Correlated dynamics in aqueous proton diffusion.

The aqueous proton displays an anomalously large diffusion coefficient that is up to 7 times that of similarly sized cations. There is general consensus that the proton achieves its high diffusion through the Grotthuss mechanism, whereby protons hop from one molecule to the next. A main assumption concerning the extraction of the timescale of the Grotthuss mechanism from experimental results has been that, on average, there is an equal probability for the proton to hop to any of its neighboring water molecules. Herein, we present ab initio simulations that show this assumption is not generally valid. Specifically, we observe that there is an increased probability for the proton to revert back to its previous location. These correlations indicate that the interpretation of the experimental results need to be re-examined and suggest that the timescale of the Grotthuss mechanism is significantly shorter than was previously thought.

Orbital angular momentum eigenfunctions for fast and numerically stable evaluations of closed-form pseudopotential matrix elements.

The computation of s-type Gaussian pseudopotential matrix elements involving low powers of the distance from the pseudopotential center using Gaussian orbitals can be reduced to familiar integrals. They may be directly expressed as either simple three-center overlap integrals for even powers of the radial distance from the pseudopotential center or related to the three-center nuclear integrals of a Gaussian charge distribution for odd powers. Orbital angular momentum about each atom is added to these integrals by solid-harmonic differentiation with respect to its center. The solid-harmonic addition theorem allows all the integrals to be factored into products of invariant one-dimensional integrals involving the Gaussian exponents and angular factors that contain the azimuthal quantum numbers but are independent of all Gaussian exponents. Precomputing the angular factors allow looping over all Gaussian exponents about the three centers. The fact that solid harmonics are eigenstates of angular momentum removes the singularities seen in previous treatments of pseudopotential matrix elements.

Sb@Ni12@Sb20-/+ and Sb@Pd12@Sb20n Cluster Anions, Where n = +1, -1, -3, -4: Multi-Oxidation-State Clusters of Interpenetrating Platonic Solids.

K5Sb4 and K3Sb7 Zintl ion precursors react with Pd(PPh3)4 in ethylenediamine/toluene/PBu4+ solutions to give crystals of Sb@Pd12@Sb20n-/PBu4+ salts, where n = 3, 4. The clusters are structurally identical in the two charge states, with nearly perfect Ih point symmetry, and can be viewed as an Sb@Pd12 icosahedron centered inside of an Sb20 dodecahedron. The metric parameters suggest very weak Sb-Sb and Pd-Pd interactions with strong radial Sb-Pd bonds between the Sb20 and Pd12 shells. All-electron DFT analysis shows the 3- ion to be diamagnetic with Ih symmetry and a 1.33 eV HOMO-LUMO gap, whereas the 4- ion undergoes a Jahn-Teller distortion to an S = 1/2 D3d structure with a small 0.1 eV gap. The distortion is predicted to be small and is not discernible by crystallography. Laser desorption-ionization time-of-flight mass spectrometry (LDI-TOF MS) studies of the crystalline samples show intense parent Sb@Pd12@Sb20- ions (negative ion mode) and Sb@Pd12@Sb20+ (positive ion mode) along with series of Sb@Pd12-y@Sb20-x-/+ ions. Ni(cyclooctadiene)2 reacts with K3Sb7 in en/tol/Bu4PBr solvent mixtures to give black precipitates of Sb@Ni12@Sb20n- salts that give similar Sb@Ni12@Sb20-/+ parent ions and Sb@Ni12-y@Sb20-x-/+ degradation series in the respective LDI-TOF MS studies. The solid-state and gas-phase studies of the icosahedral Sb@M12@Sb20n-/n+ ions show that the clusters can exist in the -4, -3, -1, +1 (M = Pd) and +1, -1 (M = Ni) oxidation states. These multiple-charge-state clusters are reminiscent of redox-active fullerenes (e.g., C60n, where n = +1, 0, -1, -2, -3, -4, -5, -6).

Density perturbation theory.

Despite the fundamental importance of electron density in density functional theory, perturbations are still usually dealt with using Hartree-Fock-like orbital equations known as coupled-perturbed Kohn-Sham (CPKS). As an alternative, we develop a perturbation theory that solves for the perturbed density directly, removing the need for CPKS. This replaces CPKS with a true Hohenberg-Kohn density perturbation theory. In CPKS, the perturbed density is found in the basis of products of occupied and virtual orbitals, which becomes ever more over-complete as the size of the orbital basis set increases. In our method, the perturbation to the density is expanded in terms of a series of density basis functions and found directly. It is possible to solve for the density in such a way that it makes the total energy stationary even if the density basis is incomplete.

