Questions tagged [hartree-fock]

For any questions about (or related to) the Hartree-Fock method.

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What is the physical meaning of the term "non-local interaction"?

This term pops up through out Hartree-Fock and DFT. Does this term have any physical significance to actual(real) system or it is a mathematical by-product?
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Continuously-varying Hartree-Fock transition matrix?

Suppose we have a parametrized molecular Hamiltonian $H(R)$, where $R$ are the nuclear coordinates. If we let $B(R)$ be some chosen atomic basis set (like STO-3G) centred at $R$, then using $B(R)$, we ...
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4 votes
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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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Is it possible to obtain the current-voltage characteristic for a crystal using the Hartree–Fock (or DFT) calculation?

In continuation of the question of obtaining an electrical conductivity tensor (ECT) from the “first characteristics”, will my following suggestion be correct? Since a crystal with an applied-to-it ...
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Simple question about Hartree-Fock algorithm

Classically in Hartree-Fock implementations we define the wave-function in term of a basis set: $$\phi_i = \sum_{\alpha} C_{\alpha i}\chi_\alpha$$ If I understand correctly the problem is reduced to ...
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Can the electrical conductivity tensor of a crystal be obtained from a Hartree-Fock calculation?

Let’s assume that a crystal has been calculated by Hartree–Fock (HF) method (or DFT one), i.d., so to speak, the "first characteristics", which are eigenvalues and eigenvectors, as well as ...
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In which part of the Hartree–Fock algorithm (or DFT one) could a neural network be most effectively used?

I understand that the task of implementing machine learning in DFT and Hartree–Fock (HF) algorithm has already been solved, perhaps to some extent, but it is interesting to think about how to ...
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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 ...
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4 votes
2 answers
548 views

Which formalism is better suited to model a crystal with defects: Hartree–Fock, Kohn–Sham, or something else?

Let’s suppose that (1) it’s required to calculate a crystal with certain parameters of a crystal lattice; (2) this crystal has some defects (let it be Frenkel defects for simplicity); (3) these ...
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Hartree-Fock Method: Projection of density matrix onto a larger basis set

I am implementing a Hartree-Fock SCF program with an educational purpose. Although the code works fine using a Core Hamiltonian guess for the SCF iterative process, I want to implement a more accurate ...
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About the order of indices in basis set expansion

In many books, e.g., Szabo and Ostlund, Helgaker Jorgensen and Olsen, etc etc, the expansion of Hartree-Fock orbital by basis set is written as a kind of $$ \phi_i = \sum_{\mu} C_{\mu i} \chi_{\mu} $$ ...
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17 votes
4 answers
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What are the physical reasons if the SCF doesn't converge?

I've been mostly using ab initio methods as a routine calculation tool, so even though I know some things from the theoretical side, I still have mostly hands-on experience. One of the things that I ...
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7 votes
0 answers
127 views

Evaluating Coulomb and exchange integrals in practice using cartesian coordinates

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 ...
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8 votes
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322 views

What do size-extensivity and size-consistency mean?

I have heard both terms in various lectures and books on quantum chemistry, however, I have not found a proper explanation of them. As I understand now, size consistency of a method means for example, ...
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6 votes
1 answer
285 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 ...
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7 votes
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Is the formula of a Dyson orbital independent of whether there is degeneracy or not in the HOMO of the neutral?

A Dyson orbital is defined as: $$ \textrm{Dy}(x) = \int dx_1 \ldots dx_{N-1} \, (\Psi^+(x_1,\ldots,x_{N-1}))^* \, \Psi^0(x_1,\ldots,x_{N-1}, x),\tag{1} $$ where $\Psi^0$ and $\Psi^+$ are the total ...
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1 answer
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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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6 votes
0 answers
114 views

Differences between DFTB3 energy and HF energy

I was performing DFTB3 calculation with DFTB+ on water monomer. This is my input. ...
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17 votes
3 answers
1k views

Why is uncertainty not a big problem in computational chemistry?

The molecular Hamiltonian (or, for simplicity, the Fock operator) contains coulomb potentials as well as momentum operators. To evaluate the coulomb potential, we need to know where the electrons are. ...
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For DFT and Hartree-Fock, how can we know that we have a true minimum? Is there an equivalent to the "frequency analysis" for geometry optimization?

