Broken-symmetry Methods Research Articles

Unveiling the Low-Lying Spin States of [Fe3S4] Clusters via the Extended Broken-Symmetry Method.

Photosynthetic water splitting, when synergized with hydrogen production catalyzed by hydrogenases, emerges as a promising avenue for clean and renewable energy. However, theoretical calculations have faced challenges in elucidating the low-lying spin states of iron-sulfur clusters, which are integral components of hydrogenases. To address this challenge, we employ the Extended Broken-Symmetry method for the computation of the cubane-[Fe3S4] cluster within the [FeNi] hydrogenase enzyme. This approach rectifies the error caused by spin contamination, allowing us to obtain the magnetic exchange coupling constant and the energy level of the low-lying state. We find that the Extended Broken-Symmetry method provides more accurate results for differences in bond length and the magnetic coupling constant. This accuracy assists in reconstructing the low-spin ground state force and determining the geometric structure of the ground state. By utilizing the Extended Broken-Symmetry method, we further highlight the significance of the geometric arrangement of metal centers in the cluster's properties and gain deeper insights into the magnetic properties of transition metal iron-sulfur clusters at the reaction centers of hydrogenases. This research illuminates the untapped potential of hydrogenases and their promising role in the future of photosynthesis and sustainable energy production.

Theoretical elucidation of the structure, bonding, and reactivity of the CaMn4Ox clusters in the whole Kok cycle for water oxidation embedded in the oxygen evolving center of photosystem II. New molecular and quantum insights into the mechanism of the O-O bond formation.

This paper reviews our historical developments of broken-symmetry (BS) and beyond BS methods that are applicable for theoretical investigations of metalloenzymes such as OEC in PSII. The BS hybrid DFT (HDFT) calculations starting from high-resolution (HR) XRD structure in the most stable S1 state have been performed to elucidate structure and bonding of whole possible intermediates of the CaMn4Ox cluster (1) in the Si (i = 0 ~ 4) states of the Kok cycle. The large-scale HDFT/MM computations starting from HR XRD have been performed to elucidate biomolecular system structures which are crucial for examination of possible water inlet and proton release pathways for water oxidation in OEC of PSII. DLPNO CCSD(T0) computations have been performed for elucidation of scope and reliability of relative energies among the intermediates by HDFT. These computations combined with EXAFS, XRD, XFEL, and EPR experimental results have elucidated the structure, bonding, and reactivity of the key intermediates, which are indispensable for understanding and explanation of the mechanism of water oxidation in OEC of PSII. Interplay between theory and experiments have elucidated important roles of four degrees of freedom, spin, charge, orbital, and nuclear motion for understanding and explanation of the chemical reactivity of 1 embedded in protein matrix, indicating the participations of the Ca(H2O)n ion and tyrosine(Yz)-O radical as a one-electron acceptor for the O-O bond formation. The Ca-assisted Yz-coupled O-O bond formation mechanisms for water oxidation are consistent with recent XES and very recent time-resolved SFX XFEL and FTIR results.

The Nature of the Chemical Bonds of High-Valent Transition-Metal Oxo (M=O) and Peroxo (MOO) Compounds: A Historical Perspective of the Metal Oxyl-Radical Character by the Classical to Quantum Computations.

This review article describes a historical perspective of elucidation of the nature of the chemical bonds of the high-valent transition metal oxo (M=O) and peroxo (M-O-O) compounds in chemistry and biology. The basic concepts and theoretical backgrounds of the broken-symmetry (BS) method are revisited to explain orbital symmetry conservation and orbital symmetry breaking for the theoretical characterization of four different mechanisms of chemical reactions. Beyond BS methods using the natural orbitals (UNO) of the BS solutions, such as UNO CI (CC), are also revisited for the elucidation of the scope and applicability of the BS methods. Several chemical indices have been derived as the conceptual bridges between the BS and beyond BS methods. The BS molecular orbital models have been employed to explain the metal oxyl-radical character of the M=O and M-O-O bonds, which respond to their radical reactivity. The isolobal and isospin analogy between carbonyl oxide R2C-O-O and metal peroxide LFe-O-O has been applied to understand and explain the chameleonic chemical reactivity of these compounds. The isolobal and isospin analogy among Fe=O, O=O, and O have also provided the triplet atomic oxygen (3O) model for non-heme Fe(IV)=O species with strong radical reactivity. The chameleonic reactivity of the compounds I (Cpd I) and II (Cpd II) is also explained by this analogy. The early proposals obtained by these theoretical models have been examined based on recent computational results by hybrid DFT (UHDFT), DLPNO CCSD(T0), CASPT2, and UNO CI (CC) methods and quantum computing (QC).

