Perspective: multi-configurational methods in bio-inorganic chemistry.

Transition metal ions play crucial roles in the structure and function of numerous proteins, contributing to essential biological processes such as catalysis, electron transfer, and oxygen binding. However, accurately modeling the electronic structure and properties of metalloproteins poses significant challenges due to the complex nature of their electronic configurations and strong correlation effects. Multiconfigurational quantum chemistry methods are, in principle, the most appropriate tools for addressing these challenges, offering the capability to capture the inherent multi-reference character and strong electron correlation present in bio-inorganic systems. Yet their computational cost has long hindered wider adoption, making methods such as density functional theory (DFT) the method of choice. However, advancements over the past decade have substantially alleviated this limitation, rendering multiconfigurational quantum chemistry methods more accessible and applicable to a wider range of bio-inorganic systems. In this perspective, we discuss some of these developments and how they have already been used to answer some of the most important questions in bio-inorganic chemistry. We also comment on ongoing developments in the field and how the future of the field may evolve.

Understanding the initial events of the oxidative damage and protection mechanisms of the AA9 lytic polysaccharide monooxygenase family.

Lytic polysaccharide monooxygenase (LPMO) is a new class of oxidoreductases that boosts polysaccharide degradation employing a copper active site. This boost may facilitate the cost-efficient production of biofuels and high-value chemicals from polysaccharides such as lignocellulose. Unfortunately, self-oxidation of the active site inactivates LPMOs. Other oxidoreductases employ hole-hopping mechanisms as protection against oxidative damage, but little is generally known about the details of these mechanisms. Herein, we employ highly accurate theoretical models based on density functional theory (DFT) molecular mechanics (MM) hybrids to understand the initial steps in LPMOs' protective measures against self-oxidation; we identify several intermediates recently proposed from experiment, and quantify which are important for protective hole-hopping pathways. Investigations on two different LPMOs show consistently that a tyrosine residue close to copper is crucial for protection: this explains recent experiments, showing that LPMOs without this tyrosine are more susceptible to self-oxidation.

Theoretical and Numerical Comparison of Quantum- and Classical Embedding Models for Optical Spectra.

Quantum-mechanical (QM) and classical embedding models approximate a supermolecular quantum-chemical calculation. This is particularly useful when the supermolecular calculation has a size that is out of reach for present QM models. Although QM and classical embedding methods share the same goal, they approach this goal from different starting points. In this study, we compare the polarizable embedding (PE) and frozen-density embedding (FDE) models. The former is a classical embedding model, whereas the latter is a density-based QM embedding model. Our comparison focuses on solvent effects on optical spectra of solutes. This is a typical scenario where super-system calculations including the solvent environment become prohibitively large. We formulate a common theoretical framework for PE and FDE models and systematically investigate how PE and FDE approximate solvent effects. Generally, differences are found to be small, except in cases where electron spill-out becomes problematic in the classical frameworks. In these cases, however, atomic pseudopotentials can reduce the electron-spill-out issue.

Molecular Mechanism of Substrate Oxidation in Lytic Polysaccharide Monooxygenases: Insight from Theoretical Investigations.

Lytic polysaccharide monooxygenases (LPMOs) are copper enzymes that today comprise a large enzyme superfamily, grouped into the distinct members AA9-AA17 (with AA12 exempted). The LPMOs have the potential to facilitate the upcycling of biomass waste products by boosting the breakdown of cellulose and other recalcitrant polysaccharides. The cellulose biopolymer is the main component of biomass waste and thus comprises a large, unexploited resource. The LPMOs work through a catalytic, oxidative reaction whose mechanism is still controversial. For instance, the nature of the intermediate performing the oxidative reaction is an open question, and the same holds for the employed co-substrate. Here we review theoretical investigations addressing these questions. The applied theoretical methods are usually based on quantum mechanics (QM), often combined with molecular mechanics (QM/MM). We discuss advantages and disadvantages of the employed theoretical methods and comment on the interplay between theoretical and experimental results.

Polarizable Embedding Complex Polarization Propagator in Four- and Two-Component Frameworks.

