Fast Evaluation of Two-Center Integrals over Gaussian Charge Distributions and Gaussian Orbitals with General Interaction Kernels

We present efficient algorithms for computing two-center integrals and integral derivatives, with general interaction kernels K(r12), over Gaussian charge distributions of general angular momenta l. While formulated in terms of traditional ab initio integration techniques, full derivations and required secondary information, as well as a reference implementation, are provided to make the content accessible to other fields. Concretely, the presented algorithms are based on an adaption of the McMurchie–Davidson Recurrence Relation (MDRR) combined with analytical properties of the solid harmonic transformation; this obviates all intermediate recurrences except the adapted MDRR itself, and allows it to be applied to fully contracted auxiliary kernel integrals. The technique is particularly well-suited for semiempirical molecular orbital methods, where it can serve as a more general and efficient replacement of Slater–Koster tables, and for first-principles quantum chemistry methods employing density fitting. But the formalism’s high efficiency and ability of handling general interaction kernels K(r12) and multipolar Gaussian charge distributions may also be of interest for modeling electrostatic interactions and short-range exchange and charge penetration effects in classical force fields and model potentials. With the presented technique, a 4894 × 4894 univ-JKFIT Coulomb matrix JAB = (A|1/r12|B) (183 MiB) can be computed in 50 ms on a Q2′2018 notebook CPU, without any screening or approximations

Fast Evaluation of Two-Center Integrals over Gaussian Charge Distributions and Gaussian Orbitals with General Interaction Kernels

We present efficient algorithms for computing two-center integrals and integral derivatives, with general interaction kernels K(r12), over Gaussian charge distributions of general angular momenta l. While formulated in terms of traditional ab initio integration techniques, full derivations and required secondary information, as well as a reference implementation, are provided to make the content accessible to other fields. Concretely, the presented algorithms are based on an adaption of the McMurchie–Davidson Recurrence Relation (MDRR) combined with analytical properties of the solid harmonic transformation; this obviates all intermediate recurrences except the adapted MDRR itself, and allows it to be applied to fully contracted auxiliary kernel integrals. The technique is particularly well-suited for semiempirical molecular orbital methods, where it can serve as a more general and efficient replacement of Slater–Koster tables, and for first-principles quantum chemistry methods employing density fitting. But the formalism’s high efficiency and ability of handling general interaction kernels K(r12) and multipolar Gaussian charge distributions may also be of interest for modeling electrostatic interactions and short-range exchange and charge penetration effects in classical force fields and model potentials. With the presented technique, a 4894 × 4894 univ-JKFIT Coulomb matrix JAB = (A|1/r12|B) (183 MiB) can be computed in 50 ms on a Q2′2018 notebook CPU, without any screening or approximations

Fast Evaluation of Two-Center Integrals over Gaussian Charge Distributions and Gaussian Orbitals with General Interaction Kernels

We present efficient algorithms for computing two-center integrals and integral derivatives, with general interaction kernels K(r12), over Gaussian charge distributions of general angular momenta l. While formulated in terms of traditional ab initio integration techniques, full derivations and required secondary information, as well as a reference implementation, are provided to make the content accessible to other fields. Concretely, the presented algorithms are based on an adaption of the McMurchie–Davidson Recurrence Relation (MDRR) combined with analytical properties of the solid harmonic transformation; this obviates all intermediate recurrences except the adapted MDRR itself, and allows it to be applied to fully contracted auxiliary kernel integrals. The technique is particularly well-suited for semiempirical molecular orbital methods, where it can serve as a more general and efficient replacement of Slater–Koster tables, and for first-principles quantum chemistry methods employing density fitting. But the formalism’s high efficiency and ability of handling general interaction kernels K(r12) and multipolar Gaussian charge distributions may also be of interest for modeling electrostatic interactions and short-range exchange and charge penetration effects in classical force fields and model potentials. With the presented technique, a 4894 × 4894 univ-JKFIT Coulomb matrix JAB = (A|1/r12|B) (183 MiB) can be computed in 50 ms on a Q2′2018 notebook CPU, without any screening or approximations

