Quantum chemical molecular descriptors

A specific class of molecular descriptors is the one based on quantum chemical calculations. These descriptors may or may not be observables themselves. They may correspond to a computed value for some experimentally verifiable quantity, or they may be purely conceptual descriptors. A review of quantum chemical molecular descriptors has been given by Karelson et al. [9,10]. 

Bultinck, R, Langenaeker, W., Carb6-Dorca, R. and Tollenaere, J.P., Fast calculation of quantum chemical molecular descriptors from the electronegativity equalization method, J. Chem. Inf. Comput. Sci., 43, 422-428, 2003. 

QUANTUM-CHEMICAL MOLECULAR DESCRIPTORS 2.1. Energy-Related Descriptors... 

Quantum-chemical molecular descriptors have been actively used in the quantitative structure-activity relationship studies of biological activities [1,2,72]. In the following, examples of QSARs involving quantum-chemical descriptors and applied on the enzymatic reactivity, pharmacological activity, and toxicity of compounds are discussed. 

The quantum-chemical molecular descriptors have been widely used in the development of quantitative structure-activity relationships for various pharmacological activities of compounds. Again, most of the QSARs developed include the electrostatic and/or MO-related descriptors. 

Quantum-chemical descriptors The quantum-chemical molecular descriptors are derived from the eigenvalues and eigenvectors. Descriptors based on the eigenvalues are the HOMO and LUMO. Atomic charges, dipole moment, bond orders, and frontier orbital indices are derived from the coefficients of the eigenvectors of the atomic orbitals. The superdelocalizability index is based on both the values of the eigenvalues and eigenvectors. 

For structure-property and structure-activity studies, one should use solely structure invariants, and when structures are represented by molecular graphs, graph invariants could serve as structure descriptors. The mathematical term invariant means any quantity that is independent o/graphical representation of a molecule or adopted numbering of atoms. In other words, invariants represent intrinsic mathematical properties of molecular structure. They differ from the physicochemical molecular properties in that they are either obtained by counting or can be expressed with mathematical formulas and are always therefore numerically exact. The same can be said for quantum chemical molecular descriptors. In contrast, physicochemical molecular descriptors that are molecular properties are obtained by measuring, which may be sufficiently precise and thus numerically satisfactory nevertheless, with time, they may undergo some, even if minor, revisions. 

Hutter [21] Molecular size, polarizability, hydrogen-bonding, and many quantum-chemically derived descriptors... 

Recent progress in computational hardware and the development of efficient algorithms have assisted the routine development of molecular quantum-mechanical calculations. New semiempirical methods calculate realistic quantum-chemical molecular quantities in a relatively short computational time frame. Quantum-chemical calculations are thus an attractive source for molecular descriptors that can express all of the electronic and geometric properties of molecules and their interactions. Quantum-chemical methods can be applied to QSARs by direct derivation of electronic descriptors from the molecular wave function. 

Several different kinds of quantum-chemical descriptors have been defined, and these can be broadly divided into energy-based descriptors, local quantum-chemical properties, descriptors based on the Density Functional Theory, molecular orbital energies, superdelocalizability indices, frontier orbital electron densities, and polarizabilities [Cartier and Rivail, 1987 Bergmann and Hinze, 1996 Karelson et al, 1996]. 

J. M.G., Marin, P.N., Crespo-Otero, R., Zaragoza, E.T. and Garci a-Domenech, R. (2007) Applying pattern recognition methods plus quantum and physico-chemical molecular descriptors to analyze the anabolic activity of structurally diverse steroids. J. Comput. Chem., 29, 317-333. 

Other pharmacological activities have also been correlated with quantum-chemically derived descriptors. For instance, the quantitative structure-activity relationship developed for the antibacterial activity of a series of monocyclic (i-lactam antibiotics included the atomic charges, the bond orders, the dipole moment, and the first excitation energy of the compound [103]. The fungicidal activity of A3-l,2,4-thiadiazolines has been correlated with an index of frontier orbital electron density derived from semi-empirical PM3 molecular orbital calculations [104],... 

