Rotating full- and reduced-dimensional quantum chemical models of molecules

Abstract

A flexible protocol, applicable to semirigid as well as floppy polyatomic systems, is developed for the variational solution of the rotational-vibrational Schrödinger equation. The kinetic energy operator is expressed in terms of curvilinear coordinates, describing the internal motion, and rotational coordinates, characterizing the orientation of the frame fixed to the nonrigid body. Although the analytic form of the kinetic energy operator might be very complex, it does not need to be known a priori within this scheme as it is constructed automatically and numerically whenever needed. The internal coordinates can be chosen to best represent the system of interest and the body-fixed frame is not restricted to an embedding defined with respect to a single reference geometry. The features of the technique mentioned make it especially well suited to treat large-amplitude nuclear motions. Reduced-dimensional rovibrational models can be defined straightforwardly by introducing constraints on the generalized coordinates. In order to demonstrate the flexibility of the protocol and the associated computer code, the inversion-tunneling of the ammonia ((14)NH(3)) molecule is studied using one, two, three, four, and six active vibrational degrees of freedom, within both vibrational and rovibrational variational computations. For example, the one-dimensional inversion-tunneling model of ammonia is considered also for nonzero rotational angular momenta. It turns out to be difficult to significantly improve upon this simple model. Rotational-vibrational energy levels are presented for rotational angular momentum quantum numbers J = 0, 1, 2, 3, and 4.

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].…”

Modelling rotations, vibrations, and rovibrational couplings in astructural molecules – a case study based on the H+5 molecular ion

“…The vibrational and rovibrational levels of H + 5 have been computed both by variational nuclear motion [29,30,32,33] and diffusion Monte Carlo (DMC) [31,34,35] techniques. The full-and reduced-dimensional variational computations performed by three of the present authors [18] utilised the GENIUSH algorithm and code [36][37][38].…”

Modelling non-adiabatic effects in ${\rm H}_3^+$H3+: Solution of the rovibrational Schrödinger equation with motion-dependent masses and mass surfaces

“…dq D . 27,28 [Ĵ a ,Ĵ b ] + is the anticommutator ofĴ a andĴ b . If an N-particle system is treated in full vibrational dimensionality, then D = 3N − 6.…”

“…In GENIUSH, this general formulation is implemented in a quasi-variational procedure using discrete variable representation (DVR) for the internal degrees of freedom, Wang functions for the rotational part, a numerical construction for the kinetic energy terms over the DVR grid, and a Lanczos iterative eigensolver for the solution of the vibrational 27 and rovibrational 28 Schrödinger equation of the atomic nuclei.…”

“…The answer we provide is based on the extension of the fourth-age 26 quantum chemical code GENIUSH. 27,28 The GENIUSH protocol is based on a numerical construction of the kinetic energy operator and its matrix representation for the (quasi-)variational solution of the Schrödinger equation. This fully numerical approach allows us to solve the rovibrational Schrödinger equation using arbitrary internal coordinates, arbitrary embeddings, and arbitrary choices of reduced-and full-dimensional models of molecules.…”