Performance of CASPT2 and DFT for Relative Spin-State Energetics of Heme Models

Toward Highly Accurate Spin State Energetics in First-Row Transition Metal Complexes: A Combined CASPT2/CC Approach

In previous work on the performance of multiconfigurational second-order perturbation theory (CASPT2) in describing spin state energetics in first-row transition metal systems [ Pierloot et al. J. Chem. Theory Comput. 2017 , 13 , 537 - 553 ], we showed that standard CASPT2 works well for valence correlation but does not describe the metal semicore (3s3p) correlation effects accurately. This failure is partially responsible for the well-known bias toward high-spin states of CASPT2. In this paper, we expand our previous work and show that this bias could be partly removed with a combined CASPT2/CC approach: using high-quality CASPT2 with extensive correlation-consistent basis sets for valence correlation and low-cost CCSD(T) calculations with minimal basis sets for the metal semicore (3s3p) correlation effects. We demonstrate that this approach is efficient by studying the spin state energetics of a series of iron complexes modeling important intermediates in oxidative catalytic processes in chemistry and biochemistry. On the basis of a comparison with bare CCSD(T) results from this and previous work, the average error of the CASPT2/CC approach is estimated at around 2 kcal mol^-1 in favor of high spin states.

Spin states of Mn(III) meso-tetraphenylporphyrin chloride assessed by density functional methods

The present work assessed several exchange-correlation functionals (including GGA, meta-GGA and hybrid functionals), in combination with a variety of basis sets and effective core potentials (ECP) for their ability to predict the ground spin state of Mn(III) meso-tetraphenylporphyrin chloride complex, labeled Mn(III)TPPCl, for which experimental data support the quintet high spin state. Geometry optimization of Mn(III)TPPCl was performed for three possible spin states (singlet state, LS; triplet state, IS; and quintet state, HS) at the TPSSh level using the LANL2DZ ECP for Mn and the 6-311G(d) basis set for C, N, Cl and H. Afterwards, single-point energy calculations were conducted by applying 18 exchange-correlation functionals (BLYP, B3LYP, PW91, BPW91, BP86, OLYP, OPBE, OPW91, O3LYP, PBE0, PBEh1PBE, HSEH1PBE, TPSS, TPSSh, M06 L, M06, M062X and M06HF). The influence of the basis set for the metal center was assessed using a smaller group of functionals and varying between the Pople basis set 6-31G(d), its newer formulation m6-31G(d) and the larger Def2-QZVP basis set. All functionals in combination with Pople basis sets predict the quintet state as the ground spin state. In addition, the BLYP, BP86, BPW91, PW91, PBEh1PBE, TPSS and TPSSh functionals predicted the IS lying at most ~60 kJ mol^-1 above the HS, which agrees with the reference data. Results including Def2-QZVP basis set were inconsistent, since only BLYP and B3LYP predict HS as the ground spin state. The recommended methodology for the treatment of such systems seems to be exchange-correlations functionals with few or none Hartree-Fock exchange and modest size basis sets. Graphical Abstract MnTPPCl molecule and the energy ordering of its spin states assessed by 18 functionals.

The mechanism for oxygen reduction in cytochrome c dependent nitric oxide reductase (cNOR) as obtained from a combination of theoretical and experimental results

Bacterial NO-reductases (NOR) belong to the heme-copper oxidase (HCuO) superfamily, in which most members are O₂-reducing, proton-pumping enzymes. This study is one in a series aiming to elucidate the reaction mechanisms of the HCuOs, including the mechanisms for cellular energy conservation. One approach towards this goal is to compare the mechanisms for the different types of HCuOs, cytochrome c oxidase (CcO) and NOR, reducing the two substrates O₂ and NO. Specifically in this study, we describe the mechanism for oxygen reduction in cytochrome c dependent NOR (cNOR). Hybrid density functional calculations were performed on large cluster models of the cNOR binuclear active site. Our results are used, together with published experimental information, to construct a free energy profile for the entire catalytic cycle. Although the overall reaction is quite exergonic, we show that during the reduction of molecular oxygen in cNOR, two of the reduction steps are endergonic with high barriers for proton uptake, which is in contrast to oxygen reduction in CcO, where all reduction steps are exergonic. This difference between the two enzymes is suggested to be important for their differing capabilities for energy conservation. An additional result from this study is that at least three of the four reduction steps are initiated by proton transfer to the active site, which is in contrast to CcO, where electrons always arrive before the protons to the active site. The roles of the non-heme metal ion and the redox-active tyrosine in the active site are also discussed.

