Quantum chemistry descriptors

MODEL Molecular Descriptor Lab (MODEL) (http //jing.cz3.nus.edu.sg/ cgi-bin/model/model.cgi) is a free Web-based server for computing a comprehensive set of 3778 molecular descriptors, which can be divided into 6 classes constitutional descriptors, electronic descriptors, physical chemistry properties, topological indexes, geometrical molecular descriptors, and quantum chemistry descriptors [73], Compounds can be provided to the server in various molecular formats such as PDB, MDL, MOL2, and COR, and the computed molecular descriptors are displayed in a few seconds or less. Cross-links to the relevant sections of the reference manual page are also provided for some of the descriptors and descriptor classes. 

The HF results generated for representative polyatomic molecules have used the /V-derivatives estimated by finite differences, while the -derivatives have been calculated analytically, by standard methods of quantum chemistry. We have examined the effects of the electronic and nuclear relaxations on specific charge sensitivities used in the theory of chemical reactivity, e.g., the hardness, softness, and Fukui function descriptors. New concepts of the GFFs and related softnesses, which include the effects of molecular electronic and/or nuclear relaxations, have also been introduced. 

Basak, S. C., Mills, D., Gute, B. D. Predicting bioactivity and toxicity of chemicals from mathematical descriptors A chemical-cum-biochemical approach. In Advances in Quantum Chemistry, Klein, D. J., Brandas, E., Eds., Elsevier, Amsterdam, 2004, in press. 

Descriptors derived via quantum chemistry are fundamentally different from experimentally measured quantities although there is some natural overlap. Unlike experimental measurements, quantum-chemical calculations have no statistical error. An inherent error is associated with the assumptions required to facilitate the calculations, but the computational error is considered to be approximately constant throughout the series when using quan-tum-chemistry-based descriptors with a series of related compounds. In most studies, the direction but not the magnitude of the error is known. The major weakness of quantum-chemical descriptors is the failure to directly address bulk effects of a molecule. 

In recent years, molecular descriptors such as the energy of the highest occupied molecular orbital (EHomo) ar d the energy of the lowest unoccupied molecular orbital ( IUMO) have gained in popularity for QSAR analysis, as these descriptors are readily calculated from PC-based software such as SPARTAN. Before we discuss EHomo ar d ELumo further, a brief discussion of quantum chemistry is necessary. 

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. 

Famini, G.R. and Wilson, L.Y., Linear free energy relationships using quantum mechanical descriptors, in Reviews in Computational Chemistry, Vol. 18, Lipkowitz, K.B. and Boyd, D.B., Eds., Wiley-VCH, New York, 2002, pp. 211-255. 

Arbitrariness One hears comments that graph descriptors being arbitrary, do not have a deep physicochemical significance A misconception here is in confusing an input with an output of a mathematical treatment of a problem Surely die choice of descriptors selected to characterize grains is at the disposal of an investigator, hence arbitary But the same is true of a choice of coordinate systems used to describe a system of classical physics, or the choice of basis functions to compute a molecular structure in quantum chemistry I In each case we speak of input information, and the outcome of the analysis undertaken (when a complete basis is taken) does not depend on the choice of descriptors (coordinates) However, the amount of work, even its mere feasibility, will differ A poor selection of basis functions may... 

These are - electronic descriptors defined in terms of atomic charges and used to describe electronic aspects both of the whole molecule and of particular regions, such as atoms, bonds, and molecular fragments. Charge descriptors are ealculated by - computational chemistry and therefore can be considered among - quantum-chemical descriptors [Lowe, 1978 Streitweiser, 1961],... 

Theoretical chemistry and, especially, quantum chemistry constitute the basic core of computational chemistry, and their success covers the field of molecular geometries and energies, reactivity, spectroscopic properties, behaviour of electrons in atoms and molecules, and various other fundamental chemical topics [Lipkowitz and Boyd, 1990]. Therefore, the term computational chemistry is also used in a more restricted sense to denote the mathematical approaches (and their software implementations) to the calculation of molecular properties from theoretical chemistry. -> Quantum-chemical descriptors are derived from computational chemistry in this restricted sense. 

