A new expression for the direct quantum mechanical evaluation of the thermal rate constant

Based on the formalism of Miller, Schwartz, and Tromp [J. Chem. Phys. 79, 4889(1983)], we derive a new expression for the thermal rate constant for a chemical reaction. The expression involves an unperturbed, i.e., reactant or product channel Boltzmann operator for the imaginary time propagation, making it possible to compute efficiently the rate constant for a range of temperatures. We illustrate numerical aspects with an extensive study of the one-dimensional Eckart barrier problem, as well as a study of the three-dimensional (J = 0) D + H2 problem.     

Existence of rank 3 vector bundles with given chern classes on homogeneous rational 3-folds

One proves that any rank 3 topological vector bundle on a homogeneous rational 3-fold has an algebraic structure. The proof uses extensions of ideals by rank 2 vector bundles. The paper also contains a construction of rank 3 vector bundles on 3-folds using extensions of ideals by rank 2 reflexive sheaves.