Molecular continuum, theoretical methods

S. J. Mo, T. Vreven, B. Mennucci, K. Morokuma and J. Tomasi, Theoretical study of the Sn2 reaction of C1-(H20) +CH3C1 using our own n-layered integrated molecular orbitals and molecular mechanics polarizable continuum model method (ONIOM-PCM), Theor. Chem. Acc., Ill (2004) 154-161. 

The ASEP/MD method, acronym for Averaged Solvent Electrostatic Potential from Molecular Dynamics, is a theoretical method addressed at the study of solvent effects that is half-way between continuum and quantum mechanics/molecular mechanics (QM/MM) methods. As in continuum or Langevin dipole methods, the solvent perturbation is introduced into the molecular Hamiltonian through a continuous distribution function, i.e. the method uses the mean field approximation (MFA). However, this distribution function is obtained from simulations, i.e., as in QM/MM methods, ASEP/MD combines quantum mechanics (QM) in the description of the solute with molecular dynamics (MD) calculations in the description of the solvent. 

The QM theory of chemical shielding was originally developed many years ago [22,23], but only later have ab initio methods and density functional theories (DFT) been reliably used for the prediction of NMR properties of isolated molecular systems, and finally of solvated systems. The latter step has been achieved by extending the gas-phase theoretical methods to continuum solvation models (see Ref. [11] for a sufficiently updated list of papers). 

Theoretical Methods for the Liquid. The approaches to be described all attempt to calculate the response functions for a central water molecule influenced by the surrounding medium. The older methods represent the surrounding medium through a continuum parametrized by a dielectric function but more recently the medium has been described by molecular mechanics (MM). In both cases the central molecule is the subject of a full correlated quantum mechanical treatment. 

In the thermodynamic cycle (1.92), the Gibbs energies of transfer AG° (i) can be calculated by theoretical methods. Two main classes of methods have been developed for modelling solvent effects. Molecular dynamics and Monte Carlo methods use a discrete representation of the solvent molecules whereas, in the second class of so-called SCRF (self-consistent reaction field) methods, the solvent is represented as a dielectric continuum surrounding the solute cavity. These methods are outside the scope of this book. They are described in reviews [105, 107, 108] and books [109, 110]. Examples of their application to Lewis acid/base complexes can be found in the following references hydrogen-bonded complexes [111-113], BF3 and BH3 complexes [114] and diiodine complexes [115]. 

In literature, some researchers regarded that the continuum mechanic ceases to be valid to describe the lubrication behavior when clearance decreases down to such a limit. Reasons cited for the inadequacy of continuum methods applied to the lubrication confined between two solid walls in relative motion are that the problem is so complex that any theoretical approach is doomed to failure, and that the film is so thin, being inherently of molecular scale, that modeling the material as a continuum ceases to be valid. Due to the molecular orientation, the lubricant has an underlying microstructure. They turned to molecular dynamic simulation for help, from which macroscopic flow equations are drawn. This is also validated through molecular dynamic simulation by Hu et al. [6,7] and Mark et al. [8]. To date, experimental research had "got a little too far forward on its skis however, theoretical approaches have not had such rosy prospects as the experimental ones have. Theoretical modeling of the lubrication features associated with TFL is then urgently necessary. 

Sometimes the theoretical or computational approach to description of molecular structure, properties, and reactivity cannot be based on deterministic equations that can be solved by analytical or computational methods. The properties of a molecule or assembly of molecules may be known or describable only in a statistical sense. Molecules and assemblies of molecules exist in distributions of configuration, composition, momentum, and energy. Sometimes, this statistical character is best captured and studied by computer experiments molecular dynamics, Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. Interaction potentials based on quantum mechanics, classical particle mechanics, continuum mechanics, or empiricism are specified and the evolution of the system is then followed in time by simulation of motions resulting from these direct... 

Photodissociation of small polyatomic molecules is an ideal field for investigating molecular dynamics at a high level of precision. The last decade has seen an explosion of many new experimental methods which permit the study of bond fission on the basis of single quantum states. Experiments with three lasers — one to prepare the parent molecule in a particular vibrational-rotational state in the electronic ground state, one to excite the molecule into the continuum, and finally a third laser to probe the products — are quite usual today. State-specific chemistry finally has become reality. The understanding of such highly resolved measurements demands theoretical descriptions which go far beyond simple models. 

The MFA [1] introduces the perturbation due to the solvent effect in an averaged way. Specifically, the quantity that is introduced into the solute molecular Hamiltonian is the averaged value of the potential generated by the solvent in the volume occupied by the solute. In the past, this approximation has mainly been used with very simplified descriptions of the solvent, such as those provided by the dielectric continuum [2] or Langevin dipole models [3], A more detailed description of the solvent has been used by Ten-no et al. [4], who describe the solvent through atom-atom radial distribution functions obtained via an extended version of the interaction site method. Less attention has been paid, however, to the use of the MFA in conjunction with simulation calculations of liquids, although its theoretical bases are well known [5]. In this respect, we would refer to the papers of Sese and co-workers [6], where the solvent radial distribution functions obtained from MD [7] calculations and its perturbation are introduced a posteriori into the molecular Hamiltonian. 

Solvent effects can significantly influence the function and reactivity of organic molecules.1 Because of the complexity and size of the molecular system, it presents a great challenge in theoretical chemistry to accurately calculate the rates for complex reactions in solution. Although continuum solvation models that treat the solvent as a structureless medium with a characteristic dielectric constant have been successfully used for studying solvent effects,2,3 these methods do not provide detailed information on specific intermolecular interactions. An alternative approach is to use statistical mechanical Monte Carlo and molecular dynamics simulation to model solute-solvent interactions explicitly.4 8 In this article, we review a combined quantum mechanical and molecular mechanical (QM/MM) method that couples molecular orbital and valence bond theories, called the MOVB method, to determine the free energy reaction profiles, or potentials of mean force (PMF), for chemical reactions in solution. We apply the combined QM-MOVB/MM method to... 

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