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

Multiphoton Ionization Spectroscopy of AlAr_N Clusters

Experimental and theoretical studies are reported of the multiphoton ionization spectroscopy of selected AlAr_N clusters (N = 2−54). Resonantly enhanced 1_(uv) + 1_(vis) and 2_(vis) + 1_(vis) ionization spectra are recorded of neutral clusters employing a laser-ablation/pulsed supersonic expansion source and time-of-flight mass spectrometric cluster-ion detection. The spectra are dominated by broad red- and blue-shifted asymmetric bands in the neighborhood of the 308 and 303 nm atomic Al 3p → 3d and 4p lines. The detailed structures of these bands and the observed degree of their spectral shifts with increasing cluster size are attributed on the basis of concomitant ab initio theoretical calculations to interplay among a number of factors, including (i) the comparable strengths of spin−orbit-split anisotropic (^2P_(1/2))Al−(^1S_0)Ar interactions and Ar−Ar mutual attractions, responsible for predicted external-site Al atom locations on distorted icosahedral Ar_N structures, (ii) avoided crossings in the nearly degenerate AlAr_N potential energy surfaces accessed by one- and two-photon atomic Al 3p → 3d and 4p excitations, giving rise to the red- and blue-shifted spectral profiles, and (iii) significant dynamical rearrangement and parent cluster-ion fragmentation following ionization, resulting in Al+Ar_M signals that generally reflect the absorption cross sections of an ensemble of larger prior clusters (AlAr_N, N > M). Additionally, nonuniformity in the cluster-size distribution of the incident molecular beam is inferred from the calculated and measured spectra and must be incorporated in the development for a completely satisfactory accounting between theory and experiment. Comparisons with the results of earlier experimental studies of the ionization potentials of AlAr_N clusters also underscore the importance of dynamical parent-ion rearrangement and fragmentation, consequent of the increased Ar solvation of the Al+ radical in the equilibrium Al+Ar_M cluster-ion structures. The reported multiphoton ionization cluster-ion spectra are evidently highly sensitive to the details of the atomic Ar arrangements around the Al chromophore and accordingly provide a spectroscopic probe of the nature and evolution of the Al trapping sites and cluster geometries with increasing cluster size when the complex electronic and vibrational phenomena underlying the measurements are appropriately interpreted

Theoretical Study of Cu/Mg Core–shell Nanocluster Formation

In a recently reported helium droplet-mediated deposition experiment to produce copper-coated magnesium core–shell nanoclusters, structural inversion was observed, which resulted in copper in the nanocluster interior, surrounded by oxidized magnesium on the copper surface. This study utilizes density functional theory methods to model the migration of copper atoms into the interior of a magnesium nanocluster to probe the energetics of this process and to compare it to the complementary process of magnesium atom migration into the interior of a copper nanocluster. Potential energy surfaces describing the forced migration of copper (magnesium) atoms into the interior of a 30-atom magnesium (copper) cluster were generated using the B3PW91 hybrid generalized gradient approximation functional with the augmented correlation consistent core–valence polarized triple-ζ basis set for magnesium and a pseudopotential plus valence-only basis set for copper. The estimated barrier for atomic copper to penetrate the surface of Mg₃₀ is 0.6 kcal mol^–1. In contrast, the migration of atomic magnesium into the interior of Cu₃₀ crosses an estimated barrier of 6 kcal mol^–1. These results are qualitatively consistent with the observed structural inversion of copper-coated magnesium nanoclusters and also suggest that inversion of a magnesium-coated copper cluster is less likely to occur

On the XeF(+)/H(2)O System: Synthesis and Characterization of the Xenon(II) Oxide Fluoride Cation, FXeOXeFXeF(+)

Gerken M, Moran MD, Mercier HPA, et al. On the XeF(+)/H(2)O System: Synthesis and Characterization of the Xenon(II) Oxide Fluoride Cation, FXeOXeFXeF(+). JOURNAL OF THE AMERICAN CHEMICAL SOCIETY. 2009;131(37):13474-13489

Atomic spectral methods for ab initio molecular electronic energy surfaces: transitioning from small-molecule to biomolecular-suitable approaches

