Electronic Ground States of Iron Porphyrin and of the First Species in the Catalytic Reaction Cycle of Cytochrome P450s

Electron Correlation in the Iron(II) Porphyrin by Natural Orbital Functional Approximations

The relative stability of the singlet, triplet, and quintet spin states of iron(II) porphyrin (FeP) represents a challenging problem for electronic structure methods. While it is currently accepted that the ground state is a triplet, multiconfigurational wave function-based methods predict a quintet, and density functional approximations vary between triplet and quintet states, leading to a prediction that highly depends on the features of the method employed. The recently proposed Global Natural Orbital Functional (GNOF) aims to provide a balanced treatment between static and dynamic correlation, and together with the previous Piris Natural Orbital Functionals (PNOFs), allowed us to explore the importance of each type of correlation in the stability order of the states of FeP with a method that conserves the spin of the system. It is noteworthy that GNOF correlates all electrons in all available orbitals for a given basis set; in the case of the FeP with a double-ζ basis set as used in this work, this means that GNOF can properly correlate 186 electrons in 465 orbitals, significantly increasing the sizes of systems amenable to multiconfigurational treatment. Results show that PNOF5, PNOF7s, and PNOF7 predict the quintet to have a lower energy than the triplet state; however, the addition of dynamic correlation via second-order Møller-Plesset corrections (NOF-MP2) turns the triplet state to be lower than the quintet state, a prediction also reproduced by GNOF that incorporates much more dynamic correlation than its predecessors.

Reliably assessing the electronic structure of cytochrome P450 on today's classical computers and tomorrow's quantum computers

Chemical simulation is one of the most promising applications for future quantum computers. It is thought that quantum computers may enable accurate simulation for complex molecules that are otherwise impossible to simulate classically; that is, it displays quantum advantage. To better understand quantum advantage in chemical simulation, we explore what quantum and classical resources are required to simulate a series of pharmaceutically relevant molecules. Using classical methods, we show that reliable classical simulation of these molecules requires significant resources and therefore is a promising candidate for quantum simulation. We estimate the quantum resources, both in overall simulation time and the size. The insights from this study pave the way for future quantum simulation of complex molecules.

An accurate assessment of how quantum computers can be used for chemical simulation, especially their potential computational advantages, provides important context on how to deploy these future devices. To perform this assessment reliably, quantum resource estimates must be coupled with classical computations attempting to answer relevant chemical questions and to define the classical algorithms simulation frontier. Herein, we explore the quantum computation and classical computation resources required to assess the electronic structure of cytochrome P450 enzymes (CYPs) and thus define a classical–quantum advantage boundary. This is accomplished by analyzing the convergence of density matrix renormalization group plus n-electron valence state perturbation theory (DMRG+NEVPT2) and coupled-cluster singles doubles with noniterative triples [CCSD(T)] calculations for spin gaps in models of the CYP catalytic cycle that indicate multireference character. The quantum resources required to perform phase estimation using qubitized quantum walks are calculated for the same systems. Compilation into the surface code provides runtime estimates to compare directly to DMRG runtimes and to evaluate potential quantum advantage. Both classical and quantum resource estimates suggest that simulation of CYP models at scales large enough to balance dynamic and multiconfigurational electron correlation has the potential to be a quantum advantage problem and emphasizes the important interplay between classical computations and quantum algorithms development for chemical simulation.

Revisiting the Orbital Energy-Dependent Regularization of Orbital-Optimized Second-Order Møller-Plesset Theory

Optimizing orbitals in the presence of electron correlation, as in orbital-optimized second-order Møller-Plesset perturbation theory (OOMP2), can remove artifacts associated with mean-field orbitals such as spin contamination and artificial symmetry-breaking. However, OOMP2 is known to suffer from divergent correlation energies in regimes of small orbital energy gaps. To address this issue, several approaches to amplitude regularization have been explored, with those featuring energy-gap-dependent regularizers appearing to be most transferable and physically justifiable. For instance, κ-OOMP2 was shown to address the energy divergence issue in, for example, bond-breaking processes while offering a significant improvement in accuracy for the W4-11 thermochemistry data set, and a parameter of κ = 1.45 was recommended. A more recent investigation of regularized MP2 with Hartree-Fock orbitals revealed that stronger regularization (i.e., smaller values of κ) than what had previously been recommended for κ-OOMP2 may offer huge improvements in certain cases such as noncovalent interactions while retaining a high level of accuracy for main-group thermochemistry data sets. In this study, we investigate the transferability of those findings to κ-OOMP2 and assess the implications of stronger regularization on the ability of κ-OOMP2 to diagnose strong static correlation. We found similar results using κ-OOMP2 for several main-group thermochemistry, barrier height, and noncovalent interaction data sets including both closed shell and open shell species. However, stronger regularization yielded substantially higher accuracy for open-shell transition-metal (TM) thermochemistry and is necessary to provide qualitatively correct spin symmetry breaking behavior for several large and electrochemically relevant TM systems. We therefore find a single κ value insufficient to treat all systems using κ-OOMP2.

