On the universality of the long-/short-range separation in multiconfigurational density-functional theory.

In many cases, the dynamic correlation can be calculated quite accurately and at a fairly low computational cost in Kohn-Sham density-functional theory (KS-DFT), using current standard approximate functionals. However, in general, KS-DFT does not treat static correlation effects (near degeneracy) adequately which, on the other hand, can be described in wave-function theory (WFT), for example, with a multiconfigurational self-consistent field (MCSCF) model. It is therefore of high interest to develop a hybrid model which combines the best of both WFT and DFT approaches. The merge of WFT and DFT can be achieved by splitting the two-electron interaction into long-range and short-range parts. The long-range part is then treated by WFT and the short-range part by DFT. In this work the authors consider the so-called "erf" long-range interaction erf(micror12)/r12, which is based on the standard error function, and where mu is a free parameter which controls the range of the long-/short-range decomposition. In order to formulate a general method, they propose a recipe for the definition of an optimal microopt parameter, which is independent of the approximate short-range functional and the approximate wave function, and they discuss its universality. Calculations on a test set consisting of He, Be, Ne, Mg, H2, N2, and H2O yield microopt approximately 0.4 a.u.. A similar analysis on other types of test systems such as actinide compounds is currently in progress. Using the value of 0.4 a.u. for micro, encouraging results are obtained with the hybrid MCSCF-DFT method for the dissociation energies of H2, N2, and H2O, with both short-range local-density approximation and PBE-type functionals.

[1]  Kerstin Andersson,et al.  Second-order perturbation theory with a CASSCF reference function , 1990 .

[2]  A. D. McLean,et al.  Contracted Gaussian basis sets for molecular calculations. I. Second row atoms, Z=11–18 , 1980 .

[3]  J. Ángyán,et al.  Potential curves for alkaline-earth dimers by density functional theory with long-range correlation corrections , 2005 .

[4]  G. Scuseria,et al.  Importance of short-range versus long-range Hartree-Fock exchange for the performance of hybrid density functionals. , 2006, The Journal of chemical physics.

[5]  K. Hirao,et al.  A long-range correction scheme for generalized-gradient-approximation exchange functionals , 2001 .

[6]  Andreas Savin,et al.  van der Waals forces in density functional theory: Perturbational long-range electron-interaction corrections , 2005, cond-mat/0505062.

[7]  Andreas Savin,et al.  Properties of short-range and long-range correlation energy density functionals from electron-electron coalescence , 2006 .

[8]  A. Savin,et al.  Short-Range Exchange-Correlation Energy of a Uniform Electron Gas with Modified Electron-Electron Interaction , 2004, cond-mat/0611559.

[9]  Gustavo E Scuseria,et al.  Assessment and validation of a screened Coulomb hybrid density functional. , 2004, The Journal of chemical physics.

[10]  Enrico Clementi,et al.  Study of the electronic structure of molecules. XXII. Correlation energy corrections as a functional of the Hartree‐Fock type density and its application to the homonuclear diatomic molecules of the second row atoms , 1974 .

[11]  Andreas Savin,et al.  Density functionals for the Yukawa electron-electron interaction , 1995 .

[12]  H. Werner,et al.  A short-range gradient-corrected density functional in long-range coupled-cluster calculations for rare gas dimers. , 2005, Physical Chemistry, Chemical Physics - PCCP.

[13]  Jorge M. Seminario,et al.  Recent developments and applications of modern density functional theory , 1996 .

[14]  Andreas Savin,et al.  Combining long-range configuration interaction with short-range density functionals , 1997 .

[15]  D. Cremer,et al.  The combination of density functional theory with multi-configuration methods - CAS-DFT , 2000 .

[16]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[17]  G. Scuseria,et al.  Hybrid functionals based on a screened Coulomb potential , 2003 .

[18]  J. B. Hasted,et al.  Liquid Water: Dielectric Properties , 1972 .

[19]  Celestino Angeli,et al.  Introduction of n-electron valence states for multireference perturbation theory , 2001 .

[20]  B. Roos.  The Complete Active Space Self‐Consistent Field Method and its Applications in Electronic Structure Calculations , 2007 .

[21]  P. Gori-Giorgi,et al.  A short-range gradient-corrected spin density functional in combination with long-range coupled-cluster methods: Application to alkali-metal rare-gas dimers , 2006 .

[22]  G. Scuseria,et al.  Assessment of a long-range corrected hybrid functional. , 2006, The Journal of chemical physics.

[23]  B. Roos,et al.  Correlation potentials for a multiconfigurational-based density functional theory with exact exchange , 2004 .

[24]  T. H. Dunning.  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[25]  A. Savin,et al.  On degeneracy, near-degeneracy and density functional theory , 1996 .

[26]  Björn O. Roos,et al.  Second-order perturbation theory with a complete active space self-consistent field reference function , 1992 .

[27]  A. Savin,et al.  Combining multideterminantal wave functions with density functionals to handle near-degeneracy in atoms and molecules , 2002 .

[28]  David E. Woon,et al.  Gaussian basis sets for use in correlated molecular calculations. IV. Calculation of static electrical response properties , 1994 .

[29]  Andreas Savin,et al.  Long-range/short-range separation of the electron-electron interaction in density functional theory , 2004 .

[30]  Felix Franks,et al.  Water:A Comprehensive Treatise , 1972 .

[31]  K. Hirao,et al.  A long-range-corrected time-dependent density functional theory. , 2004, The Journal of chemical physics.

[32]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[33]  Enrico Clementi,et al.  Study of the electronic structure of molecules. XXI. Correlation energy corrections as a functional of the Hartree‐Fock density and its application to the hydrides of the second row atoms , 1974 .

[34]  Davidson,et al.  Ground-state correlation energies for atomic ions with 3 to 18 electrons. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[35]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[36]  J. Ángyán,et al.  Hybrid functional with separated range , 2005 .