Molecular descriptor quantum chemical method

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. 

The aforementioned macroscopic physical constants of solvents have usually been determined experimentally. However, various attempts have been made to calculate bulk properties of Hquids from pure theory. By means of quantum chemical methods, it is possible to calculate some thermodynamic properties e.g. molar heat capacities and viscosities) of simple molecular Hquids without specific solvent/solvent interactions [207]. A quantitative structure-property relationship treatment of normal boiling points, using the so-called CODESS A technique i.e. comprehensive descriptors for structural and statistical analysis), leads to a four-parameter equation with physically significant molecular descriptors, allowing rather accurate predictions of the normal boiling points of structurally diverse organic liquids [208]. Based solely on the molecular structure of solvent molecules, a non-empirical solvent polarity index, called the first-order valence molecular connectivity index, has been proposed [137]. These purely calculated solvent polarity parameters correlate fairly well with some corresponding physical properties of the solvents [137]. 

None of this can be detected by standard geometric criteria. First-principles simulations like CPMD allow for new wave-function-based descriptors [231] as the electronic structure is - in addition to the positions of all atomic nuclei involved -available on the fly . Of course, the above mentioned fundamental problem that the interaction energy is not an observable quantity is in first-principle simulations as apparent as in static calculations. However, the wavefunction naturally tracks all electronic changes in an aggregate. A wavefunction-based descriptor would also be helpful in traditional molecular dynamics because snapshots can be calculated with advanced static quantum chemical methods. 

As an alternative to ab initio methods, the semi-empirical quantum-chemical methods are fast and applicable for the calculation of molecular descriptors of long series of structurally complex and large molecules. Most of these methods have been developed within the mathematical framework of the molecular orbital theory (SCF MO), but use a number of simplifications and approximations in the computational procedure that reduce dramatically the computer time [6]. The most popular semi-empirical methods are Austin Model 1 (AMI) [7] and Parametric Model 3 (PM3) [8]. The results produced by different semi-empirical methods are generally not comparable, but they often do reproduce similar trends. For example, the electronic net charges calculated by the AMI, MNDO (modified neglect of diatomic overlap), and INDO (intermediate neglect of diatomic overlap) methods were found to be quite different in their absolute values, but were consistent in their trends. Intermediate between the ab initio and semi-empirical methods in terms of the demand in computational resources are algorithms based on density functional theory (DFT) [9]. 

Depending on the quantum chemical method used and grouping the terms in Hamiltonian, other schemes for the decomposition of the energy of molecule have been suggested, especially for the description of intermo-lecular interactions (2015CSR3177). The terms arising from such decompositions are also appHcable as molecular descriptors in QSAR/QSPR. 

The molecular descriptors obtained by computation of molecular mechanics and quantum chemical methods are used to describe the molecular structures of A -(3-Oxo-3,4-dihydro-2//-benzo[l,4]oxazine-6-carbonyl) guanidines. The three-dimensional structures of the molecules are optimized with the software Hyperchem. Prior to the semi-empirical quantum chemical computation, all structures of the compounds are submitted to MM+ computation of molecular mechanics for energy optimization. The structural descriptors are obtained via the computation of semi-empirical method PM3. The computations are carried out at restricted Hartree-Fock level without configuration interaction. 

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. 

While there are reviews of the application of various quantum chemical parameters in QSARs (Karelson et al., 1996 Famini and Wilson, 2002), little attention has been paid so far to the dependence of descriptor values on the level of theory. This holds true in particular with respect to potential discrepancies between semiempirical and ab initio methods when calculating parameters such as frontier orbital energies and descriptors that characterize the molecular charge distribution. 

Because of convention, the symbols for the chemical potential, used in Equation 6.44 and Equation 6.45, and the dipole moment are the same. Further evaluation of Equation 6.48 proceeds through introduction of the LCAO-MO expansion (Equation 6.18) and, dependent on the level of theory, consideration of relevant approximations such as the NDDO formalism (Equation 6.31) in the case of semiempirical MNDO-type methods. Because the calculation of the dipole moment is usually considered a somewhat demanding test of the quality of the wavefunctions employed in the quantum chemical model, this property is included in the comparative statistical analysis of various methods to calculate molecular descriptors as presented in Section V. 

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. 

In our contribution we have focused the discussion on descriptors. The understanding of descriptors is essential for transparency of models and can also lead to mechanistic interpretation of models. Several questions are associated with descriptors. First of all, nowadays thousand of descriptors are defined and can be easily calculated with available software and the first question is how to the select the most relevant descriptors. The topological descriptors are sometimes promising, but there is no clear physicochemical interpretation for them. 3D molecular structure is a problematic quantity as it depends on the media where the molecule is, or on the method of determination. Quantum chemical descriptors, which have a clear physicochemical interpretation, are difficult to calculated. In the cases studies we have addressed some of those questions. We have discussed the sensitivity of the models, and particularly predictions, to descriptors used. According to the critical review of Snyder and Smith [87] on QSAR models for mutagenicity prediction a lot of work still remains to be done. 

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. 

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-... 

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