{"product_id":"beyond-bornoppenheimer-electronic-nonadiabatic-coupling-terms-and-conical-intersections-9780471778912","title":"Beyond BornOppenheimer Electronic Nonadiabatic Coupling Terms and Conical Intersections","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eINTRODUCING 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"…a good introductory guide to the world of nonadiabatic chemistry and can therefore be recommended to the scientists and students…\" (\u003ci\u003eZentralblatt MATH\u003c\/i\u003e, 2007)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.  \u003cp\u003eAbbreviations.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1. Mathematical Introduction.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eI.A. The Hilbert Space.\u003c\/p\u003e \u003cp\u003eI.A.1. The Eigenfunction and the Electronic non-Adiabatic Coupling Term.\u003c\/p\u003e \u003cp\u003eI.A.2. The Abelian and the non-Abelian Curl Equation.\u003c\/p\u003e \u003cp\u003eI.A.3. The Abelian and the non-Abelian Div-Equation.\u003c\/p\u003e \u003cp\u003eI.B. The Hilbert Subspace.\u003c\/p\u003e \u003cp\u003eI.C. The Vectorial First Order Differential Equation and the Line Integral.\u003c\/p\u003e \u003cp\u003eI.C.1. The Vectorial First Order Differential Equation.\u003c\/p\u003e \u003cp\u003eI.C.1.1. The Study of the Abelian Case.\u003c\/p\u003e \u003cp\u003eI.C.1.2. The Study of the non-Abelian Case.\u003c\/p\u003e \u003cp\u003eI.C.1.3. The Orthogonality.\u003c\/p\u003e \u003cp\u003eI.C.2. The Integral Equation.\u003c\/p\u003e \u003cp\u003eI.C.2.1. The Integral Equation along an Open Contour.\u003c\/p\u003e \u003cp\u003eI.C.2.2. The Integral Equation along an Closed Contour.\u003c\/p\u003e \u003cp\u003eI.C.3. Solution of the Differential Vector Equation.\u003c\/p\u003e \u003cp\u003eI.D. Summary and Conclusions.\u003c\/p\u003e \u003cp\u003eI.E. Exercises.\u003c\/p\u003e \u003cp\u003eI.F. References.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2. Born-Oppenheimer Approach: Diabatization and Topological Matrix.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eII.A. The Time Independent Treatment for Real Eigenfunctions.\u003c\/p\u003e \u003cp\u003eII.A.1. The Adiabatic Representation.\u003c\/p\u003e \u003cp\u003eII.A.2. The Diabatic Representation.\u003c\/p\u003e \u003cp\u003eII.A.3. The Adiabatic-to-Diabatic Transformation.\u003c\/p\u003e \u003cp\u003eII.A.3.1. The Transformation for the Electronic Basis Set.\u003c\/p\u003e \u003cp\u003eII.A.3.2. The Transformation for the Nuclear Wave-Functions.\u003c\/p\u003e \u003cp\u003eII.A.3.3. Implications due to the Adiabatic-to-Diabatic Transformation.\u003c\/p\u003e \u003cp\u003eII.A.3.4. Final Comments.\u003c\/p\u003e \u003cp\u003eII.B. Application of Complex Eigenfunctions.\u003c\/p\u003e \u003cp\u003eII.B.1. Introducing Time-Independent Phase Factors.\u003c\/p\u003e \u003cp\u003eII.B.1.1. The Adiabatic Schrödinger Equation.\u003c\/p\u003e \u003cp\u003eII.B.1.2. The Adiabatic-to-Diabatic Transformation.\u003c\/p\u003e \u003cp\u003eII.B.2. Introducing Time-Dependent Phase Factors.\u003c\/p\u003e \u003cp\u003eII.C. The Time Dependent Treatment.\u003c\/p\u003e \u003cp\u003eII.C.1. The Time-Dependent Perturbative Approach.\u003c\/p\u003e \u003cp\u003eII.C.2. The Time-Dependent non-Perturbative Approach.\u003c\/p\u003e \u003cp\u003eII.C.2.1. The Adiabatic Time Dependent Electronic Basis set.\u003c\/p\u003e \u003cp\u003eII.C.2.2. The Adiabatic Time-Dependent Nuclear Schrödinger Equation.\u003c\/p\u003e \u003cp\u003eII.C.2.3. The Time Dependent Adiabatic-to-Diabatic Transformation.