Development of analytic gradients for the Huzinaga quantum embedding method and its applications to large-scale hybrid and double hybrid DFT forces.

The theory of analytic gradients is presented for the projector-based density functional theory (DFT) embedding approach utilizing the Huzinaga-equation. The advantages of the Huzinaga-equation-based formulation are demonstrated. In particular, it is shown that the projector employed does not appear in the Lagrangian, and the potential risk of numerical problems is avoided at the evaluation of the gradients. The efficient implementation of the analytic gradient theory is presented for approaches where hybrid DFT, second-order Møller-Plesset perturbation theory, or double hybrid DFT are embedded in lower-level DFT environments. To demonstrate the applicability of the method and to gain insight into its accuracy, it is applied to equilibrium geometry optimizations, transition state searches, and potential energy surface scans. Our results show that bond lengths and angles converge rapidly with the size of the embedded system. While providing structural parameters close to high-level quality for the embedded atoms, the embedding approach has the potential to relax the coordinates of the environment as well. Our demonstrations on a 171-atom zeolite and a 570-atom protein system show that the Huzinaga-equation-based embedding can accelerate (double) hybrid gradient computations by an order of magnitude with sufficient active regions and enables affordable force evaluations or geometry optimizations for molecules of hundreds of atoms.

Polarizable AMOEBA Model for Simulating Mg2+·Protein·Nucleotide Complexes.

Molecular mechanics (MM) simulations have the potential to provide detailed insights into the mechanisms of enzymes that utilize nucleotides as cofactors. In most cases, the activities of these enzymes also require the binding of divalent cations to catalytic sites. However, modeling divalent cations in MM simulations has been challenging. The inclusion of explicit polarization was considered promising, but despite improvements over nonpolarizable force fields and despite the inclusion of "Nonbonded-fix (NB-fix)" corrections, errors in interaction energies of divalent cations with proteins remain large. Importantly, the application of these models fails to reproduce the experimental structural data on Mg2+·Protein·ATP complexes. Focusing on these complexes, here we provide a systematic assessment of the polarizable AMOEBA model and recommend critical changes that substantially improve its predictive performance. Our key results are as follows. We first show that our recent revision of the AMOEBA protein model (AMOEBABIO18-HFC), which contains high field corrections (HFCs) to induced dipoles, dramatically improves Mg2+-protein interaction energies, reducing the mean absolute error (MAE) from 17 to 10 kcal/mol. This further supports the general applicability of AMOEBABIO18-HFC. The inclusion of many-body NB-fix corrections further reduces MAE to 6 kcal/mol, which amounts to less than 2% error. The errors are estimated with respect to vdW-inclusive density functional theory that we benchmark against CCSD(T) calculations and experiments. We also present a new model of ATP with revised polarization parameters to better capture its high field response, as well as new vdW and dihedral parameters. The ATP model accurately predicts experimental Mg2+-ATP binding free energy in the aqueous phase and provides new insights into how Mg2+ associates with ATP. Finally, we show that molecular dynamics (MD) simulations of Mg2+·Kinase·ATP complexes carried out with these improvements lead to a better agreement in global and local catalytic site structures between MD and X-ray crystallography.

Many-Body Methods for Surface Chemistry Come of Age: Achieving Consensus with Experiments.

The adsorption energy of a molecule onto the surface of a material underpins a wide array of applications, spanning heterogeneous catalysis, gas storage, and many more. It is the key quantity where experimental measurements and theoretical calculations meet, with agreement being necessary for reliable predictions of chemical reaction rates and mechanisms. The prototypical molecule-surface system is CO adsorbed on MgO, but despite intense scrutiny from theory and experiment, there is still no consensus on its adsorption energy. In particular, the large cost of accurate many-body methods makes reaching converged theoretical estimates difficult, generating a wide range of values. In this work, we address this challenge, leveraging the latest advances in diffusion Monte Carlo (DMC) and coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] to obtain accurate predictions for CO on MgO. These reliable theoretical estimates allow us to evaluate the inconsistencies in published temperature-programed desorption experiments, revealing that they arise from variations in employed pre-exponential factors. Utilizing this insight, we derive new experimental estimates of the (electronic) adsorption energy with a (more) precise pre-exponential factor. As a culmination of all of this effort, we are able to reach a consensus between multiple theoretical calculations and multiple experiments for the first time. In addition, we show that our recently developed cluster-based CCSD(T) approach provides a low-cost route toward achieving accurate adsorption energies. This sets the stage for affordable and reliable theoretical predictions of chemical reactions on surfaces to guide the realization of new catalysts and gas storage materials.

