Adiabatic approximation and nonadiabatic corrections in the discrete variable representation

Highly excited vibrational states of triatomic molecules

J. C. Light, Zlatko Bacic

Research output: Contribution to journalArticle

Abstract

An adiabatic approximation for the calculation of excited vibrational (J = 0) levels of triatomic molecules is developed using the discrete variable representation (DVR). The DVR is in the large amplitude bending motion coordinate which is taken to be the adiabatic degree of freedom. We show that the adiabatic treatment in the DVR has some major advantages over the usual formulation in the finite basis representation (FBR), namely improved accuracy and broader range of applicability. An adiabatic rearrangement of the full Hamiltonian matrix in the DVR-ray eigenvector (REV) basis is defined, such that the diagonal blocks provide the rigorous matrix representation of the adiabatic bend Hamiltonian; their diagonalization yields bending level progressions corresponding to various stretching states. The off-diagonal blocks contain all nonadiabatic coupling matrix elements. The nonadiabatic corrections to the adiabatic vibrational levels are readily taken into account via second-order perturbation theory. One unique feature of our approach is that, in contrast to the FBR formulation, evaluation of the adiabatic and nonadiabatic matrix elements does not require evaluation of derivatives of the stretching wave functions with respect to the adiabatic variable. This approach is tested on the two-mode LiCN/LiNC (fixed CN distance) and the three-mode HCN/HNC. The adiabatic vibrational levels are in good agreement with accurate variational results. When corrected by second-order perturbative treatment, many levels are given very accurately (to within 0.1%) even for energies above the isomerization barriers. More localized states are better represented in the adiabatic approximation then delocalized vibrational states.

Original languageEnglish (US)
Pages (from-to)4008-4019
Number of pages12
JournalThe Journal of chemical physics
Volume87
Issue number7
StatePublished - 1987

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triatomic molecules
vibrational states
Hamiltonians
Molecules
approximation
Stretching
Wave functions
Isomerization
Eigenvalues and eigenfunctions
matrices
formulations
Derivatives
evaluation
progressions
isomerization
rays
eigenvectors
perturbation theory
degrees of freedom
wave functions

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

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title = "Adiabatic approximation and nonadiabatic corrections in the discrete variable representation: Highly excited vibrational states of triatomic molecules",
abstract = "An adiabatic approximation for the calculation of excited vibrational (J = 0) levels of triatomic molecules is developed using the discrete variable representation (DVR). The DVR is in the large amplitude bending motion coordinate which is taken to be the adiabatic degree of freedom. We show that the adiabatic treatment in the DVR has some major advantages over the usual formulation in the finite basis representation (FBR), namely improved accuracy and broader range of applicability. An adiabatic rearrangement of the full Hamiltonian matrix in the DVR-ray eigenvector (REV) basis is defined, such that the diagonal blocks provide the rigorous matrix representation of the adiabatic bend Hamiltonian; their diagonalization yields bending level progressions corresponding to various stretching states. The off-diagonal blocks contain all nonadiabatic coupling matrix elements. The nonadiabatic corrections to the adiabatic vibrational levels are readily taken into account via second-order perturbation theory. One unique feature of our approach is that, in contrast to the FBR formulation, evaluation of the adiabatic and nonadiabatic matrix elements does not require evaluation of derivatives of the stretching wave functions with respect to the adiabatic variable. This approach is tested on the two-mode LiCN/LiNC (fixed CN distance) and the three-mode HCN/HNC. The adiabatic vibrational levels are in good agreement with accurate variational results. When corrected by second-order perturbative treatment, many levels are given very accurately (to within 0.1{\%}) even for energies above the isomerization barriers. More localized states are better represented in the adiabatic approximation then delocalized vibrational states.",
author = "Light, {J. C.} and Zlatko Bacic",
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T1 - Adiabatic approximation and nonadiabatic corrections in the discrete variable representation

T2 - Highly excited vibrational states of triatomic molecules

AU - Light, J. C.

AU - Bacic, Zlatko

PY - 1987

Y1 - 1987

N2 - An adiabatic approximation for the calculation of excited vibrational (J = 0) levels of triatomic molecules is developed using the discrete variable representation (DVR). The DVR is in the large amplitude bending motion coordinate which is taken to be the adiabatic degree of freedom. We show that the adiabatic treatment in the DVR has some major advantages over the usual formulation in the finite basis representation (FBR), namely improved accuracy and broader range of applicability. An adiabatic rearrangement of the full Hamiltonian matrix in the DVR-ray eigenvector (REV) basis is defined, such that the diagonal blocks provide the rigorous matrix representation of the adiabatic bend Hamiltonian; their diagonalization yields bending level progressions corresponding to various stretching states. The off-diagonal blocks contain all nonadiabatic coupling matrix elements. The nonadiabatic corrections to the adiabatic vibrational levels are readily taken into account via second-order perturbation theory. One unique feature of our approach is that, in contrast to the FBR formulation, evaluation of the adiabatic and nonadiabatic matrix elements does not require evaluation of derivatives of the stretching wave functions with respect to the adiabatic variable. This approach is tested on the two-mode LiCN/LiNC (fixed CN distance) and the three-mode HCN/HNC. The adiabatic vibrational levels are in good agreement with accurate variational results. When corrected by second-order perturbative treatment, many levels are given very accurately (to within 0.1%) even for energies above the isomerization barriers. More localized states are better represented in the adiabatic approximation then delocalized vibrational states.

AB - An adiabatic approximation for the calculation of excited vibrational (J = 0) levels of triatomic molecules is developed using the discrete variable representation (DVR). The DVR is in the large amplitude bending motion coordinate which is taken to be the adiabatic degree of freedom. We show that the adiabatic treatment in the DVR has some major advantages over the usual formulation in the finite basis representation (FBR), namely improved accuracy and broader range of applicability. An adiabatic rearrangement of the full Hamiltonian matrix in the DVR-ray eigenvector (REV) basis is defined, such that the diagonal blocks provide the rigorous matrix representation of the adiabatic bend Hamiltonian; their diagonalization yields bending level progressions corresponding to various stretching states. The off-diagonal blocks contain all nonadiabatic coupling matrix elements. The nonadiabatic corrections to the adiabatic vibrational levels are readily taken into account via second-order perturbation theory. One unique feature of our approach is that, in contrast to the FBR formulation, evaluation of the adiabatic and nonadiabatic matrix elements does not require evaluation of derivatives of the stretching wave functions with respect to the adiabatic variable. This approach is tested on the two-mode LiCN/LiNC (fixed CN distance) and the three-mode HCN/HNC. The adiabatic vibrational levels are in good agreement with accurate variational results. When corrected by second-order perturbative treatment, many levels are given very accurately (to within 0.1%) even for energies above the isomerization barriers. More localized states are better represented in the adiabatic approximation then delocalized vibrational states.

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