Explicit embedding methods combined with the complex polarization propagator (CPP) enable the modeling of spectroscopy for increasingly complex systems with a high density of states. We present the first derivation and implementation of the CPP in four- and exact-two-component (X2C) polarizable embedding (PE) frameworks. We denote the developed methods PE-4c-CPP and PE-X2C-CPP, respectively. We illustrate the methods by estimating the solvent effect on ultraviolet-visible (UV-vis) and X-ray atomic absorption (XAS) spectra of [Rh(H2O)6]3+ and [Ir(H2O)6]3+ immersed in aqueous solution. We moreover estimate solvent effects on UV-vis spectra of a platinum complex that can be photochemically activated (in water) to kill cancer cells. Our results clearly show that the inclusion of the environment is required: UV-vis and (to a lesser degree) XAS spectra can become qualitatively different from vacuum calculations. Comparison of PE-4c-CPP and PE-X2C-CPP methods shows that X2C essentially reproduces the solvent effect obtained with the 4c methods.

Engineering the Oxidative Potency of Non-Heme Iron(IV) Oxo Complexes in Water for C-H Oxidation by a cis Donor and Variation of the Second Coordination Sphere.

A series of iron(IV) oxo complexes, which differ in the donor (CH2py or CH2COO-) cis to the oxo group, three with hemilabile pendant donor/second coordination sphere base/acid arms (pyH/py or ROH), have been prepared in water at pH 2 and 7. The νFe═O values of 832 ± 2 cm-1 indicate similar FeIV═O bond strengths; however, different reactivities toward C-H substrates in water are observed. HAT occurs at rates that differ by 1 order of magnitude with nonclassical KIEs (kH/kD = 30-66) consistent with hydrogen atom tunneling. Higher KIEs correlate with faster reaction rates as well as a greater thermodynamic stability of the iron(III) resting states. A doubling in rate from pH 7 to pH 2 for substrate C-H oxidation by the most potent complex, that with a cis-carboxylate donor, [FeIVO(Htpena)]2+, is observed. Supramolecular assistance by the first and second coordination spheres in activating the substrate is proposed. The lifetime of this complex in the absence of a C-H substrate is the shortest (at pH 2, 3 h vs up to 1.3 days for the most stable complex), implying that slow water oxidation is a competing background reaction. The iron(IV)═O complex bearing an alcohol moiety in the second coordination sphere displays significantly shorter lifetimes due to a competing selective intramolecular oxidation of the ligand.

Estimating the accuracy of calculated electron paramagnetic resonance hyperfine couplings for a lytic polysaccharide monooxygenase.

Lytic polysaccharide monooxygenases (LPMOs) are enzymes that bind polysaccharides followed by an (oxidative) disruption of the polysaccharide surface, thereby boosting depolymerization. The binding process between the LPMO catalytic domain and polysaccharide is key to the mechanism and establishing structure-function relationships for this binding is therefore crucial. The hyperfine coupling constants (HFCs) from EPR spectroscopy have proven useful for this purpose. Unfortunately, EPR does not provide direct structural data and therefore the experimental EPR parameters have to be supported with parameters calculated with density functional theory. Yet, calculated HFCs are extremely sensitive to the employed computational setup. Using the LPMO Ls(AA9)A catalytic domain, we here quantify the importance of several choices in the computational setup, ranging from the use of specialized basis, the underlying structures, and the employed exchange-correlation functional. We show that specialized basis sets are an absolute necessity, and also that care has to be taken in the optimization of the underlying structure: only by allowing large parts of the protein around the active site to structurally relax could we obtain results that uniformly reproduced experimental trends. We compare our results to previously published X-ray structures and experimental HFCs for Ls(AA9)A as well as to recent experimental/theoretical results for another (AA10) family of LPMOs.

Dalton Project: A Python platform for molecular- and electronic-structure simulations of complex systems.

