China
Africa
Explore chapters and articles related to this topic
Families of Molecular Descriptors
Published in Mihai V. Putz, New Frontiers in Nanochemistry, 2020
Lorentz Jäntschi, Sorana D. Bolboacă
Four atomic properties (Ap an atomic property) are taken into calculation, M (AP = M) as relative atomic mass; E (AP = E) as electronegativity (Sanderson scale, Sanderson, 1983); C (AP = C) as (set) cardinality; P (AP = P) as partial charge (class I, seeCramer, 2002, from Mulliken population analysis, Mulliken, 1955). Eight property descriptor (PD a property descriptor) expressions account atomic properties, p (PD = p) – atomic property; d (PD = d) – distance; PD = 1/p; PD = 1/d; PD = pd; PD = p/d; PD = p/d2; PD = p2/d2. Five overlapping methods (SM – superposing method) overlap atomic properties to provide the fragmental property, S (SM = S) – sum; P (SM = P) – multiplication; A (SM = A) – arithmetic mean; G (SM = G) – geometric mean; H (SM = H) – harmonic mean. Two models of interaction give transform in a vector a descriptor (IM – interaction model), R (IM = R) – rare (uses the assumption that the property of all atoms are approximately located in the fragment center of property, of which position is consequently obtained and used to express the descriptor vector); D (IM = D) – dense (the effect of each atom are superposed using vector summation). Two distance metrics (DM – metric of distance) provides the distance for expressing the descriptor values, T (DM = T) – topological (from connectivity) and D (DM = D) – topographical (from 3D model of the molecule obtained from different levels of theory - for a discussion about, seeClark, 1985). Four square-matrix based indices (MI-matrix index) collects overall molecular property, P_ (MI = P_) - half-sum of matrix elements; P2 (MI = P2) - half-sum of squared matrix elements; E_ (MI = E_) - half-sum of Hadamard product of matrix with adjacency matrix; E2 (MI = E2) - half-sum of squared Hadamard product of matrix with adjacency matrix. Finally, a molecular descriptor is obtained via a linearization operator (LO - linearization operator) meant to transform nonlinearities to linearity at relationships, I (LO = I) - identity function; R (LO = R) - reciprocal function (f(x) = 1/x); L (LO = L) - logarithm function (f(x) = ln(x)). Thus, FPIF family of molecular descriptors puts together a total number of individuals equal with the number of all multiplications described above (2·2·4·8·6·5·4·3-46080) – seeTable 15.4.
A comprehensive study of the structural, elastic, electronic, and optical properties of the tetragonal sodium chalcogenides NaAlX 2 (X = O, S, Se, Te)
Published in Philosophical Magazine, 2022
T. Helaimia, A. Benmakhlouf, M. Bouchenafa, I. Messahli, S. Maabed, F. Khamloul, M. Sidoumou, A. Bouhemadou
Mulliken population analysis [29] is an important tool commonly used to characterise the distribution of electronic charge in a molecule and to determine the nature of the interatomic bonding of a specific pair of atoms. In particular, the bond (overlap) population, which is one of the essential parameters drawn from this technique, is a great quantitative criterion for investigating the strength and the nature of the bond between a pair of neighbouring atoms in materials. According to Segall et al. [30], a positive (negative) value of the overlap population indicates bonding (antibonding) states. A value of zero of the bond population implies an ideal ionic bond and a value greater than zero indicates the presence of a degree of covalency. In order to understand the interatomic bonding behaviours of the NaAlX2 tetragonal compounds, bond population and Mulliken charge population of some selected interatomic bonds are carried out using Mulliken population analysis. From the data given in Table 4, one appreciates that all the calculated Na-X and Al-X bond lengths are in agreement with the corresponding experimental ones. One notices that the Na-X bond is longer than the Al-X one. The relatively large positive bond population values of the Al–O and Al-S bonds in NaAlO2 and NaAlS2 demonstrate a predominant covalent character of these bonds, while the low positive bond population values of the Na-O and Na-S bonds confirm their dominant ionic character. The negative bond population values of the Al-Se and Al-Te bonds in the NaAlSe2 and NaAlTe2 compounds constitute an indication of the antibonding interaction between the Na and Se atoms as well as between Na and Te atoms. The weak positive values of the bond population of the Al-Se and Al-Te bonds are a sign of a significant contribution of the ionic character in these bonds. The calculated charge transfer from the Na and Al cations to the X (X = O, S, Se, Te) anions is given in Table 4. Note that the anionic charge depends on the electronegativity of X atom; the transferred charge increases with the increasing electronegativity.