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Showing papers on "Monte Carlo molecular modeling published in 1982"



Journal ArticleDOI
TL;DR: In this paper, a Monte Carlo procedure based on a discrete point representation of the path integral for the density matrix is explored, and it is found that the variance of the estimator used to evaluate the energy grows as the square root of the number of discrete points used, and is therefore to be avoided in highly quantum mechanical systems.
Abstract: A Monte Carlo procedure based on a discrete point representation of the path integral for the density matrix is explored. It is found that the variance of the estimator used to evaluate the energy grows as the square root of the number of discrete points used, and is therefore to be avoided in highly quantum mechanical systems, where the number of discrete points must be large. A new energy estimator based on the virial theorem is proposed and shown to be well behaved. The main points of the paper are illustrated, using the harmonic oscillator as an example.

422 citations


Journal ArticleDOI
TL;DR: In this article, the authors derived exact statistical mechanical relations for polyelectrolyte systems within the primitive model using the cell model and determined the osmotic pressure through an explicit evaluation of the derivative of the partition function.
Abstract: Some exact statistical mechanical relations have been derived for polyelectrolyte systems within the primitive model. Using the cell model, the osmotic pressure is determined through an explicit evaluation of the derivative of the partition function. Planar, cylindrical, and spherical systems are considered and for a planar charged wall the contact value theorem [Henderson and Blum, J. Chem. Phys. 69, 5441 (1978)] is obtained as a special case. Analogous relations are derived for the cylindrical and spherical geometries. It is argued that the exact relations can be used as consistency tests for analytical approximations. It is pointed out that one merit of the Poisson–Boltzmann approximation is that the validity of the exact equations is retained. Finally, a simple method is devised for determining the osmotic pressure from Monte Carlo simulations. Results from such simulations are used to assess the accuracy of the osmotic pressure calculated using the Poisson–Boltzmann equation. For monovalent ions, the pressure is overestimated by 10%–50% in the cases studied, while with divalent counterions the error is substantially larger and a discrepancy of one order of magnitude is found.

282 citations


Journal ArticleDOI
TL;DR: In this paper, the dynamics of interfaces where the normal component of an interface velocity is proportional to the curvature of the interface is studied and the dynamic structure function due to the motion of random interfaces is shown to satisfy a scaling law.
Abstract: The dynamics of interfaces where the normal component of an interface velocity is proportional to the curvature is studied. The dynamic structure function due to the motion of random interfaces is shown to satisfy a scaling law. The results are compared with Monte Carlo simulations of the kinetics of the order-disorder transition in a quenched system.

258 citations


Journal ArticleDOI
TL;DR: The internal energy of the classical one-component plasma is calculated using a Monte Carlo technique for 128, 250, 432, 686, and 1024 particles for 1.
Abstract: We calculate the internal energy of the classical one-component plasma using a Monte Carlo technique for 128, 250, 432, 686, and 1024 particles for $1l\ensuremath{\Gamma}l300$ in order to determine the effect of a differing number of particles on the thermodynamics. By fitting the internal energy to a function of $\ensuremath{\Gamma}$ and $N$ (the particle number), we find the free energy for both the liquid and solid for an infinite number of particles.

207 citations


Journal ArticleDOI
TL;DR: The first numerical determination of the thermodynamic isotropic-nematic transition in a simple three-dimensional model fluid, viz., a system of infinitely thin hard platelets, is reported in this article.
Abstract: The first numerical determination of the thermodynamic isotropic-nematic transition in a simple three-dimensional model fluid, viz., a system of infinitely thin hard platelets, is reported. Thermodynamic properties were studied with use of the constant-pressure Monte Carlo method; Widom's particle-insertion method was used to measure the chemical potential. The phase diagram is found to differ considerably from predictions of a second-virial ("Onsager") theory. Virial coefficients up to the fifth were computed; b5 is found to be negative.

