Factors influencing proton positions in biomolecules

Results of quantum mechanical calculations are presented that suggest a number of mechanisms whereby protons may be shifted from one group to another along an H bond. The first factor to be considered is a stretching of the bond that drastically raises the energy barrier to transfer. It is possible to predict barriers for an arbitrary system based only on results for a simple system and knowledge of the relevant bond length in the isolated subsystems. Factors that increase the intrinsic basicity of the B group in A-H-B lead not only to a lowering of the energy of the A-HB state relative to AH-B but also to a reduction in the barrier to transfer of the proton from A to B. Ions in the vicinity of the H bond exert a powerful influence and can shift the proton to the less basic group across a gradient of several pK units. Rather than shielding the proton from the external ion, the H bond acts instead to amplify the effects of the electric field. Reorientation of the A and B groups relative to one another, i.e., bends of the H bond, also produce surprisingly large changes in the relative energies of the AH-B and A-HB states. Such bends are capable of pushing the proton across to the normally less basic group, providing a mechanism of coupling conformational changes to proton ‘pumping’ activity. It is found that the high and low pH states of a given H bond can have dramatically differnt relative populations of the AH-B and A-HB configurations. These observations are explained in terms of fundamental concepts involving electrostatic interaction energies.     

Investigation of the use of B3LYP zero-point energies and geometries in the calculation of enthalpies of formation

The use of B3LYP/6–31G^* zero-point energies and geometries in the calculation of enthalpies of formation has been investigated for the enlarged G2 test set of 148 molecules [J. Chem. Phys. 106 (1997) 1063]. A scale factor of 0.96 for the B3LYP zero-point energies gives an average absolute deviation nearly the same as scaled HF/6–31G^* zero-point energies for G2, G2(MP2), and B3LYP/6–311 + G(3df,2p) enthalpies. A scale factor of 0.98, which has been recommended in some studies, increases the average absolute deviation by about 0.2 kcal/mol. Geometries from B3LYP/6–31G^* are found to do as well as MP2/6–31G^* geometries in the calculation of the enthalpies of formation.     

Wiener distributions and white noise analysis

The paper describes the structure of a new space of generalized Wiener functionals, , called the Wiener algebra, or space of Wiener distributions, and demonstrates its use in the white noise analysis. The concepts of derivatives and integrals for multi-time parameter generalized stochastic process:^N are introduced, and a derivative version of Itô's lemma is proved. The algebraic structure of and its lattice of subspaces is elaborated, and within this framework a generalized version of the Malliavin calculus is presented.