Nonclassical Single-State Reactivity of an Oxo-Iron(IV) Complex Confined to Triplet Pathways

C-H bond activation mediated by oxo-iron (IV) species represents the key step of many heme and nonheme O₂-activating enzymes. Of crucial interest is the effect of spin state of the Fe^IV(O) unit. Here we report the C-H activation kinetics and corresponding theoretical investigations of an exclusive tetracarbene ligated oxo-iron(IV) complex, [L^NHCFe^IV(O)(MeCN)]²⁺ (1). Kinetic traces using substrates with bond dissociation energies (BDEs) up to 80 kcal mol^-1 show pseudo-first-order behavior and large but temperature-dependent kinetic isotope effects (KIE 32 at -40 °C). When compared with a topologically related oxo-iron(IV) complex bearing an equatorial N-donor ligand, [L^TMCFe^IV(O) (MeCN)]²⁺ (A), the tetracarbene complex 1 is significantly more reactive with second order rate constants k'₂ that are 2-3 orders of magnitude higher. UV-vis experiments in tandem with cryospray mass spectrometry evidence that the reaction occurs via formation of a hydroxo-iron(III) complex (4) after the initial H atom transfer (HAT). An extensive computational study using a wave function based multireference approach, viz. complete active space self-consistent field (CASSCF) followed by N-electron valence perturbation theory up to second order (NEVPT2), provided insight into the HAT trajectories of 1 and A. Calculated free energy barriers for 1 reasonably agree with experimental values. Because the strongly donating equatorial tetracarbene pushes the Fe-d_x²-y² orbital above d_z², 1 features a dramatically large quintet-triplet gap of ∼18 kcal/mol compared to ∼2-3 kcal/mol computed for A. Consequently, the HAT process performed by 1 occurs on the triplet surface only, in contrast to complex A reported to feature two-state-reactivity with contributions from both triplet and quintet states. Despite this, the reactive Fe^IV(O) units in 1 and A undergo the same electronic-structure changes during HAT. Thus, the unique complex 1 represents a pure "triplet-only" ferryl model.

Assessment of electronic structure methods for the determination of the ground spin states of Fe(ii), Fe(iii) and Fe(iv) complexes

We studied spin states of Fe²⁺ ion, gaseous FeO, and 14 Fe(ii), Fe(iii) and Fe(iv) complexes using density functional theory.

Diffusion Monte Carlo Perspective on the Spin-State Energetics of [Fe(NCH)6](2.)

The energy difference between the high spin and the low spin state of the model compound [Fe(NCH)6](2+) is investigated by means of Diffusion Monte Carlo (DMC), where special attention is dedicated to analyzing the effect of the fix node approximation on the accuracy of the results. For this purpose, we compare several Slater-Jastrow and multireference Slater-Jastrow trial wave functions. We found that a Slater-Jastrow trial wave function constructed with the generalized Kohn-Sham orbitals from hybrid DFT represents the optimal choice. This is understood by observing that hybrid functionals account for the subtle balance between exchange and correlation effects and the respective orbitals accurately describe the ligand-metal hybridization as well as the charge reorganization accompanying the spin transition. Finally the DMC results are compared with those obtained by Hartree-Fock, DFT, CASSCF, and CASPT2. While there is no clear reference value for the high spin-low spin energy difference, DMC and high level CCSD(T) calculations agree within around 0.3 eV.

