Abstract-This is a survey on graph visualization and navigation techniques, as used in information visualization. Graphs appear in numerous applications such as web browsing, state-transition diagrams, and data structures. The ability to visualize and to navigate in these potentially large, abstract graphs is often a crucial part of an application. Information visualization has specific requirements, which means that this survey approaches the results of traditional graph drawing from a different perspective.

The S22 test set of interaction energies for small model complexes [Phys. Chem. Chem. Phys. 8, 1985 (2006)] has been very valuable for benchmarking new and existing methods for noncovalent interactions. However, the basis sets utilized to compute the CCSD(T) interaction energies for some of the dimers are insufficient to obtain converged results. Here we consistently extrapolate all CCSD(T)/complete basis set (CBS) interaction energies using larger basis sets for the CCSD(T) component of the computation. The revised values, which we designate S22A, represent the most accurate results to date for this set of dimers. The new values appear to be within a few hundredths of 1 kcal mol(-1) of the true CCSD(T)/CBS limit at the given geometries, but the former S22 values are off by as much as 0.6 kcal mol(-1) compared to the revised values. Because some of the most promising methods for noncovalent interactions are already achieving this level of agreement (or better) compared to the S22 data, more accurate benchmark values would clearly be helpful. The MP2, SCS-MP2, SCS-CCSD, SCS(MI)-MP2, and B2PLYP-D methods have been tested against the more accurate benchmark set. The B2PLYP-D method outperforms all other methods tested here, with a mean average deviation of only 0.12 kcal mol(-1). However, the consistent, slight underestimation of the interaction energies computed by the SCS-CCSD method (an overall mean absolute deviation and mean deviation of 0.24 and -0.23 kcal mol(-1), respectively) suggests that the SCS-CCSD method has the potential to become even more accurate with a reoptimization of its parameters for noncovalent interactions.

In benchmark-quality studies of non-covalent interactions, it is common to estimate interaction energies at the complete basis set (CBS) coupled-cluster through perturbative triples [CCSD(T)] level of theory by adding to CBS second-order perturbation theory (MP2) a "coupled-cluster correction," δ(MP2)(CCSD(T)), evaluated in a modest basis set. This work illustrates that commonly used basis sets such as 6-31G*(0.25) can yield large, even wrongly signed, errors for δ(MP2)(CCSD(T)) that vary significantly by binding motif. Double-ζ basis sets show more reliable results when used with explicitly correlated methods to form a δ(MP2-F12)(CCSD(T(*))-F12) correction, yielding a mean absolute deviation of 0.11 kcal mol(-1) for the S22 test set. Examining the coupled-cluster correction for basis sets up to sextuple-ζ in quality reveals that δ(MP2)(CCSD(T)) converges monotonically only beyond a turning point at triple-ζ or quadruple-ζ quality. In consequence, CBS extrapolation of δ(MP2)(CCSD(T)) corrections before the turning point, generally CBS (aug-cc-pVDZ,aug-cc-pVTZ), are found to be unreliable and often inferior to aug-cc-pVTZ alone, especially for hydrogen-bonding systems. Using the findings of this paper, we revise some recent benchmarks for non-covalent interactions, namely the S22, NBC10, HBC6, and HSG test sets. The maximum differences in the revised benchmarks are 0.080, 0.060, 0.257, and 0.102 kcal mol(-1), respectively.

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High-quality benchmark computations are critical for the development and assessment of approximate methods to describe noncovalent interactions. Recent advances in the treatment of dispersion by density functional theory and also the development of more efficient wave function techniques to reliably address noncovalent interactions motivate new benchmark computations of increasing accuracy. This work considers focal point approximations to estimate the complete basis set limit of coupled-cluster theory through perturbative triples [CCSD(T)/CBS] and evaluates how this approach is affected by the use or absence of counterpoise (CP) correction or, as has recently gained traction, the average of those values. Current benchmark protocols for interaction energies are computed with all CP procedures and assessed against the A24 and S22B databases and also to highly converged results for formic acid, cyanogen, and benzene dimers. Whether CP correction, no correction, or the average is favored depends upon the theoretical method, basis set, and binding motif. In recent high-quality benchmark studies, interaction energies often use second-order perturbation theory with extrapolated aug-cc-pVTZ (aTZ) and aug-cc-pVQZ (aQZ) basis sets [MP2/aTQZ] combined with a "coupled-cluster correction," δ MP2 CCSD(T), evaluated in an aug-cc-pVDZ basis. For such an approach, averaging CP-corrected and uncorrected values for the MP2 component and using CP-corrected δ MP2 CCSD(T) values offers errors more balanced among binding motifs and generally more favorable overall. Other combinations of counterpoise correction are not quite as accurate. When employing MP2/aQ5Z extrapolations and an aTZ basis for δ MP2 CCSD(T) , using CP-corrected or averaged MP2 estimates are about equally effective (and slightly superior to uncorrected MP2 values), but the counterpoise treatment of δ MP2 CCSD(T) makes little difference. Focal point estimates at this level achieve benchmark quality results otherwise accessible only with CCSD(T)/aQZ or better.

Accurate potential energy surfaces for benzene.M complexes (M = Li+, Na+, K+, and NH4+) are obtained using coupled-cluster theory through perturbative triple excitations, CCSD(T). Our computations show that off-axis cation-pi interactions, where the cation is not directly above the aromatic ring, can be favorable and may influence molecular recognition. Even perpendicular, side-on interactions retain 18-32% of their pi-face interaction energy in the gas phase, making their bond strengths comparable to hydrogen bonds in the gas phase. Solvent effects have been explored for each complex using the polarizable continuum model.

A largely unsolved problem in computational biochemistry is the accurate prediction of binding affinities of small ligands to protein receptors. We present a detailed analysis of the systematic and random errors present in computational methods through the use of error probability density functions, specifically for computed interaction energies between chemical fragments comprising a protein-ligand complex. An HIV-II protease crystal structure with a bound ligand (indinavir) was chosen as a model protein-ligand complex. The complex was decomposed into twenty-one (21) interacting fragment pairs, which were studied using a number of computational methods. The chemically accurate complete basis set coupled cluster theory (CCSD(T)/CBS) interaction energies were used as reference values to generate our error estimates. In our analysis we observed significant systematic and random errors in most methods, which was surprising especially for parameterized classical and semiempirical quantum mechanical calculations. After propagating these fragment-based error estimates over the entire protein-ligand complex, our total error estimates for many methods are large compared to the experimentally determined free energy of binding. Thus, we conclude that statistical error analysis is a necessary addition to any scoring function attempting to produce reliable binding affinity predictions.

Background: A fundamental goal of the U.S. National Institute of Health (NIH) "Roadmap" is to strengthen Translational Research, defined as the movement of discoveries in basic research to application at the clinical level. A significant barrier to translational research is the lack of uniformly structured data across related biomedical domains. The Semantic Web is an extension of the current Web that enables navigation and meaningful use of digital resources by automatic processes. It is based on common formats that support aggregation and integration of data drawn from diverse sources. A variety of technologies have been built on this foundation that, together, support identifying, representing, and reasoning across a wide range of biomedical data. The Semantic Web Health Care and Life Sciences Interest Group (HCLSIG), set up within the framework of the World Wide Web Consortium, was launched to explore the application of these technologies in a variety of areas. Subgroups focus on making biomedical data available in RDF, working with biomedical ontologies, prototyping clinical decision support systems, working on drug safety and efficacy communication, and supporting disease researchers navigating and annotating the large amount of potentially relevant literature.