133 citations


Journal ArticleDOI
TL;DR: In this article, the chemical potential of the L-J, sf3 fluid was evaluated by molecular-dynamics simulation for a Lennard-Jones (L-J) fluid and for a shifted-force fluid over a wide range of temperature and density by Widom's [6] particleinsertion energy method.
Abstract: We have evaluated the chemical potential by molecular-dynamics simulation for a Lennard-Jones (L-J) fluid and for a Lennard-Jones shifted-force (L-J, sf) fluid over a wide range of temperature and density by Widom's [6] particle-insertion-energy method. We have also investigated, in some detail, more recent methods [10, 11] using the energy of a real particle, and combinations of both methods using the energy-distribution functions. We find that these methods are accurate, convenient and economical but are no better than the straightforward Widom method. We confirm that the molecular-dynamics method is as good, if not better, than the corresponding Monte-Carlo techniques and the grand-canonical Monte-Carlo method. We present results for the properties of the L-J, sf3 fluid, in particular the liquid-vapour co-existence curve, including the critical point, and compare them with those for the L-J fluid and for liquid argon. The method is of general application and, in particular, may be directly used for mol...

133 citations


Journal ArticleDOI
TL;DR: In this article, a Monte Carlo method for simulation of the stepwise polyreaction generating treelike polymer structures and admitting intramolecular reactions inside the largest particle (identified with the gel) has been developed.
Abstract: A Monte Carlo method for simulation of the stepwise polyreaction generating treelike polymer structures and admitting intramolecular reactions inside the largest particle (identified with the gel) has been developed. The method is equivalent to the kinetic theory of network formation applied to finite systems. The limiting properties of an infinite system are obtained by extrapolation; among those best accessible are the critical conversion of gelation and weight fractions of sol and gel. Polymerization of a trifunctional monomer with a first-shell substitution effect was used as an example to demonstrate that, with the exception of some special cases, the results obtained by the kinetic method are virtually identical with those provided by the statistical method based on the treelike model and cascade substitution.

99 citations


Journal ArticleDOI
TL;DR: In this paper, the GFMC method was used to obtain the lowest energy state of the ground state of a few-body system, which was shown to be computationally feasible for several-body systems.
Abstract: The Green’s function Monte Carlo method used for obtaining exact solutions to the Schrodinger equation of boson systems is generalized to treat systems of several fermions. We show that when it is possible to select eigenfunctions of the Hamiltonian based on physical symmetries, the GFMC method can be used to yield the lowest energy state of that symmetry. In particular, the lowest totally antisymmetric eigenfunction, the fermion ground state, can be obtained. Calculations on several two‐ and three‐body model problems show the method to be computationally feasible for few‐body systems.

89 citations


Journal ArticleDOI
TL;DR: By the use of umbrella sampling technique in the Monte Carlo method proposed by Torrie and Valleau, reliable data have been established for the Helmoholtz free energy of mixing in some selected models of Lennard-Jones liquid mixtures.
Abstract: By the use of umbrella‐sampling technique in the Monte Carlo method proposed by Torrie and Valleau, reliable data have been established for the Helmoholtz free energy of mixing in some selected models of Lennard‐Jones liquid mixtures. The variational method in perturbation theory is found to account for these Monte Carlo data. Validity of some representative semiempirical theories is discussed and it is found that none of them can reproduce the present Monte Carlo results reasonably well. Finally the phase stability of the present models is discussed in terms of both the free energy of mixing and local composition values recently obtained from our molecular dynamics calculations.

85 citations



Journal ArticleDOI
TL;DR: In this article, the phase diagram of the two-dimensional, three-state chiral Potts or asymmetric clock model is studied using Monte Carlo techniques. And the phase boundaries are compared to those obtained using the finite-size renormalization group and the free fermion approximation.
Abstract: The phase diagram of the two-dimensional, three-state chiral Potts or asymmetric clock model is studied using Monte Carlo techniques. The phase boundaries are compared to those obtained using the finite-size renormalization group and the free fermion approximation. The incommensurate phase is described in detail and crossover effects near the Lifshitz point are discussed.

