Quantum Information Driven Ansatz (QIDA): Shallow-Depth Empirical Quantum Circuits from Quantum Chemistry.

Hardware-efficient empirical variational ansätze for Variational Quantum Eigensolver (VQE) simulations of quantum chemistry often lack a direct connection to classical quantum chemistry methods. In this work, we propose a method to bridge this gap by introducing a novel approach to constructing a starting point for variational quantum circuits, leveraging quantum mutual information from classical quantum chemistry states to design simple yet effective heuristic ansätze with a topology reflecting the molecular system's correlations. As a first step, we make use of quantum chemistry calculations, such as MoÌ·ller-Plesset (MP2) perturbation theory, to initially provide approximate Natural Orbitals, which have been shown to be the best candidate one-electron basis for developing compact empirical wave functions.1 Second, we evaluate the quantum mutual information matrix, which provides insights about the main correlations between qubits of the quantum circuit, and enables a direct design of entangling blocks for the circuit. The resulting ansatz is then used with a VQE to obtain a short-depth variational ground state of the electronic Hamiltonian. To validate our approach, we perform a comprehensive statistical analysis through simulations of various molecular systems (H2, LiH, H2O) and apply it to the more complex NH3 molecule. The reported results demonstrate that the proposed methodology gives rise to highly effective ansätze, outperforming the standard empirical ladder-entangler ansatz. Overall, our approach can be used as an effective state preparation, providing a promising route for designing efficient variational quantum circuits for large molecular systems.

Unravelling Mn4Ca cluster vibrations in the S1, S2 and S3 states of the Kok-Joliot cycle of photosystem II.

Vibrational spectroscopy serves as a powerful tool for characterizing intermediate states within the Kok-Joliot cycle. In this study, we employ a QM/MM molecular dynamics framework to calculate the room temperature infrared absorption spectra of the S1, S2, and S3 states via the Fourier transform of the dipole time auto-correlation function. To better analyze the computational data and assign spectral peaks, we introduce an approach based on dipole-dipole correlation function of cluster moieties of the reaction center. Our analysis reveals variation in the infrared signature of the Mn4Ca cluster along the Kok-Joliot cycle, attributed to its increasing symmetry and rigidity resulting from the rising oxidation state of the Mn ions. Furthermore, we successfully assign the debated contributions in the frequency range around 600 cm-1. This computational methodology provides valuable insights for deciphering experimental infrared spectra and understanding the water oxidation process in both biological and artificial systems.

Natural Orbitals and Sparsity of Quantum Mutual Information.

Natural orbitals, defined in electronic structure and quantum chemistry as the molecular orbitals diagonalizing the one-particle reduced density matrix of the ground state, have been conjectured for decades to be the perfect reference orbitals to describe electron correlation. In the present work we applied the Wave function-Adapted Hamiltonian Through Orbital Rotation (WAHTOR) method to study correlated empirical ansätze for quantum computing. In all representative molecules considered, we show that the converged orbitals are coinciding with natural orbitals. Interestingly, the resulting quantum mutual information matrix built on such orbitals is also maximally sparse, providing a clear picture that such orbital choice is indeed able to provide the optimal basis to describe electron correlation. The correlation is therefore encoded in a smaller number of qubit pairs contributing to the quantum mutual information matrix.

Unveiling the Influence of Hydrated Deep Eutectic Solvents on the Dynamics of Water-Soluble Proteins.

Deep eutectic solvents (DESs) are mixtures of two or more pure compounds (e.g., Lewis or Brønsted acids and bases, anionic and/or cationic species) in a well-defined stoichiometric proportion, with a melting point lower to that of an ideal liquid mixture. These neoteric solvents are highly tunable through varying the structure or relative ratio of parent components and have been evaluated as solvents able to improve biomolecules' performance, specifically their stability and biocatalytic properties. Inspired by a recent crystallographic study, we have explored through molecular dynamics (MD) simulations the dynamic properties of two different proteins (hen egg-white lysozyme and the human VH antibody fragment HEL4) in a (20% w/w) hydrated solution of choline chloride-glycerol (1:2). We have developed proper force fields to account for DES, protein, and DES-protein interactions, which have been calibrated using pair distribution function measurements of pure DES solutions. MD results show that the presence of DES quenches the protein motion, increasing the rigidity of the overall protein structure. Specific interactions among DES components and protein residues, such as those between choline ions and two Tryptophan residues of lysozyme, may amplify the protein-DES interactions and lead to protein crystallization in the presence of hydrated DES. These findings open new horizons to improve or achieve control on protein properties by a proper choice of hydrated DESs used as solvents.

