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What's up with all that magic? (A chapter formerly known as Introduction)
The hunt for for the holy grail of density functional theory (DFT) has come a long way.[1] Becke states in the introduction of the cited paper:
Density-functional theory (DFT) is a subtle, seductive, provocative business. Its basic premise, that all the intricate motions and pair ...
31
This is a great question and I love it. Thank you for taking the time to not only post the question but each attempted response. I will try to address the parts of this question that I can at the moment. I will list, in order, your attempted answer along with my response.
Carbene H2C: has two singlet configurations that contribute to the ground ...
29
When people say that Kohn-Sham orbitals bear no physical meaning, they mean it in the sense that nobody has proved mathematically that they mean anything. However, it has been empirically observed that many times, Kohn-Sham orbitals often do look very much like Hartree-Fock orbitals, which do have accepted physical interpretations in molecular orbital theory....
26
PBE
The PBE functional${}^{[1]}$ belongs to the class of generalized gradient approximation (GGA) functionals for the exchange-correlation energy $E_{\mathrm{xc}}$. Considering that the dependence $E_{\mathrm{xc}}[\rho]$ may be non-local, i.e. $E_{\mathrm{xc}}$ may depend on the density $\rho$ at a given point (locality), but also on $\rho$ nearby (non-...
23
First note that the acronym DFA I used in my comment originates from Axel D. Becke paper on 50 year anniversary of DFT in chemistry:
Let us introduce the acronym DFA at this point for “density-functional
approximation.” If you attend DFT meetings, you will know that Mel
Levy often needs to remind us that DFT is exact. The failures we
report at ...
20
There are many tricks. Since I'm not a developer, I'm not privy to all of them, but there are some simple things to start.
Some integrals are predictably close to zero: Even in fully first-principals calculations, there are parts of the code that prune out integrals that will clearly be negligible. This cuts out a lot of work. Consider, for example, overlap ...
18
This is a complex issue, particularly because people often like to think in terms of an indepedent-particle picture (i.e. the aufbau filling up orbitals), even though the exact many-body wavefunction has strong electron-electron correlations. So let me rephrase your question:
What is the relationship between the KS eigenfunctions and the exact many-body ...
17
For Structures and Energies: Answer Hazy, Try Again Later
People can talk on this subject for literally days.
It mostly comes down to computational expense vs accuracy - if you have a larger system, you can't afford the fancier functionals. The absolute highest accuracy state of the art functional-wise would probably be those using the Random-Phase ...
17
There are no wavefunctions in DFT.
I don't like that "wave function" is used here in the plural form and I feel like it reflects OP's misconception. The right way to say this is
There is no wave function in DFT.
See, there exist only one wave function, the function that describes the state of a system in question and can be used to calculate its ...
15
The designation PBEPBE is an actual terrible artefact from researchers using Gaussian. The actual publication[1, 2] only refers to it as PBE, and most other program packages (I know) implement it as such. Often they make the correlation and exchange parts separately available via PBEC and PBEX, or similar. Unfortunately this designation also made it into the ...
14
Depending on what you're after, you might want to look for programs using libxc, so you can completely define your own functionals.
From the libxc section of the Octopus wiki, these include:
Abinit – plane-wave code
APE – an atomic code
Atomistix ToolKit – numerical orbitals code
AtomPAW – projector augmented wave functions generator
BigDFT – ...
14
There are many good review articles, but I really like the freely available "The ABC of DFT" by Kieron Burke (and friends) and a recent review article that tries to keep to understandable language.
The problem is treating the Coulomb interactions. Conventional DFT is not "asymptotically correct." That is, at long range, the 1/r behavior is not met, and ...
13
It is generally recommended not to use a cc basis set with a DFT method (and I guess conversely, a basis set aimed at DFT should not be used with a coupled cluster method).
This statement glosses over some specifics that might be important.
There is nothing technically wrong with using correlation-consistent or ANO basis sets with DFT, unless the basis is ...
12
There are many criteria that you can follow to choose a functional, in no special order:
Availability: Do you have access to a software package in which the functional is implemented? If yes, are analytic derivatives also implemented? Do you need extra dispersion corrections? Are they available?
Computational cost: Functionals in different steps of "Jacob's ...
12
As in geometry optimization, you are searching for stationary point on the potential energy surface (PES). Not for local minimum, but for saddle point, therefore in GAMESS, you specify RUNTYP=SADPOINT. You would also need the correct (non-guess) Hessian matrix, which you can calculate separately with RUNTYP=HESSIAN. In transition state (TS), you should have ...
12
What the exchange-correlation hole means in common words?
