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Particulate methane monooxygenase (pMMO) is the most efficient of the two groups of enzymes that can hydroxylate methane. The enzyme is membrane bound and therefore hard to study experimentally. For that reason, there is still no consensus regarding the location and nature of the active site. We have used combined quantum mechanical and molecular mechanical (QM/MM) methods to study the reactivity of the Cu B site with a histidine brace and two additional histidine ligands. We compare it with the similar active site of lytic polysaccharide monooxygenases. We show that the Cu B site can form a reactive [CuO] + state by the addition of three electrons and two protons, starting from a resting Cu(II) state, with a maximum barrier of 72 kJ mol -1 . The [CuO] + state can abstract a proton from methane, forming a Cu-bound OH - group, which may then recombine with the CH 3 group, forming the methanol product. The two steps have barriers of 59 and 52 kJ mol -1 , respectively. However, in many of the steps, formation and dissociation of H 2 O 2 or HO 2 - compete with the formation of the [CuO] + state and the former steps are typically more favourable. Thus, our calculations indicate that the Cu B site is not employed for methane oxidation, but may rather be used for the formation of hydrogen peroxide. This conclusion concurs with recent experimental investigations that excludes the Cu B site as the site for methane oxidation.

We present the theory and implementation of a fully variational wave function-density functional theory (DFT) hybrid model, which is applicable to many cases of strong correlation. We denote this model as the multiconfigurational self-consistent on-top pair-density functional theory (MC-srPDFT) model. We have previously shown how the multiconfigurational short-range DFT (MC-srDFT) hybrid model can describe many multiconfigurational cases of any spin symmetry and also state-specific calculations on excited states [Hedegård et al., J. Chem. Phys. 148(21), 214103 (2018)]. However, the srDFT part of the MC-srDFT has some deficiencies that it shares with Kohn-Sham DFT; in particular, (1) self-interaction errors (albeit reduced because of the range separation), (2) that different MS states incorrectly become non-degenerate, and (3) that singlet and non-singlet states dissociating to the same open-shell fragments incorrectly lead to different electronic energies at dissociation. The model that we present in this paper corrects these deficiencies by introducing the on-top pair density as an auxiliary variable replacing the spin density. Unlike other models in the literature, our model is fully variational and employs a long-range version of the on-top pair density. The implementation is a second-order optimization algorithm ensuring robust convergence to both ground and excited states. We show how MC-srPDFT solves the mentioned challenges by sample calculations on the ground state singlet curve of H2, N2, and Cr2 and the lowest triplet curves for N2 and Cr2. Furthermore, the rotational barrier for ethene is investigated for the S0 and T1 states. The calculations show correct degeneracy between the singlet and triplet curves at dissociation and the results are invariant to the choice of the MS value for the triplet curves., (© 2025 Author(s). Published under an exclusive license by AIP Publishing.)

Lytic polysaccharide monooxygenases (LPMOs) form a copper-dependent family of enzymes classified under the auxiliary activity (AA) superfamily. The LPMOs are known for their boosting of polysaccharide degradation through oxidation of the glycosidic bonds that link the monosaccharide subunits. This oxidation has been proposed to be dependent on either O 2 or H 2 O 2 as cosubstrate. Theoretical investigations have previously supported both mechanisms, although this contrasts with recent experiments. A possible explanation is that the theoretical results critically depend on how the Cu active site is modeled. This has also led to different results even when employing only H 2 O 2 as cosubstrate. In this paper, we investigate both the O 2 - and H 2 O 2 -driven pathways, employing Ls AA9 as the underlying LPMO and a theoretical model based on a quantum mechanics/molecular mechanics (QM/MM) framework. We ensure to consistently include all residues known to be important by using extensive QM regions of up to over 900 atoms. We also investigate several conformers that can partly explain the differences seen in previous studies. We find that the O 2 -driven reaction is unfeasible, in contrast with our previous QM/MM calculations with smaller QM regions. Meanwhile, the H 2 O 2 -driven pathway is feasible, showing that for Ls AA9, only H 2 O 2 is a viable cosubstrate as proposed experimentally.

