CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecu- lar simulation program. It has been developed over the last three decades with a primary focus on molecules of bio- logical interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estima- tors, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numer- ous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

/pdf/charmm-the-biomolecular-simulation-program-4kexem0xkx.pdf

CHARMM: the biomolecular simulation program.

A new algorithm called Mersenne Twister (MT) is proposed for generating uniform pseudorandom numbers. For a particular choice of parameters, the algorithm provides a super astronomical period of 219937 −1 and 623-dimensional equidistribution up to 32-bit accuracy, while using a working area of only 624 words. This is a new variant of the previously proposed generators, TGFSR, modified so as to admit a Mersenne-prime period. The characteristic polynomial has many terms. The distribution up to v bits accuracy for 1 ≤ v ≤ 32 is also shown to be good. An algorithm is also given that checks the primitivity of the characteristic polynomial of MT with computational complexity O(p2) where p is the degree of the polynomial.We implemented this generator in portable C-code. It passed several stringent statistical tests, including diehard. Its speed is comparable to other modern generators. Its merits are due to the efficient algorithms that are unique to polynomial calculations over the two-element field.

/pdf/mersenne-twister-a-623-dimensionally-equidistributed-uniform-2blcriv47b.pdf

Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator

We introduce a powerful method for exploring the properties of the multidimensional free energy surfaces (FESs) of complex many-body systems by means of coarse-grained non-Markovian dynamics in the space defined by a few collective coordinates. A characteristic feature of these dynamics is the presence of a history-dependent potential term that, in time, fills the minima in the FES, allowing the efficient exploration and accurate determination of the FES as a function of the collective coordinates. We demonstrate the usefulness of this approach in the case of the dissociation of a NaCl molecule in water and in the study of the conformational changes of a dialanine in solution.

https://www.pnas.org/content/pnas/99/20/12562.full.pdf

Escaping free-energy minima

Statistical physics has proven to be a fruitful framework to describe phenomena outside the realm of traditional physics. Recent years have witnessed an attempt by physicists to study collective phenomena emerging from the interactions of individuals as elementary units in social structures. A wide list of topics are reviewed ranging from opinion and cultural and language dynamics to crowd behavior, hierarchy formation, human dynamics, and social spreading. The connections between these problems and other, more traditional, topics of statistical physics are highlighted. Comparison of model results with empirical data from social systems are also emphasized.

Statistical physics of social dynamics

The hydrophobic effect — the tendency for oil and water to segregate — is important in diverse phenomena, from the cleaning of laundry, to the creation of micro-emulsions to make new materials, to the assembly of proteins into functional complexes. This effect is multifaceted depending on whether hydrophobic molecules are individually hydrated or driven to assemble into larger structures. Despite the basic principles underlying the hydrophobic effect being qualitatively well understood, only recently have theoretical developments begun to explain and quantify many features of this ubiquitous phenomenon.

/pdf/interfaces-and-the-driving-force-of-hydrophobic-assembly-2hgxjxkvur.pdf

Interfaces and the driving force of hydrophobic assembly

We present a new Monte Carlo algorithm that produces results of high accuracy with reduced simulational effort. Independent random walks are performed (concurrently or serially) in different, restricted ranges of energy, and the resultant density of states is modified continuously to produce locally flat histograms. This method permits us to directly access the free energy and entropy, is independent of temperature, and is efficient for the study of both 1st order and 2nd order phase transitions. It should also be useful for the study of complex systems with a rough energy landscape.

Efficient, multiple-range random walk algorithm to calculate the density of states.

Preface 1. Introduction 2. Some necessary background 3. Simple sampling Monte Carlo methods 4. Importance sampling Monte Carlo methods 5. More on importance sampling Monte Carlo methods of lattice systems 6. Off-lattice models 7. Reweighting methods 8. Quantum Monte Carlo methods 9. Monte Carlo renormalization group methods 10. Non-equilibrium and irreversible processes 11. Lattice gauge models: a brief introduction 12. A brief review of other methods of computer simulation 13. Monte Carlo simulations at the periphery of physics and beyond 14. Monte Carlo studies of biological molecules 15. Outlook Appendix Index.

