Hybrid gausslet/Gaussian basis sets.

We introduce hybrid gausslet/Gaussian basis sets, where a standard Gaussian basis is added to a gausslet basis in order to increase accuracy near the nuclei while keeping the spacing of the grid of gausslets relatively large. The Gaussians are orthogonalized to the gausslets, which are already orthonormal, and approximations are introduced to maintain the diagonal property of the two electron part of the Hamiltonian so that it continues to scale as the second power of the number of basis functions rather than the fourth. We introduce several corrections to the Hamiltonian designed to enforce certain exact properties, such as the values of certain two-electron integrals. We also introduce a simple universal energy correction that compensates for the incompleteness of the basis stemming from the electron-electron cusps based on the measured double occupancy of each basis function. We perform a number of Hartree Fock and full configuration interaction (full-CI) test calculations on two electron systems and Hartree Fock on a ten-atom hydrogen chain to benchmark these techniques. The inclusion of the cusp correction allows us to obtain complete basis set full-CI results for the two electron cases at the level of several micro-Hartrees, and we see similar apparent accuracy for Hartree Fock on the ten-atom hydrogen chain.

Bypassing the Energy Functional in Density Functional Theory: Direct Calculation of Electronic Energies from Conditional Probability Densities.

Density functional calculations can fail for want of an accurate exchange-correlation approximation. The energy can instead be extracted from a sequence of density functional calculations of conditional probabilities (CP DFT). Simple CP approximations yield usefully accurate results for two-electron ions, the hydrogen dimer, and the uniform gas at all temperatures. CP DFT has no self-interaction error for one electron, and correctly dissociates H_{2}, both major challenges. For warm dense matter, classical CP DFT calculations can overcome the convergence problems of Kohn-Sham DFT.

Projected coupled cluster theory: Optimization of cluster amplitudes in the presence of symmetry projection.

Methods which aim at universal applicability must be able to describe both weak and strong electronic correlation with equal facility. Such methods are in short supply. The combination of symmetry projection for strong correlation and coupled cluster theory for weak correlation offers tantalizing promise to account for both on an equal footing. In order to do so, however, the coupled cluster portion of the wave function must be optimized in the presence of the symmetry projection. This paper discusses how this may be accomplished, and shows the importance of doing so for both the Hubbard model Hamiltonian and the molecular Hamiltonian, all with a computational scaling comparable to that of traditional coupled cluster theory.

Projected coupled cluster theory.

Coupled cluster theory is the method of choice for weakly correlated systems. But in the strongly correlated regime, it faces a symmetry dilemma, where it either completely fails to describe the system or has to artificially break certain symmetries. On the other hand, projected Hartree-Fock theory captures the essential physics of many kinds of strong correlations via symmetry breaking and restoration. In this work, we combine and try to retain the merits of these two methods by applying symmetry projection to broken symmetry coupled cluster wave functions. The non-orthogonal nature of states resulting from the application of symmetry projection operators furnishes particle-hole excitations to all orders, thus creating an obstacle for the exact evaluation of overlaps. Here we provide a solution via a disentanglement framework theory that can be approximated rigorously and systematically. Results of projected coupled cluster theory are presented for molecules and the Hubbard model, showing that spin projection significantly improves unrestricted coupled cluster theory while restoring good quantum numbers. The energy of projected coupled cluster theory reduces to the unprojected one in the thermodynamic limit, albeit at a much slower rate than projected Hartree-Fock.

Spin polynomial similarity transformation for repulsive Hamiltonians: interpolating between coupled cluster and spin-projected unrestricted Hartree-Fock.

Our overarching goal is to be able to describe both weak and strong correlation with a single, computationally affordable method without sacrificing important qualities of the wavefunction, e.g. symmetries of the Hamiltonian. We know that coupled cluster theory with low-order excitations is excellent at describing weakly-correlated systems near equilibrium, but breaks down as systems become more strongly correlated. Projected Hartree-Fock on the other hand is inherently capable of describing multireference character, but misses weak correlation. We are thus exploring how best to combine coupled cluster and projected Hartree-Fock in our search for a computationally feasible method that is applicable across a wide range of correlation strengths. In this manuscript, we adapt our earlier work on the pairing Hamiltonian to repulsive Hamiltonians, resulting in the spin polynomial similarity transformation (SpinPoST) interpolation. SpinPoST parameterizes the wavefunction in order to interpolate between the coupled cluster and spin-projected unrestricted Hartree-Fock ansätze self consistently, and is a spin-symmetry adapted model which involves only single and double excitations. We employ a unique approach of optimizing the wavefunction by minimizing the effect of connected quadruple excitations, resulting in a method which is spin-symmetry adapted and is comparable energetically to coupled cluster with singles and doubles for weak correlation and spin-projected Hartree-Fock for strong correlation.

Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian.

