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.

Histogram filtering as a tool in variational Monte Carlo optimization

Optimization of wave functions in quantum Monte Carlo is a difficult task because the statistical uncertainty inherent to the technique makes the absolute determination of the global minimum difficult. To optimize these wave functions we generate a large number of possible minima using many independently generated Monte Carlo ensembles and perform a conjugate gradient optimization. Then we construct histograms of the resulting nominally optimal parameter sets and "filter" them to identify which parameter sets "go together" to generate a local minimum. We follow with correlated-sampling verification runs to find the global minimum. We illustrate this technique for variance and variational energy optimization for a variety of wave functions for small systellls. For such optimized wave functions we calculate the variational energy and variance as well as various non-differential properties. The optimizations are either on par with or superior to determinations in the literature. Furthermore, we show that this technique is sufficiently robust that for molecules one may determine the optimal geometry at tIle same time as one optimizes the variational energy.

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 and variational monte-carlo interaction potentials for li2 (x1-sigma-g+)

Optimized trial functions are used in quantum Monte Carlo and variational Monte Carlo calculations of the Li₂(X ¹Σ⁺_g) potential curve. The trial functions used are a product of a Slater determinant of molecular orbitals multiplied by correlation functions of electron—nuclear and electron—electron separation. The parameters of the determinant and correlation functions are optimized simultaneously by reducing the deviations of the local energy E_L (E_L  Ψ⁻¹_THΨ_T, where Ψ_T denotes a trial function) over a fixed sample. At the equilibrium separation, the variational Monte Carlo and quantum Monte Carlo methods recover 68% and 98% of the correlation energy, respectively. At other points on the curves, these methods yield similar accuracies.

Optimization of tried wave-function in quantum monte-carlo method

A method for optimizing tried wave functions in quantum Monte Carlo method has been found and used to calculate the energies of molecules, such as H-2, Li-2, H-3+, H-3 and H-4. Good results were obtained.

Development of a Cell Size Relaxed Scheme for the Direct Simulation Monte Carlo Method

The conventional direct simulation Monte Carlo (DSMC) method has a strong restriction on the cell size because simulated particles are selected randomly within the cell for collisions. Cells with size larger than the molecular mean free path are generally not allowed in correct DSMC simulations. However, the cell-size induced numerical error can be controlled if the gradients of flow properties are properly involved during collisions. In this study, a large cell DSMC scheme is proposed to relax the cell size restriction. The scheme is applied to simulate several test problems and promising results are obtained even when the cell size is greater than 10 mean free paths of gas molecules. However, it is still necessary, of course, that the cell size be small with respect to the flow field structures that must be resolved.

Improved sampling techniques for the direct simulation Monte Carlo method

The direct simulation Monte Carlo (DSMC) method is a widely used approach for flow simulations having rarefied or nonequilibrium effects. It involves heavily to sample instantaneous values from prescribed distributions using random numbers. In this note, we briefly review the sampling techniques typically employed in the DSMC method and present two techniques to speedup related sampling processes. One technique is very efficient for sampling geometric locations of new particles and the other is useful for the Larsen-Borgnakke energy distribution.

A markov chain Monte Carlo method for estimating population mixing using Y-chromosome markers: Mixing of the Han people in China

We present a new approach for estimating mixing between populations based on non-recombining markers, specifically Y-chromosome microsatellites. A Markov chain Monte Carlo (MCMC) Bayesian statistical approach is used to calculate the posterior probability

Strong electronic correlation in the hydrogen chain: A variational Monte Carlo study

In this paper, we report a fully ab initio variational Monte Carlo study of the linear and periodic chain of hydrogen atoms, a prototype system providing the simplest example of strong electronic correlation in low dimensions. In particular, we prove that numerical accuracy comparable to that of benchmark density-matrix renormalization-group calculations can be achieved by using a highly correlated Jastrow-antisymmetrized geminal power variational wave function. Furthermore, by using the so-called "modern theory of polarization" and by studying the spin-spin and dimer-dimer correlations functions, we have characterized in detail the crossover between the weakly and strongly correlated regimes of this atomic chain. Our results show that variational Monte Carlo provides an accurate and flexible alternative to highly correlated methods of quantum chemistry which, at variance with these methods, can be also applied to a strongly correlated solid in low dimensions close to a crossover or a phase transition.

An efficient scheme for the evaluation of coding performance of high speed links incorporating joint error behaviour based on Monte Carlo Method

While channel coding is a standard method of improving a system’s energy efficiency in digital communications, its practice does not extend to high-speed links. Increasing demands in network speeds are placing a large burden on the energy efficiency of high-speed links and render the benefit of channel coding for these systems a timely subject. The low error rates of interest and the presence of residual intersymbol interference (ISI) caused by hardware constraints impede the analysis and simulation of coded high-speed links. Focusing on the residual ISI and combined noise as the dominant error mechanisms, this paper analyses error correlation through concepts of error region, channel signature, and correlation distance. This framework provides a deeper insight into joint error behaviours in high-speed links, extends the range of statistical simulation for coded high-speed links, and provides a case against the use of biased Monte Carlo methods in this setting

Estimation of the probability of congestion using Monte Carlo method in OPS networks

In networks with small buffers, such as optical packet switching based networks, the convolution approach is presented as one of the most accurate method used for the connection admission control. Admission control and resource management have been addressed in other works oriented to bursty traffic and ATM. This paper focuses on heterogeneous traffic in OPS based networks. Using heterogeneous traffic and bufferless networks the enhanced convolution approach is a good solution. However, both methods (CA and ECA) present a high computational cost for high number of connections. Two new mechanisms (UMCA and ISCA) based on Monte Carlo method are proposed to overcome this drawback. Simulation results show that our proposals achieve lower computational cost compared to enhanced convolution approach with an small stochastic error in the probability estimation

A Monte Carlo method for accelerating the computation of animated radiosity sequences

Realistic rendering animation is known to be an expensive processing task when physically-based global illumination methods are used in order to improve illumination details. This paper presents an acceleration technique to compute animations in radiosity environments. The technique is based on an interpolated approach that exploits temporal coherence in radiosity. A fast global Monte Carlo pre-processing step is introduced to the whole computation of the animated sequence to select important frames. These are fully computed and used as a base for the interpolation of all the sequence. The approach is completely view-independent. Once the illumination is computed, it can be visualized by any animated camera. Results present significant high speed-ups showing that the technique could be an interesting alternative to deterministic methods for computing non-interactive radiosity animations for moderately complex scenarios