pKa prediction from an ab initio bond length: part 2--phenols.

The prediction of pK(a) continues to attract much attention with ongoing investigations into new ways to predict pK(a) accurately, where predicted pK(a) values deviate less than 0.50 log units from experiment. We show that a single descriptor, i.e. an ab initio bond length, can predict pK(a). The emphasis was placed on model simplicity and a demonstration that more accurate predictions emerge from single-bond-length models. A data set of 171 phenols was studied. The carbon-oxygen bond length, connecting the OH to the phenyl ring, consistently provided accurate predictions. The pK(a) of meta- and para-substituted phenols is predicted here by a single-bond-length model within 0.50 log units. However, accurate prediction of the pK(a) of ortho-substituted phenols necessitated their splitting into groups called high-correlation subsets in which the pK(a) of the compounds strongly correlated with a single bond-length. The highly compound-specific single-bond-length models produced better predictions than models constructed with more compounds and more bond lengths. Outliers were easily identified using single-bond-length models and in most cases we were able to determine the reason for the outlier discrepancy. Furthermore, the single-bond-length models showed better cross-validation statistics than the PLS models constructed using more than one bond length. For all of the single-bond-length models, RMSEE was less than 0.50. For the majority of the models, RMSEP was less than 0.50. The results support the use of multiple high-correlation subsets and a single bond-length to predict pK(a). Six one-term linear equations are listed as a starting point for the construction of a more comprehensive list covering a larger variety of compound classes.

pKa prediction from an ab initio bond length: part 3--benzoic acids and anilines.

The prediction of pK(a) from a single ab initio bond length has been extended to provide equations for benzoic acids and anilines. The HF/6-31G(d) level of theory is used for all geometry optimisations. Similarly to phenols (Part 2 of this series of publications), the meta-/para-substituted benzoic acids can be predicted from a single model constructed from one bond length. This model had an impressive RMSEP of 0.13 pK(a) units. The prediction of ortho-substituted benzoic acids required the identification of high-correlation subsets, where the compounds in the same subset have at least one of the same (e.g. halogens, hydroxy) ortho substituent. Two pK(a) equations are provided for o-halogen benzoic acids and o-hydroxybenzoic acids, where the RMSEP values are 0.19 and 0.15 pK(a) units, respectively. Interestingly, the bond length that provided the best model differed between these two high-correlation subsets. This demonstrates the importance of investigating the most predictive bond length, which is not necessarily the bond involving the acid hydrogen. Three high-correlation subsets were identified for the ortho-substituted anilines. These were o-halogen, o-nitro and o-alkyl-substituted aniline high-correlation subsets, where the RMSEP ranged from 0.23 to 0.44 pK(a) units. The RMSEP for the meta-/para-substituted aniline model was 0.54 pK(a) units. This value exceeded our threshold of 0.50 pK(a) units and was higher than both the m-/p-benzoic acids in this work and the m-/p-phenols (RMSEP = 0.43) of Part 2. Constructing two separate models for the meta- and para- substituted anilines, where RMSEP values of 0.63 and 0.33 pK(a) units were obtained respectively, revealed it was the meta-substituted anilines that caused the large RMSEP value. For unknown reasons the RMSEP value increased with the addition of a further twenty meta-substituted anilines to this model. The C-N bond always produced the best correlations with pK(a) for all the high-correlation subsets. A higher level of theory and an ammonia probe improved the statistics only marginally for the hydroxybenzoic acid high-correlation subsets.

Convergence of the multipole expansion for 1,2 Coulomb interactions: The modified multipole shifting algorithm.

A force field that accounts for the quantum chemical reality of interacting atoms must include Coulomb interactions between bonded atoms. The short-range nature of such 1,2 interactions necessitates atomic multipole moments in addition to point charges. However, the close proximity of bonded atoms would normally lead to a divergent multipolar expansion. A special algorithm presented here, within the scope of the previously presented multipole shifting method [M. Rafat and P. L. A. Popelier, J. Chem. Phys. 124, 144102 (2006)], shows that convergence can nevertheless be achieved by a suitable selection of multipole displacements. The algorithm is applied to improve the convergence of the multipolar expansion within the quantum theory of atoms in molecules approach.

