Dipole error statistics

The so called G2 set of molecules is nowadays considered a standard for the validation of new quantum chemical approaches [72]. Table V collects an error statistic for several quantum mechanical approaches concerning the geometric and thermodynamic parameters of 32 molecules belonging to the G2 set, together with dipole moments and harmonic vibrational frequencies. 

To illustrate how well DFT or ab initio methods predict the dipole moments. Table 1 illustrates the comparison between theory and experiment for eight small molecules. The error statistics are summarized in Table 2. In general, the quality of the basis set plays an important role in the prediction of dipole moments. We see that the 6-3IG basis set provides poor predictions, even when applied with a QCISD level of theory. The performances of the double-zeta basis set plus polarization functions (6-3IG, DZVPD (double-zeta valence orbitals plus polarization and diffuse functions on heavy atoms), and cc-pVDZ (correlation-consistent polarized valence double-zeta)) are poorer than those from the polarized triple-zeta basis sets. The only exception is B-P/DZVPD (B-P = Becke-Perdew), from which we obtained an average absolute deviation of 0.040 debye, lower than that (0.053 debye) from B-P/TZVPD (triple-zeta valence orbitals plus polarization and diffuse functions on heavy atoms). It can be seen that the inclusion of correlation effects through either ab initio or DFT approaches significantly improves the agreement. 

Heats of formation, molecular geometries, ionization potentials and dipole moments are calculated by the MNDO method for a large number of molecules. The MNDO results are compared with the corresponding MINDO/3 results on a statistical basis. For the properties investigated, the mean absolute errors in MNDO are uniformly smaller than those in MINDO/3 by a factor of about 2. Major improvements of MNDO over MINDO/3 are found for the heats of formation of unsaturated systems and molecules with NN bonds, for bond angles, for higher ionization potentials, and for dipole moments of compounds with heteroatoms. 

Figures 4.29 and 4.30 display the co-evolution of the formamide dipole moment and of the oxygen(formamide)-oxygen(water) radial distribution function during the polarization process [12]. As the dipole moment of the formamide increases, the position of the first peak of the RDF is shifted inward and its height increases. Once the dipole moment has reached its equilibrium value, it begins to fluctuate. Fluctuations are related to the statistical error associated with the finite length of the simulations. From Figures 4.29 and 4.30 it is clear that (1) ASEP/MD permits one to simultaneously equilibrate the...

Fig. 16.3 Histogram and normal distribution of calculated values for the dipole polarizability of liquid Ar, using Model 1. Average polarizability is (a) = 11.59 ao3 and statistical error, v=0.03 ao3. Also shown (below) are the individually calculated mean dipole polarizabilities of the different configurations used...

Unfortunately, Eq. 20 is of limited practical use since, at high dipole moments, the value of s depends sensitively on the statistical error on (M ). Other expressions for the dielectric constant can be derived by considering an internal energy of the form [20]... 

The results and their statistical analysis are collected in Table 1 for a set of small molecules taken from the database compiled by Tkatchenko and Scheffler [16], as used in [58]. The experimental dispersion coefficients have been determined from dipole oscillator strength distributions (DOSD) [59-71]. The percentage errors of some of the methods (LDA[M], PBE[M], RHF[M] and RSHLDA[M]) are shown in Fig. 3. 

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