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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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 ...
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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:
$$\chi = \sum_i c_i \...
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Implementation of one-elecron integrals in a Hartree-Fock program
Absolute newbie in quantum chemistry here. I was recently looking through some Fortran libraries from my university to see if I understand all of the mathematics. In a Hartree-Fock library, I found ...
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How to read two electron integrals from pyscf
This is a follow-up question to this one I asked a few days ago. I in the meantime talked to my teacher and generate all the necessary integrals in PySCF. For the one electron integrals that isn't an ...
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What is the best algorithm for ERIs of contracted gaussian atomic orbitals
I am currently working on python script that does Hartree-Fock-Calculations. I try to avoid packages as good as possible. I've figured out how to calculate the one electron integrals when it comes to ...
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Molecular orbital values on grid points in PySCF?
I am looking for a way to easily evaluate individual molecular orbitals on a grid(assuming a single determinant method for now) in PySCF.
I am aware on how to generate efficient grids for real-space ...
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How to transform the two-dimensional Berry curvature integral into a loop integral along Fermi circle?
The Hall conductivity is given by
$$\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} $$
in which $f$ is the Fermi distribution function and ...
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Rys Quadrature method for integrating over Gaussian basis functions: 1D integral recursion relation [closed]
I'm trying to implement the Rys Quadrature method for integrations of Gaussians, from scratch. I'm using this paper as a reference.
So, how does the overall recursion relation for evaluating 1D ...
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Evaluating Coulomb and exchange integrals in practice using cartesian coordinates [closed]
Many software packages provide means to calculate the Coulomb and exchange integrals, for example, the exchange
$$\int \phi^*(1) \, \psi^*(2) \frac{1}{|\mathbf{r_1} - \mathbf{r_2}|} \, \psi(1) \, \phi(...
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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
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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 ...
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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 ...
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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 ...
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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
$$-\left\...
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How are 1-electron and 2-electron integrals done in PySCF?
I am right now using the PySCF for some quantum chemistry problems. I need to get the parameters, which are labeled $h_{ij}$ and $V_{ijkl}$. How can I get this done with PySCF?
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Which software is good with generally contracted basis sets?
Recently, I learnt that basis sets can be contracted as segmented (like def2 or 6-31G) or general (like cc-PVTZ, or ANO). The general contraction allows all the primitives to appear in all shells, ...
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PySCF: 2-index and 3-index matrix
The 4-index 2-electron integral can be obtained for the He atom with the following code:
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Why is my quantum chemistry software not printing as many 2e- integrals as I expect?
Background:
In Hartree-Fock theory, the two-electron integral is given by:
$[ij|kl]$ = $\int dx_{1}dx_{2}(\chi_{i}(x_{1})\chi_{j}(x_{1})\frac{1}{r_{12}}\chi_{k}^{*}(x_2)\chi_{l}(x_{2})$
I am ...
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What do the indices mean in an FCIDUMP file?
I generated an FCIDUMP file, which is copied below
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How is group theory used to deduce which of these integrals are equal to 0?
The number of all two-electron integrals:
$$
\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 ...
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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 ...
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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.
...
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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)...
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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 ...
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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, ...
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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 ...
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