21
votes
How does the Hartree-Fock method improve on Hartree after considering the wavefunction that takes the anti-symmetry property into account?
Both Hartree and Hartree-Fock have a self-consistent field method, as does density functional theory, too; the difference is just that Hartree theory uses a bosonic wave function (symmetric with ...
- 20k
18
votes
Accepted
Why is CPHF/CPKS necessary for calculating second derivatives?
It comes down to the fact that HF and KS both are variational methods. This short article by Julien Toulouse gives a great description of ways to compute static/dynamic response properties. I'll just ...
- 15.7k
17
votes
Accepted
Why is uncertainty not a big problem in computational chemistry?
Following your arguments, we would see also a 'violation' of the Heisenberg uncertainty principle (HUP) in single-particle quantum mechanics, e.g. in a Hamiltonian of a particle in an external ...
- 757
16
votes
How does the Hartree-Fock method improve on Hartree after considering the wavefunction that takes the anti-symmetry property into account?
The procedure to find the Hartree equations and the Hartree-Fock equations is very similar, we have to minimize the expectation value of the Hamiltonian under the orthonormalization constraint. ...
- 2,741
15
votes
Hartree-Fock density vs Kohn-Sham density
Kieron Burke and co-workers have shown that in many cases one can get better results by using the HF density as input to a DFT-XC evaluation of the energy, as opposed to using the DFT-XC to generate a ...
- 1,806
15
votes
Accepted
What are the physical reasons if the SCF doesn't converge?
I have written a section in the BDF user manual on this issue. It is in Chinese but I'll roughly translate the key parts to English as below.
Common reasons for the SCF procedure to fail to converge ...
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14
votes
Accepted
Convert reduced density matrix from M.O. to A.O. basis
Only the first line is correct, as long as the AO basis is not orthogonal.
The point is: the AO $\leftrightarrow$ MO transformations of density matrices and Fock matrices require different formulas. ...
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13
votes
Accepted
One-center two-electron integrals between 1s STO
Your Octave code is trying to do the integral by quadrature, which makes very little sense since it will have a huge problems with the cusp.
Since this is a one-center problem, the best approach is ...
- 20k
12
votes
Accepted
Optimization of Gaussian basis sets within the Hartree-Fock Method
There are a lot of different methods, but a good starting point to understand how this might be done is the method of steepest descent. First we take the generalised eigenvalue expression you cite and ...
- 8,277
12
votes
What is the mathematical condition that ensure that the self-consistent field (SCF) procedure must converge?
This question is a bit ill-defined: what do you mean by "the self-consistent field procedure"? If you mean the original Roothaan procedure, then the question makes sense, but it is uninteresting: ...
- 20k
12
votes
What are the types of SCF?
GHF: Generalized Hartree Fock
In Restricted Hartree-Fock (RHF), the molecular orbitals are constructed as pairs, with a single spacial function being used to describe both an $\alpha$ and $\beta$ spin ...
- 15.7k
12
votes
Why is uncertainty not a big problem in computational chemistry?
Indeed, due to the uncertainty relation, the electrons in a molecule do not have a definite potential energy, nor do they have a definite kinetic energy (yet they have well-defined expectation values ...
- 9,981
11
votes
Accepted
What are the types of SCF?
DHF: Dirac-Hartree-Fock (or "Dirack-Fock")
the DHF (Dirac-Hartree-Fock) or Dirac-Fock is the SCF method based upon four-component spinors (simply four-spinors), because of the four-component ...
- 351
11
votes
Accepted
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?
You're right about the ability to change the initial guess repeatedly until you get the lowest energy, and this is how it's done in software like MOLPRO which don't offer "stability analysis"...
11
votes
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?
Just like geometry optimization, there is no practical way to be 100% sure that you have the global minimum of SCF solutions.
But there are checks you can do to make sure that the SCF solution you got ...
- 7,161
11
votes
Accepted
Is there a simple free working code that implements Hartree–Fock or DFT?
