SCINE-Software for chemical interaction networks.

The software for chemical interaction networks (SCINE) project aims at pushing the frontier of quantum chemical calculations on molecular structures to a new level. While calculations on individual structures as well as on simple relations between them have become routine in chemistry, new developments have pushed the frontier in the field to high-throughput calculations. Chemical relations may be created by a search for specific molecular properties in a molecular design attempt, or they can be defined by a set of elementary reaction steps that form a chemical reaction network. The software modules of SCINE have been designed to facilitate such studies. The features of the modules are (i) general applicability of the applied methodologies ranging from electronic structure (no restriction to specific elements of the periodic table) to microkinetic modeling (with little restrictions on molecularity), full modularity so that SCINE modules can also be applied as stand-alone programs or be exchanged for external software packages that fulfill a similar purpose (to increase options for computational campaigns and to provide alternatives in case of tasks that are hard or impossible to accomplish with certain programs), (ii) high stability and autonomous operations so that control and steering by an operator are as easy as possible, and (iii) easy embedding into complex heterogeneous environments for molecular structures taken individually or in the context of a reaction network. A graphical user interface unites all modules and ensures interoperability. All components of the software have been made available as open source and free of charge.

Uncertainty-Aware First-Principles Exploration of Chemical Reaction Networks.

Exploring large chemical reaction networks with automated exploration approaches and accurate quantum chemical methods can require prohibitively large computational resources. Here, we present an automated exploration approach that focuses on the kinetically relevant part of the reaction network by interweaving (i) large-scale exploration of chemical reactions, (ii) identification of kinetically relevant parts of the reaction network through microkinetic modeling, (iii) quantification and propagation of uncertainties, and (iv) reaction network refinement. Such an uncertainty-aware exploration of kinetically relevant parts of a reaction network with automated accuracy improvement has not been demonstrated before in a fully quantum mechanical approach. Uncertainties are identified by local or global sensitivity analysis. The network is refined in a rolling fashion during the exploration. Moreover, the uncertainties are considered during kinetically steering of a rolling reaction network exploration. We demonstrate our approach for Eschenmoser-Claisen rearrangement reactions. The sensitivity analysis identifies that only a small number of reactions and compounds are essential for describing the kinetics reliably, resulting in efficient explorations without sacrificing accuracy and without requiring prior knowledge about the chemistry unfolding.

Corresponding Active Orbital Spaces along Chemical Reaction Paths.

The accuracy of reaction energy profiles calculated with multiconfigurational electronic structure methods and corrected by multireference perturbation theory depends crucially on consistent active orbital spaces selected along the reaction path. However, it has been challenging to choose molecular orbitals that can be considered corresponding in different molecular structures. Here, we demonstrate how active orbital spaces can be selected consistently along reaction coordinates in a fully automatized way. The approach requires no structure interpolation between reactants and products. Instead, it emerges from a synergy of the Direct Orbital Selection orbital mapping ansatz combined with our fully automated active space selection algorithm autoCAS. We demonstrate our algorithm for the potential energy profile of the homolytic carbon-carbon bond dissociation and rotation around the double bond of 1-pentene in the electronic ground state. However, our algorithm also applies to electronically excited Born-Oppenheimer surfaces.

On the accuracy of orbital based multi-level approaches for closed-shell transition metal chemistry.

In this work, we investigate the accuracy of the local molecular orbital molecular orbital (LMOMO) scheme and projection-based wave function-in-density functional theory (WF-in-DFT) embedding for the prediction of reaction energies and barriers of typical reactions involving transition metals. To analyze the dependence of the accuracy on the system partitioning, we apply a manual orbital selection for LMOMO as well as the so-called direct orbital selection (DOS) for both approaches. We benchmark these methods on 30 closed shell reactions involving 16 different transition metals. This allows us to devise guidelines for the manual selection as well as settings for the DOS that provide accurate results within an error of 2 kcal mol-1 compared to local coupled cluster. To reach this accuracy, on average 55% of the occupied orbitals have to be correlated with coupled cluster for the current test set. Furthermore, we find that LMOMO gives more reliable relative energies for small embedded regions than WF-in-DFT embedding.

