Hybrid Density Functional Theory Methods Research Articles

Shaping Magnetite Nanoparticles from First Principles.

Iron oxide magnetic nanoparticles (NPs) are stimuli-responsive materials at the forefront of nanomedicine. Their realistic finite temperature simulations are a formidable challenge for first-principles methods. Here, we use density functional tight binding to open up the required time and length scales and obtain global minimum structures of Fe_{3}O_{4} NPs of realistic size (1400 atoms, 2.5nm) and of different shapes, which we then refine with hybrid density functional theory methods to accomplish proper electronic and magnetic properties, which have never been accurately described in simulations. On this basis, we develop a general empirical formula and prove its predictive power for the evaluation of the total magnetic moment of Fe_{3}O_{4} NPs. By converting the total magnetic moment into the macroscopic saturation magnetization, we rationalize the experimentally observed dependence with shape. We also reveal interesting reconstruction mechanisms and unexpected patterns of charge ordering.

Site occupation and 4f → 5d transitions of Ce3+ ions at mixed Ca2+/Y3+ sites in CaYAlO4: Insights from first-principles calculations

The first-principles calculations in the combination of hybrid density functional theory (DFT) and multiconfigurational quantum-chemical methods are carried out to investigate geometric structures, electronic structures and 4f → 5d transitions of Ce3+ ions at mixed Ca2+/Y3+ sites in the CaYAlO4 (CYAO). The most energetically stable unit cell among three nonequivalent configurations is firstly determined according to the total energies from DFT calculations. The calculated defect formation energies of lanthanide dopants and complexes in the host (with relatively stable configurations) then reveal the preferred substitution of Ce3+ ions in the host. Moreover, the energies and relative oscillator strengths of the 4f → 5d transitions of Ce3+ at both Ca2+ and Y3+ sites are derived from the embedded-cluster quantum-chemical calculations at the CASSCF/CASPT2/RASSI−SO level. By comparison, the excitation bands in the experimental spectra of Ce3+-doped CYAO phosphors are mainly attributed to 4f → 5d transitions of Ce3+ ions at Ca2+ sites, which is well consistent with the conclusions attained from the calculations on defect formation energies. The computational framework presented in this study is beneficial to identify the occupation sites of lanthanide ions and assign the excitation bands of the experimental spectra for the phosphors with mixed sites or solid-solution structures.

Assessment of the exact-exchange-only Kohn-Sham method for the calculation of band structures for transition metal oxide and metal halide perovskites

In the present paper we assess the performance of the exact-exchange-only (EXX) Kohn-Sham method to predict band structures of transition metal oxide and metal halide perovskites with the main emphasis on band gaps. For the considered set of prototypical systems with cubic structure, the performance of the EXX method for the prediction of band gaps is comparable with other popular methods for this purpose like density-functional calculations with the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional and one-shot $GW$ (${G}_{0}{W}_{0}$). Comparison with experimental values suggests that in the case of perovskites the EXX method, like HSE and $GW$ methods, should be supplemented by a treatment of electron-phonon effects. The EXX method is computationally more efficient than ${G}_{0}{W}_{0}$ and also provides post-self-consistent access to one-electron wave functions and band structures within the complete Brillouin zone with much lower computational effort than both ${G}_{0}{W}_{0}$ and hybrid DFT methods. We confirm the importance of including the higher-lying semicore shells within the explicitly treated states for halide perovskites which was already noted by earlier studies. Calculations taking into account only the valence space without the semicore states, however, remain still a reasonable option in practice. Spin-orbit coupling effects seem to be slightly underestimated in DFT calculations both with respect to $GW$ and experiment. The source of this underestimation can be of both technical and formal nature, and this point requires more critical consideration. For ${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}{\mathrm{PbI}}_{3}$, sizable Rashba spin splittings appear for the structure with the C-N bond of the methylammonium ion not lying along the long diagonal of the cubic unit cell.

Uranyl-Bound Tetra-Dentate Non-Innocent Ligands: Prediction of Structure and Redox Behaviour Using Density Functional Theory.

