Paul L. A. Popelier

MORPHY, a program for an automated "atoms in molecules" analysis

The operating manual for a structured FORTAN 77 program called MORPHY is presented. This code performs an automated topological analysis of a molecular electron density and its Laplacian. The program is written in a stylistically homogeneous, transparant and modular manner. The input is compact but flexible and allows for multiple jobs in one deck. The output is detailed and has an attractive lay-out. Critical points in the charge density and its Laplacian can be located in a robust and economic way and are displayed via an external on-line visualisation package. The gradient vector field of the charge density can be traced with great accuracy, planar contour, relief and one-dimensional line plots of many scalar properties can be generated. Non-bonded radii are calculated and analytical expressions for interatomic surfaces are computed (with error estimates) and plotted. MORPHY is interfaced with the AIMPAC suite of programs. The capabilities of the program are illustrated with two test runs and five selected figures.

THE EXISTENCE OF AN INTRAMOLECULAR C-H-O HYDROGEN-BOND IN CREATINE AND CARBAMOYL SARCOSINE

Abstract The theory of atoms in molecules demonstrates the existence of an intramolecular hydrogen bond between a methyl group and a negatively charged oxygen in the biomolecules creatine and its competitive inhibitor carbamoyl sarcosine. In addition to the topological evidence, other properties of the charge density are in quantitative agreement with those previously found for intermolecular hydrogen bonding. It is suggested that this hydrogen bond provides a prestabilization of the hydrolysis product sarcosine. The analysis of the charge density presented here and its correlation with properties of a hydrogen bond, including its dissociation energy, can be applied to experimentally determined charge distributions.

A robust algorithm to locate automatically all types of critical points in the charge density and its Laplacian

Abstract The location of critical points in the charge density and its Laplacian using the Newton—Raphson technique can be unsatisfactory for molecules and molecular complexes with a more challenging topology. An eigenvector following method is proposed to locate reliably all types of critical points without the need for good starting points. A completely automatic algorithm for the full analysis of critical points has been implemented in the program MORPHY.

On the full topology of the Laplacian of the electron density

Abstract In this work we briefly review the use of the function L ( r ), which is defined as minus the Laplacian of the electron density, ∇ 2 ρ , in the context of the theory of ‘atoms in molecules’. The topology of L ( r ) can be almost faithfully mapped onto the electron pairs of the VSEPR model. The computation of the gradient vector field L ( r ) opens new avenues for the further quantification of this mapping. Although major questions are still outstanding this contribution explores for the first time the full topology of L ( r ) for a molecule. In water there are four regions: the Core Shell Charge Concentration (CSCC), the Core Shell Charge Depletion (CSCD), the Valence Shell Charge Concentration (VSCC) and the Valence Shell Charge Depletion (VSCD). Each region has a set of L ( r ) critical points coagulating in a graph, except the CSCC. In analogy with the topology of the electron density we propose the term basin interaction line for the pair of gradient paths linking two basins in L ( r ), and the term interbasin surface for the surface separating two basins. We present a systematic study of the water molecule, which possesses 43 critical points in L ( r ). The question is raised how a basin in L ( r ) can be linked with the domain of the VSEPR model.

Potential energy surfaces fitted by artificial neural networks

Molecular mechanics is the tool of choice for the modeling of systems that are so large or complex that it is impractical or impossible to model them by ab initio methods. For this reason there is a need for accurate potentials that are able to quickly reproduce ab initio quality results at the fraction of the cost. The interactions within force fields are represented by a number of functions. Some interactions are well understood and can be represented by simple mathematical functions while others are not so well understood and their functional form is represented in a simplistic manner or not even known. In the last 20 years there have been the first examples of a new design ethic, where novel and contemporary methods using machine learning, in particular, artificial neural networks, have been used to find the nature of the underlying functions of a force field. Here we appraise what has been achieved over this time and what requires further improvements, while offering some insight and guidance for the development of future force fields.

