17

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 interchange of particles), while Hartree-Fock uses a fermionic wave function i.e. a Slater determinant that is the correct one for electrons. In both cases, the ...


14

NSCF stands for non-self-consistent field calculation and, as explicit by its name, the calculation is not performed in a self-consistent fashion as the SCF (self-consistent field) one. The latter performs the solution trying to minimize the density charge functional until a predetermined limit in the energy difference between two consecutive steps. The ...


13

Psi4 and PySCF Psi4 and PySCF are free, open source programs that can do both parallel integrals and SCF. MPI parallellization is quite rare in quantum chemistry codes, since the algorithms don't tend to parallellize easily across nodes.. MPQC If you really want to do massively parallel calculations, then the Massively Parallel Quantum Chemistry (MPQC) ...


13

A few materials/simulation boxes I've had some proper trouble with: HSE06 + noncollinear magnetism + antiferromagnetism, Vasp noncollinear: This was a strongly antiferro material (4 Fe atoms, in an up-down-up-down configuration). HSE06 is apparently difficult to converge anyway. Noncollinear magnetism/antiferromagnetism apparently creates problems for any ...


12

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: nobody uses the Roothaan procedure, since it usually doesn't converge, and you need to do something smarter like use damping or other convergence acceleration ...


12

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. However, both methods differ in the form of the wavefunction. Hartree Method In the Hartree method, the total wavefunction is a Hartree product: $$ \Phi(\mathbf{r}...


12

First, make sure that the structure is correct. Second, make sure that the structure is relaxed. Third, make sure that all the parameters in your input card are reasonable and the used pseudopotentials are matched with your structure. Fourth, make sure that the self-consistent loop is complete, namely, the convergence threshold of the electronic step is ...


12

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". However in software like GAUSSIAN and CFOUR, you can do something called stability analysis, which is described for example in the GAUSSIAN documentation ...


11

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 electron. Unrestricted Hartree-Fock (UHF) lifts this requirement, forming a unique set of MOs for $\alpha$ and $\beta$ spin. Generalized Hartree-Fock takes ...


11

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 to use the Legendre expansion for $|r_1-r_2|^{-1}$, which decomposes the interaction into a radial part and an angular part: $r_{12}^{-1} = \frac {4\pi} {r_>} ...


11

Yes! The Schroedinger equation for a molecule is just a differential equation, so you can solve it numerically "on a grid" or in "real-space", and there is a review paper on the topic: "Real-space numerical grid methods in quantum chemistry". You can also simply model the wavefunction $|\psi\rangle$ with some formula, and ...


10

This will be a long answer, so I will divide it in parts. Woods paper A significant limitation of the Woods et al paper is that it excludes atomic-basis set calculations where convergence acceleration is much more powerful than in plane wave codes. Namely, the update schemes discussed in the article talk about just the input and output densities, whereas ...


10

LASSCF: Localized Active Space SCF An approximation to or generalization of (depending on how you look at it) CASSCF. In CASSCF, the wave function consists of an antisymmetrized product of two factors defined in two non-overlapping sets of orbitals: a single determinant of occupied inactive orbitals, and a general correlated wave function describing the ...


10

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 Dirac-Coulomb(-Breit/Gaunt) Hamiltonian. The 4-spinors decribe both positive - electronic - solutions as well as negative, or "positronic" solutions....


10

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 is a reasonable minimum. One of them is checking the electronic hessian at the SCF solution and determining the lowest eigenvalues. If one or more negative ...


9

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 equation. The electron-electon interaction is modeled as a field influencing all electrons in the system, which are otherwise independent particles. Their "...


9

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 particle approximation to the electronic Hamilton operator of the system (with other approximations beyond the scope of this Q&A). The rows/columns (the matrix ...


9

This is an excellent question! The reality is complicated even in LCAO calculations: every code has different defaults, which also depend on the run type. It seems that older LCAO codes simultaneously look at the convergence of the energy, and of the density matrix. Looking only at the change in energy is really bad behavior, since it doesn't tell you ...


9

The central goal of KS-DFT is solving Kohn-Sham equation: $$H\psi_i(\vec{r})=\left( -\dfrac{\nabla^2}{2}+V_{ks}[\vec{r};\psi_i(\vec{r})] \right)\psi_i(\vec{r})=E_i\psi_i(\vec{r})$$ Here the atomic unit has been adopted. Note that the Kohn-Sham equation is a nonlinear differential equation and hence we need to solve it self-consistently. The workflow can be ...


8

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 freedom for both electrons, so TAR86 is correct. In the derivation at the link, the distance between the electrons ($\mid r_1 - r_2 \mid \equiv r_{12}$) is better ...


8

Looking at your input and output files, I think the most likely explanation is a different local minimum in the energy, as mentioned by Andrew in the comments. If you look at the final scf step in the vc-relax output, it uses the starting magnetization from the last bfgs step, not the initial values you used at the start of the vc-relax. I would try two ...


8

Edit: This no longer seems to be the issue, as the atomic positions are apparently essentially unchanged, per @KevinJ.M.'s comment. I will nonetheless keep the answer here because it is still important to consider going forward. It looks like you are getting a different magnetization because the structures are not identical. Your first structure is fully ...


8

What you're describing is very common, and is not limited to GAMESS and Q-Chem. First, here's how to do it in MOLPRO, MRCC, GAMESS, Q-Chem (in fact the only electronic structure software that I regularly use which doesn't allow this type of projection into a bigger basis set, is CFOUR): 1) MOLPRO: basis=cc-pVDZ hf basis=cc-pVQZ hf The HF ...


8

Supplementing Nike's answer above.. This is actually quite elementary math. Let's say I have an orbital in a basis $|\psi\rangle = \sum_i c_i |i\rangle$ and I want to find the expansion in some other basis set $|J\rangle$. How do I do this? In the new basis set, one has the resolution of the identity $\sum_{JK} |J\rangle \langle J|K\rangle^{-1} \langle K|\...


8

I wouldn't recommend that you go above $10^{-8}$, what you have in your current calculation. With SCF calculations, you definitely need a lower convergence threshold compared to say relaxing procedures. I suspect your problem is rooted elsewhere. Try: Lowering 'mixing-beta' Removing 'verbosity' as it just prints energy levels and takes up time, which you ...


7

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 "touch" the Hamiltonian, and the permutations of the orbitals "kill off" the normalization constant. Now, when you have the energy expression, ...


7

RASSCF: Restricted Active Space SCF In a Complete Active Space (CAS) calculation, one chooses a set of occupied/virtual orbitals (the active space) from an initial Slater determinant and forms additional configurations from all the possible rearrangements (hence, complete active space) of the electrons among those orbitals. As the name suggests, a RAS ...


7

Generally you want to use the same settings when trying to combine results from different jobs. However, below is the general procedure that I have seen performed for a basic, publishable PES. 1) Perform geometry optimization 2) Perform solvent/frequency calculations 3) Combine solvent energy and enthalpy (from frequency calculation "Total Enthalp...") 4)...


7

If by "the SCF method" you mean the simple SCF, the answer is: no, usually it does not converge (unless the problem is very simple; basically the gap is huge, so that the system does not respond very much to potentials). The damped SCF problem on the other hand does converge, for damping parameters small enough (unless you run into fractional occupations). ...


7

MRCC There are more programs with parallel SCF capability, but it is quite hard to scale SCF (with HF exchange) to large number of cores. MRCC indeed has a recent hybrid multi-node (MPI) & multi-threaded (OpenMP) parallel HF/hybrid DFT code relying on an integral direct density fitting algorithm, but you should not expect great scaling above few hundred ...


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