Geometry optimizations of benzene clusters using a modified genetic algorithm

A modified genetic algorithm with real-number coding, non-uniform mutation and arithmetical crossover operators was described in this paper. A local minimization was used to improve the final solution obtained by the genetic algorithm. Using the exp-6-1 interatomic energy function, the modified genetic algorithm with local minimization (MGALM) was applied to the geometry optimization problem of small benzene clusters (C6H6)N(N = 2-7) to obtain the global minimum energy structures. MGALM is simple but the structures optimized are comparable to the published results obtained by parallel genetic algorithms.     

The implementation of ab initio quantum chemistry calculations on transputers

Summary The RHF and geometry optimization sections of the ab initio quantum chemistry code, GAMESS, have been optimized for a network of parallel microprocessors, Inmos T800-20 transputers, using both indirect and direct SCF techniques. The results indicate great scope for implementation of such codes on small parallel computer systems, very high efficiencies having been achieved, particularly in the cases of direct SCF and geometry optimization with large basis sets.The work, although performed upon one particular parallel system, the Meiko Computing Surface, is applicable to a wide range of parallel systems with both shared and distributed memory.     

On the use of constraints in molecular mechanics. II. The Lagrange multiplier method and non-full-matrix Newton-Raphson minimization

It is shown how the Lagrange Multiplier method for constrained minimization can be implemented in a molecular mechanics program using the common approximations to the full-matrix Newton-Raphson minimization. The method reduces the number of cycles to achieve convergence, and also stabilizes the refinement process. Increases in computer memory requirements are small. As an application, the conformational surface of cycloheptane is calculated.     

Variance minimization of free energy estimates from optimized expanded ensembles

We explored the possibility of improving the accuracy and precision of free-energy differences estimated via expanded ensembles by manipulation of the biasing weights. Three different weighing approaches were compared: the flat histogram (FH) method, the optimized ensemble (OE) method, and a method introduced in this work, denoted MinVar, which aims to explicitly minimize the expected variance. The performance of these three methods was tested for the simulation of chemical potentials in systems of symmetric diblock copolymers with chain lengths of either 10 or 4 beads, and a system of one large hard sphere of diameter 10 d immersed in a fluid of hard spheres of diameter d. In addition, the effect of the weighing method on the observed accuracy was investigated for different choices of macrostate staging and for both optimized and nonoptimized acceptance ratio methods for calculating free-energy differences. In the diblock copolymer systems, we found that the maximum attainable accuracy can be limited by correlations between the samples, causing the "real" observed variances to be much larger than the expected "ideal" ones. Hence, if the formal minimization of the variance, as aimed by the MinVar method, occurs at the expense of increasing the correlations in the data, the accuracy may actually decrease. Although maximizing the number of round trips between initial and final macrostates (as aimed by the OE method) was found to be directly related to data decorrelation, this only translates into increased accuracy if the correlations are the major source of errors in the free energy estimates. Finally, for the hard sphere system, we found that the MinVar method performs better than both the OE and FH methods even though the MinVar method in this case never completes a round trip, illustrating that maximizing the number of round trips for fixed computational cost does not necessarily lead to increased precision.     

Optimizing the sampling and staging for simulations of rare events via forward flux sampling schemes

In this work, we present an adaptive algorithm to optimize the phase space sampling for simulations of rare events in complex systems via forward flux sampling (FFS) schemes. In FFS, interfaces are used to partition the phase space along an order parameter lambda connecting the initial and final regions of interest. Since the kinetic "bottleneck" regions along the order parameter are not usually known beforehand, an adaptive procedure is used that first finds these regions by estimating the rate constants associated with reaching subsequent interfaces; thereafter, the FFS simulation is reset to concentrate the sampling on those bottlenecks. The approach can optimize for either the number and position of the interfaces (i.e., optimized lambda phase staging) or the number M of fired trial runs per interface (i.e., the {M(i)} set) to minimize the statistical error in the rate constant estimation per simulation period. For example, the optimization of the lambda staging leads to a net constant flux of partial trajectories between interfaces and hence a constant flux of connected paths throughout the region between the two end states. The method is demonstrated for several test systems, including the folding of a lattice protein. It is shown that the proposed approach leads to an optimized lambda staging and {M(i)} set which increase the computational efficiency of the sampling algorithm.     

