State-specific approach

Linear response function approaches were introduced into the chemistry literature about thirty years ago Ref. [1,2]. At that time they were referred to as Green functions or propagator approaches. Soon after the introduction it became apparent that they offered a viable and attractive alternative to the state specific approaches for obtaining molecular properties as excitation energies, transition moments and second order molecular properties. 

An illustrative example of the comparison between the vertical (nonequilibrium) absorption energy obtained with the standard PCM-linear response, its corrected version, and with the wavefunction State-Specific approach based is reported in Table 7-5. 

C.A. Nicolaides, and N.A. Piangos, State-specific approach and computation of resonance states. Identification and properties of the lowest and triply excited states o(He, Phys. Rev. A 64 (2001) 052505. 

C.A. Nicolaides, The state-specific approach to the solution of problems of electronic structure and dynamics involving excited states, Int. J. Quantum Chem. 60 (1996) 119. 

Because there is a central theme that pervades the formalisms and applications of this work, its framework has been given the generic name of The state-specific approach (SSA) (Nicolaides, int. J. Quantum Chem. 60, (1996) 119 ibid, 71, (1999) 209). According to the SSA, critical to the development of formalism which is physically helpful as well as computationally practical is, first, the choice of appropriate for each problem forms of the trial wavefunctions and, second, the possibility of employing corresponding function spaces that are as specific and optimal as possible for the state and property of interest. A salient feature of the SSA is that it makes the interplay between electronic structure and dynamics transparent. 

Formalism and polyelectronic methods in the framework of the state-specific approach... 

The effects of intruder states are generally more severe for molecules than for atoms, due to more dense energy levels. Therefore, even if there are ways of avoiding - or at least reducing - the effect of intruder states in the multi-reference approach, it is when the interest lies entirely in one or a few particular states, more advantageous to study one state at a time in a state-specific approach. 

Guido CA, Jacquemin D, Adamo C, Mennucci B. Electronic excitations in solution the interplay between state specific approaches and a time-dependent density functional... 

In any case, it is clear that proper treatment of the solvent effect, both static and dynamical, is fundamental for reliable evaluation of the CT transition s stability in the condensed phase. When using continuum solvation models, a state-specific approach combined with an accurate description of the excited-state electron density (averaging procedures of the excited-state density such as those usually employed in CASPT2 should be avoided) is mandatory, since LR-PCM/TD-DFT strongly underestimates the stability of transition with even partial CT character. 

The excitation energies obtained from the CAS(6,5) wave functions depend very little on whether (a) they are calculated in MCSCF, VMC or DMC, (b) the state-average or the state-specific approach is employed, and (c) fhe CSF and orbital coefficients are reoptimized or not in the presence of the Jastrow factor. In contrast, the excitation energies obtained from CAS(2,2) wave functions do depend on all of the above and, in particular the reoptimization of the CSF and orbital coefficients in the presence of the Jastrow factor significantly improves the VMC and DMC excitation energies, to 3.80(2) and 3.83(l)eV, respectively. The importance of reoptimizing in VMC the CAS(2,2) expansions but not the CAS(6,5) expansions suggests that the Jastrow factor includes important correlation effects that are present in CAS(6,5) but not in CAS(2,2). 

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