Properties from Quantum Mechanical Calculations

All the techniques described above can be used to calculate molecular structures and energies. Which other properties are important for chemoinformatics Most applications have used semi-empirical theory to calculate properties or descriptors, but ab-initio and DFT are equally applicable. In the following, we describe some typical properties and descriptors that have been used in quantitative structure-activity (QSAR) and structure-property (QSPR) relationships. 

Population anaiysis methods of assigning charges rely on the LCAO approximation and express the numbers of electrons assigned to an atom as the sum of the populations of the AOs centered at its nucleus. The simplest of these methods is the Coulson analysis usually used in semi-empirical MO theory. This analysis assumes that the orbitals are orthogonal, which leads to the very simple expression for the electronic population of atom i that is given by Eq. (53), where N jcc is the number of occupied MOs, and are the first and last atomic orbitals centered 

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In addition to the obvious structural information, vibrational spectra can also be obtained from both semi-empirical and ab initio calculations. Computer-generated IR and Raman spectra from ab initio calculations have already proved useful in the analysis of chloroaluminate ionic liquids [19]. Other useful information derived from quantum mechanical calculations include and chemical shifts, quadru-pole coupling constants, thermochemical properties, electron densities, bond energies, ionization potentials and electron affinities. As semiempirical and ab initio methods are improved over time, it is likely that investigators will come to consider theoretical calculations to be a routine procedure. 

MolSurf parameters [33] are descriptors derived from quantum mechanical calculations. These descriptors are computed at a surface of constant electron density, with which a very fine description of the properties of a molecule at the Van der Waals surface can be obtained. They describe various electrostatic properties such as hydrogen-bonding strengths and polarizability, as well as Lewis base and acid strengths. MolSurf parameters are computed using the following protocol. 

Quantitative estimates of E are obtained the same way as for the collision theory, from measurements, or from quantum mechanical calculations, or by comparison with known systems. Quantitative estimates of the A factor require the use of statistical mechanics, the subject that provides the link between thermodynamic properties, such as heat capacities and entropy, and molecular properties (bond lengths, vibrational frequencies, etc.). The transition state theory was originally formulated using statistical mechanics. The following treatment of this advanced subject indicates how such estimates of rate constants are made. For more detailed discussion, see Steinfeld et al. (1989). 

Molecular mechanics lies conceptually between quantum mechanics and classical mechanics, in that data obtained from quantum mechanical calculations are incorporated into a theoretical framework established by the classical equations of motion. The Bom-Oppenheimer approximation, used in quantum mechanics, states that Schrddinger s equation can be separated into a part that describes the motion of electrons and a part that describes the motion of nuclei, and that these can be treated independently. Quantum mechanics is concerned with the properties of electrons molecular mechanics is concerned with the nuclei, while electrons are treated in a classical electrostatic manner. 

In summary, all bis(dithiolene) complexes are redox active most of them undergo two or three reversible, one-electron redox reactions. The dithiolene ligand itself is also redox active, which contributes significantly to the redox properties of the metal complex. Molecular orbital pictures derived from quantum mechanical calculations are consistent with the observed redox potential data. 

Computational quantum mechanics continues to be a rapidly developing field, and its range of application, and especially the size of the molecules that can be studied, progresses with improvements in computer hardware. At present, ideal gas properties can be computed quite well, even for moderately sized molecules. Complete two-body force fields can also be developed from quantum mechanics, although generally only for small molecules, and this requires the study of pairs of molecules in a large number of separations and orientations. Once developed, such a force field can be used to compute the second virial coefficient, which can be used as a test of its accuracy, and in simulation to compute phase behavior, perhaps with corrections for multibody effects. However, this requires major computational effort and expert advice. At present, a much easier, more approximate method of obtaining condensed phase thermodynamic properties from quantum mechanics is by the use of polarizable continuum models based on COSMO calculations. 

Secondly, we see from Eq. (1) that we need to maximize the molecular hyperpolaiiz-ability, zzz- This hyperpolarizability is a fundamental molecular property which, in principle, can be estimate from quantum mechanical calculations. Howeva , a very simple two-level quantum mechanical model has proven extremely useful for first-ordCT estimates from easily measured or estimated molecular properties. According to this model, we may write... 

Electrostatic interactions can be most simply modeled as the Coulomb interaction between partial atomic charges, while the repulsion-dispersion part is usually described by a Lennard-Jones or, more accurately, an exp-6 form, each of which contains parameters that must be fixed. High-quality empirically fitted parameter sets have been developed, where the atom-atom interactions are parameterized to reproduce the structures, sublimation enthalpies and, sometimes, further observable properties of organic molecular crystals [73,74]. Their use has been very effective in CSP. Nonempirical approaches to fitting intermolecular force fields, where the parameters are derived from quantum mechanical calculations, have occasionally been applied for CSP [75-78], but these are currently limited to small molecules, so currently lack relevance for typical pharmaceutical molecules. 

In this book we make frequent use of molecular models derived from quantum mechanical calculations. These models will help us visualize the shapes of molecules as well as understand their properties and reactivity. A useful type of model... 

To parameterize a force field, the molecular modeler must usually rely on chemical intuition to establish atom types for the molecular system under study from the beginning. Parameters can then be derived by means of the standard fitting procedure outlined below. With these parameters, properties of the system known experimentally or derived from quantum mechanical calculations can then be calculated and compared. If significant deviations exist between computed and known values, it is necessary either to introduce new atom types or to use different functional forms for the force field. To ensure accurate predictions from a given force field, this fitting process must be repeated until the deviations between computed and observed values are sufficiently small. 

Atomic orbitals represent the locations of electrons in atoms, and are derived from quantum mechanical calculations. The calculations are only briefly outlined in this chapter, but the results are described in some detail because atomic orbitals are the basis of the understanding of atomic properties. 

Using a more conventional interpretation of molecular properties as derived from quantum mechanical calculations, Reddy and Locke calculated log Poet for 90 herbicides. Their equation included terms for the van der Waals volume, dipole moment, superdelocalizability of the highest occupied molecular orbital (5homo). and nucleophilic superdelocalizability (5n). The regression equation had an SE of 0.705 and an of 0.67. 

If generic properties of polymers need to be determined, it is often sufficient to rely on lattice models. For comparison with experiments of particular melts and blends, more sophisticated off-lattice models are typically applied. These models are described by force fields that determine the interactions between atoms or groups of atoms, and the quality of the modeling is essential for the predictive quality of the simulations. Force field parameters can be derived from direct comparison with experimental data, from quantum mechanical calculations, or both. In the first part of this section, we present generic polymer models that are commonly used in molecular simulations without focussing on any particular substance. Emphasis is placed on lattice and simple off-lattice models that will also be discussed in the next three sections. Section 1.5 is dedicated to chemically realistic descriptions. 

The principal idea behind the CSP approach is to use input from Classical Molecular Dynamics simulations, carried out for the process of interest as a first preliminary step, in order to simplify a quantum mechanical calculation, implemented in a subsequent, second step. This takes advantage of the fact that classical dynamics offers a reasonable description of many properties of molecular systems, in particular of average quantities. More specifically, the method uses classical MD simulations in order to determine effective... 

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