SlowQuant
There's dozens of free, working, open source codes for Hartree-Fock and DFT available online. See Susi Lehtola's review paper about open source quantum chemistry software. I'm not sure which ...
10
votes
Accepted
Semi-canonicalisation vs canonicalisation of the Fock matrix and orbitals
For simplicity, I will stick to the restricted Hartree-Fock level of theory since the question of canonical and semi-canonical orbitals already exists there.
Let's remember the SCF equations: ${\bf F ...
- 20k
10
votes
Accepted
What is the physical meaning of the term "non-local interaction"?
The non-local operator in Hartree Fock is the Exchange operator. Locality is a mathematical property. Look at the Coulomb operator first which acts like this:
$$ \hat v_H\;\varphi_s(r) = \sum_i^{N_\...
- 543
9
votes
What are the types of SCF?
RHF: Restricted Hartree-Fock / RKS: Restricted Kohn-Sham
Restricted Hartree-Fock (RHF) is a self-consistent field approach: a mean-field approximation to the electronic, non-relativistic Schrödinger ...
- 1,698
9
votes
Accepted
Analog computing in matter modeling today: Any applications?
I don't think analog computers are quite at the level they need to be yet, but there are people working to make them applicable to matter modeling applications.
Dr. Rahul Sarpeshkar at MIT developed ...
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9
votes
Accepted
What do the rows and columns of a Fock matrix represent?
The short answer is: it is the matrix representation of the Fock operator in the given basis set, in this case, the atomic orbital (AO) basis. The Fock operator itself is a mean-field, independent ...
- 1,698
9
votes
One-center two-electron integrals between 1s STO
This can be solved analytically, a complete solution can be found here
To refrain from rewriting the entire derivation I will only say that you need to integrate over all 3 dimensional degrees of ...
- 8,015
9
votes
Visualize electron density using pyscf
This is just the Gaussian cube format. It's essentially a voxel dump of the wave function evaluated on a grid. You can find some documentation at http://paulbourke.net/dataformats/cube/ and https://...
- 20k
9
votes
Why is uncertainty not a big problem in computational chemistry?
A common textbook statement of the uncertainty principle is:
$$\tag{1}
\Delta x \Delta p \ge \frac{\hbar}{2},
$$
where $\Delta x$ and $\Delta p$ are the uncertainties in measurements of the position $...
9
votes
Accepted
How is the zero energy defined for molecular orbitals?
The zero point of orbital energies is usually defined as the vacuum level, i.e. the energy of a hypothetical orbital that is infinitely diffuse and does not come close to any nuclei or other electron. ...
- 9,981
9
votes
Free and optimized code for Hartree-Fock calculation in solids
Quantum ESPRESSO (QE) is a plane wave basis and various types of pseudopotential-based density functional theory (DFT) code. The PWscf package in it can perform both DFT and Hartree-Fock calculations. ...
8
votes
Optimization of Gaussian basis sets within the Hartree-Fock Method
Short answer: don't do it.
While optimizing the exponents in a basis set for your system is possible in principle, the optimization is very expensive. You may also end up ruining the accuracy of your ...
- 20k
8
votes
Accepted
Normalization constant and Roothaan Equations
The normalization constant is built into the Roothaan-Hall equation. Namely, when you derive the Hartree-Fock energy expression from the wave function, you integrate out all the orbitals that don't &...
- 20k
8
votes
Does Kohn-Sham DFT use Slater determinants?
A couple of comments perhaps to clarify some points.
The first Hohenberg-Kohn theorem states that the one-electron density determines uniquely the energy, for a non-degenerate ground state. The second ...
- 1,806
8
votes
Accepted
Does Kohn-Sham DFT use Slater determinants?
As Nike has already mentioned, Slater determinants occur in KS-DFT in much the same way that they do in Hartree-Fock as a way to combine a set of one-electron orbitals into an antisymmetric many-...
- 15.7k
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