In a geometry optimisation, one can check if they have reached a minimum by checking the phonons. And to a certain extent, the global minimum can be confirmed by relaxing from different starting ...
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8 votes
1 answer
604 views

Convert reduced density matrix from M.O. to A.O. basis

I am interested in converting the one-particle reduced matrix (rdm1) from the molecular orbital (M.O.) basis to the atomic orbital (A.O.) basis. Is the following method correct (in an identical ...
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9 votes
2 answers
587 views

Visualize electron density using pyscf

I found the following example of code which uses density functional theory to compute the electron density $\rho$: ...
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9 votes
1 answer
264 views

'Exchange' in Hartree-Fock and Kohn-Sham DFT

I am a bit confused about the notions of exchange in the Hartree-Fock and Kohn-Sham Density Functional Theory schemes. In Hartree-Fock, one just writes down the many-electron wavefunction as a hartree-...
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8 votes
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460 views

Does Kohn-Sham DFT use Slater determinants?

In the Hartree method, it is known that the wavefunction of the system does not obey the antisymmetry principle of fermions - that is when you swap two particles, they don't up a negative sign. ...
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16 votes
1 answer
485 views

Why is CPHF/CPKS necessary for calculating second derivatives?

This question is coming from an answer to one of my previous questions. During optimizations, QM programs usually compute the gradient(first derivative) analytically, and take a guess of the hessian (...
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14 votes
2 answers
260 views

Optimization of Gaussian basis sets within the Hartree-Fock Method

I am revisiting some exercises in Thijssen's Computational Physics book, particularly chapter 4 on the Hartree-Fock method. I am interested in the method of nonlinear optimisation for its own purposes,...
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6 votes
1 answer
449 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 ...
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9 votes
2 answers
314 views

Normalization constant and Roothaan Equations

Roothaan Hall Equations: The Hartree-Fock equations are a set of modified Schrodinger equations: $f_{i}\psi_{m}=\epsilon_{m}\psi_{m}$ where: The Fock operator ($f_{i}$) is given by (restricted case): ...
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8 votes
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242 views

Semi-canonicalisation vs canonicalisation of the Fock matrix and orbitals

I have seen the terms semi-canonicalized and canonicalized used in relation to the Fock matrix, density matrices, and orbitals; however, I am unsure what these terms actually describe. For instance: ...
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9 votes
1 answer
121 views

Muonic Modeling

I have seen an article[1] that describes a HF approach to working with exotic muonic atoms. I am curious about how far DFT has been extended for modeling muonic chemistry. Are there psuedopotentials ...
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18 votes
5 answers
753 views

What are the types of SCF?

Many of us know the most common types of SCF (though we can do better than Wikipedia at explaining them): RHF (Restricted Hartree-Fock), RKS (Restricted Kohn-Sham) [link to answer] UHF (Unrestricted ...
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12 votes
1 answer
209 views

Analog computing in matter modeling today: Any applications?

When we think about computers and computing today, almost invariably we think about digital computers, the ever-present objects today. But reading this question in the Chemistry stackexchange, How are ...
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11 votes
1 answer
630 views

How to calculate the Fock matrix in the molecular orbital basis PySCF?

I am interested in calculating the Fock matrix in the molecular orbital basis with PySCF, though I am not clear on the methodology behind this task. In my attempt, I use the following script (for the ...
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12 votes
2 answers
789 views

What do the rows and columns of a Fock matrix represent?

I am using the pyscf code, where the Fock matrix can be obtained by: ...
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15 votes
2 answers
606 views

Hartree-Fock density vs Kohn-Sham density

Hartree-Fock density is free of self-interaction but lacks electron correlation effects, while the density from KS-DFT (using an xc functional or potential, both which are explicitly density-dependent ...
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12 votes
2 answers
337 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)...
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  • 305
12 votes
2 answers
188 views

What is the mathematical condition that ensure that the self-consistent field (SCF) procedure must converge?

We know that there is convergence issue of DFT method on study real molecular system. It would be conducive if people could pre-determine if the SCF procedure is converge analytically before starting ...
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15 votes
2 answers
605 views

How does the Hartree-Fock method improve on Hartree after considering the wavefunction that takes the anti-symmetry property into account?

I am not able to understand the math of this. After taking the Slater determinant as a wavefunction in Hartree-Fock, does the procedure to find wavefunctions remain the same as in the Hartree method ...
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