\u003c\/p\u003e \u003cp\u003eII.C.3. Summary.\u003c\/p\u003e \u003cp\u003eII.D. Appendices.\u003c\/p\u003e \u003cp\u003eII.D.1. The Dressed Non-Adiabatic Coupling Matrix.\u003c\/p\u003e \u003cp\u003eII.D.2. Analyticity of the Adiabatic-to-Diabatic Transformation matrix, Ã, in Space-Time Configuration.\u003c\/p\u003e \u003cp\u003eII.E. References.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3. Model Studies.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIII.A. Treatment of Analytical Models.\u003c\/p\u003e \u003cp\u003eIII.A.1 Two-State Systems.\u003c\/p\u003e \u003cp\u003eIII.A.1.1. The Adiabatic-to-Diabatic Transformation Matrix.\u003c\/p\u003e \u003cp\u003eIII.A.1.2. The Topological Matrix.\u003c\/p\u003e \u003cp\u003eIII.A.1.3. The Diabatic Potential Matrix.\u003c\/p\u003e \u003cp\u003eIII. A.2. Three-State Systems.\u003c\/p\u003e \u003cp\u003eIII.A.2.1. The Adiabatic-to-Diabatic Transformation Matrix.\u003c\/p\u003e \u003cp\u003eIII.A.2 2. The Topological Matrix.\u003c\/p\u003e \u003cp\u003eIII. A.3. Four-State Systems.\u003c\/p\u003e \u003cp\u003eIII.A.3.1. The Adiabatic-to-Diabatic Transformation Matrix.\u003c\/p\u003e \u003cp\u003eIII.A.3 2. The Topological Matrix.\u003c\/p\u003e \u003cp\u003eIII.A.4 Comments Related to the General Case.\u003c\/p\u003e \u003cp\u003eIII.B. The Study of the 2x2 Diabatic Potential Matrix and Related Topics.\u003c\/p\u003e \u003cp\u003eIII.B.1. Treatment of the General Case.\u003c\/p\u003e \u003cp\u003eIII.B.2. The Jahn-Teller Model.\u003c\/p\u003e \u003cp\u003eIII.B.3. The Elliptic Jahn-Teller Model.\u003c\/p\u003e \u003cp\u003eIII.B.4. On the Distribution of Conical Intersections and the Diabatic Potential Matrix.\u003c\/p\u003e \u003cp\u003eIII.C. The Adiabatic-to-Diabatic Transformation Matrix and the Wigner Rotation Matrix.\u003c\/p\u003e \u003cp\u003eIII.C.1. The Wigner Rotation Matrices.\u003c\/p\u003e \u003cp\u003eIII.C.2. The Adiabatic-to-Diabatic Transformation Matrix and the Wigner dj-Matrix.\u003c\/p\u003e \u003cp\u003eIII. D. Exercise.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4. Studies of Molecular Systems.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIV.A. Introductory Comments.\u003c\/p\u003e \u003cp\u003eIV.B. Theoretical Background.\u003c\/p\u003e \u003cp\u003eIV. C. Quantization of the Non-adiabatic Coupling Matrix: Studies of \u003ci\u003eab-initio\u003c\/i\u003e Molecular Systems.\u003c\/p\u003e \u003cp\u003eIV.C.1. Two-State Quasi-Quantization.\u003c\/p\u003e \u003cp\u003eIV.C.1.1. The {H\u003csub\u003e2\u003c\/sub\u003e,H} system.\u003c\/p\u003e \u003cp\u003eIV.C.1.2. The {H\u003csub\u003e2\u003c\/sub\u003e,O} system.\u003c\/p\u003e \u003cp\u003eIV.C.1.3. The {C\u003csub\u003e2\u003c\/sub\u003eH\u003csub\u003e2\u003c\/sub\u003e) Molecule.\u003c\/p\u003e \u003cp\u003eIV.C.2. Multi-State Quasi-Quantization.\u003c\/p\u003e \u003cp\u003eIV.C.2.1. The {H\u003csub\u003e2\u003c\/sub\u003e,H} system.\u003c\/p\u003e \u003cp\u003eIV.C.2.2. The {C\u003csub\u003e2\u003c\/sub\u003e,H} system.\u003c\/p\u003e \u003cp\u003eIV.D. References. \u003c\/p\u003e \u003cp\u003e\u003cb\u003e5.\u003c\/b\u003e \u003cb\u003eDegeneracy Points and Born—Oppenheimer Coupling Terms as Poles.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eV.A. On the Relation between the Electronic Non-Adiabatic Coupling Terms and the Degeneracy Points.\u003c\/p\u003e \u003cp\u003eV.B. The Construction of Hilbert Subspaces.\u003c\/p\u003e \u003cp\u003eV.C. The Sign Flips of the Electronic Eigenfunctions.