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Questions tagged [mathematical-modeling]

Questions related to mathematical modeling of materials systems.

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Proof that equilibrium phase fraction(s) is a continuous function of composition

It seems that the equilibrium phase fractions (i.e., relative amounts of phase A1, A2, ..., Aq for a system in which there are q total phases) as a function of composition (for a constant pressure and ...
sgp45's user avatar
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A problem to simulate the kinetic energy operator using some field going through a crystal

We know about a differentiation and integration operations and also other ones can be simulated by an analog way using electric circuits with operational amplifiers (here are articles of the ...
SFriendly's user avatar
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12 votes
4 answers
979 views

Are there non-antisymmetric solutions to the electronic Hamiltonian?

In electronic structure theory, one seeks solutions of the molecular electronic Hamiltonian $$ H_e(\vec{R}) = T_n(\vec{r}) + V_{ne}(\vec{r};\vec{R}) + V_{ee}(\vec{r}) + const, $$ where $\vec{r}$ are ...
Solarflare0's user avatar
6 votes
1 answer
202 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 ...
Jaafar Mehrez's user avatar
5 votes
1 answer
170 views

Is the electron-electron interaction to blame, for the added complexity of using "orbitals" for an N-electron system?

In a one-electron system such as the H atom, we are able to say that the orbitals are valid wavefunctions. But for complex systems with N-electrons, I have heard people say that they are just ...
Jaafar Mehrez's user avatar
3 votes
0 answers
30 views

How can I compute the longest relaxation time?

Cross-posted on Stats.SE and on SciComp. In the case of Monte Carlo simulations: Autocorrelation Time ($\tau_{\text{int}}$): A measure of how many steps are needed for the correlations in the chain ...
user366312's user avatar
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6 votes
2 answers
149 views

How do I get the energy, if I have the wavefunction?

I recently wrote a simple HF SCF program for my understanding and realized that I do not fully understand such QM calculations. Suppose I have the ground state gaussian wave function of a system, $$ \...
ipcamit's user avatar
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6 votes
1 answer
191 views

Speed of atom from kinetic energy of molecule

What is the velocity of each hydrogen atom in an H2 molecule, given a kinetic energy of hydrogen molecule is 0.12 eV, when expressed in angstroms per femtosecond and assuming equal velocities for both ...
Rubi Agrawal's user avatar
3 votes
1 answer
189 views

Why does the C6z operator have 6 eigenvectors in this paper?

In this paper, I couldn't understand this line in the 3rd section (i.e. III. SYMMETRY ARGUMENTS): In the absence of SOC, the eigenvalues of $C_{6z}$ rotation operator are $e^{i2\pi n/6}$ where $n = 0$...
user192399's user avatar
5 votes
1 answer
55 views

Correct expressions for one-center Gaussian radial two-electron integrals

I am working on a new atomic solver library, for which I need expressions for the one-center two-electron integrals. Pitzer has furnished the necessary expressions for Slater-type and Gaussian-type ...
Susi Lehtola's user avatar
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5 votes
1 answer
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Evaluating analytic gradients for overlap integrals

I have been working on a toy HF code for some time. From this reference I am trying to work out an analytic expression for the first derivatives of overlap integrals. The original expression for ...
Hemanth Haridas's user avatar
3 votes
0 answers
36 views

Convex hull calculations with WIEN2k

How does one do the calculation of a convex hull with the WIEN2k code for the formation energy of alloys?
Moussa Rabah's user avatar
4 votes
0 answers
43 views

Gauge constraint in the definition of the Z2 invariant

Cross-posted at Physics.SE. In Fu and Kane's paper from 2006, the authors define the $\mathbb{Z}_2$ invariant for time-reversal invariant topological insulators as an obstruction to Stoke's theorem, $$...
Sounak Sinha's user avatar
5 votes
2 answers
154 views

How is the equation for the position of a virtual site derived?

Cross posted on Math SE I am trying to understand virtual sites in MD simulations, and I came across this configuration: Here, coordinate $\mathbf{s}$ represents the virtual site, which is formed by ...
Vasista's user avatar
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11 votes
1 answer
374 views

Inconsistencies in a famous point group table

The original resource "Tables for Group Theory" By Peter Atkins, Mark Child and Courtenay Phillips (1970). I have been using this 2008 version, in which Pg. 37 has the following table: Some ...
Nike Dattani - No Free Time's user avatar
3 votes
1 answer
52 views

Is the following description talking about the simulation box or the boundary condition?

Is the following description talking about the simulation box or the boundary condition? To prevent the argon atoms in the gas phase from running off to infinity, we enclose the system in a "...
user366312's user avatar
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5 votes
0 answers
248 views

How can I properly plot this .cube file in Python?

