83
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Accepted
Did the 2019 discovery of O(N log(N)) multiplication have a practical outcome?
What are the state-of-the-art algorithms for long-integer multiplication?
First let me address the point you raised about the schoolbook algorithm having $\mathcal{O}(n^2)$ scaling, by saying that ...
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38
votes
Accepted
Was Walter Kohn wrong about this?
Kohn is easily one of my favorite humans of all time, and he was a role model to whom I looked up in great admiration for most of my academic life; in fact before this site was created, I proposed ...
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35
votes
Did the 2019 discovery of O(N log(N)) multiplication have a practical outcome?
This $O(n\ln n)$ integer multiplication algorithm is a galactic algorithm, meaning that it won't be used despite being "of lower complexity" because it only becomes more efficient than ...
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29
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What are some recent developments in density functional theory?
2006 (Grimme): Double hybrid functionals
The timeline of milestones you have given, includes a hybrid functional called B3LYP, which mixes a Hartree-Fock exchange functional with a GGA exchange-...
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27
votes
What are some recent developments in density functional theory?
2015 (Sun et al.): SCAN functional
The SCAN meta-GGA functional is an extension of the popular PBE GGA [1] and the TPSS [2] and revTPSS [3] meta-GGAs, SCAN adheres to all 17 known exact XC ...
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26
votes
Accepted
What is matter modeling?
"Matter modeling" is a term that was coined by Stack Exchangers!
That's why the words "matter" and "modeling" next to each other, don't seem to exist in any of the ...
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23
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Did the 2019 discovery of O(N log(N)) multiplication have a practical outcome?
To take a slight detour, we can also look at the progress of matrix multiplication algorithms. As mentioned in a few comments here, standard matrix multiplication is $O(n^{3})$ and any exact method ...
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23
votes
What are some recent developments in density functional theory?
2013: Density-Corrected DFT (DC-DFT)
The goal of Density-Corrected DFT (DC-DFT) is not only to get better accuracy but also to understand and correct the true error in the functional approximation.[1,...
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22
votes
What are some recent developments in density functional theory?
Dispersion corrected methods (2007/2010)
Lots of answers already, I would say the main ones are covered. However, in the spirit of the question, I don't think anyone has done dispersion corrections ...
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20
votes
What are some recent developments in density functional theory?
2004 (Yanai et al.): Range separation
Often, the source of DFT improvement comes from Hartree-Fock as is also obvious from the answer involving double hybrid functionals. So too it is with range-...
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19
votes
Did the 2019 discovery of O(N log(N)) multiplication have a practical outcome?
Can someone explain in detail the impact of any of the multiplication algorithms scaling better than N2, for some practical application?
An actual application is right in front of our eyes: digital ...
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19
votes
What are some recent developments in density functional theory?
1993 (Becke): Hybrid Functionals
Axel D. Becke introduced the adiabatic-connection model, which allows for mixing of DFT exchange and Fock-like exchange via the formula
$$
E_{\text{x}} = a \cdot E^{\...
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18
votes
What are some recent developments in density functional theory?
1995 (Casida): TD-DFRT
Time-Dependent Density Functional Response Theory is a linear response formulation of TDDFT for the calculation of excitation energies and corresponding transition amplitudes, ...
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17
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Mathematical expression of SCAN (Strongly Constrained and Appropriately Normed) constraints in DFT
Constraint #13: Size-Extensivity
While the Wikipedia page for size-consistency and size-extensivity gives a clear formula for the definition of size-consistency, unfortunately they did not give a ...
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16
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Did the 2019 discovery of O(N log(N)) multiplication have a practical outcome?
Even the simplest better-than-schoolbook (O(n^2)) algorithms like Karatsuba are only useful in practice for large n. But what is ...
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15
votes
Did the 2019 discovery of O(N log(N)) multiplication have a practical outcome?
Practical importance: compactifying explanations
It is widely believed that $\mathcal{O}(n \log n)$ is the best possible result, and therefore we no longer have to say $\mathcal{O}(n\log n\cdot 2^{2\...
13
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What are some recent developments in density functional theory?
2005 (Bartlett): ab initio DFT
Basically one takes the xc functional from a wave function approach such as MBPT(2), CC, etc. and constructs an xc potential from them using density conditions or a ...
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12
votes
What are some recent developments in density functional theory?
I would add some developments in TDDFT that came around 1996 and resonated only later such as:
the Casida equation (Casida 1995) that allows to calculate excitation energies and electronic spectra
...
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11
votes
What is matter modeling?
First of all, we assume the matter is constituted by nuclei and electrons, as illustrated by the following figure:
Mathematically, the matter is mapped into the following Hamiltonian:
$$H=T_e + T_n + ...
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10
votes
What is the role of a chemist in computational chemistry?
In terms of the role of chemists for what you call the "most essential task":
"What I understand is that the most essential task is the improvement
of exchange correlation functionals ...
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10
votes
What are some recent developments in density functional theory?
Most chemists' point of view could be condensed as follows:
Implementation of DFT in Gaussian (Pople et al, 1992)
LDAs and GGAs were implemented in Gaussian 92/DFT by Pople, Gill and Johnson [Chem ...
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9
votes
What are some recent developments in density functional theory?
1997 (Marzari & Vanderbilt): MLWF
These methods enable a more qualitative view of the electron density by projecting the Bloch wavefunctions into localized Wannier functions [1], which is ...
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9
votes
What is the role of a chemist in computational chemistry?
As a computational chemist, I find my role is to act as a translator. In a molecular dynamics simulation, I need to know enough physics and maths to translate chemical structures into a physical model,...
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9
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Accepted
Analog computing in matter modeling today: Any applications?
I don't think analog computers are quite at the level they need to be yet, but there are people working to make them applicable to matter modeling applications.
Dr. Rahul Sarpeshkar at MIT developed ...
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8
votes
Accepted
Examples of matter modeling in fiction
The Last Question by Isaac Asimov is a short story where a computer is tasked with solving the problem of entropy.
It's a brilliant story and definitely worth listening to and reading
https://youtu.be/...
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8
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What are some recent developments in density functional theory?
2020 Furness et al: r$^2$SCAN functional
The SCAN functional is the most recent meta-GGA functional constructed from first principles, which satisfies all known bounds. However, SCAN is also ...
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8
votes
What is the role of a chemist in computational chemistry?
The role of the chemist in computational chemistry is to ask the right questions. Then, the computational chemist can step in, and start computing. The computational chemist should know which models ...
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8
votes
Accepted
Why is the planewave codes ecosystem healthier on free/opensource software adoption, when compared to codes supporting atom-centered orbitals?
Disclaimer: These are just some observations; I don't claim to know the answer to this question.
There's a lot of overlap between both camps, but I think people tend to stick mostly with one kind of ...
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7
votes
What are some recent developments in density functional theory?
2001 (Taylor et al.): DFT+NEGF
Combining density functional theory (NEGF) with nonequilibrium Green's function method (NEGF), a self-consistent first-principles technique for modeling quantum ...
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6
votes
What are some recent developments in density functional theory?
2014 (Gagliardi): MPCDFT
Multiconfiguration Pair-Density Functional Theory (MC-PDFT) is a theoretical framework that combines multiconfigurational wave functions with a generalization of density ...
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