Predicted dipole moments

The dipole moment (A) of a molecule is the first moment of the elec tric charge density of a molecule. Paraffins have dipole moments of zero, while dipole moments of almost all hydrocarbons are small. McClellan lists many dipole moments. The computer method of Dixon and Jurs" is the most useful method for predicting dipole moments. Lyman et al. give other methods of calculation. 

Gaussian also predicts dipole moments and higher multipole moments (through hexadecapole). The dipole moment is the first derivative of the energy with respect to an applied electric field. It is a measure of the asymmetry in the molecular charge distribution, and is given as a vector in three dimensions. For Hartree-Fock calculations, this is equivalent to the expectation value of X, Y, and Z, which are the quantities reported in the output. 

Here are the predicted dipole moments and atomic charges ... 

The MM3(2000) force field is the basis of this chapter. The program includes an induced dipole calculation that allows for the treatment of induction.69 This improvement in the electrostatics yields better predicted dipole moments than in previous versions of MM3. It should be pointed out that most other force fields use point charges whereas the MM series of programs is based on point dipoles. 

Karelson et al. [268] used the AMI D02 method with a spherical cavity of 2.5 A radius to study tautomeric equilibria in the 4-hydroxyisoxazole system (they did not specify which hydroxyl rotamer they examined). Tautomer 17 predominates in aqueous solution. Although AMI predicts 16 to be about 10 kcal/mol more stable in the gas-phase than 17, its dipole moment is only predicted to be 0.68 D. Tautomer 17 has a predicted dipole moment of 2.83 D in the gas-phase. With the small cavity, the two dipole moments increase to 0.90 and 4.56 D, respectively, and this is sufficient to make 17 0.3 kcal/mol more stable than 16 in solution. Zwitterion 18 is much better solvated than either of the other two tautomers, but AMI predicts its gas-phase relative energy to be so high that it plays no equilibrium role in either the gas phase of solution. 

From this point of view, let us wander a little from the subject to discuss briefly the comparison of the computed and experimental values of a dipole moment. Too often, people compare their theoretical results with experimental values obtained in solution, and if there is a discrepancy between the two sets, they generally blame the so-called failure of quantum chemistry to predict dipole moments. 

It is well established that the average lengths of CH bonds are consistently 0.003 to 0.004 A longer than the corresponding CD bonds in the ground vibrational state (see Fig. 12.1, its caption, and Section 12.2.3). It remains only to establish the dipole moment derivative, (9p/9r), at the equilibrium bond length. That is available from theoretical calculation or spectroscopic measurement (via precise measurements of IR intensities of vibration-rotation bands). Calculations based on Equation 12.7 yield predicted dipole moment IE s in reasonable agreement with experiment. 

Dipole moments and Ionization potentials. Semiempirical methods predict dipole moments vdthin about 0.4 D of that observed experimentally. 

Over the 108 molecules in Test Set B of Table 8.5, Scheiner, Baker, and Andzelm computed the mean unsigned errors in predicted dipole moments to be 0.23, 0.20, 0.23, 0.19, and 0.16 D at the HF, MP2, SVWN, BPW91, and B3PW91 levels of theory, respectively, using the 6-31G(d,p) basis set. These results were improved somewhat for the DFT levels of theory when more complete basis sets were employed. 

The calculations (Table XV) indicate that this betaine tautomer is predicted to be about 50 kcal/mole less stable than the usual tautomers of guanine. From this point of view its existence would therefore be surprising. Moreover, if existing it should possess two other striking features its predicted dipole moment should be of the order of 15 D and its spectrum should exhibit an enormous bathochromic shift with respect to the spectra of the usual guanines. No information is available about the dipole moment of this molecule but its absorption spectrum (Amax = 264 mg at pH 1 273 mg at pH 11) does not exhibit any extraordinary feature. 

Whereas the dipole moments of thieno[3,2-b]thiophene (3) and selenolo[3,2-6]selenophene (4) are 0.00 D, the mixed system selenolo[3,2-6]thiophene (29) exhibits a dipole moment of 0.30 D. Perturbation of the symmetry of (3) by the introduction of an ethyl group in the molecule at C-2 generates a dipole moment of 0.30 D. A study of the other classical thienothiophenes, selenoloselenophenes and selenolothiophenes shows that the [2,3-6]-annelated systems exhibit a slightly higher dipole moment compared to the [3,4-6]- or [2,3-c]-annelated systems (76AHC(19)123). In the case of the nonclassical thiophenes (Id X = Y = S), (Id X = S, Y=NH) and (Id X = S, Y = 0) the predicted dipole moments are 0.00, 0.15 and 3.21 D respectively (74JA1817). Experimental verification is not possible since none of these compounds are known although it should be of interest to determine the dipole moments of the tetraphenyl derivatives (6) and (12) and the pentaphenyl compound (13). 

Table IV. Effect of Correlation on Predicted Dipole Moment, Polarizability, and Electron Affinity of HF(R = 1.7328 bohr), L1F(R - 2.9549 bohr), and BeO(R - 2.5150 bohr).