The Dalton Project provides a uniform platform access to the underlying full-fledged quantum chemistry codes Dalton and LSDalton as well as the PyFraME package for automatized fragmentation and parameterization of complex molecular environments. The platform is written in Python and defines a means for library communication and interaction. Intermediate data such as integrals are exposed to the platform and made accessible to the user in the form of NumPy arrays, and the resulting data are extracted, analyzed, and visualized. Complex computational protocols that may, for instance, arise due to a need for environment fragmentation and configuration-space sampling of biochemical systems are readily assisted by the platform. The platform is designed to host additional software libraries and will serve as a hub for future modular software development efforts in the distributed Dalton community.

Is density functional theory accurate for lytic polysaccharide monooxygenase enzymes?

The lytic polysaccharide monooxygenase (LPMO) enzymes boost polysaccharide depolymerization through oxidative chemistry, which has fueled the hope for more energy-efficient production of biofuel. We have recently proposed a mechanism for the oxidation of the polysaccharide substrate (E. D. Hedegård and U. Ryde, Chem. Sci., 2018, 9, 3866-3880). In this mechanism, intermediates with superoxide, oxyl, as well as hydroxyl (i.e. [CuO2]+, [CuO]+ and [CuOH]2+) cores were involved. These complexes can have both singlet and triplet spin states, and both spin-states may be important for how LPMOs function during catalytic turnover. Previous calculations on LPMOs have exclusively been based on density functional theory (DFT). However, different DFT functionals are known to display large differences for spin-state splittings in transition-metal complexes, and this has also been an issue for LPMOs. In this paper, we study the accuracy of DFT for spin-state splittings in superoxide, oxyl, and hydroxyl intermediates involved in LPMO turnover. As reference we employ multiconfigurational perturbation theory (CASPT2).

The role of the active site tyrosine in the mechanism of lytic polysaccharide monooxygenase.

Catalytic breakdown of polysaccharides can be achieved more efficiently by means of the enzymes lytic polysaccharide monooxygenases (LPMOs). However, the LPMO mechanism has remained controversial, preventing full exploitation of their potential. One of the controversies has centered around an active site tyrosine, present in most LPMO classes. Recent investigations have for the first time obtained direct (spectroscopic) evidence for the possibility of chemical modification of this tyrosine. However, the spectroscopic features obtained in the different investigations are remarkably different, with absorption maximum at 420 and 490 nm, respectively. In this paper we use density functional theory (DFT) in a QM/MM formulation to reconcile these (apparently) conflicting results. By modeling the spectroscopy as well as the underlying reaction mechanism we can show how formation of two isomers (both involving deprotonation of tyrosine) explains the difference in the observed spectroscopic features. Both isomers have a [TyrO-Cu-OH]+ moiety with the OH in either the cis- or trans-position to a deprotonated tyrosine. Although the cis-[TyrO-Cu-OH]+ moiety is well positioned for oxidation of the substrate, preliminary calculations with the substrate reveal that the reactivity is at best moderate, making a protective role of tyrosine more likely.

Mechanism of hydrogen peroxide formation by lytic polysaccharide monooxygenase.

Lytic polysaccharide monooxygenases (LPMOs) are copper-containing metalloenzymes that can cleave the glycosidic link in polysaccharides. This could become crucial for production of energy-efficient biofuels from recalcitrant polysaccharides. Although LPMOs are considered oxygenases, recent investigations have shown that H2O2 can also act as a co-substrate for LPMOs. Intriguingly, LPMOs generate H2O2 in the absence of a polysaccharide substrate. Here, we elucidate a new mechanism for H2O2 generation starting from an AA10-LPMO crystal structure with an oxygen species bound, using QM/MM calculations. The reduction level and protonation state of this oxygen-bound intermediate has been unclear. However, this information is crucial to the mechanism. We therefore investigate the oxygen-bound intermediate with quantum refinement (crystallographic refinement enhanced with QM calculations), against both X-ray and neutron data. Quantum refinement calculations suggest a Cu(ii)-O-2 system in the active site of the AA10-LPMO and a neutral protonated -NH2 state for the terminal nitrogen atom, the latter in contrast to the original interpretation. Our QM/MM calculations show that H2O2 generation is possible only from a Cu(i) center and that the most favourable reaction pathway is to involve a nearby glutamate residue, adding two electrons and two protons to the Cu(ii)-O-2 system, followed by dissociation of H2O2.