A broken-symmetry density functional study of structures, energies, and protonation states along the catalytic O-O bond cleavage pathway in ba3 cytochrome c oxidase from Thermus thermophilus

Broken-symmetry density functional calculations have been performed on the [Fea3, CuB] dinuclear center (DNC) of ba3 cytochrome c oxidase from Thermus thermophilus in the states of [Fea3(3+)-(HO2)(-)-CuB(2+), Tyr237(-)] and [Fea3(4+)[double bond, length as m-dash]O(2-), OH(-)-CuB(2+), Tyr237˙], using both PW91-D3 and OLYP-D3 functionals. Tyr237 is a special tyrosine cross-linked to His233, a ligand of CuB. The calculations have shown that the DNC in these states strongly favors the protonation of His376, which is above propionate-A, but not of the carboxylate group of propionate-A. The energies of the structures obtained by constrained geometry optimizations along the O-O bond cleavage pathway between [Fea3(3+)-(O-OH)(-)-CuB(2+), Tyr237(-)] and [Fea3(4+)[double bond, length as m-dash]O(2-)HO(-)-CuB(2+), Tyr237˙] have also been calculated. The transition of [Fea3(3+)-(O-OH)(-)-CuB(2+), Tyr237(-)] → [Fea3(4+)[double bond, length as m-dash]O(2-)HO(-)-CuB(2+), Tyr237˙] shows a very small barrier, which is less than 3.0/2.0 kcal mol(-1) in PW91-D3/OLYP-D3 calculations. The protonation state of His376 does not affect this O-O cleavage barrier. The rate limiting step of the transition from state A (in which O2 binds to Fea3(2+)) to state PM ([Fea3(4+)[double bond, length as m-dash]O(2-), OH(-)-CuB(2+), Tyr237˙], where the O-O bond is cleaved) in the catalytic cycle is, therefore, the proton transfer originating from Tyr237 to O-O to form the hydroperoxo [Fea3(3+)-(O-OH)(-)-CuB(2+), Tyr237(-)] state. The importance of His376 in proton uptake and the function of propionate-A/neutral-Asp372 as a gate to prevent the proton from back-flowing to the DNC are also shown.

Influence of mutations at the proximal histidine position on the Fe-O2 bond in hemoglobin from density functional theory

Four mutated hemoglobin (Hb) variants and wild type hemoglobin as a reference have been investigated using density functional theory methods focusing on oxygen binding. Dispersion-corrected B3LYP functional is used and found to provide reliable oxygen binding energies. It also correctly reproduces the spin distribution of both bound and free heme groups as well as provides correct geometries at their close vicinity. Mutations in hemoglobin are not only an intrigued biological problem and it is also highly important to understand their effects from a clinical point of view. This study clearly shows how even small structural differences close to the heme group can have a significant effect in reducing the oxygen binding of mutated hemoglobins and consequently affecting the health condition of the patient suffering from the mutations. All of the studied mutated Hb variants did exhibit much weaker binding of molecular oxygen compared to the wild type of hemoglobin.

Ammonia-modified Co(II) sites in zeolites: spin and electron density redistribution through the Co(II)-NO bond

Electronic factors essential for the bonding of a non-innocent NO ligand to ammonia-modified Co(2+) sites in cobalt-exchanged zeolites are examined for small cluster models using DFT and advanced correlated wave function calculations. The analysis of charge transfer processes between the NO ligand and the cobalt center involves two protocols: valence-bond expansion of the multiconfiguration CASSCF wave function (in terms of fragment-localized active orbitals) and spin-resolved natural orbitals for chemical valence (SR-NOCV). Applicability of SR-NOCV analysis to transition metal complexes involving non-innocent fragments is critically assessed and the approach based on the CASSCF wave function turns out to be much more robust and systematic for all studied models. It is shown that the character and direction of electron density redistribution through the Co-N-O bond, quantified by relative share of the Co(II)-NO(0), Co(III)-NO(-), and Co(I)-NO(+) resonance structures in the total wave function, fully rationalize the activation of the N-O bond upon NH3 co-ligation (evidenced by calculated and measured red-shift of the NO stretching frequency and commonly ascribed to enhanced backdonation). The huge red-shift of νN-O is attributed to an effective electron transfer between the ammonia-modified Co(ii) centers and the NO antibonding π*-orbitals (related to the increased share of the Co(III)-NO(-) form). Unexpectedly, the effect is stronger for the singlet complex with three NH3 ligands than for that with five NH3 ligands bound to the cobalt center. Our results also indicate that high-efficiency electron transfers between the Co(ii) center and the NO ligand may be enabled for the selected spin state and disabled for the other spin state of the adduct. This illustrates how the cobalt center may serve to fine-tune the electronic communication between the NO ligand and its binding site.