Thermodynamic and kinetic stabilities of CO2 oligomers.

Density-functional and coupled cluster calculations suggest that the stability, against unimolecular dissociation, of the cyclic D(3h) trimer of CO2, 1,3,5-trioxetanetrione, is greater than all but one other chemically bound oligomer of CO2. It requires far less energy to produce, on a per CO2 basis, than the low-symmetry cyclic 1,2 dioxetanedione dimer, but its kinetic stability against unimolecular dissociation is much lower. The extreme stability of the dimer, which makes it an excellent intermediate in chemiluminescence, is caused by an extreme range of geometric change to its transition state leading to a trapezoidal potential energy surface. The thermodynamically more stable trimer affords a low pressure pathway from molecular carbon dioxide to the extended covalent structure at high pressure.

Shattering dissociation in high-energy molecular collisions between nitrate esters.

We present ab initio molecular dynamics simulations of head-on collisions between ethyl nitrate molecules at collisional energies from 200 to 1200 kJ/mol. Above a threshold energy, an increasing fraction of the collisions led to rapid dissociation on impact--"shattering." The probability of the shattering dissociation was derived from the quasiclassical trajectories sampling the initial vibrational motion at T(vib) = 300 K. Even for the zero impact parameter and a fixed orientation considered, the observed dissociation probability exhibited a wide spread (much larger than kT(vib)) as a function of the collision energy. This is attributed to variations in the initial vibrational phase. We propose a closed-form expression for the energy-dependent dissociation probability that captures the dependence on the phase and use it to analyze the probability of the shattering dissociation of a larger nitrate ester, pentaerythritol tetranitrate.

Molecular dynamics simulation of yttria-stabilized zirconia (YSZ) crystalline and amorphous solids.

An empirically fitted atomic potential allows a classical molecular dynamics study of the static and dynamic properties of both crystalline and amorphous yttria-stabilized zirconia (YSZ) with typical dilute Y(2)O(3) concentrations (i.e. 3.0-12.0 mol% Y(2)O(3)) in the temperature range 300-1400 K. Based on the rigid ion model approximation, we find, regardless of the distinctly different geometries, that the oxygen ionic conductivity shows a maximum at ∼ 8.0 mol% Y(2)O(3), close to the experimental maximum. A lower absolute ionic conductivity is found for the high density YSZ amorphous solid, relative to crystalline YSZ, consistent with the trends observed in crystalline and stabilized amorphous thin films of YSZ reported in experiments. Different from YSZ crystals, intriguing features of mutual diffusion among the heavy cations and mobile anions are found in the amorphous phase.

Self-consistent, constrained linear-combination-of-atomic-potentials approach to quantum mechanics.

Variational fitting gives a stationary linear-combination of atomic potentials (LCAP) approximation to the Kohn-Sham (KS) potential, V. That potential is central to density-functional theory because it generates all orbitals, occupied as well as virtual. Perturbation theory links two self-consistent field (SCF) calculations that differ by the perturbation. Using the same variational LCAP methods and basis sets in the two SCF calculations gives precise KS potentials for each order. Variational V perturbation theory, developed herein through second order, gives stationary potentials at each order and stationary even-order perturbed energies that precisely link the two SCF calculations. Iterative methods are unnecessary because the dimension of the matrix that must be inverted is the KS basis size, not the number of occupied times virtual orbitals of coupled-perturbed methods. With variational perturbation theory, the precision of derivatives and the fidelity of the LCAP KS potential are not related. Finite differences of SCF calculations allow the precision of analytic derivatives from double-precision code to be verified to roughly seven significant digits. For a simple functional, the fourth derivatives of the energy and the first and second derivative of the KS potentials with respect to orbital occupation are computed for a standard set of molecules and basis sets, with and without constraints on the fit to the KS potential. There is no significant difference between the constrained and unconstrained calculations.

Optical excitation energies, Stokes shift, and spin-splitting of C24H72Si14.

