Connected moments expansion calculations of the correlation energy in small molecules

The second-order connected moments expansion (CMX(2)) approach to calculation of the correlation energy is tested numerically on several closed-shell di- and tri-atomic molecules. Benchmark computations performed within 6–31G⁷ basis set reveal that CMX(2) usually recovers more than 50% of the MP3 correlation energy and improves the SCF molecular geometries at a cost comparable to the MP3 calculations.     

Graph theoretical approach to the topological spin hamiltonian applied to conjugated molecules

Approximate formulae for the total π-electron energy calculated within the topological spin Hamiltonian are derived using the connected moments expansion (CMX) technique up to the third order. This provides the first reported graph theoretical approach to the topological Hamiltonian other than the Hückel one. The formulae, valid for alternant, singlet ground state hydrocarbons, are used to estimate the total π-electron energy of some large molecules     

The connected moments expansion for the zero-point energy of coupled anharmonic oscillators

The connected moment expansion (CMX) technique is used to calculate the zero-point energy of an arbitrary system of coupled anharmonic oscillators. When the anharmonic term has the form of a polynomial with respect to the normal coordinates, it is possible to calculate the zero-point energy in a completely automated way. A numerical example is presented, demonstrating the power of the new method.     

Encapsulation and survival of a chondrocyte cell line within xanthan gum derivative

A chemical derivative of xanthan gum polysaccharide is investigated as a new artificial matrix for the encapsulation of chondrocytic cells. Toward this goal, a novel micro-droplet generator is developed to produce microcapsules. Microcapsules with an average diameter of 500 μm, smooth surface, and homogeneous size distribution are obtained. ATDC5 cells encapsulated in carboxymethyl xanthan (CMX) microcapsules remain viable and are observed to proliferate for prolonged culture periods with enhanced metabolic activity. Furthermore, retention of the chondrogenic phenotype is exhibited by the cells within CMX, suggesting the ability of this material to be applied in cell-delivery therapies.     

Invariance properties of the multipole expansion with respect to the choice of the coordinate system

The physical interpretation of intermolecular interactions is usually based on the well-known multipole expansion of the inverse of the interparticle distance. The interaction energy is then interpreted as a sum of terms arising from the interaction of various multipole moments of both systems. It is supposed that the interaction energy calculated via the truncated multipole expansion generally depends on the choice of local coordinate systems through the coordinate dependence of the multipole moments. In this paper we prove that each term of the multipole expansion given in the form ∑_{k = 1} C_k/R^k is invariant with respect to identical translations and arbitrary rotations of the local coordinate systems. The invariant form of the convergence criterion of the multipole expansion is given and discussed.     

Heterogeneity of Ion-Exchange Membranes: The Effects of Membrane Heterogeneity on Transport Properties

The heterogeneity of different cation-exchange membranes (Neosepta CMX, Selemion CMV, and HJC heterogeneous membrane) and their effects on transport properties were investigated using chronopotentiometry, membrane conductivity, and current-voltage curves. Modifying the classical Sand equation, a method has been developed to determine the fraction of the conducting region (epsilon) of the ion-exchange membrane. The epsilon values of the CMX, CMV, and HJC membranes were 0.93, 0.95, and 0.75, respectively. Considering the characteristics of each membrane-the CMX and CMV are reinforced homogeneous membranes, while the HJC is a heterogeneous membrane-the epsilon values determined in this study seem to be reasonable. The dependence of membrane conductivities and the limiting current densities on the fraction of conducting region of each membrane have also been studied. Copyright 2001 Academic Press.     

Halogen bonding: a theoretical study based on atomic multipoles derived from quantum theory of atoms in molecules

Atomic multipole moments derived from quantum theory of atoms in molecules are used to study halogen bonds in dihalogens (with general formula YX, in which X refers to the halogen directly interacted with the Lewis base) and some molecules containing C–X group. Multipole expansion is used to calculate the electrostatic potential in a vicinity of halogen atom (which is involved in halogen bonding) in terms of atomic monopole, dipole, and quadrupole moments. In all the cases, the zz component of atomic traceless quadrupole moments (where z axis taken along Y–X or C–X bonds) of the halogens plays a stabilizing role in halogen bond formation. The effects of atomic monopole and dipole moments on the formation of a halogen bond in YX molecules depend on Y and X atoms. In Br₂ and Cl₂, the monopole moment of halogens is zero and has no contribution in electrostatic potential and hence in halogen bonding, while in ClBr, FBr, and FCl it is positive and therefore stabilize the halogen bonds. On the other hand, the negative sign of dipole moment of X in all the YX molecules weakens the corresponding halogen bonds. In the C–X-containing molecules, monopole and dipole moments of X atom are negative and consequently destabilize the halogen bonds. So, in these molecules the quadrupole moment of X atom is the only electrostatic term which strengthens the halogen bonds. In addition, we found good linear correlations between halogen bonds strength and electrostatic potentials calculated from multipole expansion.     