QSAR with quantum topological molecular similarity indices: toxicity of aromatic aldehydes to Tetrahymena pyriformis.

Extensive production and utilization of aromatic aldehydes and their derivatives without proper certification is alarming with regard to environmental safety. This concern motivated our construction of predictive quantitative structure-activity relationship (QSAR) models for the toxicity of aldehydes to the ecologically important species Tetrahymena pyriformis. Quantum topological molecular similarity (QTMS) descriptors, along with the lipid-water partition coefficient (log K(o/w)), were used as predictor variables. The QTMS descriptors were calculated at different levels of theory including AM1, HF/3-21G(d), HF/6-31G(d), B3LYP/6-31 + G(d,p), B3LYP/6-311 + G(2d,p) and MP2/6-311+G(2d,p). The data set of 77 aromatic aldehydes was divided into a training set (n = 58) and a test (n = 19) set, and 58 models were developed using partial least squares (PLS) and genetic partial least squares (G/PLS). We evaluated the overall predictive capacity of the models based on leave-one-out predictions for the training set compounds and model derived predictions for the test set compounds. For both PLS and G/PLS, the models built at the HF/6-31G(d) level show better predictivity (based on overall prediction) than the models developed at any of the other five levels. Further validation was also performed utilizing (process and model) randomization tests. We show that improved predictive QSAR models for aldehydic toxicity to Tetrahymena pyriformis can be generated using QTMS descriptors along with log K(o/w).

pK(a) prediction from "Quantum Chemical Topology" descriptors.

Knowing the pK(a) of a compound gives insight into many properties relevant to many industries, in particular the pharmaceutical industry during drug development processes. In light of this, we have used the theory of Quantum Chemical Topology (QCT), to provide ab initio descriptors that are able to accurately predict pK(a) values for 228 carboxylic acids. This Quantum Topological Molecular Similarity (QTMS) study involved the comparison of 5 increasingly more expensive levels of theory to conclude that HF/6-31G(d) and B3LYP/6-311+G(2d,p) provided an accurate representation of the compounds studies. We created global and subset models for the carboxylic acids using Partial Least Square (PLS), Support Vector Machines (SVM), and Radial Basis Function Neural Networks (RBFNN). The models were extensively validated using 4-, 7-, and 10-fold cross-validation, with the validation sets selected based on systematic and random sampling. HF/6-31G(d) in conjunction with SVM provided the best statistics when taking into account the large increase in CPU time required to optimize the geometries at the B3LYP/6-311+G(2d,p) level. The SVM models provided an average q(2) value of 0.886 and an RMSE value of 0.293 for all the carboxylic acids, a q(2) of 0.825 and RMSE of 0.378 for the ortho-substituted acids, a q(2) of 0.923 and RMSE of 0.112 for the para- and meta-substituted acids, and a q(2) of 0.906 and RMSE of 0.268 for the aliphatic acids. Our method compares favorably to ACD/Laboratories, VCCLAB, SPARC, and ChemAxon's pK(a) prediction software based of the RMSE calculated by the leave-one-out method.

Visualization and integration of quantum topological atoms by spatial discretization into finite elements.

We present a novel algorithm to integrate property densities over the volume of a quantum topological atom. Atoms are grown outward, starting from a sphere centered on the nucleus, by means of a finite element meshing algorithm. Bond critical points and ring critical points require special treatment. The overall philosophy as well as intricate features of this meshing algorithm are given, followed by details of the quadrature over the finite elements. An effort has been made to design a streamlined and compact algorithm, focusing on the core of challenges arising in tracing the electron density's gradient vector field. The current algorithm also generates a new type of pictures that can be a Graphical User Interface. Excellent integration errors, L(Omega), are obtained, even for atoms with (narrow) tails or sharp corners.

The effects of hydrogen-bonding environment on the polarization and electronic properties of water molecules.

Adequate representation of the interactions that take place between water molecules has long been a goal of force field design. A full understanding of how the molecular charge distribution of water is altered by adjacent water molecules and by the hydrogen-bonding environment is a vital step toward achieving this task. For this purpose we generated ab initio electron densities of pure water clusters and hydrated serine and tyrosine. Quantum chemical topology enabled the study of a well-defined water molecule inside these clusters, by means of its volume, energy, and multipole moments. Intra- and intermolecular charge transfer was monitored and related to the polarization of water in hydrogen-bonded networks. Our analysis affords a way to define different types of water molecules in clusters.

