Born–Oppenheimer Approximation

2019 ◽  
Author(s):  
Marek S. Wartak ◽  
Ching-Yao Fong
Keyword(s):  
Oppenheimer Approximation

Introduction

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Degrees Of Freedom ◽  
State Level ◽  
Boltzmann Distribution ◽  
Theoretical Description ◽  
Time Dependent ◽  
Nuclear Dynamics ◽  
Molecular Reaction ◽  
Oppenheimer Approximation

This introductory chapter considers first the relation between molecular reaction dynamics and the major branches of physical chemistry. The concept of elementary chemical reactions at the quantized state-to-state level is discussed. The theoretical description of these reactions based on the time-dependent Schrödinger equation and the Born–Oppenheimer approximation is introduced and the resulting time-dependent Schrödinger equation describing the nuclear dynamics is discussed. The chapter concludes with a brief discussion of matter at thermal equilibrium, focusing at the Boltzmann distribution. Thus, the Boltzmann distribution for vibrational, rotational, and translational degrees of freedom is discussed and illustrated.

scholarly journals Full-dimensional quantum stereodynamics of the non-adiabatic quenching of OH(A2Σ+) by H2

2021 ◽  
Author(s):  
Bin Zhao ◽  
Shanyu Han ◽  
Christopher L. Malbon ◽  
Uwe Manthe ◽  
David. R. Yarkony ◽  
...  
Keyword(s):  
Quantum Dynamics ◽  
Previous Analysis ◽  
Branching Ratio ◽  
Energy Matrix ◽  
Elastic Channel ◽  
Electronically Excited ◽  
Oppenheimer Approximation ◽  
Electronic Motion ◽  
Adiabatic Dynamics ◽  
Good Agreement

AbstractThe Born–Oppenheimer approximation, assuming separable nuclear and electronic motion, is widely adopted for characterizing chemical reactions in a single electronic state. However, the breakdown of the Born–Oppenheimer approximation is omnipresent in chemistry, and a detailed understanding of the non-adiabatic dynamics is still incomplete. Here we investigate the non-adiabatic quenching of electronically excited OH(A2Σ+) molecules by H2 molecules using full-dimensional quantum dynamics calculations for zero total nuclear angular momentum using a high-quality diabatic-potential-energy matrix. Good agreement with experimental observations is found for the OH(X2Π) ro-vibrational distribution, and the non-adiabatic dynamics are shown to be controlled by stereodynamics, namely the relative orientation of the two reactants. The uncovering of a major (in)elastic channel, neglected in a previous analysis but confirmed by a recent experiment, resolves a long-standing experiment–theory disagreement concerning the branching ratio of the two electronic quenching channels.

High-Fidelity First Principles Nonadiabaticity: Diabatization, Analytic Representation of Global Diabatic Potential Energy Matrices, and Quantum Dynamics

2021 ◽  
Author(s):  
Yafu Guan ◽  
Changjian Xie ◽  
David R. Yarkony ◽  
Hua Guo
Keyword(s):  
Potential Energy ◽  
Excited States ◽  
First Principles ◽  
Quantum Dynamics ◽  
Chemical Processes ◽  
High Fidelity ◽  
Nonadiabatic Dynamics ◽  
Electronically Excited States ◽  
Electronically Excited ◽  
Oppenheimer Approximation

Nonadiabatic dynamics, which goes beyond the Born-Oppenheimer approximation, has increasingly been shown to play an important role in chemical processes, particularly those involving electronically excited states. Understanding multistate dynamics requires...

scholarly journals An Investigation into the Approximations Used in Wave Packet Molecular Dynamics for the Study of Warm Dense Matter

Plasma ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 294-308
Author(s):  
William A. Angermeier ◽  
Thomas G. White
Keyword(s):  
Molecular Dynamics ◽  
Wave Packet ◽  
Hydrogen Plasma ◽  
Valence Bond ◽  
Dense Matter ◽  
Basis Set ◽  
Warm Dense Matter ◽  
Scaling Parameters ◽  
Oppenheimer Approximation ◽  
Semi Empirical

Wave packet molecular dynamics (WPMD) has recently received a lot of attention as a computationally fast tool with which to study dynamical processes in warm dense matter beyond the Born–Oppenheimer approximation. These techniques, typically, employ many approximations to achieve computational efficiency while implementing semi-empirical scaling parameters to retain accuracy. We investigated three of the main approximations ubiquitous to WPMD: a restricted basis set, approximations to exchange, and the lack of correlation. We examined each of these approximations in regard to atomic and molecular hydrogen in addition to a dense hydrogen plasma. We found that the biggest improvement to WPMD comes from combining a two-Gaussian basis with a semi-empirical correction based on the valence-bond wave function. A single parameter scales this correction to match experimental pressures of dense hydrogen. Ultimately, we found that semi-empirical scaling parameters are necessary to correct for the main approximations in WPMD. However, reducing the scaling parameters for more ab-initio terms gives more accurate results and displays the underlying physics more readily.

Adiabatische Korrektur der Born-Oppenheimer-Näherung beim GeS und GeSe / Adiabatic Correction of the Born-Oppenheimer Approximation for GeS and GeSe

1976 ◽  
Vol 31 (3-4) ◽  
pp. 374-380 ◽  
Author(s):  
W. U. Stieda ◽  
E. Tiemann ◽  
T. Törring ◽  
J. Hoeft
Keyword(s):  
Dipole Moment ◽  
High Precision ◽  
Electric Dipole Moment ◽  
Electric Dipole ◽  
Rotational Constant ◽  
Frequency Range ◽  
Rotational Spectra ◽  
Oppenheimer Approximation

Abstract The rotational spectra of GeS and GeSe were measured in the frequency range of 66 GHz to 110 GHz with high precision. The breakdown of the Born-Oppenheimer approximation was observed for the rotational constant yol. With the known molecular 37-factor and the electric dipole moment the adiabatic part of the Born-Oppenheimer correction can be extracted from the primary observa-tion on y01. The adiabatic correction is very similar in both molecules but differs from the results in the earlier measurements on PbS.

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