Double-zeta plus polarization basis set

Although there is no strict relationship between the basis sets developed for, and used in, conventional ah initio calculations and those applicable in DFT, the basis sets employed in molecular DFT calculations are usually the same or highly similar to those. For most practical purposes, a standard valence double-zeta plus polarization basis set (e.g. the Pople basis set 6-31G(d,p) [29] and similar) provides sufficiently accurate geometries and energetics when employed in combination with one of the more accurate functionals (B3LYP, PBEO, PW91). A somewhat sweeping statement is that the accuracy usually lies mid-way between that of M P2 and that of the CCSD(T) or G2 conventional wave-function methods. 

The number of basis functions (defined by the chosen basis sets) used to construct the molecular orbitals also strongly affects the effort/accuracy ratio. The use of minimal basis sets yielded wrong results (56), whereas reasonable agreement with experiment is obtained when double zeta plus polarization basis sets are applied. Correlated methods require larger basis sets to include as much electron correlation as possible. This implies that in addition to the increased computational demand of such methods, a further increase of the computational cost results due to the requirement of using larger basis sets. 

In calculations on molecules within the matrix Hartree-Fock approximation, it is found to be important to add polarization functions to double-zeta basis sets. Such basis functions do not improve the energies of the isolated component atomic species but contribute significantly to calculated bond energies and to the accuracy of calculated equilibrium bond angles. Double-zeta plus polarization basis sets (usually designated DZP or DZ + P) became widespread in quantum chemistry in the 1970s. In such a basis set the hydrogen atom is described by two s functions and one set of p functions the... 

HB=BH, diborene, has been studied by ab initio configuration interaction calculations using a double zeta plus polarization basis set. The D h molecule has three low-lying electronic states, 1 Ag, and Zg, just like the O2 molecule, but BgHg has only eight valence electrons. 

Table II summarizes the predictions of a number of semi-empirical FH2 surfaces for the H + FH barrier. The final entry indicates that rather reliable Cl calculations (19), using a better than double zeta plus polarization basis set, predict a barrier of 49 kcal. B6S concluded in their paper (1 ) that the true col linear barrier is no less than 40 kcal. Thus, it is seen that the two "best" semi-empirical F + Ho surfaces, Muckerman V and Polanyi-Schreiber SE-I, fail miserably for the coll inear H + FH channel. This is perhaps the strongest evidence to date for the importance of ab initio information in potential energy surface calibration.

In comparison, ab initio SCF calculation of /r(CO) with the correct sign, at -0.077 D, requires a double-zeta-plus-polarization basis set with 138 doubly excited configurations plus 62 single excitations [30]. The chemical principles involved here are hard to visualize. 

In all calculations we have used DZP (double zeta plus polarization) basis set for Zn 4s and DZ (double zeta) basis sets for Zn 3d, S 3s, S 3p, and SZ (single zeta) for S 3d. The cutoff radius for s, p, and d components of pseudopotential are (1) 2.03, 2.30, and 1.75 a.u. for Zn (2) 1.50, 1.70, and 1.70 a.u. for S. Here we also found that ring-like clusters have lower energies than the corresponding hollow clusters. The SIESTA results of total energy of ring-like and hollow clusters are given in Table 12.3 for comparison. 

Full configuration interaction (FCI) by definition gives the exact n-particle energy within the given basis set. (Since it is the exact solution, this happens irrespective of the quality of the zero-order wave function.) Because its computational requirements ascend factorially with the size of the system, application to practical systems using one-particle basis sets of useful size will be essentially impossible for the foreseeable future. Even using the fastest available computational hardware and parallelized codes, an FCI calculation on H2O in a double-zeta plus polarization basis set is about the state of the art at present. ... 

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