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.

Core-electron excitations in solvated systems, influenced by solvent geometry and hydrogen bonding, make X-ray absorption spectroscopy (XAS) a valuable tool for assessing solvent-solute interactions. However, calculating XAS spectra with electronic-structure methods has proven challenging due to a delicate interplay between correlation and solvation effects. This study provides a computational procedure for XAS modeling in solvated systems, with water-solvated ammonia and ammonium systems serving as probes. Exploring methodological challenges, we investigate explicit embedding models, specifically the polarizable embedding family, including polarizable density embedding and extended polarizable density embedding. Our linear-response time-dependent density functional theory (LR-TDDFT) XAS calculations reveal the efficiency of this approach, with extended polarizable density embedding emerging as a robust improvement over polarizable density embedding. Contrary to some recent literature, our study challenges the belief that LR-TDDFT cannot accurately describe XAS spectra of ammonia and ammonium solvated in water.

Lytic polysaccharide monooxygenases (LPMOs) are copper enzymes that oxidatively cleave the strong C-H bonds in recalcitrant polysaccharide substrates, thereby playing a crucial role in biomass degradation. Recently, LPMOs have also been shown to be important for several pathogens. It is well established that the Cu(II) resting state of LPMOs is inactive, and the electronic structure of the active site needs to be altered to transform the enzyme into an active form. Whether this transformation occurs due to substrate binding or due to a unique priming reduction has remained speculative. Starting from four different crystal structures of the LPMO Ls AA9A with well-defined oxidation states, we use a frontier molecular orbital approach to elucidate the initial steps of the LPMO reaction. We give an explanation for the requirement of the unique priming reduction and analyse electronic structure changes upon substrate binding. We further investigate how the presence of the substrate could facilitate an electron transfer from the copper active site to an H 2 O 2 co-substrate. Our findings could help to control experimental LPMO reactions.

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., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

The recently developed extended polarizable density embedding (PDE-X) model is evaluated for the spectroscopic properties of organic chromophores solvated in water, including both one- and two-photon absorption properties. The PDE-X embedding model systematically improves vertical excitation energies over the preceding polarizable density embedding model (PDE). PDE-X shows more modest improvements over existing embedding models for oscillator strengths and two-photon absorption cross-sections, which are more sensitive properties. We argue that the origin of these discrepancies is related to the description of polarization effects, suggesting directions for future development of the embedding model.

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.

The lytic polysaccharide monooxygenases (LPMOs) comprise a super-family of copper enzymes that boost the depolymerisation of polysaccharides by oxidatively disrupting the glycosidic bonds connecting the sugar units. Industrial use of LPMOs for cellulose depolymerisation has already begun but is still far from reaching its full potential. One issue is that the LPMOs self-oxidise and thereby deactivate. The mechanism of this self-oxidation is unknown, but histidine residues coordinating to the copper atom are the most susceptible. An unusual methyl modification of the NE2 atom in one of the coordinating histidine residues has been proposed to have a protective role. Furthermore, substrate binding is also known to reduce oxidative damage. We here for the first time investigate the mechanism of histidine oxidation with combined quantum and molecular mechanical (QM/MM) calculations, with outset in intermediates previously shown to form from a reaction with peroxide and a reduced LPMO. We show that an intermediate with a [Cu-O] + moiety is sufficiently potent to oxidise the nearest C-H bond on both histidine residues, but methylation of the NE2 atom of His-1 increases the reaction barrier of this reaction. The substrate further increases the activation barrier. We also investigate a [Cu-OH] 2+ intermediate with a deprotonated tyrosine radical. This intermediate was previously proposed to have a protective role, and we also find it to have higher barriers than the corresponding a [Cu-O] + intermediate., (© 2023. The Author(s).)

