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For 1- and 2-electron integrals in electronic structure calculations, before Hartree-Fock or some other type of self-consistent-field calculation, or the integral transformation which is done after HF or SCF.

6 votes
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Reintegrate calculation results from ORCA using finer grid?

The standard solution is to run a new ORCA calculation with a larger grid, and read your current wavefunction (from the GBW files that you got) as initial guess: ! (level of theory etc...) ! DefGrid3 …
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6 votes

Exploiting 8-fold symmetry of ERI tensor for building Coulomb and Exchange matrices

The above tricks (plus OpenMP parallelization) should already give you a code that rivals the best codes in terms of efficiency (but note that the contraction of integrals with density matrix elements … is usually not the rate-determining step; rather, the bottleneck is usually the calculation of the integrals and/or the I/O of the FCIDUMP file), at least for molecules that are small enough such that …
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4 votes

Simplifying double integrals of isotropic functions

The work is a single integral over $|r_1-r_2|$, not a double integral over $r_1$ and $r_2$. As you are fixing particle 1, you shouldn't integrate over particle 1. Moreover, the work is $w(r) = \int Fd …
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