Linear-Scaling Local Natural Orbital CCSD(T) Approach for Open-Shell Systems: Algorithms, Benchmarks, and Large-Scale Applications.

The extension of the highly optimized local natural orbital (LNO) coupled cluster (CC) with single-, double-, and perturbative triple excitations [LNO-CCSD(T)] method is presented for high-spin open-shell molecules based on restricted open-shell references. The techniques enabling the outstanding efficiency of the closed-shell LNO-CCSD(T) variant are adopted, including the iteration- and redundancy-free second-order Møller-Plesset and (T) formulations as well as the integral-direct, memory- and disk use-economic, and OpenMP-parallel algorithms. For large molecules, the efficiency of our open-shell LNO-CCSD(T) method approaches that of its closed-shell parent method due to the application of restricted orbital sets for demanding integral transformations and a novel approximation for higher-order long-range spin-polarization effects. The accuracy of open-shell LNO-CCSD(T) is extensively tested for radicals and reactions thereof, ionization processes, as well as spin-state splittings, and transition-metal compounds. At the size range where the canonical CCSD(T) reference is accessible (up to 20-30 atoms), the average open-shell LNO-CCSD(T) correlation energies are found to be 99.9 to 99.95% accurate, which translates into average absolute deviations of a few tenths of kcal/mol in the investigated energy differences already with the default settings. For more extensive molecules, the local errors may grow, but they can be estimated and decreased via affordable systematic convergence studies. This enables the accurate modeling of large systems with complex electronic structures, as illustrated on open-shell organic radicals and transition-metal complexes of up to 179 atoms as well as on challenging biochemical systems, including up to 601 atoms and 11,000 basis functions. While the protein models involve difficulties for local approximations, such as the spin states of a bounded iron ion or an extremely delocalized singly occupied orbital, the corresponding single-node LNO-CCSD(T) computations were feasible in a matter of days with 10s to 100 GB of memory use. Therefore, the new LNO-CCSD(T) implementation enables highly accurate computations for open-shell systems of unprecedented size and complexity with widely accessible hardware.

Basis Set Limit CCSD(T) Energies for Extended Molecules via a Reduced-Cost Explicitly Correlated Approach.

Several approximations are introduced and tested to reduce the computational expenses of the explicitly correlated coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method for both closed and open-shell species. First, the well-established frozen natural orbital (FNO) technique is adapted to explicitly correlated CC approaches. Second, our natural auxiliary function (NAF) scheme is employed to reduce the size of the auxiliary basis required for the density fitting approximation regularly used in explicitly correlated calculations. Third, a new approach, termed the natural auxiliary basis (NAB) approximation, is proposed to decrease the size of the auxiliary basis needed for the expansion of the explicitly correlated geminals. The performance of the above approximations and that of the combined FNO-NAF-NAB approach are tested for atomization and reaction energies. Our results show that overall speedups of 7-, 5-, and 3-times can be achieved with double-, triple-, and quadruple-ζ basis sets, respectively, without any loss in accuracy. The new method can provide, e.g., reaction energies and barrier heights well within chemical accuracy for molecules with more than 40 atoms within a few days using a few dozen processor cores, and calculations with 50+ atoms are still feasible. These routinely affordable computations considerably extend the reach of explicitly correlated CCSD(T).

Stability of Carbocyclic Phosphinyl Radicals: Effect of Ring Size, Delocalization, and Sterics.

