# Questions tagged [integrals]

For 1- and 2-electron integrals in electronic structure calculations, before Hartree-Fock or some other type of self-consistent-field calculation, or the integral transformation which is done after HF or SCF.

24 questions
Filter by
Sorted by
Tagged with
106 views

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

Absolute newbie in quantum chemistry here. I was recently looking through some Fortran libraries from my university to see if I understand all of the mathematics. In a Hartree-Fock library, I found ...
• 53
67 views

### How to read two electron integrals from pyscf

This is a follow-up question to this one I asked a few days ago. I in the meantime talked to my teacher and generate all the necessary integrals in PySCF. For the one electron integrals that isn't an ...
• 125
91 views

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

I am currently working on python script that does Hartree-Fock-Calculations. I try to avoid packages as good as possible. I've figured out how to calculate the one electron integrals when it comes to ...
• 125
97 views

### Molecular orbital values on grid points in PySCF?

I am looking for a way to easily evaluate individual molecular orbitals on a grid(assuming a single determinant method for now) in PySCF. I am aware on how to generate efficient grids for real-space ...
• 178
75 views

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

The Hall conductivity is given by $$\sigma_{xy}^{2D}=\frac{e^2}{\hbar} \int \frac{d\vec{k}}{(2\pi)^d} f(\epsilon(\vec{k}))\Omega_{k_xk_y} \tag{1}$$ in which $f$ is the Fermi distribution function and ...
• 14k
41 views

### Rys Quadrature method for integrating over Gaussian basis functions: 1D integral recursion relation

I'm trying to implement the Rys Quadrature method for integrations of Gaussians, from scratch. I'm using this paper as a reference. So, how does the overall recursion relation for evaluating 1D ...
144 views

• 3,937
969 views

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

I am right now using the PySCF for some quantum chemistry problems. I need to get the parameters, which are labeled $h_{ij}$ and $V_{ijkl}$. How can I get this done with PySCF?
• 425
1k views

### Which software is good with generally contracted basis sets?

Recently, I learnt that basis sets can be contracted as segmented (like def2 or 6-31G) or general (like cc-PVTZ, or ANO). The general contraction allows all the primitives to appear in all shells, ...
• 5,834
144 views

### PySCF: 2-index and 3-index matrix

The 4-index 2-electron integral can be obtained for the He atom with the following code: ...
• 1,829
481 views

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

Background: In Hartree-Fock theory, the two-electron integral is given by: $[ij|kl]$ = $\int dx_{1}dx_{2}(\chi_{i}(x_{1})\chi_{j}(x_{1})\frac{1}{r_{12}}\chi_{k}^{*}(x_2)\chi_{l}(x_{2})$ I am ...
• 1,829
296 views

### What do the indices mean in an FCIDUMP file?

I generated an FCIDUMP file, which is copied below ...
• 221
491 views

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

The number of all two-electron integrals:  \tag{1} \langle \phi_1 \phi_2|\phi_3\phi_4 \rangle = \int d^3\mathbf r' \int d^3\mathbf r'' \, \phi_1(\mathbf r'') \, \phi_2(\mathbf r') \frac{1}{|\mathbf ...
• 595
129 views

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

Complementary to this question: How do the various programs read or write integrals in FCIDUMP format? which attempts to list all electronic structure packages that support the ...
• 29.1k
268 views

### How do the various programs read or write integrals in FCIDUMP format?

The FCIDUMP format was created by Peter Knowles and Nick Handy circa 1989 and now allows many electronic structure software packages to interact with each other. ...
• 29.1k
356 views

### One-center two-electron integrals between 1s STO

As per @user1271772 's suggestion I am asking this question here again. I am trying to understand SCF cycle by trying to code up solved example from Quantum Chemistry by Levine (page 443, 5th edition)...
• 305
185 views

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

I've been doing some calculations for a water molecule, with a big uncontracted basis set: For oxygen I am using aug-cc-pV9Z supplemented with the "tight" functions from cc-pCV7Z. The s-type exponents ...
• 29.1k