A flexible approach to vibrational perturbation theory using sparse matrix methods

Abstract

A sparse linear algebra based implementation of Rayleigh–Schrödinger vibrational perturbation theory is presented. This implementation allows for flexibility in the coordinates used to expand the vibrational Hamiltonian as well as the order to which the perturbation theory is performed. It also provides a powerful tool for investigating the origin of spectral intensity and transition frequencies. Specifically, this flexibility allows for the analysis of which terms in the expansions of the Hamiltonian and dipole surface lead to the largest corrections to the energies and transition intensities, and how these conclusions depend on the coordinates used for these expansions. Comparisons of corrections to transition frequencies are reported for the Morse oscillator when the potential is expanded in Δr and Morse coordinates as well as for water, water dimer, and peroxynitrous acid when the molecular Hamiltonians and dipole surfaces are expanded in Cartesian displacement coordinates and in the displacements of the bond-angle-dihedral internal coordinates. Further comparisons of the corrections to the transitions moments are made for H2O and (H2O)2. It is found that while the transition frequencies and intensities are independent of coordinate choice, a good choice of coordinates leads to a cleaner interpretation of the origins of the anharmonicities in these systems.

Exploring Expansions of the Potential and Dipole Surfaces Used for Vibrational Perturbation Theory

“…All of the calculations in this study were performed using the PyVibPT n program package , developed in our group, and in all cases the VPT calculations will be performed in the normal mode coordinates that are constructed as linear combinations of the displacements of internal coordinates. We use the deperturb and diagonalize approach to handle resonances (sometimes referred to as generalized VPT or GVPT). ,,, In our implementation of this approach, states are considered to be in resonance with the state of interest if the contribution to the perturbative expansion to the wave function exceeds 0.3 .…”

Preparation and Characterization of the Halogen-Bonding Motif in the Isolated Cl–·IOH Complex with Cryogenic Ion Vibrational Spectroscopy

“…In this study, we isolate the X-bonded Cl − • IOH binary complex and characterize the XB interaction using cryogenic ion vibrational spectroscopy, electronic structure calculations performed at the MP2/aug-cc-pVTZ level (with the corresponding aug-cc-pVTZ-pp basis set and effective core potential for I), 26,27 and anharmonic analysis of the vibrational level structure using an implementation of vibrational perturbation theory developed in one of our groups. 28,29 The [IHOCl] − binary complexes were prepared by reaction between gaseous HOCl and I − •(H 2 O) n cluster ions in the first quadrupole guide of the Yale cryogenic photofragmentation mass spectrometer as described in the Supporting Information. The dominant observed species correspond to the uptake of HOCl onto the parent I − (H 2 O) n clusters to yield clusters with stoichiometry [IHOCl] − •(H 2 O) n .…”

“…acknowledges support from the Chemistry Division of the National Science Foundation (CHE-1856125 for scientific work and OAC-1663636 for perturbation theory code development). Parts of this work were performed by using the Ilahie cluster at the University of Experimental (exp., Accurate to within ±4 cm −1 ) and Calculated (calc., MP2/aug-cc-pVTZ with Anharmonic Corrections)28 Frequencies (in Bold) and Calculated Structural Parameters for Neutral HOX (X = Cl, I) and the [IHOCl] − Complexes Reported in This Study, Where R is the Bond Length (Å) and ∠ is the Bond Angle (deg)…”

“…Calculated partial charges (Table S1) demonstrate that the negative charge on I – significantly increases from −0.48 e in I – ·ClOH to −0.84 e in the more stable I – ·HOCl (HB) form, which may also contribute to the larger binding energy of the latter. In this study, we isolate the X-bonded Cl – ·IOH binary complex and characterize the XB interaction using cryogenic ion vibrational spectroscopy, electronic structure calculations performed at the MP2/aug-cc-pVTZ level (with the corresponding aug-cc-pVTZ-pp basis set and effective core potential for I), , and anharmonic analysis of the vibrational level structure using an implementation of vibrational perturbation theory developed in one of our groups. , …”

“…The second pattern (c) consists of only a single feature at 3641 cm –1 , which is the expected behavior of either the X-bonded Cl – ·IOH or I – ·ClOH isomers. Stick spectra calculated at the MP2/aug-cc-pVTZ level of theory/basis with anharmonic corrections based on VPT2 calculations are presented above each experimental spectrum in (b) and (c) with minimum-energy structures inset. The literature values of the free OH stretching mode for neutral HOCl (ref , v OH f HOCl ) and HOI (ref , v OH f HOI ) are indicated by the black arrows in (a).…”