Self-consistent reaction field calculation

The Poisson equation has been used for both molecular mechanics and quantum mechanical descriptions of solvation. It can be solved directly using numerical differential equation methods, such as the finite element or finite difference methods, but these calculations can be CPU-intensive. A more efficient quantum mechanical formulation is referred to as a self-consistent reaction field calculation (SCRF) as described below. 

J Li, MR Nelson, CY Peng, D Bashford, L Noodleman. Incorporating protein environments in density functional theory A self-consistent reaction field calculation of redox potentials of [2Ee2S] clusters in feiTedoxm and phthalate dioxygenase reductase. J Phys Chem A 102 6311-6324, 1998. 

Figure 2-4 Comparison of electrostatic solvation energies obtained with the PCM and MPE methods for 18 polar molecules in aqueous solution (see text). Left self-consistent reaction field calculations at the HF-6-31 G level. Right calculations using gas-phase CM2 net atomic charges...

G. P, Ford and B. Wang, J. Comput. Chem., 13, 229 (1992). The Optimized Ellipsoidal Cavity and Its Application to the Self-Consistent Reaction Field Calculation of Hydration Energies of Cations and Neutral Molecules. 

Grunenberg, J. and Herges, R. (1995). Prediction of Chromatographic Retention Values (Rm) and Partition Coefficients (log OCt) Using a Combination of Semiempirical Self-Consistent Reaction Field Calculations and Neural Networks. J.Chem.lnf.Comput.ScL,35, 905-911. 

Dehu, C., Meyers, F., Hendrickx. E.. Clays, K., Persoons, A., Marder, S.R., Bredas, J.L. Solvent effects on the second-order nonlinear optical response of tr-conjugated molecules A combined evaluation through self-consistent reaction field calculations and hyper-Rayleigh scaterring measurements. J. Am. Chem. Soc. 117, 10127-10128 (1995)... 

Similarly, tautomerism of 20 was studied by theoretical molecular orbital calculations with total and relative energies in the gas phase indicating that tautomers 20 and 21 are more stable than 22 and 23. The relative low stability and lower dipole moments of the latter pair should make 20 and 21 favored in aqueous media. Self-consistent reaction field calculations indicate 20 is more stable (9-12 kcal moP ) in water than 21 <1998H(48)1833>. 

Ziegler and co-workers reported DFT with self-consistent reaction field calculations on multielectron redox reactions for dinuclear iron complexes [Fe2(CO)6(/x2-PR2)2]° (R=CH3, CF3). They did calculations on all three oxidation states for the complexes to construct energy profiles for the addition of two electrons to the = 0 oxidation state. It was found that inclusion of solvent and/or ion pairing effects was necessary to predict the experimentally observed disproportionation reaction of the singly reduced complex. It was also found that CO ligands are important in the deloealization of added electron density due to reduction. Interestingly, the authors also conclude that ion pairing with the anionic complexes should be modeled to produce the most realistic calculations. 

J. Parra-Mouchet, R.R. Contreras and A. Aizman, Self-consistent reaction field calculations on the proton transfer in ammonia-formic acid systems as a model for hydrogen bonding in amino acids in solution, Int. J. Quantum Chem., 33 (1988) 41. 

The calculation of redox potentials for bacteriochlorophyll and bacteriopheophytin molecules described in Ref. 43 at the HF 6-3 Ig level using the PS-GVB solvation module represents the largest tJt initio self-consistent reaction field calculation to date. The calculations performed an a workstation involved up to 889 basis functions and were successful in predicting the correct relative redox energies. 

SCRF (self-consistent reaction field) method for including solvation effects in ah initio calculations... 

An ab initio MO calculation by Jorgensen revealed enhanced hydrogen bonding of a water molecule to the transition states for the Diels-Alder reactions of cyclopentadiene with methyl vinyl ketone and acrylonitrile, which indicates that the observed rate accelerations for Diels-Alder reactions in aqueous solution arise from the hydrogenbonding effect in addition to a relatively constant hydrophobic term.7,76 Ab initio calculation using a self-consistent reaction field continuum model shows that electronic and nuclear polarization effects in solution are crucial to explain the stereoselectivity of nonsymmetrical... 

Conceptually, the self-consistent reaction field (SCRF) model is the simplest method for inclusion of environment implicitly in the semi-empirical Hamiltonian24, and has been the subject of several detailed reviews24,25,66. In SCRF calculations, the QM system of interest (solute) is placed into a cavity within a polarizable medium of dielectric constant e (Fig. 2.2). For ease of computation, the cavity is assumed to be spherical and have a radius ro, although expressions similar to those outlined below have been developed for ellipsoidal cavities67. Using ideas from classical electrostatics, we can show that the interaction potential can be expressed as a function of the charge and multipole moments of the solute. For ease... 