It turns out that the dipole moment calculated for AuR (at R = 2.8794 au) using the relativistic wavefunction is smaller (by about 40% to 50%) than that predicted by the corresponding NRL wavefunction, depending upon the basis set used in the calculation of the wavefunction. Rowever, the predicted dipole moments (using the relativistic chemical basis set wavefunctions) of 0.976, 0.323 and 0.371 au differ considerably from the values of 1.372, -0.120 and 0.019 au, predicted by the NRL wavefunctions, for AuR, TiR and BiR, respectively. In the case of TiR, although the dipole moment calculated with the relativistic (CB set) wavefunction predicts the expected polarity viz Ti R the value of dipole moment (-0.12 au)... 

CONTEXT Once we ve solved a Schrodinger equation to get the wavefunction for the electrons in an atom or molecule, we can calculate the distribution of the electrons. This tells us, for example, how much charge from the electron is at each point in the system, allowing us to predict dipole moments or nuclear magnetic resonance spectra (such as the spectrum below more on this topic in Section 5.5). In this example, we show how the wavefunction for a 2p electron, if properly normalized, can tell us how much electron density lies close to the plane through the middle of the orbital. 

Rotamers N and O have very similar quadrupole coupling constants comparison of their values with those predicted ab initio indicate that they are necessarily conformers la and III a (see Tables 1 and 2). Because of the similar orientation of the amino group in these forms (see Fig. 6), they cannot be discriminated on the basis of the quadrupole constants. We can distinguish them from their selection rules and intensities of the observed transitions. The rotational spectrum of rotamer N shows strong Pa typc transitions and fairly weak Pc-type transitions, while form O presents strong Pa type transitions and medium-strength pb- and Pc-type transitions. No pb-type transitions have been detected for conformer N. Considering the predicted dipole moment components of Table 1, these data are consistent with... 

Experimental dipole moments may be used to check the validity of electrostatic calculations. In the past, dipole moments of proteins were often characterized by measurements of dielectric relaxation. More information may be obtained by measurements of the electric dichroism because these measurements provide not only the magnitude of the dipole moment but also the optical anisotropy with respect to the dipole vector. Thus, measurements of the electric dichroism provide a more rigorous test for calculations of electrostatic parameters of proteins. Using the calculations described earlier for pK s of titratable groups, one can predict dipole moments of proteins and their axes given by the principal axes of the rotational diffusion tensor and compare them with electrooptical data. ° One important aspect of comparison of computed and experimental dipole moment is that computations of dipole moments, optical anisotropy, and rotational diffusion coefficients can be used in combination with experimental electrooptical procedures to determine the long-range structure of biomacromolecular assemblies, such as the complexes of DNA and proteins described by Pbrschke et al. so... 

In Table 17, we compare the computed results of water dimer, which is probably the most extensively studied hydrogen-bonded system, The predicted dipole moment fj. of water dimer from DFT and MP2 approaches agree quite well with the experimental fj. of water dimer. Rq-q is the distance between two oxygen atoms as shown in Figure 2, while the donor proton resides in between and forms a near linear O-H-0 bonding, Gradient-corrected functionals and MP2 predict very accurately for this geometrical parameter, while local S-VWN predicts a value for Rq-q that is much too short 0.27 A shorter than the experimental observation. 

In the present section, we shaU therefore proceed differently, comparing our calculated dipole moments with a set of predicted dipole moments, obtained from our best calculated values (obtained at the CCSD(T) level in the aug-cc-pVQZ basis) by adding corrections for higher-order correlation effects and basis-set incompleteness. The best calculated and predicted dipole moments are both listed in Table 15.10. Note that the uncertainties in the predicted /u (mostly 0.01 or 0.02 D) are smaller than the differences between the experimental p. and po, substantiating further our assumption that a comparison with the predicted Pe is more satisfactory than a direa comparison with the experimental pq. 

The predicted dipole moments in Table 15.10 were obtained in the following manner. For each dipole moment calculated at the CCSD(T) level in the aug-cc-pVQZ basis, we first added a correction for the connected quadruples, obtained by assuming that the ratio between the quadruples and triples corrections is the same as the ratio between the triples and doubles corrections. Obviously, this procedure can give only a crude estimate of the quadruples correction, but it may at least serve as a rough indication of the error in the calculated dipole moments. 

Let us now compare the predicted equilibrium dipole moments with experiment Of the four experimental values in Table 15.10, the dipole moments for CO, HF and H2O are within 0.01 D of the predicted value. For NH3, on the other hand, the dipole moment differs by as much as 0.04 D from the predicted value. It has been argued, however, that the experimental He of NH3 is too large by several hundredths of a debye, suggesting that this discrepancy arises from an error in the experimental rather than predicted dipole moment [5]. 

Fig. 15.8. The mean errors, standard deviations, mean absolute errors and maximum absolute errors of the aug-cc-pVXZ dipole moments relative to the predicted dipole moments in Table 15.10 (in D). The Hartree-Fock, MP2, CCSD jnd CCSD(T) models use the line patterns described in the legend of Figure 15.3.

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