Rapid quantification of acid value in frying oil using iron tetraphenylporphyrin fluorescent sensor coupled with density functional theory and multivariate analysis

Metalloporphyrin-based fluorescent sensor was developed for the acid value in frying oil. The electronic and structural performances of iron tetraphenylporphyrin (FeTPP) were theoretically investigated using time-dependent density functional theory (TD-DFT) and DFT at the B3LYP/LANL2DZ level. The quantified FeTPP-based fluorescent sensor results revealed its excellent performance in discriminating different analytes. In the present work, the acid value of palm olein was determined after every single frying cycle. A total of 10 frying cycles were conducted each day for 10 consecutive days. The FeTPP-based fluorescent sensor was used to quantify the acid value and the results were compared with the chemical data obtained by conventional titration method. The synchronous fluorescence spectrum for each sample was recorded. Parallel factor analysis (PARAFAC) was used to decompose the three-dimensional spectrum data. Then, the support vector regression (SVR), partial least squares (PLS), and back-propagation artificial neural network (BP-ANN) methods were applied to build the regression models. After the comparison of the constructed models, the SVR models exhibited the highest correlation coefficients among all models, with 0.9748 and 0.9276 for the training and test set, respectively. The findings suggested the potential of FeTPP-based fluorescent sensor in rapid monitoring of the used frying oil quality and perhaps also in other foods with higher oil content.

iCISCF: An Iterative Configuration Interaction-Based Multiconfigurational Self-Consistent Field Theory for Large Active Spaces

An iterative configuration interaction (iCI)-based multiconfigurational self-consistent field (SCF) theory, iCISCF, is proposed to handle systems that require large active spaces. The success of iCISCF stems from three ingredients: (1) efficient selection of individual configuration state functions spanning the active space while maintaining full spin symmetry; (2) the use of Jacobi rotation for optimization of the active orbitals in conjunction with a quasi-Newton algorithm for the core/active-virtual and core-active orbital rotations; (3) a second-order perturbative treatment of the residual space left over by the selection procedure (i.e., iCISCF(2)). Several examples that go beyond the capability of CASSCF are taken as showcases to reveal the efficacy of iCISCF and iCISCF(2), facilitated by iCAS for imposed automatic selection and localization of active orbitals.

Stochastic Generalized Active Space Self-Consistent Field: Theory and Application

An algorithm to perform stochastic generalized active space calculations, Stochastic-GAS, is presented, that uses the Slater determinant based FCIQMC algorithm as configuration interaction eigensolver. Stochastic-GAS allows the construction and stochastic optimization of preselected truncated configuration interaction wave functions, either to reduce the computational costs of large active space wave function optimizations, or to probe the role of specific electron correlation pathways. As for the conventional GAS procedure, the preselection of the truncated wave function is based on the selection of multiple active subspaces while imposing restrictions on the interspace excitations. Both local and cumulative minimum and maximum occupation number constraints are supported by Stochastic-GAS. The occupation number constraints are efficiently encoded in precomputed probability distributions, using the precomputed heat bath algorithm, which removes nearly all runtime overhead of GAS. This strategy effectively allows the FCIQMC dynamics to a priori exclude electronic configurations that are not allowed by GAS restrictions. Stochastic-GAS reduced density matrices are stochastically sampled, allowing orbital relaxations via Stochastic-GASSCF, and direct evaluation of properties that can be extracted from density matrices, such as the spin expectation value. Three test case applications have been chosen to demonstrate the flexibility of Stochastic-GAS: (a) the Stochastic-GASSCF [5·(6, 6)] optimization of a stack of five benzene molecules, that shows the applicability of Stochastic-GAS toward fragment-based chemical systems; (b) an uncontracted stochastic MRCISD calculation that correlates 96 electrons and 159 molecular orbitals, and uses a large (32, 34) active space reference wave function for an Fe(II)-porphyrin model system, showing how GAS can be applied to systematically recover dynamic electron correlation, and how in the specific case of the Fe(II)-porphyrin dynamic correlation further differentially stabilizes the ³E_g over the ⁵A_1g spin state; (c) the study of an Fe₄S₄ cluster's spin-ladder energetics via highly truncated stochastic-GAS [4·(5, 5)] wave functions, where we show how GAS can be applied to understand the competing spin-exchange and charge-transfer correlating mechanisms in stabilizing different spin-states.

