Charge dependent Hamiltonian

[awvwgk]

Electrostatic interactions enter DFTB/xTB Hamiltonian as charge dependent energy expression. Allows evaluation of electronic energy, which is calculated from core Hamiltonian, H0 (see #2) and charge-dependent Hamiltonian, H1.

Workflow:

1. solve eigenvalue problem with Hamiltonian
2. obtain density matrix
3. calculate populations / partial charges
4. evaluate (charge-dependent) energy expression
5. obtain potential / field, i.e. derivative of energy expression w.r.t. populations / partial charges (sign convention!)
6. create charge-dependent Hamiltonian
7. repeat until convergence is reached

Fortran reference implementation:

• storage for density matrix, populations / partial charges: src/tblite/wavefunction/type.f90
• population analysis / partial charge calculation from density matrix: src/tblite/wavefunction/mulliken.f90
• container prototype for evaluating (charge-dependent) energy expression: src/tblite/container/type.f90
  • actual implementation of second-order electrostatic energy: src/tblite/coulomb/charge.f90
  • actual implementation of third-order electrostatic energy: src/tblite/coulomb/thirdorder.f90
• evaluation of charge-dependent Hamiltonian: src/tblite/scf/potential.f90
• iterator for converging self-consistent field problem: src/tblite/scf/iterator.f90
  • requires convergence accelerator, usually Broyden mixing: src/tblite/scf/broyden.f90

Note:

• ignore multipole electrostatics (only GFN2-xTB)

[awvwgk]

Now available with #41