Self-consistent reaction field approach

F. J. Luque, M. Orozco, P. K. Bhadane and S. R. Gadre, Effect of solvation on the shapes, sizes, and anisotropies of polyatomic anions via molecular electrostatic potential topography An ab initio self-consistent reaction field approach, J. Chem. Phys., 100 (1994) 6718-6726. 

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 parity violating potentials in alanine in gas phase and solution have been studied in [106] within the framework of the multi-configuration linear response approach. Several low-energy conformers of neutral alanine as well as the zwitterionic form have been studied therein and solvent effects on structures and, for the first time, also on parity violating potentials have been accounted for within a multi-configuration self-consistent reaction field approach on the RPA and the CASSCF level of theory. The main result of these higher level calculations was, that they provided no... 

Solvation energies were computed at the double-c level using a self-consistent reaction field approach based on numerical solutions of the Poisson-Boltzmann equation 58-60). These were computed at the optimized gas-phase geometry utilizing an appropriate dielectric constant for comparison to the experimental conditions (e = 37.5 for acetonitrile e = 20.7 for acetone). The standard set of optimized radii in Jaguar were employed Mo (1.526 A), W (1.534 A), H (1.150 A), C (1.900 A), O (1.600 A). Vibrational analyses using analytical frequencies were computed at the double-q level, ensuring all stationary points to be minima. 

ABSTRACT. The effect of a macroscopic phase (solvent or adsorbent) interacting with a molecule can be taken into account in quantum chemical computations hy means of a self-consistent reaction field approach. The macroscopic phase is represented by a continuum with macroscopic dielectric properties. The molecule undergoes an electric potential arising from the polarization by the molecular charge distribution of the macroscopic pliase. 

Here we discuss a joint theoretical and experimental study of the influence of solvent polarity on the second-order molecular polarizability p of p-nitroaniline and the push-pull polyene l,l-dicyano-6-dibutylamine-hexa-triene [144]. The calculations are carried out at the Har-tree-Fock ab initio level on the basis of an expanded self-consistent reaction field approach and are compared to hyper-Rayleigh scattering measurements performed in solvents with a wide range of dielectric constants. 

One femily of models for systems in non-aqueous solution are referred to as Self-Consistent Reaction Field (SCRF) methods. These methods all model the solvent as a continuum of uniform dielectric constant e the reaction field. The solute is placed into a cavity within the solvent. SCRF approachs differ in how they define the cavity and the reaction field. Several are illustrated 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.)... 

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. 

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. 

The details on the operators introduced in the two schemes will be given below, here we only want to add that the addition of Henv to the solute Hamiltonian automatically leads to a modification of the solute wavefunction which has now to be determined by solving the effective Eq. (1-1). This can be done using exactly the same methods used for isolated molecules here in particular we shall mainly focus on the standard self-consistent field (SCF) approach (either in its Hartree-Fock or DFT formulation). Due to the presence of Hem the modified SCF scheme is generally known as self-consistent reaction field (SCRF). Historically the term SCRF has been coined for the QM/continuum approach but here, due the parallelism between the two schemes which will be made clear in the following sections, it will be used indistinctly for both. 

Among the few determinations of of molecular crystals, the CPHF/ INDO smdy of Yamada et al. [25] is unique because, on the one hand, it concerns an open-shell molecule, the p-nitrophenyl-nitronyl-nitroxide radical (p-NPNN) and, on the other hand, it combines in a hybrid way the oriented gas model and the supermolecule approach. Another smdy is due to Luo et al. [26], who calculated the third-order nonlinear susceptibility of amorphous thinmultilayered films of fullerenes by combining the self-consistent reaction field (SCRF) theory with cavity field factors. The amorphous namre of the system justifies the choice of the SCRF method, the removal of the sums in Eq. (3), and the use of the average second hyperpolarizability. They emphasized the differences between the Lorentz Lorenz local field factors and the more general Onsager Bbttcher ones. For Ceo the results differ by 25% but are in similar... 

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