3. Defining Basis Sets, Molecular Geometries, and Hamiltonians

• 3.1. Preliminaries
• 3.2. Molecular Hamiltonians
  • 3.2.1. Specifying the molecular geometry
    • 3.2.1.1. Reading the molecular geometry from file
    • 3.2.1.2. Constructing a molecular geometry from scratch
  • 3.2.2. Specifying the atomic basis set
    • 3.2.2.1. Supported atomic basis sets in the PyBEST basis set library
    • 3.2.2.2. The same basis set for different atoms
    • 3.2.2.3. Loading user-defined basis sets from file
    • 3.2.2.4. Loading geometry and basis set information from another file or external program
  • 3.2.3. Loading point charges and embedding potentials from another file
    • 3.2.3.1. Point charges
    • 3.2.3.2. Embedding potential
  • 3.2.4. Specifying dummy or ghost atoms and active fragments
    • 3.2.4.1. Dummy or ghost atoms
    • 3.2.4.2. Active fragments
    • 3.2.4.3. Combining ghost atoms and active fragments
  • 3.2.5. Computing the matrix representation of the Hamiltonian
    • 3.2.5.1. The Schrödinger Hamiltonian
    • 3.2.5.2. The DKH Hamiltonian
    • 3.2.5.3. The X2C Hamiltonian
  • 3.2.6. Computing the overlap matrix and defining the orbitals
  • 3.2.7. Computing the multipole moment integrals
  • 3.2.8. Example Python script
    • 3.2.8.1. The molecular Hamiltonian for the water molecule
    • 3.2.8.2. The DKH2 Hamiltonian for the hydrogen molecule
    • 3.2.8.3. The X2C Hamiltonian for the hydrogen molecule
    • 3.2.8.4. The DKH2 Hamiltonian, dipole moment integrals, and point charges
• 3.3. Model Hamiltonians
  • 3.3.1. Supported Features
  • 3.3.2. Preliminaries
  • 3.3.3. Computing the Hamiltonian
    • 3.3.3.1. Specifying Model Hamiltonian Parameters
  • 3.3.4. Hückel Hamiltonian
    • 3.3.4.1. Usage Example
  • 3.3.5. Hubbard Hamiltonian
    • 3.3.5.1. Usage Example
  • 3.3.6. PPP Hamiltonian
    • 3.3.6.1. Usage Example
    • 3.3.6.2. Dipole Moment
  • 3.3.7. Contact Interaction Hamiltonian
    • 3.3.7.1. Usage Example
  • 3.3.8. Example Python script
    • 3.3.8.1. The Hückel Model
    • 3.3.8.2. The Hubbard Model
    • 3.3.8.3. The 1D-Hubbard Model
    • 3.3.8.4. The PPP Model
    • 3.3.8.5. The 1D Contact Interaction Model
• 3.4. Dumping/Loading a Hamiltonian to/from a file
  • 3.4.1. PyBEST’s internal format
    • 3.4.1.1. Dumping
    • 3.4.1.2. Loading
  • 3.4.2. FCIDUMP format
    • 3.4.2.1. Dumping
    • 3.4.2.2. Loading
  • 3.4.3. Example Python scripts
    • 3.4.3.1. Dumping in the FCIDUMP format: the Ne dimer
• 3.5. The AO/MO Transformation of the Hamiltonian
  • 3.5.1. Transform integrals for restricted orbitals
  • 3.5.2. Transform integrals for unrestricted orbitals
• 3.6. Defining an Active Space Hamiltonian
  • 3.6.1. Defining the molecular Hamiltonian for an active orbital space
  • 3.6.2. Dumping the active space Hamiltonian to disk
• 3.7. List of Supported One- and Two-Electron Integrals
  • 3.7.1. One-electron integrals
  • 3.7.2. Two-electron integrals