Efficient methods for the quantum chemical treatment of protein structures: The effects of London-dispersion and basis-set incompleteness on peptide and water-cluster geometries

We demonstrate how quantum chemical Hartree-Fock (HF) or density functional theory (DFT) optimizations with small basis sets of peptide and water cluster structures are decisively improved if London-dispersion effects, the basis-set-superposition error (BSSE), and other basis-set incompleteness errors are addressed. We concentrate on three empirical corrections to these problems advanced by Grimme and co-workers that lead to computational strategies that are both accurate and efficient. Our analysis encompasses a reoptimized version of Hobza's P26 set of tripeptide structures, a new test set of conformers of cysteine dimers, and isomers of the water hexamer. These systems reflect features commonly found in protein crystal structures. In all cases, we recommend Grimme's DFT-D3 correction for London-dispersion. We recommend usage of large basis sets such as cc-pVTZ whenever possible to reduce any BSSE effects and, if this is not possible, to use Grimme's gCP correction to account for BSSE when small basis sets are used. We demonstrate that S-S and C-S bond lengths are very prone to basis-set incompleteness and that polarization functions should always be used on S atoms. At the double-ζ level, the PW6B95-D3-gCP DFT method combined with the SVP and 6-31G* basis sets yields accurate results. Alternatively, the HF-D3-gCP/SV method is recommended, with inclusion of polarization functions for S atoms only. Minimal basis sets offer an intriguing route to highly efficient calculations, but due to significant basis-set incompleteness effects, calculated bond lengths are seriously overestimated, making applications to large proteins very difficult, but we show that Grimme's newest HF-3c correction overcomes this problem and so makes this computational strategy very attractive. Our results provide a useful guideline for future applications to the optimization, quantum refinement, and dynamics of large proteins. © 2013 American Chemical Society

Problems, successes and challenges for the application of dispersion-corrected density-functional theory combined with dispersion-based implicit solvent models to large-scale hydrophobic self-assembly and polymorphism

© 2015 Taylor & Francis. The recent advent of dispersion-corrected density-functional theory (DFT) methods allows for quantitative modelling of molecular self-assembly processes, and we consider what is required to develop applications to the formation of large self-assembled monolayers (SAMs) on hydrophobic surfaces from organic solution. Focus is on application of the D3 dispersion correction of Grimme combined with the solvent dispersion model of Floris, Tomasi and Pascual-Ahuir to simulate observed scanning-tunnelling microscopy (STM) images of various polymorphs of tetraalkylporphyrin SAMs on highly oriented pyrolytic graphite surfaces. The most significant problem is identified as the need to treat SAM structures that are incommensurate with those of the substrate, providing a challenge to the use of traditional periodic-imaging boundary techniques. Using nearby commensurate lattices introduces non-systematic errors into calculated lattice constants and free energies of SAM formation that are larger than experimental uncertainties and polymorph differences. Developing non-periodic methods for polymorph interface simulation also remains a challenge. Despite these problems, existing methods can be used to interpret STM images and SAM atomic structures, distinguishing between multiple feasible polymorph types. They also provide critical insight into the factors controlling polymorphism. All this stems from a delicate balance that the intermolecular D3 and solvent Floris, Tomasi and Pascual-Ahuir corrections provide. Combined optimised treatments should yield fully quantitative approaches in the future

Algorithm Engineering in Robust Optimization

Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions. To this end we go through the algorithm engineering cycle of design and analysis of concepts, development and implementation of algorithms, and theoretical and experimental evaluation. We show that many ideas of algorithm engineering have already been applied in publications on robust optimization. Most work on robust optimization is devoted to analysis of the concepts and the development of algorithms, some papers deal with the evaluation of a particular concept in case studies, and work on comparison of concepts just starts. What is still a drawback in many papers on robustness is the missing link to include the results of the experiments again in the design

From chaos to order: Chain-length dependence of the free energy of formation of meso-tetraalkylporphyrin self-assembled monolayer polymorphs

© 2016 American Chemical Society. We demonstrate that systematic errors can be reduced and physical insight gained through investigation of the dependence of free energies for meso-tetraalkylporphyrin self-assembled monolayers (SAMs) polymorphism on the alkyl chain length m. These SAMs form on highly ordered pyrolytic graphite (HOPG) from organic solution, displaying manifold densities and atomic structures. SAMs with m = 11-19 are investigated experimentally while those with m = 6-28 are simulated using density-functional theory (DFT). It is shown that, for m = 15 or more, the alkyl chains crystallize to dominate SAM structure. Meso-tetraalkylporphyrin SAMs of length less than 11 have never been observed, a presumed effect of inadequate surface attraction. Instead, we show that free energies of SAM formation actually enhance as the chain length decreases. The inability to image regular SAMs stems from the appearance of many polymorphic forms of similar free energy, preventing SAM ordering. We also demonstrate a significant odd/even effect in SAM structure arising from packing anomalies. Comparison of the chain-length dependence of formation free energies allows the critical dispersion interactions between molecules, solvent, and substrate to be directly examined. Interpretation of the STM data combined with measured enthalpies indicates that Grimme's D3 explicit-dispersion correction and the implicit solvent correction of Floris, Tomasi and Pascual Ahuir are both quantitatively accurate and very well balanced to each other

