primitive_gaussian

class primitive_gaussian.PrimitiveGaussian(exponent=0.0, coefficient=1.0, l=array([0, 0, 0], dtype=int32), origin=array([0.0, 0.0, 0.0]))

Defines a Cartesian primitive Gaussian type orbital (GTO).

Following Obara and Saika (1986) we write an unnormalized primitive Cartesian Gaussian function centered at \(\bf A\) as

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

where \({\bf r}\) is the coordinate vector of the electron, \(\zeta\) is the orbital exponent, and \(\bf n\) is a set of non-negative integers. The sum of \(n_x\), \(n_y\), and \(n_z\) is denoted as \(\bf n\) and be referred to as the angular momentum or orbital quantum number of the Gaussian function.

Parameters

• exponent (double) – GTO exponent.

• coefficient (double) – GTO coefficients.

• origin (ndarray) – coordinates (cartesian)

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

compute(coord)

Computes the value of the object at coord.

property l

The angular moment of the object

property origin

The center of the function

overlap(other)

Calculates analytically the overlap integral between two primitives.

Parameters

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