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This thesis presents a compilation of recent work on benchmarking, applying, and developing Auxiliary Field Quantum Monte Carlo (AFQMC) for use in ab initio simulations of the electronic structure of molecules. With Chapter 1 I begin with a benchmark of phaseless AFQMC versus experiment in obtaining gas phase ligand dissociation energies of a set of tetrahedral and octahedral transition metal complexes. ph-AFQMC is shown to acquire chemical accuracy through the use of correlated sampling (CS) and CASSCF trial wave functions selected via a black box procedure. This is followed in Chapter 2 with another gas phase benchmark of ph-AFQMC versus experiment, this time calculating the redox potentials for a set of metallocenes, where we find a mix of correlated sampling and large CASSCF trials necessary to reproduce gas phase experimental values to within 1.7 ± 1.0 kcal/mol. Additionally, the inclusion of QZ ph-AFQMC values, either using UHF or CASSCF trials, was found to be necessary for a few systems, as opposed to using a hybrid approach with alternate methods such as coupled cluster to extrapolate to the basis set limit. In Chapter 3, having established protocols to obtain decent results on transition metal complexes with known experimental values, I apply ph-AFQMC to successfully predict the activity of a set of new annihilators for optical upconversion. For a set of functionalized anthracene molecules, I report agreement within statistics between ph-AFQMC and a localized approximation to coupled cluster singles doubles and perturbative triples (DLPNO-CCSD(T0)), and develop intuitive guidelines for tuning the excited state energies of anthracene. For a single molecule in an additional set of functionalized benzothiadiazole (BTD) molecules, Ph-BTD, ph-AFQMC and DLPNO-CCSD(T) disagree significantly; subsequent experimental testing validates the ph-AFQMC result. In Chapter 4 I present an approach based on localized orbitals to reduce the scaling with system size from quartic to cubic for the energy evaluation, the functional bottleneck for the majority of AFQMC calculations. Additionally, I describe the practical implementation of such an algorithm to be run on large GPU clusters. This allows AFQMC to be run for both larger systems and trials at a significantly decreased cost, while still reproducing full AFQMC results within the statistics of the method. With Chapter 5, I conclude with the development and characterization of a novel constraint, linecut (lc-) AFQMC, which exhbits distinct behavior versus the phaseless constraint. We demonstrate benchmarks for a variety of weakly to strongly correlated molecules for which we have the exact total energies, and observe that lc-AFQMC outperforms ph-AFQMC for the majority of systems studied. I conclude with the description of a systematic method to remove the linecut constraint, partially removing the bias and re-introducing the fermionic sign problem while still maintaining a practicable signal to noise ratio. This allows for us to recover the exact energy of FeO with a fraction of the cost of converging the trial wave function within ph-AFQMC.

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No description available.

Multivariate statistical methods have been strongly recommended in behavioral research employing multiple dependent variables. While the techniques are readily available, there is still controversy as to the proper use of the methods that have been developed for analyzing and interpreting data after finding a significant pairwise difference with a multivariate analog of the two group t-test, known as Hotelling's T². A Monte Carlo simulation was conducted to investigate the relative power of four post-MANOVA tests under violations of multivariate homoscedasticity and normality. The four methods for analyzing multivariate group differences following a significant Hotelling's T² were: (1) univariate F; (2) Bonferroni; (3) multiple Bonferroni; and (4) simultaneous F. Depending on the conditions examined, either the univariate F test or the multiple Bonferroni procedure was shown to be the most powerful for detecting a true difference between two groups. The following are the major conclusions drawn from the investigation: (1) Power levels of post-MANOVA tests remain constant under violations of multivariate normality, however, they change considerably in the presence of heterogeneity; (2) The univariate F test provides the most liberal power levels and the simultaneous F test provides the most conservative, regardless of sample size, effect size, distribution shape, and degree of violation; (3) As the size of the effect increases, the rate of correct rejections of a false null hypothesis increases; (4) As sample size increases, the rate of correct rejections of a false null hypothesis increases; (5) Regardless of heterogeneity level, power is always larger at larger group size levels; and (6) Within each group size level, power decreases as heterogeneity increases. Analytical comparisons show simultaneous F tests have the least power, Bonferroni methods to be intermediate, and univariate F tests most powerful under violations of multivariate heterogeneity. / Ph. D.

The 250 Kev Cockroft - Walton accelerator currently under construction at Virginia Polytechnic Institute is to be used as a pulsed neutron source. The time dependence of neutron flux, energy spectrum as a function of time, and various reactor parameters such as Fermi Age, slowing dotm time, and diffusion length in graphite will be measured using the pulsed source method. This thesis is a Monte Carlo calculation of the results to be expected in such an experiment. The neutron flux and energy spectrum was calculated at 1, 2, 5, and 10 microseconds after a burst of fast neutrons. The neutrons were “tracked" to thermal and the Fermi Age and slowing down time were determined. / Master of Science

