# 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.

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### How are 2-electron integrals usually computed?

I want to compute 2-electron coulomb integrals. When the Primitive Gaussian is not centered at 0, my quadrature scheme fails unless I increase the number of quadrature points. I am currently using a ...
145 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 ...
752 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 ...
948 views

### How to compute the overlap matrix in Python

I want to calculate the overlap integral (S), I made the code, but it is only worked when I use a basis function that describe 1s and when I include 2s orbital, I start to get error. The First Problem ...
81 views

### Analytical derivative of nuclear-electron attraction integrals over gaussian functions

I'm currently writing a program which evaluates the first derivatives of molecular integrals (over gaussian basis sets) with respect to the cartesian coordinates of the nucleus. I'm somewhat stuck ...
71 views

### Reintegrate calculation results from ORCA using finer grid?

I have made a bunch of calculations in ORCA to compare them to results from this paper. The original calculations from this paper were done in TurboMole. I tried to recreate the method as best I could ...
203 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 ...
168 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 ...
122 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 ...
262 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: ...
44 views

### Correct expressions for one-center Gaussian radial two-electron integrals

I am working on a new atomic solver library, for which I need expressions for the one-center two-electron integrals. Pitzer has furnished the necessary expressions for Slater-type and Gaussian-type ...
42 views

### How can I get 2c2e and 3c2e integrals using the erf kernel in PySCF? [closed]

I want to reproduce the calculation procedure of density fitting in PySCF. I know how to get the 2c2e/3c2e integrals matrix/tensor with $1/r_{12}$ kernel by using ...
268 views

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### Molecular integrals in spherical harmonics?

I have been trying to write a basic HF code that can compute the MOs and total energy of a molecule. I followed the following reference for overlap and kinetic integrals. During a conversation with a ...
223 views

### Becke partitioning : Computing integrals with Lebedev and Gauss-Chebyshev quadrature

Preface: This question is a follow up post from a previous question on MMSE: Usual way of computing exchange-correlation potential on a simple case H2 (RHF, LDA). The radial variable substitution and ...
25 views

### PySCF two-electron integrals between two fragments

I am trying to compute integrals of the form $(pq|rs)$ where the orbitals $p$ and $q$ are orthogonalized atomic orbitals for a fragment $A$ and $r,s$ are orthogonalized on fragment $B$. I was thinking ...
59 views

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