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El. knyga: Bond Orders and Energy Components: Extracting Chemical Information from Molecular Wave Functions

  • Formatas: 239 pages
  • Išleidimo metai: 14-Oct-2016
  • Leidėjas: CRC Press Inc
  • ISBN-13: 9781420090123
Kitos knygos pagal šią temą:
Bond Orders and Energy Components: Extracting Chemical Information from Molecular Wave FunctionsDidesnis paveikslėlis
  • Formatas: 239 pages
  • Išleidimo metai: 14-Oct-2016
  • Leidėjas: CRC Press Inc
  • ISBN-13: 9781420090123
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For thirty years Mayer has been investigating the quantum mechanical meaning of the bond order, the actual valence of an atom in a molecule, and the different atomic and diatomic energy components reflecting the energetics of molecule formation. Here he gathers his findings that have previously been published in various journals and presents all the results with complete derivations. Most results use a common theoretical framework called the atomic resolution of identity, and reside within the Hilbert space approach to analyzing quantum chemical calculations. Annotation ©2016 Ringgold, Inc., Portland, OR (protoview.com)

While modern computational methods can provide us with the wave function of a molecule in numerical form, most computer programs lack the sophisticated tools needed to extract chemical concepts from these wave functions. Saving researchers vast time and potential confusion, this volume collects and organizes those validated tools currently scattered throughout the literature and details their application. It provides immediate access for those needing to calculate such critical factors as bond order and valence indices, and atomic and diatomic contributions to molecular energy. Supporting material is available for download from the authors' continually updated website.

Preface ix
1 Introduction
1(12)
1.1 Why a posteriori analysis?
1(2)
1.2 A prelude: The simple Huckel theory
3(10)
1.2.1 An application: Huckel's "4n+2 rule"
8(5)
2 Basic ideas of Hilbert space analysis
13(6)
3 A common framework: Atomic resolution of identity
19(14)
3.1 The definition
19(2)
3.2 Different atomic operators
21(2)
3.3 Population analysis
23(3)
3.4 Decomposition of electron density and of exchange density
26(7)
4 Analysis of the first-order density in Hilbert space
33(16)
4.1 The LCAO representation of the first-order density matrix
33(6)
4.2 Mulliken charges and overlap populations: Invariance
39(4)
4.3 Lowdin charges and the problem of rotational invariance
43(6)
5 Effective AOs and effective minimal basis sets
49(16)
5.1 Definition of effective AOs
49(8)
5.2 Some calculations of effective AOs
57(8)
6 Bond order and valence indices in the Hilbert space
65(40)
6.1 Predecessor: The Wiberg Index in CNDO Theory
65(4)
6.2 Exchange and bonding
69(1)
6.3 Exchange density and the bond order
70(4)
6.4 Ab initio bond order indices of homonuclear diatomics
74(4)
6.5 Bond orders in three-center bonds
78(4)
6.6 The charge-fluctuation definition of bond order
82(1)
6.7 Bond order in the correlated case
83(6)
6.8 An example: Dimethylformamide
89(3)
6.9 An application: Predicting primary mass spectrometric cleavages
92(3)
6.10 Valences and free valences
95(5)
6.11 Hydrogen bonded systems
100(2)
6.12 Partial valences and some remarks on hypervalency
102(3)
7 Open-shell systems and local spins
105(22)
7.1 Effective number of unpaired electrons
105(3)
7.2 Effective number of unpaired electrons and the cumulant
108(3)
7.3 Local spins
111(16)
7.3.1 Local spins for single determinant wave functions
116(6)
7.3.2 Local spins for correlated wave functions
122(5)
8 Energy components in the Hilbert space
127(50)
8.1 Energy partitioning based on the virial theorem
128(4)
8.2 Atomic promotion energies in molecules
132(3)
8.3 Role of hybridization and the VSEPR rules
135(3)
8.4 The CECA method and related schemes
138(23)
8.4.1 The problem of multicenter integrals: The projective integral expansion scheme
138(4)
8.4.2 The integrals in the CECA method
142(3)
8.4.3 The CECA energy components
145(5)
8.4.4 The three-and four-center corrections
150(3)
8.4.5 Remarks about kinetic energy
153(1)
8.4.6 Physical analysis of the diatomic CECA energy components
154(7)
8.5 Improved CECA method
161(11)
8.6 Decomposition of the correlation energy
172(5)
9 Analysis in the three-dimensional space
177(28)
9.1 Different weight functions
178(4)
9.2 Population analysis in the 3D space
182(3)
9.3 Bond orders and valences from the 3D space analysis
185(5)
9.4 Effective AOs from the 3D space analysis
190(1)
9.5 Interrelation between Hilbert-space and 3D analyses
191(6)
9.6 Energy components in the 3D space
197(5)
9.7 Local spins in the 3D space
202(3)
A APPENDICES
205(16)
A.1 "Mixed" second quantization for non-orthogonal basis functions
205(15)
A.1.1 Second quantization for orthogonal functions
205(9)
A.1.2 "Mixed" second quantization for non-orthogonal functions
214(6)
A.2 Calculation of Becke's weight functions
220(1)
Bibliography 221(6)
Index 227
Istvan Mayer, he was working three months with the late Professor Per-Olov Lowdin in Gainesville, Florida, and between 1997 and 1999 he had spent three semesters at the Grenoble University, France.
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