Three pillars for achieving quantum mechanical molecular dynamics simulations of huge systems: Divide‐and‐conquer,density‐functional tight‐binding,and massively parallel computation

The linear‐scaling divide‐and‐conquer (DC) quantum chemical methodology is applied to the density‐functional tight‐binding (DFTB) theory to develop a massively parallel program that achieves on‐the‐fly molecular reaction dynamics simulations of huge systems from scratch. The functions to perform large scale geometry optimization and molecular dynamics with DC‐DFTB potential energy surface are implemented to the program called DC‐DFTB‐K. A novel interpolation‐based algorithm is developed for parallelizing the determination of the Fermi level in the DC method. The performance of the DC‐DFTB‐K program is assessed using a laboratory computer and the K computer. Numerical tests show the high efficiency of the DC‐DFTB‐K program, a single‐point energy gradient calculation of a one‐million‐atom system is completed within 60 s using 7290 nodes of the K computer. © 2016 Wiley Periodicals, Inc.     

Parallel implementation of efficient charge–charge interaction evaluation scheme in periodic divide‐and‐conquer density‐functional tight‐binding calculations

A low‐computational‐cost algorithm and its parallel implementation for periodic divide‐and‐conquer density‐functional tight‐binding (DC‐DFTB) calculations are presented. The developed algorithm enables rapid computation of the interaction between atomic partial charges, which is the bottleneck for applications to large systems, by means of multipole‐ and interpolation‐based approaches for long‐ and short‐range contributions. The numerical errors of energy and forces with respect to the conventional Ewald‐based technique can be under the control of the multipole expansion order, level of unit cell replication, and interpolation grid size. The parallel performance of four different evaluation schemes combining previous approaches and the proposed one are assessed using test calculations of a cubic water box on the K computer. The largest benchmark system consisted of 3,295,500 atoms. DC‐DFTB energy and forces for this system were obtained in only a few minutes when the proposed algorithm was activated and parallelized over 16,000 nodes in the K computer. The high performance using a single node workstation was also confirmed. In addition to liquid water systems, the feasibility of the present method was examined by testing solid systems such as diamond form of carbon, face‐centered cubic form of copper, and rock salt form of sodium chloride. © 2017 Wiley Periodicals, Inc.     

Rapid and accurate assessment of GPCR–ligand interactions Using the fragment molecular orbital‐based density‐functional tight‐binding method

The reliable and precise evaluation of receptor–ligand interactions and pair‐interaction energy is an essential element of rational drug design. While quantum mechanical (QM) methods have been a promising means by which to achieve this, traditional QM is not applicable for large biological systems due to its high computational cost. Here, the fragment molecular orbital (FMO) method has been used to accelerate QM calculations, and by combining FMO with the density‐functional tight‐binding (DFTB) method we are able to decrease computational cost 1000 times, achieving results in seconds, instead of hours. We have applied FMO‐DFTB to three different GPCR–ligand systems. Our results correlate well with site directed mutagenesis data and findings presented in the published literature, demonstrating that FMO‐DFTB is a rapid and accurate means of GPCR–ligand interactions. © 2017 Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Three‐body expansion of the fragment molecular orbital method combined with density‐functional tight‐binding

The three‐body fragment molecular orbital (FMO3) method is formulated for density‐functional tight‐binding (DFTB). The energy, analytic gradient, and Hessian are derived in the gas phase, and the energy and analytic gradient are also derived for polarizable continuum model. The accuracy of FMO3‐DFTB is evaluated for five proteins, sodium cation in explicit solvent, and three isomers of polyalanine. It is shown that FMO3‐DFTB is considerably more accurate than FMO2‐DFTB. Molecular dynamics simulations for sodium cation in water are performed for 100 ps, yielding radial distribution functions and coordination numbers. © 2017 Wiley Periodicals, Inc.     

Performance of density‐functional tight‐binding models in describing hydrogen‐bonded anionic‐water clusters

Density‐functional tight‐binding (DFTB) models are computationally efficient approximations to density‐functional theory that have been shown to predict reliable structural and energetic properties for various systems. In this work, the reliability and accuracy of the self‐consistent‐charge DFTB model and its recent extension(s) in predicting the structures, binding energies, charge distributions, and vibrational frequencies of small water clusters containing polyatomic anions of the Hofmeister series (carbonate, sulfate, hydrogen phosphate, acetate, nitrate, perchlorate, and thiocyanate) have been carefully and systematically evaluated on the basis of high‐level ab initio quantum‐chemistry [MP2/aug‐cc‐pVTZ and CCSD(T)/aug‐cc‐pVQZ] reference data. Comparison with available experimental data has also been made for further validation. The self‐consistent‐charge DFTB model, and even more so its recent extensions, are shown to properly account for the structural properties, energetics, intermolecular polarization, and spectral signature of hydrogen‐bonding in anionic water clusters at a fraction of the computational cost of ab initio quantum‐chemistry methods. This makes DFTB models candidates of choice for investigating much larger systems such as seeded water droplets, their structural properties, formation thermodynamics, and infrared spectra. © 2014 Wiley Periodicals, Inc.     