The electron-proton bottleneck of photosynthetic oxygen evolution.

Photosynthesis fuels life on Earth by storing solar energy in chemical form. Today's oxygen-rich atmosphere has resulted from the splitting of water at the protein-bound manganese cluster of photosystem II during photosynthesis. Formation of molecular oxygen starts from a state with four accumulated electron holes, the S4 state-which was postulated half a century ago1 and remains largely uncharacterized. Here we resolve this key stage of photosynthetic O2 formation and its crucial mechanistic role. We tracked 230,000 excitation cycles of dark-adapted photosystems with microsecond infrared spectroscopy. Combining these results with computational chemistry reveals that a crucial proton vacancy is initally created through gated sidechain deprotonation. Subsequently, a reactive oxygen radical is formed in a single-electron, multi-proton transfer event. This is the slowest step in photosynthetic O2 formation, with a moderate energetic barrier and marked entropic slowdown. We identify the S4 state as the oxygen-radical state; its formation is followed by fast O-O bonding and O2 release. In conjunction with previous breakthroughs in experimental and computational investigations, a compelling atomistic picture of photosynthetic O2 formation emerges. Our results provide insights into a biological process that is likely to have occurred unchanged for the past three billion years, which we expect to support the knowledge-based design of artificial water-splitting systems.

Investigation of the Entry Pathway and Molecular Nature of σ1 Receptor Ligands.

The σ1 receptor (σ1-R) is an enigmatic endoplasmic reticulum resident transmembrane protein implicated in a variety of central nervous system disorders and whose agonists have neuroprotective activity. In spite of σ1-R's physio-pathological and pharmacological importance, two of the most important features required to fully understand σ1-R function, namely the receptor endogenous ligand(s) and the molecular mechanism of ligand access to the binding site, have not yet been unequivocally determined. In this work, we performed molecular dynamics (MD) simulations to help clarify the potential route of access of ligand(s) to the σ1-R binding site, on which discordant results had been reported in the literature. Further, we combined computational and experimental procedures (i.e., virtual screening (VS), electron density map fitting and fluorescence titration experiments) to provide indications about the nature of σ1-R endogenous ligand(s). Our MD simulations on human σ1-R suggested that ligands access the binding site through a cavity that opens on the protein surface in contact with the membrane, in agreement with previous experimental studies on σ1-R from Xenopus laevis. Additionally, steroids were found to be among the preferred σ1-R ligands predicted by VS, and 16,17-didehydroprogesterone was shown by fluorescence titration to bind human σ1-R, with significantly higher affinity than the prototypic σ1-R ligand pridopidine in the same essay. These results support the hypothesis that steroids are among the most important physiological σ1-R ligands.

Molecular dynamics simulations and kinetic measurements provide insights into the structural requirements of substrate size-dependent specificity of oligogalacturonide oxidase 1 (OGOX1).

Oligogalacturonides (OGs) are pectin fragments released from the breakdown of the homogalacturonan during pathogenesis that act as Damage-Associated Molecular Patterns. OG-oxidase 1 (OGOX1) is an Arabidopsis berberine bridge enzyme-like (BBE-l) oligosaccharide oxidase that oxidizes OGs, impairing their elicitor activity and concomitantly releasing H2O2. The OG-oxidizing activity of OGOX1 is markedly pH-dependent, with optimum pH around 10, and is higher towards OGs with a degree of polymerization higher than two. Here, the molecular determinants of OGOX1 responsible for the binding of OGs with different lengths have been investigated through molecular dynamics simulations and enzyme kinetics studies. OGOX1 was simulated in complex with OGs with different degree of polymerization such as di-, tri-, tetra- and penta-galacturonide, in water solution at alkaline pH. Our simulations revealed that, among the four OGOX1/OG combinations, the penta-galacturonide (OG5) showed the best conformation in the active site to be efficiently oxidized by OGOX1. The optimal conformation can be stabilized by salt-bridges formed between the carboxyl groups of OG5 and five positively charged amino acids of OGOX1, highly conserved in all OGOX paralogs. Our results suggest that these interactions limit the mobility of OG5 as well as longer OGs, contributing to maintain the terminal monomer of OGs in the optimal orientation in order to be oxidized by the enzyme. In accordance with these results, the enzyme efficiency (Kcat/KM) of OGOX1 on OG5 (40.04) was found to be significantly higher than that on OG4 (13.05) and OG3 (0.6).

