Comparison of CBS-QB3, CBS-APNO, and G3 predictions of gas phase deprotonation data

The G3, CBS-QB3, and CBS-APNO methods have been used to calculate ΔH and ΔG values for deprotonation of seventeen gas-phase reactions where the experimental values are reported to be accurate within one kcal/mol. For these reactions, the mean absolute deviation of these three methods from experiment is 0.84 to 1.26 kcal/mol, and the root-mean-square deviation for ΔG and ΔH is 1.43 and 1.49 kcal/mol for the CBS-QB3 method, 1.06 and 1.14 kcal/mol for the CBS-APNO method, and 1.16 and 1.28 for the G3 method. The high accuracy of these methods makes them reliable for calculating gas-phase deprotonation reactions, and allows them to serve as a valuable check on the accuracy of experimental data reported in the National Institutes of Standards and Technology database.

A Closed-Form Solution for the Optimal Time Evolution of an Exponentially Decaying Signal with Thermal Noise

The signal-to-noise ratio of a monoexponentially decaying signal exhibits a maximum at an evolution time of approximately 1.26 T-2. It has previously been thought that there is no closed-form solution to express this maximum. We report in this note that this maximum can be represented in a specific, analytical closed form in terms of the negative real branch of an inverse function known as the Lambert W function. The Lambert function is finding increasing use in the solution of problems in a variety of areas in the physical sciences. (C) 2014 Wiley Periodicals, Inc.