Exact solution of the Schrödinger equation with a Lennard–Jones potential

The Schrödinger equation with a Lennard–Jones potential is solved by using a procedure that treats in a rigorous way the irregular singularities at the origin and at infinity. Global solutions are obtained thanks to the computation of the connection factors between Floquet and Thomé solutions. The energies of the bound states result as zeros of a function defined by a convergent series whose successive terms are calculated by means of recurrence relations. The procedure gives also the wave functions expressed either as a linear combination of two Laurent expansions, at moderate distances, or as an asymptotic expansion, near the singular points. A table of the critical intensities of the potential, for which a new bound state (of zero energy) appears, is also given.     

Method of moments approach and coupled cluster theory

Summary The single reference coupled cluster (CC) approach to the many-electron correlation problem is examined from the viewpoint of the method of moments (MM). This yields generally an inconsistent (overcomplete) set of equations for cluster amplitudes, which can be solved either in the least squares sense or by selective projection process restricting the number of equations to that of the unknowns. These resulting generalized MM-CC equations always contain the standard CC equations as a special case. Since, in the MM-CC formalism, the Schrödinger equation will be approximately satisfied on a subspace spanned by non-canonical configurations, this procedure may be helpful in extending the standard single reference CC theory to quasi-degenerate situations. To examine the potential usefulness of this idea, we explore the linear version of the CC approach for systems with a quasi-degenerate reference, in which case the standard linear theory is plagued with singularities due to the intruder states. Implications of this analysis for the structure of the wavefunction are also briefly discussed.Killam Research Fellow 1987–89     

A convergent multipole expansion for 1,3 and 1,4 Coulomb interactions

Traditionally force fields express 1,3 and 1,4 interactions as bonded terms via potentials that involve valence and torsion angles, respectively. These interactions are not modeled by point charge terms, which are confined to electrostatic interactions between more distant atoms (1,n where n>4). Here we show that both 1,3 and 1,4 interactions can be described on the same footing as 1,n (n>4) interactions by a convergent multipole expansion of the Coulomb energy of the participating atom pairs. The atomic multipole moments are generated by the theory of quantum chemical topology. The procedure to make the multipole expansion convergent is based on a "shift procedure" described in earlier work [L. Joubert and P. L. A. Popelier, Molec. Phys. 100, 3357 (2002)].     

The electrostatic potential generated by topological atoms. II. Inverse multipole moments

Quantum chemical topology defines finite atoms, whose bounded electron density generates a well-defined electrostatic potential. A multipole expansion based on spherical tensors provides a potential that is formally convergent outside the divergence sphere. Part I of this series [P. L. A. Popelier and M. Rafat, Chem. Phys. Lett.376, 148 (2003)] showed that a continuous multipole expansion expands the convergence region, thereby allowing the electrostatic potential to be evaluated at short range. Here, we propose a different method, based on "inverse" multipole moments, enabling an expansion that converges everywhere. These moments are defined by inverse (i.e., negative) powers of the magnitude of the position vector describing the electron density inside the atom. We illustrate this technique on nitrogen in N(2), oxygen in H(2)O, and oxygen in the phenolic group of the amino acid tyrosine. The proposed method constitutes a considerable advance over the method presented in Part I.     

Dipole moment functions of van der waals complexes of HF and HCl with rare gas atoms

A simple electrostatic model based on a single-centre multipole expansion is applied to derive the dipole moment functions of complexes formed by the HF (DF) and HCl (DCl) molecules with rare gas atoms. Vibrationally averaged ground state dipole moments agree quite well with the available experimental data. Some transition dipole moments for the internal modes of complexes are also estimated.     

