Christoph Riplinger

Natural triple excitations in local coupled cluster calculations with pair natural orbitals

In this work, the extension of the previously developed domain based local pair-natural orbital (DLPNO) based singles- and doubles coupled cluster (DLPNO-CCSD) method to perturbatively include connected triple excitations is reported. The development is based on the concept of triples-natural orbitals that span the joint space of the three pair natural orbital (PNO) spaces of the three electron pairs that are involved in the calculation of a given triple-excitation contribution. The truncation error is very smooth and can be significantly reduced through extrapolation to the zero threshold. However, the extrapolation procedure does not improve relative energies. The overall computational effort of the method is asymptotically linear with the system size O(N). Actual linear scaling has been confirmed in test calculations on alkane chains. The accuracy of the DLPNO-CCSD(T) approximation relative to semicanonical CCSD(T0) is comparable to the previously developed DLPNO-CCSD method relative to canonical CCSD. Relative energies are predicted with an average error of approximately 0.5 kcal∕mol for a challenging test set of medium sized organic molecules. The triples correction typically adds 30%-50% to the overall computation time. Thus, very large systems can be treated on the basis of the current implementation. In addition to the linear C150H302 (452 atoms, >8800 basis functions) we demonstrate the first CCSD(T) level calculation on an entire protein, Crambin with 644 atoms, and more than 6400 basis functions.

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. II. Linear scaling domain based pair natural orbital coupled cluster theory

Domain based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)) is a highly efficient local correlation method. It is known to be accurate and robust and can be used in a black box fashion in order to obtain coupled cluster quality total energies for large molecules with several hundred atoms. While previous implementations showed near linear scaling up to a few hundred atoms, several nonlinear scaling steps limited the applicability of the method for very large systems. In this work, these limitations are overcome and a linear scaling DLPNO-CCSD(T) method for closed shell systems is reported. The new implementation is based on the concept of sparse maps that was introduced in Part I of this series [P. Pinski, C. Riplinger, E. F. Valeev, and F. Neese, J. Chem. Phys. 143, 034108 (2015)]. Using the sparse map infrastructure, all essential computational steps (integral transformation and storage, initial guess, pair natural orbital construction, amplitude iterations, triples correction) are achieved in a linear scaling fashion. In addition, a number of additional algorithmic improvements are reported that lead to significant speedups of the method. The new, linear-scaling DLPNO-CCSD(T) implementation typically is 7 times faster than the previous implementation and consumes 4 times less disk space for large three-dimensional systems. For linear systems, the performance gains and memory savings are substantially larger. Calculations with more than 20 000 basis functions and 1000 atoms are reported in this work. In all cases, the time required for the coupled cluster step is comparable to or lower than for the preceding Hartree-Fock calculation, even if this is carried out with the efficient resolution-of-the-identity and chain-of-spheres approximations. The new implementation even reduces the error in absolute correlation energies by about a factor of two, compared to the already accurate previous implementation.

Mechanistic Contrasts between Manganese and Rhenium Bipyridine Electrocatalysts for the Reduction of Carbon Dioxide

[Re(bpy)(CO)3](-) is a well-established homogeneous electrocatalyst for the reduction of CO2 to CO. Recently, substitution of the more abundant transition metal Mn for Re yielded a similarly active electrocatalyst, [Mn(bpy)(CO)3](-). Compared to the Re catalyst, this Mn catalyst operates at a lower applied reduction potential but requires the presence of a weak acid in the solution for catalytic activity. In this study, we employ quantum chemistry combined with continuum solvation and microkinetics to examine the mechanism of CO2 reduction by each catalyst. We use cyclic voltammetry experiments to determine the turnover frequencies of the Mn catalyst with phenol as the added weak acid. The computed turnover frequencies for both catalysts agree to within one order of magnitude of the experimental ones. The different operating potentials for these catalysts indicate that different reduction pathways may be favored during catalysis. We model two different pathways for both catalysts and find that, at their respective operating potentials, the Mn catalyst indeed is predicted to take a different reaction route than the Re catalyst. The Mn catalyst can access both catalytic pathways, depending on the applied potential, while the Re catalyst does not show this flexibility. Our microkinetics analysis predicts which intermediates should be observable during catalysis. These intermediates for the two catalyzed reactions have qualitatively different electronic configurations, depending on the applied potential. The observable intermediate at higher applied potentials possesses an unpaired electron and therefore should be EPR-active; however, the observable intermediate at lower applied potentials, accessible only for the Mn catalyst, is diamagnetic and therefore should be EPR-silent. The differences between both catalysts are rationalized on the basis of their electronic structure and different ligand binding affinities.

