# Questions tagged [mathematical-modeling]

Questions related to mathematical modeling of materials systems.

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### Difference between Phase Diagram and Convex Hull

in literature I sometimes see a mixed use of the words Phase Diagram and Convex Hull. However from my current knowledge, there are some differences between them. A phase diagram views the difference ...
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### What is the real form of p-type gaussian basis functions?

I am attempting to write my own Hartree-Fock program, and I am currently working on implementing the STO-3G basis set for a few atoms. For C, it is of the form ...
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### 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 ...
• 1,592
57 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-...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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2k 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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1 vote
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### 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"...
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1 vote
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### 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 ...
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### 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 ...
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### 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) ...
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### 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....
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### 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 &...
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### 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 ...
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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 ...
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