RT-TDDFT basis set convergence
Clicked A Few Times
7:48:32 AM PST - Thu, Dec 10th 2015
I am running a RT-TDDFT simulation to study charge transfer between the molecules of a H2 dimer with an extra electron on the bottom H2 molecule. The input file is

title "H2 dimer"

start H2
echo

geometry "mol1" units angstroms noautosym nocenter noautoz
H    0.000   0.000   0.000
H    0.740   0.000   0.000
end

geometry "mol2" units angstroms noautosym nocenter noautoz
H    0.000   0.000   1.800
H    0.740   0.000   1.800
end

geometry "dimer" units angstroms noautosym nocenter noautoz
H    0.000   0.000   0.000
H    0.740   0.000   0.000
H    0.000   0.000   1.800
H    0.740   0.000   1.800
end

BASIS spherical
* library cc-pVDZ
END

set geometry "mol1"
charge -1
dft
  odft
  mult 2
  vectors input atomic output "mol1.movecs"
end
task dft energy

set geometry "mol2"
charge 0
dft
  odft
  mult 1
  vectors input atomic output "mol2.movecs"
end
task dft energy

set geometry "dimer"
charge -1
dft
  odft
  mult 2
  vectors input fragment "mol1.movecs" "mol2.movecs" output "dimer.movecs"
  noscf
end
task dft energy

rt_tddft
  tmax 200.0
  dt 0.2
  load vectors "dimer.movecs"
  print *
end
task dft rt_tddft


I have tried many basis sets from sto-2g to aug-cc-pVTZ and the results are very different:

H2.png

Shouldn't the results converge as we go to bigger basis sets? If not, how could we be certain that our basis set is the right one for the particular chemical system?

tcne.png

However, i also tried the tetracyanoethylene dimer example on your website with multiple basis sets, and the results are in very good agreement, especially if one considers how different are the basis sets used. So, the question is why in my very simple example above RT-TDDFT fails to produce consistent results with basis set changes? Is there any parameter that could help convergence, or am i totally missing something here?

Forum Regular
12:42:10 PM PST - Thu, Dec 10th 2015
There is nothing wrong with your simulation from the standpoint of calculation set up. The results you have for H2 will appear more in line with your expectation if you separate the basis sets with diffuse functions from those without diffuse functions. Remember that for this kind of simulation, the results will not just depend on the number of basis functions, but the spatial extent of the basis set as well. The difference between your H2 case and the TCNE case is mostly related to the distance between the molecules, i.e. try putting the H2 molecules 3 Angstrom apart as in the TCNE case and the H2 results should look much more like the TCNE results.

Best,
Sean

Clicked A Few Times
3:44:31 PM PST - Thu, Dec 10th 2015
Thank you very much for your reply.

I have put the H2 molecules 3A apart and rerun the simulations:

h2.png

With sto-2g basis set there is no appreciable charge oscillation; i guess this (very) small basis set does not fill the space between the 2 molecules, so they are effectively isolated and no charge tranfer can occur. 3-21g and 6-31g predict some charge transfer, but amplitude of charge oscillations is still small. Basis sets with diffuse functions, as well as the larger Dunning basis sets cc-pVDZ and cc-pVTZ show full oscillations.

Charge oscillation frequencies are lower than the previous example, as expected for the increased separation. Generally, for small separation distances, the small and spatially confined basis sets perform relatively well, while for larger separation distances the bigger, more extended basis sets are required.

So, i do see a pattern in the above results; however, lacking any experimental data to compare with, i cannot figure out how one could reliably determine the best basis set for a specific system. Obviously, as seen before, the larger, more extended basis set is not always the best choice. Is there anything that can be done to minimize the basis set dependence?


Thanks again,
Andreas

Forum Regular
4:45:35 PM PST - Thu, Dec 10th 2015
The other aspect to consider is that the long range behavior of most density functionals (especially pure DFT ones like LDA) is incorrect and decays too quickly. For instance, just using HF exchange with this same set up (H2 molecules 3 Angstrom apart) with the 3-21G basis set results in complete oscillation of the charge as opposed to the partial oscillation that LDA gives.

In general you want to use the largest basis set that you can afford; although, cancellation of errors can result in a smaller basis set giving numbers that agree better with a reference than a larger basis set.

Some systems just have a strong dependence on the basis set.

Clicked A Few Times
10:28:10 AM PST - Fri, Dec 11th 2015
Thank you for the suggestions.

It does make sense to use a range-separated functional, especially for larger distances. I wanted to test if it would make any difference in shorter separation distances as well, so i ran again the simulations with 1.8A separation and the CAM-B3LYP popular range-separated functional.

H2.png

The results are quite similar: basis sets with diffuse functions give much slower oscillations; extrapolating from aug-cc-pVTZ results we would expect a charge oscillation at about 200THz. Is there any chance that non-diffuse basis sets would also converge to that limit, if one could perform cc-pV6Z simulations? In other words, is it better to perform that kind of simulations with diffuse basis sets, since they seem to converge faster?

Also, i noticed an overshooting/undershooting with aug-cc-pVTZ basis set, i.e. not only the excess charge is transfered, but also a small portion of valence charge as well. Does this type of charge transfer has a physical meaning, or it is just an artifact that should be ignored? I have also observed the same kind of overshooting with charge oscillations in O2 dimer with 2A separation. I think, that happens when the separation distance is relatively small. Strange enough, in this example, the largest basis sets aug-cc-pVDZ and cc-pVTZ do not give a complete oscillation:

O2.png

Forum Regular
10:46:56 AM PST - Mon, Dec 14th 2015
Your basis set needs to be flexible enough to capture the physics you are interested in simulating. Given that you are simulating a negatively charged system and are looking at long range interactions, I would think a basis set with diffuse functions would be required to get an accurate picture.

You are starting from a non-physical initial state so to me it is suspect to classify parts of the subsequent dynamics as physical and other parts as non-physical. If you are worried about artifacts, you can tighten the thresholds in the calculation and decrease the time step in the dynamics to see if the results change.

Clicked A Few Times
9:30:36 AM PST - Wed, Dec 16th 2015
Thank you for your support.

I tightened the thresholds and halved the time step and no noticeable change occurred. I will also consider using CDFT for the initial state to get more physically meaningful results.

However, the basis set convergence problem still persists; i managed to run the simulations with diffuse Dunning basis sets all the way up to aug-cc-pV6Z, but i keep getting larger oscillation periods with bigger basis sets:

H2.png

So, the question is what is the best way to estimate the oscillation frequency in a situation like this?

Forum Regular
10:13:52 AM PST - Thu, Dec 17th 2015
You need to consider the physics of the situation; you are dealing with an electron that is most likely unbound (or at least very loosely bound). This electron wants to delocalize in space, which the larger, more diffuse basis sets let it do. This is why your frequency keeps decreasing: an electron delocalized over both molecules is not going to show much of an oscillation between the molecules.


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