Atom-in-molecule similarity

A special note should be made concerning the use of atom-in-molecule densities. The basic aspects of atom-density-based similarity continue to be valid. The reader is referred to the section on atoms-in-molecules similarity and chirality for an in-depth discussion of these domains of research. 

In the Atoms In Molecules approach (Section 9.3), the Laplacian (trace of the second derivative matrix with respect to the coordinates) of the electron density measures the local increase or decrease of electrons. Specifically, if is negative, it marks an area where the electron density is locally concentrated, and therefore susceptible to attack by an electrophile. Similarly, if is positive, it marks an area where the electron density is locally depleted, and therefore susceptible to attack by a... 

The final part is devoted to a survey of molecular properties of special interest to the medicinal chemist. The Theory of Atoms in Molecules by R. F.W. Bader et al., presented in Chapter 7, enables the quantitative use of chemical concepts, for example those of the functional group in organic chemistry or molecular similarity in medicinal chemistry, for prediction and understanding of chemical processes. This contribution also discusses possible applications of the theory to QSAR. Another important property that can be derived by use of QC calculations is the molecular electrostatic potential. J.S. Murray and P. Politzer describe the use of this property for description of noncovalent interactions between ligand and receptor, and the design of new compounds with specific features (Chapter 8). In Chapter 9, H.D. and M. Holtje describe the use of QC methods to parameterize force-field parameters, and applications to a pharmacophore search of enzyme inhibitors. The authors also show the use of QC methods for investigation of charge-transfer complexes. 

Cioslowski et al. used fragment similarity indices to compute the degree of similarity between atoms of the same element in different molecules, where the atoms were those derived from Bader s atoms in molecules theory [68,69]. They introduced a novel atomic similarity index for atom A in molecule X and atom B in molecule Y defined as [70]... 

Gottingen. At this time, Pauling had just recently met Heitler and London in Munich, and he saw them again in Zurich. Mulliken, who as early as 1925 showed that there are multiple electronic levels in molecules similar to those in atoms, became friends with Hund at Gottingen in 1927.39... 

We have used the electronic energy levels for atomic hydrogen to serve as a model for other atoms. In a similar way, we can use the interaction of two hydrogen atoms giving the hydrogen molecule as a model for bonding between other atoms. In its simplest form, we can consider the bond between... 

Assigning atom charges and bond orders involves calculating the number of electrons belonging to an atom or shared between two atoms, i.e. the population of electrons on or between atoms hence such calculations are said to involve population analysis. Earlier schemes for population analysis bypassed the problem of defining the space occupied by atoms in molecules, and the space occupied by bonding electrons, by partitioning electron density in a somewhat arbitrary way. The earliest such schemes were utilized in the simple Hiickel or similar methods [256], and related these quantities to the basis functions (which in these methods are essentially valence, or even just p, atomic orbitals see Section 4.3.4). The simplest scheme used in ab initio calculations is Mulliken population analysis [257]. 

The atoms-in-molecules (AIM) analysis of electron density, using ab initio calculations, was considered in Section 5.5.4. A comparison of AIM analysis by DFT with that by ab initio calculations by Boyd et al. showed that results from DFT and ab initio methods were similar, but gradient-corrected methods were somewhat better than the SVWN method, using QCISD ab initio calculations as a standard. DFT shifts the CN, CO, and CF bond critical points of HCN, CO, and CH3F toward the carbon and increases the electron density in the bonding regions, compared to QCISD calculations [107]. 

Here Ha and Hb are the Hamiltonians of the isolated reactant molecules, Hso is the Hamiltonian of the pure solvent, and Vmt is the interaction energy between reactants and between reactant and solvent molecules, i.e., it contains the solute-solute as well as the solute-solvent interactions, qa and reactant molecules A and B, respectively, and pa and pb are the conjugated momenta. If there are na atoms in molecule A and tib atoms in molecule B, then there will be, respectively, 3ua coordinates c/a and 3rt j coordinates c/b Similarly, R are the coordinates for the solvent molecules and P are the conjugated momenta. In the second line of the equation, we have partitioned the Hamiltonians Hi into a kinetic energy part T) and a potential energy part V). 

The two independent molecules of monoclinic Et2Sn(DMIT) 25b have quite different arrangements tin atoms in molecule A (Table 7) form two relatively weak intermolecular thione S —> Sn bonds of 3.567 and 3.620 A, with the formation of sheets, while those in molecule B form a similar bond, S — Sn = 3.555 A to give chains, with a much longer contact, S Sn = 3.927 A to another chain. The latter is only ca 0.03 A less than the van der Waals radii sum for Sn and S (Table 1). 

R.F. Nalewajski, R.G. Parr, Information theory, atoms-in-molecules, and molecular similarity, Proc. Natl. Acad. Sci. USA 97 (2000) 8879. 

Beyond similarity-based applications, machine learning techniques may pick the specific descriptor elements that appear to correlate with the observed activity trends throughout a training set. Unlike in overlay models, where there is an obvious link between pharmacophore spheres or fields in space and their source atoms, the actual pairs (triplets, etc) of atoms in molecules that incarnate the picked descriptor elements must be first established, to gain any potential insights into the binding mechanisms. 

Considerations similar to those made about electric dipole moments apply to other one-electron properties, for instance the nuclear spin-spin coupling constants between non-bonded hydrogen atoms in molecules like methane. These quantities are approximately equal to zero in the simple molecular orbital theory, as it is easily proved by using equivalent orbitals corresponding to the CH bonds instead of the usual delocalized MO s (34). Actually, the nuclear spins of protons cannot interact wta the electrons, since a localized MO cannot be large on two hydrogens at the same time, and correlation should be primarily responsible for all coupling constants, except perhaps for those observed for directly bonded atoms (see Sec. 4). 

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