Mechanism of Oxygen Reduction in Cytochrome c Oxidase and the Role of the Active Site Tyrosine

Cytochrome c oxidase, the terminal enzyme in the respiratory chain, reduces molecular oxygen to water and stores the released energy through electrogenic chemistry and proton pumping across the membrane. Apart from the heme-copper binuclear center, there is a conserved tyrosine residue in the active site (BNC). The tyrosine delivers both an electron and a proton during the O-O bond cleavage step, forming a tyrosyl radical. The catalytic cycle then occurs in four reduction steps, each taking up one proton for the chemistry (water formation) and one proton to be pumped. It is here suggested that in three of the reduction steps the chemical proton enters the center of the BNC, leaving the tyrosine unprotonated with radical character. The reproprotonation of the tyrosine occurs first in the final reduction step before binding the next oxygen molecule. It is also suggested that this reduction mechanism and the presence of the tyrosine are essential for the proton pumping. Density functional theory calculations on large cluster models of the active site show that only the intermediates with the proton in the center of the BNC and with an unprotonated tyrosyl radical have a high electron affinity of similar size as the electron donor, which is essential for the ability to take up two protons per electron and thus for the proton pumping. This type of reduction mechanism is also the only one that gives a free energy profile in accordance with experimental observations for the amount of proton pumping in the working enzyme.

Spin-state energies of heme-related models from spin-flip TDDFT calculations

The spin-state energies of heme-related models were calculated by using the spin-flip TDDFT method avoiding spin contamination.

A DFT and multi-configurational perturbation theory study on O2 binding to a model heme compound via the spin-change barrier

Potential energy surface of the O₂ binding to a model heme compound via minimum energy intersystem crossing point (MEISCP) was investigated with DFT and MS-CASPT2. The porphyrin's symmetric shrinking vibration mode contributes to reach the MESICP from the T₁ minimum.

Theoretical Study of the Dissociation Energy of First-Row Metallocenium Ions

The bond dissociation energy of a series of metallocenium ions, i.e., the energy difference of the reaction MCp2(+) → MCp(+) + Cp· (with M = Ti, V, Cr, Mn, Fe, Co, and Ni), was studied by means of multiconfigurational perturbation theory (CASPT2, RASPT2, NEVPT2) and restricted coupled cluster theory (CCSD(T)). From a comparison between the results obtained from these different methods, and a detailed analysis of their treatment of electron correlation effects, a set of MCp(+)-Cp binding energies are proposed with an accuracy of 5 kcal/mol. The computed results are in good agreement with the experimental data measured by threshold photoelectron photoion coincidence (TPEPICO) spectroscopy but disagree with the more recent threshold collision-induced dissociation (TCID) experiments.

Broken Symmetry DFT Calculations/Analysis for Oxidized and Reduced Dinuclear Center in Cytochrome c Oxidase: Relating Structures, Protonation States, Energies, and Mössbauer Properties in ba3 Thermus thermophilus