Motivation for Post: I saw a question about how to plot a .cube file recently on the Mathematica & Wolfram Language Stack Exchange. It was marked "off-...
D_C's user avatar
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3 votes
1 answer
93 views

Cubic spline interpolation through a series of images

Cubic spline interpolation is used in a lot of methods like Nudged Elastic Band (NEB), or String or Growing String Method (GSM) either to reparameterize the path, or to estimate the position of the ...
S R Maiti's user avatar
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2 votes
1 answer
55 views

What is the meaning of a "free energy per unit surface area" vs "pressure" plot?

I don't understand this graph. From the graph, does it mean that at high pressures the oxide layer is stable and this stability reduces at low pressures and temperatures?
Nana Kofi Boakye's user avatar
4 votes
0 answers
100 views

Why are some point groups for single atoms listed as Oh in the CCCBDB?

Does anyone know why the CCCBDB database lists the tin cation and antimony atom as having the Oh point group (please see the screenshot below from CCCBDB when I look at "All molecules sorted by ...
Xiong Sichao's user avatar
4 votes
0 answers
47 views

Why, if the potential is different from the Coulomb one, but has spherical symmetry, the eigenvalues of the system are non-degenerate? [closed]

Question duplicated from here https://mathematica.stackexchange.com/questions/287433/why-if-the-potential-is-different-from-the-coulomb-one-but-has-spherical-symme and here https://physics....
Mam Mam's user avatar
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4 votes
0 answers
148 views

Help with Mathematica for optimizing a Gaussian basis set for a hydrogen atom in a magnetic field

This is a follow-up to my previous question: Optimal Gaussian basis set for hydrogen atom in magnetic field Brief description of the problem I would like to find the ground and excited states of the ...
Mam Mam's user avatar
  • 253
3 votes
1 answer
55 views

Why is strain rate used instead of absolute strain for modelling stress relaxation of a viscoelastic material using the Maxwell model?

I don't quite fully understand the derivation of the Maxwell model for prediction of stress relaxation for viscoelstic materials. usually the governing equation can be described in terms of strain ...
Yourhelpismuchapprecciated's user avatar
4 votes
0 answers
98 views

Predict if a group will be acceptor/donor of H bonds [closed]

Context: I am a student of cheminformatics, and I am trying to solve a problem in predicting whether atom can be an acceptor/donor of hydrogen bonds, using Python programming language and RDKit ...
Gianmarco Luchetti 's user avatar
3 votes
1 answer
95 views

Molecular integrals in spherical harmonics?

I have been trying to write a basic HF code that can compute the MOs and total energy of a molecule. I followed the following reference for overlap and kinetic integrals. During a conversation with a ...
Hemanth Haridas's user avatar
5 votes
0 answers
99 views

How can one determine the time-step for imaginary time evolution?

The real-time evolution of a quantum system described by the state $\psi(t)$ is formally given by, $$ \psi(t+\Delta t) = \exp^{- i \hat{H} \Delta t / \hbar} \psi(t)\tag{1}$$ For dynamical simulations ...
squareroottwo's user avatar
4 votes
1 answer
118 views

Inverse Matrix Calculation

I am working on the charge transport calculation, based on the non-equilibrium green function method, for the Hamiltonian with the non-orthogonal basis. Suppose $H$ and $S$ are the Kohn-Sham ...
Kieran's user avatar
  • 703
3 votes
1 answer
77 views

Estimate the time between different residues?

Imagine now, I have 5 structures, and I want to estimate the time when the 5 structures are closer to each other at the same time. I thought I could extract the distance between the different ...
Abd-Elazeem Mohamed's user avatar
7 votes
0 answers
55 views

Database (or table) of functions obeying symmetry properties of space groups

I'm looking for a table or database containing mathematical functions that belong to crystallographic space groups by having the same symmetry elements. Imagine a 2D square planar lattice. It has a 4-...
Mika R.'s user avatar
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6 votes
1 answer
81 views

What is the X in Almlöf and Taylor's "Unified treatment of energy derivatives?"

I have been studying the possible methods for basis set optimizations. One notable paper is "Energy-optimized GTO basis sets for LCAO Calculations. A Gradient Approach" by Knut Faegri Jr. ...
John's user avatar
  • 268
5 votes
1 answer
212 views

Constrained optimisation on a hypersphere

I am currently trying to implement a GS2 (Gonzalez-Schlegel second order) IRC algorithm in a python code. I am following the original paper ref(1). The main problem is in the constrained optimisation ...
S R Maiti's user avatar
  • 7,011
2 votes
1 answer
107 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 ...
kevin's user avatar
  • 61
3 votes
0 answers
184 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 ...
kevin's user avatar
  • 61
5 votes
1 answer
1k views

Numerical Evaluation of Hessian?