Wave Function Adapted Hamiltonians for Quantum Computing.

The use of the variational quantum eigensolver (VQE) for quantum chemistry is one of the most promising applications for noisy intermediate-scale quantum (NISQ) devices. A major limitation is represented by the need to build compact and shallow circuit ansatzes having the variational flexibility to catch the complexity of the electronic structure problem. To alleviate this drawback, we introduce a modified VQE scheme in which the form of the molecular Hamiltonian is adapted to the circuit ansatz through an optimization procedure. Exploiting the invariance of the Hamiltonian by molecular orbital rotations, we can optimize it using gradients that can be calculated without significant computational overload. The proposed method, named Wavefunction Adapted Hamiltonian Through Orbital Rotation (WAHTOR), has been applied to small molecules in numerical state vector simulations. The results demonstrate that, at variance with standard VQE, the method is less dependent on circuit topology and less prone to be trapped into high-energy local minima. It is able to recover a significant amount of electron correlation even with only empirical ansatzes with shallow circuit depth. Noisy calculations demonstrate the robustness and feasibility of the proposed methodology and indicate the hardware requirements to effectively apply the procedure using forthcoming NISQ devices.

Molecular Modelling and Simulations of Light-Harvesting Decanuclear Ru-Based Dendrimers for Artificial Photosynthesis.

The structure of a decanuclear photo- and redox-active dendrimer based on Ru(II) polypyridine subunits, suitable as a light-harvesting multicomponent species for artificial photosynthesis, has been investigated by means of computer modelling. The compound has the general formula [Ru{(µ-dpp)Ru[(µ-dpp)Ru(bpy)2 ]2 }3 ](PF6 )20 (Ru10; bpy=2,2'-bipyridine; dpp=2,3-bis(2'-pyridyl)pyrazine). The stability of possible isomers of each monomer was investigated by performing classical molecular dynamics (MD) and quantum mechanics (QM) simulations on each monomer and comparing the results. The number of stable isomers is reduced to 36 with a prevalence of MER isomerism in the central core, as previously observed by NMR experiments. The simulations on decanuclear dendrimers suggest that the stability of the dendrimer is not linked to the stability of the individual monomers composing the dendrimer but rather governed by the steric constrains originated by the multimetallic assembly. Finally, the self-aggregation of Ru10 and the distribution of the counterions around the complexes is investigated using Molecular Dynamics both in implicit and explicit acetonitrile solution. In representative examples, with nine and four dendrimers, the calculated pair distribution function for the ruthenium centers suggests a self-aggregation mechanism in which the dendrimers are approaching in small blocks and then aggregate all together. Scanning transmission electron microscopy complements the investigation, supporting the formation of different aggregates at various concentrations.

Structural and dynamic insights into Mn4Ca cluster-depleted Photosystem II.

In the first steps of natural oxygenic photosynthesis, sunlight is used to oxidize water molecules to protons, electrons and molecular oxygen. This reaction takes place on the Mn4Ca cluster located in the reaction centre of Photosystem II (PSII), where the cluster is assembled and continuously repaired through a process known as photoactivation. Understanding the molecular details of such a process has important implications in different fields, in particular inspiring synthesis and repair strategies for artificial photosynthesis devices. In this regard, a detailed structural and dynamic characterization of Photosystem II lacking a Mn4Ca cluster, namely apo PSII, is a prerequisite for the full comprehension of the photoactivation. Recently, the structure of the apo PSII was resolved at 2.55 Å resolution [Zhang et al., eLife, 2017, 6, e26933], suggesting a pre-organized structure of the protein cavity hosting the cluster. Anyway, the question of whether these findings are a feature of the method used remains open. Here, by means of classical Molecular Dynamics simulations, we characterized the structural and dynamic features of the apo PSII for different protonation states of the cluster cavity. Albeit an overall conformational stability common to all investigated systems, we found significant deviations in the conformation of the side chains of the active site with respect to the X-ray positions. Our findings suggest that not all residues acting as Mn ligands are pre-organized prior to the Mn4Ca formation and previous local conformational changes are required in order to bind the first Mn ion in the high-affinity binding site.

A molecular dynamics-guided mutagenesis identifies two aspartic acid residues involved in the pH-dependent activity of OG-OXIDASE 1.

