Diffuse polarization functions

Accordingly, dipole moment and polarizability calculations are sensitive to both the quantum chemistry method and the basis set used. Accurate calculations typically require the use of D FTor Hartree-Fock methods with the inclusion of M P2 treatment of electron correlation [53, 54]. Furthermore, Gaussian basis sets should be augmented with diffuse polarization functions to provide an adequate description of the tail regions of density (the most easily polarized regions of the molecule). 

Weak intermolecular interactions Large Diffuse polarization functions in addition to common polarization functions counterpoise correction should be tested... 

REF17 Tsuzuki, S., Uchimaru, T., Mikami, M. and Tanabe K. (1996) Basis set effects on the calculated bonding energies of neutral benzene dimers importance of diffuse polarization functions, Chem. Phys. Lett., 252, 206-210... 

An attempt at an ab initio calculation of the pNA hyperpolarizability by Sim et a/.38 using double zeta quality basis sets with diffuse polarizing functions within the finite field/HF/MP2 regime gave values which are even lower than those obtained by the semi-empirical methods. These calculations are at zero frequency but have been corrected to 1064 nm using the usual two state model. Bartlett and Sekino90,91 have discussed the relationship between hyperpolarizabilities calculated by ab initio methods and by SOS formalisms. They conclude that only the most powerful recent methods for correlated calculations can be expected to produce accuracy of about 10% for gas phase hyperpolarizabilities, while ab initio calculations interpreted in terms of the SOS expansion give very poor results when the equivalent number of states is small. 

The choice of basis functions, particularly the inclusion of diffuse polarization functions, is important in the calculation of 3 and Y. TT-electron contribution to optical nonlinearity dominates. 

It is also necessary to include electron correlation in any accurate calculation of intermolecular interactions, since the dispersion interaction is a correlation effect, and is usually an important component of the interaction energy. Moreover the dispersion interaction describes correlated fluctuations of the charge distributions in the two molecules, and this calls for an accurate description of the molecular polarizability, which in turn requires a large basis set containing a large number of diffuse polarization functions. 

While polarization functions are necessary for a qualitatively correct description of transition dipole moments, additional diffuse polarization functions can account for radial nodes in the first-order KS orbitals, which further improves computed transition moments and oscillator strengths. These benefits are counterbalanced with a significant increase of the computational cost involved In our example, the aug-SV(P) basis increased the computation time by about a factor of 4. For molecules with more than 30-40 atoms, most excitations of interest are valence excitations, and the use of diffuse augmentation may become prohibitively expensive because the large spatial extent of these functions confounds integral prescreening. 

It has been widely accepted that the BSSE at the self-consistent field (SCF) level can be eliminated or reduced drastically if large enough basis sets with additional diffuse and diffuse polarization functions are added.Examples are presented below (see Case Studies section). It has also been shown that the BSSE is larger at correlated levels, and thus several studies " " " have been conducted, mainly at the second-order Moller-Plesset level, to try to prove or disprove that the FCP does or does not produce an overcorrection to the interaction energy. 

The predicted stacking energies are sensitive both to the size of the basis set and to the inclusion of higher-order electron correlation contributions. Diffuse polarization functions on the second row elements must always be used. The present MP2/medium-sized basis set level of theory is nevertheless sufficient to reveal, for the first time, the nature of base stacking interactions and to validate and/or rule out various models of base stacking. The calculations are probably very close to the actual values due to a compensation of errors (MP2 vs. CCSD(T) level, medium vs. large basis set, see method section and [35b]). 

Similar calculations were reported for A- and B-DNA geometries by Alhambra et al. [67]. However, by not using diffuse polarization functions, the result is an underestimation of the stabilization energies. It explains why Alhambra et al. reported weaker base pair step stacking even though they have made calculations for larger system having methylated N1/N9 positions of bases. 

The basis set requirements for the calculation of first hyperpolarizabilities are much the same as for the linear polarizability. However, as the first hyperpolarizabUity probes even higher-order electric-field-perturbed densities of the molecule, care should be exercised to ensure that the basis set is sufficiently saturated with respect to diffuse polarizing functions. Special basis sets have been developed for the calculation of hyperpolarizabilities by Pluta and Sadie) (1998), though the same basis sets that can be used for polarizabilities in most cases give reliable estimates also for first hyperpolarizabUities. 

In order to get accurate properties, large and carefully chosen basis sets are needed. The hyperpolarizabilities are sensitive to the tail, or outer regions, of the wavefunction, and so higher order diffuse polarization functions are needed to converge the properties. Basis sets that give good results for lu, may be poor for a and useless for In general correlated calculations demand more of a basis set than uncorrelated ones. 

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