Increase and decrease of tunneling by variation of the barrier height

We show, based on some results from classical analysis, that time-dependent perturbations can either increase or decrease the tunneling probability. The results depend on the form of the function T(√V), where T is the transmission coefficient and V the potential. If T(√V) is convex, the perturbation will always result in a decrease of the tunneling; if T(√V) is concave, both increase as well as decrease occur.     

Calculation of energies of excited states using MNDO

The energies of the lowest singlet (S₁) and triplet (T₁) states of 28 molecules have been calculated by the “half-electron” (MNDO -HE ) and spin-unrestricted (UMNDO ) versions of MNDO . While most of the calculated values are too negative, because of overestimation of the correlation energy in MNDO -HE and UMNDO , the errors are systematic and depend in an understandable way on the nature of the molecular orbitals (MO S) involved. When appropriate corrections are applied, the calculated energies agree with experiment almost as well as they do for ground states. This justifies the use of MNDO -HE or UMNDO for studies of excited state processes.     

Second-kind integral formulations of the capacitance problem

The standard approach to calculating electrostatic forces and capacitances involves solving a surface integral equation of the first kind. However, discretizations of this problem lead to ill-conditioned linear systems and second-kind integral equations usually solve for the dipole density, which can not be directly related to electrostatic forces. This paper describes a second-kind equation for the monopole or charge density and investigates different discretization schemes for this integral formulation. Numerical experiments, using multipole accelerated matrix–vector multiplications, demonstrate the efficiency and accuracy of the new approach. This revised version was published online in June 2006 with corrections to the Cover Date.