Hybrid functional issues

[xuan wang]

Dear all,

I learned that in CP2K, the use of HSE06 for periodic calculations is not allowed to use POTENTIAL_TYPE TRUNCATED, but POTENTIAL_TYPE SHORTANGE. However, even SHORTANGE will also assume a cutoff_radius which is not defined by users. 

I am wondering about how many functionals behave like such HSE06? 

Thank you! 

Best regards,

Garrett

[Frederick Stein]

Dear Garrett,

If I understand your question correctly, this affects all range-separated hybrid functionals, i.e. all functionals with an explicit short/long-range Coulomb or Gaussian potential contribution. This warning is relevant if you as a user have to choose some parameters of the functional on your own. If all parameters of the functionals (CUTOFF_RADIUS, OMEGA) are pre-defined by the functional like in HSE06, you may ignore this warning. In the case of HSE06 with omega=0.11, you will probably not be able to get rid of this warning in real-case scenarios because with usual values of EPS_DEFAULT of at most 1.0E-10, this cutoff radius is at least at the order of 20 A.

HTH,

Frederick

[xuan wang]

Thank you, Frederick,

In detail, for range-separated functional, I am allowed to use POTENTIAL_TYPE MIX_CL_TRUNC for wB7XD, CAM-B3LYP. The _TRUNC is truncated for HF exchange, and can be truncated by CUTOFF_RADIUS from our self-definition. But for HSE06, I can only use  POTENTIAL_TYPE SHORTRANGE rather than type with truncated condition, because I am acquired that the CUTOFF_RADIUS is defined by CP2K, not users, where this  CUTOFF_RADIUS is relevant with  EPS_DEFAULT,  omega=0.11,as you said. 

For range-separated functional, the coulomb operator can be seen as 1/r = [1-α-βerf(wr)]/r + [α+βerf(wr)]/r. In terms of wB7XD, α = 0.222036，β = 0.777964，of CAM-B3LYP, α = 0.19，β = 0.46. While in principle, HSE06 can also be seen α = 0.25，β = -0.25, that we can use  POTENTIAL_TYPE MIX_CL_TRUNC. But not the condition, only recommeded to use POTENTIAL_TYPE SHORTRANGE. 

I don't know why. I am dying for understanding why. 

[Frederick Stein]

I am not entirely sure what exactly you do not understand. If α = -β , then the potential operator for HF simplifies to [α+βerf(wr)]/r = [α- α erf(wr)]/r = α [1-erf(wr)]/r = α erfc(wr)/r , i.e. the short-range operator. The shortrange operator has the advantage that it is shortranged, much simpler and does not need any artificial truncation whereas in the representation with the Coulomb and the longrange operator, you have to artificially truncate the Coulomb operator to obey the minimum image convention and ensure numerical stability (convergence issues and/or too large exchange energies).

[xuan wang]

Oh, yes, I understand why use shortrange type

upon noticing the αerfc（wr），this is the shortrange because of α=-β！

heartful thanks to Frederick～

Frederick Stein <f.s...@hzdr.de>于2024年5月3日 周五21:48写道：

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