6.2.2. Definition of Effective Properties 3064 6.3. Response Properties to Magnetic Fields 3066 6.3.1. Nuclear Shielding 3066 6.3.2. Indirect Spin−Spin Coupling 3067 6.3.3. EPR Parameters 3068 6.4. Properties of Chiral Systems 3069 6.4.1. Electronic Circular Dichroism (ECD) 3069 6.4.2. Optical Rotation (OR) 3069 6.4.3. VCD and VROA 3070 7. Continuum and Discrete Models 3071 7.1. Continuum Methods within MD and MC Simulations 3072

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Quantum mechanical continuum solvation models.

We present a new continuum solvation model based on the quantum mechanical charge density of a solute molecule interacting with a continuum description of the solvent. The model is called SMD, where the “D” stands for “density” to denote that the full solute electron density is used without defining partial atomic charges. “Continuum” denotes that the solvent is not represented explicitly but rather as a dielectric medium with surface tension at the solute−solvent boundary. SMD is a universal solvation model, where “universal” denotes its applicability to any charged or uncharged solute in any solvent or liquid medium for which a few key descriptors are known (in particular, dielectric constant, refractive index, bulk surface tension, and acidity and basicity parameters). The model separates the observable solvation free energy into two main components. The first component is the bulk electrostatic contribution arising from a self-consistent reaction field treatment that involves the solution of the nonho...

Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions.

The polarizable continuum model (PCM), used for the calculation of molecular energies, structures, and properties in liquid solution has been deeply revised, in order to extend its range of applications and to improve its accuracy. The main changes effect the definition of solute cavities, of solvation charges and of the PCM operator added to the molecular Hamiltonian, as well as the calculation of energy gradients, to be used in geometry optimizations. The procedure can be equally applied to quantum mechanical and to classical calculations; as shown also with a number of numerical tests, this PCM formulation is very efficient and reliable. It can also be applied to very large solutes, since all the bottlenecks have been eliminated to obtain a procedure whose time and memory requirements scale linearly with solute size. The present procedure can be used to compute solvent effects at a number of different levels of theory on almost all the chemical systems which can be studied in vacuo.

New developments in the polarizable continuum model for quantum mechanical and classical calculations on molecules in solution

Implicit Solvation Models: Equilibria, Structure, Spectra, and Dynamics.

Continuum solvation models are appealing because of the simplified yet accurate description they provide of the solvent effect on a solute, described either by quantum mechanical or classical methods. The polarizable continuum model (PCM) family of solvation models is among the most widely used, although their application has been hampered by discontinuities and singularities arising from the discretization of the integral equations at the solute-solvent interface. In this contribution we introduce a continuous surface charge (CSC) approach that leads to a smooth and robust formalism for the PCM models. We start from the scheme proposed over ten years ago by York and Karplus and we generalize it in various ways, including the extension to analytic second derivatives with respect to atomic positions. We propose an optimal discrete representation of the integral operators required for the determination of the apparent surface charge. We achieve a clear separation between “model” and “cavity” which, together with simple generalizations of modern integral codes, is all that is required for an extensible and efficient implementation of the PCM models. Following this approach we are now able to introduce solvent effects on energies, structures, and vibrational frequencies (analytical first and second derivatives with respect to atomic coordinates), magnetic properties (derivatives with respect of magnetic field using GIAOs), and in the calculation more complex properties like frequency-dependent Raman activities, vibrational circular dichroism, and Raman optical activity.

Continuous surface charge polarizable continuum models of solvation. I. General formalism

We present the full implementation of the integral equation formalism (IEF) we have recently formulated to treat solvent effects. The method exploits a single common approach for dielectrics of very different nature:  standard isotropic liquids, intrinsically anisotropic media like liquid crystals, and ionic solutions. We report here an analysis of its both formal and technical details as well as some numerical applications addressed to state the achieved generalization to all kinds of molecular solutes and to show the equally reliable performances in treating such different environmental systems. In particular, we report, for isotropic liquids, data of solvation free energies and static (hyper)polarizabilities of various molecular solutes in water, for anisotropic dielectrics, a study of an SN2 reaction, and finally, for ionic solution, a study of some structural aspects of ion pairing.

Evaluation of Solvent Effects in Isotropic and Anisotropic Dielectrics and in Ionic Solutions with a Unified Integral Equation Method: Theoretical Bases, Computational Implementation, and Numerical Applications

and E. Cancès

Papers

Evaluation of Solvent Effects in Isotropic and Anisotropic Dielectrics and in Ionic Solutions with a Unified Integral Equation Method: Theoretical Bases, Computational Implementation, and Numerical Applications