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I am trying to evaluate 1- and 2-electron integrals using PySCF trough this code:

Hij = mol.intor('int1e_kin') + mol.intor('int1e_nuc')
Vijkl = mol.intor('int2e') 

where I previously defined mol in a particular basis.

I am new in this software and I am reading the basic tutorials that offers the project's site here, but so far I can't find if the elements Vijkl of the 2-electron integrals are define in the chemist's notation, $$ V_{ijkl} = (ij|kl) = \int \frac{\phi^*_i(\mathbf{r}_1)\phi_j(\mathbf{r}_1)\,\phi^*_k(\mathbf{r}_2)\phi_l(\mathbf{r}_2)}{|\mathbf{r}_1 - \mathbf{r}_2|}\,d\mathbf{r}_1d\mathbf{r}_2, $$ or physicist's notation, which is $$ V_{ijkl} = \langle ij|kl \rangle = \int \frac{\phi^*_i(\mathbf{r}_1)\phi_j^*(\mathbf{r}_2)\,\phi_k(\mathbf{r}_1)\phi_l(\mathbf{r}_2)}{|\mathbf{r}_1 - \mathbf{r}_2|}\,d\mathbf{r}_1d\mathbf{r}_2. $$

I am assuming that the program uses chemist's notation. Am I right? And, if so, is it a way to easily convert the array into the other convention? Thank you all in advanced.

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    $\begingroup$ A quick google search with the keywords pyscf chemist notation and electron integrals gave these hits for fci and cc. From these pages, they mention that MO integrals are treated in chemist’s notation. $\endgroup$ Jun 1, 2023 at 5:01
  • $\begingroup$ @HemanthHaridas you can write an answer (please do!) and others can add more answers if they have anything more to add :) $\endgroup$ Jun 1, 2023 at 8:10

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You are right that pyscf uses chemist's notation. A quick google search with the keywords pyscf chemist notation and electron integrals returned these two hits for FCI and CC. Reading through the documentation, it is mentioned that the integrals are treated in chemist's notation.

To address the point that Prof. Dattani made, if you instead search for physicist's notation, you will find that as an argument for this function pyscf.cc.gintermediates.get_t3p2_imds_slow in the page for CC. I also found the mention of physicist's notation in this page.

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    $\begingroup$ What about if you search "pyscf physicist notation"? $\endgroup$ Jun 1, 2023 at 13:49
  • $\begingroup$ Thank you Prof. Dattani for raising an important point. I have added that in the answer. $\endgroup$ Jun 1, 2023 at 15:12

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