We have recently developed a method based on relativistic time-dependent density functional theory (TD-DFT) that allows the calculation of electronic spectra in solution (Creutzberg, Hedegård, J. Chem. Theory Comput. 18 , 2022, 3671). This method treats the solvent explicitly with a classical, polarizable embedding (PE) description. Furthermore, it employs the complex polarization propagator (CPP) formalism which allows calculations on complexes with a dense population of electronic states (such complexes are known to be problematic for conventional TD-DFT). Here, we employ this method to investigate both the dynamic and electronic effects of the solvent for the excited electronic states of trans-trans-trans -[Pt(N 3 ) 2 (OH) 2 (NH 3 ) 2 ] in aqueous solution. This complex decomposes into species harmful to cancer cells under light irradiation. Thus, understanding its photo-physical properties may lead to a more efficient method to battle cancer. We quantify the effect of the underlying structure and dynamics by classical molecular mechanics simulations, refined with a subsequent DFT or semi-empirical optimization on a cluster. Moreover, we quantify the effect of employing different methods to set up the solvated system, e.g. , how sensitive the results are to the method used for the refinement, and how large a solvent shell that is required. The electronic solvent effect is always included through a PE potential.

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., (© 2022 The Authors. Chemistry - A European Journal published by Wiley-VCH GmbH.)

We extend the polarizable density embedding (PDE) model to support the calculation of nuclear magnetic resonance (NMR) shielding constants using gauge-including atomic orbitals (GIAOs) within a density functional theory (DFT) framework. The PDE model divides the total system into fragments, describing some by quantum mechanics (QM) and the others through an embedding model. The PDE model uses anisotropic polarizabilities, inter-fragment two-electron Coulomb integrals, and a non-local repulsion operator to emulate the QM effects. The terms involving Coulomb integrals are straightforwardly extended with GIAOs. In contrast, we consider two approaches to handle the gauge dependency of the non-local operator, employing either simple symmetrization or a gauge transformation. We find the latter approach to be most stable with respect to increasing the basis set size of the QM region. We examine the accuracy of the PDE model for calculating NMR shielding constants on several solutes in a water solution. The performance is compared with the classical polarizable embedding (PE) model in addition to supermolecular reference calculations. Based on these systems, we address the basis set convergence characteristics and the QM region size requirements. Furthermore, we investigate the performance of the PDE model for a system with significant electron spill-out. In many cases, we find that the PDE model outperforms the PE model, especially regarding the accuracy of nuclear shielding constants when using small QM region sizes and in systems with significant electron spill-out.

The inorganic platinum complexes currently in clinical use for cancer treatment have severe side effects, and complexes with fewer side effects are required. One option is to use complexes that are inactive until they are light-activated. Theoretical chemistry can contribute to the design of these complexes, but most current theoretical methods lack explicit treatment of relativistic effects (since the target complexes often contain heavy elements). In particular, spin-orbit coupling is required for accurate predictions of the complexes' photo-physical properties. In this perspective, we summarize relativistic methods developed in recent years that can contribute to our understanding of light-induced reactivity and thereby help predict new, suitable complexes.

In this paper, we present the theory and implementation of nuclear magnetic resonance shielding constants with gauge-including atomic orbitals for the hybrid multiconfigurational short-range density functional theory model. As a special case, this implementation also includes Hartree-Fock srDFT (HF-srDFT). Choosing a complete-active space (CAS) wave function as the multiconfigurational parameterization of the wave function, we investigate how well CAS-srDFT reproduces experimental trends of nuclear shielding constants compared to DFT and complete active space self-consistent field (CASSCF). Calculations on the nucleobases adenine and thymine show that CAS-srDFT performs on average the best of the tested methods, much better than CASSCF but only marginally better than HF-srDFT. The performance, compared to regular DFT, is similar when functionals containing exact exchange are used. We generally find that the inclusion of exact exchange is important for an accurate description of the shielding constants. In cases where no exact exchange is included, we observe that the HF- and CAS-srDFT often outperform regular DFT. For calculations on transition metal nuclei in organometallic compounds with significant static correlation, the CAS-srDFT method again outperforms CASSCF compared to experimental shielding constants, and the change from HF-srDFT is substantial. In conclusion, the static correlation posed by the metal complexes seems to be captured by CAS-srDFT, which is promising since this type of correlation is not well described by regular DFT.

