  Modern quantum chemistry can make quantitative predictions on an immense
array of chemical systems. However, the interpretation of those predictions is
often complicated by the complex wave function expansions used. Here we show
that an exceptionally simple algebraic construction allows for defining atomic
core and valence orbitals, polarized by the molecular environment, which can
exactly represent self-consistent field wave functions. This construction
provides an unbiased and direct connection between quantum chemistry and
empirical chemical concepts, and can be used, for example, to calculate the
nature of bonding in molecules, in chemical terms, from first principles.
