MRCC is a package of ab initio and density functional quantum chemistry programs for accurate electronic structure calculations. The suite has efficient implementations of both low- and high-level correlation methods, such as second-order Møller–Plesset (MP2), random-phase approximation (RPA), second-order algebraic-diagrammatic construction [ADC(2)], coupled-cluster (CC), configuration interaction (CI), and related techniques. It has a state-of-the-art CC singles and doubles with perturbative triples [CCSD(T)] code, and its specialties, the arbitrary-order iterative and perturbative CC methods developed by automated programming tools, enable achieving convergence with regard to the level of correlation. The package also offers a collection of multi-reference CC and CI approaches. Efficient implementations of density functional theory (DFT) and more advanced combined DFT-wave function approaches are also available. Its other special features, the highly competitive linear-scaling local correlation schemes, allow for MP2, RPA, ADC(2), CCSD(T), and higher-order CC calculations for extended systems. Local correlation calculations can be considerably accelerated by multi-level approximations and DFT-embedding techniques, and an interface to molecular dynamics software is provided for quantum mechanics/molecular mechanics calculations. All components of MRCC support shared-memory parallelism, and multi-node parallelization is also available for various methods. For academic purposes, the package is available free of charge.

An optimized implementation of the local natural orbital (LNO) coupled-cluster (CC) with single-, double-, and perturbative triple excitations [LNO-CCSD(T)] method is presented. The integral-direct, in-core, highly efficient domain construction technique of our local second-order Møller-Plesset (LMP2) scheme is extended to the CC level. The resulting scheme, which is also suitable for general-order LNO-CC calculations, inherits the beneficial properties of the LMP2 approach, such as the asymptotically linear-scaling operation count, the asymptotically constant data storage requirement, and the completely independent domain calculations. In addition to integrating our recent redundancy-free LMP2 and Laplace-transformed (T) algorithms with the LNO-CCSD(T) code, the memory demand, the domain and LNO construction, the auxiliary basis compression, and the previously rate-determining two-external integral transformation have been significantly improved. The accuracy of all of the approximations is carefully examined on medium-sized to large systems to determine reasonably tight default truncation thresholds. Our benchmark calculations, performed on molecules of up to 63 atoms, show that the optimized method with the default settings provides average correlation and reaction energy errors of less than 0.07% and 0.34 kcal/mol, respectively, compared to the canonical CCSD(T) reference. The efficiency of the present LNO-CCSD(T) implementation is demonstrated on realistic, three-dimensional examples. Using the new code, an LNO-CCSD(T) correlation energy calculation with a triple-ζ basis set is feasible on a single processor for a protein molecule including 2380 atoms and more than 44000 atomic orbitals.

An integral-direct, iteration-free, linear-scaling, local second-order Møller-Plesset (MP2) approach is presented, which is also useful for spin-scaled MP2 calculations as well as for the efficient evaluation of the perturbative terms of double-hybrid density functionals. The method is based on a fragmentation approximation: the correlation contributions of the individual electron pairs are evaluated in domains constructed for the corresponding localized orbitals, and the correlation energies of distant electron pairs are computed with multipole expansions. The required electron repulsion integrals are calculated directly invoking the density fitting approximation; the storage of integrals and intermediates is avoided. The approach also utilizes natural auxiliary functions to reduce the size of the auxiliary basis of the domains and thereby the operation count and memory requirement. Our test calculations show that the approach recovers 99.9% of the canonical MP2 correlation energy and reproduces reaction energies with an average (maximum) error below 1 kJ/mol (4 kJ/mol). Our benchmark calculations demonstrate that the new method enables MP2 calculations for molecules with more than 2300 atoms and 26000 basis functions on a single processor.

Experiments have been carried out to compare the stabilization effect of two flavonoid type natural antioxidants, dihydromyricetin (DHM) and quercetin (Q) in polyethylene (PE). Additive concentrations changed between 0 and 500 ppm in several steps and 1000 ppm Sandostab PEPQ phosphorus containing secondary stabilizer was also added to each compound. Both antioxidants are very efficient stabilizers for PE, sufficient melt stability was achieved already at 50 ppm DHM content. At small concentrations dihydromyricetin proved to be more efficient melt stabilizer and it protected the secondary antioxidant better than quercetin. In spite of its better efficiency in melt stabilization, polymers containing DHM had the same residual stability as those prepared with quercetin. Accordingly, the larger efficiency does not result from the larger number of active phenolic hydroxyls in the molecule, but from interactions with the phosphorous secondary stabilizer that is stronger or at least different for DHM than quercetin. In spite that DHM is a white powder, it gave the polymer a brownish color which became deeper with increasing number of extrusions and additive content. Nevertheless, both natural antioxidants can be used efficiently for the stabilization of polymers in applications in which color is of secondary importance.

