High accuracy calculations on coulombic few particle systems in a basis of explicitly correlated gaussian functions

9 CHAPTER 1: INTRODUCTION 10 LI Explicitly Correlated Gaussian Basis Functions 10 1.2 Non-Born-Oppenheimer Calculations 13 1.3 Overview of Current Work 14 1.4 A Note on Mathematical Background 15 CHAPTER 2: SPIN-FREE HAMILTONIAN FOR COULOMBIC SYSTEMS 17 2.1 Non-Relativistic Hamiltonian 17 2.2 The Dipole Approximation 18 2.3 Transformation to Center of Mass Coordinates 19 2.4 Adiabatic and Born-Oppenheimer Approximations 21 CHAPTER 3: THE CORRELATED GAUSSIAN BASIS SET 24 3.1 Expansion of the Wave Function 24 3.2 Point Group Symmetry of Born-Oppenheimer Molecules 26 3.3 Projection onto the Irreducible Representations of the n-th Order Symmetric Group 26 3.4 Projection Operators obtained by the Operator Method 30 3.5 Projection Operators obtained by the Representation Method ... 31 3.6 Decomposition of in Cosets of S„-i 33 3.7 Effects of Permutations on Basis Functions 33 3.8 Born-Oppenheimer Integrals Over Correlated Gaussians 35