Journal ArticleDOI
TL;DR: A Monte Carlo method of simulation of the grand canonical ensemble based on the concept of maximum number of molecules is applied to the 6 : 12 Lennard-Jones fluid and the results compared with Adams' [1] at T*=1·15 and 1·25 as discussed by the authors.
Abstract: A Monte Carlo method of simulation of the grand canonical ensemble based on the concept of maximum number of molecules is applied to the 6 : 12 Lennard-Jones fluid and the results compared with Adams' [1] at T*=1·15 and 1·25. The method generates equally reliable data using a much smaller number of molecules. Fluid states near a phase transition are simulated.


Journal ArticleDOI
TL;DR: In this article, Monte Carlo simulations of dislocation vector systems with long-range interactions reveal two possible types of phase transitions depending on the core energy of dislocations, and the Kosterlitz-Thouless theory agrees well with the simulation results.
Abstract: Monte Carlo simulations of dislocation vector systems with long-range interactions reveal two possible types of phase transitions depending on the core energy of dislocations. For dislocations with a large core energy the melting transition is found to be continuous and due to dislocation unbinding. The Kosterlitz-Thouless theory agrees well with the simulation results. For a small core energy the melting transition is caused by the nucleation of grain boundary loops and is found to be first order. The latter transition may correspond to the previous computer experiments on various atomic systems. In addition to thermodynamic quantities such as the energy and specific heat, microscopic configurations and orientational correlation functions are also calculated.


Journal ArticleDOI
TL;DR: In this article, the Monte Carlo method was used to predict the behavior of the lattice gas model for particular values of the D-D interactions, and it was shown that for repulsive first nearest-neighbour (V1) and second nearest neighbor (V2) interactions with V2=0.25 V1, the Monte-Carlo method gave similar results to those obtained by a cluster variation method calculation.
Abstract: In alpha ' Pd-D at low temperatures the deuterons become ordered on the octahedral sites of the Pd lattice due to D-D interactions. As this process does not measurably disrupt the palladium lattice the system provides an excellent approximation to a lattice gas. The Monte Carlo method of predicting the behaviour of the lattice gas model for particular values of the D-D interactions is described and it is shown that for repulsive first nearest-neighbour (V1) and second nearest-neighbour (V2) interactions with V2=0.25 V1, the Monte Carlo method gives similar results to those obtained by a cluster variation method calculation. However, the latter method only predicts the transition temperature accurately near stoichiometric compositions. The above choice of interactions also gives a good description of the real system for D concentrations between 64 and 68% and it is suggested how agreement at higher concentrations could be achieved by introducing longer range interactions. A method of estimating the values of Vn from diffuse neutron scattering above the transition temperature is also proposed.

Journal ArticleDOI
TL;DR: In this article, the excess free energy and entropy of three water models (ST2, MCY and SPC) were determined using Monte Carlo thermodynamic integration, with soft spheres as a reference system.
Abstract: The excess free energy and entropy of three water models (ST2, MCY and SPC) are determined using Monte Carlo thermodynamic integration, with soft spheres as a reference system. The method used is compared with two other methods, the umbrella sampling and the overlap ratio methods. A simple self check for the umbrella sampling method is proposed.

Journal ArticleDOI
TL;DR: In this article, a self consistent Monte Carlo particle model for simulation of semiconductor devices is presented, which is capable of correctly reproducing laboratory measurements and can be used as a design tool to evaluate novel ideas.

