Finite Field Method for Nonlinear Optical Property Prediction Using Rational Function Approximants.

The finite field (FF) method is a quick, easy-to-implement tool for the prediction of nonlinear optical properties. Here, we present and explore a novel variant of the FF method, which uses a rational function to fit a molecule's energy with respect to an electric field. Similarly to previous FF methods, factors crucial for the method's accuracy were tuned. These factors include the number of terms in the function, the distribution of fields used to construct the approximation, and the initial field in the approximation. It was found that the approximant form that best fits the energy has four numerator terms and three denominator terms. To determine a reasonable field distribution, the common ratio of a geometric progression was optimized to √2. Finally, an algorithm for determining a good initial field guess was devised. The optimized FF method was used to compute the polarizability and second hyperpolarizability for a set of 121 molecules and the first hyperpolarizability for a set of 91 molecules. The results from this were compared to a previous polynomial-based FF method. It was found that using a rational function gives higher errors compared to the polynomial model. However, unlike the polynomial model, no subsequent refinement steps were needed to obtain usable results. An overall comparison of the behavior of the two methods also shows that the rational function is less sensitive to the chosen initial field, making it a good choice for new quantum chemistry codes.

Benchmarking pKa prediction methods for Lys115 in acetoacetate decarboxylase.

Three different pKa prediction methods were used to calculate the pKa of Lys115 in acetoacetate decarboxylase (AADase): the empirical method PROPKA, the multiconformation continuum electrostatics (MCCE) method, and the molecular dynamics/thermodynamic integration (MD/TI) method with implicit solvent. As expected, accurate pKa prediction of Lys115 depends on the protonation patterns of other ionizable groups, especially the nearby Glu76. However, since the prediction methods do not explicitly sample the protonation patterns of nearby residues, this must be done manually. When Glu76 is deprotonated, all three methods give an incorrect pKa value for Lys115. If protonated, Glu76 is used in an MD/TI calculation, the pKa of Lys115 is predicted to be 5.3, which agrees well with the experimental value of 5.9. This result agrees with previous site-directed mutagenesis studies, where the mutation of Glu76 (negative charge when deprotonated) to Gln (neutral) causes no change in Km, suggesting that Glu76 has no effect on the pKa shift of Lys115. Thus, we postulate that the pKa of Glu76 is also shifted so that Glu76 is protonated (neutral) in AADase. Graphical abstract Simulated abundances of protonated species as pH is varied.

Communication: Two types of flat-planes conditions in density functional theory.

Using results from atomic spectroscopy, we show that there are two types of flat-planes conditions. The first type of flat-planes condition occurs when the energy as a function of the number of electrons of each spin, Nα and Nß, has a derivative discontinuity on a line segment where the number of electrons, Nα + Nß, is an integer. The second type of flat-planes condition occurs when the energy has a derivative discontinuity on a line segment where the spin polarization, Nα - Nß, is an integer, but does not have a discontinuity associated with an integer number of electrons. Type 2 flat planes are rare-we observed just 15 type 2 flat-planes conditions out of the 4884 cases we tested-but their mere existence has implications for the design of exchange-correlation energy density functionals. To facilitate the development of functionals that have the correct behavior with respect to both fractional number of electrons and fractional spin polarization, we present a dataset for the chromium atom and its ions that can be used to test new functionals.