Variational Monte Carlo study of core-valence separation schemes for first-row atoms and positive ions /

All-electron partitioning of wave functions into products ^core^vai of core and valence parts in orbital space results in the loss of core-valence antisymmetry, uncorrelation of motion of core and valence electrons, and core-valence overlap. These effects are studied with the variational Monte Carlo method using appropriately designed wave functions for the first-row atoms and positive ions. It is shown that the loss of antisymmetry with respect to interchange of core and valence electrons is a dominant effect which increases rapidly through the row, while the effect of core-valence uncorrelation is generally smaller. Orthogonality of the core and valence parts partially substitutes the exclusion principle and is absolutely necessary for meaningful calculations with partitioned wave functions. Core-valence overlap may lead to nonsensical values of the total energy. It has been found that even relatively crude core-valence partitioned wave functions generally can estimate ionization potentials with better accuracy than that of the traditional, non-partitioned ones, provided that they achieve maximum separation (independence) of core and valence shells accompanied by high internal flexibility of ^core and Wvai- Our best core-valence partitioned wave function of that kind estimates the IP's with an accuracy comparable to the most accurate theoretical determinations in the literature.

Optimization of the valence energy variance of the CuH molecule

We developed the concept of split-'t to deal with the large molecules (in terms of the number of electrons and nuclear charge Z). This naturally leads to partitioning the local energy into components due to each electron shell. The minimization of the variation of the valence shell local energy is used to optimize a simple two parameter CuH wave function. Molecular properties (spectroscopic constants and the dipole moment) are calculated for the optimized and nearly optimized wave functions using the Variational Quantum Monte Carlo method. Our best results are comparable to those from the single and double configuration interaction (SDCI) method.

Fluorescence spectra and ab initio theoretical studies of HCOOH /

A fluorescence excitation spectrum of formic acid monomer (HCOOH) , has been recorded in the 278-246 nm region and has been attributed to an n >7r* electron promotion in the anti conformer. The S^< S^ electronic origins of the HCOOH/HCOOD/DCOOH/DCOOD isotopomers were assigned to weak bands observed at 37431.5/37461.5/37445.5/37479.3 cm'''. From a band contour analysis of the 0°^ band of HCOOH, the rotational constants for the excited state were estimated: A'=1.8619, B'=0.4073, and C'=0.3730 cm'\ Four vibrational modes, 1/3(0=0), j/^(0-C=0) , J/g(C-H^^^) and i/,(0-H^yJ were observed in the spectrum. The activity of the antisymmetric aldehyde wagging and hydroxyl torsional modes in forming progressions is central to the analysis, leading to the conclusion that the two hydrogens are distorted from the molecular plane, 0-C=0, in the upper S. state. Ab initio calculations were performed at the 6-3 IG* SCF level using the Gaussian 86 system of programs to aid in the vibrational assignments. The computations show that the potential surface which describes the low frequency OH torsion (twisting motion) and the CH wagging (molecular inversion) motions is complex in the S^ excited electronic state. The OH and CH bonds were calculated to be twisted with respect to the 0-C=0 molecular frame by 63.66 and 4 5.76 degrees, respectively. The calculations predicted the existence of the second (syn) rotamer which is 338 cm'^ above the equilibrium configuration with OH and CH angles displaced from the plane by 47.91 and 41.32 degrees.

The normal co-ordinate analysis, vibrational spectra and theoretical infrared intensities of some thiocarbonyl halide molecules /

TITLE: The normal co-ordinate analysis, vibrational spectra and theoretical infrared intensities of some thiocarbonyl halides. AUTHOR: J. L. Brema SUPERVISOR: Dr. D. C. Moule NUMBER OF PAGES: 89 ABSTRACT: The vibrational assignment of the five-in-plane fundamental modes of CSClBr has been made on the basis of infrared gas phase and liquid Raman spectral analyses to supplement our earlier vibrational studies. Even though the one out-of-plane fundamental was not observed spectroscopically an attempt has been made to predict its frequency. The vibrational spectra contained impurity bands and the CSClBr assignment was made only after a thorough analysis of the impurities themselves. A normal co-ordinate analysis calculation was performed assuming a Urey-Bradley force field. This calculation yielded the fundamental frequencies in good agreement with those observed after refinement of the originally transferred force constants. The theoretical frequencies are the eigenvalues of the secular equation and the calculation also gave the corresponding eigenvectors in the form of the very important LLj matrix. The [l] matrix is the transfoirmation between internal co-ordinates and normal co-ordinates and it is essential for Franck-Condon calculations on electronically excited molecules and for infrared Integrated band intensity studies. Using a self-consistent molecular orbital calculation termed "complete neglect of differential overlap" (CNDO/2) , theoretical values of equilibrium bond lengths and angleswere calcuted for a series of carbonyl and thlocarbonyl molecules. From these calculations valence force field force constants were also determined but with limited success. With the CNIX)/2 method theoretical dipole moment derivatives with respect to symmetrized internal co-ordinates were calculated and the results should be useful in a correlation with experimentally determined values.

Quantum Monte Carlo : some theoretical and numerical studies

In Part I, theoretical derivations for Variational Monte Carlo calculations are compared with results from a numerical calculation of He; both indicate that minimization of the ratio estimate of Evar , denoted EMC ' provides different optimal variational parameters than does minimization of the variance of E MC • Similar derivations for Diffusion Monte Carlo calculations provide a theoretical justification for empirical observations made by other workers. In Part II, Importance sampling in prolate spheroidal coordinates allows Monte Carlo calculations to be made of E for the vdW molecule var He2' using a simplifying partitioning of the Hamiltonian and both an HF-SCF and an explicitly correlated wavefunction. Improvements are suggested which would permit the extension of the computational precision to the point where an estimate of the interaction energy could be made~

Understanding the Origin of Selectivity in the Asymmetric Lithiation Reaction of N-Heterocycles: A Theoretical Study

The natural abundance of the N-heterocycle containing compounds has pushed the synthetic community toward the invention of new synthetic methods that result in the structural diversity of N-heterocycles. Among this, is the efficient and highly selective diamine mediated asymmetric lithiation process. Amongst the diamine chiral ligands, (-)-sparterine, which is a naturally occurring alkaloid proved to be an efficient one. Many successful, good yielding and highly selective lithiation reactions have been accomplished with the mediation by this chiral diamine base. Although, there are some examples of experimental and theoretical mechanistic studies in the literature, there is a lack of detailed understanding as to how it exactly induces the chirality. In this thesis is described a systematic investigation of how (-)-sparteine influences the stereoselectivity in the course of asymmetric lithiation reaction. This led us to the establishment of the function of A-ring’s β-CH2 effect and D-ring effect. Consequently, the importance of the A-ring and D-ring portions of (-)-sparteine in the stereoselectivity is unraveled. Another part of this thesis deals with the asymmetric lithiation of BF3-activated N,N- dimethylaminoferrocene in the presence of (1R, 2R)-N1,N2-bis(3,3-dimethylbutyl)-N1,N2-dimethylcyclohexane-1,2-diamine ( a (R,R)-TMCDA surrogate) with i-PrLi. Computational findings were in full accord with the experimental observations. Subsequently, the theoretically provided insights into the mechanism of the reaction were exploited in computational design of a new ligand. Unfortunately, the outcome of this design was not experimentally robust and an updated approach towards a successful design was explained.

Spectroscopic and theoretical considerations of cyclopropenone

Please consult the paper edition of this thesis to read. It is available on the 5th Floor of the Library at Call Number: Z 9999 P65 D53 2007