Atom-atom partitioning of total (super)molecular energy: the hidden terms of classical force fields.

Classical force fields describe the interaction between atoms that are bonded or nonbonded via simple potential energy expressions. Their parameters are often determined by fitting to ab initio energies and electrostatic potentials. A direct quantum chemical guide to constructing a force field would be the atom-atom partitioning of the energy of molecules and van der Waals complexes relevant to the force field. The authors used the theory of quantum chemical topology to partition the energy of five systems [H2, CO, H2O, (H2O)2, and (HF)2] in terms of kinetic, Coulomb, and exchange intra-atomic and interatomic contributions. The authors monitored the variation of these contributions with changing bond length or angle. Current force fields focus only on interatomic interaction energies and assume that these purely potential energy terms are the only ones that govern structure and dynamics in atomistic simulations. Here the authors highlight the importance of self-energy terms (kinetic and intra-atomic Coulomb and exchange).

QSAR models based on quantum topological molecular similarity.

A new method called quantum topological molecular similarity (QTMS) was fairly recently proposed [J. Chem. Inf. Comp. Sc., 41, 2001, 764] to construct a variety of medicinal, ecological and physical organic QSAR/QSPRs. QTMS method uses quantum chemical topology (QCT) to define electronic descriptors drawn from modern ab initio wave functions of geometry-optimised molecules. It was shown that the current abundance of computing power can be utilised to inject realistic descriptors into QSAR/QSPRs. In this article we study seven datasets of medicinal interest : the dissociation constants (pK(a)) for a set of substituted imidazolines , the pK(a) of imidazoles , the ability of a set of indole derivatives to displace [(3)H] flunitrazepam from binding to bovine cortical membranes , the influenza inhibition constants for a set of benzimidazoles , the interaction constants for a set of amides and the enzyme liver alcohol dehydrogenase , the natriuretic activity of sulphonamide carbonic anhydrase inhibitors and the toxicity of a series of benzyl alcohols. A partial least square analysis in conjunction with a genetic algorithm delivered excellent models. They are also able to highlight the active site, of the ligand or the molecule whose structure determines the activity. The advantages and limitations of QTMS are discussed.

A convergent multipole expansion for 1,3 and 1,4 Coulomb interactions.

Traditionally force fields express 1,3 and 1,4 interactions as bonded terms via potentials that involve valence and torsion angles, respectively. These interactions are not modeled by point charge terms, which are confined to electrostatic interactions between more distant atoms (1,n where n>4). Here we show that both 1,3 and 1,4 interactions can be described on the same footing as 1,n (n>4) interactions by a convergent multipole expansion of the Coulomb energy of the participating atom pairs. The atomic multipole moments are generated by the theory of quantum chemical topology. The procedure to make the multipole expansion convergent is based on a "shift procedure" described in earlier work [L. Joubert and P. L. A. Popelier, Molec. Phys. 100, 3357 (2002)].

The cytotoxicity of ortho alkyl substituted 4-X-phenols: a QSAR based on theoretical bond lengths and electron densities.

A new method called quantum topological molecular similarity (QTMS) was recently proposed [O'Brien, S. E.; Popelier, P. L. A. J. Chem. Inf. Comp. Sci.2001, 41, 764] and has been shown to be successful in a variety of medicinal, ecological and physical organic QSAR/QSPRs. QTMS method uses electronic descriptors drawn from ab initio wavefunctions of geometry-optimized molecules. We investigated a remarkable and unusual set of ortho alkyl-substituted phenols [Selassie, C. D.; Verma, R. P.; Kapur, S.; Shusterman, A. J.; Hansch, C. J. Chem. Soc., Perkin2002, II, 1112], recently studied by the Hansch group. Our results do not support their proposal that a steric factor is important in the determination of the cytotoxicity of this set of substituted phenols. Thus, we conclude that the cytotoxicity of these sterically encumbered phenols is dependent primarily on electronic and radical effects, and that steric issues do not appear to be a critical distinguishing factor.

The electrostatic potential generated by topological atoms. II. Inverse multipole moments.

