The optimum contraction of basis sets for calculating spin–spin coupling constants

The previously proposed pcJ-n basis sets, optimized for calculating indirect nuclear spin–spin coupling constants using density functional methods, are re-evaluated for finding the optimum contraction scheme as a compromise between computational efficiency and minimizing contraction errors. An exhaustive search is performed for the H₂, F₂ and P₂ molecules, and candidates for optimum contraction schemes are evaluated for a larger test set of 21 molecules. Using the criterion that the contraction error should not exceed the basis set error relative to the basis set limit, the optimum contraction is defined for each basis set. The results show that it is difficult to contract basis sets for calculating spin–spin coupling constants to any significant degree without losing the inherent accuracy. The work provides guidelines for searching for optimum contraction schemes for other properties and/or at theoretical levels where a systematic search is impractical.     

Truncation of the correlation consistent basis sets: an effective approach to the reduction of computational cost?

The systematic reduction of commonly used basis sets as a means to reduce computational cost is examined for a small test set of molecules, which includes H(2), CH(4), NH(3), H(2)O, HF, and HCN. Coupled cluster with single, double, and quasiperturbative triple excitations calculations were performed using both the correlation consistent basis sets, and a set of systematically reduced basis sets to examine both the impact of the reduction upon the accuracy of the structures and energies, and the computational cost savings achieved. The effect of several truncation scenarios upon basis set convergence is also examined. Overall, for the systems studied, a reduction can occur which preserves the well-established systematic convergence behavior of the correlation consistent basis sets.     

Are predefined decoy sets of ligand poses able to quantify scoring function accuracy?

Due to the large number of different docking programs and scoring functions available, researchers are faced with the problem of selecting the most suitable one when starting a structure-based drug discovery project. To guide the decision process, several studies comparing different docking and scoring approaches have been published. In the context of comparing scoring function performance, it is common practice to use a predefined, computer-generated set of ligand poses (decoys) and to reevaluate their score using the set of scoring functions to be compared. But are predefined decoy sets able to unambiguously evaluate and rank different scoring functions with respect to pose prediction performance? This question arose when the pose prediction performance of our piecewise linear potential derived scoring functions (Korb et al. in J Chem Inf Model 49:84–96, 2009) was assessed on a standard decoy set (Cheng et al. in J Chem Inf Model 49:1079–1093, 2009). While they showed excellent pose identification performance when they were used for rescoring of the predefined decoy conformations, a pronounced degradation in performance could be observed when they were directly applied in docking calculations using the same test set. This implies that on a discrete set of ligand poses only the rescoring performance can be evaluated. For comparing the pose prediction performance in a more rigorous manner, the search space of each scoring function has to be sampled extensively as done in the docking calculations performed here. We were able to identify relative strengths and weaknesses of three scoring functions (ChemPLP, GoldScore, and Astex Statistical Potential) by analyzing the performance for subsets of the complexes grouped by different properties of the active site. However, reasons for the overall poor performance of all three functions on this test set compared to other test sets of similar size could not be identified.     

Unified treatment of electric multipole transition radial matrix elements using radial parts of STO and complete orthonormal sets of ψα-ETO

A new method is proposed for evaluating electric multipole transition radial (EMTR) matrix elements of the hydrogen-like atoms using the expansion formulae suggested by one of the authors for the radial parts of ψ^α-exponential type orbitals (ψ^α-ETO) in terms of radial parts of Slater type orbitals (STO), where α is the frictional quantum number (?∞<α≤2). A comparative study is carried out between the proposed analytical computations and other numerical simulations. The effectiveness and accuracy of the obtained analytical expressions are demonstrated by calculation of concrete cases.     

Reduced–size polarized basis sets for calculations of molecular electric properties. III. Second–row atoms

Reduced–size polarized (ZmPolX) basis sets are developed for the second–row atoms X = Si, P, S, and Cl. The generation of these basis sets follows from a simple physical model of the polarization effect of the external electric field which leads to highly compact polarization functions to be added to the chosen initial basis set. The performance of the ZmPolX sets has been investigated in calculations of molecular dipole moments and polarizabilities. Only a small deterioration of the quality of the calculated molecular electric properties has been found. Simultaneously the size of the present reduced–size ZmPolX basis sets is about one-third smaller than that of the usual polarized (PolX) sets. This reduction considerably widens the range of applications of the ZmPolX sets in calculations of molecular dipole moments, dipole polarizabilities, and related properties.     

Auxiliary basis sets for density fitting second-order Møller-Plesset perturbation theory: correlation consistent basis sets for the 5d elements Hf-Pt

Auxiliary basis sets specifically matched to the correlation consistent cc-pVnZ-PP, cc-pwCVnZ-PP, aug-cc-pVnZ-PP, and aug-cc-pwCVnZ-PP orbital basis sets (used in conjunction with pseudopotentials) for the 5d transition metal elements Hf-Pt have been optimized for use in density fitting second-order M?ller-Plesset perturbation theory and other correlated ab initio methods. Calculations of the second-order M?ller-Plesset perturbation theory correlation energy, for a test set of small to medium sized molecules, indicate that the density fitting error when utilizing these sets is negligible at three to four orders of magnitude smaller than the orbital basis set incompleteness error.     

