CONTENTS
������������ . . . ix
���������, ����������� ��� ����� . . . xv
� ������ 1 1 ������������ ������� ��������� 3 1.1 �e Dirac equation . . . 3
1.2 Relativistic Molecular Electronic-Structure �eory . . . 7
1.3 Mean-field approximation . . . 11
1.4 Basis set expansions and kinetic balance . . . 16
1.5 Relativity as the third dimension of Quantum Chemistry . . . 19
2 ����������� ��������� ����� 23 2.1 �e Problem of Solvation . . . 23
2.2 From Maxwell’s equations to Continuum models . . . 27
2.3 Discretization Procedures . . . 31
2.4 �e free energy and its decomposition . . . 33
3 ������������ ���-��� ������ 35 3.1 �e PCM e�ective Hamiltonian . . . 35
3.2 �e variation principle . . . 38
3.3 �e PCM contribution in SCF theory . . . 39
3.4 Discretization and basis set projection . . . 43
4 �������� ������ ��� � ������������ ���-��� ����� 45 4.1 �e time-dependent e�ective Hamiltonian . . . 45
4.2 Quasi-free energy, response functions and response equations . . . 47
4.3 �e Relativistic PCM-SCF Linear Response Function . . . 51
4.4 Solution of the first-order response equation . . . 54
�� �������������� 59 5 �������������� ������� 61 5.1 Integral engine . . . 62
5.2 PCMSolver . . . 64
5.2.1 Cavity surface generation and discretization . . . 65
5.2.2 Minimal input description . . . 68
5.3 Interfaces . . . 69
6 ������� 73 6.1 �e integral engine . . . 73
6.1.1 �e nuclear electrostatic potential . . . 75
6.1.2 �e electronic electrostatic potential . . . 76
vii
viii ��������
6.2 PCMSolver . . . 78
6.3 �e SCF algorithm . . . 81
6.4 �e SCF response algorithm . . . 82
7 ��� ����� 16 ���������� 85 7.1 Methods . . . 85
7.2 Geometries and electric dipole moments . . . 86
7.3 Electric dipole polarizabilities . . . 92
8 ����������� ��� ������������ 97 A��������� 99 � �������� �������� ����������� �� ��� ����������� ��������� ����� 101 �.1 �e Lemma of Integral Representation . . . 101
�.2 Derivation of the IEF-PCM equation . . . 103
�.3 Limiting Behaviours of the IEF-PCM Equation . . . 108
� ������ ������������ ��� ����-���������� ����� ������ 111 �.1 Basic Second Quantization . . . 111
�.2 �e electronic free energy gradient . . . 113
�.3 �e electronic free energy Hessian . . . 114
�.3.1 �eAmatrix . . . 114
�.3.2 �eBmatrix . . . 115
�.4 �e DFT contributions . . . 115
�.5 S-term in the time-averaged quasi-free energy . . . 116
������������ 119
