2. Defining Basis Sets, Molecular Geometries, and Hamiltonians

• 2.1. Preliminaries
• 2.2. Molecular Hamiltonians
  • 2.2.1. Specifying the molecular geometry
    • 2.2.1.1. Reading the molecular geometry from file
    • 2.2.1.2. Constructing a molecular geometry from scratch
  • 2.2.2. Specifying the atomic basis set
    • 2.2.2.1. Supported atomic basis sets in the PyBEST basis set library
    • 2.2.2.2. The same basis set for different atoms
    • 2.2.2.3. Loading user-defined basis sets from file
    • 2.2.2.4. Loading geometry and basis set information from another file or external program
  • 2.2.3. Specifying dummy or ghost atoms and active fragments
    • 2.2.3.1. Dummy or ghost atoms
    • 2.2.3.2. Active fragments
    • 2.2.3.3. Combining ghost atoms and active fragments
  • 2.2.4. Computing the matrix representation of the Hamiltonian
    • 2.2.4.1. The Schrödinger Hamiltonian
    • 2.2.4.2. The DKH Hamiltonian
  • 2.2.5. Computing the overlap matrix and defining the orbitals
  • 2.2.6. Computing the multipole moment integrals
  • 2.2.7. Example Python script
    • 2.2.7.1. The molecular Hamiltonian for the water molecule
• 2.3. Model Hamiltonians
  • 2.3.1. Supported features
  • 2.3.2. The Hubbard model Hamiltonian
    • 2.3.2.1. Preliminaries
    • 2.3.2.2. Defining the Hamiltonian and boundary conditions (open or periodic)
    • 2.3.2.3. Filling the lattice
    • 2.3.2.4. Generating the orbital basis and the overlap matrix
  • 2.3.3. Example Python script
    • 2.3.3.1. The 1-dim Hubbard model Hamiltonian with PBC
• 2.4. Dumping/Loading a Hamiltonian to/from a file
  • 2.4.1. PyBEST’s internal format
    • 2.4.1.1. Dumping
    • 2.4.1.2. Loading
  • 2.4.2. FCIDUMP format
    • 2.4.2.1. Dumping
    • 2.4.2.2. Loading
  • 2.4.3. Example Python scripts
    • 2.4.3.1. Dumping in the FCIDUMP format: the Ne dimer
• 2.5. The AO/MO Transformation of the Hamiltonian
  • 2.5.1. Transform integrals for restricted orbitals
  • 2.5.2. Transform integrals for unrestricted orbitals
• 2.6. Defining an Active Space Hamiltonian
  • 2.6.1. Defining the molecular Hamiltonian for an active orbital space
  • 2.6.2. Dumping the active space Hamiltonian to disk
• 2.7. List of Supported One- and Two-Electron Integrals
  • 2.7.1. One-electron integrals
  • 2.7.2. Two-electron integrals