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28 lines
3.4 KiB
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28 lines
3.4 KiB
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basis_correction
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This module proposes the various flavours of the DFT-based basis set correction originally proposed in J. Chem. Phys. 149, 194301 (2018); https://doi.org/10.1063/1.5052714.
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This basis set correction relies mainy on :
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+) The definition of a range-separation function \mu(r) varying in space to mimic the incompleteness of the basis set used to represent the coulomb interaction. This procedure needs a two-body rdm representing qualitatively the spacial distribution of the opposite spin electron pairs.
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Two types of \mu(r) are proposed, according to the strength of correlation, through the keyword "mu_of_r_potential" in the module "mu_of_r":
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a) "mu_of_r_potential = hf" uses the two-body rdm of a HF-like wave function (i.e. a single Slater determinant developped with the MOs stored in the EZFIO folder).
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When HF is a qualitative representation of the electron pairs (i.e. weakly correlated systems), such an approach for \mu(r) is OK.
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See for instance JPCL, 10, 2931-2937 (2019) for typical flavours of the results.
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Thanks to the trivial nature of such a two-body rdm, the equation (22) of J. Chem. Phys. 149, 194301 (2018) can be rewritten in a very efficient way, and therefore the limiting factor of such an approach is the AO->MO four-index transformation of the two-electron integrals.
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b) "mu_of_r_potential = cas_full" uses the two-body rdm of CAS-like wave function (i.e. linear combination of Slater determinants developped in an active space with the MOs stored in the EZFIO folder).
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If the CAS is properly chosen (i.e. the CAS-like wave function qualitatively represents the wave function of the systems), then such an approach is OK for \mu(r) even in the case of strong correlation.
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+) The use of DFT correlation functionals with multi-determinant reference (Ecmd). These functionals are originally defined in the RS-DFT framework (see for instance Theor. Chem. Acc.114, 305(2005)) and design to capture short-range correlation effects. A important quantity arising in the Ecmd is the exact on-top pair density of the system, and the main differences of approximated Ecmd relies on different approximations for the exact on-top pair density.
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The two main flavours of Ecmd depends on the strength of correlation in the system:
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a) for weakly correlated systems, the ECMD PBE-UEG functional based on the seminal work of in RSDFT (see JCP, 150, 084103 1-10 (2019)) and adapted for the basis set correction in JPCL, 10, 2931-2937 (2019) uses the exact on-top pair density of the UEG at large mu and the PBE correlation functional at mu = 0. As shown in JPCL, 10, 2931-2937 (2019), such a functional is more accurate than the ECMD LDA for weakly correlated systems.
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b) for strongly correlated systems, the ECMD PBE-OT, which uses the extrapolated on-top pair density of the CAS wave function thanks to the large \mu behaviour of the on-top pair density, is accurate, but suffers from S_z dependence (i.e. is not invariant with respect to S_z) because of the spin-polarization dependence of the PBE correlation functional entering at mu=0.
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An alternative is ECMD SU-PBE-OT which uses the same on-top pair density that ECMD PBE-OT but a ZERO spin-polarization to remove the S_z dependence. As shown in ???????????, this strategy is one of the more accurate and respects S_z invariance and size consistency if the CAS wave function is correctly chosen.
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