The redox potential of a heme cofactor in Nitrosomonas europaea cytochrome c peroxidase: a polarizable QM/MM study

Redox reactions are crucial to biological processes that protect organisms against oxidative stress. Metalloenzymes, such as peroxidases which reduce excess reactive oxygen species into water, play a key role in detoxification mechanisms. Here we present the results of a polarizable QM/MM study of the reduction potential of the electron transfer heme in the cytochrome c peroxidase of Nitrosomonas europaea. We have found that environment polarization does not substantially affect the computed value of the redox potential. Particular attention has been given to analyzing the role of electrostatic interactions within the protein environment and the solvent on tuning the redox potential of the heme co-factor. We have found that the electrostatic interactions predominantly explain the fluctuations of the vertical ionization/attachment energies of the heme for the sampled configurations, and that the long range electrostatic interactions (up to 40 Å) contribute substantially to the absolute values of the vertical energy gaps.

ONETEP + TOSCAM: Uniting Dynamical Mean Field Theory and Linear-Scaling Density Functional Theory

We introduce the unification of dynamical mean field theory (DMFT) and linear-scaling density functional theory (DFT), as recently implemented in ONETEP, a linear-scaling DFT package, and TOSCAM, a DMFT toolbox. This code can account for strongly correlated electronic behavior while simultaneously including the effects of the environment, making it ideally suited for studying complex and heterogeneous systems that contain transition metals and lanthanides, such as metalloproteins. We systematically introduce the necessary formalism, which must account for the nonorthogonal basis set used by ONETEP. In order to demonstrate the capabilities of this code, we apply it to carbon monoxide ligated iron porphyrin and explore the distinctly quantum-mechanical character of the iron 3d electrons during the process of photodissociation.

CASSCF with Extremely Large Active Spaces Using the Adaptive Sampling Configuration Interaction Method

The complete active space self-consistent field (CASSCF) method is the principal approach employed for studying strongly correlated systems. However, exact CASSCF can only be performed on small active spaces of ∼20 electrons in ∼20 orbitals due to exponential growth in the computational cost. We show that employing the Adaptive Sampling Configuration Interaction (ASCI) method as an approximate Full CI solver in the active space allows CASSCF-like calculations within chemical accuracy (<1 kcal/mol for relative energies) in active spaces with more than ∼50 active electrons in ∼50 active orbitals, significantly increasing the sizes of systems amenable to accurate multiconfigurational treatment. The main challenge with using any selected CI-based approximate CASSCF is the orbital optimization problem; they tend to exhibit large numbers of local minima in orbital space due to their lack of invariance to active-active rotations (in addition to the local minima that exist in exact CASSCF). We highlight methods that can avoid spurious local extrema as a practical solution to the orbital optimization problem. We employ ASCI-SCF to demonstrate a lack of polyradical character in moderately sized periacenes with up to 52 correlated electrons and compare against heat-bath CI on an iron porphyrin system with more than 40 correlated electrons.

Theoretical Study on Electronic Structural Properties of Catalytically Reactive Metalloporphyrin Intermediates

Metalloporphyrins have attracted great attention in the potential application of biomimetic catalysis. Especially, they were widely investigated as green catalysts in the chemical oxidation of various hydrocarbons through the catalytic activation of molecular oxygen. The structural properties of active central metal ions were reported to play a decisive role in catalytic activity. However, those delicate structural changes are difficult to be experimentally captured or elucidated in detail. Herein, we explored the electronic structural properties of metalloporphyrins (metal porphyrin (PMII, PMIIICl)) and their corresponding catalytically active intermediates (metal(III)-peroxo(PMIII-O2), metal(III)-hydroperoxo(PMIII-OH), and metal(IV)-oxo(PMIV=O), (M=Fe, Mn, and Co)) through the density functional theory method. The ground states of these intermediates were determined based on the assessment of relative energy and the corresponding geometric structures of ground states also further confirmed the stability of energy. Furthermore, our analyses of Mulliken charges and frontier molecular orbitals revealed the potential catalytic behavior of reactive metalloporphyrin intermediates.