Synthesis, Structure, and Magnetic Properties of an Fe36 Dimethylarsinate Cluster: The Largest "Ferric Wheel".

The synthesis and characterization of a high-nuclearity FeIII/O/arsinate cluster is reported within the salt [Fe36O12(OH)6(O2AsMe2)63(O2CH)3(H2O)6](NO3)12 (1). The compound was prepared from the reaction of Fe(NO3)3·9H2O, dimethylarsinic acid (Me2AsO2H), and triethylamine in a 1:2:4 molar ratio in acetonitrile. The Fe36 cation of 1 is an unprecedented structural type consisting of nine Fe4 butterfly units of two types, three {FeIII4(μ3-O)2} units A, and six {FeIII4(μ3-O)(μ3-OH)} units B, linked by multiple bridging Me2AsO2- groups into an Fe36 triangular wheel/loop with C3 crystallographic and D3 virtual symmetry that looks like a guitar plectrum. The unusual structure has been rationalized on the basis of the different curvatures of units A and B, the presence of intra-Fe36 hydrogen bonding, and the tendency of Me2AsO2- groups to favor μ3-bridging modes. The cations stack into supramolecular nanotubes parallel to the crystallographic c axis and contain badly disordered solvent and NO3- anions. The cation of 1 is the highest-nuclearity "ferric wheel" to date and also the highest-nuclearity Fe/O cluster of any structural type with a single contiguous Fe/O core. Variable-temperature direct-current magnetic susceptibility data and alternating-current in-phase magnetic susceptibility data indicate that the cation of 1 possesses an S = 0 ground state and dominant antiferromagnetic interactions. The Fe2 pairwise Ji,j couplings were estimated by the combined use of a magnetostructural correlation for high-nuclearity FeIII/oxo clusters and density functional theory calculations using broken-symmetry methods and the Green's function approach. The three methods gave satisfyingly similar Ji,j values and allowed the identification of spin-frustration effects and the resulting relative spin-vector alignments and thus rationalization of the S = 0 ground state of the cation.

Magnetic Properties of High-Nuclearity Fex-oxo (x = 7, 22, 24) Clusters Analyzed by a Multipronged Experimental, Computational, and Magnetostructural Correlation Approach.

The synthesis, structure, and magnetic properties of three related iron(III)-oxo clusters are reported, [Fe7O3(O2CPh)9(mda)3(H2O)] (1), [Fe22O14(OH)3(O2CMe)21(mda)6](ClO4)2 (2), and [Fe24O15(OH)4(OEt)(O2CMe)21(mda)7](ClO4)2 (3), where mdaH2 is N-methyldiethanolamine. 1 was prepared from the reaction of [Fe3O(O2CPh)6(H2O)3](NO3) with mdaH2 in a 1:2 ratio in MeCN, whereas 2 and 3 were prepared from the reaction of FeCl3/NaO2CMe/mdaH2 in a 2:∼13:2 ratio and FeCl3/NaO2CMe/mdaH2/pyridine in a 2:∼13:2:25 ratio, respectively, both in EtOH. The core of 1 consists of a central octahedral FeIII ion held within a nonplanar Fe6 loop by three μ3-O2- and three μ2-RO- arms from the three mda2- chelates. The cores of the cations of 2 and 3 consist of an A:B:A three-layer topology, in which a central Fe6 (2) or Fe8 (3) layer B is sandwiched between two Fe8 layers A. The A layers structurally resemble 1 with the additional Fe added at the center to retain virtual C3 symmetry. The central Fe6 layer B of 2 consists of a {Fe4(μ4-O)2(μ3-OH)2}6+ cubane with an Fe on either side attached to cubane O2- ions, whereas that of 3 has the same cubane but with an {Fe3(μ3-O)(μ-OH)} unit attached on one side and a single Fe on the other. Variable-temperature dc and ac magnetic susceptibility studies revealed dominant antiferromagnetic coupling in all complexes leading to ground-state spins of S = 5/2 for 1 and S = 0 for 2 and 3. All Fe2 pairwise exchange parameters (Jij) for 1-3 were estimated by two independent methods: density functional theory (DFT) calculations using broken symmetry methods and a magnetostructural correlation previously developed for high-nuclearity FeIII/O complexes. The two approaches gave satisfyingly similar Jij values, and the latter allowed rationalization of the experimental ground states by identification of the spin frustration effects operative and the resultant relative spin vector alignments at each FeIII ion.

