Search results for "Cardinal number"
showing 3 items of 3 documents
The accuracy of molecular dipole moments in standard electronic structure calculations
2000
Abstract A systematic investigation has been carried out of the accuracy of calculated molecular equilibrium dipole moments of 11 polar closed-shell molecules, using the HF, MP2, CCSD and CCSD(T) models and correlation-consistent basis sets. Augmented basis sets are important for improving the basis-set convergence, but the quality of the results depends more on the correlation treatment than on the cardinal number of the basis set. Augmented triple-zeta basis sets are sufficient for most calculations. The mean absolute error of the HF calculations is 0.16 D, which is reduced at the MP2 and CCSD levels to 0.048 and 0.025 D, respectively. The CCSD(T) errors are small – typically
Basis-set extrapolation techniques for the accurate calculation of molecular equilibrium geometries using coupled-cluster theory
2006
To reduce remaining basis-set errors in the determination of molecular equilibrium geometries, a basis-set extrapolation (BSE) scheme is suggested for the forces used in geometry optimizations. The proposed BSE scheme is based on separating the Hartree-Fock and electron-correlation contributions and uses expressions obtained by straightforward differentiation of well established extrapolation formulas for energies when using basis sets from Dunning's hierarchy of correlation-consistent basis sets. Comparison with reference data obtained at the R12 coupled-cluster level [CCSD(T)-R12] demonstrates that BSE significantly accelerates the convergence to the basis-set limit, thus leading to impro…
On the space of all regular operators from C(K) into C(K)
1988
AbstractIt is known that Lr(E, C(K)), the space of all regular operators from E into C(K), is a Riesz space for all Riesz spaces E if and only if K is Stonian. We prove that this statement holds if E is replaced by C(K), where K is a compact space, the cardinal number of which satisfies a certain condition.