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WIREs Comput Mol Sci
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Restricted active space configuration interaction methods for strong correlation: Recent developments

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Abstract In this review we outline the theory and recent progress of the restricted active space configuration interaction (RASCI) methodology within the hole and particle approximation. The RASCI is a single reference approach based on the splitting of the orbital space in different subsets, in which the target CI space is expressed by the concomitant number of electrons and empty orbitals in each subspace. Initially, the method was born as a spin complete version of the spin‐flip ansatz able to deal with any number of unpaired electrons. Since then, the method has experienced several improvements related to its theoretical foundations, its efficient implementation, in the characterization of RASCI wave functions, and in the calculation of molecular properties. It has shown to be especially suitable for the characterization of medium to large molecular diradicals and polyradicals, and to the study of photophysical processes involving open‐shell species and/or multiexcitonic states, like in the singlet fission reaction. But, despite this success, several limitations emerge from the sever truncation of the excitation operator, which might translate into inaccurate relative energies between different regions of the potential energy surface, and overestimated (or underestimated) excitation energies. These errors are associated with the lack of dynamic correlation, which has motivated the development and implementation of various improvements based on multi‐reference perturbation theory and to blend the RASCI wave function with density functional theory through range separation of electron–electron interactions. Finally, we discuss some of the properties available from RASCI wave functions and give potential future developments. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Quantum Chemistry Quantum Computing > Theory Development
Schematic representation of the RASCI orbital partitioning into RAS1, RAS2, and RAS3 subspaces
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Hole and particle contributions to the spinless triplet NTOs with the largest singular values () between , , and of MEK computed at the RASCI/cc‐pVTZ. Adapted from Reference 49
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Length of the transition dipole moment (full red circles in a.u.) and norm of the transition density matrix (empty blue circles) between the ground and lowest excited singlet along the ethene molecular torsion computed at the RAS‐SF/6‐31G(d)
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(a) Energies of 11B2g and 21Ag and the LE, TT, and CR diabatic, and (b) state decomposition () in the eclipsed ethylene dimer as a function of intermolecular distance. Details of the calculations can be found in Reference 48. Figure adapted from Reference 48
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Ground state FOD of phenalenyl and triangulene computed at the RAS‐SF/6‐311G(d,p) level with n electrons in n orbitals in RAS2 (n = 7 for phenalenyl and n = 10 for triangulene). Adapted from Reference 21
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Representation of , , and for occupation values between 0 and 2 electrons
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Ortho (o), meta (m) and para (p) benzyne isomers featuring two unpaired electrons
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RASCI and RASCI(2) errors (in eV) for 18 vertical singlet transition energies in small organic molecules with respect to best estimates in the literature.68 RASCI(2) errors obtained with the EN partition with , 0.25, 0.50, and 0.75 a.u. Computational details can be found in Reference 45
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Structure of the RASCI(2) matrix. The Hamiltonian matrix including 0, H, and P is explicitly diagonalized (orange), whereas the couplings of with HP, 2H, 2P, 2HP, H2P, and 2H2P terms enter at the second‐order correction (blue)
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Correlation energy (in %) with respect to CCSD(T) for the ground state of the ethene molecule. All values obtained with the def2‐TZVP basis set at the ground state geometry optimized at the MP2/6‐31G(d) level.68 CASCI, RASCI(h,p), and RASCI(2) (labeled as RAS(h,p) and RAS(2) for simplicity) have been computed with two electrons in two frontier ‐orbitals. The second order perturbative correction RAS(2) (see next section) has been computed with the Davidson–Kapuy partitioning and a level shift energy of
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Schematic representation of the restricted active space orbitals: RAS1, RAS2, and RAS3, in RASCI for a general excitation operator (X = EE, SF, IP, or AE) within the hole and electron approximation applied to the complementary reference configurations ()
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