Reduced density matrix
functional theory (RDMFT), a promising direction
in the problem of describing strongly correlated systems, is currently
limited by its explicit dependence on natural orbitals and, by extension,
the costly need to construct two-electron integrals in the molecular
orbital basis. While a resolution-of-the-identity approach can reduce
the asymptotic scaling behavior from O(N
5) to O(N
4), this is still prohibitively expensive for large systems, especially
considering the usually slow convergence and the resulting high number
of orbital optimization steps. In this work, efficient integral-direct
methods are derived and benchmarked for various approximate functionals.
Furthermore, we show how these integral-direct methods can be integrated
into existing self-consistent energy minimization frameworks in an
efficient manner, including improved methods for calculating diagonal
elements of the two-electron integral tensor as required in self-interaction-corrected
functionals and second derivatives of the energy with respect to the
occupation numbers. In combination, these methods provide speedups
of up to several orders of magnitude while greatly diminishing memory
requirements, enabling the application of RDMFT to large molecular
systems of general chemical interest, such as the challenging triplet–quintet
gap of the iron(II) porphyrin complex.
An alternative and
complementary transformation for the synthesis
of aryl- and heteroaryl-substituted alkynes is presented that relies
on a chemoselective electrocoupling process. Tetraorganoborate substrates
were logically designed and simply accessed by transmetalations using
readily or commercially available organotrifluoroborate salts.
Chiral β‐aminoalkylzinc halides were prepared starting from optically pure commercial β‐amino‐alcohols. These amino‐alcohols were converted to the corresponding
N
‐pyrrolyl‐protected alkyl iodides which undergo a zinc insertion in the presence of LiCl (THF, 25 °C, 10–90 min). Subsequent Negishi cross‐coupling or acylation reactions with acid chlorides produced amino‐derivatives with retention of chirality. Diastereoselective CBS‐reductions of some prepared
N
‐pyrrolyl‐ketones provided 1,3‐subsituted
N
‐pyrrolyl‐alcohols with high diastereoselectivity. Additionally, a deprotection procedure involving an ozonolysis allowed the conversion of the pyrrole‐ring into a formamide without loss of optical purity.
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