Properties

This section containts information about atomic and molecular properties that can be calculated.

Molecular dipole

The molecular dipole in one dimension is found as:

\[\mu_{x}=-\sum_{i}\sum_{j}D_{i,j}\left(i\left|x\right|j\right)+\sum_{A}Z_{A}X_{A}\]

FUNCTION:

  • Properties.dipolemoment(input, D, mux, muy, muz)
  • return ux, uy, uz, u

Input:

  • input, inputfile object
  • D, density matrix
  • mux, dipolemoment integrals in x direction
  • muy, dipolemoment integrals in y direction
  • muz, dipolemoment integrals in z direction

Output:

  • ux, dipolemoment in x direction
  • uy, dipolemoment in y direction
  • uz, dipolemoment in z direction
  • u, total dipolemoment

Refrence:

  • Szabo and Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory

Mulliken charges

The atomic charge of the A’th atom can be found as:

\[q_{A}=Z_{A}-\sum_{i\in A}\left(D\cdot S\right)_{i,i}\]

FUNCTION:

  • Properties.MulCharge(basis, input, D, S)
  • return qvec

Input:

  • basis, basisset object
  • input, inputfile object
  • D, density matrix
  • S, overlap matrix

Output:

  • qvec, vector of Mulliken charges

Refrence:

  • Szabo and Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory

Lowdin charges

The atomic charge of the A’th atom can be found as:

\[q_{A}=Z_{A}-\sum_{i\in A}\left(S^{1/2}\cdot D\cdot S^{1/2}\right)_{i,i}\]

FUNCTION:

  • Properties.LowdinCharge(basis, input, D, S)
  • return qvec

Input:

  • basis, basisset object
  • input, inputfile object
  • D, density matrix
  • S, overlap matrix

Output:

  • qvec, vector of Lowdin charges

Refrence:

  • Szabo and Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory

Random-Phase Approximation Excitation energy

The excitation energies can be calculated by using the random-phase approximation also known as time dependent Hartree-Fock. The exciation energy is found by diagonalizing the following equation:

\[\left(A+B\right)\left(A-B\right)X=E^{2}X\]

with the elements given as:

\[A_{ia,jb}=f_{ab}\delta_{ij}-f_{ij}\delta_{ab}+\left\langle aj\left|\right|ib\right\rangle\]
\[B_{ia,jb}=\left\langle ab\left|\right|ij\right\rangle\]

All of the elements are in spin basis.

FUNCTION:

  • Properties.RPA(occ, F, C, VeeMOspin)
  • return Exc

Input:

  • occ, number of occupied MOs in spinbasis
  • F, fock matrix in spatial basis
  • C, MO coeffcients in spatial basis
  • VeeMOspin, MO integrals in spin basis

Output:

  • Exc, single excitation energies

References: