Calculation of nondifferential properties for atomic ground states /

A new method for sampling the exact (within the nodal error) ground state distribution and nondiflPerential properties of multielectron systems is developed and applied to firstrow atoms. Calculated properties are the distribution moments and the electronic density at the nucleus (the 6 operator). For this purpose, new simple trial functions are developed and optimized. First, using Hydrogen as a test case, we demonstrate the accuracy of our algorithm and its sensitivity to error in the trial function. Applications to first row atoms are then described. We obtain results which are more satisfactory than the ones obtained previously using Monte Carlo methods, despite the relative crudeness of our trial functions. Also, a comparison is made with results of highly accurate post-Hartree Fock calculations, thereby illuminating the nodal error in our estimates. Taking into account the CPU time spent, our results, particularly for the 8 operator, have a relatively large variance. Several ways of improving the eflSciency together with some extensions of the algorithm are suggested.

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.

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.

The electronic spectra and the determination of the excited state geometry of 3A" propynal /|nby Chhiu-Tsu Lin. -- 260 St. Catharines, Ont. : [s. n.],

Impurity free eluission spectra of HCCCHO and DCCCHO have been rephotographed using the electronic-energy-exchange method with benzene as a carrier gas. The near ultraviolet spectra of ReeCHO and DCCCHO were photographed in a sorption under conditions of high resolution with absorption path lengths up to 100 meters. The emission and absorption spectra of Propynal resulting from 3 n 1 t 1\ - A excitation has been reanalyzed in som.e detail. Botrl of the eH out-of-plane wagging modes were found to have negative anharmonicity. A barrier height of 56.8/0.0 cm- 1 and a nonplanar oft , , equilibrium angle of 17 3 /30 are calculated for the V 10/ lJ 11 modes. The in-plane and out-of-plane v1. brational modes in the 3A." and 1a~. ' elec ronic states of Propynal were subjected to a normal coordinate treatment in the approximat :on of tIle Urey-Bradley force field. From the relative oscillator strengths of the trans1·t1·0ns connect i ng t he v ibrat1•0n1ess lA' , state and t,he V1· bron1·C 3· if levels of the A state, the differences in equilibrium configuration were evaluated from an approximate Franck-Condon analysis based on the ground state normal coordinates. As this treatment gave 512 possible geometrical structures for the upper state, it 4 was necessary to resort to a comparison of the observed and calculated moments of inertia along with chemical intuition to isolate the structure. A test of the correctness of the calculated structure change and the vibrational assignment was raade by evaluating the intensities of the inplane and out-oi-plane fundarnental, sequence, and cross sequellce transitions y the exact Franck-Condon method.

The vibrational spectra and the normal coordinate analysis of thiocarbonye halides /|nby C. R. Subramaniam. -- 260 St. Catharines, Ont. : [s. n.],

The infrared and the Raman spectra of eSelF has been obtained for the first time and has been analysed to give the in-plane normal vibrational frequencies of the molecule, in the ground state. A normal co-ordinate analysis has been carried out for the molecules CSF2, CSClF and eSel 2 using a Urey-Bradley type of potential function and the elements of the [L] matrix elements, the distribution of the potential energy in Urey-Bradley space, and the displacement vector diagrams for the normal modes of vibration for these molecules, have been obtained. The bond for~e constants obtained through the normal co-ordinate analysis, have given some interesting results. The stretching force constant, Kes ' varies markedly with halogen substitution and the force constants KeF and Keel also vary with substitution.

Analysis Of The A11a22 X 11a11 And A 33a22 X 1 electronic transitions in selenocarbonyl difluoride

The absorption spectrum of F2CSe in the 18800-21900 cm-1 region has been recorded at -770 C and 220 C under the conditions of medium resolution. The responsible electronic promotion is TI* + n excitation which leads to 3A2 and lA2 excited states. Progressions in vI', v2', v3" v4' and v4" have been identified in the spectrum and have been analyzed in terms of vibronic transitions between a planar ground state and a nQnplanar excited state. The - 3 - 1 - 1 - 1 origins of the a A2 + X Al and A A2 + X Al systems were assigned to the bands at 19018 cm-l and 19689 cm-l . This has given a singlet-triplet splittl. n g lA2 - 3A2 P f 671 cm -1 The out-of-plane wagging levels were found to be anharmonic. 1 -1 Barrier heights of 2483 cm- and 2923 cm were obtained for the lA2 and 3A2 upper states from a fitting of the energy levels of a Lorentzian-quadratic function to the observed levels in the out-of-plane wagging modes. 1 3 For the A2 and A2 states nonplanar equilibrium angles of 30.10 and 31.40 have been evaluated respectively. i

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.