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals

In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implements sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in quantum chemistry and beyond.

Electronic Structure Analysis of the Oxygen‐Activation Mechanism by FeII‐ and α‐Ketoglutarate (αKG)‐Dependent Dioxygenases

α-Ketoglutarate (αKG)-dependent nonheme iron enzymes utilize a high-spin (HS) ferrous center to couple the activation of oxygen to the decarboxylation of the cosubstrate αKG to yield succinate and CO(2), and to generate a high-valent ferryl species that then acts as an oxidant to functionalize the target C-H bond. Herein a detailed analysis of the electronic-structure changes that occur in the oxygen activation by this enzyme was performed. The rate-limiting step, which is identical on the septet and quintet surfaces, is the nucleophilic attack of the distal O atom of the O(2) adduct on the carbonyl group in αKG through a bicyclic transition state ((5, 7) TS1). Due to the different electronic structures in (5, 7) TS1, the decay of (7)TS1 leads to a ferric oxyl species, which undergoes a rapid intersystem crossing to form the ferryl intermediate. By contrast, a HS ferrous center ligated by a peroxosuccinate is obtained on the quintet surface following (5)TS1. Thus, additional two single-electron transfer steps are required to afford the same Fe(IV)-oxo species. However, the triplet reaction channel is catalytically irrelevant. The biological role of αKG played in the oxygen-activation reaction is dual. The αKG LUMO (C=O π*) serves as an electron acceptor for the nucleophilic attack of the superoxide monoanion. On the other hand, the αKG HOMO (C1-C2 σ) provides the second and third electrons for the further reduction of the superoxide. In addition to density functional theory, high-level ab initio calculations have been used to calculate the accurate energies of the critical points on the alternative potential-energy surfaces. Overall, the results delivered by the ab initio calculations are largely parallel to those obtained with the B3LYP density functional, thus lending credence to our conclusions.

Mechanism of Olefin Asymmetric Hydrogenation Catalyzed by Iridium Phosphino-Oxazoline: A Pair Natural Orbital Coupled Cluster Study

Since the development of chiral phosphino-oxazoline iridium catalysts, which hydrogenate unfunctionalized alkenes enantioselectively, the asymmetric hydrogenation of prochiral olefins has become important in the production of chiral compounds. For the last 10 years, details of the mechanism, including formal oxidation state assignment of the metal center and the nature of intermediates and transition states have been debated. Various contributions have been given from a theoretical point of view, but due to the size of the structures, these have been forced to rely on density functional theory (DFT) methods. In our investigation of the catalytic cycle, we employ both DFT and a correlated ab initio method, namely, the newly implemented domain-based local pair natural orbital coupled-cluster theory with single and double excitations and the inclusion of perturbative triples correction (DLPNO-CCSD(T)). Our results show that the most likely active paths involve the formation of an intermediate Ir(V) species. Furthermore, we have been able to predict the absolute configuration of the major products, and where comparison to experiment is possible, the results of our calculations agree with the enantiomeric excess obtained from hydrogenating five prochiral substrates. This work also shows that it is now possible to study catalytic reactions with untruncated models (having up to 88 atoms) at the CCSD(T) level of theory.

SparseMaps—A systematic infrastructure for reduced-scaling electronic structure methods. IV. Linear-scaling second-order explicitly correlated energy with pair natural orbitals

We present a formulation of the explicitly correlated second-order Møller-Plesset (MP2-F12) energy in which all nontrivial post-mean-field steps are formulated with linear computational complexity in system size. The two key ideas are the use of pair-natural orbitals for compact representation of wave function amplitudes and the use of domain approximation to impose the block sparsity. This development utilizes the concepts for sparse representation of tensors described in the context of the domain based local pair-natural orbital-MP2 (DLPNO-MP2) method by us recently [Pinski et al., J. Chem. Phys. 143, 034108 (2015)]. Novel developments reported here include the use of domains not only for the projected atomic orbitals, but also for the complementary auxiliary basis set (CABS) used to approximate the three- and four-electron integrals of the F12 theory, and a simplification of the standard B intermediate of the F12 theory that avoids computation of four-index two-electron integrals that involve two CABS indices. For quasi-1-dimensional systems (n-alkanes), the ON DLPNO-MP2-F12 method becomes less expensive than the conventional ON(5) MP2-F12 for n between 10 and 15, for double- and triple-zeta basis sets; for the largest alkane, C200H402, in def2-TZVP basis, the observed computational complexity is N(∼1.6), largely due to the cubic cost of computing the mean-field operators. The method reproduces the canonical MP2-F12 energy with high precision: 99.9% of the canonical correlation energy is recovered with the default truncation parameters. Although its cost is significantly higher than that of DLPNO-MP2 method, the cost increase is compensated by the great reduction of the basis set error due to explicit correlation.

