Direct reaction field

In spectroscopy we may distinguish two types of process, adiabatic and vertical. Adiabatic excitation energies are by definition thermodynamic ones, and they are usually further defined to refer to at 0° K. In practice, at least for electronic spectroscopy, one is more likely to observe vertical processes, because of the Franck-Condon principle. The simplest principle for understandings solvation effects on vertical electronic transitions is the two-response-time model in which the solvent is assumed to have a fast response time associated with electronic polarization and a slow response time associated with translational, librational, and vibrational motions of the nuclei.92 One assumes that electronic excitation is slow compared with electronic response but fast compared with nuclear response. The latter assumption is quite reasonable, but the former is questionable since the time scale of electronic excitation is quite comparable to solvent electronic polarization (consider, e.g., the excitation of a 4.5 eV n — n carbonyl transition in a solvent whose frequency response is centered at 10 eV the corresponding time scales are 10 15 s and 2 x 10 15 s respectively). A theory that takes account of the similarity of these time scales would be very difficult, involving explicit electron correlation between the solute and the macroscopic solvent. One can, however, treat the limit where the solvent electronic response is fast compared to solute electronic transitions this is called the direct reaction field (DRF). 49,93 The accurate answer must lie somewhere between the SCRF and DRF limits 94 nevertheless one can obtain very useful results with a two-time-scale version of the more manageable SCRF limit, as illustrated by a very successful recent treatment... 

A. G. Angy n and G. Jensen, Are direct reaction field methods appropriate for describing dispersion interactions , Chem. Phys. Lett. 175 313 (1990). 

Our QM/MM model—the discrete (or direct) reaction field (DRF) model—treats the various terms in Eq. (3-1) separately and on the basis of their own intrinsic physical meaning [3,10,31,32,38,59,74], Historically, DRF was developed to study biochemical problems, in particular for unraveling the reaction mechanism of papain. For that we went stepwise from a model active site [75] to a model active site plus a point charge representation of an a-helix [76,77,78], then to a model with a polarizable helix [78,79], and finally to an all-atom treatment of the enzyme [41]. Furthermore, we extended these studies with an exercise—with the continuum version—to show that a solvent-exposed residue has no effect on the reaction mechanism [80], Up to then we considered the protein as a peculiar solvent the real solvents, requiring extensive MC or MD simulations, came later. 

Duijnen, P.Th. van, Vries A.H. de, Swart M. and Grozema F.C., Polarizabilities in the Condensed Phase and the Local Fields Problem. A Direct Reaction Field formulation. J.Chem.Phys. (2002) 117 8442-8453. 

Thole, B.T. and Duijnen P.Th. van, The direct reaction field hamiltonian analysis of the dispersion term and application to the water dimer. Chem.Phys. (1982) 71 211-220. 

Grozema, F., Zijlstra R.W.J. and Duijnen RTh. van, Many-body interactions calculated with the direct reaction field model. Chem.Phys. (1999) 246 217—227. 

Duijnen, P.Th. van and Vries A.H. de, The direct reaction field force field a consistent way to connect and combine quantum-chemical and classical descriptions of molecules. Int. J. Quantum Chem. (1996)60 1111-1132. 

Zijlstra, R. W.J., Grozema F. C., Swart M., Feringa B. L. and Duijnen R Th. van, Solvent Induced Charge Separation in the Excited States of Symmetrical Ethylene A Direct Reaction Field Study. J.Phys.Chem.A (2001) 105 3583-3590. 

Rullman et al. (1989) studied the initial proton transfer of Cys to His with a Hartee-Fock SCF direct reaction field (DRF) method, based on the refined X-ray structure of papain (Kamphuis et al., 1984). Parts of the active site residues were represented quantum mechanically and the environment was represented by partial charges and polarizabilities. The "QM motif consisted of methanethiol (modeling Cys-25), imidazole (for His-159) and formamide (for Asn-175). All atoms at the vicinity of the active site were included, except for atoms that are too close to the active site atoms, which were deleted from the structure... 

Swart et al.169 have reported RHF, TD-DFT and Direct Reaction Field (DRF) calculations on the polarizabilities of a set of 15 organic molecules. They find that the RHF results are inferior to those of the other two methods and that the DFT method with the LB94 functional gives the best results for the polarizability anisotropy in molecules with -bonds. Howard et al.,7° have calculated the static polarizabilities of alkylsiloxanate and methoxysiloxanate anions using DFT with the BLYP functional. 

Within the direct reaction field (DRF) method,the classical part of the solute-sol-vent system (solvent) is treated as a distribution of the polarizable point dipoles, interacting with each other. The DRF Hamiltonian of the solute-solvent system is thus given by the following formula ... 

Finally the problem of dispersion forces can be mentioned. The so-called direct reaction field model has been proposed by Thole and van Duijnen [209, 213]. This... 

The key issue of incorporating solvent effects in the quantum mechanical calculation has not been solved satisfactorily in MC and molecular dynamics studies overviewed above. Warshefs empirical valence bond approach, van Duijnen s direct reaction field method, and Tapia s ISCRF theory, by including these solvent effects, are steps forward in this direction. Although the key theoretical issue cannot be considered satisfactorily solved, the applications made are most interesting. 

The effects of the solvent may be modeled using the direct reaction field (DRF) method (de Vries et al. 1995 Duijnen and de Vries 1996). 

Van Duijnen et al. in a set of papers have developed a version of a QM/classical approach in which classical solvent (water) molecules are treated as point polarizable dipoles. The portion of space with discrete water molecules is kept small and surrounded by a continuum dielectric. More attention is paid here to boundary conditions. The method makes use of a direct reaction field (RF) (in contrast with almost all other continuum methods which use an averaged RF) the average is given later with the aid of MC calculations, where the classical particles are also provided with a repulsive potential to avoid collapse of the particles. Not many details are given, however. 

A novel SCRF approach by van Duijnen and coworkers uses the direct reaction field Hamiltonian that represents the total solute plus solvent energy, the solvent being described in terms of a polarizability transfer matrix, viz. generalized point polarizabilities. Thus, a discrete set of point dipoles develop in response to the solute s field, providing a complex reaction field. The resulting electrostatic interaction, in addition to induction, includes dispersion contributions as well. 

---