Advances in methods and algorithms in a modern quantum chemistry program package.

Advances in theory and algorithms for electronic structure calculations must be incorporated into program packages to enable them to become routinely used by the broader chemical community. This work reviews advances made over the past five years or so that constitute the major improvements contained in a new release of the Q-Chem quantum chemistry package, together with illustrative timings and applications. Specific developments discussed include fast methods for density functional theory calculations, linear scaling evaluation of energies, NMR chemical shifts and electric properties, fast auxiliary basis function methods for correlated energies and gradients, equation-of-motion coupled cluster methods for ground and excited states, geminal wavefunctions, embedding methods and techniques for exploring potential energy surfaces.

SG-0: a small standard grid for DFT quadrature on large systems.

We report the development of a new standard quadrature grid for DFT calculations. Standard Grid 0 (SG-0) is designed to be approximately half as large as, and to provide approximately half the accuracy of, the established SG-1 grid. It is based on MultiExp and Lebedev quadrature for radial and angular coordinates, respectively. We find that SG-0 is typically 50% faster than SG-1 for energy, gradient, and hessian calculations for the exchange-correlation energy. This leads to a 35-38% speedup in the total gradient and hessian computations, and we particularly recommend its use for preliminary calculations on moderately large biochemical systems. It has been implemented as the default grid for DFT calculations in the Q-Chem 3.0 package.

Theoretical study of the Diels-Alder reactions between singlet (1Delta g) oxygen and acenes.

The G3(MP2) method has been employed to study the 1,4-addition reactions between singlet oxygen and five acenes, including benzene, naphthalene, anthrecene, tetracene, and pentacene. In all, nine pathways between O(2) and the five acenes have been investigated. Our calculated results indicate that all nine pathways are concerted and exothermic and that the most reactive sites on the acenes are the center ring's meso-carbons. In addition, reactivity increases along the series benzene < naphthalene < anthrecene < tetracene < pentacene. This trend is identical to that of aromaticity for the five acenes. A correlation between reactivity and aromaticity is briefly rationalized with natural bond orbital (NBO) analysis and frontier molecular orbital (FMO) analysis. Furthermore, some experimental kinetics data from the literature supporting the calculated results are cited.

Radial quadrature for multiexponential integrands.

We introduce a Gaussian quadrature, based on the polynomials that are orthogonal with respect to the weight function ln(2)x on the interval [0, 1], which is suitable for the evaluation of radial integrals. The quadrature is exact if the non-Jacobian part of the integrand is a linear combination of a geometric sequence of exponential functions. We find that the new scheme is a useful alternative to existing approaches, particularly for integrands that exhibit multiexponential behavior.