A new near-linear scaling, efficient and accurate, open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory

The Coupled-Cluster expansion, truncated after single and double excitations (CCSD), provides accurate and reliable molecular electronic wave functions and energies for many molecular systems around their equilibrium geometries. However, the high computational cost, which is well-known to scale as O(N6) with system size N, has limited its practical application to small systems consisting of not more than approximately 20-30 atoms. To overcome these limitations, low-order scaling approximations to CCSD have been intensively investigated over the past few years. In our previous work, we have shown that by combining the pair natural orbital (PNO) approach and the concept of orbital domains it is possible to achieve fully linear scaling CC implementations (DLPNO-CCSD and DLPNO-CCSD(T)) that recover around 99.9% of the total correlation energy [C. Riplinger et al., J. Chem. Phys. 144, 024109 (2016)]. The production level implementations of the DLPNO-CCSD and DLPNO-CCSD(T) methods were shown to be applicable to realistic systems composed of a few hundred atoms in a routine, black-box fashion on relatively modest hardware. In 2011, a reduced-scaling CCSD approach for high-spin open-shell unrestricted Hartree-Fock reference wave functions was proposed (UHF-LPNO-CCSD) [A. Hansen et al., J. Chem. Phys. 135, 214102 (2011)]. After a few years of experience with this method, a few shortcomings of UHF-LPNO-CCSD were noticed that required a redesign of the method, which is the subject of this paper. To this end, we employ the high-spin open-shell variant of the N-electron valence perturbation theory formalism to define the initial guess wave function, and consequently also the open-shell PNOs. The new PNO ansatz properly converges to the closed-shell limit since all truncations and approximations have been made in strict analogy to the closed-shell case. Furthermore, given the fact that the formalism uses a single set of orbitals, only a single PNO integral transformation is necessary, which offers large computational savings. We show that, with the default PNO truncation parameters, approximately 99.9% of the total CCSD correlation energy is recovered for open-shell species, which is comparable to the performance of the method for closed-shells. UHF-DLPNO-CCSD shows a linear scaling behavior for closed-shell systems, while linear to quadratic scaling is obtained for open-shell systems. The largest systems we have considered contain more than 500 atoms and feature more than 10 000 basis functions with a triple-ζ quality basis set.

Direct Detection and Characterization of Chloride in the Active Site of the Low-pH Form of Sulfite Oxidase Using Electron Spin Echo Envelope Modulation Spectroscopy, Isotopic Labeling, and Density Functional Theory Calculations

Electron spin echo envelope modulation (ESEEM) investigations were carried out on samples of the low-pH (lpH) form of vertebrate sulfite oxidase (SO) prepared with (35)Cl- and (37)Cl-enriched buffers, as well as with buffer containing the natural abundance of Cl isotopes. The isotope-related changes observed in the ESEEM spectra provide direct and unequivocal evidence that Cl(-) is located in close proximity to the Mo(V) center of lpH SO. The measured isotropic hyperfine interaction constant of about 4 MHz ((35)Cl) suggests that the Cl(-) ion is either weakly coordinated to Mo(V) at its otherwise vacant axial position, trans to the oxo ligand, or is hydrogen-bonded to the equatorial exchangeable OH ligand. Scalar relativistic all-electron density functional theory (DFT) calculations of the hyperfine and nuclear quadrupole interaction parameters, along with steric and energetic arguments, strongly support the possibility that Cl(-) is hydrogen-bonded to the equatorial OH ligand rather than being directly coordinated to the Mo(V).

The Reaction Mechanism of Cytochrome P450 NO Reductase: A Detailed Quantum Mechanics/Molecular Mechanics Study

A detailed QM/MM study on the reaction mechanism of Cytochrome P450 NO reductase is reported. Two reaction pathways connecting the two well-characterized intermediates as well as two putative intermediates that represent the unknown third intermediate are explored, with emphasis on the unusual direct reduction of the enzymatic active site by the cofactor NADH. Activation barriers and kinetic isotope effect are calculated and reveal that reduction of the NO-bound species occurs in form of a hydride ion transfer. Furthermore, the impact of different hydrogen bonds in the active site to binding and reactivity of NADH is explored. The calculated kinetic and thermodynamic properties for both modelled pathways are used for the kinetic simulation of the entire reaction course. It is thus shown that the unknown key intermediate is the singlet diradical Fe(III)-NHOH(⋅). It is also found that the mechanism of the N-N bond formation is spin-recoupling, which is only possible due to the diradical character of the key intermediate.