Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications

Second-Order Self-Consistent-Field Density-Matrix Renormalization Group

“…In this work, we employ a matrix product state (MPS) and matrix product operator (MPO) formalism which allows us to formulate the calculation of the RDM derivatives in a straightforward fashion. With these quantities at hand, we outline briefly how to derive the coupling terms in the Hessian for a simultaneous update of the wave function and orbital parameters 1,35 .…”

Methods for describing open-shell systems: Following the trail of Rosa Caballol's research

“…This means that while the calculation of the total energy requires the full summation over all excited Slater determinants, the excitation energies can be obtained from a smaller subset. This idea is one of the ingredients of the CIPSI method, [37] one of the first successful computational schemes to treat electron correlation effects in a multiconfigurational setting, and the predecessor of the spectroscopy-oriented CI (SORCI) of Neese [38] and the complementary space perturbative approach (CSPA) of Barone and et al [39,40] The direct perturbative calculation of the energy difference was applied in the landmark article by de Loth et al [41] to analyze the origin of the singlet-triplet energy difference in the copper acetate dimer Cu 2 (CH 3 COO) 4 (H 2 O) 2 . Using a reference wave function containing the determinants with up-down and down-up coupling of the unpaired electrons of Cu 21 , it was demonstrated that the only differential contributions to the second-order correction to the energy arise from the determinants with not more than two changes in the orbitals that are doubly occupied (inactive) or empty (virtual) in the reference wave function.…”

“…The methods proposed in the 1990s concerning a dressed (multiconfigurational) CI and its bridge to CC based techniques for treating open-shell systems have been recognized by the scientific community, [4,84] but unfortunately not explored in an extensive way. It would be highly desirable to see how these methods perform in cases that go beyond the strict model systems [85] and to what extent they can provide an alternative to the DDCI method, which-although much less than standard MR-SDCI-suffers from the size-consistency problem and is only applicable to vertical excitation energies.…”

“…The key to an accurate and conceptually satisfactory description of the electronic structure is found behind the single-determinantal description, and taking into account the multideterminantal or multiconfigurational character from the start. [1][2][3][4] In almost all cases, such descriptions of the electronic structure can be divided in two steps. First a reference wave function is constructed that accounts for the multideterminantal or multiconfigurational character of the wave function.…”

“…The recent article of Szalay and coworkers [4] gives an excellent overview of the different variants of MR methods to treat dynamic electron correlation, and we refer the reader to this review for more details. The highest precision is in principle obtained with MR-CC but among the many different implementations of the theory, there does not seem to emerge a generally applicable scheme capable to tackle medium-sized systems.…”