04836nam 2200685 a 450 991101985790332120200520144314.0978661041143697812804114341280411430978047032705004703270579780471780083047178008197804717800760471780073(CKB)1000000000354665(EBL)257071(SSID)ssj0000110838(PQKBManifestationID)11142744(PQKBTitleCode)TC0000110838(PQKBWorkID)10065552(PQKB)11333831(MiAaPQ)EBC257071(OCoLC)163175453(Perlego)2753265(EXLCZ)99100000000035466520050725d2006 uy 0engur|n|---|||||txtrdacontentcrdamediacrrdacarrierBeyond Born-Oppenheimer electronic non-adiabatic coupling terms and conical intersections /by Michael BaerHoboken, N.J. Wileyc20061 online resource (254 p.)Includes index.9780471778912 0471778915 BEYOND 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 Contour1.3.2.2 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 Eigenfunctions2.2.1 Introducing Time-Independent Phase Factors2.2.1.1 Adiabatic Schrödinger 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 Schrödinger Equation; 2.3.2.3 Time-Dependent Adiabatic-to-Diabatic Transformation; 2.3.3 Summary; Problem; 2A Appendixes; 2A.1 Dressed Nonadiabatic Coupling Matrix2A.2 Analyticity of Adiabatic-to-Diabatic Transformation Matrix à 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 Case4.3 Quantization of Nonadiabatic Coupling Matrix: Study of Ab Initio Molecular SystemsINTRODUCING 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 anMolecular dynamicsMathematicsBorn-Oppenheimer approximationAdiabatic invariantsMolecular dynamicsMathematics.Born-Oppenheimer approximation.Adiabatic invariants.541/.28Baer M(Michael),1937-1838443MiAaPQMiAaPQMiAaPQBOOK9911019857903321Beyond Born-Oppenheimer4419986UNINA02113nam0 22003973i 450 CFI006517520251003044117.020020610d1984 ||||0itac50 baitaitaitz01i xxxe z01nz01ncRDAcarrierˆI ‰ceti dirigenti in Italia in età moderna e contemporaneaatti del Convegno, Cividale del Friuli, 10-12 settembre 1983a cura di Amelio TagliaferriUdineDel Bianco1984539 p.25 cm.Serie monografica di storia moderna e contemporaneaIstituto di storia dell'Università di Udine8001CFI00428122001 Serie monografica di storia moderna e contemporaneaIstituto di storia dell'Università di Udine871201Università degli studi <Udine> : Istituto di storiaCFIV019175ˆI ‰ceti dirigenti in Italia in età moderna e contemporaneaTSA18596811280763Classe dirigenteItaliaSec. 16.-20.Congressi1983FIRCFIC022791I945STORIA. ITALIA23IT/X438.0CLASSI CETI CONFLITTUALITA SOCIALE ITALIARIT/X438.3CETI IMPRENDITORIALI ITALIARX0.8/1983CONFERENZE CONGRESSI CONVEGNI (ATTI DI) 1983RConvegniCongressi e convegniCongressiConvegniCongressiCongressi e convegniTagliaferri, AmelioCFIV023484ITIT-00000020020610IT-BN0095 NAP 01POZZO LIB.Vi sono collocati fondi di economia, periodici di ingegneria e scienze, periodici di economia e statistica e altri fondi comprendenti documenti di economia pervenuti in dono. CFI0065175Biblioteca Centralizzata di Ateneo1 v. 01POZZO LIB.F. ASSANTE 189 0101 0060012975E VMA 1 v. 1 v. (Precedente collocazione A 166)B 2022091620220916 01Ceti dirigenti in Italia in età moderna e contemporanea1280763UNISANNIO