# Tag Info

## Hot answers tagged density-functional-theory

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There are many reasons why so many different scientific packages have been developed These packages were developed by individual researchers who were in competition with each other and also work mostly independently. It was natural that different packages sprung out of different regions (e.g. NWChem stands for NorthWest Chem, because it’s based at Pacific ...

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Below is a summary of what I have found: What is meant by "Exact exchange"$\,$? The question mentions the following (in order of how they were presented in the question): Exact exchange-correlation potential (used in this 2019 paper in Nature Communications). Exact Hartree-Fock exchange energy functional (only 4 results, 3 from the same authors). Exact ...

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Disclaimer and warning: long and likely biased answer. Background: The Pople style basis sets were defined almost 50 years ago. The 6-31G was designed for HF calculations, the 6-311G for MP2 calculations. For computational efficiency reasons, the s- and p-exponents were constrained to be identical. Polarization functions were defined for 1d, 2d, 3d and 1f. ...

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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 that we name it after him. However I completely disagree with the sentence that you have quoted. Keep in mind that even though the Nobel Lecture was in 1999, Kohn ...

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I think this question somewhat comes down to what "camp" of DFT progression you subscribe to. I should specify upfront that this summary is mainly centered around molecular systems, so some of the recommendations likely vary for materials where the computational workload can often be much greater. One side really emphasizes accuracy with respect to ...

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Understanding, deriving, writing, testing and debugging an ab initio code can be a lenghty and tedious task. I'd like to provide a starting point for you here. If you just to it for pedagocial reasons, it might be advisable to start with the atomic problem and try to solve it with DFT. The effort for that is not too big, but it covers nearly all the nesseary ...

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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-functional. In 2006, Stefan Grimme introduced what later became known as "double hybrid functionals", which not only mix the Hartree-Fock exchange functional with a ...

