Optimization of trial wave functions for use in quantum Monte Carlo with application to LiH

Methods for both partial and full optimization of wavefunction parameters are explored, and these are applied to the LiH molecule. A partial optimization can be easily performed with little difficulty. But to perform a full optimization we must avoid a wrong minimum, and deal with linear-dependency, time step-dependency and ensemble-dependency problems. Five basis sets are examined. The optimized wavefunction with a 3-function set gives a variational energy of -7.998 + 0.005 a.u., which is comparable to that (-7.990 + 0.003) 1 of Reynold's unoptimized \fin ( a double-~ set of eight functions). The optimized wavefunction with a double~ plus 3dz2 set gives ari energy of -8.052 + 0.003 a.u., which is comparable with the fixed-node energy (-8.059 + 0.004)1 of the \fin. The optimized double-~ function itself gives an energy of -8.049 + 0.002 a.u. Each number above was obtained on a Bourrghs 7900 mainframe computer with 14 -15 hrs CPU time.

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~

The investigation of the reduction mechanism of the 5a-reductase enzyme of Penicillium decumbens /

The 5a-reductase of Penicillium decumbens ATCC 10436 was used as a model for the mammalian enzyme to investigate the mechanism of reduction of testosterone to 5adihydrotestosterone . The purpose of this study was to search for specific 5a-reductase inhibitors which antagonize prostate cancer . In a whole-cell biotransformation mode, this organism reduced testosterone (1) to 5a-dihydrosteroids (8) and 5aandrostane- 3, 17-dione (9) in yields of 28% and 37% respectively. Control experiments have shown that 5aandrostane- 3, 17-dione (9) can be produced from the corresponding alcohol (8) in a subsequent reaction separate from that catalysed by the 5a-reductase enzyme . Androst-4- ene-3, 17-dione (2) is reduced to give only (9) with a recovery of 80% The stereochemistry of the reduction was determined by 500 MHz ^H NMR analysis of the products resulting from the deuterium labelled substrates. The results were obtained by an analysis of the NOE difference spectra, double-quantum filtered phase sensitive COSY 2-D spectra, and ^^c-Ir 2-D shift correlation spectra of deuterium labelled products. According to the unambiguous assignment of the signals due to H-4a and H-4Ii in 5a-dihydro steroids, the NMR data show clearly that addition of hydrogen to the 4{5)K bond has occurred in a trans manner at positions 413 and 5a. To Study the reduction mechanism of this enzyme, several substrates were prepared as following; 3-methyleneandrost-4-en- 17fi-ol(3), androst-4-en-17i5-ol(5) , androst-4-en-3ii, 17fi-diol (6) and 4, 5ii-epoxyandrostane-3, 17-dione (7) . Results suggest that this enzyme system requires an oxygen atom at the 3-position of the steroid in order to bind the substrate. Furthermore, the mechanism of this 5a-reductase may proceed via direct addition of hydrogen at the 4,5 position without involvement of a carbonyl group as an intermediate.

Large amplitude motions in the S1 state of formic acid /

A detailed theoretical investigation of the large amplitude motions in the S, excited electronic state of formic acid (HCOOH) was done. This study focussed on the the S, «- So electronic band system of formic acid (HCOOH). The torsion and wagging large amplitude motions of the S, were considered in detail. The potential surfaces were simulated using RHF/UHF ab-initio calculations for the two electronic states. The energy levels were evaluated by the variational method using free rotor basis functions for the torsional coordinates and harmonic oscillator basis functions for the wagging coordinates. The simulated spectrum was compared to the slit-jet-cooled fluorescence excitation spectrum allowing for the assignment of several vibronic bands. A rotational analysis of certain bands predicted that the individual bands are a mixture of rotational a, b and c-type components.The electronically allowed transition results in the c-type or Franck-Condon band and the electronically forbidden, but vibronically allowed transition creates the a/b-type or Herzberg-Teller components. The inversion splitting between these two band types differs for each band. The analysis was able to predict the ratio of the a, b and c-type components of each band.

