A correlation-energy density functional for multideterminantal wavefunctions

Abstract

A density functional for dynamical correlation, to be used in connection with wavefunctions of the complete-active-space self-consistent ® eld type, is described, and ® rst applications to the series of two-and four-electron atomic ions as well as to the H2 potential curve are given. IntroductionDensity functional theory (DFT) has been very successful for both an economic and an accurate description of electronic structure in atomic, molecular and solid-state physics (for example [1]); electron correlation e ects are implicitly included while formally retaining an independent-particle Hartree± Fock (HF)-like picture. The HF picture, on the other hand, is just the starting point for an explicit electron correlation treatment with the wavefunction-based quantum-chemical ab initio methods (for example [2]); in contrast with DFT, a systematic improvement towards the exact results is possible, but at the expense of a heavy computational burden caused by long con® guration interaction (CI) expansions. However, long CI expansions are usually related to dynamical correlation e ects which have to do with the short-range description of the electron correlation hole (electron± electron cusp), while static (longrange) correlation e ects caused by near-degeneracies of ground and low-lying excited states of the same symmetry very often can e ciently be covered by quite short optimized expansions (of the multicon® guration self-consistent ® eld (MCSCF) or complete-active-space self-consistent ® eld (CASSCF) type). Since de® ciencies of DFT, if any, are likely to occur just with the description of near-degeneracies which are special to individual molecules and not easily covered by a universal functional, the idea of a CI± DFT coupling combining the advantages of the two approaches seems to be rewarding.

The DFT/MRCI method

“…47,48 While WFT-in-DFT methods aim at a multiscale description of large systems, MC-PDFT as well as sr-DFT-lr-WFT methods pursue similar objectives as DFT/MRCI. In the beginning, the combinations of generalized valence bond theory in perfect-pairing approximation 57,58 or minimal CASSCF or CASCI with DFT [59][60][61][62][63][64] were mostly thought to provide a proper description of bond dissociation processes in the electronic ground state. Later approaches used larger active spaces and additionally addressed electronically excited states [65][66][67][68][69] or strived for correcting the long-range behavior of TDDFT in describing CT states.…”

“…Several work groups used the ratio of the reference density and the total density as a measure of the active space in the construction of the residual correlation density 59,60 Alternatively, natural orbitals and their occupation numbers were engaged to define electron densities in conjunction with multideterminantal wave functions. 75 Instead of directly employing the on-top pair density (1) as auxiliary parameter, recent developments in MC-PDFT methodology 67,68,76 utilize a normalized form of the on-top density…”

Capturing static and dynamic correlations by a combination of projected Hartree-Fock and density functional theories

“…[4][5][6][7][8][9][10][11] Blends of DFT with complete active space [12][13][14] (CAS), configuration interaction 15 (CI), multiconfiguration self-consistent field 16 (MCSCF), and constrainedpairing mean-field theory 17,18 (CPMFT) have emerged in the literature during the last decade. Compared to these methods, PHF has the advantage of being a "black box" tool in the sense that it does not require the specification of the number of active orbitals or electrons from the user.…”

Activation of the B−F Bond by Diphenylcarbene: A Reversible 1,2‐Fluorine Migration between Boron and Carbon

“…Computational details.G as-phase geometry optimizations and frequencyc alculationsw ere performed using the B3LYP func-tional [21][22][23] with D3 dispersion corrections, [24] employing the cc-pVTZ and 6-311 ++g(d,p) basis sets as implemented in Gaussian 09 (Revision D.01). [25] …”