Theoretical dipole moments

The triplet nitrenium ion, however, lacks symmetry but, unlike the excited triplet states of other azaaromatic systems such as pyridine, is surprisingly planar.283 Theoretical dipole moments for cyclopent[c]- and cyclopent[rf]azepine, and the molecular geometry of cyclopent[rf]-azepine, have been calculated using semiempirical ab initio methods.3... 

Table 2 Theoretical dipole moments and relative energies of tetrazole tautomers, R—CN4H.

Inorganic Compds State or Solvent Expt l Dipole Moment Debyes Ref Theoretical Dipole Moment Debyes Ref... 

Table I. Theoretical Dipole Moments and Second-Order Hyperpolarizabilities for Selected Methylsulfonyl and Nitro Compounds (A = 1907 nm)...

A previous study of the charge distribution in cyclopropene using the 6-3IG basis set suggested that jr-electrons are withdrawn from the double bond into the methylene group. ) This led to a theoretical dipole moment with its negative end at the CH2 group and the following n-orbital populations... 

Aziridine has been examined in a number of previous ah initio molecular orbital studies. > > > 5.38,39,53,54,59,60) Energies and dipole moments from some of these are compared with our results and with experiment in Table 9. The theoretical dipole moments are all somewhat higher tham the experimental value except for the result obtained by Bonaccorsi, Scrocco and Tomasi with a minimal Slater basis. The latter (1.77D) is quite close to our STO-3G value (1.82D, Table 2). 

There have been several previous ab initio molecular orbital studies of oxirane using the experimental geometry.30.3it34,35,38,39,63) These have been mostly concerned with ionization potentials and first order properties such as multipole moments. Some details are given in Table 10. As with aziridine, all the theoretical dipole moments except those calculated with the minimal Slater basis 33) are higher than the experimental value. 

The results of various electron density calculations for pyrazolo[l,5-a]pyridine are collected in Table 1. All successfully predict the observed electrophilic attack at C(3). The CNDO/2 values ( ) lead to a theoretical dipole moment of 2.6 D and those of C ) to 2.5 D. These compare favourably with the experimental value (2.18 D). The values are also consistent with delocalization of the bridgehead nitrogen lone pair over the lOir-electron system. 

The experimental dipole moment of COF j, as measured from the Stark effect upon the microwave spectrum, is 0.951 D (3.17 x 10 3° C m) [1215]. Many theoretical dipole moments for COF have been reported [463,472,486,513,673,921,1414,1532,2037,2234], and the range of values is commensurate with the range of techniques used to calculate them. 

FIGURE 4 Experimental (x-ray) and theoretical dipole moments for uracil (after Stewart ). 

Frequently the work involved conjugated molecules to which Electronic population analysis was usually added to the energy calculations and a theoretical dipole moment was obtained that could be compared with the experimental data. With the advent of NMR. and ESR. spectroscopy other observables became available, and theory was successfully applied to the interpretation of these spectra. However, very little was done in the field of real chemistry, that is, in the study of reaction mechanisms and reaction rates. Over the last decade the availability of large electronic computers, the introduction of approximate but reliable quantum mechanical methods which include all the electrons, or at least all valence electrons in a molecular system and the discovery of the rules of orbital symmetry have led to a significant change of the situation. 

The DFT dipole moments are often significantly in error, by amounts comparable to the errors for the conventional ab initio procedures. These discrepancies are at least partially due to the deficiencies in the 6-31G(d) orbital basis set. For the lone-pair molecules NH3, H2O and HF, theoretical dipole moments are too large by almost all methods. The theoretical values for... 

If we know the distance d between two atoms, we can calculate a theoretical dipole moment on the assumption that the atoms bear a full single charge this value is /hheor 4.8d debyes. The percent ionic character of the bond can then... 

Table 13 Experimental and theoretical dipole moments p№ and dipole polarizability anisotropy for some small molecules. The theoretical results have been obtained using Hartree-Fock (HF), LDA, and GGA methods, and all quantities are given in atomic units. From ref. 80...

One of the deficiencies of the MO methods, especially the simple ones, is that they tend to exaggerate uneven distribution of electrons in a molecule and thus make it more polar (with a higher dipole moment) than it actually is. The result is that dipole moments which are based on charge densities obtained from eigenfunctions of the MO approximations are usually considerably higher than the actual experimental dipole moments. Two old, well-known examples of theoretical dipole moments obtained by the HMO method are fiilvene (11) whose calculated dipole moment is 4.7 D [72-74] and the experimental value is 1.2 D [68], and azulene (15), with a calculated dipole moment of 6.9 D [72] and the experimental value of 1.0 D [68]. 

The above material represents a concise overview devoted to experimental and theoretical dipole moments of aromatic heterocycles, their determination and computation. Only selected relevant references are included, with a particular attention to our own work. The coverage is not exhaustive. 

All these physical data on diazomethane are explainable with the conclusion that this compound is a mesomeric hybrid of structures 5.1a, 5.1b, and 5.1c, with a decreasing importance in that sequence. Moore and Pimentel (1964 c) calculated the theoretical dipole moments for 5.1a to be 5.46 D and for 5.1b to be 6.24 D (with opposite signs). They deduced from these values that 5.1a predominates over 5.1b. From these data only, the mesomeric structure 5.1c is actually not necessary. It was, however, added a long time ago (e. g., Eistert, 1938) because of the reactivity of N(2) as an electrophilic center (for other mesomeric structures see Sect. 4.4, 4.32a-4.32e). 

From Equation 20 one predicts a value of m = 2.15 D for 48, in excellent agreement with the experimental value (Table 2). However, in view of the crudeness of the approximations in the calculation this excellent agreement between experimental and theoretical dipole moments of 48 must be regarded as fortuitous. 

Good agreement has also been achieved between experimental results and theoretical dipole moments, quadrupole moments, diamagnetic susceptibilities, and electronic second moments obtained by non-empirical calcula-tion. But, following Bloor et al., the good agreement of the latter values should not be considered as a test for the quality of the molecular wavefunction, as these depend predominantly on the molecular geometry (CNDO/2 calculation of thiophen and other sulphur compounds). 

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