The Fea3(3+)···CuB(2+) dinuclear center (DNC) structure of the as-isolated oxidized ba3 cytochrome c oxidase (CcO) from Thermus thermophilus (Tt) is still not fully understood. When the proteins are initially crystallized in the oxidized state, they typically become radiolyticly reduced through X-ray irradiation. Several X-ray crystal structures of reduced ba3 CcO from Tt are available. However, depending on whether the crystals were prepared in a lipidic cubic phase environment or in detergent micelles, and whether the CcO's were chemically or radiolyticly reduced, the X-ray diffraction analysis of the crystals showed different Fea3(2+)···CuB(+) DNC structures. On the other hand, Mössbauer spectroscopic experiments on reduced and oxidized ba3 CcOs from Tt (Zimmermann et al., Proc. Natl. Acad. Sci. USA 1988, 85, 5779-5783) revealed multiple (57)Fea3(2+) and (57)Fea3(3+) components. Moreover, one of the (57)Fea3(3+) components observed at 4.2 K transformed from a proposed "low-spin" state to a different high-spin species when the temperature was increased above 190 K, whereas the other high-spin (57)Fea3(3+) component remained unchanged. In the current Article, in order to understand the heterogeneities of the DNC in both Mössbauer spectra and X-ray crystal structures, the spin crossover of one of the (57)Fea3(3+) components, and how the coordination and spin states of the Fea3(3+/2+) and Cu(2+/1+) sites relate to the heterogeneity of the DNC structures, we have applied density functional OLYP calculations to the DNC clusters established based on the different X-ray crystal structures of ba3 CcO from Tt. As a result, specific oxidized and reduced DNC structures related to the observed Mössbauer spectra and to spectral changes with temperature have been proposed. Our calculations also show that, in certain intermediate states, the His233 and His283 ligand side chains may dissociate from the CuB(+) site, and they may become potential proton loading sites during the catalytic cycle.

The Importance of the MM Environment and the Selection of the QM Method in QM/MM Calculations: Applications to Enzymatic Reactions

In this chapter, we discuss the influence of an anisotropic protein environment on the reaction mechanisms of saccharopine reductase and uroporphyrinogen decarboxylase, respectively, via the use of a quantum mechanical and molecular mechanical (QM/MM) approach. In addition, we discuss the importance of selecting a suitable DFT functional to be used in a QM/MM study of a key intermediate in the mechanism of 8R-lipoxygenase, a nonheme iron enzyme. In the case of saccharopine reductase, while the enzyme utilizes a substrate-assisted catalytic pathway, it was found that only through treating the polarizing effect of the active site, via the use of an electronic embedding formalism, was agreement with experimental kinetic data obtained. Similarly, in the case of uroporphyrinogen decarboxylase, the effect of the protein environment on the catalytic mechanism was found to be such that the calculated rate-limiting barrier is in good agreement with related experimentally determined values for the first decarboxylation of the substrate. For 8R-lipoxygenase, it was found that the geometries and energies of the multicentered open-shell intermediate complexes formed during the mechanism are quite sensitive to the choice of the density functional theory method. Thus, while density functional theory has become the method of choice in QM/MM studies, care must be taken in the selection of a particular high-level method.

How cytochrome c oxidase can pump four protons per oxygen molecule at high electrochemical gradient

Experiments have shown that the A-family cytochrome c oxidases pump four protons per oxygen molecule, also at a high electrochemical gradient. This has been considered a puzzle, since two of the reduction potentials involved, Cu(II) and Fe(III), were estimated from experiments to be too low to afford proton pumping at a high gradient. The present quantum mechanical study (using hybrid density functional theory) suggests a solution to this puzzle. First, the calculations show that the charge compensated Cu(II) potential for CuB is actually much higher than estimated from experiment, of the same order as the reduction potentials for the tyrosyl radical and the ferryl group, which are also involved in the catalytic cycle. The reason for the discrepancy between theory and experiment is the very large uncertainty in the experimental observations used to estimate the equilibrium potentials, mainly caused by the lack of methods for direct determination of reduced CuB. Second, the calculations show that a high energy metastable state, labeled EH, is involved during catalytic turnover. The EH state mixes the low reduction potential of Fe(III) in heme a3 with another, higher potential, here suggested to be that of the tyrosyl radical, resulting in enough exergonicity to allow proton pumping at a high gradient. In contrast, the corresponding metastable oxidized state, OH, is not significantly higher in energy than the resting state, O. Finally, to secure the involvement of the high energy EH state it is suggested that only one proton is taken up via the K-channel during catalytic turnover.

