Diffusion Monte Carlo study of electronic properties for H and Be atoms /

We examined three different algorithms used in diffusion Monte Carlo (DMC) to study their precisions and accuracies in predicting properties of isolated atoms, which are H atom ground state, Be atom ground state and H atom first excited state. All three algorithms — basic DMC, minimal stochastic reconfiguration DMC, and pure DMC, each with future-walking, are successfully impletmented in ground state energy and simple moments calculations with satisfactory results. Pure diffusion Monte Carlo with future-walking algorithm is proven to be the simplest approach with the least variance. Polarizabilities for Be atom ground state and H atom first excited state are not satisfactorily estimated in the infinitesimal differentiation approach. Likewise, an approach using the finite field approximation with an unperturbed wavefunction for the latter system also fails. However, accurate estimations for the a-polarizabilities are obtained by using wavefunctions that come from the time-independent perturbation theory. This suggests the flaw in our approach to polarizability estimation for these difficult cases rests with our having assumed the trial function is unaffected by infinitesimal perturbations in the Hamiltonian.

Interaction between vortices and impurities in a d-wave superconductor /

High temperature superconductors were discovered in 1986, but despite considerable research efforts, both experimental and theoretical, these materials remain poorly understood. Because their electronic structure is both inhomogeneous and highly correlated, a full understanding will require knowledge of quasiparticle properties both in real space and momentum space. In this thesis, we will present a theoretical analysis of the scanning tunneling microscopy (STM) data in BSCCO. We introduce the Bogoliubov-De Gennes Hamiltonian and solve it numerically on a two-dimensional 20 x 20 lattice under a magnetic field perpendicular to the surface. We consider a vortex at the center of our model. We introduce a Zn impurity in our lattice as a microscopic probe of the physical properties of BSCCO. By direct numerical diagonalization of the lattice BogoliubovDe Gennes Hamiltonian for different positions of the impurity, we can calculate the interaction between the vortex and the impurity in a d-wave superconductor.

Environmental assessment and biomonitoring of the Twelve Mile Creek watershed, Niagara Peninsula, Ontario

In light of the heavy reliance of the people of the Niagara Peninsula on the T\\'elve Mile Creek (TMC) watershed for recreational activities and for municipal and industrial uses ( e.g., drinking water, shipping and discharge of effluents), it was deemed prudent to assess the envirol1tnental health of the system by analysing the sediments total and exchangeable metal, and TPH contents. The MOEE has set guidelines with limits for the protection and management of aquatic sediments, and the sediments from the headwaters of the TMC have total metal and TPH (subset of O&G) contents well below the lower provincial limits. Areas of environmental concern where total metal contents in sediments, either individually or collectively, exceed the guideline, are the south side of Lake Gibson, the Old WeIland Canal, a segment of TMC just south of the QEW and Martindale Pond. The total metal content of sediments does not in all instances identify areas of biological concern. Instead, it has been found that the exchangeable metal fraction of sediments is a better indicator of metal availability and thus potential accumulation in organisms. In some instances, the exchangeable metal fraction agrees with the total metal fraction defining areas of environmental concern, but it does vary from site to site reflecting the natural variability of the ambient environment. Overall, the exchangeable metal fraction of sediments appears to be a better indicator of anthropogenic pollution and ecosystem impact. A histochemical study of Anodon.ta sp., Elliptio sp. and zebra mussels (Dreissena polyn'101pha) was done in conjunction with passive biomonitoring of zebra and quagga mussels (Dreissena bugensis) from the Twelve Mile Creek watershed and Lake 51. Clair (Jeanette's Creek, Chatham, Ontario). The highest concentrations of divalent metals such as Cu, Ni, Cd, and Zn, and trivalent Al appear to accumulate in gill and kidney tissues. Metal contents of organ tissues in Anodonta sp. vary with size class. Organ metal content varies among size classes, thus requiring consideration of size in biomonitoring studies. Shucked zebra and quagga mussel tissues, exhibited similar size class to Al content trends. In addition they reflected the Al content trends of top (approximately 10 cm) most sediments in the Twelve Mile Creek watershed. Quagga mussels appear to have higher Al concentrations than zebra mussels, thus suggesting that quagga mussels may be better passive biomonitors of AI. Cd content in zebra mussel tissues, seemed to increase with size class trends. This was not demonstrated in the quagga mussel tissues. This suggests that Cd may be regulated by quagga mussels and not by zebra mussels, and that zebra mussels may be better passivebiomonitors of Cd than are quagga mussels. Zebra mussel, quagga mussel, Anodonta sp., and Elliptio sp. were used in a two part, active (translocated) biomonitoring study of the Twelve Mile Creek watershed. There was no statistical difference in death rates between zebra and quagga mussels after 65 days of biomonitoring. However there does appear to be a difference of death rates between sites. Unfortunately the data base did not permit us to differentiate between sites. Relative to Port Colborne Harbour (Port Colborne, Ontario), the Twelve Mile Creek watershed appears to be elevated in bioavailable AI. An area near the terminus of the Twelve Mile Creek appears to be an area of environmental concern since mussels seemed to have accumulated relatively large concentrations of Cd, Zn, and Pb. In addition to possible metal loading from a nearby outfalls, or possible upstream outfalls, road salt runoff from storm sewers may have contributed to metal accumulation through cation exchanges processes. Similar trends in cumulative quagga mussel metal concentrations during the two time periods (65 and 159 days), suggest that quagga mussels may reach equilibrium within 65 days of translocation. Differences in bioaccumulated metal concentrations of the two dreissenid species demonstrate that active biomonitoring studies must use a variety of organisms to adequately assess the environmental situation of specific waterways and/or bodies.

