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# Range‐separated multiconfigurational density functional theory methods

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Abstract Range‐separated multiconfigurational density functional theory (RS MC‐DFT) rigorously combines density functional (DFT) and wavefunction (WFT) theories. This is achieved by partitioning of the electron interaction operator into long‐ and short‐range components and modeling them with WFT and DFT, respectively. In contrast to other methods, mixing wavefunctions with density functionals, RS MC‐DFT is free from electron correlation double counting. The general formulation of RS MC‐DFT allows for merging any ab initio approximation with density functionals. Implementations of RS MC‐DFT aim at increasing both versatility and accuracy of the underlying methods, while reducing the computational cost of the ab initio problem. Variants of the RS MC‐DFT approach can be divided into single‐determinant‐based range‐separated methods and range‐separated multideterminantal WFT methods. In these approaches the electron correlation energy is described both by a pertinent short‐range density functional and by the wavefunction theory. We review the short‐range functionals and correlated wavefunction theories employed in the framework of RS MC‐DFT. We discuss applications of the RS MC‐DFT methods to ground‐state properties of molecules and to noncovalent interactions. Time‐dependent linear‐response theory and direct approaches to excited states are also presented. For each area of applications, we assess advantages of RS MC‐DFT over conventional DFT and ab initio methods. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Electronic Structure Theory > Density Functional Theory
Left panel: Long‐ and short‐range electron interaction potentials, (LR) and (SR) for μ = 1.0 and μ = 0.4. Dots indicate position of the cutoff radius rc = 1/μ. Right panel: Behavior of the wavefunction in the electron–electron coalescence region for Coulomb electron interaction (1/r12) and LR erf interaction (μ = 1.0 and μ = 0.4), cf. Ref. 27. θ is the angle between position vectors r1 and r2 of two electrons and |r1| = |r2| = 1
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Mean absolute errors (MAE in kcal/mol) in AE6, G2 and AE49 atomization energies, BH6 and HTBH38/04 hydrogen transfer barrier heights, NHTBH38/04 nonhydrogen transfer barrier heights and DBH24 barrier heights. LC‐LDA and LC‐PBE denote results from LC‐ωLDA and LC‐ωPBE calculations presented in Refs. 78 and 84, respectively. The dRPA*‐srLDA label stands for LC‐ωLDA + dRPA calculations of Ref. 78, whereas dRPA*‐srPBE and SOSEX*‐srPBE denote LC‐ωPBE + dRPA and LC‐ωPBE + SOSEX results of Ref. 91. Methods marked with a star include scaling of the long‐range RPA correlation contribution. Results marked as dRPA‐srPBE, RPAx‐SO2‐srPBE, and MP2‐srPBE refer to RSH + dRPA, RSH + RPAx‐SO2, and RSH + MP2 calculations from Ref. 98
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Basis‐set dependence of the equilibrium binding energy of Ar2 for different full‐range and range‐separated methods, presented as the percentage of the binding energy recovered with respect to the CBS limit (aVTZ, aVQZ, and aV5Z stand for aug‐cc‐pVTZ, aug‐cc‐pVQZ, and aug‐cc‐pV5Z, respectively). Reprinted with permission from Ref. 51; copyright 2010 American Physical Society
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Convergence of the standard CIPSI and lrCIPSI + srPBE total variational energies (measured with respect to their respective FCI limits) as a function of the number of selected determinants for the Be2 molecule (internuclear distance of 3 bohr) with aug‐cc‐pCVTZ basis set. All electrons are correlated. The range‐separation parameter used is μ = 0.5 bohr−1. Reprinted with permission from Ref. 42; copyright 2019 AIP Publishing
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Potential energy curves of the H2 molecule in the cc‐pV5Z basis set. The CAS(2,2) wavefunction was used in both CASSCF and CAS‐srPBE calculations. The srPBE21 functional employed either the conventional density (red curve with open circles) or alternative densities defined in Equation (29) (red curve with closed circles). The μ value was set to 0.5 bohr−1. KS‐PBE corresponds to conventional spin‐restricted calculation with PBE functional.40
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