As an initial step toward the synthesis and characterization of sila-diamondoids, such as sila-adamantane (Si(10)H(16),T(d)), the synthesis of a fourfold silylated sila-adamantane molecule (C(24)H(72)Si(14),T(d)) has been reported in literature [Fischer et al., Science 310, 825 (2005)]. We present the electronic structure, ionization energies, quasiparticle gap, and the excitation energies for the Si(14)(CH(3))(24) and the exact silicon analog of adamantane Si(10)H(16) obtained at the all-electron level using the delta-self-consistent-field and transitional state methods within two different density functional models: (i) Perdew-Burke-Ernzerhof generalized gradient approximation and (ii) fully analytic density functional (ADFT) implementation with atom dependent potential. The ADFT is designed so that molecules separate into atoms having exact atomic energies. The calculations within the two models agree well, to within 0.25 eV for optical excitations. The effect of structural relaxation in the presence of electron-hole-pair excitations is examined to obtain its contribution to the luminescence Stokes shift. The spin-influence on exciton energies is also determined. Our calculations indicate overall decrease in the absorption, emission, quasiparticle, and highest occupied molecular orbital-lowest unoccupied molecular orbital gaps, ionization energies, Stokes shift, and exciton binding energy when passivating hydrogens in the Si(10)H(16) are replaced with electron donating groups such as methyl (Me) and trimehylsilyl (-Si(Me)(3)).

Electronic structure and molecular dynamics of breaking the RO-NO2 bond.

Decomposition of energetic molecules such as pentaerythritol tetranitrate is accompanied by extensive changes in their electronic configuration and thus is challenging for ab initio Born-Oppenheimer molecular dynamics simulations. The performance of single-determinant methods (in particular, density-functional theory) is validated on electronic structure and molecular dynamics simulations of RO-NO(2) bond dissociation in a smaller nitric ester, ethyl nitrate. Accurate description of dissociating molecule requires using unrestricted, spin-symmetry-broken orbitals. However, the iterative self-consistent field procedure is prone to convergence failures in the bond-breaking region even if robust convergence algorithms are employed. As a result, molecular dynamics simulations of unimolecular decomposition need to be closely monitored and manually restarted to ensure seamless transition from the closed-shell to open-shell configuration.

Lattice dielectric and thermodynamic properties of yttria stabilized zirconia solids.

A study of lattice dielectric and thermodynamic properties of yttria stabilized zirconia (YSZ) crystals as a function of yttria concentration is reported. This study is based on density functional perturbation theory, using ABINIT. Within the local density approximation and the harmonic approximation, we find excellent agreement between calculated and low temperature experimental specific heat and dielectric constants. From the variation of the specific heat of YSZ with the yttria composition, we propose a simple additivity rule that estimates the dependence of the specific heat of YSZ on the yttria concentration, whereas for the dielectric constants of YSZ, the values are bounded by the dielectric constants of cubic and amorphous zirconia.

Variational, V-representable, and variable-occupation-number perturbation theories.

Density-functional perturbation theory with variationally fitted Kohn-Sham (KS) potentials is described. Requiring the Fock matrix and density matrix to commute through each order of perturbation theory determines the off-diagonal elements of the density matrix, and thus the effect of changing occupation numbers in density-functional perturbation theory. At each order of perturbation theory, the change in occupation numbers at that order enters only the diagonal part of the density matrix. The theory contains no phases, and a limiting process relates the rest of the diagonal density matrix element, obtained from wave function perturbation theory, to the off-diagonal part, obtained by commutation. V-representable density-functional theory is most practical when the KS potential is expanded in a finite basis to create the Sambe-Felton (SF) potential of analytic density-functional theory. This reduces the dimensionality of perturbation theory from order N(2) in the orbital basis to order N in the SF basis. Computing the (occupied-virtual)(2), i.e., N(4), sum over states once at the end of a self-consistent-field molecular orbital calculation removes the orbitals from all higher orders of perturbation theory. The rank-N(2) iterative coupled-perturbed equations are replaced by rank-N matrix inversion, to fit variationally the perturbed SF potential at each order. As an example of the 2n+1 rule of perturbation theory, the variational, first-order potential is used to give precise second and third derivatives of the energy with respect to occupation number. The hardness and hyperhardness are computed for a standard set of molecules. Both are essentially independent of how the variational SF potential is constrained for four different constraint combinations. With variational fitting, the precision of derivatives and the fidelity of the fit to the SF potential are not related. Analytic derivatives are accurate to machine precision for any constraint and all fitting basis sets.

Dipole moments from atomic-number-dependent potentials in analytic density-functional theory.

Molecular dipole moments of analytic density-functional theory are investigated. The effect of element-dependent exchange potentials on these moments are examined by comparison with conventional quantum-chemical methods and experiment for the subset of the extended G2 set of molecules that have nonzero dipole moment. Fitting the Kohn-Sham [Phys. Rev. 140, A1133 (1965)] potential itself makes a mean absolute error of less than 0.1 D. Variation of alpha (Slater's [Phys. Rev. 81, 385 (1951)] exchange parameter) values has far less effect on dipole moments than on energies. It is argued that in variable alpha methods one should choose the smaller of the two rather than the geometric mean of the two alpha values for the heteroatomic part of the linear-combination-atomic-orbital density. Calculations on the dipole moment of NH(2)(CH)(24)NO(2) are consistent with earlier calculations and show that varying the differences between alpha values for atoms with different atomic numbers has only short-ranged electrostatic effects.

