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~

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).

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.

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.

Síntesis y caracterización de complejos de Sn(IV) derivados de ?-Amidofosfonatos . Evaluación de su efecto tóxico sobre artemia salina.

Tesis (Maestría en Ciencias con Orientación en Farmacia) UANL, 2012.

DETALL de la acción que el día 20 de octubre de 1961 la bri gada mixta del mando del ciudadano general Santiago Tapia libró en la sierra intermedia de Pachuca al mineral del monte,derrotado al ejercito reaccionario al mando de sus principales caudillos marquez, Mejía, Zuloaga, Zires, Guerrero, Herrea y Lozada.

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Disertationes scholasticae de Sacratissima Virgine Maria Genitrice Dei, Nostra qve etiam dilectissima Matre, ac domina, brevi, et perspicva methodo ad scolasticorum captum accomodatissima dispositae, atque eidem Beatissimae Virgini obsequenti animo consecratae

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Joannis devoti dei et apostolicae sedis gratia episcopi ananiensis,institutionum canonicarum, libri iv.

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Epistolae ad sanctissimum in Christo Patrem Pium Sextum Pont. Opt. Max. ac sacram rituum congregationem pro causa beatificationis et canonizationis Ven. Servi Dei Antonii Margil a Jesu missionarii apostolici Ord. Min. S. Francisci de observantia.

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Reflexiones critico-apologeticas sobre las obras del RR. P. maestro Fr. Benito Geronymo Feyjoo : en defensa de las milagrosas flores de S. Luis del Monte, de la constante pureza de fé admirable sabiduría,i utilissima doctrina de el iluminado doctor, i esclarecido martyr, B. Raimundo Lulio : de la gran erudición, i sólido juicio del clarissimo doctor el V. Fr. Nicolao de Lyra : de la famosa literatura, i constante veracidad historica de el Ilmo. , i V. D. Fr. Antonio de Guevara, i de otros clarissimos ingenios, que ilustraron al orbe literario

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