State-selective active-space methods

As HF and DFT procedures are based on a variational principle, they can only obtain the lowest energy of the molecular system. To obtain the energies of excited electronic states (and so be able to study photochemical processes) it is necessary to go to a Cl calculation. The simple procedure is the Cl-singles (CIS) that just considers monoelectronic excitations [7]. A more precise technique is the complete active space (CAS) method that performs a full Cl over a selected (active) space of orbitals [8]. CAS methods are very powerful in the theoretical analysis of electronic spectra but are difficult to apply to reactivity as it is difficult to ascertain that the active space remains unchanged along all the reaction paths. Within the DFT formalism it is also possible to study excited electronic states using the time-dependent (TDDFT) formalism [9,10]. 

The method can be also applied to open-shell Cl references. It has been applied for the first time to the calculation of the outer valence IPs of CO. This is a classic but by no means simple problem of theoretical studies of PES. The formalism used was the one-state one-root (SC) dressing approach. Small MR-SDCI have been used along with common sets of MOs for both the neutral and cationic systems. The results are also good, and we can reasonably expect to obtain improved results for similar problems in the future using MOs previously adapted to each ionized state. The selection of small sets of active MOs for the CAS is important to avoid very large SDCI matrices, but the results can be very sensitive to the choice of the active space. 

Hence there is a need to make SOCI more computationally efficient so that it can be used for larger chemical systems, and to develop related methods which scale better with the system size. Although the Cl space can be reduced by individual selection of references or A-electron functions, for the reasons stated above it is beneficial to select the Cl space in an a priori manner, once a minimal set of parameters, such as the active space, has been specified. For example, we have advocated a method we call CISD[TQ],16-18 which is a SOCI in which higher-than-quadruple substitutions have been excluded. For systems dominated by a single reference, CISD[TQ] performs nearly as well as SOCI.16,17... 

Among several types of the MCSCF method, the complete active space self-consistent field (CASSCF) method is commonly used at present. In fact, it has many attractive features (1) applicable to excited state as well as the ground state in a single framework (2) size-consistent (3) well defined on the whole potential energy surface if an appropriate active space is selected. However, CASSCF takes into account only nondynamic electron correlation and not dynamic correlation. The accuracy in the energy such as excitation energy and dissociation energy does not reach the chemical accuracy, that is, within several kcal/mol. A method is necessary which takes into account both the non-dynamic and dynamic correlations for quantitative description. 

The data of Table 3b have been computed by replacing the active space of the CASPT2 treatment by the CIPSI multireference space of the MRPT2 method documented in section 2.1. The selection of the components of the reference space by this technique enables us to reduce the gap between the Moller-Plesset and Epstein-Nesbet total energies to less than 0.01 a.u., and so to improve our evaluation of energy balances, disregarding a possible overestimation of the Moller-Plesset values due to intruder states, as it is the case in the ScNC system. 

The system is computed in Dunning s double-zeta polarized basis [32]. A mul-ticonfigurational reference function is provided by a CAS function with 2-electrons on two orbitals. The Full-CI solution being exclusive due to the large system size, state-selective MRCCSDT[2- -2] method [8] was computed. Since this method incorporates full triples, it is highly superior to the second-order PT methods we wish to evaluate, and serves as a good benchmark. Notation 2-1-2 refers to active indices (two-hole, two-particle) which define a reference space for MRCC. 

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