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Complete basis set extrapolations of dispersion, exchange, and coupled-clusters contributions to the interaction energy: a helium dimer study


  • Dedicated to Professor Karol Jankowski on the occasion of his 70th birthday.


Effectiveness of various extrapolation schemes in predicting complete basis set (CBS) values of interaction energies has been investigated for the helium dimer as a function of interatomic separation R. The investigations were performed separately for the leading dispersion and exchange contributions to the interaction energy and for the interaction energy computed using the coupled cluster method with single and double excitations (CCSD). For all these contributions, practically exact reference values were obtained from Gaussian-type geminal calculations. Sequences of orbital basis sets augmented with diffuse and bond functions or augmented with two sets of diffuse functions have been employed, with the cardinal numbers up to X = 7. The functional form EX = ECBS + A(Xk)−α was applied for the extrapolations, where EX is the contribution to the interaction energy computed with a basis set of cardinal number X. The main conclusion of this work is that CBS extrapolations of an appropriate functional form generally improve the accuracy of the interaction energies at a very small additional computational cost (of the order of 10%) and should be recommended in calculations of interatomic and intermolecular potentials. The effectiveness of the extrapolations significantly depends, however, on the interatomic separation R and on the composition of the basis set. Basis sets with midbond functions, well known to provide at a given size much more accurate nonextrapolated results than bases lacking such functions, have been found to perform best also in extrapolations. The X−1 extrapolations of dispersion energies computed with midbond function turned out to be very efficient (except at large R), reducing the errors by an order of magnitude for small X and a factor of two for large X (where the errors of nonextrapolated results are already very small). If midbond functions are not used, the X−3 formula is most appropriate for the dispersion energies. For the exchange component of the interaction energy, the best results are obtained—in both types of basis sets—with the X−4 extrapolation, which leads (in both cases) to almost an order of magnitude reduction of the error. The X−3 and (X − 1)−3 extrapolations work also well, but give smaller improvements. The correlation component of the CCSD interaction energy extrapolates best with α between 2 and 3 for bases with midbond functions and between 3 and 4 for bases without such functions. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008