Studies on structure and conformational stability of free canonical 2′‐deoxyribonucleosides: Approximate SCC‐DFTB and LMP2 methods

The molecular structure of free canonical 2′‐deoxyribonucleosides have been studied by applying the electron‐correlated local second‐order Møller–Plesset perturbation theory (LMP2) and self‐consistent‐charge density‐functional tight‐binding (SCC‐DFTB) methods. The variation of structural parameters for C2, C3 endo and exo conformations, and anti, syn orientation of the base unit with furanose ring have been discussed. The relative energies have been calculated for the anti and syn conformations of dT, dC, dG, and dA. Conformational analysis has been performed using the results of the LMP2 and SCC‐DFTB methods. Chemical hardness and chemical potential have been used to study the conformational stability of the conformers. The maximum hardness principle is obeyed for the furanose ring conformations and not for the nucleosides. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Establishing effective simulation protocols for β‐ and α/β‐peptides. III. Molecular mechanical model for acyclic β‐amino acids

All‐atom molecular mechanics (MM) force field parameters are developed for the backbone of acyclic β‐amino acid using an improved version of the multiobjective evolutionary algorithm (MOEA). The MM model is benchmarked using β³‐homo‐Alanine (β³‐hAla) diamide in water with SCC‐DFTB/MM simulations as the reference. Satisfactory agreements are found between the MM and SCC‐DFTB/MM results regarding the distribution of key dihedral angles for the β³‐hAla diamide in water. The MM model is further applied to a β‐hepta‐peptide in methanol solution. The calculated NOE values and ³J coupling constants averaged over different trajectories are consistent with experimental data. By contrast, simulations using parameters directly transferred from the CHARMM22 force field for proteins lead to much worse agreement, which highlights the importance of careful parameterization for non‐natural peptides, for which the improved MOEA is particularly useful. Finally, as an initial application of the new force field parameters, the behaviors of a short random copolymer consisting of β amino acids in bulk solution and membrane/water interface are studied using a generalized Born implicit solvent model (GBSW). Results for four selected sequences show that segregation of hydrophobic and cationic groups occur easily at the membrane/solution interface for all sequences. The sequence that features alternating short blocks exhibits signs of lower stability at the interface compared to other sequences. These results confirm the hypothesis in recent experimental studies that β‐amino‐acid based random copolymers can develop a high degree of amphiphilicity without regular three‐dimensional structure. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

The self‐consistent charge density functional tight‐binding theory study of carbon adatoms using tuned Hubbard U parameters

The self‐consistent charge density functional tight‐binding (DFTB) theory is a useful tool for realizing the electronic structures of large molecular complex systems. In this study, the electronic structure of C₆₁ formed by fullerene C₆₀ with a carbon adatom is analyzed, using the fully localized limit and pseudo self‐interaction correction methods of DFTB to adjust the Hubbard U parameter (DFTB + U). The results show that both the methods used to adjust U can significantly reduce the molecular orbital energy of occupied states localized on the defect carbon atom and improve the gap between highest occupied molecular orbital(HOMO) and lowest unoccupied molecular orbital(LUMO) of C₆₁. This work will provide a methodological reference point for future DFTB calculations of the electronic structures of carbon materials.     

Automatized Parameterization of the Density‐functional Tight‐binding Method. II. Two‐center Integrals

We present an efficient numerical integration scheme (TWOCENT) to be used in the context of automatized parameterization of the density‐functional tight‐binding (DFTB) method. The accuracy of the integration process is assessed and its range of applicability is discussed. The functionality of the developed code is tested by reproducing the electronic portion of the existing mio parameter sets and by reproducing a series of reference DFT band structures of elemental solids.     

