GaInt 0.1.0

GaInt is the abbreviation of Gaussian Integral, it is a python package for the non-normalizecd molecular integrals over Primitive Cartesian Gaussian orbitals. This is a particularly naive implementation in python: little attempt is made to conserve memory or CPU time. Nevertheless, it is useful for small test calculations, in particular for investigating ideas quantum chemistry.

To begin a quantum chemistry calculation, first build the Hamiltonian of a system. In terms of second quantization operators, a time-independent non-relativistic Hamiltonian gives:

\(H = - \sum_{ij} t_{ij}\hat{c}^{\dagger}_{i}\hat{c}_{j} + \frac{1}{2} \sum_{ijkl} V_{ijkl}\hat{c}^{\dagger}_{i}\hat{c}^{\dagger}_{k}\hat{c}_{l}\hat{c}_{j}\)

There are many integration schemes including McMurchie–Davidson, Obara–Saika and Rys schemes. Here Obara-Saika and McMurchie–Davidson scheme is shown in this note.

Contents

USER DOCUMENTATION:

• 1. Installation
  • 1.1. Prerequisites
  • 1.2. Compiling from source code
• 2. Molecule
  • 2.1. Build
  • 2.2. Geometry Methods
  • 2.3. Point Group
• 3. Basis Set
  • 3.1. Primitive Gaussian Type Orbital
• 4. Mcmurchie Davidson Scheme
  • 4.1. Overlap
  • 4.2. Kinetic
  • 4.3. Nuclear Attraction
  • 4.4. Electron Repulsion
• 5. Obara Saika Scheme
  • 5.1. Overlap
  • 5.2. Kinetic
  • 5.3. Nuclear Attraction
  • 5.4. Electron Repulsion

Indices and tables

• Index

• Module Index