I am new to PSI4 and do not really understand if I can use PSI4 for solving my problem. I calculated analytically transition amplitudes with Slater Condon rules. Now I am looking for a possibility to solve my matrix elements. I will be very thankful for any advice how to do this.

I don’t understand the question. Depending on what the operator is, Psi4 can (probably) give you the integrals. Is that what you’re looking for? If so, what operator is this? If not, I need more context about the question. In particular, where is this wavefunction coming from, and what is the “big picture” problem?

Sounds good if PSI4 can give me the integrals. I used HF but the only operator which survives is the Coulomb operator. It is a transition from a 1h state to a 1p-2h State. The matrix Elements are part of the formula for the decay rate so it will be usefull for me to have a value for it. That ist the reason why I want to solve the integrals.

This sounds like a photoelectron study. While I’m not an expert, I will warn you that assuming the same set of orbitals is a quantiatively accurate approximation for multiple electronic states sounds very risky to me. If you haven’t already, check for an existing method that does what you need.

How are you determining your molecular orbitals? Are you getting these from Psi, or do you have the MO coefficients in the AO basis from some independent source?

Yes, it is. In the moment the wave functions are only described by second quantizatin. I am still looking for a way how to go on and I thought that I can get the atomic orbitals from Psi4?! I do not know if that is a good Idea. Do you suggest something else?

Assuming you want to go this route (and again, make sure there isn’t a better way to compute this number!), Psi should be fine for getting the MOs. I just needed to double-check that before I could give detailed instructions. The post I linked below gives instructions for getting the alpha alpha alpha alpha block of orbitals. I imagine you have UHF wavefunctions, so replace ca with cb to turn an alpha to a beta. The ERIs are integrals and thus not antisymmetrized. They are in chemist’s notation, for orbital indexing.

While I’m at it, I also renamed the topic title, since your question isn’t about the Slater-Condon rules.

Okay. It will take some time until I can try it. At first I have to get familiar with Psi4. But then I will mark the topic as solved. Thanks for your advice and your help.

Your code really does what I want and thanks to your explanations and the tutorial I can understand what every line of the code do but nevertheless I do not understand it in much detail. In the tutorial for integrals the Obara-Saika scheme is applied which makes the script for me only more complicated and confusing. I cannot really figure your code out of this tutorial. Do you know some other tutorials or literature which explain your approach?

You don’t need the integrals tutorial for your problem. That tutorial is about computing integrals yourself. You want to let Psi do that for you. Look at the first three tutorials instead.