On the relationship between the local tracking procedures and monotonic schemes in quantum optimal control

Numerical simulations of (bilinear) quantum control often rely on either monotonically convergent algorithms or tracking schemes. However, despite their mathematical simplicity, very limited intuitive understanding exists at this time to explain the former type of algorithms. Departing from the usual mathematical formalization, we present in this paper an interpretation of the monotonic algorithms as finite horizon, local in time, tracking schemes. Our purpose is not to present a new class of procedures but rather to introduce the necessary rigorous framework that supports this interpretation. As a by-product we show that at each instant, estimates of the future quality of the current control field are available and used in the optimization. When the target is expressed as reaching a prescribed final state, we also present an intuitive geometrical interpretation as the minimization of the distance between two correlated trajectories: one starting from the given initial state and the other backward in time from the target state. As an illustration, a stochastic monotonic algorithm is introduced. Numerical discretizations of the two procedures are also presented.     

氢气和氧气生成气态水反应热力学函数的高水平量化计算研究——介绍一个计算化学实验

On the basis of teaching practice, we introduce a computational chemistry experiment for highgrade undergraduate students. This experiment uses Gaussian 09, GaussView and UltraEdit softwares to calculate the changes of thermodynamic parameters for generation of vaporous water from hydrogen and oxygen, including the internal energy, enthalpy, entropy and Gibbs free energy. Through this experiment, students will learn how to perform the geometry optimization, frequency calculation and energy calculation with the high-level quantum chemistry calculation methods.     

Sampling Potential Energy Surfaces in the Condensed Phase with Many-Body Electronic Structure Methods

Sampling potential energy surfaces (PES) is pivotal for understanding chemical structure, energetics and reactivity and is of special importance for complex condensed-phase systems. Until recently such simulations based on electronic structure theory have been performed only by density functional theory and semiempirical methods. Many-body electronic structure methods, almost routinely used for molecules, have been practically unavailable for sampling PES in the condensed-phase. This has changed during the last few years, as efficient algorithms and software implementations for the evaluation of electronic energies and forces on atoms have been developed, allowing for geometry optimization, molecular dynamics and Monte-Carlo simulations, which was previously unthinkable. Herein, we introduce the theory and software developments and overview the applications in the field, the most encouraging results being obtained for aqueous chemistry. Requiring state-of-the-art computer resources PES sampling with many-body electronic structure methods in the condensed phase provides high-quality benchmarks and will gradually become more available due to fast progress in reduced scaling algorithms and computational technologies.     

用界面几何约束的多起点蒙特卡罗方法对蛋白质/ 短肽识别体系的对接计算

提出了一个界面几何约束的多起点蒙特卡罗构象搜索方法,并把这个方法用于三个丝氨酸蛋白酶/短肽抑制剂体系的刚性、部分柔性和全部柔性对接计算中。我们的方法成功地预测出了接近晶体结构的配体构象。与没有几何约束相比,我们的几何约束蒙特卡罗方法显示出了更好的收敛性质。     

Optimization of quantum Monte Carlo wave functions by energy minimization

We study three wave function optimization methods based on energy minimization in a variational Monte Carlo framework: the Newton, linear, and perturbative methods. In the Newton method, the parameter variations are calculated from the energy gradient and Hessian, using a reduced variance statistical estimator for the latter. In the linear method, the parameter variations are found by diagonalizing a nonsymmetric estimator of the Hamiltonian matrix in the space spanned by the wave function and its derivatives with respect to the parameters, making use of a strong zero-variance principle. In the less computationally expensive perturbative method, the parameter variations are calculated by approximately solving the generalized eigenvalue equation of the linear method by a nonorthogonal perturbation theory. These general methods are illustrated here by the optimization of wave functions consisting of a Jastrow factor multiplied by an expansion in configuration state functions (CSFs) for the C2 molecule, including both valence and core electrons in the calculation. The Newton and linear methods are very efficient for the optimization of the Jastrow, CSF, and orbital parameters. The perturbative method is a good alternative for the optimization of just the CSF and orbital parameters. Although the optimization is performed at the variational Monte Carlo level, we observe for the C2 molecule studied here, and for other systems we have studied, that as more parameters in the trial wave functions are optimized, the diffusion Monte Carlo total energy improves monotonically, implying that the nodal hypersurface also improves monotonically.     

Parallel iterative reaction path optimization in ab initio quantum mechanical/molecular mechanical modeling of enzyme reactions

