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The quantum chemical topology (QCT) is able to propose atom types by direct computation rather than by chemical intuition. In previous work, molecular electron densities of 20 amino acids and smaller derived molecules were partitioned into a set of 760 topological atoms. Each atom was characterised by seven atomic properties and subjected to cluster analysis element by element, that is, C, H, O, N, and S. From the respective dendrograms, 21 carbon atom types were distinguished, 7 hydrogen, 2 nitrogen, 6 oxygen, and 6 sulfur atom types. Herein, we contrast the QCT atom types with those of the assisted model building with energy refinement (AMBER) force field. We conclude that in spite of fair agreement between QCT and AMBER atom types, the latter are sometimes underdifferentiated and sometimes overdifferentiated. In summary, we suggest that QCT is a useful guide in designing new force fields or improving existing ones. The computational origin of QCT atom types makes their determination unbiased compared to atom type determination by chemical intuition and a priori assumptions. We provide a list of specific recommendations.

Reliable atomic properties can be obtained via the theory of "Atoms in Molecules" (AIM) via integration over a finite volume. These integrations are challenging because of the variety and complexity of the shape of the AIM atoms. In practice the integration of a large number of atoms (100-1000, sampled from many molecules) yields integration errors L(Ω) of varying magnitude. We prove that it is impossible to predict the size of an angular Gauss-Legendre grid (outside the β sphere) that guarantees a pre-set error. Hence it is incorrect to assume that a large grid (~23 000 angular grid points) will automatically yield a low L(Ω) value. The erratic relationship between the integration error and the grid size prompts a statistical interpretation of atomic integration, at a purely practical level. More importantly we have investigated the relationship between L(Ω) and seven atomic properties which include volume, energy, and the magnitudes of five electrostatic multipole moments. The electronic population (N(Ω)) and the volume (v(Ω)) of carbon is linearly correlated with L(Ω), enabling the interpolation or extrapolation of N(Ω) and v(Ω). Other properties of carbon and other atoms (N, O, and S) yield low correlation coefficients but occasionally trends can be observed. For example, we find that some properties are systematically underestimated if L(Ω) is negative. This work has led to an estimate of safe error bars of atomic properties for atoms occurring in biological molecules with reasonably sized integration grids. The most stable properties were found to be the energy and the population. Finally, we have observed that the influence of the grid orientation is less if L(Ω) is small, and that population and energy are the least affected.Key words: electron density, topology, atoms in molecules, atomic properties, amino acids.

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.

Molecular electron densities are generated at B3LYP/6-311+G(2d,p)//HF/6-31G(d) level for 57 molecules, including one conformation of each naturally occurring amino acid and smaller derived molecules. The electron densities are partitioned into atomic fragments according to the approach of quantum chemical topology (QCT). A set of 547 unique topological atoms is obtained, containing 421 hydrogens, 63 oxygens, 57 nitrogens and 6 sulfurs. Each atom is described by seven properties: volume, kinetic energy, monopole, dipole, quadrupole, octupole and hexadecapole moment. Cluster analysis groups atoms into atom types based on their similarity expressed in the discrete 7D space of atomic properties. Using a separation criterion we distinguish seven hydrogen, six oxygen, two nitrogen and six sulfur atom types.

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