DePrince Lab


The Hartree-Fock Self-Consistent Field Procedure



Overview


Hartree-Fock theory holds a special place in quantum chemistry, as it forms the mathematical foundation for molecular orbital theory and is also a starting point for many other, more sophisticated electronic structure theories. This project provides an overview of the theoretical aspects of the Hartree-Fock approach and a detailed derivation of the Hartree-Fock-Roothaan equations. Python code for an unrestricted Hartree-Fock solver is provided, with all of the required integrals taken from the Psi4 electronic structure package. The outline of the project is

  1. The Electronic Hamiltonian
  2. Slater Determinants
  3. The Hartree-Fock-Roothaan Equations
  4. Spin and Unrestricted Hartree-Fock (UHF) Theory
  5. The UHF Procedure
    • Obtain Required Integrals
    • Symmetric Orthogonalization
    • Construct Guess Orbitals and Density
    • Iterating Toward Convergence
  6. Convergence Acceleration
  7. Convergence to the Complete Basis Set Limit
  8. Breaking Spin Symmetry

You can download the Jupyter notebook for this project here. test