[en] The development of reliable theoretical models for calculating the decay of quasi-stationary states of molecular systems has become an important endeavor for theoretical chemists. The understanding and analysis of a wide variety of physical and chemical phenomena depend on a knowledge of the behavior of these states in both collisional and photoionization problems. In this article we describe the theory and calculation of these cross sections using our Linear Algebraic/Optical Potential method. The theory makes optimal use of the numerical methods developed to solve large sets of coupled integral equations and the bound state techniques used by quantum chemists. Calculations are presented for a representative class of diatomic and triatomic molecules at varying levels of sophistication and for collisional and photoionization cross sections. 48 references, 11 figures