F-type polarization

There is an additional problem that must be considered for radicals that escape an original geminate radical pair. Such radicals are polarized. If they form new (encounter) radical pairs, they could yield combination products after undergoing T-S mixing again. However, because of the rapidity of nuclear relaxation in free radicals, the F-type polarization generally predominates. 

Details of the extended triple zeta basis set used can be found in previous papers [7,8]. It contains 86 cartesian Gaussian functions with several d- and f-type polarisation functions and s,p diffuse functions. All cartesian components of the d- and f-type polarization functions were used. Cl wave functions were obtained with the MELDF suite of programs [9]. Second order perturbation theory was employed to select the most energetically double excitations, since these are typically too numerous to otherwise handle. All single excitations, which are known to be important for describing certain one-electron properties, were automatically included. Excitations were permitted among all electrons and the full range of virtuals. 

All of the calculations were done with GAMESS (Generalized Atomic and Molecular Electronic Structure Systems) except for the TiCU calculations with f-type polarization functions which were done with QUEST (QUantum Electronic STructure). These programs were run on a CRAY X-MP at CRAY Research in Mendota Heights, an FPS-264 at the Cornell National Supercomputer Facility, an IBM 3090/200 at Texas A M University, and the Department of Chemistry s VAX 11/780 andFPS-164. 

As we improve the TiCU wavefunction by adding f-type polarization functions to the titanium basis set the Ti-Cl bond distance shortens further. When a chlorine basis set without d-functions is used, the addition of an f-function on titanium shortens the Ti-Cl bond 0.017 A. However, when a chlorine basis set with d-functions is used, the Ti-Cl bond only shortens 0.(X)6 A to 2.181 A. Although this Ti-Cl distance is the shortest of all the optimized geometry calculations, it is still 0.011 A longer than the experiment... 

Optimization of the geometry of TiCU at the SCF level results in a Ti-Cl bond length which is longer than the experiment, even when d- and f-type polarization functions are added to the basis set. For covalently bonded systems one expects a wavefunction at the Hartree-Fock limit to give bond lengths shorter than the experiment if they are not sterically crowded. Because the Hartree-Fock wavefunction overestimates the Cl -Cl repulsions, the Ti-Cl bond distances remain long, even in large basis sets. 

A slightly different strategy lead to the basis sets for the study of gas phase clusters, Nii3. Here, a (14,9,5) basis (64) was augmented with diffuse p and d orbital functions of exponent 0.1. Since in ah initio work it was sometimes found necessary (19,26) to add f-type polarization functions to the orbital basis this possibility was investigated here, too. However, when a significantly larger... 

The answer to the first question depends on several factors such as the accuracy which is to be achieved, the nature of the problem studied and the theoretical approach adopted. For example, from Figs, 2,1 and 2,2 we know that the energies cannot approach Hartree-Fock limits without the inclusion of polarization functions. The most recent study on the convergence of the SCF energy was reported by Kari and Csizmadia who showed different limits attainable upon stepwise augmenting the basis set with p, d and f-type polarization functions. Absence of polarization functions in the wave function is also reflected in observables other than energy. Consider for example the... 

In this study, the validity of quanmm chemical methods and basis sets has been assessed for sulfonamide geometrical parameters. Comparison with experimental data showed that including f-type polarization functions into basis sets improved the geometry optimizations at the Hartree-Fock, MP2, and B3LYP levels. Semiem-pirical methods did not reproduce the experimental sulfonamide bond lengths, bond angles, and torsion angles. 

Underlined methods include f-type polarization functions in their basis set. Each method is assigned a bold-type label... 

To elucidate the role of f-type polarization functions on describing chemical bonds, natural bond orbital (NBO) analyses were carried out for the computational results of method ii. For the NBOs of S=0 bonds in all six derivatives, the contributions of f-type orbitals were largest of all 2-center bond NBOs. The second largest contributions of f-type orbitals were observed in NBOs of S-N bond. Both for S=0 and S-N, the contributions of f-type orbital of sulfur atoms were much larger than those of oxygen or nitrogen atoms. In addition, gross orbital populations of f-type... 

In this study, appropriate methods were investigated for the structural optimization of sulfonamide derivatives. The results showed that semiempirical methods were unable to reproduce the experimental bond lengths, bond angles, and torsion angles and that ab initio MO and DFT methods were indispensable to accurately predict the molecular structures of sulfonamide derivatives. Combining ab initio MO and DFT methods with low-level basis sets like 3-2IG, 4-3IG, and basis sets without f-type polarizations did not reproduce the experimental data, suggesting that... 

For accurate calculations of TM compounds, f-type polarization functions should be added to the basis set. Exponents for f-polarization functions have been optimized by us for the Hay-Wadt ECP. No other sets of f-type functions optimized for use with pseudopotentials are known to us. However, because the valence orbitals of the pseudopotentials mimic the all-electron orbitals, the f-type functions determined for all-electron cases can also be used for pseudopotential calculations. 

The exponents of the f-type polarization functions are taken from Ref. 94. 

We calculated the relative energies of the alkyne and vinylidene isomers at HF/II, HF/III, MP2/III, and MP3/III. The results are shown in Table 18. The additional f-type polarization function in basis set III has little effect on the relative energies of the isomers. Relative energies of the alkyne and vinylidene isomers are similar at the MP2 and MP3 level, so the predicted stability order should be quite reliable. The calculations predict that substitution of hydrogen by the more electronegative substituent fluorine increases the relative stability of the vinylidene isomer, which is in agreement with experimental evidence. In... 

Next consider the changes to the dipole moments of the monomers after the addition of ghost orbitals at the optimum dimer distances. In Table 3 we present a representative sample of the results on the deformation of the dipole moment by the addition of ghost orbitals to each monomer. Small basis sets such as 6-31 1-h-G do not reproduce the experimental value for the dipole moment, nor do they allow for the distortion of the dipole moment on each monomer. On the other hand, large basis sets with several sets of d- and f-type polarization functions (aug-cc-PVTZ) not only reproduce more closely the experimental parameters, but also appear to be saturated and capable of accommodating all effects that produce distortion of the electron density. Similar effects are observed at all levels of theory. 

The inclusion of correlation effects improves the contributions of these terms to the total interaction energy, as seen in Table 4 for the MP2 and DFT results. One should be careful in attaching too much meaning to the interaction energies calculated using Eq. [1] those results should be corrected for the use of incomplete basis sets first. The interaction energy obtained at the DFT level is not improved by the addition of f-type polarization functions the 6-311++G(3df,3pd) and aug-cc-PVTZ DFT values are underestimated, in contrast to the effects of adding f functions at the MP2 level. 

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