Quantum mechanical self-consistent reaction

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. 

Colominas et al. [143] published a very detailed study on the dimerization of formic and acetic acids in the gas phase and in aqueous and chloroform solutions. By using quantum mechanical self-consistent reaction field and Monte Carlo calculations, they showed that the dimerization is favored in the gas phase and in a chloroform solution (1M) basically due to double hydrogen-bonded interaction between the monomers. In aqueous solution, the dimerization does not seem to occur due to the competitive solute-solvent intermolecular interactions. The computed dimerization energies are shown in Table VII. 15... 

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 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. 

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.)... 

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. 

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). 

Continuum solvation models consider the solvent as a homogeneous, isotropic, linear dielectric medium [104], The solute is considered to occupy a cavity in this medium. The ability of a bulk dielectric medium to be polarized and hence to exert an electric field back on the solute (this field is called the reaction field) is determined by the dielectric constant. The dielectric constant depends on the frequency of the applied field, and for equilibrium solvation we use the static dielectric constant that corresponds to a slowly changing field. In order to obtain accurate results, the solute charge distribution should be optimized in the presence of the field (the reaction field) exerted back on the solute by the dielectric medium. This is usually done by a quantum mechanical molecular orbital calculation called a self-consistent reaction field (SCRF) calculation, which is iterative since the reaction field depends on the distortion of the solute wave function and vice versa. While the assumption of linear homogeneous response is adequate for the solvent molecules at distant positions, it is a poor representation for the solute-solvent interaction in the first solvation shell. In this case, the solute sees the atomic-scale charge distribution of the solvent molecules and polarizes nonlinearly and system specifically on an atomic scale (see Figure 3.9). More generally, one could say that the breakdown of the linear response approximation is connected with the fact that the liquid medium is structured [105],... 

Coupling of quantum mechanical molecular subsystems with larger classically treated subsystems has traditionally involved electronic structure models describing molecules embedded in a dielectric medium and this is a research area that has expanded tremendously over the last three decades [2-36]. Most of this work has involved electronic structure methods that have been based on uncorrelated electronic structure methods [2-12,15-19]. Accurate description of the electronic structure of molecular systems requires that the correlated electronic motion in the molecule is incorporated and therefore a number of correlated electronic structure methods have been developed such as the second order Moller-Plesset (MP2) [28,30,90,91], the multiconfigurational self-consistent reaction field (MCSCRF) [13,20] and the coupled-cluster self-consistent reaction field (CCSCRF) method [36]. 

The isomeric equilibria of 2-acyl-2-nitroenamines with primary or secondary amino group are strongly solvent-dependent, as already seen for other enamines. An increase in the polarity of the solvent increases the population of the isomer(s) with Z-configuration, as deduced from the H-NMR spectra . In 3-amino-2-nitroacry-lic esters (567-574), the IR spectra show that an increase of solvent polarity increases the population of the ZE isomer , which has the highest calculated dipole moment. The effect of solvent polarity on the isomeric equilibria of some model 2-acyl-2-nitroenamines (554, R = H, Me R = Me, OMe R = R = H) has been qualitatively predicted by quantum-mechanical calculations using the self-consistent reaction field approach . 

The study of solvatochromic shifts is of great importance and has received enormous theoretical attention in recent years. Progress has been achieved in the use of the self-consistent reaction field and cavity models. These advances have also shown several limitations. It is thus of great interest to have alternative procedures to calculate solvent effects. In this respect the use of Monte Carlo/Molecular Dynamics simulations has been growing. In this paper we suggest a procedure to allow a full quantum mechanical calculation of the solute-solvent system. The basic idea is to treat the solute, the solvent and its interaction by quantum mechanics. First a Monte Carlo simulation is performed to characterize the liquid structure. These structures are then used in the quantum mechanical calculation. As a liquid has not one but a great number of structures equally possible within a... 

In the usual quantum-mechanical implementation of the continuum solvation model, the electronic wave function and electronic probability density of the solute molecule M are allowed to change on going firom the gas phase to the solution phase, so as to achieve self-consistency between the M charge distribution and the solvent s reaction field. Any treatment in which such self-consistency is achieved is called a self-consistent reaction-field (SCRF) model. Many versions of SCRF models exist. These differ in how they choose the size and shape of the cavity that contains the solute molecule M and in how they calculate t nf... 

Despite the demands presented by such a calculation, a number of researchers have used ab initio models to treat the electronic and nuclear degrees of freedom for the quantum motif in molecular mechanics, energy minimization studies. Examples of this include the self-consistant reaction field methods developed by Tapia and coworkers [42-44], which represent only the quantum motif explicitly and use continuum models for the environmental effects (classical and boundary regions), and the methods implemented by Kollman and coworkers [45] in their studies of condensed phase (chemical and biochemical) reaction mechanisms. In both of these implementations the expectation value of the quantum motif Hamiltonian, defined in Eqs. (11) and (14) above, is treated at the Hartree Fock level with relatively small basis sets. 

The theory of solvent-effects and some of its applications have been overviewed. The generalized self-consistent reaction field theory has been used to give a unified approach to quantum chemical calculations of subsystems embedded in a given milieu. The statistical mechanical theory of projected equation of motion has been briefly described. This theory underlies applications of molecular dynamics simulations to the study of solvent and thermal bath effects on carefully defined subsystems of interest. The relationship between different approaches used so far to calculate solvent effects and the general approach advocated by this reviewer has been established. Applications to molecular properties in a time independent framework have been presented. 

Shokhen et al. [56] analyzed possible mechanisms for the reversible formation of the complex between papain, a prototype enzyme of cysteine proteases, and pep-tidy 1 aldehyde inhibitors, using the quantum mechanical (DFT)/self consistent reaction field (virtual solvent) approach. 

Here M denotes the electronic part of the quantum mechanical operator associated with the m elements of multipole of rank / The methods based on the definition given by the equation (9) are referred as self-consistent reaction field methods (SCRF). 

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