# Tag Info

11

The simplest correct answer is that DFT is in $O(N_e^3)$. This comes from the idea that you are ultimately diagonalizing a Hamiltonian with dimension proportional to the number of elections and diagonalization is technically $O(n^3)$. In reality, DFT is a bunch of steps and different steps are rate-limiting in different context. If we restrict ourselves ...

10

One of the biggest limitations of density functional theory is that it doesn't correctly treat the exchange interaction. While it has been shown that there exists a functional that will treat exchange correctly, this functional is unknown and semi-empirical methods are used to make approximations to it. The coulomb part of the functional that I see most ...

8

Aesin already answered part of your question. I can provide you with some more information on GAMESS(US). It is possible to make GAMESS(US) use the same 'type' of B3LYP as Gaussian 03. For this, you need to specify "DFT=B3LYP1" as you already mentioned in your question. This selects B3LYP with VWN formula 1 RPA local correlation which, to the best of my ...

6

Any numerical differences between A and B will become exponentially larger with time (i.e. the Lyapunov instability, as discussed in Frenkel and Smit). Even a small difference due to basis set size could result in dramatic differences in the trajectory over time. So I'm not sure that a comparison between individual trajectories will be meaningful. It may be ...

6

The Gaussian implementation of B3LYP uses the VWN3 functional, according to the manual. Making Gaussian use the VWN5 functional instead for it is a bit tricky, but can apparently be done by adding all the following to the route line: bv5lyp - to specify which functional components - Becke exchange, and VWN5 local, LYP non-local correlation. iop(3/76=...

5

An important limitation to density functional theory is DFT's characteristically poor treatment of long-range noncovalent interactions. Many functionals give very incorrect results for $\pi\cdots\pi$ stacking, hydrogen bonding and noble gas VdW dimerisation, however quite recent functionals such as the 'Minnesota' family of Trular and coworkers are ...

5

Frozen core approximations use explicit orbitals for each core electron, which leads to explicit Coulombic potential terms: $$\langle v|V_{val,core}|w\rangle = \sum_{i\in core} \int \frac{v^\ast(r)w(r)|\phi_i(r_1)|^2}{\|r-r_1\|}-\frac{v^\ast(r)\phi_i(r)\phi_i^\ast(r_1)w(r_1)}{\|r-r_1\|}d^3r_1d^3r$$ Effective core potentials model the potential directly ...

4

To specifically answer the question: The main shortcoming of Density Functional Theory is that even though it is a formally exact reformulation of quantum theory, in the current state of the theory, approximations are required for the Exchange-Correlation energy functional. All the Density-Functional approximations that we have so far fail to exactly ...

4

If you're looking for a general reference, I would recommend the book by Parr and Yang, Density Functional Theory of Atoms and Molecules. I used this book when I sat in on an advanced course in chemical kinetics which discussed how to use quantum chemistry to calculate energies and reaction rates. It's a reasonably complete overview of DFT, although it is ...

3

NWChem's built-in B3LYP is supposed to agree with Gaussian's, modulo the grid and tolerance issues noted in Thom's answer. You can prescribe any functional form for which the constituents are supported using the explicit XC interface: http://www.nwchem-sw.org/index.php/Density_Functional_Theory_for_Molecules#XC_and_DECOMP_--_Exchange-Correlation_Potentials. ...

2

I'm honestly not overly familiar with these schemes, but I believe the ADF package has a bonding energy decomposition scheme by Ziegler and Rauk implemented in it, and there's also the Morokuma scheme which looks to be available in at least GAMESS and ADF. I think these both produce the terms you're looking for.

2

Matt: Have you looked at the polymer self-consistent field theory literature? It's rather similar in spirit to classical DFT's, and discretizations of the system are routinely performed. There's a paper by Alexander-Katz et al. [JCP, 122, 014904 (2005)] that specifically discusses finite-size and discretization effects. That might be a place to start.

2

Use the Poisson equation in its differential form to obtain the Hartree potential. It has a nice form in spherical coordinates. See for example the seminal paper of Becke, in which this problem is solved for the general polyatomic case without relying on spherical symmetry.

2

There is no universal answer to this. You will have to find publications that have similar set-ups and already did the benchmarking, or you will have to do it yourself. Once you understand how the methods work, and any quantum/ computational chemistry book is sufficient for that, you have a very general understanding of what might go wrong. It is also very ...