An analysis of the photoelectron and Rydberg states of formaldehyde /|nby Carol R. Lessard. -- 260 St. Catharines [Ont.] : Dept. of Chemistry, Brock University,

Although it is generally accepted that Rydberg orbitals are very large and diffuse, and that electron promotion to a Rydberg orbital is not too different from ionization of the molecule, analysis of the two types of transitions proves otherwise. The photoelectron spectrum of the 2B2 (n) ion has very little vibrational structure attached to the origin band; on the other hand, several of the Rydberg transitions which involve the promotion of the n(bZ) electron exhibit a great deal of vibrational activity. In particular, the members of the n=3 Rydberg\ series interact with and perturb each other through pseudo-Jahn-Teller vibronic coupling. The vacuum ultraviolet spectrum contains a number of features which are difficult to explain, and two unusually sharp bands can only be identified as representing some form of electron promotion in formaldehyde.

Anharmonic Helmholtz free energy to O(lambdaâ ´) in the non- leading term approximation /|nby Leslie Wilk. -- 260 St. Catharines, Ont. : [s. n.],

Expressions for the anharmonic Helmholtz free energy contributions up to o( f ) ,valid for all temperatures, have been obtained using perturbation theory for a c r ystal in which every atom is on a site of inversion symmetry. Numerical calculations have been carried out in the high temperature limit and in the non-leading term approximation for a monatomic facecentred cubic crystal with nearest neighbour c entralforce interactions. The numbers obtained were seen to vary by a s much as 47% from thos e obtai.ned in the leading term approximati.on,indicating that the latter approximati on is not in general very good. The convergence to oct) of the perturbation series in the high temperature limit appears satisfactory.

A study of thermal decompositions of an allylic hydroperoxide /|nby Thomas A. McCarrick. -- 260 St. Catharines [Ont.] : Dept. of Chemistry, Brock University,

The thermal decomposition of 2,3-di~ethy l - J-hydr operox y- 1 - butene , p r epared f rol") singl e t oxygen, has been studied i n three solvents over the tempe r a ture r ange from 1500e to l o00e and t!1e i 111 t ial ~oncentrfttl nn r Ange from O. 01 M to 0.2 M. Analys i s of the kine tic data ind ica te s i nduced homolysis as the n ost probRble mode of d e composition, g iving rise to a 3/2 f S order dependence upon hy d.roperoxide concent :r8.tl on . Experimental activation e nergies for the decomposition were f ound to be between 29.5 kcsl./raole and 30.0 k cal./mole .• \,iith log A factors between 11 . 3 and 12.3. Product studies were conducted in R variety of solvents a s well as in the pr esence of a variety of free r adical initiators . Investigation of the kinetic ch a in length indicated a chain length of about fifty. A degenerat i ve chain branching mechanism 1s proposed which predicts the multi t ude of products which Rre observed e xperimentally as well as giving activation energies and log A factors si~il a r to those found experimentally .

On the path integral formulation and the evaluation of quantum statistical averages

Four problems of physical interest have been solved in this thesis using the path integral formalism. Using the trigonometric expansion method of Burton and de Borde (1955), we found the kernel for two interacting one dimensional oscillators• The result is the same as one would obtain using a normal coordinate transformation, We next introduced the method of Papadopolous (1969), which is a systematic perturbation type method specifically geared to finding the partition function Z, or equivalently, the Helmholtz free energy F, of a system of interacting oscillators. We applied this method to the next three problems considered• First, by summing the perturbation expansion, we found F for a system of N interacting Einstein oscillators^ The result obtained is the same as the usual result obtained by Shukla and Muller (1972) • Next, we found F to 0(Xi)f where A is the usual Tan Hove ordering parameter* The results obtained are the same as those of Shukla and Oowley (1971), who have used a diagrammatic procedure, and did the necessary sums in Fourier space* We performed the work in temperature space• Finally, slightly modifying the method of Papadopolous, we found the finite temperature expressions for the Debyecaller factor in Bravais lattices, to 0(AZ) and u(/K/ j,where K is the scattering vector* The high temperature limit of the expressions obtained here, are in complete agreement with the classical results of Maradudin and Flinn (1963) .

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.

Reduced local energy calculations on X¹Sigmaâ ½gHâ and 1¹S He /|nGerald F. Thomas. -- 260 St. Catharines [Ont.] : Dept. of Chemistry, Brock University,

The one-electron reduced local energy function, t ~ , is introduced and has the property < tL)=(~>. It is suggested that the accuracy of SL reflects the local accuracy of an approximate wavefunction. We establish that <~~>~ <~2,> and present a bound formula, E~ , which is such that where Ew is Weinstein's lower bound formula to the ground state. The nature of the bound is not guaranteed but for sufficiently accurate wavefunctions it will yield a lower bound. ,-+ 1'S I I Applications to X LW Hz. and ne are presented.

