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.

Direct observation of H2 binding to a metal oxide surface

Inelastic neutron scattering is used to probe the dynamical response of H2 films adsorbed on MgO(100) as a function of film thickness. Concomitant diffraction measurements and a reduced-dimensionality quantum dynamical model provide insight into the molecule-surface interaction potential. At monolayer thickness, the rotational motion is strongly influenced by the surface, so that the molecules behave like quasiplanar rotors. These findings have a direct impact on understanding how molecular hydrogen binds to the surface of materials used in catalytic and storage applications.

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.

Theoretical studies of cis-Pt(II)-diammine binding to duplex DNA

The binding of cis-Pt(II) diammine (cis-DP) to double-stranded DNA was studied with several kinked conformations that can accommodate the formation of a square planar complex. Molecular mechanics (MM) calculations were performed to optimize the molecular fit. These results were combined with quantum mechanical (QM) calculations to ascertain the relative energetics of ligand binding through water vs direct binding of the phosphate to the ammine and platinum, and to guide the selection of DNA conformations to model complex formation. Based on QM and MM calculations, models are proposed that may be characterized by several general features. A structure involving hydrogen bonding between each ammine and distinct adjacent phosphate groups, referred to as closed conformation (CC), has already been reported. This is also found in the crystal structure of small dimers. We report alternative conformations that may be important in platination of duplex DNA. They are characterized by an intermediate conformation (IC), involving hydrogen bonding between one ammine and phosphate group, and an open conformation (OC), without ammine phosphate hydrogen bonding. The IC and OC can be stabilized by water bridges in the space between the ammine and the phosphate groups. Sugar puckers alternate from the type C(2')-endo or C(1')-exo (S), to the type C(3')-endo or C(2')-exo (N), with intermediate types near O(1')-endo (O). In general, the sugar puckers alternate from S to N to S through the platinated region (3'-TpG*pG*p-5'), with the complexed strand exhibiting, (3')-S*-N*-S-(5') alternation, while the complementary strand shows either (3')-S*-N*-S-(5') or (3')-S*-N*-O-(5') alternation. In both the OC and IC, a hydrogen bond is found between the ammine and O4(T) on thymine (T) at the (3') end, adjacent to the complex site. There is a continuous range of backbone conformations through the platinated region which relate the OC to the IC. The models presented suggest that the dynamics of the binding of the cis-Pt(II)-diammines to adjacent N7(G) in double-stranded DNA may encompass several conformational possibilities, and that water bridges may play a roll in supporting open and intermediate conformations. Proton-proton distances are reported to assist in the experimental determination of conformations.

The binding of substituted cis-Pt(II)-diammines to duplex DNA

The results of a study of the binding to DNA of substituted cis-Pt(II) diammines, (cis-DP) are presented. Computer modeling of a series of cis-Pt(NH2R)2(+2)--where R = H, CH3, cyclopropyl, cyclobutyl, and cyclopentyl--to N7(G) atoms of two adjacent intrastrand guanine bases in a square planar complex in a pentamer duplex of DNA were performed. The stability of the complexes is studied by calculating the relative conformational energy of the cis-DP-DNA complexes with molecular mechanics (MM) and the intrinsic binding energy, which is the relative binding energy for ligand replacement in the presence of the substituents R with quantum mechanics. In the model, the receptor site geometry and the conformation of the DNA is changed little in the accommodation of the series of monosubstituted diammines. These diammines bind to one family of DNA conformations, denoted as IC in a previous study, and this suggests that a common conformational feature in the DNA may exist to explain the smooth trend in activity. The slight increase in van der Waals energy resulting from an increasing number of atoms in the substituents is countered by a larger decrease in the ligand replacement energy as the substituent increases in size. This overall decrease in relative energy is consistent with the slight decrease in activity as the substituent size increases.