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Quick Summary: There's no way around performing a convergence test. However, it is possible to obtain convergence much faster than the Phonopy approach by using nondiagonal supercells [1]. The basic quantity you build when performing a phonon calculation is the matrix of force constants, given by: $$D_{i\alpha,i^{\prime}\alpha^{\prime}}(\mathbf{R}_p,\... 26 By definition all of them, because Density Functional Theory is in principle exact. Becke states:[1] Density-functional theory (DFT) is a subtle, seductive, provocative business. Its basic premise, that all the intricate motions and pair correlations in a many-electron system are somehow contained in the total electron density alone, is so compelling it ... 26 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 constraints and is constructed to be almost exact for the noble gasses and jellium surfaces. Early evidence suggests that SCAN is more accurate than and of comparable ... 25 There are many reasons why we have so many different density functional theory programs, and it would be nigh on impossible to give a full answer encompassing all of them. A brief, select few: Scientific reasons, because you need something that can handle some very specific physics or chemistry accurately and efficiently. At a simple level it might be that ... 25 These are a few extra points to complement Andrew Rosen's comprehensive response: To be absolutely clear, typical DFT calculations are not performed at 0K, a better description of what happens is that they are performed "for a static crystal". Static crystal means that the atoms are fixed at their crystallographic positions (which is what a typical DFT ... 24 Here is a DFT simulation of a virus, in solution! "Combining Linear-Scaling DFT with Subsystem DFT in Born-Oppenheimer and Ehrenfest Molecular Dynamics simulations: from Molecules to a Virus in Solution." But I like the way Frank Neese (lead author of ORCA) described his coupled cluster calculation of a protein: "this is what I call quantum mechanical ... 22 This is a good question. In general, it often may not matter too much, but as with all aspects of numerical convergence, the only way for you to know for sure is to investigate. The concise answer is that in most cases, you can probably feel quite comfortable using the starting geometry for your convergence tests if: 1) the structure is reasonable (e.g. it's ... 22 To complement mykd's already excellent answer, I will just add that the approximant we all learn in school (the Taylor approximant) is nice to teach and easy to help students learn the concept of approximations, but in practice it's one of the worst options in terms of it's accuracy-to-complexity ratio. The Taylor approximant matches the n^{\textrm{th}} ... 21 Another thing not mentioned yet is that there are, broadly speaking, two camps of codes: those that are primarily meant for periodic (often but not exclusively plane-wave) DFT (VASP, Quantum Espresso, etc.), and those that are primarily meant for finite systems like molecules (e.g. Gaussian, ORCA). Also, there are different algorithms in each package, some ... 21 Yes, there are! One early example that's still in use today is the Universal Structure Predictor: Evolutionary Xtallography (USPEX) method. You can find many "success cases" on their website if you're curious. The First-Principles-Assisted Structure Solution (FPASS) and Prototype Electrostatic Ground States (PEGS) methods are a couple of other codes used for ... 21 I know of several papers over the million-atom mark: 2,097,152 atoms "Calculations for millions of atoms with density functional theory: linear scaling shows its potential" 1,012,500 atoms using linear-scaling orbital-free DFT: "Accurate simulations of metals at the mesoscale: Explicit treatment of 1 million atoms with quantum mechanics" "Million Atom KS-... 21 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.[1,2] In any approximate density functional, the DFT error is \Delta E = \tilde E[\tilde n] - E[n] where E and n are exact functional and density while \... 20 There isn't a single correct answer to this question, and it depends on what is slow, what kind of material you are modeling, and what you are trying to calculate. This answer is mostly going to be partially copied from my blog post here. Geometry Optimizations Don’t waste your time using super high-accuracy settings on a structure far from the local ... 20 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-separation. The electron-electron Coulomb operator for the exchange contribution is separated into a short and long range contribution. \frac{1}{... 20 You are correct that KS-DFT, strictly speaking, involves calculations of a potential energy surface at 0 K. However, if you accept that the density functional approximation you are using is sufficiently accurate, it is not too difficult of a stretch to go from 0 K to finite temperature conditions for an application of interest. The key assumption is that the ... 20 B3LYP is still a decent functional at its level of theory (single-hybrid functional), but you're right that there's a general criticism of it, which I largely hear in the form of people saying things like "all they did was B3LYP/6-31G*" to criticize non-experts that blindly use this combination which became the "default" in chemistry for ... 19 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^{\text{HF}}_x + b \cdot E^{\text{GGA}}_x $$to obtain the exchange part of the exchange-correlation energy. Typically, one imposes a+b = 1, but some authors ... 19 Let us represent the exact exchange-correlation (xc) energy as a sum of an exchange term (x) and a correlation term (c):$$ \tag{1} E_{xc} = E_x + E_c~ . $$For a uniform electron gas (UEG), we do have an exact expression for the exchange term:$$ \tag{2} E_{x} = - \frac{3}{4}\left( \frac{3}{\pi} \right)^{1/3}\int\rho(\mathbf{r})^{4/3}\ \mathrm{d}\mathbf{r}\ ...

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As previously stated, arguably the most mature and widely used set of tools is currently a combination of Pymatgen, FireWorks, Custodian, and Atomate (which is built upon the prior three Python packages). These tools were constructed as part of the Materials Project but have seen uses in other high-throughput DFT studies. Another general workflow package for ...

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First, realize that optimization is a general thing that can be done for all types of problems. In the geometry optimization of atoms and molecules, what we want to find is the configuration of the nuclei which is a minima on the potential energy surface. In other words, we want to find the positions, x which satisfy: $\min(E[x])$ Secondly, the quantum ...

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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, that in turn allows to evaluate electronic spectra of molecular and condensed matter systems. The time-dependent density functional theory (TDDFT) in the Kohn–...

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First, a word of caution: it is hard to generalize since there are so many different approximations to the exact exchange-correlation functional. Nonetheless, in my opinion: The biggest weakness of all existing (and arguably all plausible) implementations of DFT is their limited predictive power. In practice, this means that you need to know a lot about ...

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