The determination of reaction paths for enzyme systems remains a great challenge for current computational methods. In this paper we present an efficient method for the determination of minimum energy reaction paths with the ab initio quantum mechanical/molecular mechanical approach. Our method is based on an adaptation of the path optimization procedure by Ayala and Schlegel for small molecules in gas phase, the iterative quantum mechanical/molecular mechanical (QM/MM) optimization method developed earlier in our laboratory and the introduction of a new metric defining the distance between different structures in the configuration space. In this method we represent the reaction path by a discrete set of structures. For each structure we partition the atoms into a core set that usually includes the QM subsystem and an environment set that usually includes the MM subsystem. These two sets are optimized iteratively: the core set is optimized to approximate the reaction path while the environment set is optimized to the corresponding energy minimum. In the optimization of the core set of atoms for the reaction path, we introduce a new metric to define the distances between the points on the reaction path, which excludes the soft degrees of freedom from the environment set and includes extra weights on coordinates describing chemical changes. Because the reaction path is represented by discrete structures and the optimization for each can be performed individually with very limited coupling, our method can be executed in a natural and efficient parallelization, with each processor handling one of the structures. We demonstrate the applicability and efficiency of our method by testing it on two systems previously studied by our group, triosephosphate isomerase and 4-oxalocrotonate tautomerase. In both cases the minimum energy paths for both enzymes agree with the previously reported paths.     

Computer Simulation of Molecular Dynamics: Methodology,Applications, and Perspectives in Chemistry

During recent decades it has become feasible to simulate the dynamics of molecular systems on a computer. The method of molecular dynamics (MD) solves Newton's equations of motion for a molecular system, which results in trajectories for all atoms in the system. From these atomic trajectories a variety of properties can be calculated. The aim of computer simulations of molecular systems is to compute macroscopic behavior from microscopic interactions. The main contributions a microscopic consideration can offer are (1) the understanding and (2) interpretation of experimental results, (3) semiquantitative estimates of experimental results, and (4) the capability to interpolate or extrapolate experimental data into regions that are only difficultly accessible in the laboratory. One of the two basic problems in the field of molecular modeling and simulation is how to efficiently search the vast configuration space which is spanned by all possible molecular conformations for the global low (free) energy regions which will be populated by a molecular system in thermal equilibrium. The other basic problem is the derivation of a sufficiently accurate interaction energy function or force field for the molecular system of interest. An important part of the art of computer simulation is to choose the unavoidable assumptions, approximations and simplifications of the molecular model and computational procedure such that their contributions to the overall inaccuracy are of comparable size, without affecting significantly the property of interest. Methodology and some practical applications of computer simulation in the field of (bio)chemistry will be reviewed.     

The tautomers of uracil: A local correlation treatment

The relative energies of all six uracil tautomers have been determined at the MP 4(SDQ )/6-31G** level, using both conventional correlation theory and the Local Correlation method. Geometries were optimized at the SCF /6-31G* level with offset forces. Comparison of our energies with energies from structures optimized at the SCF level supports the conclusion that offset forces are an advantageous alternative to correlated geometry optimization. The Local Correlation method compares very well with conventional Møller–Plesset theory, recovering at least 98.4% of the conventional correlated energy in all cases. More importantly, the relative energies also show good agreement with the conventional results, even for these delocalized systems. CPU timings show a substantial computational savings for the Local Correlation method over the conventional method. The results of the local method using Boys localization are compared with those using Pipek–Mezey localization. The dioxo tautomer ( 1 ) is predicted to be the most stable. The ( 1 )–( 3 ) and ( 1 )–( 4 ) energy differences are found to be within the bounds estimated from experimental work. © 1993 John Wiley & Sons, Inc.     

A powerful truncated Newton method for potential energy minimization

With advances in computer architecture and software, Newton methods are becoming not only feasible for large-scale nonlinear optimization problems, but also reliable, fast and efficient. Truncated Newton methods, in particular, are emerging as a versatile subclass. In this article we present a truncated Newton algorithm specifically developed for potential energy minimization. The method is globally convergent with local quadratic convergence. Its key ingredients are: (1) approximation of the Newton direction far away from local minima, (2) solution of the Newton equation iteratively by the linear Conjugate Gradient method, and (3) preconditioning of the Newton equation by the analytic second-derivative components of the “local” chemical interactions: bond length, bond angle and torsional potentials. Relaxation of the required accuracy of the Newton search direction diverts the minimization search away from regions where the function is nonconvex and towards physically interesting regions. The preconditioning strategy significantly accelerates the iterative solution for the Newton search direction, and therefore reduces the computation time for each iteration. With algorithmic variations, the truncated Newton method can be formulated so that storage and computational requirements are comparable to those of the nonlinear Conjugate Gradient method. As the convergence rate of nonlinear Conjugate Gradient methods is linear and performance less predictable, the application of the truncated Newton code to potential energy functions is promising.     

Geometry optimizations with explicit inclusion of electron correlation

Automatic techniques for geometry optimization are applied in conjunction with configuration interaction and perturbation treatments of electron correlation. The computational effort and numerical accuracy of the optimizations are discussed, as well as problems with approximate correlation methods concerning the continuity of the potential surface. The optimized geometries of fourteen molecules obtained with different correlation treatments (MNDO SCF MOs) are compared. The configuration interaction results are reproduced satisfactorily by simple perturbation approaches. The largest change of the optimized SCF geometry is found for hydrogen peroxide.     