Exploration of H2 binding to the [NiFe]-hydrogenase active site with multiconfigurational density functional theory.

The combination of density functional theory (DFT) with a multiconfigurational wave function is an efficient way to include dynamical correlation in calculations with multiconfiguration self-consistent field wave functions. These methods can potentially be employed to elucidate reaction mechanisms in bio-inorganic chemistry, where many other methods become either too computationally expensive or too inaccurate. In this paper, a complete active space (CAS) short-range DFT (CAS-srDFT) hybrid was employed to investigate a bio-inorganic system, namely H2 binding to the active site of [NiFe] hydrogenase. This system was previously investigated with coupled-cluster (CC) and multiconfigurational methods in the form of cumulant-approximated second-order perturbation theory, based on the density matrix renormalization group (DMRG). We find that it is more favorable for H2 to bind to Ni than to Fe, in agreement with previous CC and DMRG calculations. The accuracy of CAS-srDFT is comparable to both CC and DMRG, despite much smaller active spaces were employed than in the corresponding DMRG calculations. This enhanced efficiency at the smaller active spaces shows that CAS-srDFT can become a useful method for bio-inorganic chemistry.

Targeting the reactive intermediate in polysaccharide monooxygenases.

Lytic polysaccharide monooxygenases (LPMOs) are copper metalloenzymes that can enhance polysaccharide depolymerization through an oxidative mechanism, making them interesting for the production of biofuel from cellulose. However, the details of this activation are unknown; in particular, the nature of the intermediate that attacks the glycoside C-H bond in the polysaccharide is not known, and a number of different species have been suggested. The homolytic bond-dissociation energy (BDE) has often been used as a descriptor for the bond-activation power, especially for inorganic model complexes. We have employed quantum-chemical cluster calculations to estimate the BDE for a number of possible LPMO intermediates to bridge the gap between model complexes and the actual LPMO active site. The calculated BDEs suggest that the reactive intermediate is either a Cu(II)-oxyl, a Cu(III)-oxyl, or a Cu(III)-hydroxide, which indicate that O-O bond breaking occurs before the C-H activation step.

Multiscale Modelling of Lytic Polysaccharide Monooxygenases.

Lytic polysaccharide monooxygenase (LPMO) enzymes have attracted considerable attention owing to their ability to enhance polysaccharide depolymerization, making them interesting with respect to production of biofuel from cellulose. LPMOs are metalloenzymes that contain a mononuclear copper active site, capable of activating dioxygen. However, many details of this activation are unclear. Some aspects of the mechanism have previously been investigated from a computational angle. Yet, either these studies have employed only molecular mechanics (MM), which are inaccurate for metal active sites, or they have described only the active site with quantum mechanics (QM) and neglected the effect of the protein. Here, we employ hybrid QM and MM (QM/MM) methods to investigate the first steps of the LPMO mechanism, which is reduction of CuII to CuI and the formation of a CuII-superoxide complex. In the latter complex, the superoxide can bind either in an equatorial or an axial position. For both steps, we obtain structures that are markedly different from previous suggestions, based on small QM-cluster calculations. Our calculations show that the equatorial isomer of the superoxide complex is over 60 kJ/mol more stable than the axial isomer because it is stabilized by interactions with a second-coordination-sphere glutamine residue, suggesting a possible role for this residue. The coordination of superoxide in this manner agrees with recent experimental suggestions.

Polarizable Embedding Density Matrix Renormalization Group.