During the infection, plant cells secrete different OG-oxidase (OGOX) paralogs, defense flavoproteins that oxidize the oligogalacturonides (OGs), homogalacturonan fragments released from the plant cell wall that act as Damage Associated Molecular Patterns. OGOX-mediated oxidation inactivates their elicitor nature, but on the other hand makes OGs less hydrolysable by microbial endo-polygalacturonases (PGs). Among the different plant defense responses, apoplastic alkalinization can further reduce the degrading potential of PGs by boosting the oxidizing activity of OGOXs. Accordingly, the different OGOXs so far characterized showed an optimal activity at pH values greater than 8. Here, an approach of molecular dynamics (MD)-guided mutagenesis succeeded in identifying the amino acids responsible for the pH dependent activity of OGOX1 from Arabidopsis thaliana. MD simulations indicated that in alkaline conditions (pH 8.5), the residues Asp325 and Asp344 are engaged in the formation of two salt bridges with Arg327 and Lys415, respectively, at the rim of enzyme active site. According to MD analysis, the presence of such ionic bonds modulates the size and flexibility of the cavity used to accommodate the OGs, in turn affecting the activity of OGOX1. Based on functional properties of the site-directed mutants OGOX1.D325A and OGOX.D344A, we demonstrated that Asp325 and Asp344 are major determinants of the alkaline-dependent activity of OGOX1.

Mechanism of Oxygen Evolution and Mn4CaO5 Cluster Restoration in the Natural Water-Oxidizing Catalyst.

Water oxidation occurring in the first steps of natural oxygenic photosynthesis is catalyzed by the pigment/protein complex Photosystem II. This process takes place on the Mn4Ca cluster located in the core of Photosystem II and proceeds along the five steps (S0-S4) of the so-called Kok-Joliot cycle until the release of molecular oxygen. The catalytic cycle can therefore be started afresh through insertion of a new water molecule. Here, combining quantum mechanics/molecular mechanics simulations and minimum energy path calculations, we characterized on different spin surfaces the events occurring in the last sector of the catalytic cycle from structural, electronic, and thermodynamic points of view. We found that the process of oxygen evolution and water insertion can be described well by a two-step mechanism, with oxygen release being the rate-limiting step of the process. Moreover, our results allow us to identify the upcoming water molecule required to regenerate the initial structure of the Mn4Ca cluster in the S0 state. The insertion of the water molecule was found to be coupled with the transfer of a proton to a neighboring hydroxide ion, thus resulting in the reconstitution of the most widely accepted model of the S0 state.

Improved Accuracy on Noisy Devices by Nonunitary Variational Quantum Eigensolver for Chemistry Applications.

We propose a modification of the Variational Quantum Eigensolver algorithm for electronic structure optimization using quantum computers, named nonunitary Variational Quantum Eigensolver (nu-VQE), in which a nonunitary operator is combined with the original system Hamiltonian leading to a new variational problem with a simplified wave function ansatz. In the present work, as nonunitary operator, we use the Jastrow factor, inspired from classical Quantum Monte Carlo techniques for simulation of strongly correlated electrons. The method is applied to prototypical molecular Hamiltonians for which we obtain accurate ground-state energies with shallower circuits, at the cost of an increased number of measurements. Finally, we also show that this method achieves an important error mitigation effect that drastically improves the quality of the results for VQE optimizations on today's noisy quantum computers. The absolute error in the calculated energy within our scheme is 1 order of magnitude smaller than the corresponding result using traditional VQE methods, with the same circuit depth.

Structural basis of ubiquitination mediated by protein splicing in early Eukarya.

BACKGROUND: Inteins are intervening proteins, which are known to perform protein splicing. The reaction results in the production of an intein domain and an inteinless protein, which shows no trace of the insertion. BIL2 is part of the polyubiquitin locus of Tetrahymena thermophila (BUBL), where two bacterial-intein-like (BIL) domains lacking the C + 1 nucleophile, are flanked by two independent ubiquitin-like domains (ubl4/ubl5). METHODS: We solved the X-ray structures of BIL2 in both the inactive and unprecedented, zinc-induced active, forms. Then, we characterized by mass spectrometry the BUBL splicing products in the absence and in the presence of T.thRas-GTPase. Finally, we investigated the effect of ubiquitination on T.thRas-GTPase by molecular dynamics simulations. RESULTS: The structural analysis demonstrated that zinc-induced conformational change activates protein splicing. Moreover, mass spectrometry characterization of the splicing products shed light on the possible function of BIL2, which operates as a "single-ubiquitin-dispensing-platform", allowing the conjugation, via isopeptide bond formation (K(εNH2)-C-ter), of ubl4 to either ubl5 or T.thRas-GTPase. Lastly, we demonstrated that T.thRas-GTPase ubiquitination occurs in proximity of the nucleotide binding pocket and stabilizes the protein active state. CONCLUSIONS: We demonstrated that BIL2 is activated by zinc and that protein splicing induced by this intein does not take place through classical or aminolysis mechanisms but via formation of a covalent isopeptide bond, causing the ubiquitination of endogenous substrates such as T.thRas-GTPase. GENERAL SIGNIFICANCE: In this "enzyme-free" ubiquitination mechanism the isopeptide formation, which canonically requires E1-E2-E3 enzymatic cascade and constitutes the alphabet of ubiquitin biology, is achieved in a single, concerted step without energy consumption.

