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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). [ABSTRACT FROM AUTHOR]

In this study, the zero-field splitting parameters ( D , E ) and effective exchange integrals ( J ) for a Mn 12 /Mn 11 Cr mixed crystal were evaluated using ab initio molecular orbital (MO) computations based on the hybrid density functional theory (DFT) methods for Mn 11 Cr ∗ -acetate cluster (Mn 12 and Mn 11 Cr mixing). In this study, Mn 12 -acetate, Mn 11 Cr-acetate, and Mn 12− n Cr n -acetate clusters were focused on. The zero-field splitting (ZFS) parameters are obtained by UB3LYP methods, i.e. −0.339 cm −1 (Mn 12 -acetate) and −0.351 cm −1 (Mn 11 Cr-acetate). The energy barriers were estimated to be 53.7 K and 50.4 K, which showed good agreement with previously reported experimental values of 68.8 K and 56.8 K, respectively. The origin of such anisotropy is assumed to be the eight Mn III ions with d 4 -electrons in their outer ring subunits, where elongated conformation along the axial direction becomes very important and leads to negative D values. The spin networks in these clusters were discussed by using the effective exchange integral sets. The J s value, as estimated by the UB3LYP method revealed that the J 2 , J 3 , and J 3 ′ interactions played important roles in describing the parallel spin ordering in cubane and ring subunits as well as the antiferromagnetic coupling between two subunits. The other interactions, i.e. J 1 , J 1 ′, J 4 , and J 4 ′ somewhat disturbed the spin ordering in the Mn 12 -acetate cluster. The substitution of Mn IV by Cr III did not change the spin network. However, the total S value changed after the substitution. [ABSTRACT FROM AUTHOR]

In 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. [ABSTRACT FROM AUTHOR]

First principle calculations of the effective exchange integrals ( J) in the Heisenberg model for diradical species are presented for both symmetry-adapted multi-reference (MR) and single-reference broken-symmetry (BS) methods. The Mukherjee-type state-specific MR coupled cluster singles and doubles (MkCCSD) method with several different reference orbitals including BS natural orbitals is used to calculate the singlet-triplet energy gaps (S-T energy gap or 2 J) and diradical characters for the antiaromatic molecules [ a cyclopropenyl anion (CPA), b cyclobutadiene (CBD), and c cyclopentadienyl cation (CPC)], the cyclobutadiene derivatives with polar substitutents [ d aminocyclobutadiene (ACBD), e formylcyclobutadiene (FCBD), and f 1-amino-2-formyl-cyclobutadiene (AFCBD)] and finally the cyclobutadine derivatives with radical substitutents [ g 1,2-bis(methylene)cyclobutadiene (1,2-BMCBD) and h 1,3-bis(methylene)cyclobutadiene (1,3-BMCBD)]. For the BS methods, the spin-unrestricted Hartree-Fock based CCSD (UHF-CCSD), the CCD with the spin-unrestricted Brueckner determinant (UBD), and BS density functional theory (UDFT) computations are performed. Comparison between MkCCSD and the UHF-CCSD results indicates that spin-contamination of UHF-CCSD solutions still remains. In comparison with UHF-CCSD, the UBD results show that spin-contamination involved in BS solutions is greatly suppressed. To eliminate the spin contamination, an approximate spin-projection (AP) scheme is applied to the BS solutions. The AP procedure with the use of the expectation value of the total-spin operator corresponding to UHF-CCSD and UBD results yields good agreement with the MkCCSD results. As for the AP correction of the UDFT methods, three different computational schemes for predicting the expectation value of the total-spin operator are examined. Systematic comparisons between these methods are presented for the S-T energy gaps (2 J). Implications of the present computational results have been discussed in relation to the design of magnetic oligomers and polymers. [ABSTRACT FROM AUTHOR]

In this article, we performed spin-unrestricted Hartree Fock (UHF) based coupled-cluster (CC) and Bruckner CC double calculations of methylene, fluorine, H&bond;He&bond;H diradical, and ozone. Mukherjee-type (Mk) Multireference coupled-cluster (MRCC) calculations of these species were also conducted by the use of UHF natural orbital (UNO) and UHF localized natural orbitals (ULO) as reference orbitals to elucidate size-consistent error. Comparing calculated results of spin-unrestricted Hartree-Fock based coupled-cluster (UCC) and spin-unrestricted Bruckner-Double (UBD) with those of MkMRCC, it was found that spin-contamination errors of UCC and UBD solutions still remained, though this type of errors for these solutions was considered to be negligible in general. The comparison also revealed scope and applicability of approximate spin-projection (AP) scheme for UCC and UBD, indicating that the AP procedure corrected spin-contamination errors to yield good agreement with MRCC in energy. We also performed pure- and hybrid- density functional theory (DFT) calculations of the same systems, and those calculations provided reasonable singlet-triplet energy gaps, which were qualitatively good agreement with those of MRCC, AP-UCC, and AP-UBD calculations. Implications of the computational results are discussed in relation to applicability of hybrid DFT to large superexchange coupled systems. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [ABSTRACT FROM AUTHOR]

