RESUMEN
Abundance mass spectra, obtained upon carefully electrospraying solutions of tert-butanol (TB) in water into a mass spectrometer, display a systematic series of peaks due to mixed H(+)(TB)m(H2O)n clusters. Clusters with m + n = 21 have higher abundance (magic number peaks) than their neighbours when m ≤ 9, while for m > 9 they have lower abundance. This indicates that the mixed TB-H2O clusters retain a core hydrogen bonded network analogous to that in the famous all-water H(+)(H2O)21 cluster up to the limit m = 9. The limiting value corresponds to the number of dangling O-H groups pointing out from the surface of the degenerated pentagonal dodecahedral, considered to be the lowest energy form of H(+)(H2O)21; the experimental findings therefore support this geometry. The experimental findings are supported by ab initio quantum chemical calculations to provide a consistent framework for the interpretation of these kinds of experiments.
RESUMEN
Three new variants of the auxiliary-density-matrix method (ADMM) of Guidon, Hutter, and VandeVondele [J. Chem. Theory Comput. 6, 2348 (2010)] are presented with the common feature that they have a simplified constraint compared with the full orthonormality requirement of the earlier ADMM1 method. All ADMM variants are tested for accuracy and performance in all-electron B3LYP calculations with several commonly used basis sets. The effect of the choice of the exchange functional for the ADMM exchange-correction term is also investigated.
RESUMEN
An analysis of Dunlap's robust fitting approach reveals that the resulting two-electron integral matrix is not manifestly positive semidefinite when local fitting domains or non-Coulomb fitting metrics are used. We present a highly local approximate method for evaluating four-center two-electron integrals based on the resolution-of-the-identity (RI) approximation and apply it to the construction of the Coulomb and exchange contributions to the Fock matrix. In this pair-atomic resolution-of-the-identity (PARI) approach, atomic-orbital (AO) products are expanded in auxiliary functions centered on the two atoms associated with each product. Numerical tests indicate that in 1% or less of all Hartree-Fock and Kohn-Sham calculations, the indefinite integral matrix causes nonconvergence in the self-consistent-field iterations. In these cases, the two-electron contribution to the total energy becomes negative, meaning that the electronic interaction is effectively attractive, and the total energy is dramatically lower than that obtained with exact integrals. In the vast majority of our test cases, however, the indefiniteness does not interfere with convergence. The total energy accuracy is comparable to that of the standard Coulomb-metric RI method. The speed-up compared with conventional algorithms is similar to the RI method for Coulomb contributions; exchange contributions are accelerated by a factor of up to eight with a triple-zeta quality basis set. A positive semidefinite integral matrix is recovered within PARI by introducing local auxiliary basis functions spanning the full AO product space, as may be achieved by using Cholesky-decomposition techniques. Local completion, however, slows down the algorithm to a level comparable with or below conventional calculations.