\u003c\/p\u003e \u003cp\u003eV.C.1. Sign-Flips in Case of a Two-State Hilbert Subspace.\u003c\/p\u003e \u003cp\u003eV.C.2. Sign-Flips in Case of a Three-State Hilbert Subspace.\u003c\/p\u003e \u003cp\u003eV.C.3. Sign-Flips in Case of a General Hilbert Subspace.\u003c\/p\u003e \u003cp\u003eV.C.4 Sign-Flips for a case of a Multi-Degeneracy Point.\u003c\/p\u003e \u003cp\u003eV.C.4.1 The General Approach.\u003c\/p\u003e \u003cp\u003eV.C.4.2 Model Studies.\u003c\/p\u003e \u003cp\u003eV.D. The Topological Spin.\u003c\/p\u003e \u003cp\u003eV.E. The Extended Euler Matrix as a Model for the Adiabatic-to-Diabatic Transformation Matrix.\u003c\/p\u003e \u003cp\u003eV.E.1. Introductory Comments.\u003c\/p\u003e \u003cp\u003eV.E.2.The Two-State Case.\u003c\/p\u003e \u003cp\u003eV.E.3 The Three-State Case.\u003c\/p\u003e \u003cp\u003eV.E.4 The Multi-State Case.\u003c\/p\u003e \u003cp\u003eV.F. Quantization of the τ-Matrix and its Relation to the Size of Configuration Space: the Mathieu Equation as a Case of Study.\u003c\/p\u003e \u003cp\u003eIV.F.1. Derivation of the Eigenfunctions.\u003c\/p\u003e \u003cp\u003eIV.F.2. The non-Adiabatic Coupling Matrix and the Topological matrix.\u003c\/p\u003e \u003cp\u003eV.G Exercises.\u003c\/p\u003e \u003cp\u003eV.H. References.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6. The Molecular Field.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eVI.A. Solenoid as a Model for the Seam.\u003c\/p\u003e \u003cp\u003eVI.B. Two-State (Abelian) System.\u003c\/p\u003e \u003cp\u003eVI.B.1. The Non-Adiabatic Coupling Term as a Vector Potential.\u003c\/p\u003e \u003cp\u003eVI.B.2. Two-State Curl Equation.\u003c\/p\u003e \u003cp\u003eVI.B.3. The (Extended) Stokes Theorem.\u003c\/p\u003e \u003cp\u003eVI.B.4. Application of Stokes Theorem for several Conical Intersections.\u003c\/p\u003e \u003cp\u003eVI.B.5. Application of Vector-Algebra to Calculate the Field of a Two-State Hilbert Space.\u003c\/p\u003e \u003cp\u003eVI.B.6. A Numerical Example: The Study of the {Na,H\u003csub\u003e2\u003c\/sub\u003e} System.\u003c\/p\u003e \u003cp\u003eVI. B.7. A Short Summary.\u003c\/p\u003e \u003cp\u003eVI.C. The Multi-State Hilbert Subspace.\u003c\/p\u003e \u003cp\u003eVI.C.1. The non-Abelian Stokes Theorem.\u003c\/p\u003e \u003cp\u003eVI.C.2. The Curl-Div Equations.\u003c\/p\u003e \u003cp\u003eVI.C.2.1. The Three-State Hilbert Subspace.\u003c\/p\u003e \u003cp\u003eVI.C.2.2. Derivation of the Poisson Equations.\u003c\/p\u003e \u003cp\u003eVI.C.2.3. The Strange Matrix Element and the Gauge Transformation.\u003c\/p\u003e \u003cp\u003eVI.D. A Numerical Study of the {H, H\u003csub\u003e2\u003c\/sub\u003e} System.\u003c\/p\u003e \u003cp\u003eVI.D.1. Introductory Comments.\u003c\/p\u003e \u003cp\u003eVI.D.2. Introducing the Fourier Expansion.\u003c\/p\u003e \u003cp\u003eVI.D.3. Imposing Boundary Conditions.\u003c\/p\u003e \u003cp\u003eVI.D.4. Numerical Results.\u003c\/p\u003e \u003cp\u003eVI.E. The Multi-State Hilbert Subspace: On the Breakup of the Non-Adiabatic Coupling Matrix.\u003c\/p\u003e \u003cp\u003eVI.F. The Pseudo-Magnetic Field.\u003c\/p\u003e \u003cp\u003eVI.F.1. Quantization of the pseudo magnetic along the seam:.\u003c\/p\u003e \u003cp\u003eVI.F.2. The Non-Abelian Magnetic Fields.\u003c\/p\u003e \u003cp\u003eVI.G. Exercises:\u003c\/p\u003e \u003cp\u003eVI.H. References.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7. Open Phase and the Berry Phase for Molecular Systems.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eVII.A. Studies of Ab-initio Systems.