14
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 ...
- 33.6k
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 ...
- 256
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 ...
- 18k
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 ...
- 18k
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 (...
- 18k
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 ...
- 18k
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 ...
- 1,431
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 ...
- 7,957
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 ...
- 18k
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 ...
- 1,643
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-...
- 206
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 ...
- 9,076
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 $\ce{Zn}$:
...
- 33.6k
6
votes
Accepted
Inputting custom STO-3G basis into PySCF
Instead of:
basis = STO-3G
you can get PySCF to read your own "custom" basis set file, for example:
...
- 33.6k
6
votes
Does PySCF use chemist's or physicist's notation for 1- and 2-electron integrals?
You are right that pyscf uses chemist's notation. A quick google search with the keywords pyscf chemist notation and ...
- 2,742
6
votes
Accepted
How are 2-electron integrals usually computed?
Integral calculation is discussed extensively in the book Molecular Electronic-Structure Theory by Helgaker, Jørgensen, and Olsen.
2-electron integrals are usually computed analytically with the ...
- 18k
6
votes
Accepted
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:
...
- 9,076
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 ...
- 33.6k
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 ...
- 15.2k
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.
<...
- 435
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 ...
- 385
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 ...
- 18k
5
votes
Reintegrate calculation results from ORCA using finer grid?
We have discussed the reproducibility of DFT calculations recently in
J. Chem. Phys. 159, 114116 (2023). The calculations in J. Am. Chem. Soc. 145, 9273–9284 (2023) were carried out with the B3LYP ...
- 18k
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 <...
4
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 $(ij|kl) \approx \sum_{PQ} (ij|P) (P|Q)^{-1} (Q|kl)$...
- 18k
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 ...
- 15.2k
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....
- 231
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 ...
- 18k
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 ...
- 9,076
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