The electronic structure of oxo-Mn(salen): Single-reference and multireference approaches

Full Configuration Interaction Excited-State Energies in Large Active Spaces from Subspace Iteration with Repeated Random Sparsification

We present a stable and systematically improvable quantum Monte Carlo (QMC) approach to calculating excited-state energies, which we implement using our fast randomized iteration method for the full configuration interaction problem (FCI-FRI). Unlike previous excited-state quantum Monte Carlo methods, our approach, which is based on an asymmetric variant of subspace iteration, avoids the use of dot products of random vectors and instead relies upon trial vectors to maintain orthogonality and estimate eigenvalues. By leveraging recent advances, we apply our method to calculate ground- and excited-state energies of challenging molecular systems in large active spaces, including the carbon dimer with 8 electrons in 108 orbitals (8e,108o), an oxo-Mn(salen) transition metal complex (28e,28o), ozone (18e,87o), and butadiene (22e,82o). In the majority of these test cases, our approach yields total excited-state energies that agree with those from state-of-the-art methods─including heat-bath CI, the density matrix renormalization group approach, and FCIQMC─to within sub-milliHartree accuracy. In all cases, estimated excitation energies agree to within about 0.1 eV.

Machine Learning-Assisted Selection of Active Spaces for Strongly Correlated Transition Metal Systems

Active space quantum chemical methods could provide very accurate description of strongly correlated electronic systems, which is of tremendous value for natural sciences. The proper choice of the active space is crucial but a nontrivial task. In this article, we present a neural network-based approach for automatic selection of active spaces, focused on transition metal systems. The training set has been formed from artificial systems composed of one transition metal and various ligands, on which we have performed the density matrix renormalization group and calculated the single-site entropy. On the selected set of systems, ranging from small benchmark molecules up to larger challenging systems involving two metallic centers, we demonstrate that our machine learning models could predict the active space orbitals with reasonable accuracy. We also tested the transferability on out-of-the-model systems, including bimetallic complexes and complexes with ligands, which were not involved in the training set. Also, we tested the correctness of the automatically selected active spaces on a Fe(II)-porphyrin model, where we studied the lowest states at the DMRG level and compared the energy difference between spin states or the energy difference between conformations of ferrocene with recent studies.

Near-Linear Scaling in DMRG-Based Tailored Coupled Clusters: An Implementation of DLPNO-TCCSD and DLPNO-TCCSD(T)

We present a new implementation of density matrix renormalization group based tailored coupled clusters method (TCCSD), which employs the domain-based local pair natural orbital approach (DLPNO). Compared to the previous local pair natural orbital (LPNO) version of the method, the new implementation is more accurate, offers more favorable scaling, and provides more consistent behavior across the variety of systems. On top of the singles and doubles, we include the perturbative triples correction (T), which is able to retrieve even more dynamic correlation. The methods were tested on three systems: tetramethyleneethane, oxo-Mn(Salen), and iron(II)-porphyrin model. The first two were revisited to assess the performance with respect to LPNO-TCCSD. For oxo-Mn(Salen), we retrieved between 99.8 and 99.9% of the total canonical correlation energy which is an improvement of 0.2% over the LPNO version in less than 63% of the total LPNO runtime. Similar results were obtained for iron(II)-porphyrin. When the perturbative triples correction was employed, irrespective of the active space size or system, the obtained energy differences between two spin states were within the chemical accuracy of 1 kcal/mol using the default DLPNO settings.

Toward the efficient local tailored coupled cluster approximation and the peculiar case of oxo-Mn(Salen)

We introduce a new implementation of the coupled cluster method with single and double excitations tailored by the matrix product state wave functions (DMRG-TCCSD), which employs the local pair natural orbital (LPNO) approach. By exploiting locality in the coupled cluster stage of the calculation, we were able to remove some of the limitations that hindered the application of the canonical version of the method to larger systems and/or with larger basis sets. We assessed the accuracy of the approximation using two systems: tetramethyleneethane (TME) and oxo-Mn(Salen). Using the default cut-off parameters, we were able to recover over 99.7% and 99.8% of the canonical correlation energy for the triplet and singlet state of TME, respectively. In the case of oxo-Mn(Salen), we found that the amount of retrieved canonical correlation energy depends on the size of the complete active space (CAS)-we retrieved over 99.6% for the larger 27 orbital CAS and over 99.8% for the smaller 22 orbital CAS. The use of LPNO-TCCSD allowed us to perform these calculations up to quadruple-ζ basis set, amounting to 1178 basis functions. Moreover, we examined dependence of the ground state of oxo-Mn(Salen) on the CAS composition. We found that the inclusion of 4d_xy orbital plays an important role in stabilizing the singlet state at the DMRG-CASSCF level via double-shell effect. However, by including dynamic correlation, the ground state was found to be triplet regardless of the size of the basis set or the composition of CAS, which is in agreement with previous findings by canonical DMRG-TCCSD in smaller basis.

