Derivation of ρ-dependent coordinate transformations for nonrigid molecules in the Hougen–Bunker–Johns formalism

Abstract

In this paper, we report a series of transformations for the construction of a Hamiltonian model for nonrigid polyatomic molecules in the framework of the Hougen-Bunker-Johns formalism (HBJ). This model is expressed in normal mode coordinates for small vibrations and in a specific coordinate ρ to describe the large amplitude motion. For the first time, a general procedure linking the "true" curvilinear coordinates to ρ is proposed, allowing to express the potential energy part in the same coordinate representation as the kinetic energy operator, whatever the number of atoms. A Lie group-based method is also proposed for the derivation of the reference configuration in the internal axis system. This work opens new perspectives for future high-resolution spectroscopic studies of nonrigid, medium-sized molecules using HBJ-type Hamiltonians. Illustrative examples and computation of vibrational energy levels on semirigid and nonrigid molecules are given to validate this method.

New Ab Initio Potential Energy Surfaces for NH3 Constructed from Explicitly Correlated Coupled-Cluster Methods

“…For this work, a hybrid model was implemented in our homemade computer code TENSOR, which consists of Taylor-expanding the kinetic energy and potential parts in terms of normal mode coordinates associated with the ν 1 , ν 3 , and ν 4 modes for each point of a numerical grid describing the nonrigid coordinate ρ. 12 Here, an 11th-order Hamiltonian composed of 8648 D 3h irreducible tensor operators was built on a grid of ρ ϵ [0.5, 2.7] rad by a step of 0.02. To properly converge the vibrational energy levels (with errors <0.01 cm −1 ) in the range of observed values, 6945, 5985, and 12 915 basis functions have been used in the variational calculation for the symmetry blocks (A 1 ′, A 2 ″), (A 2 ′, A 1 ″), and (E′, E″), respectively.…”

“…The Hamiltonian model was built using the Hougen–Bunker–Johns formalism, where the relation between the curvilinear ρ̅ and effective coordinates ρ was explicitly established in ref . For this work, a hybrid model was implemented in our homemade computer code TENSOR, which consists of Taylor-expanding the kinetic energy and potential parts in terms of normal mode coordinates associated with the ν 1 , ν 3 , and ν 4 modes for each point of a numerical grid describing the nonrigid coordinate ρ . Here, an 11th-order Hamiltonian composed of 8648 D 3 h irreducible tensor operators was built on a grid of ρ ϵ [0.5, 2.7] rad by a step of 0.02.…”

“…Concerning the nuclear motion calculations, our variational computer code TENSOR [9][10][11] has been adapted to molecules exhibiting one large amplitude motion. 12 This code was initially designed to the treatment of rigid molecules which was applied with success to the construction of accurate spectroscopic line lists (see e.g. CH4, [13][14][15] CF4, 16 PH3, 17 NF3, 18 C2H4, 19 and SF6 20 ).…”

New Theoretical Infrared Line List for the Methyl Radical with Accurate Vibrational Band Origins from High-Level Ab Initio Calculations

“…Indeed, the sign of the z component of the dipole between 0 and 90° and between 180 and 90° is different whereas it is the same for the PES (see Figure ). Consequently, a sine function will be used for the PES (here ρ e ≡ ρ̅ e , see ref ), and a cosine function will be used for the DMS, where ρ̅ can be related to the three in-plane bending angles as follows …”

“…The ab initio calculations reported in this work were performed by using the MOLPRO, , MRCC, , and CFOUR , packages while the nuclear motion calculations were carried out using our homemade variational computer code TENSOR − applied with success in refs – for computing accurate spectroscopic line lists of semirigid molecules. As in ref , a hybrid nonrigid Hamiltonian model was built in this work using the Hougen–Bunker–Johns formalism, where the relation between the curvilinear ρ̅ and effective coordinates ρ was explicitly established in ref .…”