Optimized virtual orbital space

We proposed an optimized virtual orbital space (OVOS) method once upon a time... 

Adamowicz, L. (2010). Optimized virtual orbital space (OVOS) in coupled-cluster calculations. Mol Phys. 108, pp. 3105-3112, doi 10.1080/ 00268976.2010.520752. 

Pitonak, M., Aquilante, R, Hobza, P, Neogrady, P, Noga, J., and Urban, M. (2011). Parallelized implementation ofthe CCSD(T) method in MOLCAS using optimized virtual orbitals space and Cholesky decomposed two-electron integrals. Collect Czech. Chem. Commun. 76, pp. 713-742, doi ... 

We have also added a method of calculating improved virtual orbitals. Our use of this procedure for N electron excited state virtual orbitals (8l) in the framework of the SCF calculation of the N-l electron problem closely resembles those proposed by Huzinaga (82). We have also investigated Huzinagafs recent method for improved virtual orbitals in the extended basis function space (83) This is also a useful procedure where there are convergence problems for the Hartree-Fock calculations for the N-electron occupied space of the excited states. This should also be helpful in optimizing virtual orbitals to use them in perturbation theory expressions. 

In the subsequent spin-coupled calculations [9], the < > were optimized as linear combinations of all the LMOs which correspond to X—Y bonds, plus all the virtual orbitals. This scheme is entirely equivalent to expanding the in the full basis atomic basis set, except that it maintains the orthogonality between the active orbitals and the inactive space, which consists of all the other doubly-occupied MOs. The spin function 0 was fully optimized in the full spin space. The active orbitals were thus fully optimized without constraints on their form, on the degree of localization, on the overlaps between them, or on the mode of coupling the electron spins. Nevertheless, we found for each molecule that the optimized spin-coupled orbitals consist of pairs, each clearly associated with a particular two-centre bond, and with predominantly singlet coupling of the electron spins. For example, we show in Figure 2 the pair of spin-coupled... 

Equilibrium structures of the C s nanodisk and the G144 nanocapsule were optimized by Shukla and Leszczynski [43]. D h symmetry was imposed on these structures. OVGF calculations were performed with the 6-31 lG(d) basis. The size of the basis was 1728 for C% and 2592 for C144. The active orbital space for C% consisted of 192 occupied MOs and 1025 virtual MOs. 288 occupied and 1115 virtual MOs were involved in the case of C144. Vertical lEs are presented in Tables 3.3 and 3.4, respectively. 

A special case of full Cl is the complete active space self-consistent field (CASSCF) or fully optimized reaction space (FORS) approach in which one defines an active space of orbitals and corresponding electrons that are appropriate for a chemical process of interest [20]. The FORS wavefunction is then obtained as a linear combination of all possible electronic excitations (configurations) from the occupied to the unoccupied (virtual) orbitals in the active space, so a FORS wavefunction is a full Cl within the specified active space. Since a full Cl provides the exact wavefunction for a given atomic basis, there is no need to re-optimize the component molecular orbitals. On the other hand, a FORS wavefunction generally corresponds to an incomplete Cl, in the sense that only a subset of configuration (or determinant) space is included. Therefore, one also optimizes the molecular orbital coefficients to self-consistency. The calculation of a full Cl wavefunction is extremely computationally demanding, scaling exponentially with... 

An important issue in MCSCF calculations is the selection of the configurations to be included in the wavefunction expansion. The most popular approach is the complete active space self-consistent field (CASSCF) method, also called full optimized reaction space (FORS). This approach starts Irom a zeroth order set of MOs, usually obtained via the Hartree-Fock method. The set of MOs is split into three subsets, as illustrated in Fig. 2.3. A first one containing occupied inactive orbitals, for which the occupation numbers are fixed to 2. A second one containing active orbitals, including both occupied and virtual orbitals of the reference Hartree-Fock configuration, in which all possible electron excitations are allowed. And a third one containing virtual inactive orbitals, for which the occupation numbers are fixed to 0. 

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