In this computational study, we report on the stability of cyclic phosphinyl radicals with an aim for a systematical assessment of stabilization effects. The radical stabilization energies (RSEs) were calculated using isodesmic reactions for a large number of carbocyclic radicals possessing different ring sizes and grades of unsaturation. In general, the RSE values range from -1.2 to -14.0 kcal·mol-1, and they show practically no correlation with the spin populations at the P-centers. The RSE values correlate with the reaction Gibbs free energies calculated for the dimerization of the studied simple radicals. Therefore, the more easily accessible RSE values offer a cost-effective estimation of global stability in a straightforward manner. To explore the effect of unsaturation on the RSE values, delocalization energies were determined using appropriate isodesmic reactions. Introducing unsaturations beside the P-center into the backbone of the rings leads to an additive increase in the magnitude of the delocalization energy (∼10, 20, and 30 kcal·mol-1, respectively, for radicals with one, two, and three C═C bonds in the conjugation). Parallelly, the spin populations at the P-centers also dwindle gradually by ∼0.1 e in the same order, indicating that the lone electron delocalizes over the π-system. Radicals containing exocyclic C═C π-bonds were also investigated, and all of these radicals have rather similar stabilities independently of the ring size, outlining the primary importance of the two exocyclic π-bonds in the conjugation. Among the radicals involved in our study, those with the best electronic stabilization are the unsaturated three-, five-, six-, and seven-membered rings containing the maximum number of conjugated vinyl fragments. The largest delocalization energy of 31.5 kcal·mol-1 and the lowest obtained spin population of 0.665 e were found for the fully unsaturated seven-membered radical (phosphepin derivative). Importantly, the electronic stabilization effects alone are insufficient for stabilizing the radicals in monomeric forms epitomized by the exothermic dimerization energies (-40 to -58 kcal·mol-1). Therefore, it is essential to apply sterically demanding bulky substituents on the α-C-atoms. Tweaking the steric congestion enabled us to propose radicals that are expected to be stable against dimerization and, consequently, may be realistic target species for synthetic investigations. The effects contributing to the stability of radicals having sterically encumbered substituents have also been explored.

Size-consistent explicitly correlated triple excitation correction.

A new approach is proposed to reduce the basis set incompleteness error of the triple excitation correction in explicitly correlated coupled-cluster singles and doubles with perturbative triples calculations. Our method is similar to the intuitive triples correction approach of Knizia et al. [J. Chem. Phys. 130, 054104 (2009)] but, in contrast to the latter, is size-consistent. The new approximation is easy to implement, and its overhead is negligible with respect to the conventional (T) correction. The performance of the approach is assessed for atomization, reaction, and interaction energies as well as for bond lengths and harmonic vibrational frequencies. The advantages of its size consistency are also demonstrated.

Interactions between large molecules pose a puzzle for reference quantum mechanical methods.

Quantum-mechanical methods are used for understanding molecular interactions throughout the natural sciences. Quantum diffusion Monte Carlo (DMC) and coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] are state-of-the-art trusted wavefunction methods that have been shown to yield accurate interaction energies for small organic molecules. These methods provide valuable reference information for widely-used semi-empirical and machine learning potentials, especially where experimental information is scarce. However, agreement for systems beyond small molecules is a crucial remaining milestone for cementing the benchmark accuracy of these methods. We show that CCSD(T) and DMC interaction energies are not consistent for a set of polarizable supramolecules. Whilst there is agreement for some of the complexes, in a few key systems disagreements of up to 8 kcal mol-1 remain. These findings thus indicate that more caution is required when aiming at reproducible non-covalent interactions between extended molecules.

Methyl-Induced Polarization Destabilizes the Noncovalent Interactions of N-Methylated Lysines.

Lysine methylation can modify noncovalent interactions by altering lysine's hydrophobicity as well as its electronic structure. Although the ramifications of the former are documented, the effects of the latter remain largely unknown. Understanding the electronic structure is important for determining how biological methylation modulates protein-protein binding, and the impact of artificial methylation experiments in which methylated lysines are used as spectroscopic probes and protein crystallization facilitators. The benchmarked first-principles calculations undertaken here reveal that methyl-induced polarization weakens the electrostatic attraction of amines with protein functional groups - salt bridges, hydrogen bonds and cation-π interactions weaken by as much as 10.3, 7.9 and 3.5 kT, respectively. Multipole analysis shows that weakened electrostatics is due to the altered inductive effects, which overcome increased attraction from methyl-enhanced polarizability and dispersion. Due to their fundamental nature, these effects are expected to be present in many cases. A survey of methylated lysines in protein structures reveals several cases in which methyl-induced polarization is the primary driver of altered noncovalent interactions; in these cases, destabilizations are found to be in the 0.6-4.7 kT range. The clearest case of where methyl-induced polarization plays a dominant role in regulating biological function is that of the PHD1-PHD2 domain, which recognizes lysine-methylated states on histones. These results broaden our understanding of how methylation modulates noncovalent interactions.

