Quantum-chemical parameters

Keywords solvent parameters, quantum chemical calculations, solvent effect... 

Empirical donor-acceptor parameter Quantum chemical index A B Mean square deviation Number of compounds... 

Vectors A series of scalars can be arranged in a column or in a row. Then, they are called a column or a row vector. If the elements of a column vector can be attributed to special characteristics, e.g., to compounds, then data analysis can be completed. The chemical structures of compounds can be characterized with different numbers called descriptors, variables, predictors, or factors. For example, toxicity data were measured for a series of aromatic phenols. Their toxicity can be arranged in a column arbitrarily Each row corresponds to a phenolic compound. A lot of descriptors can be calculated for each compound (e.g., molecular mass, van der Waals volume, polarity parameters, quantum chemical descriptors, etc.). After building a multivariate model (generally one variable cannot encode the toxicity properly) we will be able to predict toxicity values for phenolic compounds for which no toxicity has been measured yet. The above approach is generally called searching quantitative structure - activity relationships or simply QSAR approach. 

A fundament of the quantum chemical standpoint is that structure and reactivity are correlated. When using quantum chemical reactivity parameters for quantifying relationships between structure and reactivity one has the advantage of being able to describe the nature of the structural influences in a direct manner, without empirical assumptions. This is especially valid for the so-called Salem-Klopman equation. It allows the differentiation between the charge and the orbital controlled portions of the interaction between reactants. This was shown by the investigation of the interaction between the Lewis acid with complex counterions 18> (see part 4.4). 

Our investigations agree with arguments in earlier articles by other authors, namely that empirical reactivity indices provide the best correlation with the goal values of the cationic polymerization (lg krel, DPn, molecular weight). On the other hand, the quantum chemical parameters are often based on such simplified models that quantitative correlations with experimental goal values remain unsatisfactory 84,85>. But HMO calculations for vinyl monomers show, that it is possible to determine intervals of values for quantum chemical parameters which reflect the anionic and cationic polymerizability 72,74) (see part 4.1.1) as well as grades of the reactivity (see part 3.2). 

The ability to ionically polymerize apparently correlates in many cases with the capacity of the substituents to act as electron acceptors (anionic polymerizability) or as electron donors (cationic polymerizability) on the rt-bond of the vinyl group. These relationships should be visible in carefully chosen quantum chemical parameters. 

In the case of the anionic polymerizability it is possible to find limits of the quantum chemical parameters which separate those monomers capable of polymerization from those not (see Table 9). 

Before 1980, force field and semiempircal methods (such as CNDO, MNDO, AMI, etc.) [1] were used exclusively to study sulfur-containing compounds due to the lack of computer resources and due to inefficient quantum-chemical programs. Unfortunately, these computational methods are rather hmit-ed in their reliability. The majority of the theoretical studies under this review utilized ab initio MO methods [2]. Not only ab initio MO theory is more reliable, but also it has the desirable feature of not relying on experimental parameters. As a consequence, ab initio MO methods are apphcable to any systems of interest, particularly for novel species and transition states. 

All of these parameters (with the possible exception of SAP) are frequently used in QSAR studies or as filters in virtual screening. The SAP descriptor was included to check for correlations between PSA and quantum chemically calculated charges. 

Correlation of Log P with Calculated Quantum Chemical Parameters... 

Two models of practical interest using quantum chemical parameters were developed by Clark et al. [26, 27]. Both studies were based on 1085 molecules and 36 descriptors calculated with the AMI method following structure optimization and electron density calculation. An initial set of descriptors was selected with a multiple linear regression model and further optimized by trial-and-error variation. The second study calculated a standard error of 0.56 for 1085 compounds and it also estimated the reliability of neural network prediction by analysis of the standard deviation error for an ensemble of 11 networks trained on different randomly selected subsets of the initial training set [27]. 

MD simulations in expHcit solvents are stiU beyond the scope of the current computational power for screening of a large number of molecules. However, mining powerful quantum chemical parameters to predict log P via this approach remains a challenging task. QikProp [42] is based on a study [3] which used Monte Carlo simulations to calculate 11 parameters, including solute-solvent energies, solute dipole moment, number of solute-solvent interactions at different cutoff values, number of H-bond donors and acceptors (HBDN and HBAQ and some of their variations. These parameters made it possible to estimate a number of free energies of solvation of chemicals in hexadecane, octanol, water as well as octanol-water distribution coefficients. The equation calculated for the octanol-water coefficient is ... 