Coupled cluster and symmetry projected Hartree-Fock are two central paradigms in electronic structure theory. However, they are very different. Single reference coupled cluster is highly successful for treating weakly correlated systems but fails under strong correlation unless one sacrifices good quantum numbers and works with broken-symmetry wave functions, which is unphysical for finite systems. Symmetry projection is effective for the treatment of strong correlation at the mean-field level through multireference non-orthogonal configuration interaction wavefunctions, but unlike coupled cluster, it is neither size extensive nor ideal for treating dynamic correlation. We here examine different scenarios for merging these two dissimilar theories. We carry out this exercise over the integrable Lipkin model Hamiltonian, which despite its simplicity, encompasses non-trivial physics for degenerate systems and can be solved via diagonalization for a very large number of particles. We show how symmetry projection and coupled cluster doubles individually fail in different correlation limits, whereas models that merge these two theories are highly successful over the entire phase diagram. Despite the simplicity of the Lipkin Hamiltonian, the lessons learned in this work will be useful for building an ab initio symmetry projected coupled cluster theory that we expect to be accurate in the weakly and strongly correlated limits, as well as the recoupling regime.

On the gold-ligand covalency in linear [AuX2](-) complexes.

Gold compounds, clusters, and nanoparticles are widely used as catalysts and therapeutic medicines; the interactions between gold and its ligands in these systems play important roles in their chemical properties and functionalities. In order to elucidate the nature of the chemical interactions between Au(I) and its ligands, herein we use several theoretical methods to study the chemical bonding in a variety of linear [AuX2](-) complexes, where X = halogen atoms (F, Cl, Br, I, At and Uus), H, OH, SH, OCH3, SCH3, CN and SCN. It is shown that the most important bonding orbitals in these systems have significant contributions from the Au sd hybridized atomic orbitals. The ubiquitous linear or quasi-linear structures of [AuX2](-) are attributed to the well-balanced optimal overlap in both σ and π bonding orbitals and minimal repulsion between the two negatively charged ligands. The stability of these complexes is related to the covalency of the Au-X bond and a periodic trend is found in the evolution of covalency along the halogen group ligands. The special stability of [Au(CN)2](-) is a result of strong covalent and ionic interactions. For the superheavy element Uus, the covalency of Au-Uus is enhanced through the spin-orbit interactions.

Theoretical studies of structure and dynamics of molten salts: the LiF-ThF4 system.

LiF-ThF4 molten salt (MS) is the fuel for advanced MS reactors. Knowledge of the microscopic MS structure and dynamics is required for an understanding of the macroscopic physical and chemical properties of the MS phases. We have performed molecular dynamics simulations on LiF-ThF4 MS at different molar percentages (LiF/ThF4 = 20.0 to 0.5) and temperatures (1100 to 1400 K). Experimental deductions and recent theoretical results on the coordination structures and transport properties of the MS are well reproduced. The density of states of the [ThF8](4-) species and the character of the Th-F bonding are investigated. The interplay between the microscopic structures and the dynamical properties is elucidated. Corresponding to the smaller effective radius of Zr, the activation barrier of the M(4+)-F(-) dissociation and the lifetime of the first coordination shell of M(4+) are both smaller for M = Th than for M = Zr in the respective LiF-MF4 systems. The shorter Zr-F bond is stronger than the longer Th-F bond, while the coordination number of the predominant [ZrF7](3-) species is smaller than that of the dominant [ThF8](4-) species. An approximate formula is proposed for the lifetime of F(-) ions in the first solvation shell of molten MFn (M = Y, Zr, Th) in terms of the radial distribution function.

Probing the electronic structure and chemical bonding in tricoordinate uranyl complexes UO2X3- (X = F, Cl, Br, I): competition between Coulomb repulsion and U-X bonding.

While uranyl halide complexes [UO2(halogen)n](2-n) (n = 1, 2, 4) are ubiquitous, the tricoordinate species have been relatively unknown until very recently. Here photoelectron spectroscopy and relativistic quantum chemistry are used to investigate the bonding and stability of a series of gaseous tricoordinate uranyl complexes, UO2X3(-) (X = F, Cl, Br, I). Isolated UO2X3(-) ions are produced by electrospray ionization and observed to be highly stable with very large adiabatic electron detachment energies: 6.25, 6.64, 6.27, and 5.60 eV for X = F, Cl, Br, and I, respectively. Theoretical calculations reveal that the frontier molecular orbitals are mainly of uranyl U-O bonding character in UO2F3(-), but they are from the ligand valence np lone pairs in the heavier halogen complexes. Extensive bonding analyses are carried out for UO2X3(-) as well as for the doubly charged tetracoordinate complexes (UO2X4(2-)), showing that the U-X bonds are dominated by ionic interactions with weak covalency. The U-X bond strength decreases down the periodic table from F to I. Coulomb barriers and dissociation energies of UO2X4(2-) → UO2X3(-) + X(-) are calculated, revealing that all gaseous dianions are in fact metastable. The dielectric constant of the environment is shown to be the key in controlling the thermodynamic and kinetic stabilities of the tetracoordinate uranyl complexes via modulation of the ligand-ligand Coulomb repulsions.