Relativistic Gaussian basis sets for the elements K – Uuo

A series of energy-minimized relativistic Gaussian basis sets for the elements with atomic numbers 19–118 is presented. The basis sets have been derived at the self-consistent field level as weighted average energies of the respective electronic configurations. A spherical Gaussian charge distribution has been used to model the nucleus. The basis sets are constructed as interleaving dual family sets with shared exponents within each family. The quality of the basis sets is better than double zeta. Received: 7 July 2000 / Accepted: 21 September 2000 / Published online: 21 December 2000     

Semi-automated alignment and quantification of peaks using parallel factor analysis for comprehensive two-dimensional liquid chromatography–diode array detector data sets

Parallel factor analysis was used to quantify the relative concentrations of peaks within four-way comprehensive two dimensional liquid chromatography–diode array detector data sets. Since parallel factor analysis requires that the retention times of peaks between each injection are reproducible, a semi-automated alignment method was developed that utilizes the spectra of the compounds to independently align the peaks without the need for a reference injection. Peak alignment is achieved by shifting the optimized chromatographic component profiles from a three-way parallel factor analysis model applied to each injection. To ensure accurate shifting, components are matched up based on their spectral signature and the position of the peak in both chromatographic dimensions. The degree of shift, for each peak, is determined by calculating the distance between the median data point of the respective dimension (in either the second or first chromatographic dimension) and the maximum data point of the peak furthest from the median. All peaks that were matched to this peak are then aligned to this common retention data point. Target analyte recoveries for four simulated data sets were within 2% of 100% recovery in all cases. Two different experimental data sets were also evaluated. Precision of quantification of two spectrally similar and partially coeluting peaks present in urine was as good as or better than 4%. Good results were also obtained for a challenging analysis of phenytoin in waste water effluent, where the results of the semi-automated alignment method agreed with the reference LC–LC MS/MS method within the precision of the methods.     

From bird’s eye views to molecular communities: two-layered visualization of structure–activity relationships in large compound data sets

The analysis of structure–activity relationships (SARs) becomes rather challenging when large and heterogeneous compound data sets are studied. In such cases, many different compounds and their activities need to be compared, which quickly goes beyond the capacity of subjective assessments. For a comprehensive large-scale exploration of SARs, computational analysis and visualization methods are required. Herein, we introduce a two-layered SAR visualization scheme specifically designed for increasingly large compound data sets. The approach combines a new compound pair-based variant of generative topographic mapping (GTM), a machine learning approach for nonlinear mapping, with chemical space networks (CSNs). The GTM component provides a global view of the activity landscapes of large compound data sets, in which informative local SAR environments are identified, augmented by a numerical SAR scoring scheme. Prioritized local SAR regions are then projected into CSNs that resolve these regions at the level of individual compounds and their relationships. Analysis of CSNs makes it possible to distinguish between regions having different SAR characteristics and select compound subsets that are rich in SAR information.     

Revised relativistic basis sets for the 5d elements Hf–Hg

The relativistic double-zeta (dz) and triple-zeta (tz) basis sets for the 5d elements Hf–Hg have been revised for consistency with the recently optimized 4f basis sets. The new dz basis sets have 24 s functions instead of 22 s functions, and the new tz basis sets have 30 s functions instead of 29 s functions. New contraction patterns have been determined, including the 6p orbital.     

Optimized effective potential method: is it possible to obtain an accurate representation of the response function for finite orbital basis sets?

The optimized effective potential (OEP) equations are solved in a matrix representation using the orbital products of occupied and virtual orbitals for the representation of both the local potential and the response function. This results in a direct relationship between the matrix elements of local and nonlocal operators for the exchange-correlation potential. The effect of the truncation of the number of such products in the case of finite orbital basis sets on the OEP orbital and total energies and on the spectrum of eigenvalues of the response function is examined. Test calculations for Ar and Ne show that rather large AO basis sets are needed to obtain an accurate representation of the response function.     

Do B3LYP and CCSDT predict different hydrosilylation mechanisms? Influences of theoretical methods and basis sets on relative energies in ruthenium-silylene-catalyzed ethylene hydrosilylation

A series of density functional theory (DFT) and wave function theory (WFT) methods were used in conjunction with a series of basis sets to investigate the influence of the computational methodology on the relative energies of key intermediates and transition states in potential reaction pathways in ruthenium-silylene-catalyzed hydrosilylation reactions. A variety of DFT methods in a modest basis set and B3LYP calculations in a variety of basis sets calculated the key transition in the Glaser-Tilley (GT) pathway to be energetically favored. In contrast, with the smaller basis sets, the CCSD(T) method calculated the Chalk-Harrod (CH) pathway to be favored; however, CCSD(T) results extrapolated to larger basis sets favored the GT pathway.     

How to estimate moments and quantiles of environmental data sets with non-detected observations? A case study on volatile organic compounds in marine water samples

Concentrations of 27 priority volatile organic compounds were measured in water samples of the North Sea and Scheldt estuary during a 3-year monitoring study. Despite the use of a sensitive analytical method, a number of data were censored. That is, some concentrations were below the decision limit or critical level defined by IUPAC. To characterize the observed measurement results, an attempt was made to identify an appropriate procedure to compute summary statistics for the censored data sets. Several parametric and robust parametric approaches based on the maximum likelihood principle and probability-plot regression method were evaluated for the estimation of the mean, standard deviation, median and interquartile range using three uncensored analytes (1,1,2-trichloroethane, tetrachloroethene and o-xylene) from the monitoring survey. Performance was assessed by artificially censoring the observed concentrations and estimating moments and quantiles at each censoring level. Results showed that methods with the least distributional assumptions, such as the robust bias-corrected restricted maximum likelihood method, perform best for estimating the mean and standard deviation, while both parametric and robust parametric techniques can be used for quantiles. Hence, summary statistics could be estimated with little bias (5-10%) up to 80% of censoring for the data sets employed in this study.