contracted_gaussian

class contracted_gaussian.ContractedGaussian(exponents=array([0.5]), coefficients=array([1.0]), origin=array([0.0, 0.0, 0.0]), l=array([0, 0, 0], dtype=int32))

Defines a linear combination of Cartesian Gaussian type orbitals GTO.

A contracted Gaussian function is just a linear combination of primitive Gaussians (also termed primitives) centered at the same center \({\bf A}\) and with the same momentum indices \({\bf n}\) but with different exponents \(\zeta_i\):

\(\phi ({\bf r}; {\bf \zeta}, {\bf C}, {\bf n}, {\bf A}) = (x - A_x)^{n_x} (y - A_y)^{n_y} (z - A_z)^{n_z} \times \sum_{i=1}^M C_i \exp[-\zeta_i ({\bf r}-{\bf A})^2]\)

Contracted Gaussians form shells the same way as primitives. The contraction coefficients \(\bf C\) already include normalization constants so that the resulting combination is properly normalized. Published contraction coefficients \(\bf c\) are linear coefficients for normalized primitives, hence the normalization-including contraction coefficients \(\bf C\) have to be computed from them as;

\(C_i = c_i N(\zeta_i,{\bf n})\)

where \(N\) is:

\(N = \dfrac{1}{\sqrt{<\phi | \phi>}}\)

Parameters

  • exponents (ndarray) – GTO exponent.

  • coefficients (ndarray) – GTO coefficients.

  • origin (ndarray) – coordinates (cartesian)

  • l (ndarray) – \(\bf n\). Angular moment (x, y, and z components)

compute(coord)

Computes the value of the contracted Gaussian at coord.

Parameters

  • coord (ndarray) – array with the points where the function will be

  • calculated. –

property l

The angular moment of the object

property origin

The center of the function

overlap(other)

Calculates the overlap integral between two contractions.

Parameters

other (ContractedGaussian) – Contracted function to perform \(<\phi_{self} | \phi_{other}>\)