# 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: