Compact expressions for spherically averaged position and momentum densities

Compact expressions for spherically averaged position and momentum density integrals are given in terms of spherical Bessel functions (j(n)) and modified spherical Bessel functions (i(n)), respectively. All integrals required for ab initio calculations involving s, p, d, and f-type Gaussian functions are tabulated, highlighting a neat isomorphism between position and momentum space formulae. Spherically averaged position and momentum densities are calculated for a set of molecules comprising the ten-electron isoelectronic series (Ne-CH₄) and the eighteen-electron series (Ar-SiH₄, F₂-C₂H₆).This work was supported by an Australian Research Council grant to Professor Peter Gill Grant No. DP0664466

Computation and interpretation of molecular Omega intracules

The Omega intracule is a three-dimensional function that describes the relative positions, momenta, and directions of motion of pairs of electrons in a system. In this paper, we describe the computation of the Omega intracule for a molecular system whose electronic wave function is expanded in a Gaussian basis set. This is followed by implementation details and numerical tests. Finally, we use the Omega intracules of a number of small systems to illustrate the power of this function to extract simple physical insights from complicated wave functions.We thank the ANU and ARC Grant Nos. DP0664466 and DP0771978 for funding

Intracule functional models. II. Analytically integrable kernels

We present, within the framework of intracule functional theory (IFT), a class of kernels whose correlation integrals can be found in closed form. This approach affords three major advantages over other kernels that we have considered previously; ease of implementation, computational efficiency, and numerical stability. We show that even the simplest member of the class yields reasonable estimates of the correlation energies of 18 atomic and 56 molecular systems and we conclude that this kernel class will prove useful in the development of future IFT models

Intracule functional models. IV. Basis set effects

We have calculated position and dot intracules for a series of atomic and molecular systems, starting from an unrestricted Hartree-Fock wave function, expanded using the STO-3G, 6-31G, 6-311G, 6-311++G, 6-311++G(d,p), 6-311++G(3d,3p), and 6-311++G(3df,3pd) basis sets as well as the nonpolarized part of Dunning's cc-pV5Z basis. We find that the basis set effects on the intracules are small and that correlation energies from the dot intracule ansatz are remarkably insensitive to the basis set quality. Mean absolute errors in correlation energies across the G1 data set agree to within 2 mE(h) for all basis sets tested.P.M.W.G. thanks the APAC Merit Allocation Scheme for a generous grant of supercomputer resources and the Australian Research Council Grant Nos. DP0664466 and DP0771978 for funding

Efficiency considerations in the construction of interpolated potential energy surfaces for the calculation of quantum observables by diffusion Monte Carlo

A modified Shepard interpolation scheme is used to construct global potential energy surfaces (PES) in order to calculate quantum observables--vibrationally averaged internal coordinates, fully anharmonic zero-point energies and nuclear radial distribution functions--for a prototypical loosely bound molecular system, the water dimer. The efficiency of PES construction is examined with respect to (a) the method used to sample configurational space, (b) the method used to choose which points to add to the PES data set, and (c) the use of either a one- or two-part weight function. The most efficient method for constructing the PES is found to require a quantum sampling regime, a combination of both h-weight and rms methods for choosing data points and use of the two-part weight function in the interpolation. Using this regime, the quantum diffusion Monte Carlo zero-point energy converges to the exact result within addition of 50 data points. The vibrationally averaged O-O distance and O-O radial distribution function, however, converge more slowly and require addition of over 500 data points. The methods presented here are expected to be applicable to both other loosely bound complexes as well as tightly bound molecular species. When combined with high quality ab initio calculations, these methods should be able to accurately characterize the PES of such species.D.L.C. would like to acknowledge the financial support of an Australian Postgraduate Research Award. This work has also been supported by Large Grant No. A00104447 from the Australian Research Council and by grants of computer time from the Australian Partnership in Advanced Computing (APAC) National Merit Allocation Scheme

A classical trajectory study of the photodissociation of T₁ acetaldehyde: the transition from impulsive to statistical dynamics

Previous experimental and theoretical studies of the radical dissociation channel of T(1) acetaldehyde show conflicting behavior in the HCO and CH(3) product distributions. To resolve these conflicts, a full-dimensional potential-energy surface for the dissociation of CH(3)CHO into HCO and CH(3) fragments over the barrier on the T(1) surface is developed based on RO-CCSD(T)/cc-pVTZ(DZ) ab initio calculations. 20,000 classical trajectories are calculated on this surface at each of five initial excess energies, spanning the excitation energies used in previous experimental studies, and translational, vibrational, and rotational distributions of the radical products are determined. For excess energies near the dissociation threshold, both the HCO and CH(3) products are vibrationally cold; there is a small amount of HCO rotational excitation and little CH(3) rotational excitation, and the reaction energy is partitioned dominantly (>90% at threshold) into relative translational motion. Close to threshold the HCO and CH(3) rotational distributions are symmetrically shaped, resembling a Gaussian function, in agreement with observed experimental HCO rotational distributions. As the excess energy increases the calculated HCO and CH(3) rotational distributions are observed to change from a Gaussian shape at threshold to one more resembling a Boltzmann distribution, a behavior also seen by various experimental groups. Thus the distribution of energy in these rotational degrees of freedom is observed to change from nonstatistical to apparently statistical, as excess energy increases. As the energy above threshold increases all the internal and external degrees of freedom are observed to gain population at a similar rate, broadly consistent with equipartitioning of the available energy at the transition state. These observations generally support the practice of separating the reaction dynamics into two reservoirs: an impulsive reservoir, fed by the exit channel dynamics, and a statistical reservoir, supported by the random distribution of excess energy above the barrier. The HCO rotation, however, is favored by approximately a factor of 3 over the statistical prediction. Thus, at sufficiently high excess energies, although the HCO rotational distribution may be considered statistical, the partitioning of energy into HCO rotation is not.One of the authors D.L.C. acknowledges the financial support of an Australian Postgraduate Research Award. This work has also been supported in large by Grant No. A00104447 from the Australian Research Council and by grants of computer time from the Australian Partnership in Advanced Computing APAC National Merit Allocation Scheme

Beyond the Woodward-Hoffman rules: what controls reactivity in eliminative aromatic ring-forming reactions?

The Mallory (photocyclization) and Scholl (thermal cyclohydrogenation) reactions are widely used in the synthesis of extended conjugated π systems of high scientific interest and technological importance, including molecular wires, semiconducting polymers and nanographenes. While simple electrocyclization reactions obey the Woodward-Hoffman rules, no such simple, general and powerful model is available for eliminative cyclization reactions due to their increased mechanistic complexity. In this work, detailed mechanistic investigations of prototypical reactions reveal that there is no single rate-determining step for thermal oxidative dehydrogenation reactions, but they are very sensitive to the presence and distribution of heteroatoms around the photocyclizing ring system. Key aspects of reactivity are correlated to the constituent ring oxidation potentials. For photocyclization reactions, planarization occurs readily and/or spontaneously following photo-excitation, and is promoted by heteroatoms within 5-membered ring adjacent to the photocyclizing site. Oxidative photocyclization requires intersystem crossing to proceed to products, while reactants configured to undergo purely eliminative photocyclization could proceed to products entirely in the excited state. Overall, oxidative photocyclization seems to strike the optimal balance between synthetic convenience (ease of preparation of reactants, mild conditions, tolerant to chemical diversity in reactants) and favourable kinetic and thermodynamic properties