Descriptor molecular orbitals

The electronic properties of a molecnle include physical aspects of its chemistry, such as its ability to accept and donate hydrogen bond, ionization, dipole moment, as well as those calculated from a knowledge of electron distribution. Of the last, molecular orbital properties are easily calculated and widely used these include atomic charge, superdelocalizability, and energies of electrons in specific molecular orbitals. The calculation and use of electronic descriptors, molecular orbital properties in particular, were well reviewed by Schuurmaim (2004). 

Purdy [91] used the technique to predict the carcinogenicity of organic chemicals in rodents, although his model was based on physicochemical and molecular orbital-based descriptors as well as on substructural features and it used only a relatively small number of compounds. His decision tree, which was manual rather than computer based, was trained on 306 compounds and tested on 301 different compounds it achieved 96% correct classification for the training set and 90% correct classification for the test set. 

The COMPACT (computer-optimized molecular parametric analysis of chemical toxicity) procedure, developed by Lewis and co-workers [92], uses a form of discriminant analysis based on two descriptors, namely, molecular planarity and electronic activation energy (the difference between the energies of the highest occupied and lowest unoccupied molecular orbitals), which predict the potential of a compound to act as a substrate for one of the cytochromes P450. Lewis et al. [93] found 64% correct predictions for 100 compounds tested by the NTP for mutagenicity. 

Table 1 Calculation of some molecular-based descriptors for BOA, DIMBOA and MBOA. Physicochemical descriptor like logP (partition coefficient between octanol and water) constitutional descriptors like the number of a specified atoms or bonds (number of carbons, hydrogens, oxygens, nitrogens, single and aromatic bonds, the total number of atoms and bonds) and molecular weight quantum-mechanical descriptors like HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital).

How well can continuum solvation models distinguish changes in one or another of these solvent properties This is illustrated in Table 2, which compares solvation energies for three representative solutes in eight test solvents. Three of the test solvents are those shown in Table 1, one is water, and the other four were selected to provide useful comparisons on the basis of their solvent descriptors, which are shown in Table 3. Notice that all four solvents in Table 3 have no acidity, which makes them more suitable, in this respect, than 1-octanol or chloroform for modeling biomembranes. Table 2 shows that the SM5.2R model, with gas-phase geometries and semiempirical molecular orbital theory for the wave function, does very well indeed in reproducing all the trends in the data. 

A rigorous mathematical formalism of chemical bonding is possible only through the quantum mechanical treatment of molecules. However, obtaining analytical solutions for the Schrodinger wave equation is not possible even for the simplest systems with more than one electron and as a result attempts have been made to obtain approximate solutions a series of approximations have been introduced. As a first step, the Bom-Oppenheimer approximation has been invoked, which allows us to treat the electronic and nuclear motions separately. In solving the electronic part, mainly two formalisms, VB and molecular orbital (MO), have been in use and they are described below. Both are wave function-based methods. The wave function T is the fundamental descriptor in quantum mechanics but it is not physically measurable. The squared value of the wave function T 2dT represents probability of finding an electron in the volume element dr. 

QSAR methods can be divided into several categories dependent on the nature of descriptors chosen. In classical one-dimensional (ID) and two-dimensional (2D) QSAR analyses, scalar, indicator, or topological variables are examples of descriptors used to explain differences in the dependent variables. 3D-QSAR involves the usage of descriptors dependent on the configuration, conformation, and shape of the molecules under consideration. These descriptors can range from volume or surface descriptors to HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) energy values obtained from quantum mechanics (QM) calculations. 

Some of the earliest QSAR studies on CYPs were performed by Basak (257), Murray (258), and Marshall (205). Gao et al. (259) explored the influence of electronic parameters of CYP substrates in 1996. The findings of Basak that electronic terms would cancel out have been proven wrong by many research papers published in the following decades. Tyrakowska et al. (260) indicated via QSARs based on calculated molecular orbital descriptors that the cat (maximum velocity converted per nmol of P450 per min) for CYP catalyzed C4-hydroxylation rates of aniline derivatives of different species (rats, rabbit, mice, and human) are closely related to the highest occupied molecular orbital energy (EHOMo)> r - 0-97. Several reviews published by Lewis et al. (212,216,228,261-265) and Ekins (240) should also be mentioned. 

In this context, interesting exhaustive QSAR studies dealing with the assessment of phototoxic hazards of PAHs to aquatic organisms such as Daphnia were published some years ago [12-14]. Authors chose a descriptor based on the energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). They proposed that aromatic chemicals with a HOMO-LUMO gap energy in a window of 7.2 eV 0.4 eV have a high phototoxic potential. 

The second variant of QSAR is the use of actual structural descriptors, such as molecular orbital indices or topological codes, to define numerically the structure of a molecule and to find linear relationships with numerical biological data (Kier and Hall, 1976, 1992). 

A physical model usually predisposes to physicochemical descriptors, such as p/Ca, log P or molar volume for the whole molecule, or the equivalent descriptors for substituents on a common molecular framework. But different structures can have the same or similar property values, and we are interested in designing structures. So at some stage we must choose structural descriptors (atom types, substructural fragments, connections, or indices from molecular orbital calculations) or at least relate structure to property in order to design the appropriate structure. 

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. 

Commonly used descriptor variables for QSARs involving redox reactions include substituent constants (o), ionization potential, electron affinity, energy of the highest occupied molecular orbital (EHOMO)or lowest unoccupied molecular orbital (ELUMO), one-electron reduction or oxidation potential (E1), and half-wave potential (E1/2)- One descriptor variable (D), fit to a log-linear model, is usually sufficient to describe a redox property of P. Such a QSAR will have the form... 

Extraction of information from p may not be as elegant as from P. For example, the Woodward-Hoffmann rules follow fairly transparently from the symmetries of molecular orbitals (wavefunctions), but deriving them from p requires using a dual descriptor function [1]. 

Other chemical descriptors have been used to model other properties, or to improve the QSAR models with log P. The attempt has been to avoid the errors of the QSAR models. Indeed, some chemicals were not correctly modeled, and other descriptors have been introduced, producing multilinear relationships. The theoretical assumptions were modeled keeping into account other physico-chemical parameters, such as chemical reactivity, through chemical descriptors, such as the energy of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). 

TSARBatch for Windows Accelrys Inc. www.accelrys.com Log K, various topological, structural, 3D and molecular orbital descriptors... 

Ehomo Elumo EN HD Descriptors Based on Molecular Orbital Energies (Section IV.A and B) Energy of the highest occupied molecular orbital (Equation 6.42) Energy of the lowest unoccupied molecular orbital (Equation 6.43) Molecular electronegativity (Equation 6.45) Molecular hardness (Equation 6.46)... 

Descriptors Based on Molecular Orbital Wave Functions and Energies (Section IV.F)... 

Schuurmann, G. and Funar-Timofei, S., Multilinear regression and comparative molecular field analysis (CoMFA) of azo dye-fiber affinities. 2. Inclusion of solution-phase molecular orbital descriptors, J. Chem. Inf. Comput. Sci., 43, 1502-1512, 2003. 

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