David S. Hollman

In search of the next Holy Grail of polyoxide chemistry: Explicitly correlated ab initio full quartic force fields for HOOH, HOOOH, HOOOOH, and their isotopologues

Explicitly correlated ab initio methods have been used to compute full quartic force fields for the three chain minima for HOOOOH, which are found to lie within 1 kcal mol(-1). The CCSD(T)-F12 method with the cc-pVTZ-F12 basis set was used to compute equilibrium structures, anharmonic vibrational frequencies, and rotational constants for HOOH, HOOOH, and three chain isomers of HOOOOH, with the two former force fields being used as benchmarks for the latter three. The full quartic force fields were computed in such a way as to yield fundamental frequencies for all isotopologues at once. The present research confirms the recent experimental identification of HOOOH and provides reliable force fields in support of future experimental work on the enigmatic bonding paradigms involved in the HOOOOH chain.

A tight distance-dependent estimator for screening three-center Coulomb integrals over Gaussian basis functions

A new estimator for three-center two-particle Coulomb integrals is presented. Our estimator is exact for some classes of integrals and is much more efficient than the standard Schwartz counterpart due to the proper account of distance decay. Although it is not a rigorous upper bound, the maximum degree of underestimation can be controlled by two adjustable parameters. We also give numerical evidence of the excellent tightness of the estimator. The use of the estimator will lead to increased efficiency in reduced-scaling one- and many-body electronic structure theories.

Explicitly correlated atomic orbital basis second order Møller-Plesset theory.

The scope of problems treatable by ab initio wavefunction methods has expanded greatly through the application of local approximations. In particular, atomic orbital (AO) based wavefunction methods have emerged as powerful techniques for exploiting sparsity and have been applied to biomolecules as large as 1707 atoms [S. A. Maurer, D. S. Lambrecht, D. Flaig, and C. Ochsenfeld, J. Chem. Phys. 136, 144107 (2012)]. Correlated wavefunction methods, however, converge notoriously slowly to the basis set limit and, excepting the use of large basis sets, will suffer from a severe basis set incompleteness error (BSIE). The use of larger basis sets is prohibitively expensive for AO basis methods since, for example, second-order Møller-Plesset perturbation theory (MP2) scales linearly with the number of atoms, but still scales as O(N(5)) in the number of functions per atom. Explicitly correlated F12 methods have been shown to drastically reduce BSIE for even modestly sized basis sets. In this work, we therefore explore an atomic orbital based formulation of explicitly correlated MP2-F12 theory. We present working equations for the new method, which produce results identical to the widely used molecular orbital (MO) version of MP2-F12 without resorting to a delocalized MO basis. We conclude with a discussion of several possible approaches to a priori screening of contraction terms in our method and the prospects for a linear scaling implementation of AO-MP2-F12. The discussion includes concrete examples involving noble gas dimers and linear alkane chains.

From strong van der Waals complexes to hydrogen bonding: From CO⋯H2O to CS⋯H2O and SiO⋯H2O complexes

Structures and interaction energies of complexes valence isoelectronic to the important CO⋯H(2)O complex, namely SiO⋯H(2)O and CS⋯H(2)O, have been studied for the first time using high-level ab initio methods. Although CO, SiO, and CS are valence isoelectronic, the structures of their complexes with water differ significantly, owing partially to their widely varied dipole moments. The predicted dissociation energies D(0) are 1.8 (CO⋯H(2)O), 2.7 (CS⋯H(2)O), and 4.9 (SiO⋯H(2)O) kcal∕mol. The implications of these results have been examined in light of the dipole moments of the separate moieties and current concepts of hydrogen bonding. It is hoped that the present results will spark additional interest in these complexes and in the general non-covalent paradigms they represent.

Fast construction of the exchange operator in an atom-centred basis with concentric atomic density fitting

ABSTRACT An algorithm is presented for computing the Hartree–Fock exchange matrix using concentric atomic density fitting with data and instruction count complexities. The algorithm exploits the asymptotic distance dependence of the three-centre Coulomb integrals along with the rapid decay of the density matrix to accelerate the construction of the exchange matrix. The new algorithm is tested with computations on systems with up to 1536 atoms and a quadruple-zeta basis set (up to 15585 basis functions). Our method handles screening of high angular momentum contributions in a particularly efficient manner, allowing the use of larger basis sets for large molecules without a prohibitive increase in cost.

Arbitrary order El'yashevich-Wilson B tensor formulas for the most frequently used internal coordinates in molecular vibrational analyses.

In recent years, internal coordinates have become the preferred means of expressing potential energy surfaces. The ability to transform quantities from chemically significant internal coordinates to primitive Cartesian coordinates and spectroscopically relevant normal coordinates is thus critical to the further development of computational chemistry. In the present work, general nth order formulas are presented for the Cartesian derivatives of the five most commonly used internal coordinates--bond stretching, bond angle, torsion, out-of-plane angle, and linear bending. To compose such formulas in a reasonably understandable fashion, a new notation is developed that is a generalization of that which has been used previously for similar purposes. The notation developed leads to easily programmable and reasonably understandable arbitrary order formulas, yet it is powerful enough to express the arbitrary order B tensor of a general, N-point internal coordinate, as is done herein. The techniques employed in the derivation of such formulas are relatively straightforward, and could presumably be applied to a number of other internal coordinates as needed.