Molecular Refractivity and Polarizability

Accurate Determination of Ion Polarizabilities in Aqueous Solutions

We present a novel method for obtaining salt polarizabilities in aqueous solutions based on our recent theory for the refractive index of salt solutions, which predicts a linear relationship between the refractive index and the salt concentration at low concentrations, with a slope determined by the intrinsic values of the salt polarizability and the density of the solution. Here we apply this theory to determine the polarizabilities of 32 strong electrolyte salts in aqueous solutions from refractive index and density measurements. Setting Li⁺ as the standard ion, we then determine the polarizabilities of seven cations (Na⁺, K⁺, Rb⁺, Cs⁺, Ca²⁺, Ba²⁺, and Sr²⁺) and seven anions (F^-, Cl^-, Br^-, I^-, ClO₄^-, NO₃^-, and SO₄^2-), which can be used as important reference data. We investigate the effect of temperature on salt polarizabilities, which decreases slightly with increasing temperature. The ion polarizability is found to be proportional to the cube of bare ionic radius (r_bare³) for univalent ions, but the relationship does not hold for multivalent ions. Contrary to findings of Krishnamurti, we find no significant linear relationship between ion polarizability and the square of the atomic number (N²) for smaller ions.

Computational methods in drug discovery

Computer-aided drug discovery/design methods have played a major role in the development of therapeutically important small molecules for over three decades. These methods are broadly classified as either structure-based or ligand-based methods. Structure-based methods are in principle analogous to high-throughput screening in that both target and ligand structure information is imperative. Structure-based approaches include ligand docking, pharmacophore, and ligand design methods. The article discusses theory behind the most important methods and recent successful applications. Ligand-based methods use only ligand information for predicting activity depending on its similarity/dissimilarity to previously known active ligands. We review widely used ligand-based methods such as ligand-based pharmacophores, molecular descriptors, and quantitative structure-activity relationships. In addition, important tools such as target/ligand data bases, homology modeling, ligand fingerprint methods, etc., necessary for successful implementation of various computer-aided drug discovery/design methods in a drug discovery campaign are discussed. Finally, computational methods for toxicity prediction and optimization for favorable physiologic properties are discussed with successful examples from literature.

Effective molecular polarizabilities and crystal refractive indices estimated from x-ray diffraction data

Although it was proposed some time ago that (hyper)polarizabilities might be estimated from the results of x-ray charge density refinements, early results were unconvincing. In this work we show that the one particle density obtained from the usual multipole refinement model does not contain sufficient information to determine these response properties and instead pursue the "constrained wave function" approach of fitting to x-ray structure factors. Simplified sum-over-states expressions are derived for determining the dipole polarizability from these wave functions, and these clearly show that the earlier work ignored important two-electron expectation values for the dipole polarizability, and two- and three-electron terms for Beta, etc. Correction factors for the simplified sum-over-states polarizability tensors from the constrained wave function are obtained by calibration against coupled Hartree-Fock ab initio results to yield in-crystal effective polarizability tensors. Results obtained for benzene, urea, and 2-methyl-4-nitroaniline demonstrate that the effective molecular polarizabilities clearly include the effects of intermolecular interactions and electron correlation, especially for urea where the effects on the polarizability are known to be quite large. We also carefully consider the way in which the linear bulk susceptibility, chi((1)), and refractive indices are determined from the x-ray fitted polarizabilities, employing three models based on a rigorous treatment of the local field. Incorrect results are obtained for the sort of molecules that are of interest in nonlinear optical applications if the molecules are approximated by single point dipoles. In contrast, the use of Lorentz-factor tensors averaged over several sites yields excellent results, with refractive indices obtained using this model in remarkably good agreement with optical measurements extrapolated to zero frequency.

MOLECULES IN OPTICAL, ELECTRIC, AND MAGNETIC FIELDS: A Personal Perspective

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▪ Abstract  Physical chemistry and theoretical chemistry have advanced over the past 50 years from being largely qualitative to having a mature status based firmly on the principles of quantum and statistical mechanics. My interest in the chemical elements and their compounds has prompted me to learn more about the nature of matter through the measurement and interpretation of optical, electric, and magnetic properties of molecules. In addition to holding intrinsic interest, such properties tell us about charge and current distributions and form the basis of electro-optics, magneto-optics, and nonlinear optics. They also help us understand the nature and strength of long-range intermolecular forces, the hydrogen bond, and molecular biology—topics that are apparently forever young.