83
votes
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 ...
- 33.6k
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 ...
- 451
29
votes
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-...
- 33.6k
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 ...
- 836
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 ...
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23
votes
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 ...
- 15.2k
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,...
- 239
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 ...
- 321
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-...
- 4,306
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 ...
- 291
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^{\...
- 1,643
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, ...
- 766
16
votes
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 ...
- 461
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
votes
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 ...
- 946
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 (...
- 18k
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
...
- 766
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 ...
- 18k
10
votes
Accepted
How does charge mixing work?
Density mixing is a type of self-consistent field (SCF) method, which tries to find the closest density to the Kohn-Sham (or Hartree-Fock etc) ground state density by mixing previous densities and ...
- 6,567
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 ...
- 459
9
votes
Order of scaling for different algorithms
From my experience with Stochastic Series Expansion (SSE) QMC (a type of discrete-time QMC) the computational cost scales like $\beta L^d$.
In practice, it's often important to account for the finite-...
- 6,579
9
votes
Accepted
How to build cartesian representations of spherical Gaussian basis functions?
Following Helgaker et al. in "Molecular Electronic-Structure Theory" a real valued spherical harmonic GTO can be written as
$$\chi_{\alpha_{nl}lm}^{GTO}=N_{\alpha_{nl}lm}^{GTO}S_{lm}e^{-\...
- 763
8
votes
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 ...
- 18k
7
votes
Order of scaling for different algorithms
Conventional implementations of Kohn-Sham DFT scale cubically with system size. This is principally because at some point they:
orthonormalise a set of $N$ trial states, each expressed in a basis ...
- 6,567
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 ...
- 14.9k
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 ...
5
votes
Evaluating the MSD of my simulation
I have no prior experience with molecular dynamics really, but to get you started I have found a resource with a pretty detailed method of calculating the MSD (Mean square displacement).
Looking at ...
- 10.8k
5
votes
When is coupled cluster preferred over DFT?
Coupled cluster is theoretically more accurate that DFT, as it's limiting behaviour is an exact solution to the Schrödinger equation. By limiting behaviour, I mean including all possible excitations (...
- 890
4
votes
Evaluating the MSD of my simulation
Alright, so it turns out @TristanMaxson was right - it was the periodic boundary conditions that were messing with my computation. The solution to it was to find the unwrapped coordinates of my system....
- 4,141
4
votes
What are some recent developments in density functional theory?
2016: Reproducibility of DFT calculations (Lejaeghere et al)
Lejaeghere et al.$^1$ compared the calculated values for the equation of states for 71 elemental crystals from 15 different widely used DFT ...
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