Rapid QM/MM approach for biomolecular systems under periodic boundary conditions: Combination of the density‐functional tight‐binding theory and particle mesh Ewald method

A quantum mechanical/molecular mechanical (QM/MM) approach based on the density‐functional tight‐binding (DFTB) theory is a useful tool for analyzing chemical reaction systems in detail. In this study, an efficient QM/MM method is developed by the combination of the DFTB/MM and particle mesh Ewald (PME) methods. Because the Fock matrix, which is required in the DFTB calculation, is analytically obtained by the PME method, the Coulomb energy is accurately and rapidly computed. For assessing the performance of this method, DFTB/MM calculations and molecular dynamics simulation are conducted for a system consisting of two amyloid‐β(1‐16) peptides and a zinc ion in explicit water under periodic boundary conditions. As compared with that of the conventional Ewald summation method, the computational cost of the Coulomb energy by utilizing the present approach is drastically reduced, i.e., 166.5 times faster. Furthermore, the deviation of the electronic energy is less than . © 2016 Wiley Periodicals, Inc.     

Less is more when simulating unsulfated glycosaminoglycan 3D‐structure: Comparison of GLYCAM06/TIP3P,PM3‐CARB1/TIP3P,and SCC‐DFTB‐D/TIP3P predictions with experiment

The 3D‐structure of extracellular matrix glycosaminoglycans is central to function, but is currently poorly understood. Resolving this will provide insight into their heterogeneous biological roles and help to realize their significant therapeutic potential. Glycosaminoglycan chemical isoforms are too numerous to study experimentally and simulation provides a tractable alternative. However, best practice for accurate calculation of glycosaminoglycan 3D‐structure within biologically relevant nanosecond timescales is uncertain. Here, we evaluate the ability of three potentials to reproduce experimentally observed glycosaminoglycan monosaccharide puckering, disaccharide 3D‐conformation, and characteristic solvent interactions. Temporal dynamics of unsulfated chondroitin, chondroitin‐4‐sulfate, and hyaluronan β(1→3) disaccharides were simulated within TIP3P explicit solvent unrestrained for 20 ns using the GLYCAM06 force‐field and two semi‐empirical quantum mechanics methods, PM3‐CARB1 and SCC‐DFTB‐D (both within a hybrid QM/MM formalism). Comparison of calculated and experimental properties (vicinal couplings, nuclear Overhauser enhancements, and glycosidic linkage geometries) showed that the carbohydrate‐specific parameterization of PM3‐CARB1 imparted quantifiable benefits on monosaccharide puckering and that the SCC‐DFTB‐D method (including an empirical correction for dispersion) best modeled the effects of hexosamine 4‐sulfation. However, paradoxically, the most approximate approach (GLYCAM06/TIP3P) was the best at predicting monosaccharide puckering, 3D‐conformation, and solvent interactions. Our data contribute to the debate and emerging consensus on the relative performance of these levels of theory for biological molecules. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Double Exponential Evaluation under Non‐Pseudo–First‐Order Conditions: A Mixed Second‐Order Process Followed by a First‐Order Reaction

In this paper, a double exponential approximating approach is described for a quite common kinetic model (mixed second‐order formation of an intermediate followed by its first‐order decay) under non‐pseudo–first‐order conditions (i.e., when the initial ratio of the two reactants is between 1 and 10). For the evaluation, first the exact kinetic curves predicted by the two‐step model were calculated and then fitted to a double exponential function. The goodness of the fits and the estimated parameters of the double exponential function for both I and P concentrations were determined as a function of the rate constants and initial concentrations in the two‐step model. It was found that the fit of the double exponential function is acceptable or very good under these conditions despite the fact that none of the reagents is in a large excess. Since UV–vis absorption spectroscopy is probably the most common technique to follow kinetic traces, we also made efforts to deal with the typical properties of monitoring the process through UV–vis. It was found that the experimental curves can be fitted quite well with a double exponential function if the reagents have minor absorption compared to the intermediate and/or product. The connection between the observed rate constants and the rate constants of the above‐mentioned mechanism is also studied.     

Density-functional-based molecular-dynamics simulations of molten salts

The physicochemical properties of two molten salts, namely, KCl and NaCl, have been studied with a molecular-dynamics approach using a density-functional-based tight-binding (DFTB) model. The obtained results have been compared with a number of previously reported simulations, carried out on smaller systems and using classical force-field techniques. A good agreement has been found for both structural parameters and macroscopic properties, such as self-diffusion coefficients. Furthermore, our DFTB results are very close to the available experimental data. From a more general point of view, our results demonstrate the applicability of DFTB as an efficient tool in the modeling of melts. At the same time, the quality of the obtained results supports the use of this as a reliable alternative to the more expensive ab initio dynamics approaches, if accurate parameters are provided.     