Remark on the moment expansion of total π-electron energy

Summary The truncated expansion of the function |x| was frequently used to express the total Hückel -electron energy (E) in terms of moments. We now present an identity which connectsE with an infinite series of moments. This series is convergent. Lower and upper bounds forE are obtained, based on the same infinite moment expansion.     

Electrical conductivity of cation-and anion-exchange membranes in ampholyte solutions

Several laws governing ampholyte transport through ion-exchange membranes are established by a comparative analysis of the concentration dependence of electrical conductivity for homogeneous (CMX, AMX) and heterogeneous (MK-40, MA-41) membranes in NaCl, LysHCl, and NaH₂PO₄ solutions. The increase in the electrical conductivity of membranes in ampholyte solutions as the solutions become more dilute is explained by the increased fraction of divalent ions of the amino acid (cation-exchange membrane) or from phosphoric acid (anion-exchange membrane) in the membrane as a result of Donnan exclusion of hydrolysis products (hydroxide ions or protons, respectively).     

The discrete representation correspondence between quantum and classical spatial distributions of angular momentum vectors

This work demonstrates that the quantum mechanical moments of a state described by the density matrix correspond to discrete spherical harmonic moments of the classical multipole expansion of the spatial distribution of the angular momentum vectors. For the diagonal density matrix elements, this work exploits the fact that the quantum mechanical vector coupling (Clebsch-Gordan) coefficients become increasingly accurate discrete representations of spherical harmonics as j increases. A Schwinger-type basis accounts for nonaxially symmetric angular distributions, which result in nonzero off-diagonal elements of the density matrix. The resulting discrete minimum uncertainty picture of the classical moments has a stringent equivalence with the quantum mechanical one for all j and provides an unambiguous connection for the classical and quantum moments in the large j limit. The equivalence is numerically tested for simple models, and there is a satisfying equivalence even for small j. Applications, implications, and extensions are indicated, and the relevance of this work for the interpretation of classical mechanical simulations of inelastic and reactive molecular collisions will be documented elsewhere.     

Polymerization by alkaline earth metal compounds—II Polymerization of 2- and 4-vinylpyridine,styrene and butadiene by triphenylmethyl derivatives of calcium,strontium and barium

Investigations are reported on polymerizations of 2- and 4- vinylpyridine, styrene and butadiene by a series of related alkaline earth metal initiators, Ph₃CMX(THF)_n (M = Ca, Ba, X = Cl, n = 2; M = Ca, X = Br, n = 4; M = Sr, X = Cl, n = 4; M = Sr, X = Br, n = 5) in tetrahydrofuran (THF) or 1,2-dimethoxyethane (DME) at various temperatures and in the absence of solvent. The polymers have been examined by GPC and aspects of their microstructures determined by ¹³C and/or ¹H NMR spectroscopy and, for polybutadiene, i.r. spectroscopy. Poly-2-vinylpyridine produced by Ph₃CMX(THF)_n is rich in isotactic content; the isotacticity is higher for polymer formed in THF than DME solution, falls with change of initiator in the order M = Ca > Sr > Ba and, in DME, is greater when X = Br. The tacticities of poly-4-vinylpyridine and polystyrene are similar to those obtained from related organometallic initiators. The 1,4-content of polybutadiene decreases with initiator Ph₃CMX(THF)_n in the order M = Ba > Sr > Ca; the trans-1,4 structure generally predominates except when M = Ba from which cis-1,4 links are formed in comparable amounts.     

On the validity and applicability of the connected moments expansion

The theoretical justification, and typical convergence properties, of Cioslowski's connected moments expansion for the ground-state energy of a quantum-mechanical system are considered. This size extensive expansion is an alternative to Rayleigh-Schrodinger perturbation theory, and is expected to be useful in electronic structure calculations based on many-determinant reference functions, where perturbation theory is not applicable. It is found from example molecular electronic structure calculations that, in some cases, the expansion does not converge correctly to the true energy. An im- proved expansion derived from a padé approximant, and an analysis of its validity, is presented here.     

Cumulative potential-derived atomic multipoles

A method to derive the atomic multipole moments cumulatively up to quadrupole moments was developed. The multipole moments are obtained by least-square simulating the molecular electrostatic potentials. Only the components of the term of highest order in the atomic multipole expansion are optimized while the lower terms remain fixed. The calculations on HF, H₂O and NH₃ show that the cumulative method can give reasonable qualitative and fairly good quantitative results.