Linear-Scaling Open-Shell MP2 Approach: Algorithm, Benchmarks, and Large-Scale Applications.

A linear-scaling local second-order Møller-Plesset (MP2) method is presented for high-spin open-shell molecules based on restricted open-shell (RO) reference functions. The open-shell local MP2 (LMP2) approach inherits the iteration- and redundancy-free formulation and the completely integral-direct, OpenMP-parallel, and memory and disk use economic algorithms of our closed-shell LMP2 implementation. By utilizing restricted local molecular orbitals for the demanding integral transformation step and by introducing a novel long-range spin-polarization approximation, the computational cost of RO-LMP2 approaches that of closed-shell LMP2. Extensive benchmarks were performed for reactions of radicals, ionization potentials, as well as spin-state splittings of carbenes and transition-metal complexes. Compared to the conventional MP2 reference for systems of up to 175 atoms, local errors of at most 0.1 kcal/mol were found, which are well below the intrinsic accuracy of MP2. RO-LMP2 computations are presented for challenging protein models of up to 601 atoms and 11 000 basis functions, which involve either spin states of a complexed iron ion or a highly delocalized singly occupied orbital. The corresponding runtimes of 9-15 h obtained with a single, many-core CPU demonstrate that MP2, as well as spin-scaled MP2 and double-hybrid density functional methods, become widely accessible for open-shell systems of unprecedented size and complexity.

Accurate Reduced-Cost CCSD(T) Energies: Parallel Implementation, Benchmarks, and Large-Scale Applications.

The accurate and systematically improvable frozen natural orbital (FNO) and natural auxiliary function (NAF) cost-reducing approaches are combined with our recent coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] implementations. Both of the closed- and open-shell FNO-CCSD(T) codes benefit from OpenMP parallelism, completely or partially integral-direct density-fitting algorithms, checkpointing, and hand-optimized, memory- and operation count effective implementations exploiting all permutational symmetries. The closed-shell CCSD(T) code requires negligible disk I/O and network bandwidth, is MPI/OpenMP parallel, and exhibits outstanding peak performance utilization of 50-70% up to hundreds of cores. Conservative FNO and NAF truncation thresholds benchmarked for challenging reaction, atomization, and ionization energies of both closed- and open-shell species are shown to maintain 1 kJ/mol accuracy against canonical CCSD(T) for systems of 31-43 atoms even with large basis sets. The cost reduction of up to an order of magnitude achieved extends the reach of FNO-CCSD(T) to systems of 50-75 atoms (up to 2124 atomic orbitals) with triple- and quadruple-ζ basis sets, which is unprecedented without local approximations. Consequently, a considerably larger portion of the chemical compound space can now be covered by the practically "gold standard" quality FNO-CCSD(T) method using affordable resources and about a week of wall time. Large-scale applications are presented for organocatalytic and transition-metal reactions as well as noncovalent interactions. Possible applications for benchmarking local CCSD(T) methods, as well as for the accuracy assessment or parametrization of less complete models, for example, density functional approximations or machine learning potentials, are also outlined.

Improved description of ligand polarization enhances transferability of ion-ligand interactions.

The reliability of molecular mechanics (MM) simulations in describing biomolecular ion-driven processes depends on their ability to accurately model interactions of ions simultaneously with water and other biochemical groups. In these models, ion descriptors are calibrated against reference data on ion-water interactions, and it is then assumed that these descriptors will also satisfactorily describe interactions of ions with other biochemical ligands. The comparison against the experiment and high-level quantum mechanical data show that this transferability assumption can break down severely. One approach to improve transferability is to assign cross terms or separate sets of non-bonded descriptors for every distinct pair of ion type and its coordinating ligand. Here, we propose an alternative solution that targets an error-source directly and corrects misrepresented physics. In standard model development, ligand descriptors are never calibrated or benchmarked in the high electric fields present near ions. We demonstrate for a representative MM model that when the polarization descriptors of its ligands are improved to respond to both low and high fields, ligand interactions with ions also improve, and transferability errors reduce substantially. In our case, the overall transferability error reduces from 3.3 kcal/mol to 1.8 kcal/mol. These improvements are observed without compromising on the accuracy of low-field interactions of ligands in gas and condensed phases. Reference data for calibration and performance evaluation are taken from the experiment and also obtained systematically from "gold-standard" CCSD(T) in the complete basis set limit, followed by benchmarked vdW-inclusive density functional theory.

