Virtual orbital excitations

Valence -> virtual orbital excitation, including those leading to Rydberg states. 

Choosing the operators hi to be the state-transfer operators 4> ) (4 ol 4 o)(4 n would lead us back to the spectral representation, Eq. (23). In practical applications, however, the exact ground state of the system o) is replaced by some approximate wave function ), which is a linear combination of antisymmetrized products of molecular orbitals, so-called Slater determinants, while the operators hi replace one or more of the occupied molecular orbitals by virtual orbitals (excitations) in the Slater determinants or virtual orbitals by occupied orbitals (de-excitations). Approximations to the vertical electronic excitation energies E - Eq are then obtained by solving the generalized eigenvalue problem... 

The slow X 3 convergence cannot easily be avoided. To improve on it, one can try to describe electron correlation not only by means of virtual orbital excitations but also by means of spatial two-electron basis functions that depend explicitly on the electron-electron distances. This is the idea behind the explicitly correlated methods [69]. Indeed, in this manner, it is possible to accelerate the convergence from X 3 to X 7, greatly reducing the basis set requirements for high accuracy. Nevertheless, such calculations are complex and cannot yet be used routinely on large molecules. 

Flunt W J and Goddard W A III 1969 Excited states of FI2O using improved virtual orbitals Chem. Phys. Lett. 3 414-18... 

The il/j in Equation (3.21) will include single, double, etc. excitations obtained by promoting electrons into the virtual orbitals obtained from a Hartree-Fock calculation. The second-order energy is given by ... 

What we want to do is to find an Ajg orbital within the transition list the symmetry of the virtual orbital into which it is excited will give us the symmetry for that excited state. Orbital 7 has Ajg symmetry, and for the first excited state, the first entry is ... 

In a single substitution, a virtual orbital, say (jia, replaces an occupied orbital (ji/ within the determinant. This is equivalent to exciting an electron to a higher energy orbital. 

The reason usually advanced is that whilst the occupied orbitals are determined variationally within the HF-LCAO procedure, the virtual orbitals are not. Consequently, the virtual orbitals give a very poor description of excited states. 

It is also a common experience that traditional Cl calculations converge very poorly, because the virtual orbitals produced from an HF (or HF-LCAO) calculation are not determined by the variation principle and turn out to be very poor for representations of excited states. 

MCSCF theory is a specialist branch of quantum modelling. Over the years Jt has become apparent that there are computational advantages in treating all oossible excitations arising by promoting electron(s) from a (sub)set of the occu-orbitals to a (sub)set of the virtual orbitals. We then speak of complete active ace MCSCF, or CASSCF. 

First of all, the wavefunction has to contain the necessary ingredients to properly describe the phenomenon under investigation for example, when dealing with electronic spectra, it thus has to contain every CSFs needed to account at least qualitatively for the description of the excited states. The zeroth-order wavefunction has then to include a number of monoexcitations from the groimd state occupied orbitals to some virtual orbitals. In that sense, the choice of a Single Cl type of wavefunction as proposed by Foresman et al. [45,46] in their treatment of electronic spectra represents the minimum zeroth-order space that can be considered. 

With regard to the former, one would like to include as many important configurations as possible. Unfortunately, the definition of an important configuration is often debatable. One popular remedy is the full-valence complete active space SCF (CASSCF) approach in which configurations arising from all excitations from valence-occupied to valence-virtual orbitals are chosen. [29] Since this is equivalent to performing a full Cl within the valence space, the full-valence CASSCF method is limited to small systems. Nevertheless, the CASSCF approach using a well-chosen (often chemically motivated) subspace of the valence orbitals has been shown to yield a much improved depiction of the wave function at all points on a potential surface. Furthermore, the choice of an active space can be adjusted to describe excited state wave functions. 

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