Journal ArticleDOI
TL;DR: In this paper, the essential features of a Monte Carlo program which simulates the scattering and the retardation of energetic ions in amorphous targets are presented, and theoretical predictions obtained using the above expressions for nuclear scattering and electronic energy loss are shown to agree very well with experimental results.
Abstract: The essential features of a Monte Carlo program which simulates the scattering and the retardation of energetic ions in amorphous targets are presented. The new experimentally derived universal scattering cross-section of Kalbitzer and Oetzmann is used to describe nuclear scattering events. For electronic energy loss, the Lindhard-Scharff and Bethe formulae are used. The program was primarily developed to study the spatial distribution of ion deposited energy for lithographic applications. However, for initial verification, the program has been used to study the fundamental characteristics of ion transport for various ion-target combinations. The theoretical predictions obtained using the above expressions for nuclear scattering and electronic energy loss are shown to agree very well with experimental results.

Journal ArticleDOI
TL;DR: In this paper, an exact Monte Carlo method for calculating thermodynamic properties of quantum spin systems is described, for both one-dimensional and three-dimensional ferromagnetic and antiferromagnetic systems.
Abstract: An exact Monte Carlo method for calculating thermodynamic properties of quantum spin systems is described. Results for one-dimensional ferromagnetic and antiferromagnetic systems and for three-dimensional ferromagnetic systems show that the method can be used to study quantum spin systems as extensively as classical spin systems are studied with conventional Monte Carlo methods.


Journal ArticleDOI
TL;DR: In this paper, a formalism was presented for estimating critical cluster size as defined in classical models for nucleation phenomena, which combines Bennett's Monte Carlo technique for determining free-energy differences for clusters containingn andn- 1 atoms with the steady state nucleation rate formalism.
Abstract: A formalism is presented for estimating critical cluster size as defined in classical models for nucleation phenomena. The method combines Bennett's Monte Carlo technique for determining free-energy differences for clusters containingn andn- 1 atoms with the steady state nucleation rate formalism. A simple form for the free energy of formation of then cluster [including a termA (n)n2/3] is used to predict critical cluster size and critical supersaturation ratio, S*. This approach is applied to Lennard-Jones vapor clusters at 60 K. Results for free-energy differences for the 13, 18, 24, and 43 clusters predict a critical cluster size of 70 ± 5 atoms at a critical supersaturation ratio given bylnS*=2,45 0.15. This method is intended to provide estimates of critical cluster size for more ambitious attempts to calculate cluster free energies or for initializing conditions in microscopic simulations of nucleating systems.


Journal ArticleDOI
TL;DR: In this article, the sum of vibration-rotation states has been calculated for realistic potentials of O 3 and H 2 CO using a quasi-and random Monte Carlo method.

Journal ArticleDOI
Ulrich Gahn1
TL;DR: In this paper, a Monte Carlo model is used to simulate the thermodynamic equilibrium of a substitutional binary f.c. solid solution with pairwise interactions, which is used for the determination of ground state structures, the calculation of short-range and long-range order data at non-zero temperatures, and the computation of the uppermost ordering temperatures.


Journal ArticleDOI
TL;DR: In this article, a real space renormalization group is formulated for percolation of overlapping discs with a variety of distributions of disc radii and the Monte Carlo method is used for obtaining recursion relations.
Abstract: A real space renormalization group is formulated for continuum (off-lattice) percolation problems It is applied to the system of overlapping discs with a variety of distributions of disc radii Monte Carlo method is used for obtaining recursion relations The results support universality: The Harris criterion seems to work for percolation The position of the critical point shows stability against introducing a distribution in the disc radii


Journal ArticleDOI
TL;DR: In this article, a multispin coding technique was applied to the kinetic Ising model with size 600*600*600 and the magnetization was found to decay asymptotically as exp(-t/2.90) ift is measured in Monte Carlo steps per spin, and M(t = 0) = 1 initially.
Abstract: Rebbi's multispin coding technique is improved and applied to the kinetic Ising model with size 600*600*600. We give the central part of our computer program (for a CDC Cyber 76), which will be helpful also in a simulation of smaller systems, and describe the other tricks necessary to go to large lattices. The magnetizationM atT=1.4*T c is found to decay asymptotically as exp(-t/2.90) ift is measured in Monte Carlo steps per spin, and M(t = 0) = 1 initially.