Elliptical orbital studies of H21 and H2 molecules /|nS. K. Gupta. -- 260 St. Catharines, Ont. : [s. n.],

Calculations are performed on the \S <:Jd ground states of d ' + the H and HC) molecules using a basis set of non-integral ~ ~ I elliptical orbitals. Different variational wavefunctions constructed i- for H~ involved one parameter to three par~~eter variation. In order to l"'educe the ntunber of parameters in most commonly 0- used basis orbitals set, the importance of the term (,+~) Y\ over the term ;u 'Where n is a variational pararneter and the value of cr may be given by boundary condition or cusp condition is outlined in Chapters II and III. It is found that the two parameter -+ wavefunction for H~ including the ternl (~+~) , a- given by the bound~ condition, gives lower variational energies than any wavefunction published to date for small and moderate internuclear separations. c;. In order to find out the importance of the term (I +~ ) Y\ over ;U for the two electron problem, the variational energy is computed for the H~ molecule from unrestricted two parameter closed shell wavefunctions including the term U+ft)ground state of the hydrogen molecule for R =1.4 (equilibrium internuclear separation) is perfonaed. The results are excellent.

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.

The satellite band patterns in the near ultraviolet absorption spectra of isotopic compounds of acetaldehyde

The 3700 A - 3000 A absorption spectra of CH3CHO and its isotopic compounds such as CH3CDO, CD3CHO and CD3CDO were studied in the gas phase at room temperature and low temperatures. The low resolution spectra of the compounds were recorded by a 1.5 m Baush and Lomb grating spectrograph. The high resolution spectra were recorded by a Ebert spectrograph with the Echelle grating and the holographic grating separately. The multiple reflection cells were used to achieve the long path length. The pressure-path length used for the absorption spectrum of CH 3CHO was up to 100 mm Hg )( 91 . 43mo The emission spectrum and the excitation spectrum of CH3CHO were also recorded in this research. The calculated satellite band patterns \vhich were ob-tailied by the method of Lewis were used to compare with the observed near UV absorption spectrum of acetaldehyde. These calculated satellite band patterns belonged to two cases: namely, the barriers-in-phase case and the barriers- out-of-phase case. Each of the calculated patterns corresponded to a stable conformation of acetaldehyde in the excited state . The comparisons showed that the patterns in the observed absorption spectra corresponded to the H-H eclipsed conformations of acetaldehyde in the excited state . The least squares fitting analysis showed that the barrier heights in the excited state were higher than in the ground state. Finally, the isotopic shifts for the isotopic compounds of acetaldehyde were compared to the compounds with the similar deuterium substitution.

Variational Monte Carlo estimation of the dissociation energy of CuH using correlated sampling

A new approach to treating large Z systems by quantum Monte Carlo has been developed. It naturally leads to notion of the 'valence energy'. Possibilities of the new approach has been explored by optimizing the wave function for CuH and Cu and computing dissociation energy and dipole moment of CuH using variational Monte Carlo. The dissociation energy obtained is about 40% smaller than the experimental value; the method is comparable with SCF and simple pseudopotential calculations. The dipole moment differs from the best theoretical estimate by about 50% what is again comparable with other methods (Complete Active Space SCF and pseudopotential methods).

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.

Application of Reptation Quantum Monte Carlo and Related Methods to LiH

This work investigates mathematical details and computational aspects of Metropolis-Hastings reptation quantum Monte Carlo and its variants, in addition to the Bounce method and its variants. The issues that concern us include the sensitivity of these algorithms' target densities to the position of the trial electron density along the reptile, time-reversal symmetry of the propagators, and the length of the reptile. We calculate the ground-state energy and one-electron properties of LiH at its equilibrium geometry for all these algorithms. The importance sampling is performed with a single-determinant large Slater-type orbitals (STO) basis set. The computer codes were written to exploit the efficiencies engineered into modern, high-performance computing software. Using the Bounce method in the calculation of non-energy-related properties, those represented by operators that do not commute with the Hamiltonian, is a novel work. We found that the unmodified Bounce gives good ground state energy and very good one-electron properties. We attribute this to its favourable time-reversal symmetry in its target density's Green's functions. Breaking this symmetry gives poorer results. Use of a short reptile in the Bounce method does not alter the quality of the results. This suggests that in future applications one can use a shorter reptile to cut down the computational time dramatically.

