2011aHuang et al , 2012Sousa-Silva et al 2014;Nikitin et al 2014;Li et al 2014;Delahaye et al 2015) and by developing efficient methods for quantum nuclear motion calculations (see Schwenke & Partridge 2001;Schwenke 2002;Cassam-Chenaï et al 2012;Yurchenko et al 2007;Wang & Carrington Jr. 2013a,b;Carter et al 2009;Rey et al 2012;Bowman et al 2005). In case of triatomics, such as water isotopic species (Yurchenko et al 2009;Barber et al 2011), carbon dioxide (Huang et al 2013(Huang et al , 2014, and ozone accurate theoretical predictions led to significant extensions of spectral analyses toward higher energy ranges.…”

“…In this work, we applied vibrational normal modes and an Eckart frame representation (Watson 1968) for the nuclear motion, a basis set of wavefunctions and dipole moment expansion, the formalism of which is described in Rey et al (2010Rey et al ( , 2012. To minimize the cost of computations and loss of precision in full-dimensional variational calculations, we implemented truncation-compression techniques as described in our previous works for methane isotopologs and ethylene (see Rey et al 2013aRey et al ,b, 2014aDelahaye et al 2014).…”

Perspective: Computing (ro-)vibrational spectra of molecules with more than four atoms

“…87 SF/D/P ideas have also been extensively applied to methane. 88,89 Rey, Nikitin, and Tyuterev use the Watson normal-coordinate KEO and a SOP approximation to the methane PES. To obtain a SOP KEO, they expand the elements of the inverse of the effective moment of inertia matrix.…”

“…The basis functions are products of vibrational wavefunctions (which are contracted basis functions) and Wigner functions. 2,65,88,89,91 All SF/D calculations are limited by the size of the Hamiltonian matrix. Using commonly accessible computers it is not possible to use a direct diagonalization algorithm for matrices whose size is larger than 100'000.…”

An improved third order dipole moment surface for methane

“…Eigenstates converged to within the cm −1 accuracy (or better), up to, say, the tetradecad for a given PES have been obtained by means of various forms of configuration interactions (CI) [30][31][32][33][34] (earlier references can be found therein). We have used the vibrational mean field configuration interaction (VMFCI) method [35][36][37][38][39] to solve methane vibrational, stationary Schrödinger equation.…”