In this study we pursue the most efficient paths for the evaluation of three-center electron repulsion integrals (ERIs) over solid harmonic Gaussian functions of various angular momenta. First, the adaptation of the well-established techniques developed for four-center ERIs, such as the Obara-Saika, McMurchie-Davidson, Gill-Head-Gordon-Pople, and Rys quadrature schemes, and the combinations thereof for three-center ERIs is discussed. Several algorithmic aspects, such as the order of the various operations and primitive loops as well as prescreening strategies, are analyzed. Second, the number of floating point operations (FLOPs) is estimated for the various algorithms derived, and based on these results the most promising ones are selected. We report the efficient implementation of the latter algorithms invoking automated programming techniques and also evaluate their practical performance. We conclude that the simplified Obara-Saika scheme of Ahlrichs is the most cost-effective one in the majority of cases, but the modified Gill-Head-Gordon-Pople and Rys algorithms proposed herein are preferred for particular shell triplets. Our numerical experiments also show that even though the solid harmonic transformation and the horizontal recurrence require significantly fewer FLOPs if performed at the contracted level, this approach does not improve the efficiency in practical cases. Instead, it is more advantageous to carry out these operations at the primitive level, which allows for more efficient integral prescreening and memory layout.

The stabilization effect of a flavonoid type natural antioxidant, rutin, was compared to that of quercetin in polyethylene. Additive concentrations changed between 0 and 500 ppm in several steps and also 1000 ppm Sandostab PEPQ phosphorus secondary stabilizer was added to each compound. Stabilization efficiency was determined by changes in vinyl group content, melt flow rate, oxygen induction time, color and the consumption of the secondary antioxidant during multiple extrusions. The results showed that rutin is as efficient melt stabilizer as quercetin used as reference. On the other hand, rutin has a deteriorating effect on the stability of the polymer at small concentrations and partially decomposes during processing. The comparison of bond dissociation enthalpies indicated that the substitution of the hydroxyl group in the C ring of quercetin by saccharide moieties increases their value, but the small increase does not influence the efficiency of the stabilizer. FTIR and DSC measurements indicated the interaction of the natural antioxidant and the phosphonite secondary stabilizer, and the development of interactions was confirmed by molecular modeling. Mainly hydrogen bonds and aromatic,  electron interactions develop between the hydroxyl groups in ring A and the POC group of the phosphonite, as well as between the aromatic rings of PEPQ and the flavonoids, but they do not influence the stabilization efficiency of the antioxidants.

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The calculation of the geometrical derivatives of three-center electron repulsion integrals (ERIs) over contracted spherical harmonic Gaussians has been optimized. We compared various methods based on the Obara-Saika, McMurchie-Davidson, Gill-Head-Gordon-Pople, and Rys polynomial algorithms using Cartesian, Hermite, and mixed Gaussian integrals for each scheme. The latter ERIs contain both Hermite and Cartesian Gaussians, and they combine the advantageous properties of both types of basis functions. Furthermore, prescreening of the ERI derivatives is discussed, and an efficient approximation of the Cauchy-Schwarz bound for first derivatives is presented. Based on the estimated operation counts, the most promising schemes were implemented by automated code generation, and their relative performances were evaluated. We analyzed the benefits of computing all of the derivatives of a shell triplet simultaneously compared to calculating them just for one degree of freedom at a time, and it was found that the former scheme offers a speedup close to an order of magnitude with a triple-zeta quality basis when appropriate prescreening is applied. In these cases, the Obara-Saika method with Cartesian Gaussians proved to be the best approach, but when derivatives for one degree of freedom are required at a time the mixed Gaussian Obara-Saika and Gill-Head-Gordon-Pople algorithms are predicted to be the best performing ones.