\u003c\/p\u003e \u003cp\u003eVII.A.1. Introductory Comments.\u003c\/p\u003e \u003cp\u003eVII.A.2. The Open Phase and the Berry Phase for Single-valued Eigenfunctions ( Berry's Approach.\u003c\/p\u003e \u003cp\u003eVII.A.3. The Open Phase and the Berry Phase for Multi-valued Eigenfunctions ( the Present Approach.\u003c\/p\u003e \u003cp\u003eVII.A.3.1. Derivation of the Time-Dependent Equation.\u003c\/p\u003e \u003cp\u003eVII.A.3.2. The Treatment of the Adiabatic Case.\u003c\/p\u003e \u003cp\u003eVII.A.3.3. The Treatment of the non-Adiabatic (General) Case.\u003c\/p\u003e \u003cp\u003eVII.A.3.4. The {H\u003csub\u003e2\u003c\/sub\u003e,H} System as a Case Study.\u003c\/p\u003e \u003cp\u003eVII.B. Phase-Modulus Relations for an External Cyclic Time-Dependent Field.\u003c\/p\u003e \u003cp\u003eVII.B.1. The Derivation of the Reciprocal Relations.\u003c\/p\u003e \u003cp\u003eVII.B.2. The Mathieu equation.\u003c\/p\u003e \u003cp\u003eVII.B.2.1. The Time-Dependent Schrödinger Equations.\u003c\/p\u003e \u003cp\u003eVII.B.2.2. Numerical Study of the Topological Phase.\u003c\/p\u003e \u003cp\u003eVII.B.3. Short Summary.\u003c\/p\u003e \u003cp\u003eVII.C. Exercises.\u003c\/p\u003e \u003cp\u003eVII.D. References.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8. Extended Born-Oppenheimer Approximations.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eVIII.A. Introductory Comments.\u003c\/p\u003e \u003cp\u003eVIII.B. The Born-Oppenheimer Approximation as Applied to a Multi-State Model-System.\u003c\/p\u003e \u003cp\u003eVIII.B.1. The Extended Approximate Born-Oppenheimer Equation.\u003c\/p\u003e \u003cp\u003eVIII.B.2. Gauge Invariance Condition for the Approximate Born-Oppenheimer Equation.\u003c\/p\u003e \u003cp\u003eVIII.C. Multi-State Born-Oppenheimer Approximation: Energy Considerations to Reduce the Dimension of the Diabatic Potential Matrix.\u003c\/p\u003e \u003cp\u003eVIII.C.1. Introductory Comments.\u003c\/p\u003e \u003cp\u003eVIII.C.2. Derivation of the Reduced Diabatic Potential Matrix.\u003c\/p\u003e \u003cp\u003eVIII.C.3. Application of the Extended Euler Matrix: Introducing the N-State Adiabatic-to-Diabatic Transformation Angle.\u003c\/p\u003e \u003cp\u003eVIII.C.3.1. Introductory Comments.\u003c\/p\u003e \u003cp\u003eVIII.C.3.2. Derivation of the Adiabatic-to-Diabatic Transformation Angle.\u003c\/p\u003e \u003cp\u003eVIII.C.4. Two-State Diabatic Potential Energy Matrix.\u003c\/p\u003e \u003cp\u003eVIII.C.4.1 Derivation of the Diabatic Potential Matrix.\u003c\/p\u003e \u003cp\u003eVIII.C.4.2 A Numerical Study of the (W-Matrix Elements.\u003c\/p\u003e \u003cp\u003eVIII.C.4.3 A Different Approach: The Helmholtz Decomposition.\u003c\/p\u003e \u003cp\u003eVIII.D. A Numerical Study of a Reactive Scattering Two-Coordinate Model.\u003c\/p\u003e \u003cp\u003eVIII.D.1. The Basic Equations.\u003c\/p\u003e \u003cp\u003eVIII.D.2. A Two-Coordinate Reactive (Exchange) Model.\u003c\/p\u003e \u003cp\u003eVIII.D.3. Numerical Results and Discussion.\u003c\/p\u003e \u003cp\u003eVIII.E. Exercises.\u003c\/p\u003e \u003cp\u003eVIII.F. References.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9. Summary.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":51767552475479,"sku":"9780471778912","price":180.86,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471778912.jpg?v=1758713760","url":"https:\/\/bookcurl.com\/products\/beyond-bornoppenheimer-electronic-nonadiabatic-coupling-terms-and-conical-intersections-9780471778912","provider":"Book Curl","version":"1.0","type":"link"}