A combination of Kohn–Sham density functional theory and multi-reference configuration interaction methods

Abstract

An effective Hamiltonian in a basis of spin-and space-symmetry adapted configuration state functions ͑CSF͒, which includes information from Kohn-Sham density functional theory ͑DFT͒, is used to calculate configuration interaction ͑CI͒ wave functions for the electronic states of molecules. The method emphasizes on states of multiconfigurational character which cannot be represented by conventional DFT. The CI matrix elements are constructed empirically by using the exact operator and corrections from DFT. Both the optimized KS orbitals from the parent determinant and the corresponding KS potential from the parent state density are used. Depending on their energy gap the CI off-diagonal elements between CSF are exponentially scaled to zero to avoid double counting of electron correlation. The selection of the most important CSF describing nondynamical correlation effects and the use of an approximate resolution of the identity ͑RI͒ for the evaluation of the two-electron integrals allows a very efficient DFT/MRCI treatment of molecules with several hundreds of electrons. As applications, the prediction of excitation energies for singlet and triplet states of organic molecules and transition metal complexes, the calculation of electronic circular dichroism spectra and investigations of the energetics of diradicals are presented. It is found, that the new DFT/MRCI approach gives results of high accuracy ͑rms errors for relative energies Ͻ0.2 eV͒ comparable to those from sophisticated ab initio treatments.

Double-hybrid density functionals: merging wavefunction and density approaches to get the best of both worlds

“…As a matter of illustration, the energy barrier for the auto-isomerization of cyclobutadiene is known to be a longstanding problem [151][152][153][154]. The interconversion between two iso-energetic (rectangular) forms passes through a (square) transition state having degenerate frontier orbitals, see Figure 5, which would thus need a multiconfigurational treatment or a more generalised treatment than that provided by current methods [155][156][157]. Actually, the results provided by B2-PLYP (PBE0-DH), with the def2-QZVP basis set, severely overestimate that energy barrier: 23.5 (25.2) kcal/mol, respectively, to be compared against sophisticated multiconfigurational MR-BWCCSD(T) results (7.0 kcal/mol, taken from Ref.…”

Electronic excitations in long polyenes revisited

“…Finally, Marian and Gilka 45 applied the "density functional theory multireference configuration interaction" method (DFT/MRCI) to polyenes with 6 ≥ N ≥ 26 using extended basis sets, geometries optimized for single determinant Kohn-Sham ground states, and described dynamic correlations by MRCI expansions "kept short by extensive configuration selection at a few thousand configuration state functions." 46 According to these results the 1B − u state becomes the S 2 state for N 22 at the chosen Franck-Condon geometry, while the 3A − g singlet excitation stays above the 1B + u state in all polyenes considered. In summary, the quoted calculations 26,[43][44][45] and, here, particularly Refs.…”

“…In this case a more detailed analysis is precluded by the partially empirical procedures, by which DFT/MRCI tries to avoid double counting of dynamical correlations that are already included by the DFT. 46 The method underestimates the energy gap E BA (N) at all polyene sizes by about 0.2 eV. Concerning excitation energies (see Fig.…”

“…13(b) stems from a DFT/MRCI treatment, 46 whose references are only singly and doubly excited (like in our MRCI). In this case a more detailed analysis is precluded by the partially empirical procedures, by which DFT/MRCI tries to avoid double counting of dynamical correlations that are already included by the DFT.…”

The low-lying excited states of neutral polyacenes and their radical cations: a quantum chemical study employing the algebraic diagrammatic construction scheme of second order

“…Nevertheless, all existing methods possess individual weaknesses and drawbacks [1,2]. The success of the available methods is manifested by ample excellent applications in the fields of photochemistry and photobiology [13][14][15][16][17][18][19][20][21][22][23][24]. Even more than for closed-shell molecules, theoretical methods are urgently needed to reliably provide information about excited states of open-shell molecules, since neutral and charged radicals are of crucial importance in a broad range of chemical and biological processes.…”