High-order contact transformations of molecular Hamiltonians: general approach, fast computational algorithm and convergence of ro-vibrational polyad models

Abstract

The paper describes methods and fast computational algorithm for building effective Hamiltonians in molecular physics using perturbative approach. Various techniques of separation of fast and slow variables are considered in the general mathematical framework of contact transformations. The particular focus is on a systematic derivation of effective models for vibration-rotation spectroscopy from ab initio based potential energy surfaces with an exhaustive review of the previous studies in this field. We consider applications to various types of polyads coupled by Fermi, Coriolis, Darling-Dennison and other types of resonance interactions with the examples for asymmetric top, symmetric top and spherical top molecules. A flexible choce of the modelling operator accounts for strong coupling of various types of nuclear motion in molecules among closely lying levels including vibrational resonance schemes (2:1:2) , (2:1:2:1), (4:2:6:3), (3:2:1:2:1:1) etc that occur for C2v, C3v, and Td molecules and their isotopic species. The method is implemented in the MOL_CT program suite that offers a complementary tool to variational methods in terms of convergence and computational time. This permits an inclusion of a priori information to obtain physically meaningful values for the the resonance coupling terms in order to developing mixed "ab initio/effective" models with smaller number of adjustable parameters for analyses of molecular spectra.

Rotational Spectroscopy of 1-Cyano-2-methylenecyclopropane (C5H5N)─A Newly Synthesized Pyridine Isomer

“…This study provides spectroscopic constants for two fundamental vibrational states that can be used as benchmarks for the future development of computational methods. Despite some recent advances, − very few studies have included computational prediction of the centrifugal distortion of vibrationally excited states. In addition, we unintentionally provided a benchmark for the existing computational software.…”

Unrivaled accuracy in measuring rotational transitions of greenhouse gases: THz CRDS of CF4

“…In eqn (9), the last block H R includes all the “remaining” polyads beyond P N P . Unlike contact transformations 30 based on perturbation theory, 31 the approach proposed in ref. 19 obviates the need to make tedious algebraic calculations for the derivation of both Hamiltonian and dipole moment effective parameters.…”

“…Here, a similar experimental setup described previously 7 is used, a cavity ring-down spectroscopy (CRDS) configuration has enabled the direct measurement of the absorption coefficient. 8 R (19) to R (30) and Q (32) to Q(34) line clusters are measured both in frequency and intensity with unequalled precision. CRDS THz line frequencies and intensities are included in a global fit of the n 2 polyad (see Section 5.1) allowing an improvement of the RMS deviation and an accurate determination of the m 3,3 dipole moment parameter specific to the n 3 À n 3 CF 4 transitions.…”

From the Automated Calculation of Potential Energy Surfaces to Accurate Infrared Spectra

“…Besides this, very many vibrational states need to be considered for the simulation of a rovibrational spectrum, which leads to polyad schemes or screening approaches. However, in the recent past some progress has been made in the direction of calculating rovibrational spectra of molecules with more than 4 or 5 atoms, which at least allows for a qualitative comparison. , …”

“…However, in the recent past some progress has been made in the direction of calculating rovibrational spectra of molecules with more than 4 or 5 atoms, which at least allows for a qualitative comparison. 76,77 This shall be exemplified by RVCI calculations for formamide, 78 a molecule that can hardly be described by VPT2 calculations (cf. Table 1).…”