Development of broken-symmetry (BS) methods in chemical reactions. A theoretical view of water oxidation in photosystem II and related systems

Fundamental concepts and basic theories for the broken-symmetry (BS) methods have been reviewed in relation to theoretical elucidation and understanding of the mechanism for water oxidation in the oxygen evolving complex (OEC) of photosystem II (PSII). The HOMO-LUMO mixings by the BS method have provided the BS orbitals which are mainly localized on the metal and oxygen sites of the high-valent transition-metal oxo (MO) bonds, respectively. The oxyl-radical character (M–O) is responsible for radical reactivity such as the radical coupling in accord with various experimental results. The Lewis acids play important roles for reduction of the oxyl-radical character, indicating the participation of the water-coordinated Ca(II) ion of the CaMn3O4 cubane to stabilization of the Mn(V)=O…Ca(II) bond for essentially non-radical reactions. Several chemical indices have been calculated to elucidate the radical character for quantitative purpose. Implications of the computational results are discussed in relation to possible mechanisms of water oxidation in OEC of PSII.

How Plausible Is Getting Ferromagnetic Interactions by Coupling Blatter's Radical via Its Fused Benzene Ring?

With ongoing efforts to synthesize super-stable Blatter's diradicals having strong ferromagnetic exchange interactions, all the 10 possible isomers of di-Blatter diradical coupled through the fused benzene rings are investigated. A variety of electronic structure theory such as broken-symmetry methods in density functional theory (DFT), spin-constraint DFT (CDFT), and wave function-based multi-configurational methods, e.g., CASSCF/NEVPT2 are applied to compute the magnetic exchange interactions. Surprisingly, anti-ferromagnetic interactions are revealed for all the stable isomers of di-Blatter diradicals. Indeed, it is commensurate with the experimental observations for the only available synthesized isomer. However, the other nine isomeric diradicals in the series are yet to be synthesized. Despite a good match between theory and experiment, the anti-ferromagnetic exchange interactions could not be explained based on the spin alternation rule due to unique spin distributions in the triazinyl ring. Thus, we propose the zonal spin-alternation rule, which explains the observed ground spin-state for the conjugated di-Blatter diradicals quite accurately. Further, the fractional spin-moment localization on the N-atoms activates multiple exchange pathways and the dominating exchange interactions render anti-ferromagnetic interactions in the conjugated isomers. The study further reveals that, due to strong steric hindrance in certain coupled isomers, the exchange interaction switches from anti-ferromagnetic to weak ferromagnetic interactions with the cost of stabilization energy of the radicals. Thus, it questions the possibility of synthesizing ferromagnetic di-Blatter diradicals.

Structure, Dynamics, and Reactivity for Light Alkane Oxidation of Fe(II) Sites Situated in the Nodes of a Metal-Organic Framework.

