Page 8 - Valence Bond Methods. Theory and Applications

Preface Contents pØgexiii
Lisł of abbreviations xv

I Theory and two-electon systems
1 Introduction 3
1.1 History 3
1.2 Mathematical background 4
1.2.1 Schr¨odinger’s equation 5
1.3 The variation theorem 9
1.3.1 General variation functions 9
1.3.2 Linear variation functions 9
1.3.3 A 2 × 2 generalized eigenvalue problem 14
1.4 Weights of nonorthogonal functions 16
1.4.1 Weights without orthogonalization 18
1.4.2 Weights requiring orthogonalization 19
2H 2 and localized orbitals 23
2.1 The separation of spin and space variables 23
2.1.1 The spin functions 23
2.1.2 The spatial functions 24
2.2 The AO approximation 24
2.3 Accuracy of the Heitler–London function 27
2.4 Extensions to the simple Heitler–London treatment 27
2.5 Why is the H 2 molecule stable? 31
2.5.1 Electrostatic interactions 32
2.5.2 Kinetic energy effects 36
2.6 Electron correlation 38
2.7 Gaussian AO bases 38
2.8 A full MCVB calculation 38

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