We present a novel decomposition scheme for electronic interaction energies based on the flexible formulation of fragmentation schemes through fragment combination ranges (FCRs; J. Chem. Phys. , 2021 , 155 , 164105). We devise a clear additive decomposition with contribution of nondisjoint fragments and correction terms for overlapping fragments and apply this scheme to the metalloenzyme-substrate complex of a lytic polysaccharide monooxygenase (LPMO) with an oligosaccharide. By this, we further illustrate the straightforward adaptability of the FCR-based schemes to novel systems. Our calculations suggest that the description of the electronic structure is a larger error source than the fragmentation scheme. In particular, we find a large impact of the basis set size on the interaction energies. Still, the introduction of three-body interaction terms in the fragmentation setup improves the agreement to the supermolecular reference. Yet, the qualitative results for the decomposition scheme with two-body terms only largely agree within the investigated electronic-structure approaches and basis sets, which are B97-3c, DFT (TPSS and B3LYP), and MP2 methods. The overlap contributions are found to be small, allowing analysis of the interaction energy into individual amino acid residues: We find a particularly strong interaction between the substrate and the LPMO copper active site.

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(H 2 O) 6 ] 3+ and [Ir(H 2 O) 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.

Aqueous solutions of the iron(III) complex of N , N , N '-tris(2-pyridylmethyl)ethylenediamine- N '-acetate (tpena) react with hypochlorite (ClO - ) to produce the reactive high-valent [Fe IV (O)(tpena)] + . Under catalytic conditions, in bicarbonate-buffered media (pH 8) with a set ionic strength (10 mM NaCl), kinetic analysis shows that two equivalents of [Fe IV (O)(tpena)] + per one ClO - are produced, with benign chloride ions the only byproduct. An unprecedented supramolecular activation of ClO - by {(HCO 3 )⊂[(tpena)Fe III (μ-O)Fe III (Htpena)]} 2+ is proposed. This mode of activation has great advantage for use in the catalytic oxidation of C-H bonds in water since: (i) the catalyst scaffold is protected from oxidative degradation and (ii) undesirable radical side reactions which produce toxic chlorinated compounds are circumvented by this novel coactivation of water and ClO - . The unique activation mechanism by the Fe-tpena system makes possible the destruction of organic contaminants as an add-on technology to water disinfection by chlorination, demonstrated here through (i) the catalytic oxidation of micropollutant metaldehyde, and (ii) mineralization of the model substrate formate. The resting-state speciation at pH 3, 5, 7, and 9, as well as the catalytically active iron speciation are characterized with Mössbauer and EPR spectroscopy and supported by DFT calculations. Our study provides fundamentally new insights into the design and activation mode of iron-based catalysts relevant to applications in water remediation.

A series of iron(IV) oxo complexes, which differ in the donor (CH 2 py or CH 2 COO - ) 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 ν Fe═O values of 832 ± 2 cm -1 indicate similar Fe IV ═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 ( k H /k D = 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, [Fe IV O(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.

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., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2020 The Authors.)