The Earth Radiation Budget Experiment (ERBE) and the Clouds and Earth's Radiant Energy System (CERES) are systems that measure the earth's radiation budget, or the difference between earth-emitted radiation and radiation absorbed from the sun. Both these systems use three scanning radiometers based on a Cassegrain telescope design. Each of the three radiometers is sensitive in one of three wavelength intervals: shortwave, longwave, and total. A numerical model has been developed to investigate the radiative and optical characteristics of these instruments. The Monte-Carlo ray-trace method has been applied to the ERBE and CERES scanning radiometer instruments to calculate radiation exchange. In a radiative analysis, the surfaces of both instruments are found to emit a significant amount of radiation to the detector. In an optics analysis, both the ERBE and CERES instrument are found to have excellent directional selectivity. The field-of-view limits in the design of both instruments are verified using results from the optical analysis. / Master of Science

This study addresses the problem of assessing the value of Social Security as an investment for an individual with given characteristics. The characteristics considered are age, sex, race, marital status, and salary earning history. The problem formulation takes into account the uncertainties of human life, i.e., the probabilistic characteristics of the events that an individual may experience and may affect his tax payments and the benefits he will receive. These events are the birth of a child, death, marriage, divorce, retirement, and disability onset. The measurements used are the individual expected rate of return and the overall population rate of return. The former is expected to be more important to an individual, while the latter is more significant to the Social Security Administration. The difficulties inherent in an analytic solution procedure to obtain numerical values for these rates are shown. Using actual demographic and social security data, the use of the model is illustrated through case studies. The four cases examined, although hypothetical, represent large segments of the United States population. Additional analyses are performed to assess the value of separate components of the total benefits, including secondary, retirement, and disability-survivor benefits. The effect on the rates of return of the two factors, salary level and age of the individual’s examined. A sensitivity analysis for five types of input data, birth, death, marriage, divorce, and disability, is included. / Master of Science

In order to investigate the details of hydrogen bonding and solution molecular conformation of complex alcohols in water, isobaric-isothermal Monte Carlo simulations were carried out on several systems. The solutes investigated were ethanol, ethylene glycol, 1,2-propylene glycol, 1,3-propylene glycol and glycerol. In addition, propane, which does not hydrogen bond but does form water hydrates, was simulated in aqueous solution. The complex alcohol-water systems are very nonideal in their behavior as a function of solute concentration down to very dilute solutions. The water model employed was TIP4P water¹ and the intermolecular potentials employed are of the Jorgensen type² in which the interactions between the molecules are represented by interaction sites usually located on nuclei. The interactions are represented by a sum of Coulomb and Lennard-Jones terms between all intermolecular pairs of sites. Intramolecular rotations in the solute are modeled by torsional potential energy functions taken from ethanol, 1-propanol and 2-propanol for C-O and C-C bond rotations. Quasi-component pair correlation functions were used to analyze the hydrogen bonding. Hydrogen bonds were classified as proton acceptor and proton donor bonds by analyzing the nearest neighbor pair correlation function between hydroxyl oxygen and hydrogen and between solvent-water hydrogen and oxygen. The results obtained for partial molar heats of solution are more negative than the experimental values by 3.0 to 14 kcal/mol. In solution, all solutes reached a contracted molecular geometry with the OH groups generally on one side of the molecule. There is a tendency for the solute OH groups to hydrogen bond with water, with more proton acceptor bonds than proton donor bonds. The water-solute binding energies correlate with experimental measurements of the water-binding properties of the solute. 1. Jorgensen, W.L. et al, J. Chem. Phys., 79, 926 (1983). 2. Jorgensen, W.L., J. Phys Chem., 87, 5304 (1983). / Ph. D.

Monte Carlo algorithms can be used to estimate the state of a system given relative observations. In this dissertation, these algorithms are applied to physical layer communications system models to estimate channel state information, to obtain soft information about transmitted symbols or multiple access interference, or to obtain estimates of all of these by joint estimation. Initially, we develop and analyze a multiple access technique utilizing mutually orthogonal complementary sets (MOCS) of sequences. These codes deliberately introduce inter-chip interference, which is naturally eliminated during processing at the receiver. However, channel impairments can destroy their orthogonality properties and additional processing becomes necessary. We utilize Monte Carlo algorithms to perform joint channel and symbol estimation for systems utilizing MOCS sequences as spreading codes. We apply Rao-Blackwellization to reduce the required number of particles. However, dense signaling constellations, multiuser environments, and the interchannel interference introduced by the spreading codes all increase the dimensionality of the symbol state space significantly. A full maximum likelihood solution is computationally expensive and generally not practical. However, obtaining the optimum solution is critical, and looking at only a part of the symbol space is generally not a good solution. We have sought algorithms that would guarantee that the correct transmitted symbol is considered, while only sampling a portion of the full symbol space. The performance of the proposed method is comparable to the Maximum Likelihood (ML) algorithm. While the computational complexity of ML increases exponentially with the dimensionality of the problem, the complexity of our approach increases only quadratically. Markovian structures such as the one imposed by MOCS spreading sequences can be seen in other physical layer structures as well. We have applied this partitioning approach with some modification to blind equalization of frequency selective fading channel and to multiple-input multiple output receivers that track channel changes. Additionally, we develop a method that obtains a metric for quantifying the convergence rate of Monte Carlo algorithms. Our approach yields an eigenvalue based method that is useful in identifying sources of slow convergence and estimation inaccuracy.