Restricted Hartree-Fock (RHF) and UHF wavefunctions for beryllium-like ions with nuclear charge 3 ≤ Z ≤ 5 are found using a near-complete Slater basis set. The triplet (RHF → UHF) instability and correlation energy are investigated as a function of Z and we find that the instability vanishes for Z > 4.5. We reproduce this surprising behavior using a minimal-basis model and, by comparing with the stretched H(2) molecule, conclude that "static" (also known as nondynamical, near-degeneracy, first-order, or strong) correlation comes in two flavors: one that can be captured by UHF and another that cannot. In the former (Type A), there is an "absolute near-degeneracy"; in the latter (Type B), there is a "relative near-degeneracy." This dichotomy clarifies discussions of static correlation effects.

Diversely substituted anilines are prepared by treatment of functionalized arylboronic acids with a common, inexpensive source of electrophilic nitrogen (H2N-OSO3H, HSA) under basic aqueous conditions. Electron-rich substrates are found to be the most reactive by this method. However, even moderately electron-poor substrates are well tolerated under the room temperature conditions. Sterically hindered substrates appear to be equally effective compared to unhindered ones. Highly electron-deficient substrates afford product in very low yields at room temperature, but moderate to good yields are obtained at refluxing temperatures. Our method is also amenable to electrophilic amination of several common boronic acid derivatives (e.g., pinacol esters). We demonstrate that it can be combined with metal-halogen exchange reactions or a variety of directed ortho metalation protocols in a "one-pot" sequence for the synthesis of aromatic amines with unique substitution patterns. DFT studies, in combination with experimental results, suggest that the reaction occurs via base-mediated activation of HSA, followed by 1,2 aryl B-N migration. This mode of activation appears to be critical for the success of the reaction and allows, for the first time, a general, electrophilic amination of boronic acids at ambient temperature.

The approach used by Ahlrichs [Phys. Chem. Chem. Phys., 2006, 8, 3072] to derive the Obara-Saika recurrence relation (RR) for two-electron integrals over Gaussian basis functions, is used to derive an 18-term RR for six-dimensional integrals in phase space and 8-term RRs for three-dimensional integrals in position or momentum space. The 18-term RR reduces to a 5-term RR in the special cases of Dot and Posmom intracule integrals in Fourier space. We use these RRs to show explicitly how to construct Position, Momentum, Omega, Dot and Posmom intracule integrals recursively.

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The ∆NO method for static correlation is combined with second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster singles and doubles (CCSD) to account for dynamic correlation. The MP2 and CCSD expressions are adapted from finite-temperature CCSD, which includes orbital occupancies and vacancies, and expanded orbital summations. Correlation is partitioned with the aid of damping factors incorporated into the MP2 and CCSD residual equations. Potential energy curves for a selection of diatomics are in good agreement with extrapolated full configuration interaction results (exFCI), and on par with conventional multireference approaches.