  The finite-basis, pair formulation of the Spectral Theory of chemical bonding
is briefly surveyed. Solutions of the Born-Oppenheimer polyatomic Hamiltonian
totally antisymmetric in electron exchange are obtained from diagonalization of
an aggregate matrix built up from conventional diatomic solutions to
atom-localized problems. A succession of transformations of the bases of the
underlying matrices and the unique character of symmetric orthogonalization in
producing the archived matrices calculated "once-of-all" in the
pairwise-antisymmetrized basis are described. Application is made to molecules
containing hydrogens and a single carbon atom. Results in conventional orbital
bases are given and compared to experimental and high-level theoretical
results. Chemical valence is shown to be respected and subtle angular effects
in polyatomic contexts are reproduced. Means of reducing the size of the
atomic-state basis and improve the fidelity of the diatomic descriptions for
fixed basis size, so as to enable application to larger polyatomic molecules,
is outlined along with future initiatives and prospects.