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~

Rotation-electronic interaction in the 3p-complex Rydberg state of water

An energy theory is formulated for the rotational energy levels in a p-complex Rydberg state of an asymmetric top molecule of symmetry C2v. The effective Hamiltonian used consists of the usual rigid rotor Hamiltonian augmented with terms representing electronic spin and orbital angular momentum effects. Criteria for assigning symmetry species to the rotational energy levels, following Houganfs scheme that uses the full molecular group,are established and given in the form of a table. This is particularly suitable when eigenvectors are calculated on a digital computer. Also, an intensity theory for transitions to the Rydberg p-complex singlet states is presented and selection rules in terms of symmetry species of energy states are established. Finally, applications to HpO and DpO are given.

Exact property estimation from diffusion Monte Carlo with minimal stochastic reconfiguration /

Our objective is to develop a diffusion Monte Carlo (DMC) algorithm to estimate the exact expectation values, ($o|^|^o), of multiplicative operators, such as polarizabilities and high-order hyperpolarizabilities, for isolated atoms and molecules. The existing forward-walking pure diffusion Monte Carlo (FW-PDMC) algorithm which attempts this has a serious bias. On the other hand, the DMC algorithm with minimal stochastic reconfiguration provides unbiased estimates of the energies, but the expectation values ($o|^|^) are contaminated by ^, an user specified, approximate wave function, when A does not commute with the Hamiltonian. We modified the latter algorithm to obtain the exact expectation values for these operators, while at the same time eliminating the bias. To compare the efficiency of FW-PDMC and the modified DMC algorithms we calculated simple properties of the H atom, such as various functions of coordinates and polarizabilities. Using three non-exact wave functions, one of moderate quality and the others very crude, in each case the results are within statistical error of the exact values.

An analysis of the methyl rotation dynamics in the So (x' A) and T (a A) states of thioacetaldehyde from Pyrolysis jet spectra /

Jet-cooled, laser-induced phosphorescence excitation spectra (LIP) of thioacetaldehyde CH3CHS, CH3CDS, CD3CHS and CD3CDS have been observed over the region 15800 - 17300 cm"^ in a continuous pyrolysis jet. The vibronic band structure of the singlet-triplet n -* n* transition were attributed to the strong coupling of the methyl torsion and aldehydic hydrogen wagging modes . The vibronic peaks have been assigned in terms of two upper electronic state (T^) vibrations; the methyl torsion mode v^g, and the aldehydic hydrogen wagging mode v^^. The electronic origin O^a^ is unequivocally assigned as follows: CH3CHS (16294.9 cm"'' ), CH3CDS (16360.9 cm"'' ), CD3CHS (16299.7 cm"^ ), and CD3CDS (16367.2 cm"'' ). To obtain structural and dynamical information about the two electronic states, potential surfaces V(e,a) for the 6 (methyl torsion) and a (hydrogen wagging) motions were generated by ab initio quantum mechanical calculations with a 6-3 IG* basis in which the structural parameters were fully relaxed. The kinetic energy coefficients BQ(a,e) , B^(a,G) , and the cross coupling term B^(a,e) , were accurately represented as functions of the two active coordinates, a and 9. The calculations reveal that the molecule adopts an eclipsed conformation for the lower Sq electronic state (a=0°,e=0"') with a barrier height to internal rotation of 541.5 cm"^ which is to be compared to 549.8 cm"^ obtained from the microwave experiment. The conformation of the upper T^ electronic state was found to be staggered (a=24 . 68° ,e=-45. 66° ) . The saddle point in the path traced out by the aldehyde wagging motion was calculated to be 175 cm"^ above the equilibrium configuration. The corresponding maxima in the path taken by methyl torsion was found to be 322 cm'\ The small amplitude normal vibrational modes were also calculated to aid in the assignment of the spectra. Torsional-wagging energy manifolds for the two states were derived from the Hamiltonian H(a,e) which was solved variationally using an extended two dimensional Fourier expansion as a basis set. A torsionalinversion band spectrum was derived from the calculated energy levels and Franck-Condon factors, and was compared with the experimental supersonic-jet spectra. Most of the anomalies which were associated with the interpretation of the observed spectrum could be accounted for by the band profiles derived from ab initio SCF calculations. A model describing the jet spectra was derived by scaling the ab initio potential functions. The global least squares fitting generates a triplet state potential which has a minimum at (a=22.38° ,e=-41.08°) . The flatter potential in the scaled model yielded excellent agreement between the observed and calculated frequency intervals.