Atomic spectral-product representations of molecular electronic structure: metric matrices and atomic-product composition of molecular eigenfunctions

Recent progress is reported in development of ab initio computational methods for the electronic structures of molecules employing the many-electron eigenstates of constituent atoms in spectral-product forms. The approach provides a universal atomic-product description of the electronic structure of matter as an alternative to more commonly employed valence-bond- or molecular-orbital-based representations. The Hamiltonian matrix in this representation is seen to comprise a sum over atomic energies and a pairwise sum over Coulombic interaction terms that depend only on the separations of the individual atomic pairs. Overall electron antisymmetry can be enforced by unitary transformation when appropriate, rather than as a possibly encumbering or unnecessary global constraint. The matrix representative of the antisymmetrizer in the spectral-product basis, which is equivalent to the metric matrix of the corresponding explicitly antisymmetric basis, provides the required transformation to antisymmetric or linearly independent states after Hamiltonian evaluation. Particular attention is focused in the present report on properties of the metric matrix and on the atomic-product compositions of molecular eigenstates as described in the spectral-product representations. Illustrative calculations are reported for simple but prototypically important diatomic (H(2), CH) and triatomic (H(3), CH(2)) molecules employing algorithms and computer codes devised recently for this purpose. This particular implementation of the approach combines Slater-orbital-based one- and two-electron integral evaluations, valence-bond constructions of standard tableau functions and matrices, and transformations to atomic eigenstate-product representations. The calculated metric matrices and corresponding potential energy surfaces obtained in this way elucidate a number of aspects of the spectral-product development, including the nature of closure in the representation, the general redundancy or linear dependence of its explicitly antisymmetrized form, the convergence of the apparently disparate atomic-product and explicitly antisymmetrized atomic-product forms to a common invariant subspace, and the nature of a chemical bonding descriptor provided by the atomic-product compositions of molecular eigenstates. Concluding remarks indicate additional studies in progress and the prognosis for performing atomic spectral-product calculations more generally and efficiently.

Atomic spectral methods for molecular electronic structure calculations

Theoretical methods are reported for ab initio calculations of the adiabatic (Born-Oppenheimer) electronic wave functions and potential energy surfaces of molecules and other atomic aggregates. An outer product of complete sets of atomic eigenstates familiar from perturbation-theoretical treatments of long-range interactions is employed as a representational basis without prior enforcement of aggregate wave function antisymmetry. The nature and attributes of this atomic spectral-product basis are indicated, completeness proofs for representation of antisymmetric states provided, convergence of Schrodinger eigenstates in the basis established, and strategies for computational implemention of the theory described. A diabaticlike Hamiltonian matrix representative is obtained, which is additive in atomic-energy and pairwise-atomic interaction-energy matrices, providing a basis for molecular calculations in terms of the (Coulombic) interactions of the atomic constituents. The spectral-product basis is shown to contain the totally antisymmetric irreducible representation of the symmetric group of aggregate electron coordinate permutations once and only once, but to also span other (non-Pauli) symmetric group representations known to contain unphysical discrete states and associated continua in which the physically significant Schrodinger eigenstates are generally embedded. These unphysical representations are avoided by isolating the physical block of the Hamiltonian matrix with a unitary transformation obtained from the metric matrix of the explicitly antisymmetrized spectral-product basis. A formal proof of convergence is given in the limit of spectral closure to wave functions and energy surfaces obtained employing conventional prior antisymmetrization, but determined without repeated calculations of Hamiltonian matrix elements as integrals over explicitly antisymmetric aggregate basis states. Computational implementations of the theory employ efficient recursive methods which avoid explicit construction the metric matrix and do not require storage of the full Hamiltonian matrix to isolate the antisymmetric subspace of the spectral-product representation. Calculations of the lowest-lying singlet and triplet electronic states of the covalent electron pair bond (H(2)) illustrate the various theorems devised and demonstrate the degree of convergence achieved to values obtained employing conventional prior antisymmetrization. Concluding remarks place the atomic spectral-product development in the context of currently employed approaches for ab initio construction of adiabatic electronic eigenfunctions and potential energy surfaces, provide comparisons with earlier related approaches, and indicate prospects for more general applications of the method.

Structure of the SO(2)F(-) anion, a problem case

Recently, room-temperature crystal structures of SO(2)F(-) in its K(+) and Rb(+) salts were published in Z. Anorg. Allg. Chem. 1999, 625, 385 and claimed to represent the first reliable geometries for SO(2)F(-). However, their almost identical S-O and S-F bond lengths and O-S-O and O-S-F bond angles are in sharp contrast to the results from theoretical calculations. To clarify this discrepancy, the new [(CH(3))(2)N](3)SO(+) and the known [N(CH(3))(4)(+)], [(CH(3))(2)N](3)S(+), and K(+) salts of SO(2)F(-) were prepared and their crystal structures studied at low temperatures. Furthermore, the results from previous RHF and MP2 calculations were confirmed at the RHF, B3LYP, and CCSD(T) levels of theory using different basis sets. It is shown that all the SO(2)F(-) salts studied so far exhibit varying degrees of oxygen/fluorine and, in some cases, oxygen-site disorders, with [(CH(3))(2)N](3)SO(+)SO(2)F(-) at 113 K showing the least disorder with r(S-F) - r(S-O) = 17 pm and angle(O-S-O) - angle(F-S-O) = 6 degrees. Refinement of the disorder occupancy factors and extrapolation of the observed bond distances for zero disorder resulted in a geometry very close to that predicted by theory. The correctness of the theoretical predictions for SO(2)F(-) is further supported by the good agreement between the calculated and the experimentally observed vibrational frequencies and their comparison with those of isoelectronic ClO(2)F. A normal coordinate analysis of SO(2)F(-) confirms the weakness of the S-F bond with a stretching force constant of only 1.63 mdyn/A and shows that there is no highly characteristic S-F stretching mode. The S-F stretch strongly couples with the SO(2) deformation modes and is concentrated in the two lowest a' frequencies.