Charles A. Weatherford

A systematic study of neutral and charged 3d-metal trioxides and tetraoxides

Using density functional theory with generalized gradient approximation, we have performed a systematic study of the structure and properties of neutral and charged trioxides (MO(3)) and tetraoxides (MO(4)) of the 3d-metal atoms. The results of our calculations revealed a number of interesting features when moving along the 3d-metal series. (1) Geometrical configurations of the lowest total energy states of neutral and charged trioxides and tetraoxides are composed of oxo and∕or peroxo groups, except for CuO(3)(-) and ZnO(3)(-) which possess a superoxo group, CuO(4)(+) and ZnO(4)(+) which possess two superoxo groups, and CuO(3)(+), ZnO(3)(+), and ZnO(4)(-) which possess an ozonide group. While peroxo groups are found in the early and late transition metals, all oxygen atoms bind chemically to the metal atom in the middle of the series. (2) Attachment or detachment of an electron to∕from an oxide often leads to a change in the geometry. In some cases, two dissociatively attached oxygen atoms combine and form a peroxo group or a peroxo group transforms into a superoxo group and vice versa. (3) The adiabatic electron affinity of as many as two trioxides (VO(3) and CoO(3)) and four tetraoxides (TiO(4), CrO(4), MnO(4), and FeO(4)) are larger than the electron affinity of halogen atoms. All these oxides are hence superhalogens although only VO(3) and MnO(4) satisfy the general superhalogen formula.

Structure and properties of the aluminum borates Al(BO2)n and Al(BO2)n−, (n = 1–4)

The geometrical and electronic structures of Al(BO2)n and Al(BO2)n− (n = 1–4) clusters are computed at different levels of theory including density functional theory (DFT), hybrid DFT, double‐hybrid DFT, and second‐order perturbation theory. All aluminum borates are found to be quite stable toward the BO2 and BO2− loss in the neutral and anion series, respectively. Al(BO2)4 belongs to the class of hyperhalogens composed of smaller superhalogens, and should possess a large adiabatic electron affinity (EAad) larger than that of its superhalogen building block BO2. Indeed, the aluminum tetraborate possesses the EAad of 5.6 eV, which, however, is smaller than the EAad of 7.8 eV of the AlF4 supehalogen despite BO2 is more electronegative than F. The EAad decrease in Al(BO2)4 is due to the higher thermodynamic stability of Al(BO2)4 compared to that of AlF4. Because of its high EA and thermodynamic stability, Al(BO2)4 should be capable of forming salts with electropositive counter ions. We optimized KAl(BO2)4 as corresponding to a unit cell of a hypothetical KAl(BO2)4 salt and found that specific energy and energy density of such a salt are competitive with those of trinitrotoluol (TNT).

Density functional study of neutral and anionic AlOn and ScOn with high oxygen content

The electronic and geometrical structures of neutral and negatively charged AlO5, AlO6, AlO7, AlO8, AlO9, AlO10, AlO11, AlO12, AlO15, AlO16, and AlO18 along with the corresponding series of ScOn and ScO  n− oxides were investigated using density functional theory with generalized gradient approximation. We found that these species possess geometrically stable isomers for all values of n = 5–12, 15, 16, 18 and are thermodynamically stable for n = 5–7. The species with n = 16 are found to be octa‐dioxides M(η1‐O2)8 while the species with n = 15 and 18 are penta‐ozonides (η2‐O3)M(η1‐O3)4 and hexa‐ozonides M(η1‐O3)6, respectively. Geometrical configurations of a number of the lowest total energy states of Al and Sc oxides are different. Especially, drastic differences are found for the anion AlO  n− and ScO  n− pairs at n = 9, 10, and 11. The ScO bonds are longer than the AlO bonds by ≈0.2 Å, which, in turn, slightly affects the corresponding interoxygen bond lengths. The charges on metal atoms are close to +2e in both Al series and to +1.5e in both Sc series. As an extra electron is delocalized over ligands in the presence of a large positive charge on the metal atom of the anions, the electron affinity (EA) of the neutrals along with the ionization energies of the anions are large and exceed the EAs of the halogen atoms in a number of cases.

Interactions of a Mn atom with halogen atoms and stability of its half-filled 3d-shell

Using density functional theory with hybrid exchange-correlation potential, we have calculated the geometrical and electronic structure, relative stability, and electron affinities of MnX(n) compounds (n = 1-6) formed by a Mn atom and halogen atoms X = F, Cl, and Br. Our objective is to examine the extent to which the Mn-X interactions are similar and to elucidate if/how the half-filled 3d-shell of a Mn atom participates in chemical bonding as the number of halogen atoms increases. While the highest oxidation number of the Mn atom in fluorides is considered to be +4, the maximum number of halogen atoms that can be chemically attached in the MnX(n)(-) anions is 6 for X = F, 5 for X = Cl, and 4 for X = Br. The MnCl(n) and MnBr(n) neutrals are superhalogens for n ≥ 3, while the superhalogen behavior of MnF(n) begins with n = 4. These results are explained to be due to the way different halogen atoms interact with the 3d electrons of Mn atom.