Spin-symmetrised structures and vibrational frequencies of iron-sulfur clusters.

Calculations of relaxed geometries of multi-centre transition metal compounds are routinely carried out using Broken Symmetry Density Functional Theory. The resulting low-spin open shell electronic state is described by one single Slater determinant and is affected by spin contamination. To alleviate this symmetry breaking, the Extended Broken Symmetry (EBS) approach can be applied to complexes with an arbitrary number of local high-spin metal ions. The actual symmetry is therefore reconstructed through minimization of an effective Hamiltonian leading to a relaxed geometry consistent with the magnetic couplings. In the present work we extend the approach already introduced by [Chu et al., J. Chem. Theory Comput., 2017, 13, 4675] to the calculation of vibrational frequencies. As prototypes we have considered the iron-sulfur clusters Fe2S2Cl42- and Fe4S4Cl4. We have compared the results obtained for different spin states (high spin, broken symmetry and extended broken symmetry) and by using different DFT functionals (B3LYP, OPBE, BP, M06 and B2PLYP) and a post-HF method (SCS-MP2). The data have shown that for specific vibrational modes the EBS technique produces shifts up to 40 cm-1 with respect to the routinely used Broken Symmetry approach, indicating that the use of a consistent spin-symmetrised state is a crucial ingredient for an accurate description of vibrational properties, as certified by the comparison with the experimental data for the Fe2S2Cl42- cluster.

Molecular dynamics of an asymmetric form of GabR, a bacterial transcriptional regulator.

GabR is a bacterial transcription regulator with a dimeric structure in which each subunit includes a wHTH (winged Helix-Turn-Helix) domain connected through a peptide linker to a large C-terminal domain folded as the enzyme aspartate aminotransferase (AAT). In Bacillus subtilis, GabR activates the genes involved in the metabolism of γ-amino butyric acid (GABA) upon formation of a PLP-GABA adduct. Recently, the crystallographic structure of an asymmetric form of GabR has been solved. This form (semi-holo) has one active site binding PLP as internal aldimine and the other the PLP-GABA complex. This work reports a molecular dynamics (MD) study aimed at understanding the characteristics of the asymmetric GabR form and compare them to the dynamics properties of previously studied symmetric holo (internal PLP aldimine at both active sites) and holo-GABA (containing PLP-GABA adducts) GabRs. Standard molecular dynamics and data analysis techniques have been used. The results indicate a remarkable asymmetry in the mobility and interactions of the different structural portions of the semi-holo GabR and of a few residues at the active site. The pattern is different from that observed in the other symmetrical GabR forms. The asymmetric perturbation of the active site residues may suggest the existence of a form of allosteric interference between the two active sites.

Conformational transitions induced by γ-amino butyrate binding in GabR, a bacterial transcriptional regulator.

GabR from Bacillus subtilis is a transcriptional regulator of the MocR subfamily of GntR regulators. The MocR architecture is characterized by the presence of an N-terminal winged-Helix-Turn-Helix domain and a C-terminal domain folded as the pyridoxal 5'-phosphate (PLP) dependent aspartate aminotransferase (AAT). The two domains are linked by a peptide bridge. GabR activates transcription of genes involved in γ-amino butyrate (GABA) degradation upon binding of PLP and GABA. This work is aimed at contributing to the understanding of the molecular mechanism underlying the GabR transcription activation upon GABA binding. To this purpose, the structure of the entire GabR dimer with GABA external aldimine (holo-GABA) has been reconstructed using available crystallographic data. The structure of the apo (without any ligand) and holo (with PLP) GabR forms have been derived from the holo-GABA. An extensive 1 µs comparative molecular dynamics (MD) has been applied to the three forms. Results showed that the presence of GABA external aldimine stiffens the GabR, stabilizes the AAT domain in the closed form and couples the AAT and HTH domains dynamics. Apo and holo GabR appear more flexible especially at the level of the HTH and linker portions and small AAT subdomain.