Computational methods have been applied to understand the reduction potentials of [UO2 -salmnt-L] complexes (L=pyridine, DMSO, DMF and TPPO), and their redox behavior is compared with previous experiments in dichloromethane solution. Since the experimental results were inconclusive regarding the influence of the uranyl-bound tetra-dentate 'salmnt' ligand, here we will show that salmnt acts as a redox-active ligand and exhibits non-innocent behavior to interfere with the otherwise expected one-electron metal (U) reduction. We have employed two approaches to determine the uranyl (VI/V) reduction potentials, using a direct study of one-electron reduction processes and an estimation of the overall reduction using isodesmic reactions. Hybrid density functional theory (DFT) methods were combined with the Conductor-like Polarizable Continuum Model (CPCM) to account for solvation effects. The computationally predicted one-electron reduction potentials for the range of [UO2 -salmnt-L] complexes are in excellent agreement with shoulder peaks (∼1.4 eV) observed in the cyclic voltammetry experiments and clearly correlate with ligand reduction. Highly conjugated pi-bonds stabilize the ligand based delocalized orbital relative to the localized U f-orbitals, and as a consequence, the ligand traps the incoming electron. A second reduction step results in metal U(VI) to U(V) reduction, in good agreement with the experimentally assigned uranyl (VI/V) reduction potentials.

Molecular Structures, Rotational Barriers, and Density Functional Theory Studies on 3,5-Diamino-6-(2,3-Dichlorophenyl)-1,2,4-Triazine

In this report, different hybrid Density Functional Theory (DFT) methods were utilized to determine the geometries, total energies, Frontier molecular orbitals, atomic charges, and rotational barriers of 3,5-Diamino-6-(2,3-Dichlorophenyl)-1,2,4-Triazine, C9H7Cl2N5 molecular system. All optimized geometrical parameters (i.e. bond lengths, bond angles, and dihedral angles) were then compared with the experimental data, which reported by Sridhar and Ravikumar in 2009 [5]. Also, the results of electronic structures (i.e. total energies, Frontier molecular orbitals, atomic charges, and others) obtained by different DFT methods were compared and discussed.

Computational study of linear and nonlinear optical properties of substituted thiophene imino dyes using long-range corrected hybrid DFT methods

The molecular structures, linear and nonlinear optical properties of a series constituted by four R-substituted thiophene imino dyes, namely A(R = SO2Me), B(R = SO2Ph), C(R = NO2), and D(R = C2(CN)3) were analysed using CAM-B3LYP, ωB97XD and LC-ωPBE hybrid DFT functionals in combination of the 6-311++G(d,p) standard basis set. The dipole moments, polarisabilities, HOMO-LUMO energy gaps, maximum absorption wavelengths and first hyperpolarisabilities were calculated in the gas phase and the obtained results are in good agreement with experimental NLO activity order A < B < C. Compared to synthesised dyes A-C, the designed dye D presents a longer maximum absorption wavelength and a lower HOMO-LUMO gap because of the appreciable stabilisation of its LUMO energy. These results were confirmed by the calculation of the total second-order stabilisation energy E(2) defined in the context of the NBO population analysis. Consequently, dye D is predicted to exhibit a higher first hyperpolarisability in comparison with dyes A-C. This result can be justified by the enhanced intramolecular charge transfer in dye D due to the stronger electron-withdrawing ability and the cumulative action of the long π-conjugation of the tricyanovinyl moiety. The very high total hyperpolarisability (27 times greater than that of para-nitroaniline) of the designed dye D suggests its promising use in organic NLO devices.

Hybrid ADFT Study of the C104 and C106 IPR Isomers.

This work presents a hybrid auxiliary density functional theory (ADFT) study of the neutral and hexaanionic C104 and C106 fullerenes with the aim to determine their ground state structures. To this end, all C104 and C106 fullerene structures that obey the isolated pentagon rule (IPR) were optimized with the Perdew-Burke-Ernzerhof generalized gradient approximation followed by a single-point energy calculation with the PBE0 hybrid functional. Our studies show that this composite approach yields relative energies of giant fullerenes that are accurate to around 1 kcal/mol. As a result, the ground states of C104, C1046-, and C1066- can be assigned to the isomers 234:Cs, 821:D2, and 891:Cs, respectively. On the other hand, the energetically lowest lying IPR isomers of C106, 331:Cs, 1194:C2, 534:C1 are separated by less than 1 kcal/mol which makes an unequivocal ground state assignment by hybrid DFT methods impossible. To guide future experiments, we also report the simulated IR and Raman spectra of the most stable neutral and hexaanionic C104 and C106 fullerenes.