Transferable interactions of Li+ and Mg2+ ions in polarizable models.

Therapeutic implications of Li+, in many cases, stem from its ability to inhibit certain Mg2+-dependent enzymes, where it interacts with or substitutes for Mg2+. The underlying details of its action are, however, unknown. Molecular simulations can provide insights, but their reliability depends on how well they describe relative interactions of Li+ and Mg2+ with water and other biochemical groups. Here, we explore, benchmark, and recommend improvements to two simulation approaches: the one that employs an all-atom polarizable molecular mechanics (MM) model and the other that uses a hybrid quantum and MM implementation of the quasi-chemical theory (QCT). The strength of the former is that it describes thermal motions explicitly and that of the latter is that it derives local contributions from electron densities. Reference data are taken from the experiment, and also obtained systematically from CCSD(T) theory, followed by a benchmarked vdW-inclusive density functional theory. We find that the QCT model predicts relative hydration energies and structures in agreement with the experiment and without the need for additional parameterization. This implies that accurate descriptions of local interactions are essential. Consistent with this observation, recalibration of local interactions in the MM model, which reduces errors from 10.0 kcal/mol to 1.4 kcal/mol, also fixes aqueous phase properties. Finally, we show that ion-ligand transferability errors in the MM model can be reduced significantly from 10.3 kcal/mol to 1.2 kcal/mol by correcting the ligand's polarization term and by introducing Lennard-Jones cross-terms. In general, this work sets up systematic approaches to evaluate and improve molecular models of ions binding to proteins.

The MRCC program system: Accurate quantum chemistry from water to proteins.

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.

Integral-Direct and Parallel Implementation of the CCSD(T) Method: Algorithmic Developments and Large-Scale Applications.

A completely integral-direct, disk I/O, and network traffic economic coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] implementation has been developed relying on the density-fitting approximation. By fully exploiting the permutational symmetry, the presented algorithm is highly operation count and memory-efficient. Our measurements demonstrate excellent strong scaling achieved via hybrid MPI/OpenMP parallelization and a highly competitive, 60-70% utilization of the theoretical peak performance on up to hundreds of cores. The terms whose evaluation time becomes significant only for small- to medium-sized examples have also been extensively optimized. Consequently, high performance is also expected for systems appearing in extensive data sets used, e.g., for density functional or machine learning parametrizations, and in calculations required for certain reduced-cost or local approximations of CCSD(T), such as in our local natural orbital scheme [LNO-CCSD(T)]. The efficiency of this implementation allowed us to perform some of the largest CCSD(T) calculations ever presented for systems of 31-43 atoms and 1037-1569 orbitals using only four to eight many-core CPUs and 1-3 days of wall time. The resulting 13 correlation energies and the 12 corresponding reaction energies and barrier heights are added to our previous benchmark set collecting reference CCSD(T) results of molecules at the applicability limit of current implementations.

Reduced-Scaling Correlation Methods for the Excited States of Large Molecules: Implementation and Benchmarks for the Second-Order Algebraic-Diagrammatic Construction Approach.

A framework for reduced-scaling implementation of excited-state correlation methods is presented. An algorithm is introduced to construct excitation-specific local domains, which include all important molecular orbitals for the excitation as well as for electron correlation. The orbital space dimensions of the resulting compact domains are further decreased utilizing our reduced-cost techniques developed previously [J. Chem. Phys. 148, 094111 (2018)] based on the natural auxiliary function and local natural orbital approaches. Additional methodological improvements for the evaluation of density matrices are also discussed. Benchmark calculations are presented at the second-order algebraic-diagrammatic construction level. Compared to our reduced-cost algorithm significant, up to 3-9-fold speedups are achieved even for systems of smaller than 100 atoms. At the same time, additional errors introduced by domain approximations are highly acceptable, being about 2-4 meV on the average. The presented reduced-scaling algorithm allows us to carry out correlated excited-state calculations using triple-ζ basis sets with diffuse functions for systems of up to 400 atoms or 13 000 atomic orbitals in a matter of days using an 8-core processor.