Fig. 2.2 Self-Consistent Reaction Field (SCRF) model for the inclusion of solvent effects in semi-empirical calculations. The solvent is represented as an isotropic, polarizable continuum of macroscopic dielectric e. The solute occupies a spherical cavity of radius ru, and has a dipole moment of p,o. The molecular dipole induces an opposing dipole in the solvent medium, the magnitude of which is dependent on e.

There is a fundamental difference between Eqs. 4.12 and 4.15 despite their apparent similarity. The term electron density (see Eq. 4.13), whereas the term Vcxt in Eq. 4.12, is constant in the SCF procedure. To reflect this fact, the approach based on Eqs. 4.13-4.15 is frequently called the Self-Consistent Reaction Field method (SCRF). (Throughout the text, AXY/SCRF denotes combined quantum-mechanical/reaction field calculations where XXX specifies the quantum-mechanical method.)... 

Marten, B., K. Kim, C. Cortis, R. A. Friesner, R. B. Murphy, M. N. Ringnalda, D. Sitkoff, and B. Honig. 1996. New Model for Calculation of Solvation Free Energies Correction to Self-consistent Reaction Field Continuum Dielectric Theory for Short-Range Hydrogen-Bonding Effects. J. Phys. Chem. 100, 11775. 

Diastereoselectivity of the reactions of the cation 26 and the anion 29 derived from 25 (R2 = Me) was modeled by self-consistent reaction field solvation models obtained from ab initio SCF-MO calculations. The experimentally found cis/trans ratios confirmed the model (Scheme 1) <2002JOC2013>. 

The most common approach to solvation studies using an implicit solvent is to add a self-consistent reaction field (SCRF) term to an ab initio (or semi-empirical) calculation. One of the problems with SCRF methods is the number of different possible approaches. Orozco and Luque28 and Colominas et al27 found that 6-31G ab initio calculations with the polarizable continuum model (PCM) method of Miertius, Scrocco, and Tomasi (referred to in these papers as the MST method)45 gave results in reasonable agreement with the MD-FEP results, but the AM1-AMSOL method differed by a number of kJ/mol, and sometimes gave qualitatively wrong results. 

Abstract This chapter reviews the theoretical background for continuum models of solvation, recent advances in their implementation, and illustrative examples of their use. Continuum models are the most efficient way to include condensed-phase effects into quantum mechanical calculations, and this is typically accomplished by the using self-consistent reaction field (SCRF) approach for the electrostatic component. This approach does not automatically include the non-electrostatic component of solvation, and we review various approaches for including that aspect. The performance of various models is compared for a number of applications, with emphasis on heterocyclic tautomeric equilibria because they have been the subject of the widest variety of studies. For nonequilibrium applications, e.g., dynamics and spectroscopy, one must consider the various time scales of the solvation process and the dynamical process under consideration, and the final section of the review discusses these issues. 

Self-consistent reaction field (SCRF) models are the most efficient way to include condensed-phase effects into quantum mechanical calculations [8-11]. This is accomplished by using SCRF approach for the electrostatic component. By design, it considers only one physical effect accompanying the insertion of a solute in a solvent, namely, the bulk polarization of the solvent by the mean field of the solute. This approach efficiently takes into account the long range solute-solvent electrostatic interaction and effect of solvent polarization. However, by design, this model cannot describe local solute-solvent interactions. 

Marten B, Kim K, Cortis C, Friesner RA, Murphy RB, Ringnalda MN, Sitkoff D, Honig B. New model for calculation of solvation free energies correction of self-consistent reaction field continuum dielectric theory for short-range hydrogen-bonding effects, / Phys. Chem. 1996, 100, 11775-11788. 

These workers also calculated the relative stability of the tautomers lOa-c in the gas phase by ab initio and density functional theory (DFT) methods and in solution using several continuum solvation models such as self-consistent reaction fields (SCRF) and the Poisson-Boltzmann method. These results showed good agreement between the experimental and theoretical approaches. 

Solvation effects on the conformation of esters of three /i-snbstituted 1-phenyletha-nols with 2-flnoro-2-phenyl acetic acid (FCDA) were studied both experimentally (in five solvents ranging from CDCb to DMSO) and quantum mechanically. Semi-empiri-cal (AMI of MJS Dewar and PM3 of JJP Stewart) and ab initio (RHF/3-21 G) calculations were undertaken. Energy maps for the conformers of the esters as a function of the dihedral angles alpha (F-C-alpha acid-C=0) and beta (CO-O-C-alcohol-H) were obtained. Solvent effect calculations, through the self-consistent reaction field on the most stable conformers, were also carried out (Hamman et al., 1996). 

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