We report the first systematic investigation of relativistic effects on the UV-vis spectra of two prototype complexes for so-called photo-activated chemotherapy (PACT), trans-trans-trans-[Pt(N3)2(OH)2(NH3)2] and cis-trans-cis-[Pt(N3)2(OH)2(NH3)2]. In PACT, design of new drugs requires in-depth understanding of the photo-activation mechanisms. A first step is usually to rationalize their UV-vis spectra for which time-dependent density functional theory (TD-DFT) is an indispensable tool. We carried out TD-DFT calculations with a systematic series of non-relativistic (NR), scalar-relativistic (SR), and four-component (4c) Hamiltonians. As expected, large differences are found between spectra calculated within 4c and NR frameworks, while the most intense features (found at higher energies below 300 nm) can be reasonably well reproduced within a SR framework. It is also shown that effective core potentials (ECPs) yield essentially similar results as all-electron SR calculations. Yet the underlying transitions can be strongly influenced by spin-orbit coupling, which is only present in the 4c framework: while this can affect both intense and less intense transitions in the spectra, the effect is most pronounced for weaker transitions at lower energies, above 300 nm. Since the investigated complexes are activated with light of wavelengths above 300 nm, employing a method with explicit inclusion of spin-orbit coupling may be crucial to rationalize the activation mechanism.

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., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

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.

DIRAC is a freely distributed general-purpose program system for one-, two-, and four-component relativistic molecular calculations at the level of Hartree-Fock, Kohn-Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, electron propagator, and various flavors of coupled cluster theory. At the self-consistent-field level, a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows for the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding model, and the frozen density embedding model.

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).

Linear response theory for the multiconfigurational short-range density functional theory (MC-srDFT) model is extended to triplet response with a singlet reference wave function. The triplet linear response equations for MC-srDFT are derived for a general hybrid srGGA functional and implemented in the Dalton program. Triplet excitation energies are benchmarked against the CC3 model of coupled cluster theory and the complete-active-space second-order perturbation theory using three different short-range functionals (srLDA, srPBE, and srPBE0), both with full linear response and employing the generalized Tamm-Dancoff approximation (gTDA). We find that using gTDA is required for obtaining reliable triplet excitations; for the CAS-srPBE model, the mean absolute deviation decreases from 0.40 eV to 0.26 eV, and for the CAS-srLDA model, it decreases from 0.29 eV to 0.21 eV. As expected, the CAS-srDFT model is found to be superior to the HF-srDFT model when analyzing the calculated triplet excitations for molecules in the benchmark set where increased static correlation is expected.

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 H 2 O 2 can also act as a co-substrate for LPMOs. Intriguingly, LPMOs generate H 2 O 2 in the absence of a polysaccharide substrate. Here, we elucidate a new mechanism for H 2 O 2 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 -NH 2 state for the terminal nitrogen atom, the latter in contrast to the original interpretation. Our QM/MM calculations show that H 2 O 2 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 H 2 O 2 .

Many chemical systems cannot be described by quantum chemistry methods based on a single-reference wave function. Accurate predictions of energetic and spectroscopic properties require a delicate balance between describing the most important configurations (static correlation) and obtaining dynamical correlation efficiently. The former is most naturally done through a multiconfigurational (MC) wave function, whereas the latter can be done by, e.g., perturbation theory. We have employed a different strategy, namely, a hybrid between multiconfigurational wave functions and density-functional theory (DFT) based on range separation. The method is denoted by MC short-range DFT (MC-srDFT) and is more efficient than perturbative approaches as it capitalizes on the efficient treatment of the (short-range) dynamical correlation by DFT approximations. In turn, the method also improves DFT with standard approximations through the ability of multiconfigurational wave functions to recover large parts of the static correlation. Until now, our implementation was restricted to closed-shell systems, and to lift this restriction, we present here the generalization of MC-srDFT to open-shell cases. The additional terms required to treat open-shell systems are derived and implemented in the DALTON program. This new method for open-shell systems is illustrated on dioxygen and [Fe(H 2 O) 6 ] 3+ .

