Continuum-solvation methods

Key words Continuum models - Polarizable continuum method - Solvation... 

OPW (orthogonalized plane wave) a band-structure computation method P89 (Perdew 1986) a gradient corrected DFT method parallel computer a computer with more than one CPU Pariser-Parr-Pople (PPP) a simple semiempirical method PCM (polarized continuum method) method for including solvation effects in ah initio calculations... 

SCF (self-consistent field) procedure for solving the Hartree-Fock equations SCI-PCM (self-consistent isosurface-polarized continuum method) an ah initio solvation method... 

Given the diversity of different SCRF models, and the fact that solvation energies in water may range from a few kcal/mol for say ethane to perhaps 100 kcal/mol for an ion, it is difficult to evaluate just how accurately continuum methods may in principle be able to represent solvation. It seems clear, however, that molecular shaped cavities must be employed, the electiostatic polarization needs a description either in terms of atomic charges or quite high-order multipoles, and cavity and dispersion terms must be included. Properly parameterized, such models appear to be able to give absolute values with an accuracy of a few kcal/mol." Molecular properties are in many cases also sensitive to the environment, but a detailed discussion of this is outside the scope of this book. ... 

Pratt, L. R., Tawa, G.J., Hummer, G., Garcia, A. E., and Corcelli, S. A. (1997). Boundary integral methods for the poisson equation of continuum dielectric solvation models. Int.J. Quant. Chem. 64, 121-141. 

Prior to addressing the results of simulations on the issues exposed in the last section, we will now develop in this section a simple model perspective [5c,21,22,43]. Its purpose is both to shed light on the interpretation in terms of solvation of those results and to emphasize the interconnections (and differences) that may exist. The development given below is suitable for charge transfer reaction systems, which have pronounced solute-solvent electrostatic coupling it is not appropiate for, e.g., neutral reactions in which the solvent influence is mainly of a collisional character. (Although we do not pursue it here, the various frequencies that arise in the model can be easily evaluated by dielectric continuum methods [21,431). 

Hybrid solvation Implicit solvation plus Explicit solvation microsolvation subjected to the continuum method. Here the solute molecule is associated with explicit solvent molecules, usually no more than a few and sometimes as few as one, and with its bound (usually hydrogen-bonded) solvent molecule(s) is subjected to a continuum calculation. Such hybrid calculations have been used in attempts to improve values of solvation free energies in connection with pKp. [42], and also [45] and references therein. Other examples of the use of hybrid solvation are the hydration of the environmentally important hydroxyl radical [52] and of the ubiquitous alkali metal and halide ions [53]. Hybrid solvation has been surveyed in a review oriented toward biomolecular applications [54]. 

The inclusion in the book of this introductory section has been motivated by the remarkable advances of continuum methods. Their extension to more complex properties and to more complex systems makes it necessary to have a more detailed understanding of the way in which physical concepts have to be further developed to continue this promising line of investigation. The relatively simple procedures in use for three decades to obtain with a limited computational effort the numerical values of some basic properties, such as the solvation energy of a solute in very dilute solution, are no longer sufficient. 

To appreciate the basic reasons why continuous models are so versatile and promising for more applications, however, we have to consider again the simple systems and the simple properties mentioned above. The best way to gain this initial appreciation is to contrast the procedures given by discrete and continuum methods to obtain the solvation energy in a very dilute solution. 

Molecular solutes described within QM continuum solvation models are characterized by an effective Hamiltonian which depends on the wavefunction of the solute itself. This makes the determination of the wavefunction a nonlinear QM problem. We have shown how the standard methods of modern quantum chemistry, developed for isolated molecules, have been extended to these solvation models. The development of QM continuum methods has reached a satisfactory stage for completely variational approaches (HF/DFT/MCSFC/VB). More progress is expected for continuous solvation model based on MP or CC wavefunction approaches. 

Here we give an overview of the current status and perspectives of theoretical treatments of solvent effects based on continuum solvation models where the solute is treated quantum mechanically. It is worth noting that our aim is not to give a detailed description of the physical and mathematical formalisms that underlie the different quantum mechanical self-consistent reaction field (QM-SCRF) models, since these issues have been covered in other contributions to the book. Rather, our goal is to illustrate the features that have contributed to make QM-SCRF continuum methods successful and to discuss their reliability for the study of chemical reactivity in solution. 

This section will focus on the application of QM-SCRF continuum methods to chemical processes in solution. For brevity, however, we will limit the discussion to two kinds of chemical processes. Firstly, we will examine selected examples of tautomeric equilibria, which are well known to be highly sensitive to solvation effects. Secondly, we will move on the analysis of selected chemical reactions involving formation and breaking of bonds, whose description constitutes a challenge for any QM-SCRF continuum model. 

Sampling the conformational space of solute(s) by MC or MD algorithms requires many intramolecular and solvation calculations and accordingly simplicity in the solute Hamiltonian and computer efficiency in the continuum method used to compute solvation are key requirements. This implies that, with some exceptions [1], MD/MC algorithms are always coupled to purely classical descriptions of solvation, which in order to gain computer efficiency adopt severe approximations, such as the neglect of explicit electronic polarization contributions to solvation (for a discussion see ref. [1]). In the following we will summarize the major approaches used to couple MD/MC with continuum representations of solvation. 

In this contribution we will first outline the formalism of the ONIOM method. Although ONIOM has not yet been applied extensively to problems in the solvated phase, we will show how ONIOM has the potential to become a very valuable tool in both the explicit and implicit modeling of solvent effects. For the implicit modeling of solvent, we developed the ONIOM-PCM method, which combines ONIOM with the Polarizable Continuum Method (PCM). We will conclude with a case study on the vertical electronic transition to the it state in formamide, modeled with several explicit solvent molecules. 

E. Cances and B. Mennucci, New applications of integral equations methods for solvation continuum methods Ionic solutions and liquid crystals, J. Mater. Chem., 23 (1998) 309-326. 

Table 1-7. Comparison of the components and global solvation energies (in kcal moF1) for the four forms of the palladium complex PdH3Cl(NH3)2 in dichloromethane calculated by the discrete and continuum methods...

There are various methods for treating solvation, ranging from a detailed description at the molecular level to reaction field models where the solvent is modelled as a continuum method.125... 

In the previous sections we have briefly summarized the basic theory of QM/MM and QM/continuum methods showing their differences and similarities, now we can move on to describe their applications to the calculation of molecular response properties and the related spectroscopies for a generic solvated system. 

No systematic study of the effect of different solvation models has been performed. A few reports have compared specific cases such as the study of cationic and anionic alanines, which shows a significant improvement in the chemical shift prediction using polarized continuum method (PCM) or better stiU a hybrid solvation approach (Section 1.4.3). However, the linear scaling correction discussed below can often account for the systematic solvent effect and so sometimes one can get away without any solvent computation at all. 

Corcelli, S. A., Kress, J. D., Pratt, L. R., and Tawa, G. J., Mixed-direct-iterative methods for boundary integral formulations of continuum dielectric solvation models. In L. Hunter and T. E. Klein (eds.). Pacific Symposium on Biocomputing 1996, pp. 142-159, Singapore World Scientific (1995). 

For solvation modeling, see C. J. Cramer and D. G. Truhlar, this volume. Continuum and Solvation Models Classical and Quantum Mechanical Implementation. For molecular mechanics, see D. B. Boyd and K. Lipkowitz, /. Chem. Educ., S9, 269 (1982). Molecular Mechanics. The Method and Its Underlying Philosophy. 

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