Energy explosion when atom count increases with HFX. Issue with auxiliary basis sets?

[Nicholas Winner]

I've been looking at a couple of systems that are atomically pretty dense. For example, alpha boron and diamond.

For these systems, when I increase the supercell size too large, the energy in the SCF loop explodes to ridiculous values. For example, I am calculating diamond with 54 atom and 128 atom supercells, truncated PBE0 with 2A cutoff. 

The 54 atom case converges with no real issues. In that case I have used OT, and against common wisdom for really accurate results I screen on the initial density matrix with scf_guess atomic. The convergence seems robust to that and the aggressive (1e-6) integral screening.

Then, I move to 128 atom supercells, and I am unable to converge as the energies diverge rapidly after a few SCF steps. For this case, I have stopped screening on the initial density matrix. I was able to narrow the issue down to the auxiliary basis sets used for C. I tried cFIT3, pFIT3, cpFIT3, and FIT3, which all result in the rapid divergence of the energy. Example:

     1 OT CG       0.15E+00  141.5     0.01764397      -673.6622732538 -6.74E+02

     2 OT LS       0.60E+00   35.1                     -806.4853195301

     3 OT CG       0.60E+00   38.5    12.03779293     -4186.8334161380 -3.51E+03

     4 OT LS       0.30E+00   33.7                    -8657.0632214970

Since these all failed, but the primary basis is prohibitively large, I tried setting BASIS_SET AUX_FIT SZV-MOLOPT-SR-GTH, and this remedies the problem, and the calculation finishes.

My questions then are four-fold.

(1) Is this behavior for dense systems like diamond expected? I have not had this issue with any other system besides alpha boron.

(2) Is this un-fixable? i.e. we can't use the FIT basis sets for such systems?

(3) Would someone have another idea for why this is the case? i.e. maybe FIT basis sets can still be used if some other setting was changed. 

and finally (4) Does anyone see an issue with proceeding with using the SZV basis as the auxiliary basis?

-Nick

[S Ling]

Hi Nick,

If you read the original paper of ADMM (https://pubs.acs.org/doi/10.1021/ct1002225 ), they mentioned "the condition number of the overlap matrix with the FIT3 basis is unfavorable in the case of bulk C", see section 3.6. They produced a separate optFIT3 basis for C with much more favourable condition number. Unfortunately, I cannot find the optFIT3 basis for C. I have personally produced an optFIT3 basis for B if you want to try.

SL

#####

B OPTFIT3

6

1 0 0 1 1

         0.27763115800007     1.00000000000000E+00

1 0 0 1 1

         3.17679618980955     1.00000000000000E+00

1 0 0 1 1

         8.21086367916339     1.00000000000000E+00

1 1 1 1 1

         0.15104423596280     1.00000000000000E+00

1 1 1 1 1

         0.61295240465023     1.00000000000000E+00

1 1 1 1 1

         2.56244918405309     1.00000000000000E+00

##### 

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[Nicholas Winner]

Thank you Ling. I had read this paper and noticed this problem before. I had even asked a similar question before on here, but the manifestation was slow convergence rather than divergence. I did not know that any of these optFIT basis sets were available.

Using the optFIT you provided, I was able to converge alpha boron without much issue. Do you know of any other issues where this might pop-up? i.e. is this just an issue of boron and carbon?

[S Ling]

Hi Nick,

I don't know why the condition number of the overlap matrix with the FIT3 basis is unfavorable in the case of bulk C, so I don't know any other issues where this might pop-up. Please make sure you are happy with results before you use the optFIT3 ADMM basis for production run, as I had to sacrifice some accuracy during the basis optimisation in order to get a better conditioned basis set.

SL

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