Multigraining: an algorithm for simultaneous fine-grained and coarse-grained simulation of molecular systems

A method to combine fine-grained and coarse-grained simulations is presented. The coarse-grained particles are described as virtual particles defined by the underlying fine-grained particles are described as virtual particles defined by the underlying fine-grained particles. The contribution of the two grain levels to the interaction between particles is specified by a grain-level parameter lambda. Setting lambda = 0 results in a completely fine-grained simulation, whereas lambda = 1 yields a simulation governed by the coarse-grained potential energy surface with small contributions to keep the fine-grained covalently bound particles together. Simulations at different lambda values may be coupled using the replica-exchange molecular dynamics method to achieve enhanced sampling at the fine-grained level.     

RRS-PBC: a molecular approach for periodic systems

Technically, when dealing with a perfect crystal, methods in k-(reciprocal) space that impose periodic boundary conditions(PBC) in conjunction with plane-wave basis sets are widely used. Chemists, however, tend to think of a solid as a giant molecule, which offers a molecular way to describe a solid by using a finite cluster model(FCM). However, FCM may fail to simulate a perfect crystal due to its inevitable boundary effects. We propose an RRS-PBC method that extracts the k-space information of a perfect crystalline solid out of a reduced real space(RRS) of an FCM. We show that the inevitable boundary effects in an FCM are eliminated naturally to achieve converged high-quality band structures.     

Efficient algorithm of the transcorrelated method for periodic systems

The transcorrelated (TC) method is one of the promising wave-function-based approaches for the first-principles electronic structure calculations. In this method, the many-body wave function is approximated as the Jastrow-Slater type and one-electron orbitals in the Slater determinant are optimized with a one-body self-consistent-field equation such as that in the Hartree-Fock (HF) method. Although the TC method has yielded good results for both molecules and solids, its computational cost in solid-state calculations, being of order O(N(k)(3)N(b)(3)) with N(k) and N(b) the respective numbers of k-points and bands, has for some years hindered its wide application in condensed matter physics. Although an efficient algorithm was proposed for a Gaussian basis set, that algorithm is not applicable to a plane-wave basis that is suited to and widely used in solid-state calculations. In this paper, we present a new efficient algorithm of the TC method for the plane-wave basis or an arbitrary basis function set expanded in terms of plane waves, with which the computational cost of the TC method scales as O(N(k)(2)N(b) (2)). This is the same as that of the HF method. We applied the TC method with the new algorithm to obtain converged band structure and cell parameters of some semiconductors.     

A symbolic algorithm for periodic tridiagonal systems of equations

In the current paper, we present a novel symbolic algorithm for solving periodic tridiagonal linear systems without imposing any restrictive conditions. The computational cost of the algorithm is less than or almost equal to those of three well-known algorithms given by Chawla and Khazal (Int. J. Comput. Math. 79(4):473–484, 2002) and by El-Mikkawy (Appl. Math. Comput. 161:691–696, 2005), respectively. In addition, the solution of periodic anti-tridiagonal linear systems is also discussed. Two numerical experiments are provided in order to illustrate the performance and effectiveness of our algorithm. All of the experiments were performed on a computer with aid of programs written in MATLAB.     

A consensus line search algorithm for molecular potential energy functions

Force field based energy minimization of molecular structures is a central task in computational chemistry and biology. Solving this problem usually requires efficient local minimization techniques, i.e., iterative two‐step methods that search first for a descent direction and then try to estimate the step width. The second step, the so called line search, typically uses polynomial interpolation schemes to estimate the next trial step. However, dependent on local properties of the objective function alternative schemes may be more appropriate especially if the objective function shows singularities or exponential behavior. As the choice of the best interpolation scheme cannot be made a priori, we propose a new consensus line search approach that performs several different interpolation schemes at each step and then decides which one is the most reliable at the current position. Although a naive consensus approach would lead to severe performance impacts, our method does not require additional evaluations of the energy function, imposing only negligible computational overhead. Additionally, our method can be easily adapted to the local behavior of other objective functions by incorporating suitable interpolation schemes or omitting non‐fitting schemes. The performance of our consensus line search approach has been evaluated and compared to established standard line search algorithms by minimizing the structures of a large set of molecules using different force fields. The proposed algorithm shows better performance in almost all test cases, i.e., it reduces the number of iterations and function and gradient evaluations, leading to significantly reduced run times. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009     

A fast pairlist-construction algorithm for molecular simulations under periodic boundary conditions

A new grid-cell algorithm is presented that permits the fast construction of cutoff-based nonbonded pairlists in molecular simulations under periodic boundary conditions based on an arbitrary box shape. The key features of the method are (1) the use of a one-dimensional mask array (to determine which grid cells contain interacting atoms) that incorporates the effect of periodicity, and (2) the grouping of adjacent interacting cells of the mask array into stripes, which permits the handling of empty cells with a very low computational overhead. Testing of the algorithm on water systems of different sizes (containing about 2000 to 11,000 molecules) shows that the method (1) is about an order of magnitude more efficient compared to a standard (double-loop) algorithm, (2) achieves quasi-linear scaling in the number of atoms, (3) is weakly sensitive in terms of efficiency to the chosen number of grid cells, and (4) can be easily parallelized.     

