Beyond Born-Oppenheimer

INTRODUCING A POWERFUL APPROACH TO DEVELOPING RELIABLE QUANTUM
MECHANICAL TREATMENTS OF A LARGE VARIETY OF PROCESSES IN MOLECULAR
SYSTEMS.

The Born-Oppenheimer approximation has been fundamental to
calculation in molecular spectroscopy and molecular dynamics since
the early days of quantum mechanics. This is despite
well-established fact that it is often not valid due to conical
intersections that give rise to strong nonadiabatic effects caused
by singular nonadiabatic coupling terms (NACTs). In Beyond
Born-Oppenheimer, Michael Baer, a leading authority on molecular
scattering theory and electronic nonadiabatic processes, addresses
this deficiency and introduces a rigorous
approach--diabatization--for eliminating troublesome NACTs and
deriving well-converged equations to treat the interactions within
and between molecules.

Concentrating on both the practical and theoretical aspects of
electronic nonadiabatic transitions in molecules, Professor Baer
uses a simple mathematical language to rigorously eliminate the
singular NACTs and enable reliable calculations of spectroscopic
and dynamical cross sections. He presents models of varying
complexity to illustrate the validity of the theory and explores
the significance of the study of NACTs and the relationship between
molecular physics and other fields in physics, particularly
electrodynamics.

The first book of its king Beyond Born-Oppenheimer:

• Presents a detailed mathematical framework to treat electronic
  NACTs and their conical intersections

• Describes the Born-Oppenheimer treatment, including the concepts
  of adiabatic and diabatic frameworks

• Introduces a field-theoretical approach to calculating NACTs,
  which offers an alternative to time-consuming ab initio
  procedures

• Discusses various approximations for treating a large system of
  diabatic Schrödinger equations

• Presents numerous exercises with solutions to further clarify the
  material being discussed

Beyond Born-Oppenheimer is required reading for physicists,
physical chemists, and all researchers involved in the quantum
mechanical study of molecular systems.

Auteur
Michael Baer is one of the foremost authorities on molecular scattering theory. He wrote the seminal paper in the field of electronic nonadiabatic molecular collisions in 1975 and has continued to make fundamental contributions to electronic nonadiabatic processes in molecular systems. He also contributed significantly to developing numerical methods to treat, quantum mechanically, reactive-exchange processes and is a co-author of the negative imaginary potential approach to decoupling the dynamics in different arrangement channels, which is now used worldwide. Dr. Baer, who received his M.Sc. and Ph.D from the Hebrew University of Jerusalem, is currently associated with the Fritz Haber Center for Molecular Dynamics at the Hebrew University in Jerusalem. Before that he was a theoretical physicist and an applied mathematician for almost 40 years at the Soreq Nuclear Research Center, Israel. The author was a visiting scientist in many foreign universities and scientific institutes, among them Harvard University and the University of Oxford. He has published more than 300 scientific articles and edited several books. In 1993 he was awarded the (Senior) Meitner-Humboldt Prize in Germany for Theoretical Chemistry and in 2003 he was nominated as a Szent-Györgyi professor for physics by the National Academy of Sciences in Hungary.

Résumé
INTRODUCING A POWERFUL APPROACH TO DEVELOPING RELIABLE QUANTUM MECHANICAL TREATMENTS OF A LARGE VARIETY OF PROCESSES IN MOLECULAR SYSTEMS.

The Born-Oppenheimer approximation has been fundamental to calculation in molecular spectroscopy and molecular dynamics since the early days of quantum mechanics. This is despite well-established fact that it is often not valid due to conical intersections that give rise to strong nonadiabatic effects caused by singular nonadiabatic coupling terms (NACTs). In Beyond Born-Oppenheimer, Michael Baer, a leading authority on molecular scattering theory and electronic nonadiabatic processes, addresses this deficiency and introduces a rigorous approach--diabatization--for eliminating troublesome NACTs and deriving well-converged equations to treat the interactions within and between molecules.

Concentrating on both the practical and theoretical aspects of electronic nonadiabatic transitions in molecules, Professor Baer uses a simple mathematical language to rigorously eliminate the singular NACTs and enable reliable calculations of spectroscopic and dynamical cross sections. He presents models of varying complexity to illustrate the validity of the theory and explores the significance of the study of NACTs and the relationship between molecular physics and other fields in physics, particularly electrodynamics.

The first book of its king Beyond Born-Oppenheimer:

• Presents a detailed mathematical framework to treat electronic NACTs and their conical intersections
• Describes the Born-Oppenheimer treatment, including the concepts of adiabatic and diabatic frameworks
• Introduces a field-theoretical approach to calculating NACTs, which offers an alternative to time-consuming ab initio procedures
• Discusses various approximations for treating a large system of diabatic Schrödinger equations

• Presents numerous exercises with solutions to further clarify the material being discussed

  Beyond Born-Oppenheimer is required reading for physicists, physical chemists, and all researchers involved in the quantum mechanical study of molecular systems.

Contenu
Preface. Abbreviations.

1. Mathematical Introduction.

I.A. The Hilbert Space.

I.A.1. The Eigenfunction and the Electronic non-Adiabatic Coupling Term.

I.A.2. The Abelian and the non-Abelian Curl Equation.

I.A.3. The Abelian and the non-Abelian Div-Equation.

I.B. The Hilbert Subspace.

I.C. The Vectorial First Order Differential Equation and the Line Integral.

I.C.1. The Vectorial First Order Differential Equation.

I.C.1.1. The Study of the Abelian Case.

I.C.1.2. The Study of the non-Abelian Case.

I.C.1.3. The Orthogonality.

I.C.2. The Integral Equation.

I.C.2.1. The Integral Equation along an Open Contour.

I.C.2.2. The Integral Equation along an Closed Contour.

I.C.3. Solution of the Differential Vector Equation.

I.D. Summary and Conclusions.

I.E. Exercises.

I.F. References.

2. Born-Oppenheimer Approach: Diabatization and Topological Matrix.

II.A. The Time Independent Treatment for Real Eigenfunctions.

II.A.1. The Adiabatic Representation.

II.A.2. The Diabatic Representation.

II.A.3. The Adiabatic-to-Diabatic Transformation.

II.A.3.1. The Transformation for the Electronic Basis Set.

II.A.3.2. The Transformation for the Nuclear Wave-Functions.

II.A.3.3. Implications due to the Adiabatic-to-Diabatic Transformation.

II.A.3.4. Final Comments.

II.B. Application of Complex Eigenfunctions.

II.B.1. Introducing Time-Independent Phase Factors.

II.B.1.1. The Adiabatic Schrödinger Equation.

II.B.1.2. The Adiabatic-to-Diabatic Transformation.

II.B.2. Introducing Time-Dependent Phase Factors.

II.C. The Time Dependent Treatment.

II.C.1. The Time-Dependent Perturbative Approach.

II.C.2. The Time-Dependent non-Perturbative Approach.

II.C.2.1. The Adiabatic Time Dependent Electronic Basis set.

II.C.2.2. The Adiabatic Time-Dependent Nuclear Schrödinger Equation.

II.C.2.3. The Time Dependent Adiabatic-to-Diabatic Transformation.

II.C.3. Summary.

II.D. Appendices.

II.D.1. The Dressed Non-Adiabatic Coupling Matrix.

II.D.2. Analyticity of the Adiabatic-to-Diabatic Transformation matrix, Ã, in Space-Time Configuration.

II.E. References.

**3. Model Studie…