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.

Semi-exact concentric atomic density fitting: reduced cost and increased accuracy compared to standard density fitting.

A local density fitting scheme is considered in which atomic orbital (AO) products are approximated using only auxiliary AOs located on one of the nuclei in that product. The possibility of variational collapse to an unphysical "attractive electron" state that can affect such density fitting [P. Merlot, T. Kjærgaard, T. Helgaker, R. Lindh, F. Aquilante, S. Reine, and T. B. Pedersen, J. Comput. Chem. 34, 1486 (2013)] is alleviated by including atom-wise semidiagonal integrals exactly. Our approach leads to a significant decrease in the computational cost of density fitting for Hartree-Fock theory while still producing results with errors 2-5 times smaller than standard, nonlocal density fitting. Our method allows for large Hartree-Fock and density functional theory computations with exact exchange to be carried out efficiently on large molecules, which we demonstrate by benchmarking our method on 200 of the most widely used prescription drug molecules. Our new fitting scheme leads to smooth and artifact-free potential energy surfaces and the possibility of relatively simple analytic gradients.

Tetragermacyclobutadiene: energetically disfavored with respect to its structural isomers.

Germanium has been a central feature in the renaissance of main-group inorganic chemistry. Herein, we present the stationary-point geometries of tetragermacyclobutadiene and its related isomers on the singlet potential energy surface at the CCSD(T)/cc-pVTZ level of theory. Three of these 12 structures are reported for the first time and one of them is predicted to lie only 0.4 kcal mol(-1) above the previously reported global minimum. Focal-point analyses has provided electronic energies at the CCSD(T) level of theory, which are extrapolated to the complete basis-set limit and demonstrate the convergence behavior of the electronic energies with improving levels of theory and increasing basis-set size. The lowest-energy structure is the bicyclic structure, which lies 35 kcal mol(-1) below the "all-Ge" cyclobutadiene structure. The reaction energies for the association of known Ge hydrides (e.g., digermene) to form Ge4H4 indicate that Ge4H4 could be observed experimentally. We investigate the bonding patterns by examining the frontier molecular orbitals. Our results demonstrate that: 1) the cyclic isomers of (GeH)4 distort to maximize the mixing of the p orbitals that are involved in the π system of tetragermacyclobutadiene and 2) the lowest-energy isomers exhibit unusual bonding arrangements (e.g., bridging H bonds) that maximize the nonbonding electron density at the Ge centers.

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.

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.

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.

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.

The benzene+OH potential energy surface: intermediates and transition states.

The potential energy surface for the interaction between benzene and hydroxyl radical is studied in detail using quantum mechanical methods, with a particular focus on the hydrogen abstraction pathway. Geometric parameters are optimized using a variety of density functional methods as well as perturbation theory. Energies are refined using coupled cluster singles and doubles with perturbative triples [CCSD(T)] extrapolated to the complete basis set limit. At our most reliable level of theory, complexation energies are found to be (with zero-point corrected energies in parentheses) 3.7 (2.8) kcal/mol for the benzene-hydroxyl radical complex and 2.9 (-1.7) kcal/mol for the phenyl radical-water complex. The barrier to H abstraction lies 6.5 (4.2) kcal/mol above the infinitely separated benzene and hydroxyl radical monomers.