The lytic polysaccharide monooxygenases (LPMOs) are copper metalloenzymes that can enhance polysaccharide depolymerization through an oxidative mechanism and hence boost generation of biofuel from e.g. cellulose. By employing density functional theory in a combination of quantum mechanics and molecular mechanics (QM/MM), we report a complete description of the molecular mechanism of LPMOs. The QM/MM scheme allows us to describe all reaction steps with a detailed protein environment and we show that this is necessary. Several active species capable of abstracting a hydrogen from the substrate have been proposed previously and starting from recent crystallographic work on a substrate-LPMO complex, we investigate previously suggested paths as well as new ones. We describe the generation of the reactive intermediates, the abstraction of a hydrogen atom from the polysaccharide substrate, as well as the final recombination step in which OH is transferred back to the substrate. We show that a superoxo [CuO 2 ] + complex can be protonated by a nearby histidine residue (suggested by recent mutagenesis studies and crystallographic work) and, provided an electron source is available, leads to formation of an oxyl-complex after cleavage of the O-O bond and dissociation of water. The oxyl complex either reacts with the substrate or is further protonated to a hydroxyl complex. Both the oxyl and hydroxyl complexes are also readily generated from a reaction with H 2 O 2 , which was recently suggested to be the true co-substrate, rather than O 2 . The C-H abstraction by the oxyl and hydroxy complexes is overall favorable with activation barriers of 69 and 94 kJ mol -1 , compared to the much higher barrier (156 kJ mol -1 ) obtained for the copper-superoxo species. We obtain good structural agreement for intermediates for which structural data are available and the estimated reaction energies agree with experimental rate constants. Thus, our suggested mechanism is the most complete to date and concur with available experimental evidence.

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 H 2 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 H 2 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.

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.

The absorption spectrum of the MnO 4 - ion has been a test-bed for quantum-chemical methods over the last decades. Its correct description requires highly-correlated multiconfigurational methods, which are incompatible with the inclusion of finite-temperature and solvent effects due to their high computational demands. Therefore, implicit solvent models are usually employed. Here we show that implicit solvent models are not sufficiently accurate to model the solvent shift of MnO 4 - , and we analyze the origins of their failure. We obtain the correct solvent shift for MnO 4 - in aqueous solution by employing the polarizable embedding (PE) model combined with a range-separated complete active space short-range density functional theory method (CAS-srDFT). Finite-temperature effects are taken into account by averaging over structures obtained from ab initio molecular dynamics simulations. The explicit treatment of finite-temperature and solvent effects facilitates the interpretation of the bands in the low-energy region of the MnO 4 - absorption spectrum, whose assignment has been elusive.

Most chemistry, including chemistry where relativistic effects are important, occurs in an environment, and in many cases, this environment has a significant effect on the chemistry. In nonrelativistic quantum chemistry, a lot of progress has been achieved with respect to including environments such as a solvent or protein in the calculations, and now is the time to extend the possibilities for also doing this in relativistic quantum chemistry. The polarizable embedding (PE) model efficiently incorporates electrostatic effects of the environment by describing it as a collection of localized electric multipoles and polarizabilities obtained through quantum chemical calculations. In this article, we present the theory and implementation of four- and exact two-component Hamiltonians within a PE framework. We denote the methods the PE-4c-DFT and PE-X2C-DFT models. The models include a linear response formalism to calculate time-dependent (TD) properties: PE-TD-4c-DFT and PE-TD-X2C-DFT. With this first implementation, we calculate the PE-TD-4c-PBE0 excitation energies of the TcO 4 - and ReO 4 - ions in an explicit water solvent. This initial investigation focuses on the relative size of relativistic and solvent contributions to the excitation energies. The solvent effect is divided into an indirect solvent effect due to the structural perturbation of the XO 4 - ion and a direct electrostatic effect. The relativistic effects as well as both types of solvent effects are found to contribute to a shift in the excitation energies, but they do so to different extents depending on the ion and the electronic transition in question.

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 Cu II to Cu I and the formation of a Cu II -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., Competing Interests: The authors declare no competing financial interest.

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.

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.

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.

Reliable quantum chemical methods for the description of molecules with dense-lying frontier orbitals are needed in the context of many chemical compounds and reactions. Here, we review developments that led to our new computational toolbox which implements the quantum chemical density matrix renormalization group in a second-generation algorithm. We present an overview of the different components of this toolbox.