I am trying to understand the construction of Hessian matrix using numerical differentiation (NUMFREQ option in ORCA for example). I understand that Hessian is a square matrix containing second ...
Hemanth Haridas's user avatar
5 votes
1 answer
109 views

How to Derive the Kong-Chakrabarty Mixing Rules

Background In the world of atomistic modeling with classical force fields, one is often given a force field defined by like interactions (e.g. argon-argon interactions). If one is working with a ...
Hayden S's user avatar
  • 940
3 votes
1 answer
89 views

Decay rate of DSD-PBEPBE-D3BJ

I gave up on the wB97X-2(TQZ) functional, which would have an exact decay rate of -1/r, re: my previous question and decided to use DSD-PBEPBE-D3BJ, which is available on vanilla Psi4. I then looked ...
Kanghun Kim's user avatar
2 votes
0 answers
57 views

how to incorporate size polydispersity in colloidal suspensions [closed]

Basically, I'm working on spherical colloids and investigating the phase behavior of these monodisperse colloids using Monte Carlo simulations (Fortran 77 coding). Now I want to introduce size ...
siva ram's user avatar
1 vote
0 answers
61 views

Question on possible cancellations in the computation of Dyson orbitals from FCC/FCI wavefunctions [closed]

Dyson orbitals are mathematically meaningful, in the sense that they, unlike the DFT orbitals for instance, are actual observables of the wavefunction, instead of being "the other way around"...
Kanghun Kim's user avatar
1 vote
0 answers
50 views

Question on known expression (see post) of exact XC functional in analytic (but not closed) form [closed]

This paper analytically solves the "inverse DFT problem" of mapping the ground-state density to the exact XC functional. And the exact density, i.e. the FCC/FCI density, can be expressed as ...
Kanghun Kim's user avatar
2 votes
1 answer
92 views

Is there an analogue of the K-S theorem for double hybrids

In my previous question, I was basically asking whether the results of the double hybrid using the exact XC functional are the same as those of just the exact XC functional. Even that sentence is hard ...
Kanghun Kim's user avatar
3 votes
0 answers
32 views

Is this method of obtaining only the exact "first excited state" density correct, under select conditions that makes it mathematically non-ambiguous? [closed]

(For context, see my other question here; this has been disproven (albeit contestedly), and is not even well-defined in the first place, so I'm going to ask a slightly different (and well-defined) ...
Kanghun Kim's user avatar
3 votes
1 answer
164 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....
Kanghun Kim's user avatar
7 votes
1 answer
129 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 &...
Kanghun Kim's user avatar
3 votes
1 answer
2k views

Why is the Alphafold PAE (predicted aligned error) not symmetric?

Cross-posted on AI Stack Exchange. We are running alphafold2 multimer on Google Colab to predict the association between two proteins. It generally works fine, but we get an asymmetric PAE plot for a ...
NKGon's user avatar
  • 31
5 votes
2 answers
306 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 ...
uhoh's user avatar
  • 2,034
5 votes
2 answers
306 views

Do the cc/pc/def2 basis sets mathematically converge to the CBS limit, assuming exact CI/DFT?

The cc-, pc- and def2- basis sets are often described as "systematic", in the sense that the results of these basis sets at different cardinal numbers (i.e. the number of ζ's) can be ...
Kanghun Kim's user avatar
12 votes
3 answers
3k views

Artificial intelligence is a hot topic, but should I pursue it if I'm interested in Matter Modeling?

Since my previous question seems to have a large number of views, I would like to ask my central question. I am a student now and should decide my major to research soon. AI/ML is a very hot research ...
neco's user avatar
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1 vote
0 answers
107 views

What kind of chemistry background to get to pursue computational chemistry from an IT background?

What kind of chemistry background to get to pursue computational chemistry from an IT background? I have no background in chemistry, and there might be others like me. But I know about computer models....
mavavilj's user avatar
  • 227
5 votes
1 answer
103 views

Cross-post: Matrix elements <n,k|x|n',k'> for Bloch states

Cross posted at Physics.SE I believe this is just elementary QM, but I'm getting awfully confused. The question is drawn from this paper on Wannier-Stark localization (but is self-contained). Let: \...
dsfkgjn's user avatar
  • 51
4 votes
1 answer
226 views

What is the curve fitting model used for the "Qubit™ Protein Assay Kit"?

This is the example of Qubit™ Protein Assay curve. It relates the concentration (x-axis) with fluorescence (y-axis). What is the curve-fitting method it use for this? Clearly this is not simple linear ...
littleworth's user avatar
  • 1,674