Assuming that the probability is the common word, one could say that the exchange-correlation hole, is a region of space around an electron in which the probability of finding another electron is close to zero due to electron correlation.
How do you explain it to a non-literate person?
Long story ...
11
Time-dependent DFT can be used to predict excitation energies through a linear-response formulation.
In this Gaussian result, beyond the first line, you are looking at the largest coefficients in the configuration-interaction (CI) style expansion.
(It's not strictly CI, but the implementation of time-dependent HF or RPA is essentially the same for TDDFT or ...
11
I am afraid I do not know of a paper specifically discussing the effects of DFT dispersion corrections on intramolecular properties. However, it should be noted that for short-range descriptors (such as bond lengths and bending angles) the dispersion corrections will not influence those as they correspond to distances below the typical distance at which the ...
11
$\newcommand{\el}{_\mathrm{e}}
\newcommand{\dif}{\mathrm{d}}
\newcommand{\braket}[2]{\langle{#1}\vert{#2}\rangle}$Consider an $n$-electron system in an arbitrary electronic state represented by the electronic wave function $\psi\el(\vec{q}_{1}, \vec{q}_{1}, \dotsc, \vec{q}_{n})$, where $\vec{q}_{i}$ stands for joint spin-spatial coordinate of $i$-th electron,...
11
I will quote the paper quite a bit, but I'll try and summarize a bit after the quotes and equations. You might want to start at the bottom and work backward, a lot of this is just for later reference.
First, some background. Equation 3:
$$
E^{(2)} = \sum_{AB} \sum_{n=6,8,10,\dots} s_{n} \frac{C_{n}^{AB}}{r_{AB}^{n}} f_{d,n}(r_{AB})
$$
Here, the first ...
11
That is true: in the Kohn–Sham model electrons both in occupied and in virtual orbitals are "moving" in the field $n-1$ electrons, while in the Hartee-Fock model electrons in occupied orbitals are "moving" in the field $n-1$ electrons, but electrons in virtual orbitals are "moving" in the field all $n$ electrons. And this is simply "by construction": you ...
10
First things first, I would check your code: there is no reason 400 unique integrals should take an hour, even with the most naive implementation. You are computing at a rate of an integral every ten seconds. While I agree with all the comments pointing to increasing parallelization, I think efficient scalar code is more important. Why scale up inefficient ...
10
To further reduce storage requirement, integrals may be calculated on the fly, emplpoying different caching strategies. For some methods storing all the integrals is plainly impossible.
10
In addition to the good answers that have already been given, it is important to note that for DFT to be properly implemented, you must calibrate the functional(s) to whatever it is you are examining. While this is idealistic, it is far from common practice.
Calibrating is very tedious and time intensive than just running with a single functional. For ...
10
Electron density, is defined as the probability density of finding any of the $n$ electrons with arbitrary spin at some point $\vec{r}_{1}$ in space,
$$
\newcommand{\el}{_\mathrm{el}}
\newcommand{\dif}{\mathrm{d}}
\rho(\vec{r}_{1})
:=
n \sum_{m_{s1}} \sum_{m_{s2}} \dotsi \sum_{m_{sn}} \iint \dotsi \int
| ψ\el(\vec{q}_{1}, \vec{q}_{2}, ...
10
From a theoretical standpoint, that approach is correct:
$$
\mu_i = \sum_{a}^{N_{\text{atoms}}} \sum_{i\in\{x,y,z\}} r_{ia}q_{a},
$$
where the set of atomic partial charges $\{q\}$ could come from partitioning the density in AO space (Mulliken, Lowdin), partitioning the density in real space (Bader, Voronoi, Hirshfeld), partitioning the electrostatic ...
9
The short answer is not. You cannot define a constant force for an atom or set of atoms in a system.
If you still want to modify force constants, this is the way to do it:
Gaussian, you can modify through the keyword GEOM(IHarmonic=n), where n is part of: $\frac{n}{10^6}$ which indicates the respective force applied to the system. Its units are $\frac{...
9
First off, I would like to note that you wrongly interpreted the very first equation. Below I quote the relevant part of the paper:
In the Hartree-Fock (HF) approximation for, say, the $\ce{Na}$ atom,
the ground-state wave function has the form
$$
\Psi = \mathcal{A} (\Phi_{\mathrm{core}} \phi_\nu X) \, , \tag{1}
$$
where $\Phi_{\mathrm{core}}$ ...
8
The convention used by many is that ab initio refers solely to wave-function based methods of various sorts and that first principles refers to either wave-function or DFT methods with little approximation.
I can't find a citation at the moment, but I know this convention is fairly widely used in, e.g., J. Phys. Chem. journals.
The IUPAC gold book doesn't ...
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