Scalable Electron Correlation Methods I.: PNO-LMP2 with Linear Scaling in the Molecular Size and Near-Inverse-Linear Scaling in the Number of Processors

We propose to construct electron correlation methods that are scalable in both molecule size and aggregated parallel computational power, in the sense that the total elapsed time of a calculation becomes nearly independent of the molecular size when the number of processors grows linearly with the molecular size. This is shown to be possible by exploiting a combination of local approximations and parallel algorithms. The concept is demonstrated with a linear scaling pair natural orbital local second-order Møller–Plesset perturbation theory (PNO-LMP2) method. In this method, both the wave function manifold and the integrals are transformed incrementally from projected atomic orbitals (PAOs) first to orbital-specific virtuals (OSVs) and finally to pair natural orbitals (PNOs), which allow for minimum domain sizes and fine-grained accuracy control using very few parameters. A parallel algorithm design is discussed, which is efficient for both small and large molecules, and numbers of processors, although true inverse-linear scaling with compute power is not yet reached in all cases. Initial applications to reactions involving large molecules reveal surprisingly large effects of dispersion energy contributions as well as large intramolecular basis set superposition errors in canonical MP2 calculations. In order to account for the dispersion effects, the usual selection of PNOs on the basis of natural occupation numbers turns out to be insufficient, and a new energy-based criterion is proposed. If explicitly correlated (F12) terms are included, fast convergence to the MP2 complete basis set (CBS) limit is achieved. For the studied reactions, the PNO-LMP2-F12 results deviate from the canonical MP2/CBS and MP2-F12 values by <1 kJ mol^–1, using triple-ζ (VTZ-F12) basis sets

Characterization of the Fleeting Hydroxoiron(III) Complex of the Pentadentate TMC-py Ligand

Nonheme mononuclear hydroxoiron­(III) species are important intermediates in biological oxidations, but well-characterized examples of synthetic complexes are scarce due to their instability or tendency to form μ-oxodiiron­(III) complexes, which are the thermodynamic sink for such chemistry. Herein, we report the successful stabilization and characterization of a mononuclear hydroxoiron­(III) complex, [Fe^III(OH)­(TMC-py)]²⁺ (<b>3</b>; TMC-py = 1<i>-</i>(pyridyl-2′-methyl)-4,8,11-trimethyl-1,4,8,11-tetrazacyclotetradecane), which is directly generated from the reaction of [Fe^IV(O)­(TMC-py)]²⁺ (<b>2</b>) with 1,4-cyclohexadiene at −40 °C by H-atom abstraction. Complex <b>3</b> exhibits a UV spectrum with a λ_max at 335 nm (ε ≈ 3500 M^–1 cm^–1) and a molecular ion in its electrospray ionization mass spectrum at <i>m</i>/<i>z</i> 555 with an isotope distribution pattern consistent with its formulation. Electron paramagnetic resonance and Mössbauer spectroscopy show <b>3</b> to be a high-spin Fe­(III) center that is formed in 85% yield. Extended X-ray absorption fine structure analysis reveals an Fe–OH bond distance of 1.84 Å, which is also found in [(TMC-py)­Fe^III–O–Cr^III(OTf)₃]⁺ (<b>4</b>) obtained from the reaction of <b>2</b> with Cr­(OTf)₂. The <i>S</i> = 5/2 spin ground state and the 1.84 Å Fe–OH bond distance are supported computationally. Complex <b>3</b> reacts with 1-hydroxy-2,2,6,6-tetramethylpiperidine (TEMPOH) at −40 °C with a second-order rate constant of 7.1 M^–1 s^–1 and an OH/OD kinetic isotope effect value of 6. On the basis of density functional theory calculations, the reaction between <b>3</b> and TEMPOH is classified as a proton-coupled electron transfer as opposed to a hydrogen-atom transfer