The major contribution to the components of the D tensor as well as the deviations of the g values from 2.0023 arises from the mixing of ligand field states by SOC other contributions to D result from direct spin-spin coupling, which mixes states of the same spin S. The D tensor and the g matrix both carry chemical information as they are related to the strength and symmetry of the LF, which is competing and counteracting to the effects of SOC. Details on the chemical interpretation of the parameters by quantum chemical means is found in Chap. 5. 

The spin-Hamiltonian formalism is a crutch in the sense that it is a parameterized theory, but it provides a common theoretical frame for the various experimental techniques with a minimum number of adjustable parameters that describe the essential physics of the system under investigation. Even more important is the fact that the same parameters can be derived relatively easily from quantum chemical calculations. Therefore, theoreticians appreciate the concept as a convenient place to rest in the analysis of experimental data by theoretical means [123, 124]. 

This theory appears not to involve adjustable parameters (other than the nuclear radius parameters that were taken from the literature). In particular, it was criticized that the calibration approach involved a slope that is too high by about a factor of two. However, in actual calculations with the linear response approach, it was found that the slope of the correlation line between theory and experiment (dependent on the quantum chemical method) is close to 0.5. Thus, it also requires a scaling factor of about 2 in order to reach quantitative agreement with experiment. The standard deviations between the calibration and linear response approaches are comparable thus indicating that the major error in both approaches still stems from errors in the description of the bonding that is responsible for the actual valence shell electron distribution. 

The usefulness of quantum-chemical methods varies considerably depending on what sort of force field parameter is to be calculated (for a detailed discussion, see [46]). There are relatively few molecular properties which quantum chemistry can provide in such a way that they can be used directly and profitably in the construction of a force field. Quantum chemistry does very well for molecular bond lengths and bond angles. Even semiempirical methods can do a good job for standard organic molecules. However, in many cases, these are known with sufficient accuracy a C-C single bond is 1.53 A except under exotic circumstances. Similarly, vibrational force constants can often be transferred from similar molecules and need not be recalculated. 

The general theory of the quantum mechanical treatment of magnetic properties is far beyond the scope of this book. For details of the fundamental theory as well as on many technical aspects regarding the calculation of NMR parameters in the context of various quantum chemical techniques we refer the interested reader to the clear and competent discussion in the recent review by Helgaker, Jaszunski, and Ruud, 1999. These authors focus mainly on the Hartree-Fock and related correlated methods but briefly touch also on density functional theory. A more introductory exposition of the general aspects can be found in standard text books such as McWeeny, 1992, or Atkins and Friedman, 1997. As mentioned above we will in the following provide just a very general overview of this... 

The growing importance of quantum-chemical calculations is dealt with in a short section, with emphasis on the consideration of relativistic effects, especially in systems containing mercury. These calculations aim at optimization of structures, determination of bond energies, simulation of spectra, and estimation of spectral parameters, independent of but complementary to experiments. 

In contrast to kinetic models reported previously in the literature (18,19) where MO was assumed to adsorb at a single site, our preliminary data based on DRIFT results suggest that MO exists as a diadsorbed species with both the carbonyl and olefin groups being coordinated to the catalyst. This diadsorption mode for a-p unsaturated ketones and aldehydes on palladium have been previously suggested based on quantum chemical predictions (20). A two parameter empirical model (equation 4) where - rA refers to the rate of hydrogenation of MO, CA and PH refer to the concentration of MO and the hydrogen partial pressure respectively was developed. This rate expression will be incorporated in our rate-based three-phase non-equilibrium model to predict the yield and selectivity for the production of MIBK from acetone via CD. 

To judge the bonding properties of SiO and SiS, we compare their experimentally derived force constants and bond energies with those of CO and CS [10]. Further insight into the bonding characteristics is gained from molecular parameters such as geometry and force constant data as well as electron distributions (Tab. 1), which are derived from ab initio quantum chemical calculations. 

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