Approaching the Basis Set Limit of CCSD(T) Energies for Large Molecules with Local Natural Orbital Coupled-Cluster Methods.

Recent optimization efforts and extensive benchmark applications are presented illustrating the accuracy and efficiency of the linear-scaling local natural orbital (LNO) coupled-cluster single-, double-, and perturbative triple-excitations [CCSD(T)] method. A composite threshold combination hierarchy (Loose, Normal, Tight, etc.) is introduced, which enables black box convergence tests and is useful to estimate the accuracy of the LNO-CCSD(T) energies with respect to CCSD(T). We also demonstrate that the complete basis set limit (CBS) of LNO-CCSD(T) energies can be reliably approached via basis set extrapolation using large basis sets including diffuse functions. Where reference CCSD(T) results are available, the mean (maximum) absolute errors of the LNO-CCSD(T) reaction and intermolecular interaction energies with the default Normal threshold combination are below 0.2-0.3 (0.6-1.0) kcal/mol, while the same measures with the Tight setting are 0.1 (0.2-0.5) kcal/mol for all the tested systems including highly complicated cases. The performance of LNO-CCSD(T) is also compared with that of other popular local CCSD(T) schemes. The exceptionally low hardware requirements of the present scheme enables the routine calculation of benchmark-quality energy differences within chemical accuracy of CCSD(T)/CBS for systems including a few hundred atoms. LNO-CCSD(T)/CBS calculations can also be performed for more than 1000 atoms with 45,000 atomic orbitals using a single, six-core CPU, about 100 GB memory, and comparable disk space.

Dual Basis Set Approach for Density Functional and Wave Function Embedding Schemes.

A dual basis (DB) approach is proposed which is suitable for the reduction of the computational expenses of the Hartree-Fock, Kohn-Sham, and wave function-based correlation methods. The approach is closely related to the DB approximation of Head-Gordon and co-workers [ J. Chem. Phys. 2006 , 125 , 074108 ] but specifically designed for embedding calculations. The new approach is applied to our variant of the projector-based embedding theory utilizing the Huzinaga-equation, multilevel local correlation methods, and combined density functional-multilevel local correlation approximations. The performance of the resulting DB density functional and wave function embedding methods is evaluated in extensive benchmark calculations and also compared to that of the corresponding embedding schemes exploiting the mixed-basis approximation. Our results show that, with an appropriate combination of basis sets, the DB approach significantly speeds up the embedding calculations, and, for chemical processes where the electronic structure considerably changes, it is clearly superior to the mixed-basis approximation. The results also demonstrate that the DB approach, if integrated with the mixed-basis approximation, efficiently eliminates the major weakness of the latter, and the combination of the DB and mixed-basis schemes is the most efficient strategy to accelerate embedding calculations.

Optimization of the Linear-Scaling Local Natural Orbital CCSD(T) Method: Improved Algorithm and Benchmark Applications.

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.

Stereocontrol in Diphenylprolinol Silyl Ether Catalyzed Michael Additions: Steric Shielding or Curtin-Hammett Scenario?

The enantioselectivity of amine-catalyzed reactions of aldehydes with electrophiles is often explained by simple steric arguments emphasizing the role of the bulky group of the catalyst that prevents the approach of the electrophile from the more hindered side. This standard steric shielding model has recently been challenged by the discovery of stable downstream intermediates, which appear to be involved in the rate-determining step of the catalytic cycle. The alternative model, referred to as the Curtin-Hammett scenario of stereocontrol, assumes that the enantioselectivity is related to the stability and reactivity of downstream intermediates. In our present computational study, we examine the two key processes of the catalytic Michael reaction between propanal and ß-nitrostyrene that are relevant to the proposed stereoselectivity models, namely the C-C bond formation and the protonation steps. The free energy profiles obtained for the pathways leading to the enantiomeric products suggest that the rate- and stereodetermining steps are not identical as implied by the previous models. The stereoselectivity can be primarily controlled by C-C bond formation even though the reaction rate is dictated by the protonation step. This kinetic scheme is consistent with all observations of experimental mechanistic studies including those of mass spectrometric back reaction screening experiments, which reveal a mismatch between the stereoselectivity of the back and the forward reactions.