First-principles DFT insights into the structural, elastic, and optoelectronic properties of α and β-ZnP2: implications for photovoltaic applications

Binary II–V semiconductors are highly optically active materials, possess high intrinsic mechanical and chemical durability, and have electronic properties ideal for optoelectronic applications. Among them, zinc diphosphide (ZnP2) is a promising earth-abundant absorber material for solar energy conversion. We have investigated the structural, mechanical, and optoelectronic properties of both the tetragonal (α) and monoclinic (β) phases of ZnP2 using standard, Hubbard-corrected and screened hybrid density functional theory methods. Through the analysis of bond character, band gap nature, and absorption spectra, we show that there exist two polymorphs of the β phase (denoted as β1 and β2) with distinct differences in the photovoltaic potential. While β1 exhibits the characteristics of metallic compounds, β2 is a semiconductor with predicted thin-film photovoltaic absorbing efficiency of almost 10%. The α phase is anticipated to be an indirect gap material with a calculated efficiency limited to only 1%. We have also analysed and gained insights into the electron localization function, projected density of states and projected crystal orbital Hamilton populations for the analogue bonds between the α and β-ZnP2. In light of these calculations, a number of previous discrepancies have been solved and a solid ground for future employment of zinc diphosphides in photovoltaics has been established.

Density functional theory study of selective aerobic oxidation of cyclohexane: the roles of acetic acid and cobalt ion.

A computational study of cyclohexane autoxidation and catalytic oxidation to a cyclohexyl hydroperoxide intermediate (CyOOH), cyclohexanol, and cyclohexanone has been conducted using a hybrid density functional theory method. The activation of cyclohexane and O2 is the rate-determining step in the formation of CyOOH due to its relatively high energy barrier of 41.2kcal/mol, and the subsequent reaction behavior of CyOOH controls whether the production of cyclohexanol or cyclohexanone is favored. Using CH3COOH or (CH3COO)2Co as a catalyst reduces the energy barriers required to activate cyclohexane and O2 by 4.1 or 7.9kcal/mol, respectively. Employing CH3COOH improves the CyOOH intramolecular dehydration process, which favors the formation of cyclohexanone. The energy barrier to the decomposition of CyOOH to CyO·, an important precursor of cyclohexanol, decreases from 35.5kcal/mol for autoxidation to 25.9kcal/mol for (CH3COO)2Co catalysis. (CH3COO)2Co promotes the autoxidation process via a radical chain mechanism. The computational results agree with experimental observations quite well, revealing the underlying role of CH3COOH and Co ion in cyclohexane oxidation. Graphical abstract Through DFT analysis of cyclohexane autoxidation and catalytic oxidation, we reveal the mechanism of the effects of CH3COOH and Co2+ on the reaction routes.

A DFT/ZORA Study of Cadmium Magnetic Shielding Tensors: Analysis of Relativistic Effects and Electronic-State Approximations.

Theoretical considerations are discussed for the accurate prediction of cadmium magnetic shielding tensors using relativistic density functional theory (DFT). Comparison is made between calculations that model the extended lattice of the cadmium-containing solids using periodic boundary conditions and pseudopotentials with calculations that use clusters of atoms. The all-electron cluster-based calculations afford an opportunity to examine the importance of (i) relativistic effects on cadmium magnetic shielding tensors, as introduced through the ZORA Hamiltonian at either the scalar (SC) or spin-orbit (SO) levels and (ii) variation in the class of the DFT approximation. Twenty-three combinations of pseudopotentials or all-electron methods, DFT functionals, and relativistic treatments are assessed for the prediction of the principal components of the magnetic shielding tensors of 30 cadmium sites. We find that the inclusion of SO coupling can increase the cadmium magnetic shielding by as much as ca. 1100 ppm for a certain principal values; these effects are most pronounced for cadmium sites featuring bonds to other heavy atoms such as cadmium, iodine, or selenium. The best agreement with experimental values is found at the ZORA SO level in combination with a hybrid DFT method featuring a large admixture of Hartree-Fock exchange such as BH&HLYP. Finally, a theoretical examination is presented of the magnetic shielding tensor of the Cd(I) site in Cd2(AlCl4)2.