Coupled Cluster Method with Single and Double Excitations Tailored by Matrix Product State Wave Functions

In the past decade, the quantum chemical version of the density matrix renormalization group (DMRG) method has established itself as the method of choice for calculations of strongly correlated molecular systems. Despite its favorable scaling, it is in practice not suitable for computations of dynamic correlation. We present a novel method for accurate "post-DMRG" treatment of dynamic correlation based on the tailored coupled cluster (CC) theory in which the DMRG method is responsible for the proper description of nondynamic correlation, whereas dynamic correlation is incorporated through the framework of the CC theory. We illustrate the potential of this method on prominent multireference systems, in particular, N₂ and Cr₂ molecules and also oxo-Mn(Salen), for which we have performed the first post-DMRG computations in order to shed light on the energy ordering of the lowest spin states.

Ab initio electronic structure study of a model water splitting dimer complex

A model manganese dimer electrocatalyst bridged by μ-OH ligands is used to investigate changes in spin states that may occur during water oxidation. We have employed restricted open-shell Hartree-Fock (ROHF), second-order Møller-Plesset perturbation theory (MP2), complete active space self-consistent field (CASSCF), and multireference second-order Møller-Plesset perturbation theory (MRMP2) calculations to investigate this system. Multiconfigurational methods like CASSCF and MRMP2 are appropriate methods to study these systems with antiferromagnetically-coupled electrons. Orbital occupations and distributions have been closely analyzed to understand the electronic details and contributions to the water splitting from manganese and oxygen atoms. The presence of Mn(IV)O˙ radical moieties has been observed in this catalytic pathway. Multiple nearly degenerate excited states were found close to the ground state in all structures. This suggests competing potential energy landscapes near the ground state may influence the reactivity of manganese complexes such as the dimers studied in this work.

Communication: DMRG-SCF study of the singlet, triplet, and quintet states of oxo-Mn(Salen)

We use CheMPS2, our free open-source spin-adapted implementation of the density matrix renormalization group (DMRG) [S. Wouters, W. Poelmans, P. W. Ayers, and D. Van Neck, Comput. Phys. Commun. 185, 1501 (2014)], to study the lowest singlet, triplet, and quintet states of the oxo-Mn(Salen) complex. We describe how an initial approximate DMRG calculation in a large active space around the Fermi level can be used to obtain a good set of starting orbitals for subsequent complete-active-space or DMRG self-consistent field calculations. This procedure mitigates the need for a localization procedure, followed by a manual selection of the active space. Per multiplicity, the same active space of 28 electrons in 22 orbitals (28e, 22o) is obtained with the 6-31G(*), cc-pVDZ, and ANO-RCC-VDZP basis sets (the latter with DKH2 scalar relativistic corrections). Our calculations provide new insight into the electronic structure of the quintet.

Principal component analysis of Mn(salen) catalysts

In this work, the Jacobsen catalyst is decomposed under different truncation schemes, allowing the establishment of structure–property relationships for several Mn(salen) complexes.

A rational basis for the axial ligand effect in C-H oxidation by [MnO(porphyrin)(X)]+ (X = H2O, OH-, O2-) from a DFT study

Oxyl radical character in the MnO group of the title system is shown from a density functional theory study to be essential for efficient C-H cleavage, which is a key step in C-H oxidation. Since oxyl species have elongated Mn-O bonds relative to the more usual oxo species of type MnO, the normal expectation would be that high trans-influence ligands X should facilitate oxyl character by elongating the Mn-O bond and thus enhance both oxyl character and reactivity. Contrary to this expectation, but in line with the experimental data (Jin, N.; Ibrahim, M.; Spiro, T. G.; Groves, J. T. J. Am. Chem. Soc. 2007, 129, 12416), we find that reactivity increases along the series X = O(2-) < OH(-) < H2O for the following reasons. The ground-state singlet (S) is unreactive for all X, and only the higher-energy triplet (T) and quintet (Q) states have the oxyl character needed for reactivity, but the higher trans-influence X ligands are also shown to increase the S/T and S/Q gaps, thus making attainment of the needed T and Q states harder. The latter effect is dominant, and high trans-influence X ligands thus disfavor reaction. The higher reactivity in the presence of acid noted by Groves and co-workers is thus rationalized by the preference for having X = H2O over OH(-) or O(2-).

Assessing the performance of density functional theory for the electronic structure of metal-salens: the d2-metals

The performance of three common combinations of density functional theory has been evaluated for the geometries and relative energies of a commonly-employed model complex of the salen ligand [salen = bis(salicylaldehydo)ethylenediamine] with the d2-metals Ti(II), V(III), Cr(IV), Zr(II), Nb(III), and Mo(IV). High-level ab initio methods including complete active-space third-order perturbation theory have been employed both as benchmarks for the density functional theory results and to examine the multireference character of the low-lying electronic states in these systems. The strong multireference character of the systems has been clearly demonstrated. All of the functionals examined provide geometries that are typically within 0.2 A least root mean square deviation from the benchmark geometries. The performance of the density functionals for the relative energies of the low-lying electronic states is significantly worse, providing qualitatively different descriptions in some instances. Of the systems explored, no significant difference is observed in the multireference character or in the reliability of the density functional results when comparing 3d vs 4d transition-metal systems.