We present a new hybrid multiconfigurational method based on the concept of range-separation that combines the density matrix renormalization group approach with density functional theory. This new method is designed for the simultaneous description of dynamical and static electron-correlation effects in multiconfigurational electronic structure problems.

A series of QM/MM optimizations of the full protein of [Fe] hydrogenase were performed. The FeGP cofactor has been optimized in the water-bound resting state (1), with a side-on bound dihydrogen (2), or as a hydride intermediate (3). For inclusion of H4MPT in the closed structure, advanced multiscale modeling appears to be necessary, especially to obtain reliable distances between CH-H4MPT(+) and the dihydrogen (H2) or hydride (H(-)) ligand in the FeGP cofactor. Inclusion of the full protein is further important for the relative energies of the two intermediates 2 and 3. We finally find that hydride transfer from 3 has a significantly higher barrier than found in previous studies neglecting the full protein environment., (© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

We present here the coupling of a polarizable embedding (PE) model to the recently developed multiconfiguration short-range density functional theory method (MC-srDFT), which can treat multiconfigurational systems with a simultaneous account for dynamical and static correlation effects. PE-MC-srDFT is designed to combine efficient treatment of complicated electronic structures with inclusion of effects from the surrounding environment. The environmental effects encompass classical electrostatic interactions as well as polarization of both the quantum region and the environment. Using response theory, molecular properties such as excitation energies and oscillator strengths can be obtained. The PE-MC-srDFT method and the additional terms required for linear response have been implemented in a development version of Dalton. To benchmark the PE-MC-srDFT approach against the literature data, we have investigated the low-lying electronic excitations of acetone and uracil, both immersed in water solution. The PE-MC-srDFT results are consistent and accurate, both in terms of the calculated solvent shift and, unlike regular PE-MCSCF, also with respect to the individual absolute excitation energies. To demonstrate the capabilities of PE-MC-srDFT, we also investigated the retinylidene Schiff base chromophore embedded in the channelrhodopsin protein. While using a much more compact reference wave function in terms of active space, our PE-MC-srDFT approach yields excitation energies comparable in quality to CASSCF/CASPT2 benchmarks.

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., (Copyright © 2014 Wiley Periodicals, Inc.)

Mössbauer spectroscopy is an indispensable spectroscopic technique and analytical tool in iron coordination chemistry. The linear correlation between the electron density at the nucleus ("contact density") and experimental isomer shifts has been used to link calculated contact densities to experimental isomer shifts. Here we have investigated relativistic methods of systematically increasing sophistication, including the eXact 2-Component (X2C) Hamiltonian and a finite-nucleus model, for the calculation of isomer shifts of iron compounds. While being of similar accuracy as the full four-component treatment, X2C calculations are far more efficient. We find that effects of spin-orbit coupling can safely be neglected, leading to further speedup. Linear correlation plots using effective densities rather than contact densities versus experimental isomer shift lead to a correlation constant a = -0.294 a0(-3) mm s(-1) (PBE functional) which is close to an experimentally derived value. Isomer shifts of similar quality can thus be obtained both with and without fitting, which is not the case if one pursues a priori a non-relativistic model approach. As an application for a biologically relevant system, we have studied three recently proposed [Fe]-hydrogenase intermediates. The structures of these intermediates were extracted from QM/MM calculations using large QM regions surrounded by the full enzyme and a solvation shell of water molecules. We show that a comparison between calculated and experimentally observed isomer shifts can be used to discriminate between different intermediates, whereas calculated atomic charges do not necessarily correlate with Mössbauer isomer shifts. Detailed analysis reveals that the difference in isomer shifts between two intermediates is due to an overlap effect.

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.