Transition Metal Spin-State Energetics by MC-PDFT with High Local Exchange

The energetics of the spin states of transition metal complexes have been explored with a variety of electronic structure methods, but the calculations require a compromise between accuracy and affordability. In this work, the spin splittings of several iron complexes are studied with multiconfiguration pair-density functional theory (MC-PDFT). The results are compared to previously published results obtained by complete active space second-order perturbation theory (CASPT2) and CASPT2 with coupled-cluster semicore correlation (CASPT2/CC). In contrast to CASPT2's systematic overstabilization of high-spin states with respect to the CASPT2/CC reference, MC-PDFT with the tPBE on-top functional understabilizes high-spin states. This systematic understabilization is largely corrected by revising the exchange and correlation contributions to the on-top functional using the high local-exchange approximation (tPBE-HLE). Moreover, tPBE-HLE correctly predicts the spin of the ground state in most cases, while CASPT2 incorrectly predicts high-spin ground states in all cases. This is encouraging for practical work because tPBE and tPBE-HLE are faster than CASPT2 by a factor of 50 even in a moderately sized example.

Ground state of the Fe(ii)-porphyrin model system corresponds to quintet: a DFT and DMRG-based tailored CC study

Fe(ii)-porphyrins play an important role in many reactions, due to their closely lying spin states. We present a thorough study of a Fe(ii)-porphyrin model system, in which we examine how the geometrical parameters influence its spin state ordering.

Second-order MCSCF optimization revisited. I. Improved algorithms for fast and robust second-order CASSCF convergence

A new improved implementation of the second-order multiconfiguration self-consistent field optimization method of Werner and Knowles [J. Chem. Phys. 82, 5053 (1985)] is presented. It differs from the original method by more stable and efficient algorithms for minimizing the second-order energy approximation in the so-called microiterations. Conventionally, this proceeds by alternating optimizations of the orbitals and configuration (CI) coefficients and is linearly convergent. The most difficult part is the orbital optimization, which requires solving a system of nonlinear equations that are often strongly coupled. We present a much improved algorithm for solving this problem, using an iterative subspace method that includes part of the orbital Hessian explicitly, and discuss different strategies for performing the uncoupled optimization in a most efficient manner. Second, we present a new solver in which the orbital-CI coupling is treated explicitly. This leads to quadratic convergence of the microiterations but requires many additional evaluations of reduced (transition) density matrices. In difficult optimization problems with a strong coupling of the orbitals and CI coefficients, it leads to much improved convergence of both the macroiterations and the microiterations. Third, the orbital-CI coupling is treated approximately using a quasi-Newton approach with Broyden-Fletcher-Goldfarb-Shanno updates of the orbital Hessian. It is demonstrated that this converges almost as well as the explicitly coupled method but avoids the additional effort for computing many transition density matrices. The performance of the three methods is compared for a set of 21 aromatic molecules, an Fe(ii)-porphine transition metal complex, as well as for the [Cu₂O₂(NH₃)  ₆]²⁺, FeCl₃, Co₂(CO)₆C₂H₂, and Al₄O₂ complexes. In all cases, faster and more stable convergence than with the original implementation is achieved.

The dramatic effect of N-methylimidazole on trans axial ligand binding to ferric heme: experiment and theory

The binding energy of CO, O2 and NO to isolated ferric heme, [FeIIIP]+, was studied in the presence and absence of a σ donor (N-methylimidazole and histidine) as the trans axial ligand. This study combines the experimental determination of binding enthalpies by equilibrium measurements in a low temperature ion trap using the van't Hoff equation and high level DFT calculations. It was found that the presence of N-methylimidazole as the axial ligand on the [FeIIIP]+ porphyrin dramatically weakens the [FeIIIP-ligand]+ bond with an up to sevenfold decrease in binding energy owing to the σ donation by N-methylimidazole to the FeIII(3d) orbitals. This trans σ donor effect is characteristic of ligation to iron in hemes in both ferrous and ferric redox forms; however, to date, this has not been observed for ferric heme.

DFT investigations for the catalytic reaction mechanism of methane combustion occurring on Pd(ii)/Al-MCM-41

In this work, a theoretical analysis was carried out on the mechanism of methane combustion occurring on single site palladium oxide species [Pd]2+ supported on Al-MCM-41 silica. Single site Pd-oxo and PdO2-superoxo structures were used to represent the active centers. Activation energies for all the elementary steps involved in the oxidation of methane into formaldehyde are presented. The competition of methane/methanol substrates on active sites was examined. It was found that the formation of methanol via the reaction of methane with the superoxo species, formed via the adsorption of O2 on reduced Pd(ii) centers, facilitates the production of the very active Pd-oxo catalytic sites.

