14 votes
Accepted

How is group theory used to deduce which of these integrals are equal to 0?

The question is too broad to be answered directly so I will provide a somewhat general scheme. Basically in an integral like $$ \int d\mu A B C $$ one would seek to expand each part in irreducible ...
13 votes
Accepted

How are 1-electron and 2-electron integrals done in PySCF?

While this earlier question on our site was asking why fewer 2e- integrals were printed by PySCF than expected, and your question is simply asking how to calculate the 1e- and 2e- integrals in the ...
  • 29.7k
13 votes
Accepted

What programs can do electron integrals and SCF calculations with more than one CPU?

Psi4 and PySCF Psi4 and PySCF are free, open source programs that can do both parallel integrals and SCF. MPI parallellization is quite rare in quantum chemistry codes, since the algorithms don't tend ...
  • 15.7k
13 votes
Accepted

One-center two-electron integrals between 1s STO

Your Octave code is trying to do the integral by quadrature, which makes very little sense since it will have a huge problems with the cusp. Since this is a one-center problem, the best approach is ...
  • 15.7k
10 votes
Accepted

Predicting linear dependencies in a basis set in advance of calculating any integrals

You might be interested to know that I've recently presented a general solution to this problem in Curing basis set overcompleteness with pivoted Cholesky decompositions, J. Chem. Phys. 151, 241102 (...
  • 15.7k
9 votes

How is group theory used to deduce which of these integrals are equal to 0?

First, you have to transform all the basis functions into the irreducible representations (irreps) of the point group of the molecule. You can do this with standard projection formulas. Once, you know ...
  • 1,411
9 votes
Accepted

Exchange-Correlation Two-Electron Integrals

I assume you're referring to eq 51 of the Hirata-Head-Gordon-Bartlett paper. One should note that these are not two-electron integrals, since there is only one spatial position; these are rather ...
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8 votes

One-center two-electron integrals between 1s STO

This can be solved analytically, a complete solution can be found here To refrain from rewriting the entire derivation I will only say that you need to integrate over all 3 dimensional degrees of ...
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8 votes
Accepted

Which software is good with generally contracted basis sets?

General vs segmented contraction Unless one is using a fully decontracted a.k.a "primitive" basis set, one uses contracted Gaussian-type orbitals (cGTOs), which are given as a linear ...
  • 15.7k
8 votes

Which software is good with generally contracted basis sets?

Integral Screening It is possible to place upper bounds on integrals based on the Cauchy-Schwartz inequality: $$ \left( a a | b b \right) \ge \left( a c | b d \right) $$ If the first integral is ...
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7 votes

What programs can do electron integrals and SCF calculations with more than one CPU?

MRCC There are more programs with parallel SCF capability, but it is quite hard to scale SCF (with HF exchange) to large number of cores. MRCC indeed has a recent hybrid multi-node (MPI) & multi-...
6 votes

Which software is good with generally contracted basis sets?

MOLPRO Continuing Susi's excellent benchmarking for $\ce{Zn}$ and $\ce{Zn_2}$, MOLPRO 2012 gives for $\ce{Zn}$: ...
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6 votes

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

AFAIK the standard way is to obtain the memory efficiency at the expense of some code repetition in the innermost loop. A preliminary example goes like: Construct a nested loop that only loops over ...
  • 8,036
5 votes

How are 1-electron and 2-electron integrals done in PySCF?

Here is the code that I currently used. i hope it could be helpful for other's research. To obtain the integrals, the first step is to run a Hartree Fock approximation and check if it has converged. <...
5 votes
Accepted

What is the best algorithm for ERIs of contracted gaussian atomic orbitals

I will consider both your question and the comments to your question in this answer. I understand your motivation is related to making a high school project, you say I would use a package but since ...
5 votes
Accepted

Molecular orbital values on grid points in PySCF?

You can evaluate molecular orbitals on a grid by first evaluating the AOs on the grid with ao = mol.eval_gto('GTOval', coords) and then contracting with the ...
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5 votes

What do the indices mean in an FCIDUMP file?

"I was able to guess most of results, except the ones with value 0.663472." I am able to confirm that your integrals are correct even for the 0.663472 case, because by calculating them ...
  • 29.7k
5 votes

How is group theory used to deduce which of these integrals are equal to 0?

To start with, while it's not as necessary, you can apply symmetry arguments to one-electron integrals. Consider $\langle\mu|O_1|\nu\rangle$, where $O_1$ is some one-electron operator. If the molecule ...
  • 14.4k
4 votes

What programs can do electron integrals and SCF calculations with more than one CPU?

NWChem NWChem is an ideal package for massively parallel needs. JCP recently published a collection of articles focused on the special topic "Electronic Structure Software". Not only NWCHem, ...
  • 946
4 votes

For software that does not support FCIDUMP format, what format is used and how can we get the software to interact with FCIDUMP integrals?

MRCC MRCC stores 1- and 2-electron integrals in an ASCII file called fort.55 which is formatted very similarly to FCIDUMP. The <...
  • 29.7k
4 votes
Accepted

Why is my quantum chemistry software not printing as many 2e- integrals as I expect?

I figured it might be worthwhile to address some the misconceptions in the question, as they are probably fairly common. No SCF prior The AO two-electron integrals (and actually all the AO integrals ...
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4 votes

What do the indices mean in an FCIDUMP file?

I would like to post a partial answer that I have for now. For the indices ijkl in the FCIDUMP file, it corresponds to the integral (see https://theochem.github.io/horton/2.0.2/user_hamiltonian_io....
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4 votes

How is group theory used to deduce which of these integrals are equal to 0?

Boy, you're not starting off easy. Proper implementation of symmetry is quite a job, especially since most systems of interest nowadays have no symmetry. For a reference, you can look at e.g. Dovesi's ...
  • 15.7k
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 ...
  • 8,036
4 votes
Accepted

How to transform the two-dimensional Berry curvature integral into a loop integral along Fermi circle?

If the distribution function has a step discontinuity at the Fermi surface, its derivatives are Dirac delta functions which reduce the integral to one over the Fermi surface. I will illustrate this ...
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4 votes
Accepted

Implementation of one-elecron integrals in a Hartree-Fock program

There is a bunch of errors in your question. First of all you seem to ignore the contraction coefficients in your code snippet. If however you ignore them (set them to 1 and pick only one pair $i,j$), ...
3 votes
Accepted

How to compute the overlap matrix in Python

Here is an updated version of your code that I believe now works. I had to add in a few of the values that were computed elsewhere in your code, but otherwise it is mostly the same. ...
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3 votes
Accepted

How to read data from an input and form two-electrons integral?

I'm not sure how your current code is supposed to work. Focusing just on the first half: ...
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3 votes

PySCF: 2-index and 3-index matrix

In the density fitting / resolution-of-the-identity (RI) formalism, a two-electron integral $(ij|kl)$ in the atomic-orbital basis is approximated as $(ij|kl) \approx \sum_{PQ} (ij|P) (P|Q)^{-1} (Q|kl)$...
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3 votes

For software that does not support FCIDUMP format, what format is used and how can we get the software to interact with FCIDUMP integrals?

GAMESS(US) has this facility implemented, but this feature may not be available in the public release.

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