Townes-Dailey theory

The covalency of the bond is calculated from Townes-Dailey theory by the relation... 

In the discussion of NQR results in the frame of the Townes-Dailey theory, the influence of temperature on NQR frequencies is normally ignored. The temperature dependence of NQR spectra is considered here as a crystal field effect and in the following we shall discuss some of its aspects. 

From the Townes-Dailey theory (Eq. (II.9)) different values of (1 -/) will be calculated when frequencies measured at different temperatures are used. Comparing temperatures and T2, the relation for the covalent character is... 

In the first approximation of the Townes-Dailey theory, changes of the s-character of the bonding orbital of chlorine and also changes in the double bond character causing a different 17 are neglected. 

The modified Townes-Dailey theory takes out the influence of the different dif-fusivity of the p.-orbital on the electric field gradient [1409, 1410],... 

The asymmetry parameter in 1,2-disubstituted 5-nitroimidazoles decreases with increasing the substituent size. The n-electron density and N-l bond population is calculated according to the Townes-Dailey theory and described in detail by Dr. Lucken [1408] and Dr. Dolgushin [1409,1410] based on height with lengthening of the substituent on N-l [1411]. 

Often the Townes-Dailey approximation is used rather successfully. This approximation assumes that contributions to the EFG from nonsphericity of core electron and from lattice charge distributions offset each other. Then the EFG results from imbalances in valence electron populations. The calculations also show that the errors introduced by the approximations ofthe Townes Dailey theory do not exceed 5%. Thus Townes Dailey calculations generally do well in showing trends in quadrapole coupling constants or NQR frequencies. 

Using the Townes-Dailey theory, a relationship of the NQR frequency of a single-bonded terminal unhybridized Cl atom can be derived to the ionic character, i, of the bond to the chlorine atom, or to the partial charge of the chlorine atom, 5ci-... 

These calculations, of course, are subject to the usual limitations of Townes Dailey theory, as well as the assumption that the bond angle is effectively 90°. So they are most likely useful to show, not absolute values of <7b2, but periodic trends in those values. 

NQR data yield primarily informations on the p electron densities in the valence shells, from which the net resulting charge on the investigated atom can be easily inferred by means of some simple models, e.g. of the TOWNES-DAILEY theory. Usually the accuracy of experimental measurements is rather high, and is at present not matched by equally powerful and accurate interpretative theories. Therefore at this initial state of application in the field of coordination chemistry we are devoting more attention to the experimental results of NQR spectroscopy, their immediate interpretation and their close connection with X-ray structural data. 

Table 10 Electron tt- and cr-Populations Calculated by Townes and Dailey Theory from 14N NQR Coupling Constants for the Ring Nitrogen Atom in 4-Substituted Pyridines...

A simple semiempirical theory for the interpretation of nuclear quadrupole coupling constants in terms of chemical bonding was developed by Townes and Dailey 2 24). This theory is treated in many summary papers on NQR, e.g. 39 4S 94.i43.is9) An extension of the Townes-Dailey treatment was given by Cotton and Harris 113-123>. Besides these simple model theories, a variety of more elaborate calculations have been done on the influence of intramolecular bonding on NQR spectra (see the discussion in 143- S9)). 

Since the Townes-Dailey model is the basis of most interpretations, we shall discuss here the results of this theory. For simplicity, we consider a single bond between an element and a halogen atom. 

The determination of the coupling of a p electron appears to be more useful for the interpretation of the molecular couplings by means of the Townes and Dailey theory and through the computation of the p contribution of each molecular orbital involved in the nitrogen atom bonding43)-... 

The consideration of the exact value of the angle CNC was quite reasonable, both for the sake of completeness and because 2 - a and 2 — b are very sensitive to the value 2tpof this angle. Nevertheless, owing to the many approximations on which the Townes and Dailey theory is based, it did not always seem desirable to consider ip deviations from a 60 ° mean value 7 ). 

The paper is divided into sections as follows. First, ab initio calculations on Br2 and then some approximate supermolecule calculations on H3N Br2 are reported. Then the Townes-Dailey model for nuclear quadrupole coupling constants and its connection with response theory are briefly reprised. Finally the model is applied to the complex H3N" -Br2, and empirical and ab initio results are compared. 

The relative occupation of the 5s- and 5p-orbitals is not immediately given by the chemical isomer shift, but may be derived in conjunction with the quadrupole splitting to which does not contribute. The relevant theory is directly adopted from n.q.r. spectroscopy [78]. The Townes and Dailey theory says that the principal value of the molecular field gradient (eq od is related to the atomic electric field gradient from a 5p-hole in the 5s 5p configuration (e at) by... 

---