quemb.molbe.sparse_2el_integral.TwoElIntegral

class quemb.molbe.sparse_2el_integral.TwoElIntegral

Sparsely stores the 2-electron integrals using chemist’s notation.

This is a jitclass which can be used with numba functions.

8-fold permutational symmetry is assumed for the spatial integrals, i.e.

\[g_{ijkl} = g_{klij} = g_{jikl} = g_{jilk} = g_{lkji} = g_{lkij} = g_{ilkj} = g_{ikjl}\]

There is no boundary checking! It will not crash, but just return 0.0 if you try to access an index that is not in the dictionary.

The 2-electron integrals are stored in a dictionary. The keys of the dictionary are tuples of the form (i, j, k, l) where i, j, k, l are the indices of the basis functions. The values of the dictionary are the 2-electron integrals.

Examples

>>> g = TwoElIntegral()
>>> g[1, 2, 3, 4] = 3

We can test all possible permutations:

>>> assert g[1, 2, 3, 4] == 3
>>> assert g[1, 2, 4, 3] == 3
>>> assert g[2, 1, 3, 4] == 3
>>> assert g[2, 1, 4, 3] == 3
>>> assert g[3, 4, 1, 2] == 3
>>> assert g[4, 3, 1, 2] == 3
>>> assert g[3, 4, 2, 1] == 3
>>> assert g[4, 3, 2, 1] == 3

A non-existing index returns 0.0:

>>> assert g[1, 2, 3, 10] == 0

Attributes

class_type = jitclass.TwoElIntegral#7f3741acebd0<_data:DictType[int64,float64]<iv=None>>

Methods

__init__()
compound(b, c, d)	Return compound index given four indices using Yoshimine sort