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r²SCAN-Based Double-Hybrids

DOI

Functional Implementation

  • Pr²SCAN functionals can be build in Orca and Turbomole via the LibXC

  • r²SCAN can be used with libxc version 5.1.0 as MGGA_X_R2SCAN (id=497), MGGA_C_R2SCAN (id=498)

  • XCFun 2.1.0 also implements support for the r²SCAN functional

  • Routines for r²SCAN functional implementation can be found at https://gitlab.com/dhamil/r2scan-subroutines (Fortran), routines for Vasp are included

  • $\kappa$ Pr²SCAN functionals employ the regularized MP2 implemented in a development version of ORCA 5.0

  • $\omega$ Pr²SCAN functionals utilize the error function splitting of the two-electron operator implemented in a development version of ORCA 5.0

  • Libraries implementing DFT-D4 can be found at https://github.com/dftd4/dftd4 (Fortran) and https://github.com/dftd4/cpp-d4 (C++)

  • NL dispersion correction DFT-NL (VV10, by Vydrov and Van Voorhis) can be used in Orca and Turbomole. For program-suits that do not support the usage of a scaling factor of the NL energy, one can scale the obtained NL energy by $NLScal$ manually.

ORCA Input Files

Double-hybrids:

Range-separated hybrid:

Functional Parameters

Functional

All functionals employ the following fundamental relation.

$E_{XC}^{DH} = (1-a_{X})E_{X}^{DFT} + a_{X}E_{X}^{HF} + (1-a_{C})E_{C}^{DFT} + a_{C}(a_{SS}E_{C}^{SS-MP2}+a_{OS}E_{C}^{OS-MP2})$

Functional $a_X$ $a_C$ $a_{OS}$ $a_{SS}$ $\kappa$ $\omega$
r²SCAN0-DH $1/2$ (0.50) $1/8$ (0.13) $4/3$ 0
r²SCAN-CIDH $6^{-1/3}$ (0.55) $1/6$ (0.17) $4/3$ 0
r²SCAN-QIDH $3^{-1/3}$ (0.69) $1/3$ (0.33) $4/3$ 0
r²SCAN0-2 $2^{-1/3}$ (0.79) $1/2$ (0.50) $4/3$ 0
Pr²SCAN50 $1/2$ (0.50) $1/4$ (0.25) $4/3$ 0
Pr²SCAN69 $3^{-1/3}$ (0.69) $4/9$ (0.44) $4/3$ 0
$\kappa$ Pr²SCAN50 $1/2$ (0.50) $3/10$ (0.30) $4/3$ 0 2.7500
$\omega$ Pr²SCAN50 $1/2$ (0.50) $7/20$ (0.35) $4/3$ 0 0.2140

Dispersion Correction

Dispersion correction parameters were fitted against the S22x5, NCIBLIND10, and S66x8 (2022 revision by Martin et al.) benchmark sets for non-covalent interaction energies by least-squares Levenberg-Marquardt minimization. All parameters were fitted close to the complete basis set limit using the large def2-QZVPP quadruple-zeta basis set.

D4

Functional $s_6$ $s_8$ $s_9$ $a_1$ $a_2$
r²SCAN0-DH 0.9424 0.3856 1.0000 0.4271 5.8565
r²SCAN-CIDH 0.8666 0.5336 1.0000 0.4171 5.9125
r²SCAN-QIDH 0.7867 0.2955 1.0000 0.4001 5.8300
r²SCAN0-2 0.7386 0.0000 1.0000 0.4030 5.5142
Pr²SCAN50 0.7964 0.3421 1.0000 0.4663 5.7916
Pr²SCAN69 0.7167 0.0000 1.0000 0.4644 5.2563
$\kappa$ Pr²SCAN50 0.8402 0.1212 1.0000 0.4382 5.8232
$\omega$ Pr²SCAN50 0.8143 0.3842 1.0000 0.4135 5.8773

This Markdown table includes the provided data with appropriate formatting for GitHub. Adjustments

NL

Non-local dispersion correction makes use of a scaling factor $a_{NL}$, that is given by $a_{NL}=1-a_C$.

Method $a_{NL}$ $NL_{b}$
Pr²SCAN50 0.7500 10.9207
Pr²SCAN69 0.5556 9.0691
$\kappa$ Pr²SCAN50 0.7000 10.6723
$\omega$ Pr²SCAN50 0.6500 9.4149