An investigation of the conductivity of peptide nanotube networks prepared by enzyme-triggered self-assembly

We demonstrate that nanotubular networks formed by enzyme-triggered self-assembly of Fmoc-L3 (9-fluorenylmethoxycarbonyl-tri-leucine) show significant charge transport. FT-IR, fluorescence spectroscopy and wide angle X-ray scattering (WAXS) data confirm formation of beta-sheets that are locked together viapi-stacking interactions. Molecular dynamics simulations confirmed the pi-pi stacking distance between fluorenyl groups to be 3.6-3.8 A. Impedance spectroscopy demonstrated that the nanotubular xerogel networks possess minimum sheet resistances of 0.1 MOmega/sq in air and 500 MOmega/sq in vacuum (pressure: 1.03 mbar) at room temperature, with the conductivity scaling linearly with the mass of peptide in the network. These materials may provide a platform to interface biological components with electronics.

A method to integrate an atom in a molecule without explicit representation of the interatomic surface

A method to obtain accurate integrated properties according to the theory of “Atoms in Molecules” for any atom is proposed. Classical integration algorithms using explicit representations of the interatomic surfaces (IAS) bounding the integrated atom suffer from the presence of regions where the charge density is extremely flat. This phenomenon is typically caused by ring critical points and leads to unacceptable integration errors. The present paper extends a previously published integration algorithm (Mol. Phys. 87 (1996) 1169) by introducing a procedure that can find an atomic boundary if the interatomic surface is not explicitly known. This hybrid algorithm — which uses analytical interatomic surfaces whenever they are available and adequate but does not necessarily require them — enables the accurate and efficient integration of any atom. A robust and effective code is implemented in MORPHY97 and applied to two representative examples.

Atom–atom partitioning of intramolecular and intermolecular Coulomb energy

An atom–atom partitioning of the (super)molecular Coulomb energy is proposed on the basis of the topological partitioning of the electron density. Atom–atom contributions to the molecular intra- and intermolecular Coulomb energy are computed exactly, i.e., via a double integration over atomic basins, and by means of the spherical tensor multipole expansion, up to rank L=lA+lB+1=5. The convergence of the multipole expansion is able to reproduce the exact interaction energy with an accuracy of 0.1–2.3 kJ/mol at L=5 for atom pairs, each atom belonging to a different molecule constituting a van der Waals complex, and for nonbonded atom–atom interactions in single molecules. The atom–atom contributions do not show a significant basis set dependence (3%) provided electron correlation and polarization basis functions are included. The proposed atom–atom Coulomb interaction energy can be used both with post-Hartree–Fock wave functions and experimental charge densities in principle. The Coulomb interaction energy ...

Quantum molecular similarity. 3. QTMS descriptors.

Building on the ideas of a previous paper [part 1, J. Phys. Chem. A 1999, 103, 2883] we present a new molecular similarity method based on the topology of the electron density. This method is directly applicable to QSARs and is called quantum topological molecular similarity (QTMS). It has been tested for five sets of carboxylic systems including para- and meta-benzoic acid, para-phenylacetic acid, 4-X-bicyclo[2.2.2]octane-1-carboxylic acids, and polysubstituted benzoic acids. In combination with the partial least squares (PLS) procedure QTMS is able to produce excellent and statistically valid regressions. It is shown that QTMS avoids certain challenges of traditional Carbó-like similarity indices. Finally, QTMS is able to suggest a molecular fragment that contains the active center or the part of the molecule that is responsible for the QSAR.

Optimal construction of a fast and accurate polarisable water potential based on multipole moments trained by machine learning

To model liquid water correctly and to reproduce its structural, dynamic and thermodynamic properties warrants models that account accurately for electronic polarisation. We have previously demonstrated that polarisation can be represented by fluctuating multipole moments (derived by quantum chemical topology) predicted by multilayer perceptrons (MLPs) in response to the local structure of the cluster. Here we further develop this methodology of modeling polarisation enabling control of the balance between accuracy, in terms of errors in Coulomb energy and computing time. First, the predictive ability and speed of two additional machine learning methods, radial basis function neural networks (RBFNN) and Kriging, are assessed with respect to our previous MLP based polarisable water models, for water dimer, trimer, tetramer, pentamer and hexamer clusters. Compared to MLPs, we find that RBFNNs achieve a 14-26% decrease in median Coulomb energy error, with a factor 2.5-3 slowdown in speed, whilst Kriging achieves a 40-67% decrease in median energy error with a 6.5-8.5 factor slowdown in speed. Then, these compromises between accuracy and speed are improved upon through a simple multi-objective optimisation to identify Pareto-optimal combinations. Compared to the Kriging results, combinations are found that are no less accurate (at the 90th energy error percentile), yet are 58% faster for the dimer, and 26% faster for the pentamer.