Multiconfigurational quantum chemical methods for molecular systems containing actinides

Recent advances in computational actinide chemistry are reported in this tutorial review. Muticonfigurational quantum chemical methods have been employed to study the gas phase spectroscopy of small actinide molecules. Examples of actinide compounds studied in solution are also presented. Finally the multiple bond in the diuranium molecule and other diactinide compounds is described.     

A fast parallel clustering algorithm for molecular simulation trajectories

We implemented a GPU‐powered parallel k‐centers algorithm to perform clustering on the conformations of molecular dynamics (MD) simulations. The algorithm is up to two orders of magnitude faster than the CPU implementation. We tested our algorithm on four protein MD simulation datasets ranging from the small Alanine Dipeptide to a 370‐residue Maltose Binding Protein (MBP). It is capable of grouping 250,000 conformations of the MBP into 4000 clusters within 40 seconds. To achieve this, we effectively parallelized the code on the GPU and utilize the triangle inequality of metric spaces. Furthermore, the algorithm's running time is linear with respect to the number of cluster centers. In addition, we found the triangle inequality to be less effective in higher dimensions and provide a mathematical rationale. Finally, using Alanine Dipeptide as an example, we show a strong correlation between cluster populations resulting from the k‐centers algorithm and the underlying density. © 2012 Wiley Periodicals, Inc.     

Enforcing periodic secondary structures in hybrid peptides: a novel hybrid foldamer containing periodic gamma-turn motifs

This note describes the design, synthesis, and conformational studies of a novel hybrid foldamer that adopts a definite compact, three-dimensional structure determined by a combined effect of the special conformational properties of the foldamer constituents. The striking feature of this de novo designed foldamer is its ability to display periodic gamma-turn conformations stabilized by intramolecular hydrogen bonds. Conformational investigations by single-crystal X-ray studies, solution-state NMR, and ab initio MO theory at the HF/6-31G* level strongly support the prevalence of gamma-turn motifs in both the di- and tetrapeptide foldamers, which are presumably stabilized by bifurcated hydrogen bonds in the solid and solution states. The strategy disclosed herein for the construction of hybrid foldamers with periodic gamma-turn motifs has the potential to significantly augment the conformational space available for foldamer design with diverse backbone structures and conformations.     

Parallelization strategies for molecular simulation using the Monte Carlo algorithm

We describe the development of Metropolis Monte Carlo algorithms for a general network of multiple instruction multiple data (MIMD) parallel processors. The implementation of farm, event, and systolic parallel algorithms on transputer-based computers is detailed and their relative performance discussed. Although the emphasis is on methodology, the application of such parallel algorithms will be important for addressing computational problems such as the determination of free energy differences in complex biologically important molecular systems. © 1993 John Wiley & Sons, Inc.     

Quantum algorithm for obtaining the energy spectrum of molecular systems

Simulating a quantum system is more efficient on a quantum computer than on a classical computer. The time required for solving the Schr?dinger equation to obtain molecular energies has been demonstrated to scale polynomially with system size on a quantum computer, in contrast to the well-known result of exponential scaling on a classical computer. In this paper, we present a quantum algorithm to obtain the energy spectrum of molecular systems based on the multiconfigurational self-consistent field (MCSCF) wave function. By using a MCSCF wave function as the initial guess, the excited states are accessible. Entire potential energy surfaces of molecules can be studied more efficiently than if the simpler Hartree-Fock guess was employed. We show that a small increase of the MCSCF space can dramatically increase the success probability of the quantum algorithm, even in regions of the potential energy surface that are far from the equilibrium geometry. For the treatment of larger systems, a multi-reference configuration interaction approach is suggested. We demonstrate that such an algorithm can be used to obtain the energy spectrum of the water molecule.     

Improved delay-leaping simulation algorithm for biochemical reaction systems with delays

In biochemical reaction systems dominated by delays, the simulation speed of the stochastic simulation algorithm depends on the size of the wait queue. As a result, it is important to control the size of the wait queue to improve the efficiency of the simulation. An improved accelerated delay stochastic simulation algorithm for biochemical reaction systems with delays, termed the improved delay-leaping algorithm, is proposed in this paper. The update method for the wait queue is effective in reducing the size of the queue as well as shortening the storage and access time, thereby accelerating the simulation speed. Numerical simulation on two examples indicates that this method not only obtains a more significant efficiency compared with the existing methods, but also can be widely applied in biochemical reaction systems with delays.     

A new parallel method for molecular dynamics simulation of macromolecular systems

Short-range molecular dynamics simulations of molecular systems are commonly parallelized by replicated-data methods, in which each processor stores a copy of all atom positions. This enables computation of bonded 2-, 3-, and 4-body forces within the molecular topology to be partitioned among processors straightforwardly. A drawback to such methods is that the interprocessor communication scales as N (the number of atoms) independent of P (the number of processors). Thus, their parallel efficiency falls off rapidly when large numbers of processors are used. In this article a new parallel method for simulating macromolecular or small-molecule systems is presented, called force-decomposition. Its memory and communication costs scale as N/√P, allowing larger problems to be run faster on greater numbers of processors. Like replicated-data techniques, and in contrast to spatial-decomposition approaches, the new method can be simply load balanced and performs well even for irregular simulation geometries. The implementation of the algorithm in a prototypical macromolecular simulation code ParBond is also discussed. On a 1024-processor Intel Paragon, ParBond runs a standard benchmark simulation of solvated myoglobin with a parallel efficiency of 61% and at 40 times the speed of a vectorized version of CHARMM running on a single Cray Y-MP processor. © 1996 by John Wiley & Sons, Inc.     

