Polarisation/ polarisable basis functions

The use of polarisation basis functions is indicated by an asterisk ( ). Thus, 6-31G refers to a 6-31G basis set with polarisation functions on the heavy (i.e. non-hydrogen) atoms. Two asterisks (e.g. 6-31G ) indicate the use of polarisation (i.e. p) functions on hydrogen and helium. The 6-31G basis set is particularly useful where hydrogen acts as a bridging atom. Partial polarisation basis sets have also been developed. For example, the 3-21G basis set has the same set of Gaussians as the 3-21G basis set (i.e. three functions for the inner shell, two contracted functions and one diffuse function for the valence shell) supplemented by six d-type Gaussians for the second-row elements. This basis set therefore attempts to account for d-orbital effects in molecules containing second-row elements. There are no special polarisation functions on first-row elements, which are described by the 3-21G basis set. 

These two factors are decisive in fixing the usual basis set not as atomic orbitals but as a set of atom-centred functions which are adapted to the expansion of the AOs of each of the component atoms of the molecule under study. It will also be useful from time to time to augment these basis functions with additional atom-centred functions that allow the description of aspects of the molecular electron distribution which are specific to the molecule. For example, in any satisfactory description of the H2 molecule one would use those sets of spherically symmetric atom-centred functions which are used to expand the Is AOs of the hydrogen atoms. But one might also add to the basis one or more p functions on each atom to allow for the polarisation of the electron distribution on each atom on molecule formation functions which do not take part in the expansion of the AOs of the ground state of the component atoms of the molecule. 

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. 

Equation (2) was also used to calculate quantum chemical approach. On the basis of previous results [19], calculated electrostatic potentials were computed from ab initio wave functions obtained in the framework of the HF/SCF method using a split-valence basis set (3-21G) and a split-valence basis set plus polarisation functions on atoms other than hydrogen (6-31G ). The GAUSSIAN 90 software package [20] was used. Since ab initio calculations of the molecular wave function for the whole... 

Quadratic Configuration Interaction with Singles and Doubles Quadratic Configuration Interaction with Singles, Doubles, and Noniterative Approximation of Triples Symmetry Adapted Cluster-Configuration Interaction Split-Valence basis set plus Polarisation functions Zero-Order Regular Approximation Zero-Point Energy... 

As another example, the potential surface of the He-CH4 complex (studied in Ref. lOe) is described. In these calculations a basis set 7s6p3dlflg on the C atom, 4s3pld on the H atoms, and 8s4p2dlf on the He atom, consisting of a total 182 functions, was adopted. The s and p functions were optimised so as to reproduce energies close to the Hartree-Fock limit of the CH4 molecule and He atom, respectively. The exponents of high-order polarisation functions were determined by maximising directly the dispersion contribution. 

The evaluation of interactions between particles inside and outside the quantum mechanical region is usually achieved on the basis of molecular mechanics, i.e. by the application of parametrised potential functions. Thus, parameters for partial charges and non-Coulombic interactions are required for all QM particles although these species are treated by quantum mechanics. The constmction of these functions is a time-consuming and tedious task requiring the evaluation of thousands of solute-solvent interaction points, which afterwards have to be fitted to an analytical representation in agreement with all other MM functions like the solvent-solvent interactions. As mentioned earlier the accuracy of these functions is in many cases insufficient for the treatment of polarisable compounds such as solvated ions [4,5,6,7,8], Sometimes these insufficiencies can be partially compensated by the inclusion of correction potentials as discussed above, but the accuracy is still not always satisfactory. 

SVP Split-Valence basis set plus Polarisation functions... 

As far as the basis set is concerned, increasing its quality from split valence to double zeta does not lead to any improvement of the situation a slight increase in the energy dificrence was found on going from a (14,9,6/9,5/6) set of primitives contracted to < 6,4,3/3,2/3 > for the iron atom, the first row atoms and the hydrogen atom respectively, to the (14,11,6/10,6/6) < 8,6,3/4,2/3 > basis set (14). The addition of a p polarisation function on the hydrogen atom decreased this value somewhat, down to 1.8 kcal/mol, but in every case the trans isomer remained the most stable one (14). 

CAS SCF calculations were therefore performed with the split valence basis set incremented by a p polarisation function on the hydrogen atoms. Two different sets of active orbitals were considered. The first one was designed to account for the d - n back donation and was therefore restricted to the n type valence orbitals. The three 3d orbitals, which are strongly occupied, were each correlated by two weakly occupied orbitals, owing to the mixed 4d and tt o character of these weakly occupied orbitals. This 3 + 6 set of active orbitals referred to as CAS SCF-6 is populated by 6 electrons. The second set, hereafter referred as CAS SCF-12, took into account both a and n correlation eficcts. Twelve electrons were correlated and... 

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