Karelson et al. [124] had also carried out a comparative analysis of the molecular descriptors calculated for the isolated molecules (gas phase) and for the molecules embedded into a dielectric continuum corresponding to aqueous solution. The self-consistent reaction field method [125] was used for the latter calculations. The results indicated that, in general, the quantum-chemically derived descriptors are rather insensitive towards the change in the environment surrounding the molecule. However, the most influenced are the polarizability and several other MO-related descrip-... 

Quantum chemical descriptors such as atomic charges, HOMO and LUMO energies, HOMO and LUMO orbital energy differences, atom-atom polarizabilities, super-delocalizabilities, molecular polarizabilities, dipole moments, and energies sucb as the beat of formation, ionization potential, electron affinity, and energy of protonation are applicable in QSAR/QSPR studies. A review is given by Karelson et al. [45]. 

CODESSA can compute or import over 500 molecular descriptors. These can be categorized into constitutional, topological, geometric, electrostatic, quantum chemical, and thermodynamic descriptors. There are automated procedures that will omit missing or bad descriptors. Alternatively, the user can manually define any subset of structures or descriptors to be used. 

Although one could consider the electron density as just one of the many quantum chemical descriptors available, it deserves special attention. In QSM, it is the only descriptor used for a number of reasons. The idea of using the electron density as the ultimate molecular descriptor is founded on the basic elements of quantum mechanics. First of all, it is the all-determinmg quantity in density functional theory (DFT) [11] and also holds a very close relation to the wave function. Convincing arguments were given by Handy and are attributed to Wilson [12], although initial ideas can also be traced back to Bom [13] and von... 

Three classes of calculated molecular descriptors, viz., topological and substruc-tural descriptors, geometrical (3-D) indices, and quantum chemical (QC) indices, have been extensively used in QSAR studies pertaining to drug discovery and environmental toxicology [8-12],... 

Molecular descriptors derived solely from D, E, B, and R discriminate between different basic graphs. They do not, however, differentiate between molecules such as I, II, and III with the same basic graph but with differences in their types of atoms, bonds, or stereo- and quantum-chemical features. In the remaining part of this section, a few approaches that extend basic graph descriptors to chemically informed descriptors are introduced. 

Chemical reactivity and biological activity can be related to molecular structure and physicochemical properties. QSAR models can be established among hydrophobic-lipophilic, electronic, and steric properties, between quantum-mechanics-related parameters and toxicity and between environmental fate parameters such as sorption and tendency for bioaccumulation. The main objective of a QSAR study is to develop quantitative relationships between given properties of a set of chemicals and their molecular descriptors. To develop a valid QSAR model, the following steps are essential ... 

Quantum chemistry is the foundation of molecular chemistry dealing with structure, properties, and interaction of molecules. The basic principles are offered by quantum mechanics. Quantum-chemical calculations are able to supply information needed for molecular descriptors for QSAR analyses. The use of quantum-chemical calculations is becoming common to establish molecular equilibrium geometries and conformations and to supply quantitative thermochemical and kinetic data. 

In principle, quantum-chemical theory should be able to provide precise quantitative descriptions of molecular structures and their chemical properties however, due to mathematical and computational complexities this seems unlikely to be realized in the foreseeable future. Thus, researchers need to rely on approximate methods that have now become routine and have found wide applications. In many cases, errors due to the approximate nature of quantum-chemical calculations and the neglect of the solvation effects are largely transferable within structurally related series (Karelson and Lobanov, 1996). Thus, relative values of calculated descriptors can be meaningful even though their absolute values are not directly applicable. 

Many software packages have been developed for calculation of molecular descriptors. Table 5.5 shows some software employed for molecular modeling, quantum-chemical calculations, molecular dynamics, and QSARs. 

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