Efficient energy based modeling and experimental validation of liquid filling in planar micro-fluidic components and networks

This paper presents a model that describes how liquid flow fills micro-fluidic components and networks. As an alternative to computational fluid dynamic (CFD) simulations, we use a constrained energy minimization approach. This approach is based on two assumptions that hold in many micro-fluidic devices: (i) The length scales are small, and we consider slow filling rates, hence fluid momentum and viscous terms are small compared to surface tension forces, consequently the liquid/gas interfaces can be viewed as a succession of quasi-steady equilibrium configurations. (ii) Any equilibrium configuration corresponds to a surface tension energy minima which is constrained by the device shape and the volume of liquid in the device. The model is developed for planar micro-fluidic devices, is based on a fundamental physical principle, and shows accurate agreement with experimental data. It takes us only a few minutes to evaluate the model for a planar component of any shape using the Surface Evolver software, and this is significantly less then the computer run time required for CFD simulations. Moreover, once a library of component models has been created (which takes less than an hour of computer time) it then takes only seconds to simulate different network architectures with thousands of components. This fast "reconfigure the network and simulate in seconds" capability is essential for the design of truly complex networks that will enable the next generation of passive, micro-fluidic, lab-on-a-chip systems.     

A microfluidic device for kinetic optimization of protein crystallization and in situ structure determination

The unprecedented economies of scale and unique mass transport properties of microfluidic devices made them viable nano-volume protein crystallization screening platforms. However, realizing the full potential of microfluidic crystallization requires complementary technologies for crystal optimization and harvesting. In this paper, we report a microfluidic device which provides a link between chip-based nanoliter volume crystallization screening and structure analysis through "kinetic optimization" of crystallization reactions and in situ structure determination. Kinetic optimization through systematic variation of reactor geometry and actuation of micromechanical valves is used to screen a large ensemble of kinetic trajectories that are not practical with conventional techniques. Using this device, we demonstrate control over crystal quality, reliable scale-up from nanoliter volume reactions, facile harvesting and cryoprotectant screening, and protein structure determination at atomic resolution from data collected in-chip.     

A comparative study of semiempirical, ab initio, and DFT methods in evaluating metal-ligand bond strength, proton affinity, and interactions between first and second shell ligands in Zn-biomimetic complexes

Although theoretical methods are now available which give very accurate results, often comparable to the experimental ones, modeling chemical or biological interesting systems often requires less demanding and less accurate theoretical methods, mainly due to computer limitations. Therefore, it is crucial to know the precision of such less reliable methods for relevant models and data. This has been done in this work for small zinc-active site models including O- (H(2)O and OH(-)) and N-donor (NH(3) and imidazole) ligands. Calculations using a number of quantum mechanical methods were carried out to determine their precision for geometries, coordination number relative stability, metal-ligand bond strengths, proton affinities, and interaction energies between first and second shell ligands. We have found that obtaining chemical accuracy can be as straightforward as HF geometry optimization with a double-zeta plus polarization basis followed by a B3LYP energy calculation with a triple-zeta quality basis set including diffuse and polarization functions. The use of levels as low as PM3 geometry optimization followed by a B3LYP single-point energy calculation with a double-zeta quality basis including polarization functions already yields useful trends in bond length, proton affinities or bond dissociation energies, provided that appropriate caution is taken with the optimized structures. The reliability of these levels of calculation has been successfully demonstrated for real biomimetic cases.     

Fully quantum mechanical energy optimization for protein-ligand structure

We present a quantum mechanical approach to study protein-ligand binding structure with application to a Adipocyte lipid-binding protein complexed with Propanoic Acid. The present approach employs a recently develop molecular fractionation with a conjugate caps (MFCC) method to compute protein-ligand interaction energy and performs energy optimization using the quasi-Newton method. The MFCC method enables us to compute fully quantum mechanical ab initio protein-ligand interaction energy and its gradients that are used in energy minimization. This quantum optimization approach is applied to study the Adipocyte lipid-binding protein complexed with Propanoic Acid system, a complex system consisting of a 2057-atom protein and a 10-atom ligand. The MFCC calculation is carried out at the Hartree-Fock level with a 3-21G basis set. The quantum optimized structure of this complex is in good agreement with the experimental crystal structure. The quantum energy calculation is implemented in a parallel program that dramatically speeds up the MFCC calculation for the protein-ligand system. Similarly good agreement between MFCC optimized structure and the experimental structure is also obtained for the streptavidin-biotin complex. Due to heavy computational cost, the quantum energy minimization is carried out in a six-dimensional space that corresponds to the rigid-body protein-ligand interaction.