Setting, effects

Choosing a standard GTO basis set means that the wave function is being described by a finite number of functions. This introduces an approximation into the calculation since an infinite number of GTO functions would be needed to describe the wave function exactly. Dilferences in results due to the quality of one basis set versus another are referred to as basis set effects. In order to avoid the problem of basis set effects, some high-accuracy work is done with numeric basis sets. These basis sets describe the electron distribution without using functions with a predefined shape. A typical example of such a basis set might... 

This results in a population analysis scheme that is less basis set dependent than the Mulliken scheme. Flowever, basis set effects are still readily apparent. This is also a popular technique because it is available in many software packages and researchers find it convenient to use a method that classifies the type of orbital. 

Clearly, the 3-21G basis set reproduces the experimental results much better than STO-3G. We ll look at basis set effects in detail in Chapter 5. ... 

This mode corresponds to the IR peak associated with carbonyl stretch, used to identify the C-O double bond. Its predicted frequency is about 1810 (after scaling). This is in reasonable agreement with the experimental value of 1746. Using a larger basis set will improve this value. We ll discuss basis set effects in the next chapter. 

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. 

The normal modes associated with these frequencies are characterized by motion limited to the hydrogen atom in question. The values of the frequencies are in reasonable agreement with observations which place this peak in the range 2745-2710 cm S given our knowledge of basis set effects from the carbonyl stretch frequencies. ... 

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). 

Determine the effect of basis set on the predicted chemical shifts for benzene. Compute the NMR properties for both compounds at the B3LYP/6-31G(d) geometries we computed previously. Use the HF method for your NMR calculations, with whatever form(s) of the 6-31G basis set you deem appropriate. Compare your results to those of the HF/6-311+G(2d,p) job we ran in the earlier exercise. How does the basis set effect the accuracy of the computed chemical shift for benzene ... 

Part 2, Model Chemistries, begins with Chapter 5, Basis Set Effects. This chapter discusses the most important standard basis sets and presents principles for basis set selection. It also describes the distinction between open shell and closed shell calculations. 

Provide you with a framework for the design and implementation of the scheme. For example, by researching the needs of your employees, you will find it easier to set effective program objectives and to identify your mentee target group. 

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... 

This leaves us with a computed resuit in iess than satisfactory agreement with the experimental value of about 170 kcal/mol(57). The neglect of electron correlation and the limited basis set used are the most important sources of the discrepancy. In a previous study on monolayer graphite(56), basis set effects were found to lead to a significant underestimation of the cohesive energy. 

To investigate the basis set effect in connection with geometric strain in BF, we have performed calculations with and without d-type functions on corannulene. The d-functions improve the binding with about 10 kcal/mol per C-atom in C20H10 the corresponding improvement in coronene (C24H 2) 8 kcal/mol. 

Basis set effects were not in the ground of this study, so that the 6-31IG [22] basis set has been chosen as a compromise between reliability and computation times. 

The frequency dependence is taken into accoimt through a mixed time-dependent method which introduces a dipole-moment factor (i.e. a polynomial of first degree in the electronic coordinates ) in a SCF-CI (Self Consistent Field with Configuration Interaction) method (3). The dipolar factor, ensuring the gauge invariance, partly simulates the molecular basis set effects and the influence of the continuum states. A part of these effects is explicitly taken into account in an extrapolation procedure which permits to circumvent the sequels of the truncation of the infinite sum-over- states. 

These compounds have been the subject of several theoretical [7,11,13,20)] and experimental[21] studies. Ward and Elliott [20] measured the dynamic y hyperpolarizability of butadiene and hexatriene in the vapour phase by means of the dc-SHG technique. Waite and Papadopoulos[7,ll] computed static y values, using a Mac Weeny type Coupled Hartree-Fock Perturbation Theory (CHFPT) in the CNDO approximation, and an extended basis set. Kurtz [15] evaluated by means of a finite perturbation technique at the MNDO level [17] and using the AMI [22] and PM3[23] parametrizations, the mean y values of a series of polyenes containing from 2 to 11 unit cells. At the ab initio level, Hurst et al. [13] and Chopra et al. [20] studied basis sets effects on and y. It appeared that diffuse orbitals must be included in the basis set in order to describe correctly the external part of the molecules which is the most sensitive to the electrical perturbation and to ensure the obtention of accurate values of the calculated properties. 

These monodimensional compounds, rich in it electrons, have been the object of several experimental[35] and theoretical work[20,35,36]. Perry et al.[35], using a powder SHG technique, have studied diaryl polyynes and have shown that some of them exhibit second order hyperpolarizabilities of very high magnitude. On another hand, Jameson and Fowler[36] carried out ab initio calculations in order to study basis sets effects on the electrical properties of acetylene and diacetylene. Furthermore, Chopra et al [20], then Maroulis and Thakkar [37] have been interested in the influence of the lengthening of the... 

Boggs, J. E., and F. R. Cordell. 1981. Accurate Ab Initio Gradient Calculation of the Structures and Conformations of Some Boric and Fluoroboric Acids. Basis-Set Effects on Angles Around Oxygen. J. Mol. Struct. (Theochem) 76, 329-347. 

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