Some aspects of the chemistry of Reissert compounds / |nDurga Prasad Aysola. -- 260 St. Catharines [Ont. : s. n.],

1-(0- and m-Ohlorobenzoyl)isoquinolines have been synthesized by two routes involving Reissert compounds. One route involves condensation of 2-benzoyl-l,2-dihydroisoquinaldonitrile with the appropriate chlorobenzaldehyde and the second involves rearrangement of the appropriate Z-(chlorobenzoyl)-l,Z-dihydroisoquinaldonitrile under basic conditions. The action of potassamide in anhydrous liquid ammonia on both ketones gave unexpectedly N-(l-isoquinolyl)benzamide (67) as the major product and the use of dibenzo-18-crown-6-ether 98% substantially improved the yd..e.ld in the case of l-chloroketone. This amide (67) exhibits unusual hydrogen bonding. 1-(o-chlorobenzoyl)-6,7-dimethoxyisoquinoline (79) was prepared in very s,amll quantities by the route involving condensation of 2-benzoyll, Z-dihydro-6,7-dimethoxyisoquinaldonitrile with o-chlorobenzaldehyde. The poor yields are due to the instability of the anion of 2-benzoyl1, Z-dihydro-6,7-dimethoxyisoquinaldonitrile. Attempted preparation of the ketone (79) by rearrangement of 2-(o-chlorobenzoyl)-l,2-dihydro6,7- dimethoxyisoquinaldonitrile under basic conditions yielded the start~ng material (Reissert compound) and 6,7-dimethoxyisoquinoline. The action of potassamide in anhydrous liquid ammonia on l-(o-bromo-4,5-dimethoxybenzoyl)isoquinoline (85), which was prepared by the route involving the condensation of 2-benzoyl-l,4-dihydroisoquinaldonitrile with o-bromo-4,5-dimethoxybenzaldehyde, gave two products, which have not yet been identified. The ketone (85) and its precursors are interest~ng in that their 20 eV and 70 eV mass spectra do not show molecular ions.

Some aspects of the chemistry of 1, 3, 4 - Thiadiazolium salts and related compounds

The work described in this thesis has been divided into seven sections. The first section involves the preparation of N'-acyl-N'-arylN- benzothiohydrazides by the acylation of N'-aryl-N-benzothiohydrazides and is followed by a brief discussion of their possible conformation in solution. The second section deals with the preparation of 1,3,4-thiadiazolium salts by the action of perchloric acid/acetic anhydride on N'-acylN'- aryl-N-benzothiohydrazides and also by the reaction of N'-arylN- benzothiohydrazides with nitriles in an acidic medium. The preparation of 2-methylthio-I,3,4-thiadiazolium methosulfate by methylating the corresponding thione is also described. The third section deals with the reaction of 2-phenyl- and 2-methyl-I,3,4-thiadiazolium salts with alcohols in the presence of base. The stability and spectra of these compounds are discussed. Treatment of the 2-methyl-I,3,4-thiadiazolium salt with base was found to give rise to a dimeric anhydrobase and evidence supporting its structure is given. The anhydrobase could be trapped by a variety of acylating and thioacylating agents before dimerization occurred. In the fourth section, the reaction of N'-acyl-N'-aryl-N-benzothiohydrazides with a variety of acid anhydrides is described. These compounds were found to be identical with those obtained by acylating the anhydrobase. The mass spectral fragmentation of these compounds is described and the anomolous product obtained upon thiobenzoylation of 3-methyl-l-phenyl-pyrazal-5-one is also discussed. The fifth section deals with thioacyl derivatives of the anhydrobase which were prepared by the action of phosphorus pentasulfide upon the oxygen analogues and also obtained as the major product of the reaction of thioacetic acid with compounds related to N'-aryl-N-benzothiohydrazides. The mass spectra and p.m.r. spectra of these compounds are discussed. In the sixth section, the reaction of the 2-methylthio-l,3,4- thiadiazolium salt with active methylene compounds to give acyl and diacyl derivatives of the anhydrobase is described. Some aspects of these compounds are discussed. The seventh section describes the synthesis of ncyanine~' type dyes incorporating the l,3,4-thiadiazole ring and their spectra are briefly discussed.