Metal organic frameworks (MOFs), with their crystalline, porous structures, can be synthesized to incorporate a wide range of catalytically active metals in tailored surroundings. These materials have potential as catalysts for conversion of light alkanes, feedstocks available in large quantities from shale gas that are changing the economics of manufacturing commodity chemicals. Mononuclear high-spin (S = 2) Fe(II) sites situated in the nodes of the MOF MIL-100(Fe) convert propane via dehydrogenation, hydroxylation, and overoxidation pathways in reactions with the atomic oxidant N2O. Pair distribution function analysis, N2 adsorption isotherms, X-ray diffraction patterns, and infrared and Raman spectra confirm the single-phase crystallinity and stability of MIL-100(Fe) under reaction conditions (523 K in vacuo, 378-408 K C3H8 + N2O). Density functional theory (DFT) calculations illustrate a reaction mechanism for the formation of 2-propanol, propylene, and 1-propanol involving the oxidation of Fe(II) to Fe(III) via a high-spin Fe(IV)═O intermediate. The speciation of Fe(II) and Fe(III) in the nodes and their dynamic interchange was characterized by in situ X-ray absorption spectroscopy and ex situ Mössbauer spectroscopy. The catalytic relevance of Fe(II) sites and the number of such sites were determined using in situ chemical titrations with NO. N2 and C3H6 production rates were found to be first-order in N2O partial pressure and zero-order in C3H8 partial pressure, consistent with DFT calculations that predict the reaction of Fe(II) with N2O to be rate determining. DFT calculations using a broken symmetry method show that Fe-trimer nodes affecting reaction contain antiferromagnetically coupled iron species, andhighlight the importance of stabilizing high-spin (S = 2) Fe(II) species for effecting alkane oxidation at low temperatures (<408 K).

Seven Clues to Ligand Noninnocence: The Metallocorrole Paradigm.

Noninnocent ligands do not allow an unambiguous definition of the oxidation state of a coordinated atom. When coordinated, the ligands also cannot be adequately represented by a classic Lewis structure. A noninnocent system thus harbors oxidizing (holes) or reducing equivalents (electrons) that are delocalized over both the ligand and the coordinated atom. To a certain degree, that is true of all complexes, but the phenomenon is arguably most conspicuous in complexes involving ligands with extended π-systems. The electronic structures of such systems have often been mischaracterized, thereby muddying the chemical literature to the detriment of students and newcomers to the field. In recent years, we have investigated the electronic structures of several metallocorrole families, several of which have turned out to be noninnocent. Our goal here, however, is not to present a systematic account of the different classes of metallocorroles, but rather to focus on seven major tools (in a nod to A. G. Cairns-Smith's Seven Clues to the Origin of Life) that led us to recognize noninnocent behavior and subsequently to characterize the phenomenon in depth. (1) The optical probe: For a series of noninnocent meso-triarylcorrole derivatives with different para substituents X, the Soret maxima are typically exquisitely sensitive to the nature of X, red-shifting with increasing electron-donating character of the group. No such substituent sensitivity is observed for the Soret maxima of innocent triarylcorrole derivatives. (2) Quantum chemistry: Spin-unrestricted density functional theory calculations permit a simple and quick visualization of ligand noninnocence in terms of the spin density profile. Even for an S = 0 complex, the broken-symmetry method often affords a spin density profile that, its fictitious character notwithstanding, helps visualize the intramolecular spin couplings. (3) NMR and EPR spectroscopy: In principle, these two techniques afford experimental probes of the electronic spin density. (4) Structure/X-ray crystallography. Ligand noninnocence in metallocorroles is often reflected in small but distinct skeletal bond length alternations in and around the bipyrrole part of the macrocycle. In addition, for Cu and some Ag corroles, ligand noninnocence manifests itself via a strong saddling of the macrocycle. (5) Vibrational spectroscopy. Unsurprisingly, the aforementioned bond length alternations translate to structure-sensitive vibrational marker bands. (6) Electrochemistry. Noninnocent metallocorroles exhibit characteristically high reduction potentials, but caution should be exercised in turning the logic around. A high reduction potential does not necessarily signify a noninnocent metallocorrole; certain high-valent metal centers also undergo metal-centered reduction at quite high potentials. (7) X-ray absorption spectroscopy (XAS). By focusing on a given element, typically the central atom in a coordination complex, X-ray absorption near-edge spectroscopy (XANES) can provide uniquely detailed local information on oxidation and spin states, ligand field strength, and degree of centrosymmetry. For metallocorroles, some of the most clear-cut distinctions between innocent and noninnocent systems have come from the K-edge XANES of Mn and Fe corroles. For researchers faced with a new, potentially noninnocent system, the take-home message is to employ a good majority (i.e., at least four) of the above methods to arrive at a reliable conclusion vis-à-vis noninnocence.

Three-Dimensional Magnetic Exchange Networks in Trigonal Bisdithiazolyl Radicals.

