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.
36
questions
19
votes
4
answers
686
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
18
votes
1
answer
355
views
Exchange-Correlation Two-Electron Integrals
Do any freely available or proprietary electronic structure packages explicitly compute two-electron exchange correlation integrals?
I have found a few derivations to calculate excited state ...
- 15.2k
12
votes
2
answers
579
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)...
- 481
11
votes
2
answers
2k
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?
- 435
11
votes
1
answer
234
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 ...
- 33.6k
9
votes
4
answers
508
views
What programs can do electron integrals and SCF calculations with more than one CPU?
Similar to this question which asks for each answer to provide one software that can do CASSCF: I am interested in software that can do integrals, SCF (Hartree-Fock), and the integral transformation, ...
- 407
9
votes
3
answers
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, ...
- 6,591
9
votes
2
answers
559
views
What do the indices mean in an FCIDUMP file?
I generated an FCIDUMP file, which is copied below
...
- 231
9
votes
0
answers
182
views
Interacting with pyscf integral library from Fortran [closed]
I would like to use libcint, the integral library in pyscf from Fortran. Its webpage has a Fortran API and developer manual, but ...
- 182
8
votes
1
answer
339
views
Does PySCF use chemist's or physicist's notation for 1- and 2-electron integrals?
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')
...
8
votes
1
answer
140
views
How to read data from an input and form two-electrons integral?
I am doing a code that can calculate the hartree-fock energy. I want to form the two-electrons integral by reading the data from the input like this one below. The first four number are the indices ...
- 1,285
8
votes
1
answer
398
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.
...
- 33.6k
7
votes
1
answer
292
views
Exploiting 8-fold symmetry of ERI tensor for building Coulomb and Exchange matrices
I'm trying to write a restricted Hartree Fock code in Fortran that reads in a file of zeroth-iteration 1 and 2 electron integrals (FCIDUMP format) and uses them to do the SCF procedure from an initial ...
user4763
7
votes
0
answers
295
views
Evaluating Coulomb and exchange integrals in practice using cartesian coordinates [closed]
Many software packages provide means to calculate the Coulomb and exchange integrals, for example, the exchange
$$\int \phi^*(1) \, \psi^*(2) \frac{1}{|\mathbf{r_1} - \mathbf{r_2}|} \, \psi(1) \, \phi(...
- 593
6
votes
1
answer
122
views
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 ...
- 723
6
votes
1
answer
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 ...
- 14.9k
6
votes
1
answer
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 ...
- 2,015
6
votes
1
answer
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 ...
- 1,285
6
votes
2
answers
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 ...
- 133
5
votes
2
answers
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 ...
- 443
5
votes
2
answers
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 ...
- 33.6k
5
votes
1
answer
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 ...
- 125
5
votes
1
answer
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 ...
- 53
5
votes
1
answer
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:
...
- 2,015
5
votes
1
answer
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 ...
- 18k
5
votes
0
answers
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 ...
- 51
4
votes
1
answer
268
views
Inputting custom STO-3G basis into PySCF
A simple question about PySCF, but nonetheless I could not find out how to do it: I have a system of atoms for which I already calculated a STO-3G basis in the usual form of MOs:
$$\chi = \sum_i c_i \...
- 95
4
votes
1
answer
473
views
Molecular orbital values on grid points in PySCF?
I am looking for a way to easily evaluate individual molecular orbitals on a grid(assuming a single determinant method for now) in PySCF.
I am aware on how to generate efficient grids for real-space ...
- 400
4
votes
0
answers
77
views
Rys Quadrature method for integrating over Gaussian basis functions: 1D integral recursion relation [closed]
I'm trying to implement the Rys Quadrature method for integrations of Gaussians, from scratch. I'm using this paper as a reference.
So, how does the overall recursion relation for evaluating 1D ...
- 133
3
votes
1
answer
118
views
Simplifying double integrals of isotropic functions
Cross-posted from physics SE.
I am studying statistical mechanics, and I am studying ideas surrounding potential of mean force and n-body density functions.
In a derivation, they mention that
$$-\left\...
- 4,141
3
votes
1
answer
75
views
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 ...
- 2,762
3
votes
2
answers
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 ...
- 723
2
votes
0
answers
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 ...
- 400
2
votes
0
answers
59
views
2
votes
0
answers
378
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
1
vote
1
answer
270
views
PySCF: How to do CCSD calculations from an FCIDUMP file in HDF5 format?
Recently my question: Why does CCSD work, but not CCSD(T), after reading an FCIDUMP in PySCF? lead to a bug fix that allows users to do CCSD(T) calculations from an FCIDUMP file in PySCF. That was ...
- 33.6k