Molecular descriptor energy descriptors

Molecular descriptors must then be computed. Any numerical value that describes the molecule could be used. Many descriptors are obtained from molecular mechanics or semiempirical calculations. Energies, population analysis, and vibrational frequency analysis with its associated thermodynamic quantities are often obtained this way. Ah initio results can be used reliably, but are often avoided due to the large amount of computation necessary. The largest percentage of descriptors are easily determined values, such as molecular weights, topological indexes, moments of inertia, and so on. Table 30.1 lists some of the descriptors that have been found to be useful in previous studies. These are discussed in more detail in the review articles listed in the bibliography. 

H-bonding is an important, but not the sole, interatomic interaction. Thus, total energy is usually calculated as the sum of steric, electrostatic, H-bonding and other components of interatomic interactions. A similar situation holds with QSAR studies of any property (activity) where H-bond parameters are used in combination with other descriptors. For example, five molecular descriptors are applied in the solvation equation of Kamlet-Taft-Abraham excess of molecular refraction (Rj), which models dispersion force interactions arising from the polarizability of n- and n-electrons the solute polarity/polarizability (ir ) due to solute-solvent interactions between bond dipoles and induced dipoles overall or summation H-bond acidity (2a ) overall or summation H-bond basicity (2(3 ) and McGowan volume (VJ [53] ... 

Valko et al. [37] developed a fast-gradient RP-HPLC method for the determination of a chromatographic hydrophobicity index (CHI). An octadecylsilane (ODS) column and 50 mM aqueous ammonium acetate (pH 7.4) mobile phase with acetonitrile as an organic modifier (0-100%) were used. The system calibration and quality control were performed periodically by measuring retention for 10 standards unionized at pH 7.4. The CHI could then be used as an independent measure of hydrophobicity. In addition, its correlation with linear free-energy parameters explained some molecular descriptors, including H-bond basicity/ acidity and dipolarity/polarizability. It is noted [27] that there are significant differences between CHI values and octanol-water log D values. 

Because of the large number of chemicals of actual and potential concern, the difficulties and cost of experimental determinations, and scientific interest in elucidating the fundamental molecular determinants of physical-chemical properties, considerable effort has been devoted to generating quantitative structure-property relationships (QSPRs). This concept of structure-property relationships or structure-activity relationships (QSARs) is based on observations of linear free-energy relationships, and usually takes the form of a plot or regression of the property of interest as a function of an appropriate molecular descriptor which can be calculated using only a knowledge of molecular structure or a readily accessible molecular property. 

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. 

Figure 1. Loadings of molecular descriptors and sensory sweet score on two PlS factors. 1 = log k, 2 = Kovats index on OVIOI and (3) Caibowax-20M, 4 = molecular weight, S = dipole moment, 6 = ionization potential, 7 = electron energy, 8 = heat of formation, 9 = zero-order connectivity, 10 = first-order connectivity, 11 = first-order connectivity/n Y = sensory sweet score.

A general theory of quantitatively comparing molecular shapes using common overlap steric volume(33-36) and, more recently, descriptors derived from superimposed molecular potential energy fields of pairs of molecules(37) has been derived and tested. This theory allows a "marriage between Hansch analysis and conformational analysis. 

Let us now extend our molecular descriptor model introduced in Chapter 4 (Eqs. 4-26 and 4-27) to the aqueous activity coefficient. We should point out it is not our principal goal to derive an optimized tool for prediction of yw, but to develop further our understanding of how certain structural features determine a compound s partitioning behavior between aqueous and nonaqueous phases. Therefore, we will try to keep our model as simple as possible. For a more comprehensive treatment of this topic [i.e., of so-called linear solvation energy relationships (LSERs)] we refer to the literature (e.g., Kamlet et al., 1983 Abraham et al., 1990 Abraham, 1993 Abraham et al., 1994a and b Sherman et al., 1996). 

It should be noted that when replacing the London dispersive interactions term by other properties such as, for example, the air-hexadecane partition constant, by expressing the surface area in a more sophisticated way, and/or by including additional terms, the predictive capability could still be somewhat improved. From our earlier discussions, we should recall that we do not yet exactly understand all the molecular factors that govern the solvation of organic compounds in water, particularly with respect to the entropic contributions. It is important to realize that for many of the various molecular descriptors that are presently used in the literature to model yiw or related properties (see Section 5.5), it is not known exactly how they contribute to the excess free energy of the compound in aqueous solution. Therefore, when also considering that some of the descriptors used are correlated to each other (a fact that... 

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. 

The regression coefficient (r2) for this relationship was 0.8685. The significance of the calculated F(1/3) = 22.2 can be ascertained by consulting tables of F values. From such a table, it is found that the F(13)a0 025 distribution is 17.4. Because the F(13) of 22.2 is greater than 17.4, it can be assumed that the equation is significant at the 2.5% confidence level. This relationship showed that the kinetic rate increases as ELUMO increases. A set of aliphatic compounds was used for the correlation between ELUMO as molecular descriptor and activation energy as a predictive molecular descriptor. The dataset of... 

Taft s constants were used as molecular descriptors to correlate with activation energy and kinetic rates, respectively. They were used because they describe the inductive effects of the substituents in aliphatic compounds. Taft s constant showed a poor correlation (r2 = 0.68) for aliphatic compounds however, the correlation between activation energy and Taft s constant was... 

Various sets of aromatic compounds and three different molecular descriptors such as EHOmo/ Elumo, and Hammett s constants have been used for other QSAR models. First-order kinetic rates, pseudo first-order kinetic rates, and activation energy were used to correlate with different molecular descriptors. 

Quantitative structure/activity relationships (QSARs) for hydrolysis are based on the application of linear free energy relationships (LFERs) (Well, 1968). An LFER is an empirical correlation between the standard free energy of reaction (AG0), or activation energy (Ea) for a series of compounds undergoing the same type of reaction by the same mechanism, and the reaction rate constant. The rate constants vary in a way that molecular descriptors can correlate. 

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)... 

Table 6.4 Correlation (in terms of R2) between AM1, PM3, PM5, HF/6-31G, and B3LYP/6-31G for Molecular Descriptors Based on Orbital Energies and Net Atomic Charges9... 

The primary supposition of any toxicological QSAR is that the potency of a compound is dependent upon its molecular structure, which is typically quantified by chemical properties (Schultz et al., 2002). Chemical descriptors include a variety of types, including atom, substituent, and molecular parameters. The most transparent of these are the molecular-based empirical and quantum chemical descriptors. Empirical descriptors are measured descriptors and include physicochemical properties such as hydrophobicity (Dearden, 1990). Quantum chemical properties are theoretical descriptors and include charge and energy values (Karelson et al., 1996). Physicochemical and quantum chemical descriptors are for the most part easily interpretable with regard to how that property may be related to toxicity. The classic example of this, the partitioning of a toxicant between aqueous and lipid phases, has been used as a measure of hydrophobicity for over a century (Livingstone, 2000). 

Recently, Riviere and Brooks (2007) published a method to improve the prediction of dermal absorption of compounds dosed in complex chemical mixtures. The method predicts dermal absorption or penetration of topically applied compounds by developing quantitative structure-property relationship (QSPR) models based on linear free energy relations (LFERs). The QSPR equations are used to describe individual compound penetration based on the molecular descriptors for the compound, and these are modified by a mixture factor (MF), which accounts for the physical-chemical properties of the vehicle and mixture components. Principal components analysis is used to calculate the MF based on percentage composition of the vehicle and mixture components and physical-chemical properties. 

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