The löwdin α function and its application to the multi-center molecular integral problem over slater-type orbitals

Abstract In this paper we trace the evolution of the Lowdin α-function method in its application to multicenter molecular integrals over Slater-type orbitais (STOs). As is well-known, any STO displaced from the origin can be expanded in an infinite series of spherical harmonics; the functional coefficients have been designated as Lowdin α functions. These a functions can be represented as exponentials multiplied by polynomials in the displacement distance and the radial distance. The polynomials are used to construct a C matrix with integer elements. To avoid cancellation errors in some cases, the exponentials are expanded to obtain E matrices for interior regions and F matrices for exterior regions. We believe that this careful approach to molecular integrals will succeed in producing accurate and rapid evaluation of the integrals needed in STO basis-set methods or quantum chemistry.

Poisson's equation solution of Coulomb integrals in atoms and molecules

The integral bottleneck in evaluating molecular energies arises from the two-electron contributions. These are difficult and time-consuming to evaluate, especially over exponential type orbitals, used here to ensure the correct behaviour of atomic orbitals. In this work, it is shown that the two-centre Coulomb integrals involved can be expressed as one-electron kinetic-energy-like integrals. This is accomplished using the fact that the Coulomb operator is a Greens function of the Laplacian. The ensuing integrals may be further simplified by defining Coulomb forms for the one-electron potential satisfying Poissons equation therein. A sum of overlap integrals with the atomic orbital energy eigenvalue as a factor is then obtained to give the Coulomb energy. The remaining questions of translating orbitals involved in three and four centre integrals and the evaluation of exchange energy are also briefly discussed. The summation coefficients in Coulomb forms are evaluated using the LU decomposition. This algorithm is highly parallel. The Poisson method may be used to calculate Coulomb energy integrals efficiently. For a single processor, gains of CPU time for a given chemical accuracy exceed a factor of 40. This method lends itself to evaluation on a parallel computer. †Dedicated to Professor Nicholas Handy.

Message-passing parallel adaptive quantum trajectory method

Time-dependent wavepackets are widely used to model various phenomena in physics. One approach in simulating the wavepacket dynamics is the quantum trajectory method (QTM). Based on the hydrodynamic formulation of quantum mechanics, the QTM represents the wavepacket by an unstructured set of pseudoparticles whose trajectories are coupled by the quantum potential. The governing equations for the pseudoparticle trajectories are solved using a computationally-intensive moving weighted least squares (MWLS) algorithm, and the trajectories can be computed in parallel. This work contributes a strategy for improving the performance of wavepacket simulations using the QTM on message-passing systems. Specifically, adaptivity is incorporated into the MWLS algorithm, and loop scheduling is employed to dynamically load balance the parallel computation of the trajectories. The adaptive MWLS algorithm reduces the amount of computations without sacrificing accuracy, while adaptive loop scheduling addresses the load imbalance introduced by the algorithm and the runtime system. Results of experiments on a Linux cluster are presented to confirm that the adaptive MWLS reduces the trajectory computation time by up to 24%, and adaptive loop scheduling achieves parallel effieciencies of up to 90% when simulating a free particle.

Does N2− exist? A coupled-cluster study

Potential energy curves of the ground-state N2 molecule and its doublet N2− anion are calculated at the coupled-cluster level with single and double excitations and with noniterative triples [CCSD(T)] as well as with the multireference averaged-quadratic coupled-cluster (MR-AQCC) method. The N2− anion is shown to be temporary and decays to its neutral parent plus a free electron at bond lengths shorter than ≈1.4 and larger than ≈2.5 A. Thus, the N2− anion exists within the 1.4⩽R(N–N)⩽2.5 A range at the Born–Oppenheimer approximation.

Solution of Poisson's equation using spectral forms

A new technique is presented for the solution of Poissons equation in spherical coordinates. The method employs an expansion of the solution in a new set of functions defined herein for the first time, called ‘spectral forms’. The spectral forms have spherical harmonics as their angular part, but use a new set of radial functions that automatically statisfy the boundary conditions, up to a multiplicative constant, on the Poisson solution. The resultant problem reduces to a set of simultaneous equations for the expansion coefficients . The matrix A is block diagonal in the spherical harmonic indices l,m and is independent of any parameters. The simultaneous equations may be solved by LU decomposition. The LU decomposition only needs to be done once and multiple right hand sides (B-vectors) can be treated by a matrix-vector multiply. For a parallel computing platform, each such B-vector may be dealt with on a separate processor. Thus the algorithm is highly parallel. This technique may be used to calculate Coulomb energy integrals efficiently on a parallel computer.

Parallel adaptive quantum trajectory method for wavepacket simulations

Time-dependent wavepackets are widely used to model various phenomena in physics. One approach in simulating the wavepacket dynamics is the quantum trajectory method (QTM). Based on the hydrodynamic formulation of quantum mechanics, the QTM represents the wavepacket by an unstructured set of pseudoparticles whose trajectories are coupled by the quantum potential. The governing equations for the pseudoparticle trajectories are solved using a computationally intensive moving weighted least squares (MWLS) algorithm, and the trajectories can be computed in parallel. This paper contributes a strategy for improving the performance of wavepacket simulations using the QTM. Specifically, adaptivity is incorporated into the MWLS algorithm, and loop scheduling techniques are employed to dynamically load balance the parallel computation of the trajectories. The adaptive MWLS algorithm reduces the amount of computations without sacrificing accuracy, while adaptive loop scheduling addresses the load imbalance introduced by the algorithm and the runtime system. Results of experiments on a Linux cluster are presented to confirm that the adaptive MWLS reduces the trajectory computation time by up to 24%, and adaptive loop scheduling achieves parallel efficiencies of up to 85% when simulating a free particle.