LEADER 04748nam 2200637 a 450 001 9910143416003321 005 20190822110616.0 010 $a1-280-41143-0 010 $a9786610411436 010 $a0-470-32705-7 010 $a0-471-78008-1 010 $a0-471-78007-3 035 $a(CKB)1000000000354665 035 $a(EBL)257071 035 $a(OCoLC)71431446 035 $a(SSID)ssj0000110838 035 $a(PQKBManifestationID)11142744 035 $a(PQKBTitleCode)TC0000110838 035 $a(PQKBWorkID)10065552 035 $a(PQKB)11333831 035 $a(MiAaPQ)EBC257071 035 $a(EXLCZ)991000000000354665 100 $a20050725d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBeyond Born-Oppenheimer$b[electronic resource] $eelectronic non-adiabatic coupling terms and conical intersections /$fby Michael Baer 210 $aHoboken, N.J. $cWiley$dc2006 215 $a1 online resource (254 p.) 300 $aIncludes index 311 $a0-471-77891-5 327 $aBEYOND BORN-OPPENHEIMER; CONTENTS; PREFACE; ABBREVIATIONS; 1 MATHEMATICAL INTRODUCTION; 1.1 Hilbert Space; 1.1.1 Eigenfunction and Electronic Nonadiabatic Coupling Term; 1.1.2 Abelian and Non-Abelian Curl Equations; 1.1.3 Abelian and Non-Abelian Divergence Equations; 1.2 Hilbert Subspace; 1.3 Vectorial First-Order Differential Equation and Line Integral; 1.3.1 Vectorial First-Order Differential Equation; 1.3.1.1 Study of Abelian Case; 1.3.1.2 Study of Non-Abelian Case; 1.3.1.3 Orthogonality; 1.3.2 Integral Equation; 1.3.2.1 Integral Equation along an Open Contour 327 $a1.3.2.2 Integral Equation along a Closed Contour1.3.3 Solution of Differential Vector Equation; 1.4 Summary and Conclusions; Problem; References; 2 BORN-OPPENHEIMER APPROACH: DIABATIZATION AND TOPOLOGICAL MATRIX; 2.1 Time-Independent Treatment; 2.1.1 Adiabatic Representation; 2.1.2 Diabatic Representation; 2.1.3 Adiabatic-to-Diabatic Transformation; 2.1.3.1 Transformation for Electronic Basis Sets; 2.1.3.2 Transformation for Nuclear Wavefunctions; 2.1.3.3 Implications Due to Adiabatic-to-Diabatic Transformation; 2.1.3.4 Final Comments; 2.2 Application of Complex Eigenfunctions 327 $a2.2.1 Introducing Time-Independent Phase Factors2.2.1.1 Adiabatic Schro?dinger Equation; 2.2.1.2 Adiabatic-to-Diabatic Transformation; 2.2.2 Introducing Time-Dependent Phase Factors; 2.3 Time-Dependent Treatment; 2.3.1 Time-Dependent Perturbative Approach; 2.3.2 Time-Dependent Nonperturbative Approach; 2.3.2.1 Adiabatic Time-Dependent Electronic Basis Set; 2.3.2.2 Adiabatic Time-Dependent Nuclear Schro?dinger Equation; 2.3.2.3 Time-Dependent Adiabatic-to-Diabatic Transformation; 2.3.3 Summary; Problem; 2A Appendixes; 2A.1 Dressed Nonadiabatic Coupling Matrix 327 $a2A.2 Analyticity of Adiabatic-to-Diabatic Transformation Matrix A? in Spacetime ConfigurationReferences; 3 MODEL STUDIES; 3.1 Treatment of Analytical Models; 3.1.1 Two-State Systems; 3.1.1.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.1.2 Topological (D) Matrix; 3.1.1.3 The Diabatic Potential Matrix; 3.1.2 Three-State Systems; 3.1.2.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.2.2 Topological Matrix; 3.1.3 Four-State Systems; 3.1.3.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.3.2 Topological Matrix; 3.1.4 Comments Related to General Case 327 $a4.3 Quantization of Nonadiabatic Coupling Matrix: Study of Ab Initio Molecular Systems 330 $aINTRODUCING 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 an 606 $aMolecular dynamics$xMathematics 606 $aBorn-Oppenheimer approximation 606 $aAdiabatic invariants 608 $aElectronic books 615 0$aMolecular dynamics$xMathematics. 615 0$aBorn-Oppenheimer approximation. 615 0$aAdiabatic invariants. 676 $a539.758 676 $a541/.28 700 $aBaer$b M$g(Michael),$f1937-$0848737 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910143416003321 996 $aBeyond Born-Oppenheimer$91901119 997 $aUNINA