Pivotal role of the redox-active tyrosine in driving the water splitting catalyzed by photosystem II.

Photosynthetic water oxidation is catalyzed by the Mn4Ca cluster in photosystem II (PSII). The nearby redox-active tyrosine (YZ) serves as a direct electron acceptor of the Mn4Ca cluster and it forms a low-barrier H-bond (LBHB) with a neighboring histidine residue (D1-His190). Experimental evidence indicates that YZ oxidation triggers changes in the hydrogen bonding network that precede proton abstraction from the Mn4Ca cluster. In order to characterize such changes, we compare ab initio molecular dynamics simulations of different states of the catalytic cycle of PSII with dynamics of isolated tyrosine models (namely, p-cresol) in different oxidation states. The systematic comparison of the H-bond networks in different simulated systems suggests that the YZ oxidation leads to a water hydration pattern which is more similar to that of the neutral p-cresol rather than that of the p-cresol anion. Our simulations also reveal the twofold nature of the interactions between YZ and the Mn4Ca cluster. Firstly, the YZ oxidation triggers rapid structural changes of the H-bond pattern in the proximity of the cluster which have been observed to propagate on the ps time scale on the Ca2+ hydration shell up to other water molecules in the proximity of the cluster. Secondly, it is clear that YZ interacts with the Mn4Ca cluster also through Coulombic interactions mediated by CP43-Arg357 through the remaining positive charge of the pair. Our results are able to identify, for the first time, the structural rearrangements guided by the oxidation of YZ necessary for the evolution of the water splitting reaction in PSII. Based on these findings, we propose a mechanism of structural changes which is functional towards the progression of the catalytic cycle in PSII.

Molecular Vibrations of an Oxygen-Evolving Complex and Its Synthetic Mimic.

Bio-inspired catalysis for artificial photosynthesis has been widely studied for decades, in particular, with the purpose of using bio-disposable and non-toxic metals as building blocks. The characterisation of such catalysts has been achieved by using different kinds of spectroscopic methods, from X-ray crystallography to NMR spectroscopy. An artificial Mn4 CaO4 cubane cluster with dangling Mn4 was synthesised in 2015 [Zhang et al. Science 2015, 348, 690-693]; this cluster showed many structural similarities to that of the natural oxygen-evolving complex. An accurate structural and spectroscopic comparison between the natural and artificial systems is highly relevant to understand the catalytic mechanism. Among data from different techniques, the differential FTIR spectra (Sn+1 -Sn ) of photosystem II are still lacking a complete interpretation. The availability of IR data of the artificial cluster offers a unique opportunity to assign absolute absorption spectra on a well-defined and easier to interpret analogous moiety. The present work aims to investigate the novel inorganic compound as a model system for an oxygen-evolving complex through measurement of its spectroscopic properties. The experimental results are compared with calculations by using a variety of theoretical methods (normal mode analysis, effective normal mode analysis) in the S1 state. We underline the similarities and the differences in the computational spectra based on atomistic models of Mn4 CaO5 and Mn4 CaO4 complexes.

On the comparison between differential vibrational spectroscopy spectra and theoretical data in the carboxyl region of photosystem II.

Understanding the structural modification experienced by the Mn4 CaO5 oxygen-evolving complex of photosystem II along the Kok-Joliot's cycle has been a challenge for both theory and experiments since many decades. In particular, differential infrared spectroscopy was extensively used to probe the surroundings of the reaction center, to catch spectral changes between different S-states along the catalytic cycle. Because of the complexity of the signals, only a limited quantity of identified peaks have been assigned so far, also because of the difficulty of a direct comparison with theoretical calculations. In the present work, we critically reconsider the comparison between differential vibrational spectroscopy and theoretical calculations performed on the structural models of the photosystem II active site and an inorganic structural mimic. Several factors are currently limiting the reliability of a quantitative comparison, such as intrinsic errors associated to theoretical methods, and most of all, the uncertainty attributed to the lack of knowledge about the localization of the underlying structural changes. Critical points in this comparison are extensively discussed. Comparing several computational data of differential S2 /S1 infrared spectroscopy, we have identified weak and strong points in their interpretation when compared with experimental spectra.