The local single particle momentum is proposed as a localized-electrons detector (LED) that provides a direct three-dimensional representation of bonding interactions in molecules. It is given exclusively in terms of the electron density and its gradient. We show that the graphical representation of bonding interactions given by LED is consistent with the local curvatures of the electron density as given by the eigenvalues of the Hessian matrix, according to a local symmetry classification of the critical points here introduced. LED consistently complements the topological analysis of the electron density given by the quantum theory of atoms in molecules, by providing a graphical representation of the symmetry of the bonding interactions in molecular systems.

The structures of 19 alpha-helical alanine-based peptides, 13 amino acids in length, have been fully optimized using density functional theory and analyzed by means of the quantum theory of atoms in molecules. Two types of N-H...O bonds and one type of C-H...O bond have been identified. The value of the electron density at hydrogen bond critical points corresponding to N-H...O interactions is higher than that of C-H...O interactions. The effect of amino acid substitution at the central position of the peptide on the hydrogen bond network of the alpha-helix has been assessed. The strength of the hydrogen bond network, measured as the summation of the electron density over the hydrogen bond critical points, may be used to explain experimental relative helix propensities of amino acids in cases where solvation and entropic effects cannot.

ABSTRACT:The quantum chemistry of finite aperiodic graphene flakes is a matter of considerable interest because of the anticipated technological importance of such objects. Since real aperiodic graphene flakes will in general be composed of many thousands of carbon atoms, theoretical methods appropriate to such large molecules would need to be used for the ab initio quantum calculation of their properties. The Kernel energy method is discussed here, and it is shown to be accurately applicable to graphenes and analogous extended aromatic molecules. It is necessary to define the kernels of a graphene molecule in a new way because of the extensive aromaticity, which defines its electronic structure. The kernels used in the reconstruction of the full graphene sheet preserve the total number of p-electrons, Clar sextets, and the Correspondence to: L. Massa;

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The molecular structure can be defined quantum mechanically thanks to the theory of atoms in molecules. Here, we report a new molecular model that reflects quantum mechanical properties of the chemical bonds. This graphical representation of molecules is based on the topology of the electron density at the critical points. The eigenvalues of the Hessian are used for depicting the critical points three-dimensionally. The bond path linking two atoms has a thickness that is proportional to the electron density at the bond critical point. The nuclei are represented according to the experimentally determined atomic radii. The resulting molecular structures are similar to the traditional ball and stick ones, with the difference that in this model each object included in the plot provides topological information about the atoms and bonding interactions. As a result, the character and intensity of any given interatomic interaction can be identified by visual inspection, including the noncovalent ones. Because similar bonding interactions have similar plots, this tool permits the visualization of chemical bond transferability, revealing the presence of functional groups in large molecules.

The local quantum theory is applied to the study of the momentum operator in atomic systems. Consequently, a quantum-based local momentum expression in terms of the single-electron density is determined. The limiting values of this function correctly obey two fundamental theorems: Kato's cusp condition and the Hoffmann-Ostenhof and Hoffmann-Ostenhof exponential decay. The local momentum also depicts the electron shell structure in atoms as given by its local maxima and inflection points. The integration of the electron density in a shell gives electron populations that are in agreement with the ones expected from the Periodic Table of the elements. The shell structure obtained is in agreement with the higher level of theory computations, which include the Kohn-Sham kinetic energy density. The average of the local kinetic energy associated with the local momentum is the Weizsacker kinetic energy. In conclusion, the local representation of the momentum operator provides relevant information about the electronic properties of the atom at any distance from the nucleus.

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We explored amino acid side chains from a quantum mechanical perspective in order to identify molecular similarities and differences, for the purpose of exploring the de novo design of peptidic sequences with desired biochemical reactivities. Charge densities for the 20 genetically encoded amino acids in both R and β conformations were partitioned into molecular fragments, and their electronic properties (charge, energy, and dipole and quadrupole moments) were calculated using atoms in molecules theory. Transferability, as required by this theory, was confirmed for the side chains. Two methods were used to identify similarity: The first mapped each side chain property vector onto frequency differentiated Andrews plots, while the second used a composite measure of vectorial distance and angle as the dependent variable for hierarchical cluster analyses. We found that both methods clustered the side chains into chemically related groups only on the basis of theoretically derived variables. Both fine grained and coarse grained levels of analysis highlighted important emergent properties such as hydropathy, polarity, size, aromaticity, and the presence of carbon chains (aliphatics) and hydroxyl groups (alcohol). These results verify the hypothesis that symmetries of charge densities (as measured by the variables used here) can account for the observed chemical reactivities of amino acids.