25
votes
Accepted
What are the "smart algorithms" applied to solve the "curse of dimensionality"?
This is a very broad question, so I am going to give a very brief overview of typical exponentially-scaling problems. I am not an expert in most of these areas, so any suggestions or improvements will ...
- 1,918
20
votes
Accepted
How to determine, a priori, whether a compound has multireference character?
This is not going to be a full answer, but maybe a starting point, a pointer to somewhat troubled systems. The general keyword here is degeneracy. Whenever you have fewer electrons than fit in the ...
- 1,571
20
votes
Accepted
Total spin and/or multiplicity for transition metal ions?
Even for the simplest transition metal diatomic molecules, the most reliable way to know the ground-state spin configuration is often by doing experiments. I will give an example where it's easy to ...
- 33.5k
19
votes
What is the largest system that has been studied by the coupled cluster method?
ORCA
The local pair-natural orbital (DLPNO) based coupled cluster method have been managed to investigate large organic molecule and small proteins (linear C150H302 (452 atoms, >8800 basis ...
- 3,813
18
votes
Accepted
When should geometry relaxation not be performed?
Geometry optimization corresponds to a system in equilibrium. It is the "average" position of a molecule vibrating in a well.
However, there are many cases where the system is "non-equilibrium" ...
- 7,957
18
votes
How to incorporate the effect of spin-orbit coupling in electronic structure calculation
The inclusion of spin-orbit coupling in electronic structure calculations is done by including the interaction between the electron-spin and the orbital angular momentum in the Hamiltonian. Such ...
- 1,335
17
votes
How can quantum computing accelerate materials modeling?
Quantum computers provide the possibility of simulating systems that are so mathematically complex that classical computers cannot practically be used. The difficulty comes from the fact that the ...
- 1,463
17
votes
Accepted
How to calculate energy of a molecule in an aligned electric field?
Aligning a molecule to a particular frame of reference (e.g., with the z-axis along a particular bond) is part of Avogadro for this reason:
In Avogadro 1.x, there's an align tool
You click one atom ...
- 9,045
16
votes
How to identify a semi-metal from the band structure?
A rigorous definition of a semimetal can for example be found in the mathematical literature (e.g. this paper: arXiv:2002.01990v1 [math-ph], pdf version, assumption 2.5). The basic idea is that the ...
- 2,384
16
votes
Accepted
How to incorporate the effect of spin-orbit coupling in electronic structure calculation
Basically there are two kinds of approaches which may be found in many text books, L-S coupling and j-j coupling.
L-S coupling means that scalar electronic states (e.g. atomic L-S states and linear ...
- 176
15
votes
Accepted
How to overcome the exponential wall encountered in full configurational interaction methods?
It is hard to claim that any FCI code overcomes the exponential wall, especially for strongly correlated systems.
There are many algorithms, e.g. CDFCI, HCI, FCIQMC, ACI, etc., which significantly ...
- 1,076
15
votes
How to determine, a priori, whether a compound has multireference character?
As Martin has said a practical way to decide if a molecule requires multi-reference treatment is to calculate the unrestricted Hartree Fock natural orbitals.[1] Significant fractional occupancy of a ...
- 7,957
15
votes
Why does orbital-free DFT scale linearly with system size?
There is linear scaling DFT, where you use density matrix as your object throughout SCF iterations instead of the wavefunctions. The linear scaling comes from the sparsity assumption/truncation on the ...
- 1,076
15
votes
Accepted
When do relativistic effects need to be explicitly included?
When to include relativistic corrections or modeling of any kind in computational methods is a rather complex one. Full Dirac methods as you asked about (DHF) recapture two important factors, so ...
- 852
14
votes
How can quantum computing accelerate materials modeling?
Quantum computing has been extensively discussed as long as the first quantum computers have become a reality. As already pointed out, we are still at very early stages of such development. What we ...
- 3,238
14
votes
Accepted
How is group theory used to deduce which of these integrals are equal to 0?
The question is too broad to be answered directly so I will provide a somewhat general scheme.
Basically in an integral like
$$
\int d\mu A B C
$$
one would seek to expand each part in irreducible ...
- 256
14
votes
Accepted
Gaussian-type orbitals vs Slater-type orbitals in terms of computational efficiency
Your supervisor is correct that in almost all practical cases in quantum chemistry, the cost savings of using Gaussian-type orbitals far outweigh the disadvantages of needing more orbitals.
First of ...
- 33.5k
13
votes
Methods for visualising aromaticity
Multiwfn
The software Multiwfn can calculated four aromaticity indices, namely FLU, FLU-pi, PDI and information-theoretic index.
Multiwfn can perform wavefunction analyses based on outputted file of ...
- 22.3k
13
votes
FCI without Hartree-Fock
Yes, you can surely do full CI without Hartree-Fock. However, the reason why one typically starts from Hartree-Fock is that this guarantees a good conditioning of the FCI matrix, which becomes ...
- 17.9k
13
votes
Do bonds between the atoms influence ab-initio energies?
The bonds you draw or see in Gaussview should have no effect on the calculation (besides some minor effects in choosing internal coordinates for a geometry optimization). As you note, a bond is a ...
- 15.2k
12
votes
Accepted
Is Heisenberg model or in its simplier form Ising model a good approximation to study magnetic systems?
Introduction
Your question reminds me of a quote by Paul Dirac,
The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus ...
- 4,696
12
votes
How can quantum computing accelerate materials modeling?
Quantum computers potentially could provide a far more efficient way to solve the electronic structure problem: finding the ground state energy (or other properties) of electrons in a compound.
The ...
- 221
12
votes
Accepted
What approaches are employed to treat amorphous materials?
Creating amorphous structures is non-trivial and always rather expensive. Generally you are using large supercells such that you can achieve mid-range disorder. That means, since the cell is still ...
- 898
12
votes
What are the "smart algorithms" applied to solve the "curse of dimensionality"?
The curse of dimensionality is indeed a huge problem in quantum chemistry, since the possible ways N electrons can occupy K orbitals is a binning problem whose computational cost grows factorially (...
- 17.9k
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: ...
- 17.9k
12
votes
Derivation of Slater-Koster equations
Spherical harmonics are not themselves full atomic orbitals. Consider the Hydrogen wave function, which separates into a radial part and an angular part. The latter is a spherical harmonic, but the ...
- 4,696
12
votes
Is there an energy gap correction factor that needs to be used in DFT calculations?
I would like to add a few clarifications to Jack's answer:
Standard DFT calculations with fixed ionic positions are actually not even 0 K. A better way to describe them is that they are static ...
- 10.9k
12
votes
Accepted
Increasing k-point grid to take DOS calculation
This depends a lot on how the DOS is calculated. I don't know the options one has for this when using VASP or SIESTA, but I am aware of different approaches. The central problem is that you don't know ...
- 1,426
11
votes
Is there an energy gap correction factor that needs to be used in DFT calculations?
Is this calculated indirect bandgap at room temp. or at 0K?
QE is based on the density functional theory (DFT). DFT is a ground-state (0K) theory and hence the calculated bandstructure is 0K.
If it ...
- 14.9k
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"...
- 33.5k
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