Orbital pair selection for relative energies in the domain-based local pair natural orbital coupled-cluster method.

For the accurate computation of relative energies, domain-based local pair natural orbital coupled-cluster [DLPNO-CCSD(T0)] has become increasingly popular. Even though DLPNO-CCSD(T0) shows a formally linear scaling of the computational effort with the system size, accurate predictions of relative energies remain costly. Therefore, multi-level approaches are attractive that focus the available computational resources on a minor part of the molecular system, e.g., a reaction center, where changes in the correlation energy are expected to be the largest. We present a pair-selected multi-level DLPNO-CCSD(T0) ansatz that automatically partitions the orbital pairs according to their contribution to the overall correlation energy change in a chemical reaction. To this end, the localized orbitals are mapped between structures in the reaction; all pair energies are approximated through computationally efficient semi-canonical second-order Møller-Plesser perturbation theory, and the orbital pairs for which the pair energies change significantly are identified. This multi-level approach is significantly more robust than our previously suggested, orbital selection-based multi-level DLPNO-CCSD(T0) ansatz [M. Bensberg and J. Neugebauer, J. Chem. Phys. 155, 224102 (2021)] for reactions showing only small changes in the occupied orbitals. At the same time, it is even more efficient without added input complexity or accuracy loss compared to the full DLPNO-CCSD(T0) calculation. We demonstrate the accuracy of the multi-level approach for a total of 128 chemical reactions and potential energy curves of weakly interacting complexes from the S66x8 benchmark set.

Solvation Free Energies in Subsystem Density Functional Theory.

For many chemical processes the accurate description of solvent effects are vitally important. Here, we describe a hybrid ansatz for the explicit quantum mechanical description of solute-solvent and solvent-solvent interactions based on subsystem density functional theory and continuum solvation schemes. Since explicit solvent molecules may compromise the scalability of the model and transferability of the predicted solvent effect, we aim to retain both, for different solutes as well as for different solvents. The key for the transferability is the consistent subsystem decomposition of solute and solvent. The key for the scalability is the performance of subsystem DFT for increasing numbers of subsystems. We investigate molecular dynamics and stationary point sampling of solvent configurations and compare the resulting (Gibbs) free energies to experiment and theoretical methods. We can show that with our hybrid model reaction barriers and reaction energies are accurately reproduced compared to experimental data.

Direct orbital selection within the domain-based local pair natural orbital coupled-cluster method.

Domain-based local pair natural orbital coupled cluster (DLPNO-CC) has become increasingly popular to calculate relative energies (e.g., reaction energies and reaction barriers). It can be applied within a multi-level DLPNO-CC-in-DLPNO-CC ansatz to reduce the computational cost and focus the available computational resources on a specific subset of the occupied orbitals. We demonstrate how this multi-level DLPNO-CC ansatz can be combined with our direct orbital selection (DOS) approach [M. Bensberg and J. Neugebauer, J. Chem. Phys. 150, 214106 (2019)] to automatically select orbital sets for any multi-level calculation. We find that the parameters for the DOS procedure can be chosen conservatively such that they are transferable between reactions. The resulting automatic multi-level DLPNO-CC method requires no user input and is extremely robust and accurate. The computational cost is easily reduced by a factor of 3 without sacrificing accuracy. We demonstrate the accuracy of the method for a total of 61 reactions containing up to 174 atoms and use it to predict the relative stability of conformers of a Ru-based catalyst.

Density functional theory based embedding approaches for transition-metal complexes.

