Time Dependent Theory of Electronic Structure and Nuclear Dynamics in DIET

Abstract

Some physical processes conceptually lend themselves best to thinking within the time-domain. Direct dissociation or bond-cleavage falls into this category. However, most of quantum dynamics is formulated on the basis of the time-independent Schroedinger equation, since once knowing all the time-independent solutions the time dependence becomes trivial. Implicitly or explicitly solving the time-independent Schroedinger equation is to work within the energy (frequency) domain and to solve within the energy domain is to have knowledge for infinite time. However, many processes to be investigated (DIET included) will be effectively complete in no more than about Δt = 10(−13) sec or less. Hence, individual eigenstates separated by any less than ΔE = −t/Δt = 10(−2)eV cannot be resolved and consequently must be treated on equal footing. For extended systems this is an infinite number of states. Another way of viewing this is to think of energy states as delocalized in time; thus to form a solution which is localized in time many such states must be coherently superimposed. Similarly some physical processes conceptually lend themselves best to thinking within the spatial domain (again DIET falls into this category). However, most of solid state theory is formulated on the basis of band structure calculations, within k-space, which is to solve for inherently spatially delocalized solutions. DIET will be most influenced by the local environment of the desorbing atoms.