VertexCoulombIntegrals

Table of Contents

1. Brief description

VertexCoulombIntegrals prepares a recipe needed for the evaluation of Coulomb integrals.

2. Algorithm call

A typical input file snippet to call the VertexCoulombIntegrals algorithm is given below.

- name: VertexCoulombIntegrals
  in:
    slicedCoulombVertex: CoulombVertex
  out:
    coulombIntegrals: CoulombIntegrals

3. Algorithm input

Table 1: Input keywords
Keyword Value
slicedCoulombVertex  

4. Algorithm output

Keyword Value
coulombIntegrals  

4.1. Sample stdout

A sample output of this algorithm reads

step: 8, VertexCoulombIntegrals
number of field variables NF: 2092
realtime 0.001249174 s

4.2. Sample yaml output

A sample yaml output of this algorithm reads

floatingPointOperations: 0
flops: 0
in:
  slicedCoulombVertex: 0x24aee28
name: VertexCoulombIntegrals
out:
  coulombIntegrals: 0x247f2b8
realtime: 0.001078910

5. Computational complexity

Note that the VertexCoulombIntegrals algorithm merely defines a recipe to perform the computation of all integrals. The integrals will only be computed once their numerical values are needed. Certain types of Coulomb integrals; for example, \(V_{cd}^{ab}\) will potentially never be computed if not needed by a later algorithm. In this manner potential memory bottle-necks are avoided.

6. Theory

Coulomb integrals are evaluated using the following expression. \[ V^{pq}_{sr} = \sum_{G} {\Gamma^\ast}^{pG}_s \Gamma^q_{rG} \]

7. Literature

Created: 2022-09-19 Mon 15:00