Insights into enzymatic halogenation from computational studies

The halogenases are a group of enzymes that have only come to the fore over the last 10 years thanks to the discovery and characterization of several novel representatives. They have revealed the fascinating variety of distinct chemical mechanisms that nature utilizes to activate halogens and introduce them into organic substrates. Computational studies using a range of approaches have already elucidated many details of the mechanisms of these enzymes, often in synergistic combination with experiment. This Review summarizes the main insights gained from these studies. It also seeks to identify open questions that are amenable to computational investigations. The studies discussed herein serve to illustrate some of the limitations of the current computational approaches and the challenges encountered in computational mechanistic enzymology.

Applications of density functional theory to iron-containing molecules of bioinorganic interest

The past decades have seen an explosive growth in the application of density functional theory (DFT) methods to molecular systems that are of interest in a variety of scientific fields. Owing to its balanced accuracy and efficiency, DFT plays particularly useful roles in the theoretical investigation of large molecules. Even for biological molecules such as proteins, DFT finds application in the form of, e.g., hybrid quantum mechanics and molecular mechanics (QM/MM), in which DFT may be used as a QM method to describe a higher prioritized region in the system, while a MM force field may be used to describe remaining atoms. Iron-containing molecules are particularly important targets of DFT calculations. From the viewpoint of chemistry, this is mainly because iron is abundant on earth, iron plays powerful (and often enigmatic) roles in enzyme catalysis, and iron thus has the great potential for biomimetic catalysis of chemically difficult transformations. In this paper, we present a brief overview of several recent applications of DFT to iron-containing non-heme synthetic complexes, heme-type cytochrome P450 enzymes, and non-heme iron enzymes, all of which are of particular interest in the field of bioinorganic chemistry. Emphasis will be placed on our own work.

Revisiting the role of exact exchange in DFT spin-state energetics of transition metal complexes

Sensitivity of DFT spin-state energetics to exact exchange is rooted in the description of metal–ligand bonding.

Accurate calculations of geometries and singlet–triplet energy differences for active-site models of [NiFe] hydrogenase

The relative stability of singlet and triplet state models of [NiFe] hydrogenase have been studied by advanced quantum-mechanical methods.

Density functional study for the bridged dinuclear center based on a high-resolution X-ray crystal structure of ba3 cytochrome c oxidase from Thermus thermophilus

Strong electron density for a peroxide type dioxygen species bridging the Fea3 and CuB dinuclear center (DNC) was observed in the high-resolution (1.8 Å) X-ray crystal structures (PDB entries 3S8G and 3S8F) of ba3 cytochrome c oxidase (CcO) from Thermus thermophilus. The crystals represent the as-isolated X-ray photoreduced CcO structures. The bridging peroxide was proposed to arise from the recombination of two radiation-produced HO(•) radicals formed either very near to or even in the space between the two metals of the DNC. It is unclear whether this peroxide species is in the O2(2-), O2(•)(-), HO2(-), or the H2O2 form and what is the detailed electronic structure and binding geometry including the DNC. In order to answer what form of this dioxygen species was observed in the DNC of the 1.8 Å X-ray CcO crystal structure (3S8G), we have applied broken-symmetry density functional theory (BS-DFT) geometric and energetic calculations (using OLYP potential) on large DNC cluster models with different Fea3-CuB oxidation and spin states and with O2(2-), O2(•)(-), HO2(-), or H2O2 in the bridging position. By comparing the DFT optimized geometries with the X-ray crystal structure (3S8G), we propose that the bridging peroxide is HO2(-). The X-ray crystal structure is likely to represent the superposition of the Fea3(2+)-(HO2(-))-CuB(+) DNC's in different states (Fe(2+) in low spin (LS), intermediate spin (IS), or high spin (HS)) with the majority species having the proton of the HO2(-) residing on the oxygen atom (O1) which is closer to the Fea3(2+) site in the Fea3(2+)-(HO-O)(-)-CuB(+) conformation. Our calculations show that the side chain of Tyr237 is likely trapped in the deprotonated Tyr237(-) anion form in the 3S8G X-ray crystal structure.