Reaction mechanisms of oxygen evolution in native and artificial photosynthesis II (PSII) systems have been investigated on the theoretical grounds, together with experimental results. First of all, our previous broken-symmetry (BS) molecular orbitals (MO) calculations are reviewed to elucidate the instability of the dπ-pπ bond in high-valent (HV) Mn(X)&dbond;O systems and the dπ-pπ-dπ bond in HV Mn&dbond;O&dbond;Mn systems. The triplet instability of these bonds entails strong or intermediate diradical characters: •Mn(IV)&dbond;O• and •Mn&bond;O&bond;Mn•; the BS MO resulted from strong electron correlation, leading to the concept of electron localizations and local spins. The BS computations have furthermore revealed guiding principles for derivation of selection rules for radical reactions of local spins. As a continuation of these theoretical results, the BS MO interaction diagrams for oxygen-radical coupling reactions in the oxygen evolution complex (OEC) in the PSII have been depicted to reveal scope and applicability of local singlet diradical (LSD) and local triplet diradical (LTD) mechanisms that have been successfully utilized for theoretical understanding of oxygenation reactions mechanisms by p450 and methane monooxygenase (MMO). The manganese-oxide cluster models examined are London, Berlin, and Berkeley models of CaMn4O4 and related clusters Mn4O4 and Mn3Ca. The BS MO interaction diagrams have revealed the LSD and/or LTD mechanisms for generation of molecular oxygen in the total low-, intermediate and high-spin states of these clusters. The spin alignments are found directly corresponding to the spin-coupling mechanisms of oxygen-radical sites in these clusters. The BS UB3LYP calculations of the clusters have been performed to confirm the comprehensive guiding principles for oxygen evolution; charge and spin densities by BS UB3LYP are utilized for elucidation and confirmation of the LSD and LTD mechanisms. Applicability of the proposed selection rules are examined in comparison with a lot of accumulated experimental and theoretical results for oxygen evolution reactions in native and artificial PSII systems. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [ABSTRACT FROM AUTHOR]

The effective exchange integrals (J[sub ab(M)]) between two cation radicals of title compounds in the Heisenberg model were calculated by ab initio molecular orbital (MO) and density functional theory (DFT) methods, together with hybrid DFT methods. The J[sub ab(D)] values between two dimer mono-cation radicals were also estimated assuming J[sub ab(D)] ≈ J[sub ab(M)]/2. It is found that the spin lattice obtained by the ab initio method is square planar and linear in BEDT-TTF and BETS planes, respectively, although other previous calculations show that spin lattice in the BEDT-TTF plane is a triangular one. The J[sub ab] and overlap integrals (s[sub ab]) values by the ab initio methods were used to determine transfer integral (t[sub ab]) and Coulomb repulsion (U[sub eff]) parameters of the Hubbard model, which were compared with those of the previous results. Implications of the calculated results are discussed in relation to the spin-mediated mechanism for superconductivity. [ABSTRACT FROM AUTHOR]

We report a thorough comparison between the spin-unrestricted semi-empirical molecular orbital (SE-UMO) and density functional theory (UDFT) calculations for a variety of π-conjugated diradical molecules which exhibit through-bond magnetic exchange interactions. The spin-unrestricted neglect of diatomic differential overlap (NDDO)-based methods (UPM6 and UrPM6) and self-consistent charge density functional tight-biding (UDFTB) are examined. The UCAM-B3LYP method is used as a representative of UDFT. We have found that NDDO-based and UDFTB methods give different performances with respect to the results of UCAM-B3LYP. The degree of diradical character in the target systems decreases in the order of UPM6 > UrPM6 ≈ UCAM-B3LYP > UDFTB. The conventional UPM6 and UDFTB calculations tend to overestimate and underestimate the diradical character, respectively, whereas UrPM6 is able to provide much the same results as UCAM-B3LYP. This is convincing evidence that UrPM6 will be useful for in silico screening of materials science at much lower computational cost. [ABSTRACT FROM AUTHOR]

Abstract: We have investigated the scope and applicability of Mukherjee’s state-specific multireference coupled cluster singles and doubles (Mk-MRCCSD) method on the magnetic interactions in dichloro-, oxo-, and peroxo-bridged binuclear Cu(II) complexes. Several reference orbitals including broken-symmetry natural orbitals (BSNOs) are examined for the Mk-MRCCSD computations. We compare the effective exchange integral (J) values calculated by Mk-MRCCSD with those calculated by conventional complete active space self-consistent field (CASSCF) and MRMP2. The BS methods with approximate spin-projection (AP) method are also performed for comparison. It is found that the Mk-MRCCSD method can be applicable to the prediction of exchange couplings in binuclear copper(II) containing systems. [Copyright &y& Elsevier]

Abstract: The barrier height for automerization of cyclobutadiene (CBD) is examined by broken-symmetry (BS) HF, post-HF, and density functional methods. To remove the spin contamination error, we use an approximate spin projection (AP) method. Comparison between the results of BS methods and those of the localized UHF natural orbital (ULO) based Mukherjee’s state-specific MRCC (ULO-MkCC) method shows that spin-unrestricted Brueckner doubles including perturbative triple excitations (UBD(T)) with the AP correction performs well within a framework of single reference approaches. On the other hand, UDFT methods except for UBLYP and UM06-2X give negative barrier heights, which are not consistent with the both the experimental and MRCC results. [ABSTRACT FROM AUTHOR]