The N-methyl-4-phenyl-pyridine-bridged bisdithiazolyl radical PhBPMe is polymorphic, crystallizing from cold acetonitrile in a trigonal α-phase, space group P3121, and from hot dichloroethane in an orthorhombic β-phase, space group Pca21. The crystal structures of both phases consist of slipped π-stacks of undimerized radicals aligned laterally into herringbone arrays. In the β-phase, there are two independent radicals in the asymmetric unit, and the resulting π-stacks form corrugated layers interspersed by methyl and phenyl groups which block the approach of neighboring radicals. In the α-phase, the methyl/phenyl groups and the radical π-stacks separately form spirals about 31 axes, the latter giving rise to a 3D network of close radical/radical contacts. Variable temperature magnetic susceptibility measurements on the β-phase indicate strong antiferromagnetic coupling. Weaker but predominantly antiferromagnetic interactions (θ = -20.7 K) are observed in the α-phase. A high temperature series expansion analysis of the magnetic data for the α-phase affords antiferromagnetic exchange energies for the one- and two-step radical/radical interactions about the 31 spirals ( J1 = -1.2 K, J2 = -10.9 K, respectively), with weak ferromagnetic interactions along the π-stacks ( Jπ = +1.8 K). Despite the presence of a 3D network based on the dominant J2 interactions, which affords two independent bipartite sublattices, no evidence of bulk antiferromagnetic order has been observed above T = 2 K. The magnetic results are discussed in light of exchange energies calculated using density functional theory broken symmetry methods.

Broken Symmetry Approach to Magnetic Properties of Oligonuclear Transition-Metal Complexes: Application to Hyperfine Tensors of Mixed-Valence Manganese Compounds

The broken symmetry method is a standard approach for the calculation of isotropic exchange coupling constants in oligonuclear transition-metal compounds with density functional methods. It is most...

Electronic structure and energy decomposition of binuclear transition metal complexes containing β-diketiminate and imido ligands: spin state and metal’s nature effects

DFT calculations with full geometry optimization using BP86-D and OPBE functionals have been performed on series of [(BDI)M(NH)]2(Bz) and [(BDI)M(NH)]2(Tol) (M = Ti, V, Nb, Cr, Mn, Fe, Co, and Ni; BDI = β-diketiminate; NH = imido group; Bz = benzene; and Tol = toluene) of various spin states (singlet S = 0, triplet S = 1, quintet S = 2, and singlet S = 0 of broken symmetry method). Depending on the metal nature and its electron count and the spin state, the six-membered ring in [(BDI)M(NH)]2(Bz) and [(BDI)M(NH)]2(Tol) adopts various hapticities that involve full or partial coordination, giving rise to a flat or a distorted ring, respectively. The NH2− imido group is linear or bent with respect to its sp or sp2 hybridization acting as a six- or a four-electron donor, respectively. The (BDI)− anion is a bidentate ligand as a six-electron donor. The optimized geometries do not show direct metal-metal bonding and correspond to long separations. The optimized structures for Nb metal are comparable to the available experimental ones. The Ziegler-Rauk energy decomposition analysis scheme was employed to characterize the geometry distortion, the steric interaction (electrostatic and Pauli), and the orbital interaction terms in the total bonding energy. The results showed that the interaction terms in all the studied complexes are governed by one third covalent and two thirds ionic characters, which are in agreement with the ΔEelstat (electrostatic) and ΔEorb (orbital) contributions, respectively, into the total attractive interaction (ΔEelstat + ΔEorb).

Full-valence density matrix renormalisation group calculations on meta-benzyne based on unrestricted natural orbitals. Revisit of seamless continuation from broken-symmetry to symmetry-adapted models for diradicals

ABSTRACTIn this work, we show that the natural orbitals of unrestricted hybrid density functional theory (UHDFT) can be used as the active space orbitals to perform multireference (MR) calculations, for example, the density matrix renormalisation group (DMRG) and Mukherjee-type (Mk) MR coupled-cluster (CC) method. By including a sufficiently large number of these natural orbitals, full-valence (FV) active space can be identified without recourse of the expensive self-consistent procedures for DMRG-SCF. Several useful chemical indices are derived based on the occupation numbers of the natural orbitals for seamless continuation from broken-symmetry (BS) to symmetry-adapted (SA) methods. These procedures are used on 1,3-didehydrobenzene (meta-benzyne) to calculate its singlet (S)-triplet (T) gap. We compare our results to available experiments and computational results obtained by several other groups. We see our procedures as a seamless bridge between single-reference BS methods, such as UHDFT, and the SA MR methods, such as FV DMRG and MkMRCC.