The chemistry of heterocyclic methine bases and of their acyl and thioacyl derivatives

The work described in this thesis has been dtvided into six sections . The first section involves the reaction of 3,5-diphenyl-2-methyl-l,3,4-oxadiazolium perchlorate with acetic and benzoic anhydrides. The second section deals with the preparation and reactions of 1,3,4-thia diazolium salts. Some monomeric 1,3,4-thiadiazoline methine bases have also been prepared by reacting 1,3,4-thia d iaz ol ium s al t s with concen trated ammonium hydroxide solution. Variable temperature p.m.r. of 2-(3-acetylacetonylidene)-3,5-diphenyl-A4 -1,3,4-thiadiazoline has also been described. The third section deals with prepar a tion and reactions of some compounds in benzoxazole series. The fourth section deals with the prep a ration and reactions of N-alkyl-2-methylbenzothi azolium salts with base , a nd with some a cetylating and thioacetylating agents. Treatment of 2,3-dimethylbenzothiazolium iodide and of 3-ethyl-2-methylbenzothia zolium iodide with base wa s found to give the corresponding dimeric methine b a ses and evidence supporting their structure is also given. Thiol acetic acid was found to exchange 0 for S in its reactions with 2-acetonylidene-3-methylbenzothiazoline and 2-acetophenonylidene-3-methylbenzothi a zoline. (ii) In th e fifth section, the r eactions of 2,3-dimethylbenzselenazolium iodide with a variety of ac e tylating and thioacetylating agents has been described. The treatment of 2,3-dimethylbenzselenazolium iodide with base was found to give rise to a dimeric methine base and evidence supporting its structure is also given. The reactions of this dimeric methine b a se with benzoic anhydride and phenylisothiocyanate have also been described. The sixth section deals with the preparation and reactions of l-alkyl-2-methylquinolinium salts. Treatment of 1,2-dimethylquinolinium iodide and l-ethyl-2-methylquinolinium iodide was found to give the corresponding monomeric methine bases and evidence supporting their structure is also given. The E-type geometry of the olefinic bond in 2-acetonylidene-l-methylquinoline has been established on the basis of an N.O.E. experiment.

The crystal and molecular structure of thiamine hydroiodide /|nWilliam Edward Lee. -- 260 St. Catharines [Ont.] : Dept. of Chemistry, Brock University,

The x-ray crystal structure of thiamine hydroiodide,C1ZH18N40S12' has been determined. The unit cell parameters are a = 13.84 ± 0.03, o b = 7.44 ± 0.01, c = 20.24 ± 0.02 A, 8 = 120.52 ± 0.07°, space group P2/c, z = 4. A total of 1445 reflections having ,2 > 2o(F2), 26 < 40° were collected on a Picker four-circle diffractometer with MoKa radiation by the 26 scan technique. The structure was solved by the heavy atom method. The iodine and sulphur atoms were refined anisotropically; only the positional parameters were refined for the hydrogen atoms. Successive least squares cycles yielded an unweighted R factor of 0.054. The site of protonation of the pyrimidine ring is the nitrogen opposite the amino group. The overall structure conforms very closely to the structures of other related thiamine compounds. The bonding surrounding the iodine atoms is distorted tetrahedral. The iodine atoms make several contacts with surrounding atoms most of them at or near the van der Waal's distances A thiaminium tetrachlorocobaltate salt was produced whose molecular and crystal structure was j~dged to be isomorphous to thiaminium tetrachlorocadmate.

Quantum Monte Carlo study of electrostatic polarizabilities of H and He atoms /

The infinitesimal differential quantum Monte Carlo (QMC) technique is used to estimate electrostatic polarizabilities of the H and He atoms up to the sixth order in the electric field perturbation. All 542 different QMC estimators of the nonzero atomic polarizabilities are derived and used in order to decrease the statistical error and to obtain the maximum efficiency of the simulations. We are confident that the estimates are "exact" (free of systematic error): the two atoms are nodeless systems, hence no fixed-node error is introduced. Furthermore, we develope and use techniques which eliminate systematic error inherent when extrapolating our results to zero time-step and large stack-size. The QMC results are consistent with published accurate values obtained using perturbation methods. The precision is found to be related to the number of perturbations, varying from 2 to 4 significant digits.