Exchange-correlation potential in pyscf

Hello! Could you please explain me how does pyscf calculate exchange-correlation potential in GGA case? I analyzed code and it seems to me that pyscf uses only first-order gradients of xc energy density w.r.t. rho from libxc (vrho, vgamma). I found in file “/dft/numint.py” a function “nr_rks” and in case of GGA, for example, it slices the result obtained from “eval_xc” function: exc, vxc = ni.eval_xc(xc_code, rho, spin=0, relativity=relativity, deriv=1, verbose=verbose)[:2] And it uses only exc, vxc, but discards kxc and fxc. Does it mean that pyscf somehow calculates second-order gradients needed for exchange-correlation potential calculation? Or it uses another way for calculating exchange-correlation potential?

[zhendongli2008]

Hi Zhenyu,

As answered by others before, vxc® in GGA is usually not computed for SCF, since an equivalent simple expression for the contribution to the Fock matrix can be obtained using integration by part. If you really need it, the chain rule can be used to derive an expression for vxc®, which for example can be found in Eqs. (A1-A6) [ https://aip.scitation.org/doi/10.1063/1.3479401], where we used it for the XC kernel in spin-flip TD-DFT.

Best, Zhendong Li

Zhenyu Zhu ajz34 [e-mail] 于2020年8月12日周三 下午8:20写道：

To my understanding, doing PBE SCF process does need vxc matrix in atomic orbital form, and does not require fxc; but generating vxc® does need fxc in GGA’s case. For LDA, only vxc (i.e. xc kernel’s first derivative) is required for vxc®. Also, vxc® is actually functional of rho. It’s really tricky for me 😹

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[zhendongli2008]

Sorry, the correct reference should be https://doi.org/10.1063/1.3676736.

Zhendong Li [e-mail] 于2020年8月13日周四 上午11:58写道：

Hi Zhenyu,

As answered by others before, vxc® in GGA is usually not computed for SCF, since an equivalent simple expression for the contribution to the Fock matrix can be obtained using integration by part. If you really need it, the chain rule can be used to derive an expression for vxc®, which for example can be found in Eqs. (A1-A6) [ https://aip.scitation.org/doi/10.1063/1.3479401], where we used it for the XC kernel in spin-flip TD-DFT.

Best, Zhendong Li

Zhenyu Zhu ajz34 [e-mail] 于2020年8月12日周三 下午8:20写道：

To my understanding, doing PBE SCF process does need vxc matrix in atomic orbital form, and does not require fxc; but generating vxc® does need fxc in GGA’s case. For LDA, only vxc (i.e. xc kernel’s first derivative) is required for vxc®. Also, vxc® is actually functional of rho. It’s really tricky for me 😹

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