First-Order Response Properties in MNDO: Contents

Acknowledgments iv
Zusammenfassung v
Abstract vii
Frequently used symbols and abbreviations viii
Introduction 1

A: Theory

1.

MNDO family of semiempirical methods: approximations and expressions

2

1.1 MNDO integral approximation and electronic energy 2
1.2 Half-electron restricted open-shell method: electronic energy correction 3
1.3 Core-core repulsion energy 4
2.

First-order CPHF equations in MNDO approximation

6

2.1 General case: CPHF equations for a UHF wavefunction 6
2.2 Special case: CPHF equations for an RHF wavefunction 9
3.

Second Cartesian derivatives of the energy in MNDO methods

10

3.1 Cartesian gradient of the electronic energy of a UHF wavefunction 10
3.2 Second Cartesian derivatives of the UHF electronic energy 11
4.

Energy gradient in the MNDO half-electron open-shell treatment

12

4.1 Static and response parts of the half-electron gradient 12
4.2 Z-vector evaluation of the response contribution 13
5.

Magnetic shielding tensors in MNDO approximation

15

5.1 NMR shielding tensor and the experimentally observable parameters 15
5.2 GIAO-SCF theory of the NMR shielding tensors 16
5.3 MNDO approximation for the NMR shielding tensor expression 18

B: Implementation

6.

Solution of the CPHF equations

20

6.1 Reported iterative algorithms for the solution of the CPHF equations 20
6.2 Proposed new algorithms 22
6.3 Preconditioning of the CPHF equations 25
7.

Reduction of the integrals over real Slater AOs to elementary integrals

28

7.1 Derivatives of the overlap integrals in the local coordinate system 30
7.2 Product of a Slater AO and a dipole moment operator 30
7.3 Product of two Slater AOs at the same center 33
7.4 Action of the orbital momentum operator on a Slater AO at the same center 34
7.5 Action of the orbital momentum operator on a Slater AO at a displaced center 38
8.

Evaluation of the elementary two-center integrals

40

8.1 Two-electron repulsion integrals 40
8.2 Overlap integrals 43
8.3 Magnetic integrals 45
9.

Evaluation of the elementary three-center integrals

48

9.1 Expansion of a Slater function at a displaced origin 48
9.2 Three-center matrix elements of the r^-3 &Lhat; operator 51
9.3 Three-center matrix elements of the r^-3 r operator 54

C: Applications

10.

Mechanisms of helium incorporation into buckminsterfullerene

55

10.1 Equilibrium yield for He@C₆₀ 55
10.2 Window mechanism 58
10.3 Radical impurity mechanisms 64
11.

Exploratory parametrization for the isotropic shielding constants in MNDO

73

11.1 Reference set selection 73
11.2 Results and discussion 74
11.3 Conclusions and perspective 81

References
82
A1.

Appendix A1: Generation of the electron repulsion integrals in the local coordinate system

88

A2.

Appendix A2: Reference set for the exploratory parametrization of chemical shifts

104

Curriculum Vitae 127

		Acknowledgments	iv
		Zusammenfassung	v
		Abstract	vii
		Frequently used symbols and abbreviations	viii
		Introduction	1
		A: Theory
1.		MNDO family of semiempirical methods: approximations and expressions	2
	1.1	MNDO integral approximation and electronic energy	2
	1.2	Half-electron restricted open-shell method: electronic energy correction	3
	1.3	Core-core repulsion energy	4
2.		First-order CPHF equations in MNDO approximation	6
	2.1	General case: CPHF equations for a UHF wavefunction	6
	2.2	Special case: CPHF equations for an RHF wavefunction	9
3.		Second Cartesian derivatives of the energy in MNDO methods	10
	3.1	Cartesian gradient of the electronic energy of a UHF wavefunction	10
	3.2	Second Cartesian derivatives of the UHF electronic energy	11
4.		Energy gradient in the MNDO half-electron open-shell treatment	12
	4.1	Static and response parts of the half-electron gradient	12
	4.2	Z-vector evaluation of the response contribution	13
5.		Magnetic shielding tensors in MNDO approximation	15
	5.1	NMR shielding tensor and the experimentally observable parameters	15
	5.2	GIAO-SCF theory of the NMR shielding tensors	16
	5.3	MNDO approximation for the NMR shielding tensor expression	18
		B: Implementation
6.		Solution of the CPHF equations	20
	6.1	Reported iterative algorithms for the solution of the CPHF equations	20
	6.2	Proposed new algorithms	22
	6.3	Preconditioning of the CPHF equations	25
7.		Reduction of the integrals over real Slater AOs to elementary integrals	28
	7.1	Derivatives of the overlap integrals in the local coordinate system	30
	7.2	Product of a Slater AO and a dipole moment operator	30
	7.3	Product of two Slater AOs at the same center	33
	7.4	Action of the orbital momentum operator on a Slater AO at the same center	34
	7.5	Action of the orbital momentum operator on a Slater AO at a displaced center	38
8.		Evaluation of the elementary two-center integrals	40
	8.1	Two-electron repulsion integrals	40
	8.2	Overlap integrals	43
	8.3	Magnetic integrals	45
9.		Evaluation of the elementary three-center integrals	48
	9.1	Expansion of a Slater function at a displaced origin	48
	9.2	Three-center matrix elements of the r^-3 &Lhat; operator	51
	9.3	Three-center matrix elements of the r^-3 r operator	54
		C: Applications
10.		Mechanisms of helium incorporation into buckminsterfullerene	55
	10.1	Equilibrium yield for He@C₆₀	55
	10.2	Window mechanism	58
	10.3	Radical impurity mechanisms	64
11.		Exploratory parametrization for the isotropic shielding constants in MNDO	73
	11.1	Reference set selection	73
	11.2	Results and discussion	74
	11.3	Conclusions and perspective	81
		References	82
A1.		Appendix A1: Generation of the electron repulsion integrals in the local coordinate system	88
A2.		Appendix A2: Reference set for the exploratory parametrization of chemical shifts	104
		Curriculum Vitae	127