Kinetic and thermodynamic studies on molecular interaction of antipyrine donor and 2,3‐dichloro‐5,6‐dicyano‐1,4‐benzoquinone as an electron acceptor in different solvents

The charge–transfer (CT) complex of donor antipyrine with Π‐acceptor 2,3‐dichloro‐5,6‐dicyano‐1,4‐benzoquinone (DDQ) has been investigated spectrophotometrically in different halocarbon and acetonitrile solvents. The results indicated immediate formation of an electron donor–acceptor complex (DA), which is followed by two relatively slow consecutive reactions. The pseudo–first‐order rate constants for the formation of the ionic intermediate and the final product at various temperatures were evaluated from the absorbance–time data. The activation parameters, viz. activation energy, enthalpy, entropy, and free energy of activation, were computed from temperature dependence of rate constants. The stoichiometry of the complex was found to be 1:1 by Job's method of continuous variation. The formation constants of the resulting DA complexes were determined by the Benesi–Hildebrand equation at four different temperatures. The enthalpies and entropies of the complex formation reactions have been obtained by temperature dependence of the formation constants using Van't Hoff equation. The results indicate that DDQ complexes of antipyrine in all solvents are enthalpy stabilized but entropy destabilized. Both the kinetics of the interaction and the formation constants of the complexes are dependent upon the polarity of the solvents. © 2012 Wiley Periodicals, Inc. Int J Chem Kinet 45: 81–91, 2013     

Gas‐Phase Elimination Reaction of Ethyl (5‐cyanomethyl‐1,3,4‐thiadiazol‐2‐yl)carbamate: A Computational Study

The gas‐phase elimination reaction of ethyl (5‐cyanomethyl‐1,3,4‐thiadiazol‐2‐yl)carbamate has been studied computationally at the MP2/6–31++G(2d,p) level of theory. The values of the activation parameters and rate constants for the thermal decomposition were evaluated over a temperature range from 405.0 to 458.0 K. The temperature dependence of the rate constants was used to deduce the modified Arrhenius expression: log k_{405–458 K} = (9.01 ± 0.49) + (1.32 ± 0.16) log T – (6946 ± 30) 1/T, which is in good agreement with the expression obtained from experimental data. The results confirm that the mechanism is a cis‐concerted elimination that occurs in two steps: The first one corresponds to the formation of ethylene and an intermediate, 5‐(cyanomethyl)‐1,3,4‐thiadiazol‐2‐yl‐carbamic acid, via a six‐membered cyclic transition state, and the second one is the decarboxylation of this intermediate via a four‐membered cyclic transition step, leading to carbon dioxide and the corresponding 1,3,4‐thiadiazole derivative (5‐amino‐1,3,4‐thiadiazole‐2‐acetonitrile). The connectivity of transition states with their respective minima was verified through intrinsic reaction coordinate calculations, and the progress of the reaction was followed by means of Wiberg bond indices, resulting that both transition states have an “early” character, nearer to the reactants than to the products.     

Frequency‐Response Evidence for Parallel Diffusion Processes in the Bimodal Micropore System of an Activated Carbon

The rates of mass transport of gases such as propane, carbon dioxide, and ammonia have been studied in an activated carbon sorbent. The frequency‐response (FR) method was used to measure these rates. Small‐angle X‐ray scattering (SAXS) and nitrogen‐adsorption isotherm at 77 K showed that the activated carbon contains small micropores with diameters around 0.64 and 0.92 nm, respectively. The FR‐rate spectra distinguished two parallel diffusion processes with different time constants, suggesting that the smaller and the larger micropores were not interconnected.     

Computerized implementation of higher‐order electron‐correlation methods and their linear‐scaling divide‐and‐conquer extensions

We have implemented a linear‐scaling divide‐and‐conquer (DC)‐based higher‐order coupled‐cluster (CC) and Møller–Plesset perturbation theories (MPPT) as well as their combinations automatically by means of the tensor contraction engine, which is a computerized symbolic algebra system. The DC‐based energy expressions of the standard CC and MPPT methods and the CC methods augmented with a perturbation correction were proposed for up to high excitation orders [e.g., CCSDTQ, MP4, and CCSD(2)_TQ]. The numerical assessment for hydrogen halide chains, polyene chains, and first coordination sphere (C1) model of photoactive yellow protein has revealed that the DC‐based correlation methods provide reliable correlation energies with significantly less computational cost than that of the conventional implementations. © 2017 Wiley Periodicals, Inc.