Questions tagged [mathematical-modeling]
Questions related to mathematical modeling of materials systems.
25
questions
17
votes
6
answers
694
views
What are the applications of chemical graph theory?
Graph theory was originally introduced in computer science to study data structure. Chemists also introduced graph theory to study the relation between structure and properties for molecular compounds....
- 3,973
10
votes
1
answer
339
views
Basics of numerical energy minimization techniques used in molecular dynamics?
The question below describes my plan to make a basic molecular dynamics calculation using a Python script rather than a canned, self-contained program.
There seems to be three parts:
a model of the ...
- 2,064
9
votes
3
answers
2k
views
What are the advantages of the Davidson diagonalization method over other sparse matrix diagonalization methods?
I am interested to understand the advantages of the Davidson diagonalization method over other sparse matrix diagonalization routines. For instance, Intel MKL.
- 2,177
19
votes
4
answers
762
views
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 ...
- 605
6
votes
1
answer
203
views
Understanding derivation of discretized FIRE algorithm
Introduction/Preamble
@SusiLehtola's answer to Basics of numerical energy minimization techniques used in molecular dynamics? mentions conjugate gradients, BFGS for energy minimization, Metropolis ...
- 2,064
22
votes
0
answers
245
views
Is there a software that can do derivatives with respect to user defined vibrational modes?
I'm doing some property calculations that depend on a sum of derivatives of some quantity with respect to normal vibrational modes. I was hoping to find some physical intuition relating the type of ...
- 15.7k
20
votes
3
answers
477
views
How are continued fractions related to quantum materials?
In my spare time, I have been studying and analysing continued fractions.
I was having a conversation with someone on Discord in a Mathematics server and he was telling me that continued fractions ...
- 253
18
votes
1
answer
1k
views
Do we know for sure that all atomic and molecular wavefunctions decay exponentially as r goes to infinity?
Slater type orbitals (STO) are considered to be more accurate than gaussian type orbitals (GTO) for atomic and molecular QM calculations because - among other reasons - they decay with $e^{-\alpha r}$ ...
- 603
15
votes
1
answer
117
views
Types of Discrete molecular models
It is often assumed in cheminformatics that molecules with similar physical structure tend to have similar chemical properties [1].
Based on this, our group has used discrete graphs as a model for the ...
13
votes
1
answer
164
views
Has a form of diamond with certain properties ever been theorized?
The following is what a Penrose tiling looks like:
I know the verticies of a dodecahedron can be grouped into 5 groups each of which are the verticies of a tetrahedron. So I thought of the idea that ...
- 487
9
votes
1
answer
136
views
Which specific perturbation do we consider applying to the potential when defining the energy derivative of the log derivative?
Norm-conserving pseudopotentials are defined such that the energy derivative of the log derivative of the real and pseudo wavefunctions agree at $r>r_c$. I understand that although valence ...
- 231
9
votes
1
answer
538
views
How can I implement the Cartesian harmonics?
I'm studying the quantum chemistry calculation and now trying to implement the basic methods.
For example, given a water molecule,
$M = {(\ce{O}, R_\ce{O}), (\ce{H}, R_\ce{H}), (\ce{H}, R_\ce{H})}$,
...
- 93
8
votes
2
answers
1k
views
Functional derivative of energy with respect to density
I have read the paper of "A bird's-eye view of density-functional theory [PDF]" and I have a question about the functional derivative of the energy by the density.
I have found the following ...
- 1,789
7
votes
1
answer
210
views
Can replacing some of the atoms in a covalent network with that of the element one atomic number higher make it nonstick? [closed]
I originally made the title the question I had that is a more suitable question but then it ended up too long. I had the idea that if you replace some of the atoms in a covalent network with the atom ...
- 487
7
votes
1
answer
132
views
Is an "exact" double hybrid density the same as the "exact" DFT density?
Double hybrid approximate functionals have "unoccupied" Kohn-Sham orbitals in their formulations due to their MP2 component; however, the "exact functional" depends only on the &...
- 870
7
votes
2
answers
339
views
How to rotate polarizability tensor depending upon the molecular coordinates?
My question is somewhat related to molecular rotation. I have calculated the polarizability tensor of $\ce{HCHO}$ molecule in PSI4. The output tensor is this,
...
- 1,056
7
votes
0
answers
120
views
Deriving relations for a hard sphere phase diagram [closed]
In Torquato's book "Random Heterogeneous Materials", he has written:
$$\frac{p}{\rho kT} = 1+2^{d-1}\eta g_2 (D^{+})\tag{1}$$
where $g_2(D^+)$ is the contact value from the right-side of the ...
- 4,181
6
votes
1
answer
215
views
For one atom, what is the correct point group?
I have a concern related to the follwoing question When orbitals are labeled based on their irreps in D2h, how are the orbitals ordered for an N atom? In which the following Answer clearly states that ...
- 3,535
6
votes
0
answers
59
views
Basics of configuration initialization strategies used in molecular dynamics? [duplicate]
This answer to Basics of numerical energy minimization techniques used in molecular dynamics? mentions
conjugate gradients, BFGS for energy minimization
and
Metropolis Monte Carlo (and the) the ...
- 2,064
5
votes
1
answer
217
views
Calculating first and second derivatives of a molecular Hamiltonian?
I'm interested in computing first and second derivatives of molecular Hamiltonians with respect to nuclear coordinates. I've been using Psi4 and PySCF to perform Hartree-Fock calculations, and I was ...
- 409
5
votes
2
answers
347
views
Relationship between functional derivative and potential value at a position
Thanks to very helpful and detailed answers for my previous question,
I understand the functional derivative of the energy with respect to the density.
In addition, this functional derivative is equal ...
- 1,789
5
votes
2
answers
307
views
How to apply FIRE to many atoms where P=F·v seems to be a vector rather than a scalar?
Introduction/Preamble
@SusiLehtola's answer to Basics of numerical energy minimization techniques used in molecular dynamics? mentions conjugate gradients, BFGS for energy minimization, Metropolis ...
- 2,064
3
votes
1
answer
165
views
Is this method of obtaining only the exact "other" densities, and no other properties w.l.o.g, correct?
In Kohn-Sham DFT, the exact density of the ground-state wavefunction is given by summing the squares of the filled K-S orbitals.
Suppose now that one only needs the exact density (and nothing else w.l....
- 870
3
votes
0
answers
185
views
Understanding derivation of geminal based methods [closed]
Cross-posted on Reddit.
I have been reading through [1] to get a better understanding of geminal based methods. This is one of two questions that I'm asking about that paper on this site, the other ...
- 61
2
votes
1
answer
113
views
Understanding the complexity of geminal-based wavefunctions
Cross-posted on Reddit.
I have been reading through [1] to get a better understanding of geminal-based methods. Some short passages are included below:
The occupation of each orbital in the expansion ...
- 61