DFT Quantum Chemical Calculation of the Molecular Structures of the Metal Clusters Al2Cu3 and Al2Ag3

The hybrid density functional theory (DFT) method in the OPBE/TZVP approximation and the Gaussian 09 program were used to calculate the geometric parameters of the molecular structures of aluminum copper and aluminum silver metal clusters with the stoichiometric compositions Al2Cu3 and Al2Ag3. It was found that each of the clusters can exist as eight structural forms, which considerably differ in the stability and geometrical parameters. The bond lengths and bond and torsion (dihedral) angles were determined for each form.

Calculation of electron-impact ionization cross sections of perfluoroketone (PFK) molecules CxF2xO (x = 1–5) based on Binary-Encounter-Bethe (BEB) and Deutsch-Märk (DM) methods

Perfluoroketone (PFK) gases are widely used in industry, e.g. as an insulating medium in high-voltage apparatus and as a cleaning agent in chemical vapor deposition (CVD) chambers. A great deal of attention has been paid to them recently because of their low global warming potential (GWP). In order to describe the ionization processes in various plasmas resulting from PFK gases, the electron-impact ionization cross sections (Qion) of PFK molecules CxF2xO (x = 1–5) were calculated by the Binary-Encounter Bethe (BEB) and the Deutsch-Märk (DM) methods. The chemical structures of PFK molecules were optimized by the hybrid Density Functional Theory (DFT) method with the Austin-Petersson-Frisch functional including dispersion (APF-D). The binding and kinetic energies of electrons in molecular orbitals were also determined with the APF-D hybrid DFT method. The binding energies of valence electrons were then improved by the electron propagator theory (EPT) method. The ionization potentials of PFK molecules were calculated as the difference between the energy of a molecule and its cation using the complete basis set (CBS) method. The molecular orbital compositions were obtained by the natural atomic orbital (NAO) analysis. The results show that Qion determined by the BEB method are always larger than those by the DM method. The difference is reduced with the EPT corrections considered. The comparison between the theoretical and experimental Qion demonstrates that the EPT correction improves Qion considerably.

Clustering of hydrogen, phosphorus, and vacancies in diamond: A density functional theory analysis

Phosphorus-doped $n$-type diamond is currently one of the most promising wide-band-gap materials for next-generation high-power electronics and optoelectronics. Artificial diamond growth methods such as chemical vapor deposition involve hydrogen-containing precursors; therefore, the hydrogen atoms can be simultaneously introduced into the diamond lattice as a contamination and form complexes with other defects. In this work, we used the spin-polarized, hybrid density functional theory method to investigate the electronic structure, stability, and magnetic and optical properties of phosphorus, vacancy, and hydrogen clusters in diamond. Our results indicate a thermodynamic driving force for the formation of previously unidentified phosphorus-vacancy-hydrogen complexes that can be electrically, magnetically, or optically active centers. We found an unusual extremely large hyperfine coupling with the $^{31}\mathrm{P}$ nuclei ($Ag2$ GHz) for some of the investigated defects that requires further experimental verification. Finally, we demonstrate that the ${\text{PV}}_{2}{\text{H}}^{0}$ complex has two metastable triplets between the ground- and excited-state singlets, and it may exhibit a highly selective spin decay channel to a ground state, which makes the defect a promising candidate for realizing long-living solid-state quantum memory. These results provide deep insight into the donor compensation effect associated with vacancy-related clusters, and they may be useful in future identification of P-related defects suitable for quantum information processing applications.

Evaluation of hybrid and pure DFT methods for the binding of novel ligands in the tyrosine hydroxylase enzyme

The M06-2X, M06-L, and M06 functionals were used to evaluate the interaction energies of novel ligands in the TyrOH active site. TyrOH is the rate determining enzyme in the catecholamine-dopamine pathway, converting tyrosine to l-DOPA. The inhibition of TyrOH, however, reduces dopamine in the brain to undetectable levels (Spector et al., 1965). A crystal structure of the active site of tyrosine hydroxylase with a known inhibitor bound was obtained from the protein data bank (PDB ID: 2TOH) (Goodwill et al., 1998). In this work, dopaminergic derivatives, which could be potential treatments for Parkinson’s disease were inserted into the enzymatic active site in silico in order to test the strength of the interactions between the ligand and active site, to determine if any of these derivatives could be effective inhibitors. M06 and M06-2X are hybrid functionals, while M06-L is a pure DFT method; all of these functionals were used to optimize structures and to analyze interaction energies. The novel dopaminergic derivatives were optimized in the active site with implicit solvent with either M06-2X, M06-L, or M06 and 6-31G with relaxed amino acid side chains. Counterpoise corrected interaction energies between the ligands and protein were determined using the same DFT methods mentioned above with the 6-311+G∗ basis set. This work shows significant differences between the methods within the same complex. The analysis has also helped to determine promising ligands for the treatment of Parkinson’s disease that would not inhibit TyrOH.