Redox-modulated switching of ferro to antiferromagnetic coupling in endohedral fullerenes: A broken-symmetry approach

The redox-governed switching potency from ferro to antiferromagnetic coupling and vice versa of three already synthesized endohedral fullerenes N@C60, N@C70 and P@C60 has been studied using the broken symmetry method. The calculated exchange coupling constants for cation and anion forms of N@C60 indicate ferro and antiferromagnetic interactions respectively. In this work, several pure and hybrid functionals were examined on N@C60 to study the amount of Hartree–Fock exact exchange effect in magnetic exchange coupling constant values. Furthermore, the spin density distributions and molecular orbitals shapes have been analyzed to explain the nature of exchange-coupling interactions and their pathways respectively.

Magnetic Exchange Couplings from Noncollinear Perturbation Theory: Dinuclear CuIIComplexes

To benchmark the performance of a new method based on noncollinear coupled-perturbed density functional theory [J. Chem. Phys. 138, 174115 (2013)], we calculate the magnetic exchange couplings in a series of triply bridged ferromagnetic dinuclear Cu(II) complexes that have been recently synthesized [Phys. Chem. Chem. Phys. 15, 1966 (2013)]. We find that for any basis-set the couplings from our noncollinear coupled-perturbed methodology are practically identical to those of spin-projected energy-differences when a hybrid density functional approximation is employed. This demonstrates that our methodology properly recovers a Heisenberg description for these systems, and is robust in its predictive power of magnetic couplings. Furthermore, this indicates that the failure of density functional theory to capture the subtle variation of the exchange couplings in these complexes is not simply an artifact of broken-symmetry methods, but rather a fundamental weakness of current approximate density functionals for the description of magnetic couplings.

Diradical Character of Benzo- and Naphtho-Annelated Thiophene–Pyrrole Mixed Oligomer Dications

Benzo- and naphtho-annelated thiophene–pyrrole mixed octamers Bz8TP-Cm and Np8TP-Cm, comprising benzo- or naphthodithiophene and two dithienylpyrrole units, were synthesised. Density functional theory (DFT) calculations based on B3LYP/6–31G(d) with the broken symmetry method predicted that dications Bz8TP-C12+ and Np8TP-C12+ have stronger diradical character than previously investigated non-annelated thiophene–pyrrole mixed octamer 8TP-C12+ (R1 = R2 = H). Compounds Bz8TP-C8 and Np8TP-C8 showed a one-step, two-electron oxidation process based on cyclic voltammetry analysis. Reaction with SbCl5 involved a two-electron oxidation. Bz8TP-C82+ and Np8TP-C82+ displayed similar absorption spectra to that of nonamer 9TP-C122+ (R1 = R2 = H), rather than that of octamer 8TP-C122+, indicating the stronger diradical characters of octamers Bz8TP-C82+ and Np8TP-C82+, as enhanced by benzo- and naphtho-annelation, and were comparable with that of 9TP-C122+. Time-dependent-DFT calculations supported the conclusion obtained from the experimental results.

Density Functional Theory of Open-Shell Systems. The 3d-Series Transition-Metal Atoms and Their Cations.