Genetic evidence for multiple invasions of subterranean termites into Canada

Modern quantum chemical electronic structure methods typically applied to localized chemical bonding are developed to predict atomic structures and free energies for meso-Tetraalkylporphyrin self-Assembled monolayer (SAM) polymorph formation from organic solution on highly ordered pyrolytic graphite surfaces. Large polymorphdependent dispersion-induced substrate-molecule interactions (e.g., -100 kcal mol-1 to -150 kcal mol-1 for tetratrisdecylporphyrin) are found to drive SAM formation, opposed nearly completely by large polymorph-dependent dispersion-induced solvent interactions (70- 110 kcal mol-1) and entropy effects (25-40 kcal mol-1 at 298 K) favoring dissolution. Dielectric continuum models of the solvent are used, facilitating consideration of many possible SAM polymorphs, along with quantum mechanical/molecular mechanical and dispersion- corrected density functional theory calculations. These predict and interpret newly measured and existing high-resolution scanning tunnelling microscopy images of SAM structure, rationalizing polymorph formation conditions. A wide range of molecular condensed matter properties at room temperature now appear suitable for prediction and analysis using electronic structure calculations

Global hybrids from the semiclassical atom theory satisfying the local density linear response

We propose global hybrid approximations of the exchange-correlation (XC) energy functional which reproduce well the modified fourth-order gradient expansion of the exchange energy in the semiclassical limit of many-electron neutral atoms and recover the full local density approximation (LDA) linear response. These XC functionals represent the hybrid versions of the APBE functional [Phys. Rev. Lett. 106, 186406, (2011)] yet employing an additional correlation functional which uses the localization concept of the correlation energy density to improve the compatibility with the Hartree-Fock exchange as well as the coupling-constant-resolved XC potential energy. Broad energetical and structural testings, including thermochemistry and geometry, transition metal complexes, non-covalent interactions, gold clusters and small gold-molecule interfaces, as well as an analysis of the hybrid parameters, show that our construction is quite robust. In particular, our testing shows that the resulting hybrid, including 20\% of Hartree-Fock exchange and named hAPBE, performs remarkably well for a broad palette of systems and properties, being generally better than popular hybrids (PBE0 and B3LYP). Semi-empirical dispersion corrections are also provided.Comment: 12 pages, 4 figure

Accurate quantum chemical energies for tetrapeptide conformations: why MP2 data with an insufficient basis set should be handled with caution

This article discusses potential problems if the widely-applied MP2 approach is used in such situations with basis sets of insufficient size

Susceptibility of optimal train schedules to stochastic disturbances of process times

This work focuses on the stochastic evaluation of train schedules computed by a microscopic scheduler of railway operations based on deterministic information. The research question is to assess the degree of sensitivity of various rescheduling algorithms to variations in process times (running and dwell times). In fact, the objective of railway traffic management is to reduce delay propagation and to increase disturbance robustness of train schedules at a network scale. We present a quantitative study of traffic disturbances and their effects on the schedules computed by simple and advanced rescheduling algorithms. Computational results are based on a complex and densely occupied Dutch railway area; train delays are computed based on accepted statistical distributions, and dwell and running times of trains are subject to additional stochastic variations. From the results obtained on a real case study, an advanced branch and bound algorithm, on average, outperforms a First In First Out scheduling rule both in deterministic and stochastic traffic scenarios. However, the characteristic of the stochastic processes and the way a stochastic instance is handled turn out to have a serious impact on the scheduler performance

S66: A Well-balanced Database of Benchmark Interaction Energies Relevant to Biomolecular Structures

With numerous new quantum chemistry methods being developed in recent years and the promise of even more new methods to be developed in the near future, it is clearly critical that highly accurate, well-balanced, reference data for many different atomic and molecular properties be available for the parametrization and validation of these methods. One area of research that is of particular importance in many areas of chemistry, biology, and material science is the study of noncovalent interactions. Because these interactions are often strongly influenced by correlation effects, it is necessary to use computationally expensive high-order wave function methods to describe them accurately. Here, we present a large new database of interaction energies calculated using an accurate CCSD(T)/CBS scheme. Data are presented for 66 molecular complexes, at their reference equilibrium geometries and at 8 points systematically exploring their dissociation curves; in total, the database contains 594 points: 66 at equilibrium geometries, and 528 in dissociation curves. The data set is designed to cover the most common types of noncovalent interactions in biomolecules, while keeping a balanced representation of dispersion and electrostatic contributions. The data set is therefore well suited for testing and development of methods applicable to bioorganic systems. In addition to the benchmark CCSD(T) results, we also provide decompositions of the interaction energies by means of DFT-SAPT calculations. The data set was used to test several correlated QM methods, including those parametrized specifically for noncovalent interactions. Among these, the SCS-MI-CCSD method outperforms all other tested methods, with a root-mean-square error of 0.08 kcal/mol for the S66 data set

Random-phase approximation and its applications in computational chemistry and materials science

The random-phase approximation (RPA) as an approach for computing the electronic correlation energy is reviewed. After a brief account of its basic concept and historical development, the paper is devoted to the theoretical formulations of RPA, and its applications to realistic systems. With several illustrating applications, we discuss the implications of RPA for computational chemistry and materials science. The computational cost of RPA is also addressed which is critical for its widespread use in future applications. In addition, current correction schemes going beyond RPA and directions of further development will be discussed.Comment: 25 pages, 11 figures, published online in J. Mater. Sci. (2012