Theoretical Studies on Catalysis Mechanisms of Serum Paraoxonase 1 and Phosphotriesterase Diisopropyl Fluorophosphatase Suggest the Alteration of Substrate Preference from Paraoxonase to DFP

The calcium-dependent β-propeller proteins mammalian serum paraoxonase 1 (PON1) and phosphotriesterase diisopropyl fluorophosphatase (DFPase) catalyze the hydrolysis of organophosphorus compounds and enhance hydrolysis of various nerve agents. In the present work, the phosphotriesterase activity development between PON1 and DFPase was investigated by using the hybrid density functional theory method B3LYP. Based on the active-site difference between PON1 and DFPase, both the wild type and the mutant (a water molecule replacing Asn270 in PON1) models were designed. The results indicated that the substitution of a water molecule for Asn270 in PON1 had little effect on the enzyme activity in kinetics, while being more efficient in thermodynamics, which is essential for DFP hydrolysis. Structure comparisons of evolutionarily related enzymes show that the mutation of Asn270 leads to the catalytic Ca2+ ion indirectly connecting the buried structural Ca2+ ion via hydrogen bonds in DFPase. It can reduce the plasticity of enzymatic structure, and possibly change the substrate preference from paraoxon to DFP, which implies an evolutionary transition from mono- to dinuclear catalytic centers. Our studies shed light on the investigation of enzyme catalysis mechanism from an evolutionary perspective.

Performance of L-493 Macroprous Resin for Adsorption of Trihalomethanes from Water

The commercial resin Dowex Optipore L-493 was evaluated for the removal of the trihalomethanes (THMs) from water. Adsorption amounts were in the order CHBr3 ≈ CHBr2Cl > CHBrCl2 > CHCl3, insensitive to pH in the range 3.0–7.0, but decreased at pH higher values. They were little affected by the presence of co-existing anions and humic acid, and environmental impurities in a spiked natural water sample were only slightly lower than those obtained with pure water. In a comparison with several other commercial adsorbents, the overall performance of L-493 for adsorption of THMs was comparable with the best of those tested, and superior to IR 120, IRC 748, and powder activated carbon. THM adsorption on L-493 was endothermic, and fitted by the pseudo-second-order kinetic and Langmuir isotherm models; maximum adsorption was 228.6, 247.3, 250.6, and 253.7 μg/g, for CHCl3, CHBrCl2, CHBr2Cl, and CHBr3, respectively. Charge distributions and dipole moments were calculated for the optimized structures using the hybrid density functional theory (DFT) method. Both hydrophobic effects and electrostatic interactions play important roles in the adsorption process. The L-493 resin was easily regenerated and could be recycled using 0.1 M NaOH, with only a small decrease in its initial adsorption capacities. Overall, this research shows that L-493 is potentially a valuable adsorbent for the removal of THMs during water treatment.

Thermoelectric Properties of p-Type Cu2O, CuO, and NiO from Hybrid Density Functional Theory.

The electronic transport coefficients of three Earth-abundant metal oxides Cu2O, CuO, and NiO were investigated using hybrid density functional theory (DFT). Hybrid DFT methods combined with local Gaussian-type basis sets enabled band structure studies on both non-magnetic and magnetic p-type metal oxides without empirical corrections. The CRYSTAL code was used for obtaining the wavefunction, and the transport properties were calculated with two different methodologies to benchmark their accuracy: a numerical approach as implemented in the BoltzTraP code and an analytical approach recently implemented in CRYSTAL17. Both computational methods produce identical results in good agreement with experimental measurements of the Seebeck coefficient. The predicted electrical conductivities are overestimated, owing likely to the used approximation of a constant electronic relaxation time in the calculations, as explicit electron scattering is neglected and relaxation time is considered only as a free parameter. The obtained results enable us to critically review and complement the available theoretical and experimental literature on the studied p-type thermoelectric metal oxide materials.

