Scaled opposite-spin atomic-orbital based algebraic diagrammatic construction scheme for the polarization propagator with asymptotic linear-scaling effort: Theory and implementation.

A novel local approach for the quantum-chemical computation of excited states is presented, where the concept of the atomic-orbital formulation of the second-order Møller-Plesset energy expression is extended to the second-order algebraic diagrammatic construction scheme by virtue of the Laplace transform. The scaled opposite-spin second-order algebraic diagrammatic construction method with Cholesky decomposed densities and density-fitting, or CDD-DF-SOS-ADC(2) for short, exploits the sparsity of the two-electron repulsion integrals, the atomic ground-state density matrix, and the atomic transition density matrix to drastically reduce the computational effort. By using a local density-fitting approximation, it is shown that asymptotically linear scaling can be achieved for linear carboxylic acids. For electron-dense systems, sub-cubic scaling can be achieved if the excitation is local, and hence the transition density is sparse. Furthermore, the memory footprint and accuracy of the CDD-DF-SOS-ADC(2) method are explored in detail.

An effective sub-quadratic scaling atomic-orbital reformulation of the scaled opposite-spin RI-CC2 ground-state model using Cholesky-decomposed densities and an attenuated Coulomb metric.

An atomic-orbital reformulation of the Laplace-transformed scaled opposite-spin (SOS) coupled cluster singles and doubles (CC2) model within the resolution of the identity (RI) approximation (SOS-RI-CC2) is presented that extends its applicability to molecules with several hundreds of atoms and triple-zeta basis sets. We exploit sparse linear algebra and an attenuated Coulomb metric to decrease the disk space demands and the computational efforts. In this way, an effective sub-quadratic computational scaling is achieved with our ω-SOS-CDD-RI-CC2 model. Moreover, Cholesky decomposition of the ground-state one-electron density matrix reduces the prefactor, allowing for an early crossover with the molecular orbital formulation. The accuracy and performance of the presented method are investigated for various molecular systems.

Efficient Integral-Direct Methods for Self-Consistent Reduced Density Matrix Functional Theory Calculations on Central and Graphics Processing Units.

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(N5) to O(N4), 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.

A scaled explicitly correlated F12 correction to second-order Møller-Plesset perturbation theory.

An empirically scaled version of the explicitly correlated F12 correction to second-order Møller-Plesset perturbation theory (MP2-F12) is introduced. The scaling eliminates the need for many of the most costly terms of the F12 correction while reproducing the unscaled explicitly correlated F12 interaction energy correction to a high degree of accuracy. The method requires a single, basis set dependent scaling factor that is determined by fitting to a set of test molecules. We present factors for the cc-pVXZ-F12 (X = D, T, Q) basis set family obtained by minimizing interaction energies of the S66 set of small- to medium-sized molecular complexes and show that our new method can be applied to accurately describe a wide range of systems. Remarkably good explicitly correlated corrections to the interaction energy are obtained for the S22 and L7 test sets, with mean percentage errors for the double-zeta basis of 0.60% for the F12 correction to the interaction energy, 0.05% for the total electron correlation interaction energy, and 0.03% for the total interaction energy, respectively. Additionally, mean interaction energy errors introduced by our new approach are below 0.01 kcal mol-1 for each test set and are thus negligible for second-order perturbation theory based methods. The efficiency of the new method compared to the unscaled F12 correction is shown for all considered systems, with distinct speedups for medium- to large-sized structures.

Communication: A reduced scaling J-engine based reformulation of SOS-MP2 using graphics processing units.

We present a low-prefactor, cubically scaling scaled-opposite-spin second-order Møller-Plesset perturbation theory (SOS-MP2) method which is highly suitable for massively parallel architectures like graphics processing units (GPU). The scaling is reduced from O(N5) to O(N³) by a reformulation of the MP2-expression in the atomic orbital basis via Laplace transformation and the resolution-of-the-identity (RI) approximation of the integrals in combination with efficient sparse algebra for the 3-center integral transformation. In contrast to previous works that employ GPUs for post Hartree-Fock calculations, we do not simply employ GPU-based linear algebra libraries to accelerate the conventional algorithm. Instead, our reformulation allows to replace the rate-determining contraction step with a modified J-engine algorithm, that has been proven to be highly efficient on GPUs. Thus, our SOS-MP2 scheme enables us to treat large molecular systems in an accurate and efficient manner on a single GPU-server.

Structure assignment in the solid state by the coupling of quantum chemical calculations with NMR experiments: a columnar hexabenzocoronene derivative.

We present a quantum chemical ab initio study which demonstrates a new combined experimental and theoretical approach, whereby a comparison of calculated and experimental (1)H NMR chemical shifts allows the elucidation of structural arrangements in solid-state molecular ensembles, taking advantage of the marked sensitivity of the (1)H chemical shift to intermolecular interactions. Recently, Brown et al. have shown that, under fast magic-angle spinning (MAS) at 35 kHz, the resolution in a (1)H NMR spectrum of the solid phase of an alkyl-substituted hexabenzocoronene (HBC) derivative is sufficient to observe the hitherto unexpected resolution of three distinct aromatic resonances ( J. Am. Chem. Soc. 1999, 121, 6712). Exploiting the additional information about proton proximities provided by (1)H double-quantum (DQ) MAS NMR spectroscopy, it was shown that the results are qualitatively consistent with the aromatic cores packing in a manner similar to that in unsubstituted HBC. Using the HBC-C(12) molecule as an example, we show here that the new combined experimental and theoretical approach allows the observed (1)H chemical shifts to be related in a quantitative manner to the intermolecular structure. In the quantum chemical calculations, a series of model systems of stacked HBC oligomers are used. On account of the marked dependence of the (1)H chemical shift to ring currents arising from nearby aromatic rings, the calculated (1)H chemical shifts are found to be very sensitive to the stacking arrangement of the HBC molecules. Moreover, the ring current effect is found to be particularly long range, with a considerable influence of the second neighbor, at a distance of 700 pm, being observed.

The formation of HCS and HCSH molecules and their role in the collision of comet Shoemaker-Levy 9 with Jupiter.

The reaction of hydrogen sulfide with ground-state atomic carbon was examined with crossed molecular beams experiments and ab initio calculations. The thiohydroxycarbene molecule, HCSH, was the reactive intermediate, which fragmented into atomic hydrogen and the thioformyl radical HCS. This finding may account for the unassigned HCS source and an unidentified HCSH radical needed to match observed CS abundances from the collision of comet Shoemaker-Levy 9 into Jupiter. In the shocked jovian atmosphere, HCS could further decompose to H and CS, and CS could react with SH and OH to yield the observed CS2 and COS.

A combined experimental and theoretical study on the formation of interstellar C3H isomers.

The reaction of ground-state carbon atoms with acetylene was studied under single-collision conditions in crossed beam experiments to investigate the chemical dynamics of forming cyclic and linear C3H isomers (c-C3H and l-C3H, respectively) in interstellar environments via an atom-neutral reaction. Combined state-of-the-art ab initio calculations and experimental identification of the carbon-hydrogen exchange channel to both isomers classify this reaction as an important alternative to ion-molecule encounters to synthesize C3H radicals in the interstellar medium. These findings strongly correlate with astronomical observations and explain a higher [c-C3H]/[l-C3H] ratio in the dark cloud TMC-1 than in the carbon star IRC+10216.