Quantum chemical topology defines finite atoms, whose bounded electron density generates a well-defined electrostatic potential. A multipole expansion based on spherical tensors provides a potential that is formally convergent outside the divergence sphere. Part I of this series [P. L. A. Popelier and M. Rafat, Chem. Phys. Lett.376, 148 (2003)] showed that a continuous multipole expansion expands the convergence region, thereby allowing the electrostatic potential to be evaluated at short range. Here, we propose a different method, based on "inverse" multipole moments, enabling an expansion that converges everywhere. These moments are defined by inverse (i.e., negative) powers of the magnitude of the position vector describing the electron density inside the atom. We illustrate this technique on nitrogen in N(2), oxygen in H(2)O, and oxygen in the phenolic group of the amino acid tyrosine. The proposed method constitutes a considerable advance over the method presented in Part I.

Quantum chemical topology (QCT) descriptors as substitutes for appropriate Hammett constants.

A technique called quantum topological molecular similarity (QTMS) was recently proposed [J. Chem. Inf. Comput. Sci., 2001, 41, 764] in order to construct a variety of medicinal, ecological and physical organic QSAR/QSPRs, based on modern ab initio wave functions of geometry optimised molecules, in combination with quantum chemical topology (QCT). The current abundance of computing power can be utilised to inject realistic descriptors into QSAR/QSPRs. In previous work [J. Chem. Soc., Perkin Trans. 2, 2002, 1231] it was proven that a set of Hammett constants (sigma(p), sigma(m), sigma(I) and sigma(p)0) for a sizeable set of mono- and polysubstituted carboxylic acids can be replaced by QCT bond descriptors. Using QTMS and proper statistical validation we examined seven data sets in total. The first three sets (para-substituted phenols (sigma-), substituted toluenes (sigma+) and bromophenethylamines (sigma+)) corroborate that a wider class of Hammett constants can also be replaced by QCT descriptors. A fourth set (benzyl radicals) focuses on non-Hammett behaviour being superimposed on Hammett behaviour. QCT descriptors selectively correlate with Hammett behaviour. The QTMS analysis of the last three sets (toxicity of benzyl alcohols, chromatographic capacity factors of chalcones and herbicidal activity of 5-chloro-2,3-dicyanopyrazines) screens for false positives. This test is successfully passed in that QCT descriptors fail when lipophilicity/hydrophobicity is in charge. Hence, overall, the discriminatory capacity of QCT descriptors is established, in detecting Hammett behaviour and specifically replacing the Hammett constants by more modern and non-empirical descriptors.

Rendering of quantum topological atoms and bonds.

In this article, we describe and apply an algorithm that visualizes atoms and bonds in molecules and van der Waals complexes, based on the topology of the electron density. The theory of quantum chemical topology defines both atoms and bonds via a single consistent procedure, and enables the association of an atomic shape with an atomic property (charge, dipole moment, volume, ...). Special attention is paid to the bridging of gaps arising in interatomic surfaces, in the presence of ring critical points or high ellipticity. This algorithm, in conjunction with the graphical user interface of the computer program MORPHY enables robust and efficient rendering of complicated interatomic surfaces, as found in larger systems.

The quantum topological electrostatic potential as a probe for functional group transferability.

The electrostatic potential can be used as an appropriate and convenient indicator of how transferable an atom or functional group is between two molecules. Quantum-chemical topology (QCT) is used to define the electron density of a molecular fragment and the electrostatic potential it generates. The potential generated on a grid by the terminal aldehyde group of the biomolecule retinal is compared with the corresponding aldehyde group in smaller molecules derived from retinal. The terminal amino group in the free amino acid lysine was treated in a similar fashion. Each molecule is geometry-optimized by an ab initio calculation at B3LYP/6-311G+(2d,p)//HF/6-31G(d) level. The amino group in lysine is very little influenced by any part of the molecule further than two C atoms away. However, the aldehyde group in retinal is influenced by molecular fragments six C atoms away. This dramatic disparity is ascribed to the difference in saturation in the carbon chains; retinal contains a conjugated hydrocarbon chain but lysine an aliphatic one.

Quantitative structure-activity relationships from optimised ab initio bond lengths: steroid binding affinity and antibacterial activity of nitrofuran derivatives.

