Polarization correlation coefficient

A convenient way of displaying these correlations is the polarization correlation coefficient ... 

Fig. 3. Polarization correlation coefficient, as a function of the relative orientation of the polarizers.

These are B.C.H.S.H. inequalities, i.e. Bell s inequalities generalized by Clauser, Horne, Shimony, Holt They bear upon a combination of four polarization correlation coefficients, measured in four orientations of the polarizers. S is thus a measurable quantity. 

Here, Yx m( j) denotes a spherical harmonic, coj represents the spherical polar angles made by the symmetry axis of molecule i in a frame containing the intermolecular vector as the z axis. The choice of the x and y axes is arbitrary because the product of the functions being averaged depends on the difference of the azimuthal angles for the two molecules which are separated by distance r. At the second rank level the independent correlation coefficients are... 

QuantlogP, developed by Quantum Pharmaceuticals, uses another quantum-chemical model to calculate the solvation energy. As in COSMO-RS, the authors do not explicitly consider water molecules but use a continuum solvation model. However, while the COSMO-RS model simpUfies solvation to interaction of molecular surfaces, the new vector-field model of polar Uquids accounts for short-range (H-bond formation) and long-range dipole-dipole interactions of target and solute molecules [40]. The application of QuantlogP to calculate log P for over 900 molecules resulted in an RMSE of 0.7 and a correlation coefficient r of 0.94 [41]. 

On the other hand, the analyst might not be interested in global retention indices. Indeed, by increasing the temperature for SF3, he would obtain similar retention indices as for the other two. He will then observe that the relative retention time, i.e. the retention times of the substances compared with each other, are the same for SF, and SF3 and different from SFj. Chemically, this means that SF3 has different polarity from SFj, but the same specific interactions. This is best expressed by using the correlation coefficient as the similarity measure. Indeed, rj3 = 1, indicating complete similarity, while r 2 23 much lower. Since both... 

Fields et al. 33) examined the closely related bis (trifluoromethyl) phosphine (Table 14) and found a similar increase in Vp.H with increasing polarity of the solvent. They noted a correlation between /P H and the proton chemical shift (confidence limit of the correlation coefficient was 99.9 %). Again hydrogen bonding was suggested as the principle causative factor since correlations with dielectric constant or refractive index were not found. The two-bond 2/P F was noted to decrease while the three-bond 3/H F coupling constant was solvent invariant (vide infra). 

Pharmaceuticals Correlation coefficient, wavelength distance, polar coordinates, gravity center, scanning probability windows PRMs comparison 73... 

A high correlation coefficient ( r = 0.903, 99 percent confidence level) was found between Y c and polar group concentration ( COO) and relatively high correlation coefficients were obtained between Yc and the metallic elements (Cr and Ni), but carbon (main component of oil), oxygen, hydration degree (n) and covering rate W showed low correlation coefficient. In Fig. 11, Yc versus the polar group concentration is presented. 

A high correlation coefficient ( r = 0.969) and a relatively low intercept value (-7.053 dyne) indicate that Yc on the oiled CDC - Ni plated sheet is substantially determined by the polar group of oil and the metallic elements. 

Cotton-Mouton effect), NMR chemical shift and coupling constants, the optical rotation of polarized light and correlation coefficients between different properties. Extensions to incorporate long-range interactions have also been elaborated11 and it has even been possible to adapt RIS theory for the description of the dynamics of transitions between rotational isomeric states.12,13... 

None of the zeroth-order partial correlation coefficients involving ae was significant. It seems fairly certain that the electronic demand in the reaction in set CR2abc is 0. The rate of the reaction is accelerated by electron donor substituents and decelerated by electron acceptor groups. This situation is reversed in set CR2d. The best explanation of these observations is that the mechanism in the most polar solvent, acetonitrile, is different... 

Quinones et al. (2000) reported the successful use of neural networks to predict the half-life of a series of 30 antihistamines. The input for the network was derived from the output of CODES, a routine that generates descriptors for a structure based on atom nature, bonding, and connectivity. Attempts to correlate the half-life with the physicochemical parameters log Kow, pKa, molecular weight, molar refractivity, molar volume, parachor, and polarity were unsuccessful. In a subsequent study by Quinones-Torrelo et al. (2001), the authors correlated the half-life of 18 antihistamines with their retention in a biopartitioning micellar chromatography system with a resultant correlation coefficient (R2adj) value of 0.89. The correlation is explained in that the retention in this system is dependent on hydrophobic, electronic, and steric properties, which are also important in determining half-life. 

Most of the descriptors have been explained earlier L16 is the hexadecane-gas partition coefficient. The extremely high correlation coefficient is of some concern, and may indicate overfitting of the data. From this QSAR, it can be deduced that hydrogen bond donor ability and polarity/polariz-ability are most important in controlling K. ... 

The necessity of having two independent terms to describe the specific (or polar) interactions is relevant to the fact that most organic probes are amphoteric and may as well act as electron donors or electron acceptors, as seen in Table 9. In Table 9, it should be noted that LFERs for a general set of electron acceptors (or donors) which is the specific component of adsorption enthalpy may be closely related to LSERs of Kamlet-Taft, resulting in that the correlation coefficients are largely constant and the standard deviations are low, as below [119]... 

Recently Roe (29) reported that the p values for polymers were smaller than those for monomers. For instance, the following p values were found 3.0 for poly (ethylene oxide), 3.2 for both polyethylene and polypropylene, 3.3 for branched polyethylene, 3.5 for poly (dimethyl siloxane), and 4.1 for poly (butene). Here the relationship between p and polarity is not well defined. But if the exact value of p is known for each homolog of compounds or polymers, we should be able to obtain a higher correlation coefficient and a lower standard deviation. 

The symmetrical cis- and trans-olefins RCH=CHR (Table III) are particularly suited to this evaluation by Equation 10 because the polar reaction constant p and the steric correlation coefficient 8 reflect, in this series of olefins, the effect of varying two substituents. Hence, the expected effects (both on p and 8) are more pronounced than those expected for olefins in which only one substituent is varied. 

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