Electronic information is combined with shape and steric information to characterize molecules in - charged partial surface area descriptors. Other approaches, different from those closely related to quantum-chemistry, refer to electronic descriptors, such as - electronic substituent constants, - electrotopological state indices, -> topological charge indices. - Reactivity indices and - resonance indices are also related to electronic descriptors. 

The class of the empirical descriptors is a fuzzy, not well-defined class. In principle, empirical descriptors are those not defined on the basis of a general theory such as, for example, quantum chemistry or graph theory. Rather they are defined by practical rules derived from chemical experience, e.g. considering specific or local structural factors present in the molecules, often sets of congeneric compounds. As a consequence, in most cases, empirical descriptors represent limited subsets of compounds and cannot be extended to classes of compounds different from those for which they were defined. Empirical descriptors have not to be confused with experimentally derived descriptors even if it is well known that several of them are empirically derived. 

In analogy with solvatochromic parameters but based on quantum theoretical chemistry, a set of - quantum-chemical descriptors intended to describe the hydrogen bonding effects of molecules by theroretical linear solvation energy relationships (TLSER) were proposed. 

A nonlinear 18-parameter model based on 10 molecular descriptors calculated by semi-empirical quantum-chemistry methods, starting from optimized 3D geometries [Bodor et al, 1989 Bodor and Huang, 1992b Huang and Bodor, 1994] ... 

Although several molecular quantities were defined from the beginiming of quantum chemistry and graph theory, the term molecular descriptor has become popular with the development of structure-property correlation models. The - Platt number [Platt, 1947] and - Wiener index [Wiener, 1947c], defined in 1947, are sometimes referred to as the first molecular descriptors. 

Quantum-chemical descriptors are obtained from quantum-mechanical calculations (-> computational chemistry), in which the energy levels E, and the wave functions ijj, of a molecule are computed by solving the Schrodinger equation ... 

Bjorsvik, H.R. and Priebe, H. (1995). Multivariate Data Analysis of Molecular Descriptors Estimated by Use of Semiempirical Quantum Chemistry Methods. Principal Properties for Synthetic Screening of 2-Chloromethyloxirane and Analogous bis-Alkylating C-3 Moieties. Acta Chem.Scand.,49,446-456. 

Charge descriptors are calculated by methods of —> computational chemistry and are among —> quantum-chemical descriptors [Lowe, 1978 Streitweiser, 1961]. In the framework of quantum chemistry, population analysis is the basic tool used to calculate atomic charges and the most common approaches are the —> Mulliken population analysis and Lowdin population... 

Bjorsvik, H.R. and Priebe, H. (1995) Multivariate data analysis of molecular descriptors estimated by use of semiempirical quantum chemistry methods. Principal properties for synthetic screening of 2-chloromethyloxirane and analogous bis-alkylating C-3 moieties. Acta Chem. Scand., 49, 446-456. 

Klamt, A. and Eckert, F. (2001) COSMO-RS a novel way from quantum chemistry to free energy, solubility, and general QSAR-descriptors for partitioning, in Rational Approaches to Drug Design (eds H.-D. Hdltje and W. Sippl), Prous Science, Barcelona, Spain, pp. 195-205. 

Indeed, molecular descriptors are based on several different theories, such as quantum-chemistry, information theory, organic chemistry, graph theory, and so on, and are used to model several different properties of chemicals in scientific fields such as toxicology, analytical chemistry, physical chemistry, and medicinal, pharmaceutical, and environmental chemistry. 

Descriptors are atomic or molecular parameters or even molecular properties that contain information about the energy of each type of intermolecular interaction. They can be classified into two broad categories empirical and theoretical. Empirical descriptors depend on experimental measurements thus, they are available for a limited number of solutes (16). Theoretical descriptors are derived from the solute structure they are usually based on ab initio or semiempirical quantum chemistry calculations or on the connectivity of atoms in the molecule. With the proper use of dedicated software, the number of structural descriptors that can be assigned to a given solute is practically unlimited. Comprehensive compilations of the literature (17,18) register over 2000 known theoretical descriptors. 

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