In Computational Physics
there are a number of different theoretical approaches to our disposal that are
valid on different time and length scales. In this talk I will demonstrate that
similar computational approaches can be
used to model rather different physical problems. Moreover, I will illustrate
how a combination of different techniques that I have all worked with can be
used to describe physical problems that span time and length scales over many
orders of magnitude. In fact, such different theoretical techniques are
complementary to each other, and form a hierarchy of models.
I will focus on two examples
in this talk. In the first part, I will show how we can use density-functional
theory (DFT) to calculate the vibrational frequencies of small vanadium
clusters. DFT is a fully quantum mechanical approach that is essentially a
parameter-free theory. I will show how
comparison of calculated spectra with the once measured experimentally allow us
to determine the detailed atomistic structure of these small metal clusters.
In the second part, I will
discuss multiscale modeling of epitaxial growth. Physical processes during
epitaxial growth span length and time scales of many orders of magnitude. For
example, on the microscopic level, atoms move several Angstroms (the lattice
constant), and vibrate with a frequency of approx. 1013 1/s. On the other
hand, phenomena and applications of practical interest occur on a timescale of
seconds, with system sizes that can be microns or larger. The grand challenge is
to link those vastly different time and length scales. DFT allows us to
calculate the energetics of microscopic processes with very high accuracy. I
will show how DFT can be used to predict the stability of surface
reconstructions, and will discuss how microscopic parameters, for example
diffusion constants, can be obtained. These microscopic parameters are
indispensable input for kinetic