# Tag Info

18

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 ...

17

It is very important to differentiate between Density Functional Theory (DFT) and Density Functional Approximation (DFA). DFT is an exact theory and if we know the exact formulation for exchange-correlation functional, we should get the exact solution. However we don't have the exact formulation and hence we choose different approximations for it, ...

16

There's three scenarios that come to my mind, for when ab initio methods get abandoned: The cost becomes prohibitive (e.g. too many electrons) The insight is lost It is simply not required for what we want to do Prohibitive cost: If solving the Schrödinger equation (for example) is no longer possible, we may very well still wish we could solve the ...

12

Known failures of density functional approximations (DFAs) include anions, charge transfer systems and point defects (e.g. vacancy states). These are mainly due to self-interaction error, which can be mitigated to some level with hybrid functionals and range-separated hybrids. DFAs are also generally unreliable for systems with strong correlation, like many ...

11

First of all, MP2 (for example) is actually guaranteed to converge from above to the basis set limit even though MP2 in one specific basis set can give an energy lower than the FCI energy in that same basis set. So it's variational character in the basis set sense that matters here. Furthermore, variational character is not the most pertinent thing to ...

10

I will list 5 issues with F12/R12 methods, and then try to explain them the best I can: Need for an auxiliary basis set Most (if not all) F12/R12 methods require more than just a standard single-particle Gaussian basis set. For one of the most common elements (carbon) in electron structure calculations, you can see some of these auxiliary basis sets on Basis ...

10

In general, when computing any property with different models (e.g. level of theory, basis set, etc), if you don't have some kind of theoretical bound (like the variational principle) to determine what is a better result, you need a reference value to compare against. One choice for this reference is experimental results. At the end of the day, the goal of ...

10

This is a nice thought, but the two are not actually related. In principle, static correlation is completely accounted for in the exchange-correlation functional of Kohn-Sham DFT and there is no need for any mixing of the Kohn-Sham states, in fact it would lead to an incorrect result. In practice, the exchange-correlation functional is approximated and so ...

9

We know that the many-electron wave function has to be antisymmetric with respect to the exchange of two electrons: $\Psi (x_1,x_2,\dots,x_i,\dots,x_j,\dots)=-\Psi (x_1,x_2,\dots,x_j,\dots,x_i,\dots)$. This symmetry is satisfied by Slater determinants a.k.a. electron configurations, so the wave function can be written in terms of them as $|\Psi\rangle = \... 9 I think the best place to start is the original paper¹ proposing norm conserving pseudopotentials (NCPPs). It's very short and gives a nice explanation of why they were developed. I'll just give a brief summary here. Norm conservation (specifically of the charge density$\rho$) ensures that the electrostatic potential for$r>r_c$is accurate as a result ... 9 These two terms are quite rigorous in the way they're defined and used: Fermi correlation: This is the correlation found in the electron exchange term in a Hartree-Fock calculation, describes the correlation between electrons with parallel spins, and prevents two parallel-spin electrons from being found at the same location. Coulomb correlation: This is the ... 9 DFT is single effective correlated particle theory Problems that can be described by single determinant theory DFT in principle should able to provide a good description given that exact form of xc functional is known. It is not the problem of DFT that it fails. Failure is due to approximate nature of xc functional. One should in KS-DFT (one that uses ... 7 Yes, it is perfectly possible. As I've discussed here, it is possible to convert generally contracted basis sets into (somewhat) segmented sets without any formal loss of accuracy; next, one would discard functions with tiny coefficients and reoptimize the segmented exponents and contraction coefficients to end up with a segmented basis set. However, as you ... 7 Hylleraas' method is special to the case of the helium atom; note that the equation only has a single nucleus. When you go to more electrons, you get more and more interelectronic distances in your wave function ansatz, which will blow up the scaling; this is why the method is impractical for several electrons. (Also, I think you would need several expansion ... 6 Hylleraas wavefunctions tend only to be used for systems with up to 3 electrons. The reason for this is because the integrals have only been worked out analytically for up to 3 electrons, and they would be far too slow to do numerically. People have talked about using Hylleraas wavefunctions for 4 electrons, but when you ask them to show you results on real ... 6 I think Nike has answered to all questions adequately enough. I am sharing my understanding as one of the developers of the PNO-based local coupled-cluster (CC) methods, codes for computing response properties in particular. In coupled-cluster theory, the correlated wavefunction is described in terms of "cluster amplitudes" (which are the ... 6 I'll answer each of your three questions separately, but the one you say is "most important" will go first 😊 And most importantly, why are they used for correlation calculation? They can significantly reduce the cost of a calculation on a big system, especially when there is a large number of "virtual" orbitals (unoccupied orbitals) in ... 5 Well, Nike already answered the point about the variationality: even though methods like MP2, CCSD, and CCSD(T) are non-variational in that they may over- or underestimate the energy of the ground state (or excited states) of the Schrödinger equation, the energy reproduced by any given method typically does behave variationally with respect to the basis set.... 5 I recommend the use of Multiwfn package. This software is free with Windows/Linux versions. It uses the wave function calculated from other software. From the site: Briefly speaking, Multiwfn can perform wavefunction analyses based on outputted file of almost all well-known quantum chemistry programs, such as Gaussian, ORCA, GAMESS-US, Molpro, NWChem, ... 4 By the "metal cores", If you're referring to the overlapping of wave functions of electrons of metal ions separated by a distance, then you can in principle use quantum ESPRESSO to get some insights. You can define a CIF file with the ions separated at varying distances from each other and visualize the electronic density. Apart from quantum ... 4 What are the available methods for the calculation of reference interaction energies of layered materials? I assume that the meaning of the "reference interaction energy" is the interlayer binding energy between layers. Then you can use SCAN+rVV10 method. Reference paper: Phys. Rev. X 6, 041005 Description: The resultant SCAN+rVV10 is the only ... 3 LDA only includes local density effects. GGA also includes dependence on the gradient of the density. Meta-GGAs include dependence on the Laplacian of the density and/or the local kinetic energy density. Double hybrids include a mixture of post-Hartree-Fock correlation; typically either according to MP2 or RPA. 3 DFT can break down (like all numerical methods) if you want to model a too-large or too-complicated system. This is especially relevant if you want to study impurities, where periodic boundary conditions are less helpful. The exchange correlation functionals are a key weakness for DFT, since they are empirical approximations. Therefore the method may ... 1 An easier route to using symmetry-adapted CI with hand-derived matrix elements is to implement CI with determinant strings. That is, you construct bitstrings of which orbitals are occupied in the determinant, and you don't care about adapting your basis for$\hat{S}^2\$. This is the way most codes work, since the resulting algorithm is easy to make very fast, ...

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