The polarizable embedding (PE) approach is a flexible embedding model where a preselected region out of a larger system is described quantum mechanically, while the interaction with the surrounding environment is modeled through an effective operator. This effective operator represents the environment by atom-centered multipoles and polarizabilities derived from quantum mechanical calculations on (fragments of) the environment. Thereby, the polarization of the environment is explicitly accounted for. Here, we present the coupling of the PE approach with the density matrix renormalization group (DMRG). This PE-DMRG method is particularly suitable for embedded subsystems that feature a dense manifold of frontier orbitals which requires large active spaces. Recovering such static electron-correlation effects in multiconfigurational electronic structure problems, while accounting for both electrostatics and polarization of a surrounding environment, allows us to describe strongly correlated electronic structures in complex molecular environments. We investigate various embedding potentials for the well-studied first excited state of water with active spaces that correspond to a full configuration-interaction treatment. Moreover, we study the environment effect on the first excited state of a retinylidene Schiff base within a channelrhodopsin protein. For this system, we also investigate the effect of dynamical correlation included through short-range density functional theory.

Investigation of Multiconfigurational Short-Range Density Functional Theory for Electronic Excitations in Organic Molecules.

Computational methods that can accurately and effectively predict all types of electronic excitations for any molecular system are missing in the toolbox of the computational chemist. Although various Kohn-Sham density-functional methods (KS-DFT) fulfill this aim in some cases, they become inadequate when the molecule has near-degeneracies and/or low-lying double-excited states. To address these issues we have recently proposed multiconfiguration short-range density-functional theory-MC-srDFT-as a new tool in the toolbox. While initial applications for systems with multireference character and double excitations have been promising, it is nevertheless important that the accuracy of MC-srDFT is at least comparable to the best KS-DFT methods also for organic molecules that are typically of single-reference character. In this paper we therefore systematically investigate the performance of MC-srDFT for a selected benchmark set of electronic excitations of organic molecules, covering the most common types of organic chromophores. This investigation confirms the expectation that the MC-srDFT method is accurate for a broad range of excitations and comparable to accurate wave function methods such as CASPT2, NEVPT2, and the coupled cluster based CC2 and CC3.

Excitation Spectra of Nucleobases with Multiconfigurational Density Functional Theory.

Range-separated hybrid methods between wave function theory and density functional theory (DFT) can provide high-accuracy results, while correcting some of the inherent flaws of both the underlying wave function theory and DFT. We here assess the accuracy for excitation energies of the nucleobases thymine, uracil, cytosine, and adenine, using a hybrid between complete active space self-consistent field (CASSCF) and DFT methods. The method is based on range separation, thereby avoiding all double-counting of electron correlation and is denoted long-range CASSCF short-range DFT (CAS-srDFT). Using a linear response extension of CAS-srDFT, we compare the first 7-8 excited states of the nucleobases with perturbative multireference approaches as well as coupled cluster based methods. Our results show that the CAS-srDFT method can provide accurate excitation energies in good correspondence with the computationally more expensive methods.

Basis set error estimation for DFT calculations of electronic g-tensors for transition metal complexes.

We present a detailed study of the basis set dependence of electronic g-tensors for transition metal complexes calculated using Kohn-Sham density functional theory. Focus is on the use of locally dense basis set schemes where the metal is treated using either the same or a more flexible basis set than used for the ligand sphere. The performance of all basis set schemes is compared to the extrapolated complete basis set limit results. Furthermore, we test the performance of the aug-cc-pVTZ-J basis set developed for calculations of NMR spin-spin and electron paramagnetic resonance hyperfine coupling constants. Our results show that reasonable results can be obtain when using small basis sets for the ligand sphere, and very accurate results are obtained when an aug-cc-pVTZ basis set or similar is used for all atoms in the complex.

Damped Response Theory in Combination with Polarizable Environments: The Polarizable Embedding Complex Polarization Propagator Method.

We present a combination of the polarizable embedding (PE) scheme with the complex polarization propagator (CPP) method with the aim of calculating response properties including relaxation for large and complex systems. This new approach, termed PE-CPP, will benefit from the highly advanced description of the environmental electrostatic potential and polarization in the PE method as well as the treatment of near-resonant effects in the CPP approach. The PE-CPP model has been implemented in a Kohn-Sham density functional theory approach, and we present pilot calculations exemplifying the implementation for the UV/vis and carbon K-edge X-ray absorption spectra of the protein plastocyanin. Furthermore, technical details associated with a PE-CPP calculation are discussed.