Termodinâmica estatística de líquidos com o método de Monte Carlo. II. O líquido clorofórmio

Thermodynamic properties and radial distribution functions for liquid chloroform were calculated using the Monte Carlo method implemented with Metropolis algorithm in the NpT ensemble at 298 K and 1 atm. A five site model was developed to represent the chloroform molecules. A force field composed by Lennard-Jones and Coulomb potential functions was used to calculate the intermolecular energy. The partial charges needed to represent the Coulombic interactions were obtained from quantum chemical ab initio calculations. The Lennard-Jones parameters were adjusted to reproduce experimental values for density and enthalpy of vaporization for pure liquid. All thermodynamic results are in excelent agreement with experimental data. The correlation functions calculated are in good accordance with theoretical results avaliable in the literature. The free energy for solvating one chloroform molecule into its own liquid at 298 K and 1 atm was computed as an additional test of the potential model. The result obtained compares well with the experimental value. The medium effects on cis/trans convertion of a hypotetical solute in water TIP4P and chloroform solvents were also accomplished. The results obtained from this investigation are in agreement with estimates of the continuous theory of solvation.

Monte Carlo simulation of x-ray emission by kilovolt electron bombardment

A physical model for the simulation of x-ray emission spectra from samples irradiated with kilovolt electron beams is proposed. Inner shell ionization by electron impact is described by means of total cross sections evaluated from an optical-data model. A double differential cross section is proposed for bremsstrahlung emission, which reproduces the radiative stopping powers derived from the partial wave calculations of Kissel, Quarles and Pratt [At. Data Nucl. Data Tables 28, 381 (1983)]. These ionization and radiative cross sections have been introduced into a general-purpose Monte Carlo code, which performs simulation of coupled electron and photon transport for arbitrary materials. To improve the efficiency of the simulation, interaction forcing, a variance reduction technique, has been applied for both ionizing collisions and radiative events. The reliability of simulated x-ray spectra is analyzed by comparing simulation results with electron probe measurements.

Monte Carlo simulation of x-ray spectra generated by kilo-electron-volt electrons

We present a general algorithm for the simulation of x-ray spectra emitted from targets of arbitrary composition bombarded with kilovolt electron beams. Electron and photon transport is simulated by means of the general-purpose Monte Carlo code PENELOPE, using the standard, detailed simulation scheme. Bremsstrahlung emission is described by using a recently proposed algorithm, in which the energy of emitted photons is sampled from numerical cross-section tables, while the angular distribution of the photons is represented by an analytical expression with parameters determined by fitting benchmark shape functions obtained from partial-wave calculations. Ionization of K and L shells by electron impact is accounted for by means of ionization cross sections calculated from the distorted-wave Born approximation. The relaxation of the excited atoms following the ionization of an inner shell, which proceeds through emission of characteristic x rays and Auger electrons, is simulated until all vacancies have migrated to M and outer shells. For comparison, measurements of x-ray emission spectra generated by 20 keV electrons impinging normally on multiple bulk targets of pure elements, which span the periodic system, have been performed using an electron microprobe. Simulation results are shown to be in close agreement with these measurements.

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.

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.

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).

Étude de la formation et de l'évolution de nanostructures par méthodes Monte Carlo

