Frequently it is useful to compare experimental values of the hyperpolarizabilities β and γ with calculated values. It is also often helpful to compare experimental values of β obtained from dc-electric field induced second harmonic generation (dc-SHG) experiments, e.g., with values obtained using the solvatochromism method. In order to do this the hyperpolarizabilities must be defined using consistent conventions. In this paper, four commonly used conventions are discussed and simple factors for converting between them presented. In addition, the sum-over-states expression for the calculation of β and γ is described and its correct use in comparing with hyperpolarizabilities obtained using other experimental and theoretical techniques discussed. As an illustration of the consistent use of conventions, ab initio and semiempirical calculations on para-nitroaniline are compared with experimental dc-SHG values. This comparison highlights the difference between theoretical values of the hyperpolarizability with the molecule in a gas phase environment and experimental values obtained in polar solvents−a difference that has in the past been obscured by inconsistent choice of conventions.

The increasing availability of high-quality experimental data and first-principles calculations creates opportunities for developing more accurate empirical force fields for simulation of proteins. We developed the AMBER-FB15 protein force field by building a high-quality quantum chemical data set consisting of comprehensive potential energy scans and employing the ForceBalance software package for parameter optimization. The optimized potential surface allows for more significant thermodynamic fluctuations away from local minima. In validation studies where simulation results are compared to experimental measurements, AMBER-FB15 in combination with the updated TIP3P-FB water model predicts equilibrium properties with equivalent accuracy, and temperature dependent properties with significantly improved accuracy, in comparison with published models. We also discuss the effect of changing the protein force field and water model on the simulation results.

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We have developed the IPolQ method for fitting non-polarizable point charges to implicitly represent the energy of polarization for systems in pure water. The method involves iterative cycles of molecular dynamics simulations to estimate the water charge density around the solute of interest followed by quantum mechanical calculations at the MP2/cc-pV(T+d)Z level to determine updated solute charges. Lennard-Jones parameters are updated starting from the Amber FF99SB nonbonded parameter set to accommodate the new charge model, guided by the comparisons to experimental hydration free energies (HFEs) of neutral amino acid side chain analogs and assumptions about the computed HFEs for charged side chains. These Lennard-Jones parameter adjustments for side chain analogs are assumed to be transferable to amino acids generally, and new charges for all standard amino acids are then derived in the presence of water modeled by TIP4P-Ew. Overall, the new charges depict substantially more polarized amino acids, particularly in the backbone moieties, than previous Amber charge sets. Efforts to complete a new force field with appropriate torsion parameters for this charge model are underway. The IPolQ method is general, applicable to arbitrary solutes.

The importance of including electron correlation effects in the determination of the equilibrium structure and hyperpolarizabilities of p-nitroaniline is investigated. Second-order perturbation theory gives static hyperpolarizabilities which are 88% to 100% larger than those obtained without electron correlation. These values are scaled by a self-consistent field frequency-dependent contribution for comparison with experimental measurements.Despite the large increase in ß(-2 ; , ) from electron correlation, the theoretical result is still 3 times smaller than the experimental value obtained in solution. This difference is discussed. The finite field perturbation approach for calculating hyperpolarizabilities is discussed, and we outline a generalization of a previous method based on the solution of simultaneous equations.

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