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
| 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. \[ V^{pq}_{sr} = \sum_{G} {\Gamma^\ast}^{pG}_s \Gamma^q_{rG} \]