The Irreducible Tensor Method for Molecular

Suitable for advanced undergraduates and graduate students, this text presents a highly specific version of the irreducible tensor method for molecular symmetry groups. It was written by a distinguished chemist and biophysicist, John Stanley Griffith (1928-72), whose brief career spanned many disciplines and who developed a theory of protein self-replication that led to significant advances in genetic research.

Introduction

1

(3)

V Coefficients for the Octahedral Group

4

(21)

Introduction

4

(3)

Coupling coefficients

7

(2)

Reduced matrix elements

9

(1)

Symmetry of the coupling coefficients

9

(1)

V coefficients

10

(5)

The Kramers operator

15

(2)

Elementary properties of V coefficients

17

(1)

Orthogonal transformations of components

18

(1)

Complex transformations

19

(2)

Examples of reduced matrix elements

21

(4)

V Coefficients for Other Symmetry Groups

25

(7)

General discussion

25

(1)

Direct product groups

26

(2)

The groups T, O, and K

28

(1)

Dihedral groups Dn(n > 2), and D∞

29

(2)

Reduced matrix elements

31

(1)

W Coefficients

32

(8)

Invariants

32

(2)

Elementary properties of W coefficients

34

(1)

Relation of W to recoupling transformations

35

(2)

Equations satisfied by W coefficients

37

(3)

Irreducible Products and Their Matrix Elements

40

(9)

Definition of an irreducible product

40

(2)

Various special operators

42

(3)

Matrix elements

45

(2)

Second-order perturbation theory and an operator equivalent

47

(2)

Two-Electron Formulae for the Octahedral Group

49

(10)

Two-electron functions

49

(2)

A preliminary lemma

51

(1)

The elimination of spin

52

(1)

Simplification of the spatial matrix element

53

(1)

Other operators

54

(1)

g values for the nickel ion

55

(1)

Paramagnetic susceptibilities

56

(1)

An axial ligand field

57

(2)

Fractional Parentage

59

(9)

Coefficients of fractional parentage

59

(2)

Matrix elements of a spinindependent operator within an

61

(4)

Matrix elements of Uf φ between an and an-1b

65

(2)

Nuclear magnetic resonance for the cobaltic ion

67

(1)

X Coefficients

68

(7)

Definition and some general properties

68

(2)

Special formulae for X

70

(2)

X coefficients for the group D4

72

(1)

General equations satisfied by X coefficients

73

(2)

Spin

75

(10)

Reduced matrix elements and V coefficients

75

(3)

W coefficients

78

(1)

X coefficients

79

(1)

Double tensor operators

79

(1)

Spin-orbit coupling as a double tensor operator

80

(2)

Coupling of spin with space for octahedral (and tetrahedral) symmetry

82

(1)

Matrix of a spin-independent operator

83

(2)

Matrices of One-Electron Operators

85

(10)

The configurations an

85

(4)

Matrix elements between an and a1-1b

89

(1)

Configurationally diagonal matrix elements for ambn-1

90

(1)

Matrix elements between am-1bn and ambn-1

91

(4)

Some Special Topics

95

(8)

A trigonal ligand field for d electrons

95

(2)

Intensity calculations for centrosymmetric octahedral systems

97

(1)

Second-order spin-orbit coupling in free atoms

98

(2)

Aromatic hydrocarbons

100

(3)

Appendix A Important Remarks Conceming Phase

103

(2)

Appendix B Associated Representations for the Octahedral Group

105

(4)

Appendix C Tables for the Octahedral Group

109

(10)

Appendix D Tables for the Dihedral Groups

119

(7)

Appendix E Values of the Coefficients Ω for Spin-Orbit Coupling

126

(4)

Appendix F Acknowledgements and References

130

(2)

Index

132

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The Irreducible Tensor Method for Molecular Symmetry Groups

Summary

Table of Contents

Supplemental Materials

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

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The Irreducible Tensor Method for Molecular Symmetry Groups

Summary

Table of Contents

Supplemental Materials

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