The limitations of Slater's element-dependent exchange functional from analytic density-functional theory.

Our recent formulation of the analytic and variational Slater-Roothaan (SR) method, which uses Gaussian basis sets to variationally express the molecular orbitals, electron density, and the one-body effective potential of density-functional theory, is reviewed. Variational fitting can be extended to the resolution of identity method, where variationality then refers to the error in each two-electron integral and not to the total energy. However, a Taylor-series analysis shows that all analytic ab initio energies calculated with variational fits to two-electron integrals are stationary. It is proposed that the appropriate fitting functions be charge neutral and that all ab initio energies be evaluated using two-center fits of the two-electron integrals. The SR method has its root in Slater's Xalpha method and permits an arbitrary scaling of the Slater-Gàspàr-Kohn-Sham exchange-correlation potential around each atom in the system. The scaling factors are Slater's exchange parameters alpha. Of several ways of choosing these parameters, two most obvious are the Hartree-Fock (HF) alpha(HF) values and the exact atomic alpha(EA) values. The former are obtained by equating the self-consistent Xalpha energy and the HF energies, while the latter set reproduces exact atomic energies. In this work, we examine the performance of the SR method for predicting atomization energies, bond distances, and ionization potentials using the two sets of alpha parameters. The atomization energies are calculated for the extended G2 set of 148 molecules for different basis-set combinations. The mean error (ME) and mean absolute error (MAE) in atomization energies are about 25 and 33 kcal/mol, respectively, for the exact atomic alpha(EA) values. The HF values of exchange parameters alpha(HF) give somewhat better performance for the atomization energies with ME and MAE being about 15 and 26 kcal/mol, respectively. While both sets give performance better than the local-density approximation or the HF theory, the errors in atomization energy are larger than the target chemical accuracy. To further improve the performance of the SR method for atomization energies, a new set of alpha values is determined by minimizing the MAE in atomization energies of 148 molecules. This new set gives atomization energies half as large (MAE approximately 14.5 kcal/mol) and that are slightly better than those obtained by one of the most widely used generalized-gradient approximations. Further improvements in atomization energies require going beyond Slater's functional form for exchange employed in this work to allow exchange-correlation interactions between electrons of different spins. The MAE in ionization potentials of 49 atoms and molecules is about 0.5 eV and that in bond distances of 27 molecules is about 0.02 A. The overall good performance of the computationally efficient SR method using any reasonable set of alpha values makes it a promising method for study of large systems.

Slater's Exchange Parameters α for Analytic and Variational Xα Calculations.

Recently, we formulated a fully analytical and variational implementation of a subset of density functional theory using Gaussian basis sets to express orbital and the one-body effective potential. The implementation, called the Slater-Roothaan (SR) method, is an extension of Slater's Xα method, which allows arbitrary scaling of the exchange potential around each type of atom in a heteroatomic system. The scaling parameter is Slater's exchange parameter, α, which can be determined for each type of atom by choosing various criteria depending on the nature of problem undertaken. Here, we determine these scaling parameters for atoms H through Cl by constraining some physical quantity obtained from the self-consistent solution of the SR method to be equal to its exact value. Thus, the sets of α values that reproduce the exact atomic energies have been determined for four different combinations of basis sets. A similar set of α values that is independent of a basis set is obtained from numerical calculations. These sets of α parameters are subsequently used in the SR method to compute atomization energies of the G2 set of molecules. The mean absolute error in atomization energies is about 17 kcal/mol and is smaller than that of the Hartree-Fock theory (78 kcal/mol) and the local density approximation (40 kcal/mol) but larger than that of a typical generalized gradient approximation (∼8 kcal/mol). A second set of α values is determined by matching the highest occupied eigenvalue of the SR method to the negative of the first ionization potential. Finally, the possibility of obtaining α values from the exact atomization energy of homonuclear diatomic molecules is explored. We find that the molecular α values show much larger deviation than what is observed for the atomic α values. The α values obtained for atoms in combination with an analytic SR method allow elemental properties to be extrapolated to heterogeneous molecules. In general, the sets of different α values might be useful for calculations of different properties using the analytic and variational SR method.