  We present a method used to intuitively interpret the STM contrast by
investigating individual wave functions originating from the substrate and tip
side. We use localized basis orbital density functional theory, and propagate
the wave functions into the vacuum region at a real-space grid, including
averaging over the lateral reciprocal space. Optimization by means of the
method of Lagrange multipliers is implemented to perform a unitary
transformation of the wave functions in the middle of the vacuum region. The
method enables (i) reduction of the number of contributing tip-substrate wave
function combinations used in the corresponding transmission matrix, and (ii)
to bundle up wave functions with similar symmetry in the lateral plane, so that
(iii) an intuitive understanding of the STM contrast can be achieved. The
theory is applied to a CO dimer adsorbed on a Cu(1 1 1) surface scanned by a
single-atom Cu tip, whose STM image is discussed in detail by the outlined
method.