First Principles Calculation of the Reaction Rates for Ligand Binding to Myoglobin: The Cases of NO and CO

Ligand binding by proteins is among the most fundamental processes in nature. Among these processes the binding of small gas molecules, such as O₂ , CO and NO to heme proteins has traditionally received vivid interest, which was further boosted by their recently recognized significant role in gas sensing in the body. At the heart of the binding of these ligands to the heme group is the spinforbidden reaction between high-spin iron(II) and the ligand yielding a low-spin adduct. We use computational means to address the complete mechanism of CO and NO binding by myoglobin. Considering that it involves several steps occurring on different time scales, molecular dynamics simulations were performed to address the diffusion of the ligand through the enzyme, and DFT calculations in combination with statistical rate calculation to investigate the spin-forbidden reaction. The calculations yielded rate constants in qualitative agreement with experiments and revealed that the bottleneck of NO and CO binding is different; for NO, diffusion was found to be rate-limiting, whereas for CO, the spin-forbidden step is the slowest.

Using porphyrin–amino acid pairs to model the electrochemistry of heme proteins: experimental and theoretical investigations

Deconstructing the complex electrochemistry of heme proteins into simpler heme–amino acid interactions.

On the structures, spin states, and optical properties of titanium, platinum, and iron azacalixphyrins: a DFT study

Azacalixphyrins (ACP) constitute a new class of macrocycles isoelectronic and isostructural to porphyrins. Herein, we report the first theoretical investigation of the properties of the ACP macrocycles metallated at their centre by titanium, platinum, and iron ions. We considered both the original phenyl-type ACP and new pyridyl-type forms. Our results indicate that the metallation greatly impacts the global structure of the macrocycle through pseudo Jahn-Teller effects, giving rise to a possible conformational transition between D_2d and S₄ structures. Such an effect could not be found in the metal-free ACPs. In addition, we find that, in contrast to the purely singlet platinum ACPs, and the purely triplet iron ACPs, several spin states are energetically close in the titanium ACPs, especially when weak field ligands are bound in axial positions to the metallic centre. According to TD-DFT calculations, metallation also tunes the optical properties. In particular, the absorption band in the near infrared region undergoes a hypsochromic shift of ca. 100-200 nm when going from the D_2d to the S₄ structures. We quantify how the addition of electroactive ligands in the axial position can increase or tune down these spectral changes. This contribution therefore supports the development of ACP coordination complexes.

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.

Cholesky Decomposition-Based Multiconfiguration Second-Order Perturbation Theory (CD-CASPT2): Application to the Spin-State Energetics of Co(III)(diiminato)(NPh)

The electronic structure and low-lying electronic states of a Co(III)(diiminato)(NPh) complex have been studied using multiconfigurational wave function theory (CASSCF/CASPT2). The results have been compared to those obtained with density functional theory. The best agreement with ab initio results is obtained with a modified B3LYP functional containing a reduced amount (15%) of Hartree-Fock exchange. A relativistic basis set with 869 functions has been employed in the most extensive ab initio calculations, where a Cholesky decomposition technique was used to overcome problems arising from the large size of the two-electron integral matrix. It is shown that this approximation reproduces results obtained with the full integral set to a high accuracy, thus opening the possibility to use this approach to perform multiconfigurational wave-function-based quantum chemistry on much larger systems relative to what has been possible until now.

Quantum chemical and solution phase evaluation of metallocenes as reducing agents for the prospective atomic layer deposition of copper

We propose and evaluate the use of metallocene compounds as reducing agents for the chemical vapour deposition (and specifically atomic layer deposition, ALD) of the transition metal Cu from metalorganic precursors.

Catalytic activity of macroion-porphyrin nanoassemblies

A new type of catalytically active self-assembled nanostructures in aqueous solution is presented. Polyelectrolyte-porphyrin nanoscale assemblies consisting of anionic cylindrical poly(styrene sulfonate) brush molecules and cationic tetravalent meso-tetrakis(4-N-methyl-pyridinium)porphyrin (TMPyP) or meso-tetrakis(4-(trimethyl-ammonium)phenyl)-porphyrin (TAPP), respectively, exhibit up to 8-fold higher catalytic activity with regard to light induced iodide oxidation than the corresponding porphyrins without polymeric template. This is particularly interesting because a general concept rather than a specific binding motif is exploited. The approach introduced here hence is attractive due to its facility and versatility and bears potential, for example, in light harvesting and energy conversion.