/pdf/a-guide-to-monte-carlo-simulations-in-statistical-physics-p2g09a9ft4.pdf

A Guide to Monte Carlo Simulations in Statistical Physics

We describe an efficient Monte Carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models. The density of states is modified at each step when the energy level is visited to produce a flat histogram. By carefully controlling the modification factor, we allow the density of states to converge to the true value very quickly, even for large systems. From the density of states at the end of the random walk, we can estimate thermodynamic quantities such as internal energy and specific heat capacity by calculating canonical averages at any temperature. Using this method, we not only can avoid repeating simulations at multiple temperatures, but we can also estimate the free energy and entropy, quantities that are not directly accessible by conventional Monte Carlo simulations. This algorithm is especially useful for complex systems with a rough landscape since all possible energy levels are visited with the same probability. As with the multicanonical Monte Carlo technique, our method overcomes the tunneling barrier between coexisting phases at first-order phase transitions. In this paper, we apply our algorithm to both first- and second-order phase transitions to demonstrate its efficiency and accuracy. We obtained direct simulational estimates for the density of states for two-dimensional ten-state Potts models on lattices up to 200 x 200 and Ising models on lattices up to 256 x 256. Our simulational results are compared to both exact solutions and existing numerical data obtained using other methods. Applying this approach to a three-dimensional +/-J spin-glass model, we estimate the internal energy and entropy at zero temperature; and, using a two-dimensional random walk in energy and order-parameter space, we obtain the (rough) canonical distribution and energy landscape in order-parameter space. Preliminary data suggest that the glass transition temperature is about 1.2 and that better estimates can be obtained with more extensive application of the method. This simulational method is not restricted to energy space and can be used to calculate the density of states for any parameter by a random walk in the corresponding space.

http://phycomp.technion.ac.il/~nir/PRE56101.pdf

Determining the density of states for classical statistical models: a random walk algorithm to produce a flat histogram.

Using recently developed histogram techniques and an ultrafast multispin coding simulation algorithm, we have investigated the critical behavior of the d=3 simple-cubic Ising model We have studied lattice sizes ranging from L=8 to 96 using between 3\ifmmode\times\else\texttimes\fi{}${10}^{6}$ and 12\ifmmode\times\else\texttimes\fi{}${10}^{6}$ Monte Carlo steps (complete lattice updates) By accurately measuring the finite-size behavior of several different thermodynamic quantities, we are able to determine the critical properties with a precision comparable to that obtained with Monte Carlo renormalization-group and sophisticated series-expansion techniques The best estimate of the inverse critical temperature from our analysis is ${\mathit{K}}_{\mathit{c}}$=0221 659 5\ifmmode\pm\else\textpm\fi{}0000 002 6 The advantages of the histogram technique are discussed, as are the potential problems that can arise at this level of resolution

Critical behavior of the three-dimensional Ising model: A high-resolution Monte Carlo study.

We study the finite-size effects at a temperature-driven first-order transition by analyzing various moments of the energy distribution. The distribution function for the energy is approximated by the superposition of two weighted Gaussian functions yielding quantitative estimates for various quantities and scaling form for the specific heat. The rounding of the singularities and the shifts in the location of the specific-heat maximum are analyzed and the characteristic features of a first-order transition are identified. The predictions are tested on the ten-state Potts model in two dimensions by carrying out extensive Monte Carlo calculations. The results are found to be in good agreement with theory. Comparison is made with the second-order transitions in the two- and three-state Potts models.

David P. Landau

Papers

Efficient, multiple-range random walk algorithm to calculate the density of states.

A Guide to Monte Carlo Simulations in Statistical Physics

Determining the density of states for classical statistical models: a random walk algorithm to produce a flat histogram.

Critical behavior of the three-dimensional Ising model: A high-resolution Monte Carlo study.

Finite-size effects at temperature-driven first-order transitions.