Clementi double-zeta basis

In the 1960s, this last statement was not acceptable and, indeed, it was to minimize such discrepancies that prompted Clementi to propose his optimized double-zeta sets. That better results can be obtained using this approach is shown in Figure 1.12, wherein the comparisons are made between the optimized Clementi double-zeta function and the numerical results. The detail of this calculation requires the involvement of the variation principle to determine the relative weightings of the two components of the double-zeta basis by minimizing the calculated 2s orbital energy. This requires that the 2s function be rendered orthonormal [Chapters] to the Is function in lithium. Thus, all four Slater functions in the Clementi double-zeta basis, the two for the 1 s and the two for the 2s, contribute to... 

Figure 1.12 The better agreement in the valence region of the atom with the numerical data for the Li s radial wave function, which follows for the Clementi double-zeta basis sets for Li s and Liis mutually orthogonal.

Exercise 5.2. Calculation of the energy of the helium atom using the Clementi double-zeta basis. 

Figure 5.4b The output of each iteration to self-consistency for the Clementi double-zeta Slater basis calculation of the ground state energy of the helium atom and the final converged result of the worksheet hfs in fig5-4.xls. Further iterations lead to no improvement of the results and the energy of the helium atom is found to be 2.86167 a.u.

Double-2eta basis sets were introduced by Roetti and Clementi to provide greater flexibility in the orbital expansion and to avoid the need to reoptimize the orbital exponents when the basis set is used in a molecular calculation. Double-zeta basis sets contain two functions for every function in a minimum basis set. The accuracy which can be achieved in calculations of total energies using such basis sets is illustrated in Table IV where calculations using double-zeta basis sets are compared with those using minimum basis sets and the Hartree-Fock limit. 

In order to evidence the effects of the crystal field, the central ion must be described by a wavefunction built up with a sufficiently flexible basis set. We have selected the double-zeta set (DZ) of Slater type orbitals proposed by Clementi [3]. The wave-function for the isolated NO J ion with this basis set had been already published by us some years ago [4]. 

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