Hamiltonian SCRF model

Other semiempirical Hamiltonians have also been used within the BKO model. A Complete Neglect of Differential Overlap (CNDO/2) ° study of the effect of solvation on hydrogen bonds has appeared. o The Intermediate Neglect of Differential Overlap (INDO) °2 formalism has also been employed for this purpose.2011 Finally, the INDO/S model,which is specifically parameterized to reproduce excited state spectroscopic data, has been used within the SCRF model to explain solvation effects on electronic spectra.222,310-312 jhis last approach is a bit less intuitively straightforward, insofar as the INDO/S parameters themselves include solvation by virtue of being fit to many solution ultraviolet/visible spectroscopic data.29J... 

A scheme for the treatment of the solvent effects on the electronic absorption spectra in solution had been proposed in the framework of the electrostatic SCRF model and quantum chemical configuration interaction (Cl) method. Within this approach, the absorption of the light by chromophoric molecules was considered as an instantaneous process. Tliere-fore, during the photon absorption no change in the solvent orientational polarization was expected. Only the electronic polarization of solvent would respond to the changed electron density of the solute molecule in its excited (Franck-Condon) state. Consequently, the solvent orientation for the excited state remains the same as it was for the ground state, the solvent electronic polarization, however, must reflect the excited state dipole and other electric moments of the molecule. Considering the SCRF Hamiltonian... 

If the species is charged then an appropriate Born term must also be added. The react field model can be incorporated into quantum mechanics, where it is commonly refer to as the self-consistent reaction field (SCRF) method, by considering the reaction field to a perturbation of the Hamiltonian for an isolated molecule. The modified Hamiltoniar the system is then given by ... 

The SM1-SM3 methods model solvation in water with various degrees of sophistication. The SM4 method models solvation in alkane solvents. The SM5 method is generalized to model any solvent. The SM5.42R method is designed to work with HF, DFT or hybrid HF/DFT calculations, as well as with AMI or PM3. SM5.42R is implemented using a SCRF algorithm as described below. A description of the differences between these methods can be found in the manual accompanying the AMSOL program and in the reviews listed at the end of this chapter. Available Hamiltonians and solvents are summarized in Table 24.1. 

The solvent effects are often described within a semiempirical selfconsistent reaction field theory (SCRF)248. In this theory the free energy of solvation is obtained from a set of selfconsistent equations describing the interaction of the solute (denoted by S) with the solvent modeled by a polarizable continuum characterized by a dielectric constant e. In the SCRF formalism, as developed by Rivail and collaborators249- 250 the solute-solvent system is modeled by a polarizable continuum (characterized by a dielectric constant e) in which the solvent molecule is immersed within an ellipsoidal cavity251,252. The Hamiltonian describing the solute in the cavity is given by,... 

It should be stressed that the relation between the SCRF and SAPT approaches is not obvious, as the former describes the solvation energetics in terms of the free energy of solvation at a finite temperature T, while in the latter one considers the interaction energy between the molecule of the solute and all molecules of the solvent at T = 0 K. One should also note that in the SCRF theory the solvent is modeled by a polarizable continuum, so the SCRF Hamiltonian is semiempirical. Still, by assuming a discrete equivalent of the SCRF Hamiltonian one can get approximate relations between SAPT and SCRF at T = 0 K. A SAPT analysis of the free energy of solvation AG within the SCRF method was reported in Ref. (234). It was shown that the free energy of solvation AG is given by,... 

The schemes of solvatons and of virtual charges represent particular cases of the general theory of selfconsistent reactive field (SCRF) [21, 22, 32-35]. The model Hamiltonian has in the general theory of SCRF the form ... 

In addition, all QM models may be modified by deleting some terms, leading thus to the formulation of methods in which the use of the Hamiltonian of M and the explicit solution of the QM problem are no longer necessary. The latter set of methods belongs to another subfamily of focused models more similar to the original Onsager s formulation that we should call classical (or semiclassical) C/RF reaction field methods, even if in the literature they are sometimes denoted as SCRF methods. 

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