The present day abundance of cheap computing power enables the use of quantum chemical ab initio data in Quantitative Structure-Activity Relationships (QSARs). Optimised bond lengths are a new such class of descriptors, which we have successfully used previously in representing electronic effects in medicinal and ecological QSARs (enzyme inhibitory activity, hydrolysis rate constants and pKas). Here we use AM1 and HF/3-21G* bond lengths in conjunction with Partial Least Squares (PLS) and a Genetic Algorithm (GA) to predict the Corticosteroid-Binding Globulin (CBG) binding activity of the classic steroid data set, and the antibacterial activity of nitrofuran derivatives. The current procedure, which does not require molecular alignment, produces good r2 and q2 values. Moreover, it highlights regions in the common steroid skeleton deemed relevant to the active regions of the steroids and nitrofuran derivatives.

Distributed polarizability analysis for para-nitroaniline and meta-nitroaniline: functional group and charge-transfer contributions.

Topological partitioning of electronic properties is used to investigate the polarizability of para-nitroaniline and meta-nitroaniline. The distributed polarizabilities for atoms are combined into total local or generalized distributed contributions for the amino, ring, and nitro functional groups; generalized distributed group contributions have not been calculated before. The local group contributions are transferable between the two molecules only when charge transfer is suppressed, but the generalized distributed contributions prove surprisingly similar in the two molecules, apparently because they treat charge-transfer contributions explicitly.

Estimation of pKa using quantum topological molecular similarity descriptors: application to carboxylic acids, anilines and phenols.

The current availability of cheap computer power enables the construction of QSARs from modern ab initio quantum chemical data. Multivariate models for three classes of compounds are developed by means of the quantum topological molecular similarity (QTMS) tool, which incorporates descriptors originating from the "Atoms in Molecules" (AIM) theory. Correlations obtained outperform the Hammett and other traditional parameters. The advantage of QTMS over semiempirical and empirical descriptors is demonstrated by the following r(2)/q(2) values: 0.920/0.891 (acids), 0.974/0.953 (anilines), and 0.952/0.884 (phenols).

Quantitative structure-activity relationships of mutagenic activity from quantum topological descriptors: triazenes and halogenated hydroxyfuranones (mutagen-X) derivatives.

The mutagenic activity of 23 triazenes and, in a different set, of 24 halogenated hydroxyfuranones (MX derivatives) is quantitatively related to new features of contemporary molecular wave functions. Nowadays affordable computers are powerful enough to rapidly generate geometry-optimised ab initio wave functions at HF/3-21G*, HF/6-31G* and B3LYP/6-311 + G(2d,p) level for all molecules. The bonds of a common molecular skeleton are described by their ab initio bond lengths and local properties provided by the theory of quantum chemical topology (QCT). The chemometric analysis involves two types: one to generate a statistically validated quantitative model, and one to isolate the active center. In the former a genetic algorithm (GA) selects bond descriptors in order to optimise the cross-validation error, q2, followed by a full partial least squares (PLS) analysis, which also yields randomisation statistics. In the latter type principal components (PCs) are constructed from the original bond descriptors and their variables important to the projection (VIPs) are plotted in a histogram. This analysis suggests a preferred mechanistic pathway for the initial hydroxylation of the triazenes, an issue that has remained ambiguous so far. In the case of the hydroxyfuranones the proposed method aids the elucidation of a mechanistic ambivalence.

Atomic properties of selected biomolecules: quantum topological atom types of carbon occurring in natural amino acids and derived molecules.

We seek to recover rigorous atom types from amino acid wave functions. The atom types emerge from a cluster analysis operating on a set of seven atomic properties, including kinetic energy, volume, population, and dipole, quadrupole, octupole, and hexadecapole moments. These properties are acquired by partitioning the molecular electron density into quantum topological atoms. Wave functions are generated at the B3LYP/6-311+G(2d,p)//HF/6-31G(d) level for a sensible conformation of each of the 20 naturally occurring amino acids and smaller derived molecules, which together constitute a data set of 57 molecules. From this set 213 unique quantum topological carbons are obtained, which are linked according to the similarity of their properties. After introducing a statistical separation criterion, our cluster analysis proposes two representations: a cruder one with 5 atom types and a finer one with 21 atom types. The immediate coordination of the central carbon plays a major role in labeling the atom types.