The optimal P3M algorithm for computing electrostatic energies in periodic systems

We optimize Hockney and Eastwood's particle-particle particle-mesh algorithm to achieve maximal accuracy in the electrostatic energies (instead of forces) in three-dimensional periodic charged systems. To this end we construct an optimal influence function that minimizes the root-mean-square (rms) errors of the energies. As a by-product we derive a new real-space cutoff correction term, give a transparent derivation of the systematic errors in terms of Madelung energies, and provide an accurate analytical estimate for the rms error of the energies. This error estimate is a useful indicator of the accuracy of the computed energies and allows an easy and precise determination of the optimal values of the various parameters in the algorithm (Ewald splitting parameter, mesh size, and charge assignment order).     

Efficient formulation of the stochastic simulation algorithm for chemically reacting systems

In this paper we examine the different formulations of Gillespie's stochastic simulation algorithm (SSA) [D. Gillespie, J. Phys. Chem. 81, 2340 (1977)] with respect to computational efficiency, and propose an optimization to improve the efficiency of the direct method. Based on careful timing studies and an analysis of the time-consuming operations, we conclude that for most practical problems the optimized direct method is the most efficient formulation of SSA. This is in contrast to the widely held belief that Gibson and Bruck's next reaction method [M. Gibson and J. Bruck, J. Phys. Chem. A 104, 1876 (2000)] is the best way to implement the SSA for large systems. Our analysis explains the source of the discrepancy.     

The accuracy of ab initio molecular geometries for systems containing second-row atoms

The performance of the standard hierarchy of ab initio models--that is, Hartree-Fock theory, second-order Moller-Plesset theory, coupled-cluster singles-and-doubles theory, and coupled-cluster singles-doubles-approximate-triples theory--in combination with correlation-consistent basis sets is investigated for equilibrium geometries of molecules containing second-row elements. From an analysis on a collection of 31 molecules (yielding statistical samples of 41 bond distances and 13 bond angles), the statistical errors (mean deviation, mean absolute deviation, standard deviation, and maximum absolute deviation) are established at each level of theory. The importance of core correlation is examined by comparing calculations in the frozen-core approximation with calculations where all electrons are correlated.     

Box orbitals for extended systems

A linear scaling of the number of nonzero integrals in extended systems calculations and the solution of the difficult cutoff threshold problems in the integral evaluation of periodic HF computations could be solved by the usage of orbitals with a finite extension. The present work proposes the usage of Box orbitals, defined inside spheres centered on the nuclei. Preliminary tests on small systems (atoms and H₂⁺) were performed. The results are very encouraging, since, in most cases, the Box orbitals give better results (giving results of equivalent quality in the worse cases) than do the classical Gaussian orbitals. No spurious effects were encountered. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64 : 411–420, 1997     

Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates

An efficient simulation algorithm for chemical kinetic systems with disparate rates is proposed. This new algorithm is quite general, and it amounts to a simple and seamless modification of the classical stochastic simulation algorithm (SSA), also known as the Gillespie [J. Comput. Phys. 22, 403 (1976); J. Phys. Chem. 81, 2340 (1977)] algorithm. The basic idea is to use an outer SSA to simulate the slow processes with rates computed from an inner SSA which simulates the fast reactions. Averaging theorems for Markov processes can be used to identify the fast and slow variables in the system as well as the effective dynamics over the slow time scale, even though the algorithm itself does not rely on such information. This nested SSA can be easily generalized to systems with more than two separated time scales. Convergence and efficiency of the algorithm are discussed using the established error estimates and illustrated through examples.     

Kronecker-product periodic systems of small gas-phase molecules and the search for order in atomic ensembles of any phase

The periodic law, manifested in the chart of the elements, is so fundamental in chemistry and related areas of physics that the question arises "Might periodicity among molecules also be embodied in a periodic system?" This review paper details how a particular periodic system of gas-phase diatomic molecules, allowing for the forecasting of thousands of new data, was developed. It can include ionized and even quarked-nuclei molecules and it coincides with locality (averaging) and the additivity found in some data; it has interesting vector properties, and it may be related in challenging ways to partial order. The review then explains how periodic systems for triatomic and four-atomic species are evolving along a similar path. The systems rest largely upon exhaustive comparisons of tabulated data, relate to some extent to the octet rule, and include reducible representations of the dynamic group SO(4) in higher spaces. Finally, the paper shows how periodicity can be quantified in data for larger molecules. Data for properties of homologous or substituted molecules, in any phase, are quantified with a vector index, and the index for one set can be transformed into that for another set.