Potential energy hypersurfaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam u.a.
Elsevier
1987
|
| Series: | Studies in physical and theoretical chemistry
53 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 538 S. |
| ISBN: | 0444428879 |
Staff View
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Record in the Search Index
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| adam_text | STUDIES IN PHYSICAL AND THEORETICAL CHEMISTRY 53 POTENTIAL ENERGY
HYPERSURFACES PAULG. MEZEY DEPARTMENT OF CHEMISTRY AND DEPARTMENT OF
MATHEMATICS, UNIVERSITY OF SASKATCHEWAN, SASKATOON, CANADA S7N OWO
ELSEVIER AMSTERDAM * OXFORD * NEW YORK * TOKYO 1 987 VII CONTENTS
FOREWORD XIN INTRODUCTION 1 CHAPTERL THE MOLECULAR ENERGY EXPECTATION
VALUE 4 1.1 ENERGY, THE FUNDAMENTAL QUANTUM MECHANICAL OBSERVABLE 4 1.2
THE BORN-OPPENHEIMER APPROXIMATION AND THE CONCEPT OF NUCLEAR GEOMETRY 6
1.3. GENERALIZATIONS OF NUCLEAR COORDINATES 18 1.4 GLOBAL AND LOCAL
COORDINATE SYSTEMS AND THE CONCEPT OF NUCLEAR CONFIGURATION SPACE 21
1.4.1 GLOBAL CARTESIAN COORDINATE SYSTEMS 21 1.4.2 LOCAL INTERNAL
COORDINATE SYSTEMS 27 1.4.3 SYMMETRY COORDINATES AND NORMAL COORDINATES
OF THE SMALL AMPLITUDE VIBRATIONAL PROBLEM 30 1.4.4 SPECIAL GLOBAL
COORDINATE SYSTEMS 45 1.4.5 SPECIAL PURPOSE COORDINATE SYSTEMS FOR SMALL
MOLECULES 47 1.5 INTERSECTIONS OF ENERGY HYPERSURFACES: ADIABAT1C AND
DIABATIC REPRESENTATIONS 51 CHAPTERLL GEOMETRICAL PROPERTIES OF ENERGY
HYPERSURFACES 61 II. 1 ENERGY DERIVATIVES: FORCES AND FORCE CONSTANTS 61
II. 1.1 THE HELLMANN-FEYNMAN THEOREM 61 II.2 MINIMA, SADDLE POINTS AND
GENERAL CRITICAL POINTS 66 11.2.1 CLASSIFICATION OF CRITICAL POINTS 69
11.2.2 INTERRELATIONS AMONG CRITICAL POINTS: CRITICAL POINT INEQUALITIES
77 VIII IL 3 MINIMUM ENERGY PATH AND THE INTRINSIC REACTION COORDINATE
81 11.3.1 STEEPEST DESCENT PATHS AND STATIONARY PATHS 83 11.3.2 STEEPEST
DESCENT PATHS AND THE INTRINSIC REACTION COORDINATE 86 11.3.3 SYMMETRY
PROPERTIES OF TRANSITION STRUCTURES AND STEEPEST DESCENT PATHS 87 11.3.4
STEEPEST DESCENT APPROACH TO CRITICAL POINTS 94 II.4 DIFFERENTIAL
GEOMETRY OF ENERGY HYPERSURFACES 98 CHAPTER III CALCULATION AND
REPRESENTATION OF ENERGY HYPERSURFACES 117 III. 1 THE
HARTREE-FOCK-ROOTHAAN-HALL METHOD FOR THE CALCULATION OF MOLECULAR
WAVEFUNCTIONS 117 111.2 THE ELECTRON CORRELATION PROBLEM AND THE
CORRELATION ENERGY 143 111.3 CALCULATION OF SEMIEMPIRICAL AND EMPIRICAL
POTENTIAL FUNCTIONS 149 111.3.1 SEMIEMPIRICAL QUANTUM CHEMICAL METHODS
150 111.3.2 MOLECULAR MECHANICS METHOD AND EMPIRICAL POTENTIAL FUNCTIONS
151 111.4 THE FORCE METHOD AND CALCULATION OF HIGHER DERIVATIVES 152
111.5 MINIMUM SEARCH METHODS FOR THE DETERMINATION OF STABLE CHEMICAL
SPECIES 155 111.5.1 NON-GRADIENT METHODS OF ENERGY MINIMIZATION 156
111.5.2 GRADIENT METHODS FOR MINIMUM SEARCH 161 111.6 SADDLE POINT
SEARCH METHODS FOR THE DETERMINATION OF TRANSITION STRUCTURES 163 111.7
FITTING OF POTENTIAL ENERGY HYPERSURFACES, POLYNOMIALS, SPLINES AND