Continuing attention has addressed incorportation of the electronically dynamical attributes of biomolecules in the largely static first-generation molecular-mechanical force fields commonly employed in molecular-dynamics simulations. We describe here a universal quantum-mechanical approach to calculations of the electronic energy surfaces of both small molecules and large aggregates on a common basis which can include such electronic attributes, and which also seems well-suited to adaptation in ab initio molecular-dynamics applications. In contrast to the more familiar orbital-product-based methodologies employed in traditional small-molecule computational quantum chemistry, the present approach is based on an "ex-post-facto" method in which Hamiltonian matrices are evaluated prior to wave function antisymmetrization, implemented here in the support of a Hilbert space of orthonormal products of many-electron atomic spectral eigenstates familiar from the van der Waals theory of long-range interactions. The general theory in its various forms incorporates the early semiempirical atoms- and diatomics-in-molecules approaches of Moffitt, Ellison, Tully, Kuntz, and others in a comprehensive mathematical setting, and generalizes the developments of Eisenschitz, London, Claverie, and others addressing electron permutation symmetry adaptation issues, completing these early attempts to treat van der Waals and chemical forces on a common basis. Exact expressions are obtained for molecular Hamiltonian matrices and for associated energy eigenvalues as sums of separate atomic and interaction-energy terms, similar in this respect to the forms of classical force fields. The latter representation is seen to also provide a long-missing general definition of the energies of individual atoms and of their interactions within molecules and matter free from subjective additional constraints. A computer code suite is described for calculations of the many-electron atomic eigenspectra and the pairwise-atomic Hamiltonian matrices required for practical applications. These matrices can be retained as functions of scalar atomic-pair separations and employed in assembling aggregate Hamiltonian matrices, with Wigner rotation matrices providing analytical representations of their angular degrees of freedom. In this way, ab initio potential energy surfaces are obtained in the complete absence of repeated evaluations and transformations of the one- and two-electron integrals at different molecular geometries required in most ab inito molecular calculations, with large Hamiltonian matrix assembly simplified and explicit diagonalizations avoided employing partitioning and Brillouin-Wigner or Rayleigh-Schrödinger perturbation theory. Illustrative applications of the important components of the formalism, selected aspects of the scaling of the approach, and aspects of "on-the-fly" interfaces with Monte Carlo and molecular-dynamics methods are described in anticipation of subsequent applications to biomolecules and other large aggregates

Organic Crystal Engineering of Thermosetting Cyanate Ester Monomers: Influence of Structure on Melting Point

Key principles needed for the rational design of thermosetting monomer crystals, in order to control the melting point, have been elucidated using both theoretical and experimental investigations of cyanate esters. A determination of the thermodynamic properties associated with melting showed that the substitution of silicon for the central quaternary carbon in the di­(cyanate ester), 2,2-bis­(4-cyanatophenyl)­propane, resulted in an increase in the entropy of melting along with a decrease in the enthalpy of melting, leading to a decrease in the melting temperature of 21.8 ± 0.2 K. In contrast, the analogous silicon substitution in the tri­(cyanate ester), 1,1,1-tris­(4-cyanatophenyl)­ethane, resulted in no significant changes to the enthalpy and entropy of melting, accompanied by a small increase of 1.5 ± 0.3 K in the melting point. The crystal structure of 1,1,1-tris­(4-cyanatophenyl)­ethane was determined via single crystal X-ray diffraction, and the structures of these four di­(cyanate esters) and tri­(cyanate esters) were examined. Although both the empirical models of Lian and Yalkowsky, as well as Chickos and Acree, provided reasonable estimates of the entropy of melting of 2,2-bis­(4-cyanatophenyl)­propane, they successfully predicted only certain effects of silicon substitution and did not capture the difference in behavior between the di­(cyanate esters) and the tri­(cyanate esters). Semiempirical molecular modeling, however, helped to validate an explanation of the mechanism for the increase in the entropy of melting of the silicon-containing di­(cyanate ester), while providing insight into the reason for the difference in behavior between the di­(cyanate esters) and tri­(cyanate esters). Taken together, the results assist in understanding how freedom of molecular motions in the liquid state may control the entropy of melting and can be utilized to guide the development of compounds with optimal melting characteristics for high-performance applications