Michel Rafat

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 densitys gradient vector field. The current algorithm also generates a new type of pictures that can be a Graphical User Interface. Excellent integration errors, L(Ω), are obtained, even for atoms with (narrow) tails or sharp corners.

The electrostatic potential generated by topological atoms: A continuous multipole method leading to larger convergence regions

The electrostatic potential generated by an atom in a molecule can be conveniently expressed by traditional multipole expansions. The disadvantage of such expansions is that they introduce a divergence sphere within which the expansion diverges. Because of their finite size, atoms defined according to quantum chemical topology (QCT) yield a small divergence sphere. However the introduction of an alternative continuous multipole expansion reduces the divergence region even further. The new method allows the electrostatic potential to be evaluated accurately at short-range, which is illustrated for a pair of simple molecules.

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).

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.

Long range behavior of high‐rank topological multipole moments

The construction of a high‐rank multipolar force field (for peptides) is a complex task, leading to several intermediate questions in need of a clear answer. Here we focus on the convergence of the (electrostatic) multipolar expansion at medium and long range. Using molecular electron densities, quantum chemical topology (QCT) defines the atoms as finite volumes, each endowed with multipole moments. The terms in the multipole expansion are grouped according to powers of the internuclear distance, R−L. Given two atom types at a given distance, we determine which rank (L) is necessary for the electrostatic energy to converge to the exact interaction energy within a certain error. With this information, the rank of the expansion for each interaction can be adapted to the required accuracy and the available computing power.