Cette thèse, composée de quatre articles scientifiques, porte sur les méthodes numériques atomistiques et leur application à des systèmes semi-conducteurs nanostructurés. Nous introduisons les méthodes accélérées conçues pour traiter les événements activés, faisant un survol des développements du domaine. Suit notre premier article, qui traite en détail de la technique d'activation-relaxation cinétique (ART-cinétique), un algorithme Monte Carlo cinétique hors-réseau autodidacte basé sur la technique de l'activation-relaxation nouveau (ARTn), dont le développement ouvre la voie au traitement exact des interactions élastiques tout en permettant la simulation de matériaux sur des plages de temps pouvant atteindre la seconde. Ce développement algorithmique, combiné à des données expérimentales récentes, ouvre la voie au second article. On y explique le relâchement de chaleur par le silicium cristallin suite à son implantation ionique avec des ions de Si à 3 keV. Grâce à nos simulations par ART-cinétique et l'analyse de données obtenues par nanocalorimétrie, nous montrons que la relaxation est décrite par un nouveau modèle en deux temps: "réinitialiser et relaxer" ("Replenish-and-Relax"). Ce modèle, assez général, peut potentiellement expliquer la relaxation dans d'autres matériaux désordonnés. Par la suite, nous poussons l'analyse plus loin. Le troisième article offre une analyse poussée des mécanismes atomistiques responsables de la relaxation lors du recuit. Nous montrons que les interactions élastiques entre des défauts ponctuels et des petits complexes de défauts contrôlent la relaxation, en net contraste avec la littérature qui postule que des "poches amorphes" jouent ce rôle. Nous étudions aussi certains sous-aspects de la croissance de boîtes quantiques de Ge sur Si (001). En effet, après une courte mise en contexte et une introduction méthodologique supplémentaire, le quatrième article décrit la structure de la couche de mouillage lors du dépôt de Ge sur Si (001) à l'aide d'une implémentation QM/MM du code BigDFT-ART. Nous caractérisons la structure de la reconstruction 2xN de la surface et abaissons le seuil de la température nécessaire pour la diffusion du Ge en sous-couche prédit théoriquement par plus de 100 K.

Monte Carlo field-theoretic simulations for melts of symmetric diblock copolymer

Monte Carlo field-theoretic simulations (MCFTS) are performed on melts of symmetric diblock copolymer for invariant polymerization indexes extending down to experimentally relevant values of N̅ ∼ 10^4. The simulations are performed with a fluctuating composition field, W_−(r), and a pressure field, W_+(r), that follows the saddle-point approximation. Our study focuses on the disordered-state structure function, S(k), and the order−disorder transition (ODT). Although shortwavelength fluctuations cause an ultraviolet (UV) divergence in three dimensions, this is readily compensated for with the use of an effective Flory−Huggins interaction parameter, χ_e. The resulting S(k) matches the predictions of renormalized one-loop (ROL) calculations over the full range of χ_eN and N̅ examined in our study, and agrees well with Fredrickson−Helfand (F−H) theory near the ODT. Consistent with the F−H theory, the ODT is discontinuous for finite N̅ and the shift in (χ_eN)_ODT follows the predicted N̅^−1/3 scaling over our range of N̅.

Modelling water adsorption on Au(210) surfaces: II. Monte Carlo simulations

Canonical Monte Carlo simulations for the Au(210)/H(2)O interface, using a force field recently proposed by us, are reported. The results exhibit the main features normally observed in simulations of water molecules in contact with different noble metal surfaces. The calculations also assess the influence of the surface topography on the structural aspects of the adsorbed water and on the distribution of the water molecules in the direction normal to the metal surface plane. The adsorption process is preferential at sites in the first layer of the metal. The analysis of the density profiles and dipole moment distributions points to two predominant orientations. Most of the molecules are adsorbed with the molecular plane parallel to surface, while others adsorb with one of the O-H bonds parallel to the surface and the other bond pointing towards the bulk liquid phase. There is also evidence of hydrogen bond formation between the first and second solvent layers at the interface. (c) 2007 Elsevier B.V. All rights reserved.

Protein-Ion Binding Process on Finite Macromolecular Concentration. A Poisson-Boltzmann and Monte Carlo Study

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

C-H center dot center dot center dot O and N-H center dot center dot center dot O hydrogen bonds in liquid amides investigated by Monte Carlo simulation

Monte Carlo simulations of liquid formamide, N-methylformamide (MF), and N,N-dimethylformamide (DMF) have been performed in the isothermal and isobaric ensemble at 298 K and 1 atm, aiming to investigate the C-H ... O and N-H ... O hydrogen bonds. The interaction energy was calculated using the classical 6-12 Lennard-Jones pairwise potential plus a Coulomb term on a rigid six-site molecular model with the potential parameters being optimized in this work. Theoretical values obtained for heat of vaporization and liquid densities are in good agreement with the experimental data. The radial distribution function [RDF, g(r)] obtained compare well with R-X diffraction data available. The RDF and molecular mechanics (MM2) minimization show that the C-H ... O interaction has a significant role in the structure of the three liquids. These results are supported by ab initio calculations. This Interaction is particularly important in the structure of MF. The intensity of the N-H ... O hydrogen bond is greater in the MF than formamide. This could explain some anomalous properties verified in MF. (C) 1997 John Wiley & Sons, Inc.

