Abstract A procedure for defining virtual spaces, and the periodic one-electron and two-electron integrals, for plane-wave second quantized Hamiltonians has been developed, and it was validated using full configuration interaction (FCI) calculations, as well as executions of variational quantum eigensolver (VQE) circuits on Quantinuum’s ion trap quantum computers accessed through Microsoft’s Azure Quantum service. This work is an extension to periodic systems of a new class of algorithms in which the virtual spaces were generated by optimizing orbitals from small pairwise CI Hamiltonians, which we term as correlation optimized virtual orbitals with the abbreviation COVOs. In this extension, the integration of the first Brillouin zone is automatically incorporated into the two-electron integrals. With these procedures, we have been able to derive virtual spaces, containing only a few orbitals, that were able to capture a significant amount of correlation. The focus in this manuscript is on comparing the simulations of small molecules calculated with plane-wave basis sets with large periodic unit cells at the $$\Gamma$$ Γ -point, including images, to results for plane-wave basis sets with aperiodic unit cells. The results for this approach were promising, as we were able to obtain good agreement between periodic and aperiodic results for an LiH molecule. Calculations performed on the Quantinuum H1-1 quantum computer produced surprisingly good energies, in which the error mitigation played a small role in the quantum hardware calculations and the (noisy) quantum simulator results. Using a modest number of circuit runs (500 shots), we reproduced the FCI values for the 1 COVO Hamiltonian with an error of 11 milliHartree, which is expected to improve with a larger number of circuit runs.
Author(s): Song, Duo | Advisor(s): Weare, John H | Abstract: Reactions in the mineral surface/reservoir fluid interface control geochemical processes such as the dissolution and growth of minerals. In this dissertation we present properties of hematite bulk, AIMD simulation of structures and reactions (Fe2+ absorption) in the hematite–water interfaces region with intension of interpreting the structure of the reactive interface region, the dynamics of the water, solute molecules and atoms in this region and the electronic structure associated with hydrogen and covalent bond formations. We also study symmetry breaking in the mean field solutions to the 2 electron hydrogen molecule within Kohn Sham (KS) local spin density function theory with Dirac exchange (the XLDA model). This simplified model shows behavior related to that of the (KS) spin density functional theory (SDFT) predictions in condensed and molecular systems. The Kohn Sham solutions to the constrained SDFT variation problem undergo spontaneous symmetry breaking as the relative strength of the non-convex exchange term increases. This results in the change of the molecular ground state from a paramagnetic state to an antiferromagnetic ground states and a stationary symmetric delocalized 1st excited state. We further characterize the limiting behavior of the minimizer when the strength of the exchange term goes to infinity. The stability of the various solution classes is demonstrated by Hessian analysis. Finite element numerical results provide support for the formal conjectures. In Chapter 1 experimental and theoretical backgrounds and progress are introduced. In Chapter 2 computational methods including first principle methods and AIMD are briefly introduced. %In Chapter 3 the properties of hematite bulk are calculated and analyzed. In Chapter 3 simulations of surface and aqueous fluid interfaces of hematite (001) and (012) are carried out. Projected density of states for interfacial atoms, water adsorption process on surface, hydrogen bond analysis, electron density profiles and etc are investigated. In Chapter 4 symmetry breaking in density functional theory due to Dirac exchange for a Hydrogen molecule is studied. In Chapter 5 Dynamic Mean Field Theory method and applications are presented. In Chapter 6 summary and future work are discussed.
Many important chemical processes involve reactivity and dynamics in complex solutions. Gaining a fundamental understanding of these reaction mechanisms is a challenging goal that requires advanced computational and experimental approaches. However, important techniques such as molecular simulation have limitations in terms of scales of time, length, and system complexity. Furthermore, among the currently available solvation models, there are very few designed to describe the interaction between the molecular scale and the mesoscale. To help address this challenge, here, we establish a novel hybrid approach that couples first-principles plane-wave density functional theory with classical density functional theory (cDFT). In this approach, a region of interest described by ab initio molecular dynamics (AIMD) interacts with the surrounding medium described using cDFT to arrive at a self-consistent ground state. cDFT is a robust but efficient mesoscopic approach to accurate thermodynamics of bulk electrolyte solutions over a wide concentration range (up to 2M concentrations). Benchmarking against commonly used continuum models of solvation, such as SMD, as well as experiments, demonstrates that our hybrid AIMD–cDFT method is able to produce reasonable solvation energies for a variety of molecules and ions. With this model, we also examined the solvent effects on a prototype SN2 reaction of the nucleophilic attack of a chloride ion on methyl chloride in the solution. The resulting reaction pathway profile and the solution phase barrier agree well with experiment, showing that our AIMD/cDFT hybrid approach can provide insight into the specific role of the solvent on the reaction coordinate.