2

In the standard form, KS-DFT is solved variationally, which means that additional degrees of freedom in the basis set must lead to a lower (or equal) energy. This is a very basic property of the variational method and the math is almost certainly explained on Wikipedia or equivalent. I am assuming the same functional is used. Each DFT functional provides ...

2

First thought is to use A and B on standard validation test cases. I'm not sure what's available for validation on MD (googling "molecular dynamics validation" turned up a lot), but in CFD there's plenty of databases. If you need to validate something very specific (it sounds like you are), then you'll need to compile some statistics to convince me that A ...

1

Density functional theory optimizes the total energy with respect to the (possibly constrained) electronic density. The usual numerical procedure for this optimization is embodied by the KS method. The KS procedure will give you the optimal total energy and the ground-state (gs) density for which this optimal energy is achieved. This optimization procedure ...

1

In planewave calculations, we use a regularly spaced grid that fills the entire unit cell to perform calculations. The number of planewaves is proportional to the number of grid points used (as well as other system dependent parameters). Thus, when you add vacuum to your unit cell, you increase the number of planewave basis functions. With this in mind, you ...

1

Quantum Chemistry codes can get very complicated very fast. Even if you limit yourself to DFT, there are many functionals to support. There's going to be a trade off here for you. You can get a simple, smaller code base, but you'll end up with very few features. Or you can go with a larger, more mature code base, but it will be more complicated for you to ...

1

I don't fully understand where the problem is. Where the bonds are supposed to be, S-Se bonds? Like this, those distances don't seem much longer than Cd-S. In any case, you should not be troubled by the "sticks" connecting atoms in the visual representation: there are thresholds telling the program when to show them, and when not to show them. Actually, in ...

1

Not aware of any CPU benchmarks for DFT. This might be due to different programs being built to take advantage of different architectures etc. If you are truly looking for pure computational power and do not intend to use the computer in any other way (gaming, movies etc.) then it might be worthwhile to look into buying a server computer. A quick search in ...

1

after a short (say 10 ps) equilibration period You say yourself that the re-equilibration period is 'short'. Have you tried waiting longer to see if the two re-initialized systems converge, and if so at what rate? Velocity-rescaling is a notoriously naive thermostat. Maybe you could replace it with something more realistic? (Berendsen, Nose-Hoover, etc.) If ...

1

I think that the problem encountered in this question is not specificly for DFT. But more in general for QM methods. You say that $E(r\rightarrow \infty) \neq0$. Now let us consider the molecular Hamiltonian: $$\hat{H}=\hat{T}_N+\hat{T}_e+\hat{U}_{NN}+\hat{U}_{Ne}+\hat{U}_{ee}$$ Here: The kinetic energy of the nucleis: \hat{T}_N=-\sum_i\frac{\hbar^2}{...

1

I assume you are asking about the total energy which is printed as the final result of your DFT calculation. This energy represents the kinetic energy of all your particles (atoms and electrons) and their coulomb interaction. It does not have much physical meaning by itself. Usually, the more particles and the larger your basis set, the smaller (more ...

1

To answer your question, the most popular right now is phonopy. If you are having a technical problem you can post it on GitHub, usage issues are better suited for the mailing list. My opinion is that, if possible, using phonopy and getting it working would probably be best for the community if it is a technical problem in the code or best for you if it's ...

1

Problem can be fixed by adding this around line 395 in the config.py file, inside the build_interpreter function: define_macros.append(('_GNU_SOURCE', '1')) where the other define_macros.append commands reside.

1

Most of your answers look good. For the geometry optimization of single-reference organic systems, B3LYP/big should be fine. MPn is bad for open-shell systems in general. MCSCF is the way to go if one has truly pathological multireference effects. CCSD(T)/huge is good any time you want to treat dispersion, but you'll find in the literature that (He)2 ...

1

I found an energy decomposition scheme that does exactly what I was looking for. Here is a link to a paper describing the scheme: http://dx.doi.org/10.1063/1.3253797 The sum of the repulsive and electrostatic contribution to the interaction energy of a dimer is defined as the difference in energy between the dimer and the two separate monomers, where the ...

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