C - H ⋯ 0 and N - H ⋯ 0 hydrogen bonds in liquid amides investigated by monte carlo simulation

Monte Carlo simulations of liquid formamide, N-methylformamide (MF), and N, N-dimethytformamide (DMF) have been performed in the isothermal and isobaric ensemble at 298 K and 1 atm, aiming to investigate the C-H ⋯ O and N-H ⋯ O hydrogen bonds. The interaction energy was calculated using the classical 6-12 Lennard-Jones pairwise potential plus a Coulomb term on a rigid six-site molecular model with the potential parameters being optimized in this work. Theoretical values obtained for heat of vaporization and liquid densities are in good agreement with the experimental data. The radial distribution function [RDF, g(r)] obtained compare well with R-X diffraction data available. The RDF and molecular mechanics (MM2) minimization show that the C-H ⋯ O interaction has a significant role in the structure of the three liquids. These results are supported by ab initio calculations. This interaction is particularly important in the structure of MF. The intensity of the N - H ⋯ O hydrogen bond is greater in the MF than formamide. This could explain some anomalous properties verified in MF. © 1997 John Wiley & Sons, Inc.

Estudo de solvatocromismo em líquidos moleculares orgânicos via método seqüencial Monte Carlo/Mecânica Quântica

Utilizou-se o método seqüencial Monte Carlo / Mecânica Quântica para obterem-se os desvios de solvatocromismo e os momentos de dipolo dos sistemas de moléculas orgânicas: Uracil em meio aquoso, -Caroteno em Ácido Oléico, Ácido Ricinoléico em metanol e em Etanol e Ácido Oléico em metanol e em Etanol. As otimizações das geometrias e as distribuições de cargas foram obtidas através da Teoria do Funcional Densidade com o funcional B3LYP e os conjuntos de funções de base 6-31G(d) para todas as moléculas exceto para a água e Uracil, as quais, foram utilizadas o conjunto de funções de base 6-311++G(d,p). No tratamento clássico, Monte Carlo, aplicou-se o algoritmo Metropólis através do programa DICE. A separação de configurações estatisticamente relevantes para os cálculos das propriedades médias foi implementada com a utilização da função de auto-correlação calculada para cada sistema. A função de distribuição radial dos líquidos moleculares foi utilizada para a separação da primeira camada de solvatação, a qual, estabelece a principal interação entre soluto-solvente. As configurações relevantes da primeira camada de solvatação de cada sistema foram submetidas a cálculos quânticos a nível semi-empírico com o método ZINDO/S-CI. Os espectros de absorção foram obtidos para os solutos em fase gasosa e para os sistemas de líquidos moleculares comentados. Os momentos de dipolo elétrico dos mesmos também foram obtidos. Todas as bandas dos espectros de absorção dos sistemas tiveram um desvio para o azul, exceto a segunda banda do sistema de Beta-Caroteno em Ácido Oléico que apresentou um desvio para o vermelho. Os resultados encontrados apresentam-se em excelente concordância com os valores experimentais encontrados na literatura. Todos os sistemas tiveram aumento no momento de dipolo elétrico devido às moléculas dos solventes serem moléculas polares. Os sistemas de ácidos graxos em álcoois apresentaram resultados muito semelhantes, ou seja, os ácidos graxos mencionados possuem comportamentos espectroscópicos semelhantes submetidos aos mesmos solventes. As simulações através do método seqüencial Monte Carlo / Mecânica Quântica estudadas demonstraram que a metodologia é eficaz para a obtenção das propriedades espectroscópicas dos líquidos moleculares analisados.