Transition metal species are commonly discussed by considering the metal atom embedded in a ligand environment. This apparently makes them interesting targets for modern embedding strategies based on Kohn-Sham density functional theory (DFT), which aim at modelling accurate predictions for large systems by combining different quantum chemical methods. In this perspective, we will focus on subsystem density functional theory and projection-based embedding. We review the developments in the field for transition metal species, demonstrate benefits, drawbacks and analyse error sources of the different strategies using the example of chromium hexacarbonyle, before giving a perspective where the field is currently heading.

Orbital Alignment for Accurate Projection-Based Embedding Calculations along Reaction Paths.

In projection-based embedding (PbE) the subsystem partitioning of a chemical system is based on localized orbitals. We demonstrate how the localization step can lead to inconsistent orbital spaces along reaction paths, with severe consequences for reaction barriers and energies. We propose an orbital alignment procedure that resolves this problem without manual input. The usefulness of this alignment is demonstrated for a reaction benchmark set in combination with a direct orbital selection approach to automatize PbE calculations of double hybrid-in-nonhybrid density functional theory (DFT) and wave-function-in-DFT type for reaction energies and barriers. We show how the embedded calculations are accelerated in comparison to the corresponding supersystem calculations for realistic example reactions, using a new implementation of domain-based local pair natural orbital coupled cluster with single, double, and perturbative triple excitations [DLPNO-CCSD(T0)]. The embedded calculations yield results within an error margin below 4 kJ mol-1 for the reaction barrier and energy when compared to the supersystem calculation. The calculations can be executed in a user-friendly, black-box-like fashion with minimal manual input.

Direct orbital selection for projection-based embedding.

Projection-based embedding (PbE) has become increasingly popular in recent years due to its simplicity and robustness. It is a very promising method for highly accurate calculations of reaction barriers and reaction energies via embedding of a correlated wavefunction or sophisticated density functional theory (DFT) method for the reaction center into a more cost effective DFT description of the environment. PbE enables an arbitrary partitioning of the supersystem orbitals into subsystems. In most applications so far, the selection of orbitals for the active system was directly linked to the selection of "active atoms." We propose an inexpensive approach that automatically selects orbitals as active that change during the reaction and that assigns all remaining orbitals to the environment. This approach is directly coupled to the reaction under investigation and does not rely on any specification of active atoms. We compare different variants of this approach for the selection of orbitals along the reaction path for embedding of Adamo and Barone's hybrid functional (known as PBE0) into Perdew, Burke, and Ernzerhof's exchange-correlation functional (PBE), a method dubbed as PBE0-in-PBE embedding, based on orbitalwise partial charges and the kinetic energy. The most successful comparison scheme is based on shellwise intrinsic atomic orbital charges. We show for a set of six reactions of different types that the corresponding errors in reaction energies and barriers converge quickly to zero with the extension of the active-orbital space.

Automatic basis-set adaptation in projection-based embedding.

Projection-based embedding (PbE) is an exact embedding method within density-functional theory (DFT) that has received increasing attention in recent years. Several different variants have been described in the literature, but no systematic comparison has been presented so far. The truncation of the basis is critical for the efficiency of this class of approaches. Here, we employ a basis-set truncation scheme previously used for level-shift embedding in a top-down fashion, and we present an own basis-set extension scheme for bottom-up type PbE. We compare its accuracy for the level-shift technique [Manby et al., J. Chem. Theory Comput. 8, 2564-2568 (2012)] and an empirically corrected variant, the external-orthogonality approach by Khait and Hoffmann [Annu. Rep. Comput. Chem. 8, 53-70 (2012)] and the approach based on the Huzinaga equation transferred to the DFT context [Hégely et al., J. Chem. Phys. 145, 064107 (2016)]. Concerning the reproduction in total energies, we show that the Huzinaga method yields the most stable results concerning a basis-set truncation in top-down embedding. For the practically more relevant calculation of energy differences, the efficient level-shift technique yields very promising results due to error cancellation. In bottom-up embedding, we observe convergence issues in cases where constraints in the Lagrange formalism cannot be fulfilled due to basis-set incompleteness.