Atom-based contributions

Despite its importance, there still remain few methods to calculate log Saq. Many methods are based on the relationship between Saq and hydrophobicity (log Kow) and some measure of the enthalpy of crystallization (e.g., melting point). Other methods are based on fragment- or atom-based contributions. A full review of methods to calculate log Saq is provided by Livingstone (2003). Methods to calculate log Saq are summarized in Table 3.3. 

With the widespread application of lipophi-licity and partitioning to biophysical processes, a wide variety of tools is currently available to estimate partition coefficient. Several recent reviews of programs and methods that are commercially available have been published (25-28). Predictive methods may be broken down into the following basic approaches to partition coefficient estimation (i) group contribution methods, by use of molecular fragments (2) group contribution, by use of atom-based contributions (5) conformation-dependent or molecular methods (4) combined fragment and atom-based methods and (5)other physicochemical methods. 

Enthalpy of Formation The ideal gas standard enthalpy (heat) of formation (AHJoqs) of chemical compound is the increment of enthalpy associated with the reaction of forming that compound in the ideal gas state from the constituent elements in their standard states, defined as the existing phase at a temperature of 298.15 K and one atmosphere (101.3 kPa). Sources for data are Refs. 15, 23, 24, 104, 115, and 116. The most accurate, but again complicated, estimation method is that of Benson et al. " A compromise between complexity and accuracy is based on the additive atomic group-contribution scheme of Joback his original units of kcal/mol have been converted to kj/mol by the conversion 1 kcal/mol = 4.1868 kJ/moL... 

T Lazaridis, G Archontis, M Karplus. Enthalpic contribution to protein stability Atom-based calculations and statistical mechanics. Adv Protein Chem 47 231-306, 1995. 

Atom-based methods [40, 57-68] cut molecules down to single atoms and commonly do not apply correction rules. According to Eq. (9) they work by summing the products of the contribution of an atom type i times the frequency of its presence in a query molecule ... 

The group of Grippen [40, 61-63] has described the development of a purely atom-based procedure, which exclusively applies atomic contributions and avoids correction factors ... 

XLOGP [67, 68] is a further atom-additive method, as expressed by its almost exclusive use of atomic contributions. However, in contrast to pure atom-based methods correction rules are defined, to account for intramolecular interactions, which is typical for fragmental methods. 

The fragment/atom type contribution method does not need any descriptors based on other theoretical models it only needs to count the occurrence of functional groups or atom types in a molecule, so it is extremely time-saving. One potential disadvantage of this kind of method is that new fragments or atom types not defined in the training sets may cause substantial errors. 

Atom-based Methods As for fragmental methods, the molecule is considered as composed of fragments, but these latter are single atoms instead of functional groups. Each atom is characterized by its own lipophilicity constant and the global lipophilicity is then a sum of each contribution (Equation 5.4). 

What is meant by an identical ensemble for two different species It is helpful to return to our specific example of HCN and HNC. To determine the proper identical ensemble for HNC based on one chosen in the usual fashion for HCN, we first stipulate that all particles that are common to the two systems, i.e., all solvent molecules, the carbon atom, and the nitrogen atom, have identical positions and momenta when we evaluate the energy in system B as when we evaluate it in A. Then, the only contribution to the energy difference in Eq. (12.13) would be the different interactions that the hydrogen atom has with all of the other atoms, based on whether it is attached to C or N (see Figure 12.1). 

Illustrative Example 7.2 Estimating Octanol-Water Partition Constants from Structure Using the Atom/Fragment Contribution Method Illustrative Example 7.3 Estimating Octanol-Water Partition Constants Based on Experimental KI0W s of Structurally Related Compounds... 

T. Lazaridis, G. Archontis, and M. Karplus, Enthalpic Contribution to Protein Stability Insights from Atom-based Calculations and Statistical Mechanics , Adv. Protein Chem., 47, 231-306 (1995). 

Force-field-based scoring functions use arbitrary empirical estimates of interaction energies obtained by molecular mechanics energy functions. This simple approximation, which takes into account only enthalpic contribution often correlates well with the experiment. Solvent effects are described by atom-based solvation parameters, which are computed for the surface of both ligand and receptor which is buried upon complexation. DOCK-chemical27 and CHARMm scoring functions represent this class. 

So the additive functions must be discovered the values of the atom group contributions or increments must be derived. This derivation of group contributions is relatively easy when the shape of the additive function is known and if sufficient experimental data for a fairly large number of substances are known. The derivation is mostly based on trial and error methods or linear programming in the latter case the program contains the desired group increments as adjustable parameters. The objective function aims at minimum differences between calculated and experimental molar quantities. 

Within the last 25 years of X-ray spectroscopy on fusion devices, the theory of He-like ions has been developed to an impressive precision. The spectra can be modeled with deviations not more than 10% on all lines. For the modeling, only parameters with physical meaning and no additional approximation factors are required. Even the small effects due to recombination of H-like atoms, which contribute only a few percent to the line intensity, can be used to explain consistently the recombination processes and hence the charge state distribution in a hot plasma. The measurements on fusion devices such as tokamaks or stellarators allow the comparison to the standard diagnostics for the same parameters. As these diagnostics are based on different physical processes, they provide sensitive tests for the atomic physics used for the synthetic spectra. They also allow distinguishing between different theoretical approaches to predict the spectra of other elements within the iso-electronic series. The modeling of the X-ray spectra of astronomical objects or solar flares, which are now frequently explored by X-ray satellite missions, is now more reliable. In these experiments, the statistical quality of the spectra is limited due to the finite observation time or the lifetime of... 

Surface atoms on real catalysts reside in a variety of coordination environments depending on the exposed crystal plane (see Figure 5.1.3) and may exhibit different catalytic activities in a given reaction. Thus, a turnover frequency based on [ ]q will be an average value of the catalytic activity. In fact, the calculated turnover frequency is a lower bound to the true activity because only a fraction of the total number of surface atoms may contribute to the reaction rate. Nevertheless, the concept of a turnover frequency on a uniform surface has proven to be very useful in relating reaction rates determined on metal single crystals, metal foils, and supported metal particles. 

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