Generalized reaction field method

I. G. Tironi, R. Sperb, P. E. Smith, W. F. van Gunsteren. A generalized reaction field method for molecular dynamics simulations. J Chem Phys 702 5451, 1995. 

A Generalized Reaction Field Method for Molecular Dynamics Simulations. 

Kirkwood generalized the Onsager reaction field method to arbitrary charge distributions and, for a spherical cavity, obtained the Gibbs free energy of solvation in tenns of a miiltipole expansion of the electrostatic field generated by the charge distribution [12, 1 3]... 

Two standard methods are in common use in the MD community the reaction field method [79,80] and the Ewald summation technique [72,81-83]. There are also various hierarchical algorithms which are quite attractive in principle, but have proved to be difficult to implement efficiently in practice [67,84-87]. An alternative and potentially development interesting complement, is the summation formula developed by Lekner [88,89] which has been given an alternative and more general derivation by Sperb [90]. 

Karelson et al. [124] had also carried out a comparative analysis of the molecular descriptors calculated for the isolated molecules (gas phase) and for the molecules embedded into a dielectric continuum corresponding to aqueous solution. The self-consistent reaction field method [125] was used for the latter calculations. The results indicated that, in general, the quantum-chemically derived descriptors are rather insensitive towards the change in the environment surrounding the molecule. However, the most influenced are the polarizability and several other MO-related descrip-... 

The theoretical principles of cycloaddition reactions are well understood and there have been many computational studies (see Pericyclic Reactions The Diels-Alder Reaction). Often the hetero-cycloaddition reaction shows similar characteristics to the carbocyclic analog, but a number of special features have been noted. In heterocyclic chemistry the cycloaddition reactions are often dipolar computational studies show that a concerted mechanism is followed in the gas phase. However, a number of studies have noted that these dipolar cycloaddition reactions become stepwise when solvent effects are included (via the reaction field method), with a consequent loss of stereospecificity." Other characteristics of hetero-cycloaddition reactions which have been studied include the endo/exo selectivity" and the regiose-lectivity (for example, [2-1-2] vs. [2-1-4])." High levels of electron correlation are generally required in order to establish these selectivities. 

In the quantum mechanical continuum model, the solute is embedded in a cavity while the solvent, treated as a continuous medium having the same dielectric constant as the bulk liquid, is incorporated in the solute Hamiltonian as a perturbation. In this reaction field approach, which has its origin in Onsager s work, the bulk medium is polarized by the solute molecules and subsequently back-polarizes the solute, etc. The continuum approach has been criticized for its neglect of the molecular structure of the solvent. Also, the higher-order moments of the charge distribution, which in general are not included in the calculations, may have important effects on the results. Another important limitation of the early implementations of this method was the lack of a realistic representation of the cavity form and size in relation to the shape of the solute. 

The generalized Bom model (GBM) can be regarded as a special case of the preceding procedures the reaction field is expressed in terms of a multi-center monopole representation of the solute molecule, using the Bom formula, Eq. (32).l3 ,6, 3 "5 The centers are the atomic nuclei. The results are quite sensitive to the method used to calculate the atomic charges Cramer and Truhlar, who have applied the GBM approach extensively13,16,107 use their Class IV charges for this purpose.16,107,116 Various techniques have been utilized to determine the radii.16,95,101,107... 

A third possibility that has received extensive study in the SCRF regime is one that has seen less use at the classical level, at least within the context of general cavities, and that is representation of the reaction field by a multipole expansion. Rinaldi and Rivail (1973) presented this methodology in what is arguably the first paper to have clearly defined the SCRF procedure. While the original work focused on ideal cavities, this group later extended the method to cavities of arbitrary shape. In formalism, Eq. (11.17) is used for any choice of cavity shape, but the reaction field factors f must be evaluated numerically when the cavity is not a sphere or ellipsoid (Dillet et al. 1993). Analytic derivatives for this approach have been derived and implemented (Rinaldi et al. 2004). 

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