On the Born–Oppenheimer approximation of diatomic wave operators. II. Singular potentials

1997 ◽  
Vol 38 (3) ◽  
pp. 1373-1396 ◽  
Author(s):  
Markus Klein ◽  
André Martinez ◽  
Xue Ping Wang
Keyword(s):  
Singular Potentials ◽  
Wave Operators ◽  
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 Approximating pointwise products of quasimodes

2020 ◽  
Vol 32 (3) ◽  
pp. 541-552
Author(s):  
Mei Ling Jin
Keyword(s):  
Vector Space ◽  
Harmonic Analysis ◽  
Riemannian Manifolds ◽  
Spectral Projection ◽  
Beltrami Operator ◽  
Singular Potentials ◽  
Link Type ◽  
Right Hand ◽  
Low Degree ◽  
The Right

AbstractWe obtain approximation bounds for products of quasimodes for the Laplace–Beltrami operator on compact Riemannian manifolds of all dimensions without boundary. We approximate the products of quasimodes uv by a low-degree vector space {B_{n}}, and we prove that the size of the space {\dim(B_{n})} is small. In this paper, we first study bilinear quasimode estimates of all dimensions {d=2,3}, {d=4,5} and {d\geq 6}, respectively, to make the highest frequency disappear from the right-hand side. Furthermore, the result of the case {\lambda=\mu} of bilinear quasimode estimates improves {L^{4}} quasimodes estimates of Sogge and Zelditch in [C. D. Sogge and S. Zelditch, A note on L^{p}-norms of quasi-modes, Some Topics in Harmonic Analysis and Applications, Adv. Lect. Math. (ALM) 34, International Press, Somerville 2016, 385–397] when {d\geq 8}. And on this basis, we give approximation bounds in {H^{-1}}-norm. We also prove approximation bounds for the products of quasimodes in {L^{2}}-norm using the results of {L^{p}}-estimates for quasimodes in [M. Blair, Y. Sire and C. D. Sogge, Quasimode, eigenfunction and spectral projection bounds for Schrodinger operators on manifolds with critically singular potentials, preprint 2019, https://arxiv.org/abs/1904.09665]. We extend the results of Lu and Steinerberger in [J. F. Lu and S. Steinerberger, On pointwise products of elliptic eigenfunctions, preprint 2018, https://arxiv.org/abs/1810.01024v2] to quasimodes.

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