TRIGONOMETRIC FUNCTIONS 170 CHAPTER IV THE QUANTUM CHEMICAL CONCEPT OF
MOLECULES REVLSITED 181 IV. 1 QUANTIZATION AND CONTINUITY 181 IV. 2 WA
VE PACKET TOPOLOGY 185 IV.3 THE TOPOLOGY OF NUCLEAR CONFIGURATIONS 191
IX CHAPTERV MOLECULAR TOPOLOGY 198 V.L THE REDUCED NUCLEAR CONFIGURATION
SPACE: METRIC SPACE M 198 V.L.L AN EQUIVALENCE RELATION AND A GENERAL
CORRESPONDENCE PRINCIPLE 198 V.L.2 METRIE PROPERTIES OF THE REDUCED
NUCLEAR CONFIGURATION SPACE M 204 V.L.3 CONTINUITY OF ENERGY
HYPERSURFACES AS FUNETIONS OF INTERNAL CONFIGURATIONS K 215 V.L.4
REFLECTION PROPERTIES OF THE REDUCED NUCLEAR CONFIGURATION SPACE M: A
TANGENT CRITERION 219 V.2 CATCHMENT REGIONS OF POTENTIAL ENERGY
HYPERSURFACES: THE REPRESENTATION OF CHEMICAL SPECIES 227 V.2.1 THE
INTUITIVE CONEEPT OF CATCHMENT REGIONS 227 V.2.2 RELAXATION OF FORMAL
NUCLEAR CONFIGURATIONS IN THE LABORATORY FRAME 235 V.2.3 CATCHMENT
REGIONS IN EUCLIDEAN NUCLEAR CONFIGURATION SPACE 3N E 236 V.2.4
CATCHMENT REGIONS IN THE REDUCED NUCLEAR CONFIGURATION SPACE M 246 V.2.5
EXCIPLEX AND EXCIMER TOPOLOGIES: CATCHMENT REGIONS OF EXCITED STATE
POTENTIAL ENERGY HYPERSURFACES 257 V.3 MANIFOLD THEORY OF POTENTIAL
ENERGY SURFACES AND CATCHMENT REGIONS 262 V.3.1 MANIFOLD THEORY OF A
GENERAL NUCLEAR CONFIGURATION SPACE N R 263 V.3.2 MANIFOLD STRUCTURE OF
THE REDUCED NUCLEAR CONFIGURATION SPACE M 270 V.3.3 THE NUMBER OF
CHEMICAL SPECIES ALONG A HYPERSURFACE 280 V. 4 POTENTIAL DEFYING
CHEMICAL SPECIES 301 V.4.1 THE INTRINSIC KINETIC ENERGY ALONG POTENTIAL
ENERGY HYPERSURFACES 303 V.4.2 THE CONSTRUETION OF APPROXIMATE AEE(R)
FUNCTIONALS 308 V.4.3 LOCAL GEOMETRIC CRITERIA FOR POTENTIAL DEFYING
CHEMICAL SPECIES 313 V.4.4 GLOBAL TOPOLOGICAL CRITERIA FOR POTENTIAL
DEFYING CHEMICAL SPECIES 319 X V.5 THE ROLE OF NUCLEAR CHARGES AND
RELATIONS BETWEEN POTENTIAL SURFACES: CONVEXETY THEOREMS IN SPACE W Z
324 V.5.1 THE ABSTRACT NUCLEAR CHARGE SPACE W Z AND THE PRODUCT SPACE N
R W Z 327 V.5.2 LEVEL SETS OF THE ELECTRONIC ENERGY FUNCTIONAL IN SPACE
W Z 329 V.5.3 A SIMPLE RELATION BETWEEN NUCLEAR CHARGES AND POTENTIAL
ENERGY HYPERSURFACES: A CONCAVITY CONDITION FOR MOLECULAR TOTAL ENERGIES
346 V.6 CATCHMENT REGIONS AND SYMMETRY 364 CHAPTER VI REACTION TOPOLOGY
369 VI.L TOPOLOGICAL REACTION PATHS AND QUANTUM CHEMICAL REACTION
MECHAMSMS 369 VI.2 THE ALGEBRAIC STRUCTURE OF THE COMPLETE SET OF
REACTION PATHS 377 VI.2.1 THE FUNDAMENTAL GROUPOID OF REACTION PATHS 378
VI.2.2 TUNNELING AND THE EXTENSION OF THE FUNDAMENTAL GROUPOID OF
REACTION PATHS INTO A SEMIGROUP 382 VI.3 THE FUNDAMENTAL GROUP OF
REACTION MECHANISMS 384 VI.3.1 THE FUNDAMENTAL GROUP AND FUNDAMENTAL
REACTION MECHANISMS 385 VI.3.2 COMPARING SYSTEMS OF REACTION MECHANISMS:
HOMOMORPHISMS AND ISOMORPHISMS OF FUNDAMENTAL GROUPS 390 VI.3.3
GENERATORS FOR THE FUNDAMENTAL GROUP OF REACTION MECHANISMS 393 VI.3.4
ENERGY DEPENDENCE WITHIN THE FAMILY OF GROUPS OF REACTION MECHANISMS 401
VI.4 THE REACTION GLOBE, THE REACTION POLYHEDRON, AND HOMOLOGY GROUP
THEORY OF REACTION MECHANISMS 409 VI.4.1 THE CONSTRUCTION OF THE