Investigação da dinâmica sequêncial Monte Carlo/Mecânica Quântica para sitemas moleculares orgânicos

O principal objetivo deste trabalho é investigar teóricamente as propriedades eletrônicas e óticas de compostos orgânicos em ambiente líquido. A compreensão das interações em sistemas líquidos é muito importante para a descrição de fenômenos em muitas partes da ciência, como Física, Química, Biologia e Materiais, bem como no desenvolvimento de materiais óticos. As flutuações térmicas fazem que inumaram das configurações para os líquidos possam ser gerados. Esta é a razão do comportamento estatístico observado em sistemas líquidos. Considerando estas dificuldades, o tratamento sequencial Monte Carlo / Mecânica Quântica (SMC/QM) é usado neste trabalho. Neste procedimento, a estrutura líquida é gerada primeiramente por simulações clássicas de MC e mais tarde, somente a parte mais importante do sistema é tratada com mecânica quântica. Usando o procedimento acima, os propriedades do quantum o pirazine dimethyl do thiene Methyl da laranja (MO) e do O 2,3-dimetil tieno[3,4-b] pirazina (DTP) foram investigados. O MO é um conhecido indicador de pH e pode ser encontrado sob circunstâncias básicas e acidas. Suas geometrias de mínima energia foram obtidas mediante a Teoria do Funcional da Densidade pelo funcional B3LYP, sendo o sistema descrito pelas bases de Pople com uma função de polarização (6-31G*). Para obter as propriedades médias dos observaveis, cálculos de química quântica foram executados dentro da aproximação semi-empírica de INDO/S-CI. Com respeito ao espectro de absorção, os dados experimentais existentes na literatura científica reportam a existência de uma larga banda localizada na região de baixas energias, mais precisamente entre 400 e 600 nm. Nossos resultados teóricos para a forma alcalina mostram uma transição intensa transição π → π* aproximadamente à 432.4 ± 0.03 nm e, sob condições ácidas, esta transição aparece aproximadamente à 507.4 ± 0.12, 496.4 ± 0.28 ou 545.3 ± 0.10 nm, dependendo da estrutura, mostrando bom acordo com resultados experimentais. O DTP é um sistema particular usado na produção de polímeros de baixo gap. Suas propriedades elétricas e óticas foram obtidas através de um novo procedimento conhecido por Configuração Eletrostática Média do Solvent (ASEC). O procedimento ASEC inclui moléculas do solvente como cargas pontuais e permite o obtenção das quantidades quânticas executando somente poucos cálculos de mecânica quântica. Para o DTP, usando a teoria das perturbações de segunda ordem Mφller-Plesset (MP2) e o conjunto de bases aug-cc-pVDZ, a convergência do momento de dipolo foi alcançada com apenas quatro cálculos de mecânica quântica à 1.16 D, apresentando um aumento de 42% quando comparado ao dipolo isolado. O polarizabilidade corresponde à outra característica elétrica que pôde ser medida. Considerando o mesmo nível empregado ao cálculo do dipolo, o valor médio 132.7 a30 foi observado. A região de mais baixas da energias do espectro de absorption foi investigada também atravé de procedimento de ASEC usando ambos as aproximações, semi-empírico e DFT. Esta região de absorção é motivo de conclusões contraditórias com relação à natureza das transições n → π* e π → π*. Nossos resultados mostram que realmente que essas excitações são realmente observadas simultanemente podendo sobrepôr-se. Como exemplo, nossos resultados para DFT, encontrados usando o funcional B3LYP nos mostra que estas transições aparecem aproximadamente à 360.6 e 351.1 nm.

A Monte Carlo study of the anisotropic N=3 Ashkin-Teller model

The phase diagram of an asymmetric N = 3 Ashkin-Teller model is obtained by a numerical analysis which combines Monte Carlo renormalization group and reweighting techniques. Present results reveal several differences with those obtained by mean-field calculations and a Hamiltonian approach. In particular, we found Ising critical exponents along a line where Goldschmidt has located the Kosterlitz-Thouless multicritical point. On the other hand, we did find nonuniversal exponents along another transition line. Symmetry breaking in this case is very similar to the N = 2 case, since the symmetries associated to only two of the Ising variables are broken. However, for large values of the coupling constant ratio XW = W/K, when the only broken symmetry is of a hidden variable, we detected first-order phase transitions giving evidence supporting the existence of a multicritical point, as suggested by Goldschmidt, but in a different region of the phase diagram. © 2002 Elsevier Science B.V. All rights reserved.