The 3d-series transition metals (also called the fourth-period transition metals), Sc to Zn, are very important in industry and biology, but they provide unique challenges to computing the electronic structure of their compounds. In order to successfully describe the compounds by theory, one must be able to describe their components, in particular the constituent atoms and cations. In order to understand the ingredients required for successful computations with density functional theory, it is useful to examine the performance of various exchange-correlation functionals; we do this here for 4s(N)3d(N') transition-metal atoms and their cations. We analyze the results using three ways to compute the energy of the open-shell states: the direct variational method, the weighted-averaged broken symmetry (WABS) method, and a new broken-symmetry method called the reinterpreted broken symmetry (RBS) method. We find the RBS method to be comparable in accuracy with the WABS method. By examining the overall accuracy in treating 18 multiplicity-changing excitations and 10 ionization potentials with the RBS method, 10 functionals are found to have a mean-unsigned error of <5 kcal/mol, with ωB97X-D topping the list. For local density functionals, which are more practical for extended systems, the M06-L functional is the most accurate. And by combining the results with our previous studies of p-block and 4d-series elements as well as databases for alkyl bond dissociation, main-group atomization energies, and π-π noncovalent interactions, we find five functionals, namely, PW6B95, MPW1B95, M08-SO, SOGGA11-X, and MPWB1K, to be highly recommended. We also studied the performance of PW86 and C09 exchange functionals, which have drawn wide interest in recent studies due to their claimed ability to reproduce Hartree-Fock exchange at long distance. By combining them with four correlation functionals, we find the performance of the resulting functionals disappointing both for 3d transition-metal chemistry and in broader tests, and thus we do not recommend PW86 and C09 as components of generalized gradient approximations for general application.

Theoretical Study on the Structure and Properties of Graphdiyne

The graphdiyne, as a new stable carbon allotrope, is expected to be widely applied to nanosciences and devices due to unique structure and properties. In this paper we investigated the structural parameters, Wiberg bond indices, and the aromaticity of graphdiyne at the B3LYP/6-31+G* level. The calculating results indicated all the p-electrons of the carbons were able to form delocalized π-bonds and all the lengths of C—C bonds were to become average. The aromaticity of all the benzene rings was stronger than the scalene hexagon due to more negative the nucleus independent chemical shift (NICS) value. The topological properties of the compound were in good agreement with those discussed in Wiberg Bond Orders. The LUMO bandwidth (0.27 eV) of the title compound was larger than the HOMO bandwidth (0.24 eV), it indicates that the graphdiyne should be n-type material. The calculation of the odd electrons by the broken symmetry method showed that the compound contains 3.6 effectively unpaired electrons and possesses enhanced chemical reactivity. Keywords graphdiyne; aromaticity; Wiberg bond indices; AIM; odd electrons

Magnetic coupling constants and vibrational frequencies by extended broken symmetry approach with hybrid functionals

The description of the electronic structure and magnetic properties of multi-centers transition metal complexes, especially of mixed-valence compounds, still represents a challenge for density functional theory (DFT) methods. The energies and the geometries of the correctly symmetrized low-spin ground state are estimated using the Heisenberg-Dirac-van Vleck spin Hamiltonian within the extended broken symmetry method introduced by Marx and co-workers [Nair et al., J. Chem. Theory Comput. 4, 1174-1188 (2008)]. In the present work we extend the application of this technique, originally implemented using the DFT+U scheme, to the use of hybrid functionals, investigating the ground-state properties of di-iron and di-manganese compounds. The calculated magnetic coupling and vibrational properties of ferredoxin molecular models are in good agreements with experimental results and DFT+U calculations. Six different mixed-valence Mn(III)-Mn(IV) compounds have been extensively studied optimizing the geometry in low-spin, high-spin, and broken-symmetry states and with different functionals. The magnetic coupling constants calculated by the extended broken symmetry approach using B3LYP functional presents a remarkable agreement with the experimental results, revealing that the proposed methodology provides a consistent and accurate DFT approach to the electronic structure of multi-centers transition metal complexes.

Which oxidation state is preferable at S0 state in oxygen-evolving complex, Mn4(II, III, IV, IV) or Mn4(III, III, III, IV)? A B3LYP study

Based on the structure of 1.9Å resolved OEC, which was published as PDBid=3ARC, geometries and electronic structures of the CaMn4O5 core and surrounding water molecules at the S0 state are examined by the hybrid B3LYP and broken-symmetry methods. Two doublet states 1 and 2 with energy difference of 15.2kcal/mol were obtained. 1 is lower than 2. The oxidation states of four manganese atoms of 1 are Mn4[III, III, IV, III], while those of 2 are Mn4[III, IV, IV, II]. It is concluded that the oxidation states of Mn4(II, III, IV, IV) is ruled out at the S0 state.