# Tag Info

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### 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 ...
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### 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
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### 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 ...
• 19.8k
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### 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 ...
• 19.8k
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### 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 (...
• 19.8k

### 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 ...
• 8,017
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### 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 ...
• 19.8k

### 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
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### 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 ...
• 19.8k

### 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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### 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. <...
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### 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-...
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### 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 <...

### 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 $\ce{Zn}$: ...

### 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 ...
• 9,710
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### 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: ...

### 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 ...
• 4,017
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### 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 ...
• 19.8k
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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: ...
• 9,710
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### 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 ...
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### 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 ...
• 19.8k

### 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 ...

### 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 ...
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### 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 $(ij|kl) \approx \sum_{PQ} (ij|P) (P|Q)^{-1} (Q|kl)$...
• 19.8k
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### 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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### 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 ...
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### Using the same input (MINP) file, why does MRCC fail with a "normal" fort.55 file, but succeeds with a longer fort.55 file that has duplicate entries?

The good news I got MRCC working properly with your first fort.55 file, by a very small modification of your MINP file. ...

### 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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