Local structures predicted from protein sequences are employed extensively in every aspect of modeling and prediction of protein structure and function. For more than 50 years, they have been predicted at a low-resolution coarse-grained level (e.g. three-state secondary structure). Here, we combine a two-state classifier with real-value predictor to predict local structure in continuous representation by backbone torsion angles. The accuracy of the angles predicted by this approach is close to that derived from NMR chemical shifts. Their substitution for predicted secondary structure as restraints for ab initio structure prediction doubles the success rate. This result demonstrates the potential of predicted local structure for fragment-free tertiary-structure prediction. It further implies potentially significant benefits from employing predicted real-valued torsion angles as a replacement of or supplement to the secondary-structure prediction tools employed almost exclusively in many computational methods ranging from sequence alignment to function prediction.

A new exact representation of the quantum propagator is derived in terms of semiclassical initial value representations. The resulting expression may be expanded in a series, of which the leading order term is the semiclassical one. Motion of a Gaussian wave packet on a symmetric double well potential is used to demonstrate numerical convergence of the series and the ability to compute each element in the series using Monte Carlo methods.

A new class of prefactor free semiclassical initial value representations (SCIVR) of the quantum propagator is presented. The derivation is based on the physically motivated demand, that on the average in phase space and in time, the propagator obey the exact quantum equation of motion. The resulting SCIVR series representation of the exact quantum propagator is also free of prefactors. When using a constant width parameter, the prefactor free SCIVR propagator is identical to the frozen Gaussian propagator of Heller [J. Chem. Phys. 75, 2923 (1981)]. A numerical study of the prefactor free SCIVR series is presented for scattering through a double slit potential, a system studied extensively previously by Gelabert et al. [J. Chem. Phys. 114, 2572 (2001)]. As a basis for comparison, the SCIVR series is also computed using the optimized Herman-Kluk SCIVR. We find that the sum of the zeroth order and the first order terms in the series suffice for an accurate determination of the diffraction pattern. The same exercise, but using the prefactor free propagator series needs also the second order term in the series, however the numerical effort is not greater than that needed for the Herman-Kluk propagator, since one does not need to compute the monodromy matrix elements at each point in time. The numerical advantage of the prefactor free propagator grows with increasing dimensionality of the problem.

An analytic study of the density matrix and Wigner representation equations for dissipative electron transfer is presented. An explicit expression is derived for the off-diagonal Green’s function, which shows a very fast relaxation in time if the barrier to reaction is greater than the thermal energy. This fast relaxation invalidates previous attempts to derive coupled equations for the density in the large friction limit. The fast off-diagonal relaxation disallows an adiabatic elimination of the momentum even in the large friction limit. We then show, with the aid of the boundary layer method, how one can use the same analysis to derive a set of two coupled equations for the diagonal densities. These equations are a generalization to phase space of the large friction Zusman equations [Chem. Phys. 49, 295 (1980)]. Adiabatic elimination of the momentum from these generalized Zusman equations is correct in the large friction limit and naturally leads back to the Zusman equations. Numerical solution of the generalized Zusman equations is presented for symmetric electron transfer for weak and strong electronic coupling, moderate and high barriers, and a large range of damping. The numerical results provide new insight into the friction dependence of the rate in the weak damping regime and show that previous analytic expressions for the rate are only qualitative in nature.

Semiclassical approximations to real-time quantum-mechanical effects in correlation functions of complex molecular systems