Charge transfer excitations can be described within Time-Dependent Density Functional Theory (TD-DFT), not only by means of the Coulomb Attenuated Method (CAM) but also with a combination of wave function theory and TD-DFT based on range separation. The latter approach enables a rigorous formulation of multi-determinantal TD-DFT schemes where excitation classes, which are absent in conventional TD-DFT spectra (like for example double excitations), can be addressed. This paper investigates the combination of both the long-range Multi-Configuration Self-Consistent Field (MCSCF) and Second Order Polarization Propagator Approximation (SOPPA) ansätze with a short-range DFT (srDFT) description. We find that the combinations of SOPPA or MCSCF with TD-DFT yield better results than could be expected from the pure wave function schemes. For the Time-Dependent MCSCF short-range DFT ansatz (TD-MC-srDFT) excitation energies calculated over a larger benchmark set of molecules with predominantly single reference character yield good agreement with their reference values, and are in general comparable to the CAM-B3LYP functional. The SOPPA-srDFT scheme is tested for a subset of molecules used for benchmarking TD-MC-srDFT and performs slightly better against the reference data for this small subset. Beyond the proof-of-principle calculations comprising the first part of this contribution, we additionally studied the low-lying singlet excited states (S1 and S2) of the retinal chromophore. The chromophore displays multireference character in the ground state and both excited states exhibit considerable double excitation character, which in turn cannot be described within standard TD-DFT, due to the adiabatic approximation. However, a TD-MC-srDFT approach can account for the multireference character, and excitation energies are obtained with accuracy comparable to CASPT2, although using a much smaller active space.

We present a detailed derivation of Multi-Configuration Self-Consistent Field (MCSCF) optimization and linear response equations within the polarizable embedding scheme: PE-MCSCF. The MCSCF model enables a proper description of multiconfigurational effects in reaction paths, spin systems, excited states, and other properties which cannot be described adequately with current implementations of polarizable embedding in density functional or coupled cluster theories. In the PE-MCSCF scheme the environment surrounding the central quantum mechanical system is represented by distributed multipole moments and anisotropic dipole-dipole polarizabilities. The PE-MCSCF model has been implemented in DALTON. As a preliminary application, the low lying valence states of acetone and uracil in water has been calculated using Complete Active Space Self-Consistent Field (CASSCF) wave functions. The dynamics of the water environment have been simulated using a series of snapshots generated from classical Molecular Dynamics. The calculated shifts from gas-phase to water display between good and excellent correlation with experiment and previous calculations. As an illustration of another area of potential applications we present calculations of electronic transitions in the transition metal complex, [Fe(NO)(CN)5](2-) in a micro-solvated environment. This system is highly multiconfigurational and the influence of solvation is significant.

Even for pure substances, the deduction of the absolute configuration is not always straightforward since there is no direct link between the magnitude and sign of the optical rotation and the absolute configuration. It would be very useful to use computations of the optical rotation to link experimentally measured optical rotations to an absolute configuration. Such electronic structure calculations of the optical rotation typically employ regular energy optimized basis sets from wave function theory, and especially the aug-cc-pVDZ basis set has been popular. Here, we have carried out extrapolation of the optical rotation to the basis set limits for nine small or medium sized molecules, using basis sets developed specifically for DFT and magnetic properties (aug-pcS-n series). We suggest that assignment of absolute configuration by comparisons between theoretical and experimental optical rotations may be improved by employing different wavelengths, and accordingly the optical rotation at two wavelengths (589.3 and 355.0 nm) has been investigated. Several fitting schemes were used to estimate the optical rotations at the basis set limit. It was found that use of the aug-cc-pVDZ basis set often leads to results that deviate significantly form the basis set limit results, especially at 355.0 nm but also at 589.3 nm. The double-ζ aug-pcS-1 basis set usually provides results which are closer to the limiting values. The basis set requirements are generally more severe at 355.0 nm, where also the aug-cc-pVTZ and 6-311++G(3fd,3dp) basis sets show significant deviations from the basis set limit results, while the aug-pcS-2 basis set always leads to results within an acceptable deviation.