The 3D supramolecular architecture of copper(II) 6-methyl-2-pyridone-4-carboxylate: synthesis, structure, magnetic behavior and DFT studies

Abstract The reaction of Cu(NO3)2·3H2O and 6-methyl-2-pyridone-4-carboxylic acid (Hhmpca) under hydrothermal condition produced a new copper(II) coordination polymer [Cu(hmpca)2(H2O)2]·4H2O (1), which has been characterized by elemental analysis, infrared spectroscopy, thermogravimetric analysis and single-crystal X-ray diffraction. The Cu(II) ions are linked by coordinating water molecule bridges to generate a polymeric chain, and adjacent chains are connected to form a layer structure through interchain N–H···O hydrogen bonding. Because of the strong hydrogen bonds of free water molecules, ladder-shaped water chains are produced. Further, the layers and the water chains are linked into a three-dimensional supramolecular structure through strong O–H···O hydrogen bonds. Magnetic susceptibility measurements have indicated that compound 1 shows antiferromagnetic interactions between the adjacent Cu(II) ions. Based on the crystal structure data, compound 1 was analyzed using hybrid density functional theory (DFT) methods at the B3LYP/6-31G(d) level, and a DFT-broken symmetry approach was applied to study the magnetic coupling behavior. The calculated exchange coupling constant J is in good agreement with the experimental data.

Relative stability between the manganese hydroxide- and oxo-models for water oxidation by CCSD, DMRG CASCI, CASSCF, CASPT2 and CASDFT methods; Importance of static and dynamical electron correlation effects for OEC of PSII

Relative stability between manganese hydroxide (H2O)2(OH)4Mn(IV)OH (1) and manganese oxo (H2O)3(OH)3Mn(IV)O (2) species were investigated by coupled cluster (CC) SD and SD(T), DMRG CASCI, CASSCF, CASPT2 and CASDFT methods. The DMRG CASCI and DMRG CASSCF based on thirteen active orbitals and thirteen active electrons {13, 13} CAS space indicted the greater stability of 2 than 1. On the other hand, the relative stability between 1 and 2 was reversed by UCC SD, DLPNO-UCC SD, CASPT2 and CAS-DFT, indicating an important role of dynamical electron correlation corrections. Implications of present results are discussed to elucidate scope and applicability of hybrid DFT (HDFT) methods for 1 and 2.

Theory of chemical bonds in metalloenzymes XXI. Possible mechanisms of water oxidation in oxygen evolving complex of photosystem II

ABSTRACTPossible mechanisms for water cleavage in oxygen evolving complex (OEC) of photosystem II (PSII) have been investigated based on broken-symmetry (BS) hybrid DFT (HDFT)/def2 TZVP calculations in combination with available XRD, XFEL, EXAFS, XES and EPR results. The BS HDFT and the experimental results have provided basic concepts for understanding of chemical bonds of the CaMn4O5 cluster in the catalytic site of OEC of PSII for elucidation of the mechanism of photosynthetic water cleavage. Scope and applicability of the hybrid DFT (HDFT) methods have been examined in relation to relative stabilities of possible nine intermediates such as Mn-hydroxide, Mn-oxo, Mn-peroxo, Mn-superoxo, etc., in order to understand the O–O (O–OH) bond formation in the S3 and/or S4 states of OEC of PSII. The relative stabilities among these intermediates are variable, depending on the weight of the Hartree–Fock exchange term of HDFT. The Mn-hydroxide, Mn-oxo and Mn-superoxo intermediates are found to be preferable in the weak, intermediate and strong electron correlation regimes, respectively. Recent different serial femtosecond X-ray (SFX) results in the S3 state are investigated based on the proposed basic concepts under the assumption of different water-insertion steps for water cleavage in the Kok cycle. The observation of water insertion in the S3 state is compatible with previous large-scale QM/MM results and previous theoretical proposal for the chemical equilibrium mechanism in the S3 state . On the other hand, the no detection of water insertion in the S3 state based on other SFX results is consistent with previous proposal of the O–OH (or O–O) bond formation in the S4 state . Radical coupling and non-adiabatic one-electron transfer (NA-OET) mechanisms for the OO-bond formation are examined using the energy diagrams by QM calculations and by QM(UB3LYP)/MM calculations . Possible reaction pathways for the O–O and O–OH bond formations are also investigated based on two water-inlet pathways for oxygen evolution in OEC of PSII. Future perspectives are discussed in relation to post HDFT calculations of the energy diagrams for elucidation of the mechanism of water oxidation in OEC of PSII.