Nanoparticle self-assembly plays a key role in the formation of superlattices, which exhibit remarkable physical and chemical properties. However, controlling the assembly remains a challenge partly due to a lack of understanding of the assembly dynamics and the difficulty in linking interfacial solution properties to interparticle forces. Using liquid-cell transmission electron microscopy, the self-assembly of gold nanoparticles (NPs) into superlattices in mixtures of water and ionic liquid (IL) was visualized, revealing a dual role of the IL in the assembly process. At intermediate concentrations, the IL acts as a surfactant stabilizing the particles at a well-defined equilibrium separation corresponding to the length of hydrogen-bonded IL cations adsorbed onto neighboring NPs. Analysis of the interparticle forces reveals attractive long-range interactions of a van der Waals nature. At separations of 1–3 nm, the interactions are dominated by attractive ion correlation and repulsive hydration forces giving rise to an energy minimum at 1.5 nm separation. The superlattice is further stabilized by hydrogen bonding, which shifts the equilibrium interparticle distance to 1.1 nm. In contrast, at higher concentrations, IL accumulates and forms a structured network in the gap between nanoparticles, where it acts as a solvent that eliminates the repulsive barrier and thus promotes particle coalescence. This solvent–surfactant duality of IL opens new opportunities for its use in directing particle assembly.
Abstract Investigating the structural evolution and phase transformation of iron oxides is crucial for gaining a deeper understanding of geological changes on diverse planets and preparing oxide materials suitable for industrial applications. In this study, in‐situ heating techniques are employed in conjunction with transmission electron microscopy (TEM) observations and ex‐situ characterization to thoroughly analyze the thermal solid‐phase transformation of akaganéite 1D nanostructures with varying diameters. These findings offer compelling evidence for a size‐dependent morphology evolution in akaganéite 1D nanostructures, which can be attributed to the transformation from akaganéite to maghemite (γ‐Fe 2 O 3 ) and subsequent crystal growth. Specifically, it is observed that akaganéite nanorods with a diameter of ∼50 nm transformed into hollow polycrystalline maghemite nanorods, which demonstrated remarkable stability without arresting crystal growth under continuous heating. In contrast, smaller akaganéite nanoneedles or nanowires with a diameter ranging from 20 to 8 nm displayed a propensity for forming single‐crystal nanoneedles or nanowires through phase transformation and densification. By manipulating the size of the precursors, a straightforward method is developed for the synthesis of single‐crystal and polycrystalline maghemite nanowires through solid‐phase transformation. These significant findings provide new insights into the size‐dependent structural evolution and phase transformation of iron oxides at the nanoscale.
Many important geochemical and biogeochemical processes involve reactivity and dynamics in complex solutions. Gaining a fundamental understanding of these reaction mechanisms is a challenging goal that requires advanced computational and experimental approaches. However, important techniques such as molecular simulation have limitations in terms of scales of time, length and system complexity. Furthermore, among currently available solvation models, there are very few designed to describe the interaction between the molecular scale and mesoscale. To help address this challenge, here we establish a novel hybrid approach that couples first principle plane-wave density functional theory (DFT) with classical density functional theory (cDFT). In this approach, a region of interest described by ab initio molecular dynamics (AIMD) interacts with the surrounding medium described using cDFT to arrive at a self-consistent ground state. cDFT is a robust but efficient mesoscopic approach to accurate thermodynamics of bulk electrolyte solutions over a wide concentration range (up to 2 molar concentrations). Benchmarking against commonly used continuum models of solvation such as SMD, as well as experiment, demonstrates that our hybrid AIMD/cDFT method is able to produce reasonable solvation energies for a variety of molecules and ions. With this model, we also examined solvent effects on a prototype S$_N$2 reaction of the nucleophilic attack of a chloride ion on methyl chloride in solution. The resulting reaction pathway profile and the solution phase barrier agree well with the experiment, showing that our AIMD/cDFT hybrid approach can provide insight into the specific role of solvent on the reaction coordinate.
