Diffuse functions, effect

Figure 12.42ft shows the measurements given as a function of the Archimedes number At ATqIuq. This figure is more informative than Fig. 12.42(3. The figure shows that the temperature effectiveness is a function of the Archimedes number. An identical level of j for the two diffusers A and B at the same Archimedes number implies that the temperature effectiveness is rather independent of the diffuser design and the local induction close to the diffuser. The effectiveness is probably more dependent on other parameters that are constant in the experiments, such as heat source and heat source location.

This table provides an introduction to the basis set effects we U discuss in the next chapter. Adding diffuse functions lowers the frequency by about 20-30 cm. However, both sets of numbers are in reasonable agreement with the observed values, with the better theoretical values producing quite good agreement. However, even using the smaUer basis set, we can successfully identify the carbonyl stretch. 

Diffuse functions have very little effect on the optimized structure of methanol but do significantly affect the bond angles in negatively charged methoxide anion. We can conclude that they are required to produce an accurate structure for the anion by comparing the two calculated geometries to that predicted by Hartree-Fock theory at a very large basis set (which should eliminate basis set effects). 

Predict the structure and frequencies for this compound using two or more different DFT functionals and the LANL2DZ basis set augmented by diffuse functions (this basis set also includes effective core potentials used to include some relativistic effects for K and Cs). How well does each functional reproduce the observed spectral data ... 

The substituent effects on the H-bonding in an adenine-uracil (A-U) base pair were studied for a series of common functional groups [99JPC(A)8516]. Substitutions in the 5 position of uracil are of particular importance because they are located toward the major groove and can easily be introduced by several chemical methods. Based on DFT calculation with a basis set including diffuse functions, variations of about 1 kcal/mol were found for the two H-bonds. The solvent effects on three different Watson-Crick A-U base pairs (Scheme 100) have been modeled by seven water molecules creating the first solvation shell [98JPC(A)6167]. 

In Table 3 we have listed the results of a basis set and correlation study for the hyperpolarizability dispersion coefficients. In a previous investigation of the basis set effects on the dispersion coefficients for the first hyperpolarizability (3 of ammonia [22] we found quite different trends for the static hyperpolarizability and for the dispersion coefficients. While the static hyperpolarizability was very sensitive to the inclusion of diffuse functions, the dispersion coefficients remained almost unchanged on augmentation of the basis set with additional diffuse functions, but the results obtained with the CC2 and CCSD models, which include dynamic electron correlation, showed large changes with an increase of the... 

A main source of model bias lies in the choice of exponents in the single-exponential-type functions r exp (-ar) that are commonly used as the radial parts of the deformation functions this choice is often more of an art than a science [4]. Very little is known about the optimal values to be used for elements other than those of the first two rows. Selection of the best value for the exponents n is usually carried out by systematically varying exponents and monitoring the effects on the R indices and/or residual densities [8, 9]. The procedure can in some cases be unsatisfactory, as is the case when very diffuse functions centred on one atom are used to model most of the density in the bond, and even some of the density on neighbouring atoms [10]. 

The ECP basis sets include basis functions only for the outermost one or two shells, whereas the remaining inner core electrons are replaced by an effective core or pseudopotential. The ECP basis keyword consists of a source identifier (such as LANL for Los Alamos National Laboratory ), the number of outer shells retained (1 or 2), and a conventional label for the number of sets for each shell (MB, DZ, TZ,...). For example, LANL1MB denotes the minimal LANL basis with minimal basis functions for the outermost shell only, whereas LANL2DZ is the set with double-zeta functions for each of the two outermost shells. The ECP basis set employed throughout Chapter 4 (denoted LACV3P in Jaguar terminology) is also of Los Alamos type, but with full triple-zeta valence flexibility and polarization and diffuse functions on all atoms (comparable to the 6-311+- -G++ all-electron basis used elsewhere in this book). 

Basis set effects are similar for all models. Specifically, 6-31G basis set models, which lack diffuse functions, clearly lead to unsatisfactory results, while the corresponding 6-3II+G models, which include diffuse functions, all perform well. STO-3G and 3-21G Hartree-Fock models also lead to poor results. Individual errors (for 6-311+G models) are typically kept to 2-3 kcal/mol and are only rarely greater than 5 kcal/mol. The largest single error is 9 kcal/mol (the acidity of cyclopentadiene using the MP2/6-311+G model). In short, there is very little to distinguish from among the different models with the 6-311+G basis set. 

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