Single-Molecule Magnets and Multifunctional Molecular Magnetic Materials Based on Polynuclear Metal Complexes

Our work on single molecule magnets and multifunctional magnetic materials is presented in four projects. In the first project we show for first time that heteroatomic-type pseudohalides, such as OCN-, can be employed as structure-directing ligands and ferromagnetic couplers in higher oxidation state metal cluster chemistry. The initial use of cyanato groups in Mn cluster chemistry has afforded structurally interesting MnII/III14 (1) and MnII/III/IV16 (2) clusters in which the end-on bridging cyanates show a preference in binding through their O-atom. The Mn14 compound shows entirely visible out-of-phase alternating currect signals below 5 K and large hysteresis loops below 2 K. Furthermore, the amalgamation of azido groups with the triethanolamine tripodal ligand in manganese carboxylate cluster chemistry has led to the isolation of a new ferromagnetic, high-nuclearity and mixed-valence MnII/III15Na2 (3) cluster with a large ground-state spin value of S = 14. In the second project we demonstrate a new synthetic route to purely inorganic-bridged, transition metal-azido clusters [CoII7 (4) and NiII7 (5)] and coordination polymers [{FeII/III2}n (6)] which exhibit strong ferromagnetic, SMM and long-range magnetic ordering behaviors. We also show that access to such a unique ferromagnetic class of inorganic, N-rich and O-free materials is feasible through the use of Me3SiN3 as the azido-ligand precursor without requiring the addition of any organic chelating/bridging ligand. In the last projects we have tried to bring together molecular magnetism and optics via the synthesis of multifunctional magnetic materials based on 3d- or 4f-metal ions. We decided to approach such challenge from two different directions: firstly, in our third project, by the deliberate replacement of non-emissive carboxylato ligands in known 3d-SMMs with their fluorescent analogues, without perturbing the metal-core structure and SMM properties (complexes 7, 8, and 9). The second route (last project) involves the use of naphthalene or pyridine-based polyalcohol bridging ligands for the synthesis of new polynuclear LnIII metal clusters (Ln = lanthanide) with novel topologies, SMM behaviors and luminescent properties arising from the increased efficiency of the “antenna” organic group. This approach has led us to the isolation of two new families of LnIII8 (complexes 10-13) and LnIII4 (complexes 14-20) clusters.

The Effects of Magnetic Dilution and Applied Pressure on Several Frustrated Spinels

The effects of magnetic dilution and applied pressure on frustrated spinels GeNi2O4, GeCo2O4, and NiAl2O4 are reported. Dilution was achieved by substitution of Mg2+ in place of magnetically active Co2+ and Ni2+ ions. Large values of the percolation thresholds were found in GeNi(2-x)MgxO4. Specifically, pc1 = 0.74 and pc2 = 0.65 in the sub-networks associated with the triangular and kagome planes, respectively. This anomalous behaviour may be explained by the kagome and triangular planes behaving as coupled networks, also know as a network of networks. In simulations of coupled lattices that form a network of networks, similar anomalous percolation threshold values have been found. In addition, at dilution levels above x=0.30, there is a T^2 dependency in the magnetic heat capacity which may indicate two dimensional spin glass behaviour. Applied pressures in the range of 0 GPa to 1.2 GPa yield a slight decrease in ordering temperature for both the kagome and triangular planes. In GeCo(2-x)MgxO4, the long range magnetic order is more robust with a percolation threshold of pc=0.448. Similar to diluted nickel germanate, at low temperatures, a T^2 magnetic heat capacity contribution is present which indicates a shift from a 3D ordered state to a 2D spin glass state in the presence of increased dilution. Dynamic magnetic susceptibility data indicate a change from canonical spin glass to a cluster glass behaviour. In addition, there is a non-linear increase in ordering temperature with applied pressure in the range P = 0 to 1.0 GPa. A spin glass ground state was observed in Ni(1-x)MgxAl2O4 for (x=0 to 0.375). Analysis of dynamic magnetic susceptibility data yield a characteristic time of tau* = 1.0x10^(-13) s, which is indicative of canonical spin glass behaviour. This is further corroborated by the linear behaviour of the magnetic specific heat contribution. However, the increasing frequency dependence of the freezing temperature suggests a trend towards spin cluster glass formation.