REACTION GLOBE H(F) AND REACTION POLYHEDRON P(F) 412 VI.4.2 CHAINS,
CYCLES, AND HOMOLOGY GROUPS OF CATCHMENT REGIONS 419 XI VI.5. QUANTUM
CHEMICAL REACTION NETWORKS 429 VI.5.1 POINTED SETS OF THE NUCLEAR
CONFIGURATION SPACE N R AND REACTION NETWORKS 429 VI.5.2 ANALYSIS OF
REACTION GRAPHS AND NETWORKS OF REACTION MECHANISMS 438 VI.5.3 THEOREMS
ON SHORTEST REACTION MECHANISMS AND REACHABILITY MATRICES 445 VI. 6 THE
FUTURE OF COMPUTER BASED QUANTUM CHEMICAL SYNTHESIS DESIGN AND MOLECULAR
ENGINEERING 453 CLOSING REMARKS 459 APPENDIX 1 REVIEW OF TOPOLOGICAL
CONCEPTS 460 APPENDIX 2 PHYSICAL UNITS AND CONVERSION FACTORS 495
REFERENCES 497 SUBIECT INDEX 527
|
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| indexdate | 2024-07-09T15:20:33Z |
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| isbn | 0444428879 |
| language | English |
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| spelling | Mezey, Paul G. Verfasser aut Potential energy hypersurfaces Amsterdam u.a. Elsevier 1987 XV, 538 S. txt rdacontent n rdamedia nc rdacarrier Studies in physical and theoretical chemistry 53 Chimie des états excités Dynamique moléculaire Excited state chemistry Molecular dynamics Potenzialhyperfläche (DE-588)4267440-2 gnd rswk-swf Äquipotenzialfläche (DE-588)4141493-7 gnd rswk-swf Angeregter Zustand (DE-588)4142423-2 gnd rswk-swf Potenzialhyperfläche (DE-588)4267440-2 s Angeregter Zustand (DE-588)4142423-2 s DE-604 Äquipotenzialfläche (DE-588)4141493-7 s Studies in physical and theoretical chemistry 53 (DE-604)BV000004482 53 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000535781&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mezey, Paul G. Potential energy hypersurfaces Studies in physical and theoretical chemistry Chimie des états excités Dynamique moléculaire Excited state chemistry Molecular dynamics Potenzialhyperfläche (DE-588)4267440-2 gnd Äquipotenzialfläche (DE-588)4141493-7 gnd Angeregter Zustand (DE-588)4142423-2 gnd |
| subject_GND | (DE-588)4267440-2 (DE-588)4141493-7 (DE-588)4142423-2 |
| title | Potential energy hypersurfaces |
| title_auth | Potential energy hypersurfaces |
| title_exact_search | Potential energy hypersurfaces |
| title_full | Potential energy hypersurfaces |
| title_fullStr | Potential energy hypersurfaces |
| title_full_unstemmed | Potential energy hypersurfaces |
| title_short | Potential energy hypersurfaces |
| title_sort | potential energy hypersurfaces |
| topic | Chimie des états excités Dynamique moléculaire Excited state chemistry Molecular dynamics Potenzialhyperfläche (DE-588)4267440-2 gnd Äquipotenzialfläche (DE-588)4141493-7 gnd Angeregter Zustand (DE-588)4142423-2 gnd |
| topic_facet | Chimie des états excités Dynamique moléculaire Excited state chemistry Molecular dynamics Potenzialhyperfläche Äquipotenzialfläche Angeregter Zustand |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000535781&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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