Satomichi Nishihara

Reinvestigation of the reaction of ethylene and singlet oxygen by the approximate spin projection method. Comparison with multireference coupled-cluster calculations.

We quantify a spin contamination error caused by a broken-symmetry (BS) method on the geometry at the stationary points and barrier heights of the [2 + 2] reaction between singlet oxygen and ethylene, which goes through a diradical intermediate. Several hybrid GGA, hybrid meta-GGA, and long-range corrected hybrid functionals, O3LYP, B3LYP, PBE0, MPW1B95, BHandHLYP, and omegaB97X, are examined to elucidate their original nature without the spin contamination error. For that purpose, the geometry of each reaction step for the BS state as well as its total energy is corrected by using an approximate spin projection method. The CCSD and CCSD(T) single-point calculations are also carried out at optimized geometries at the DFT level to confirm the results of the DFT methods. The single-point calculations by means of Mukherjees multireference coupled cluster with single and double excitations at CASSCF(10e,8o)-optimized geometries are also presented to assess the DFT methods. After the energy and geometry corrections, the barrier height of each functional is consistent with conventional closed-shell-type reactions even in the reaction involving singlet diradical species. We also find that the spin contamination error on the geometric change is not negligible especially at the early stage of the reaction ( approximately 3 kcal/mol), where the triplet state is the ground state.

Multireference character of 1,3-dipolar cycloaddition of ozone with ethylene and acrylonitrile.

In the present study, the concerted and stepwise reaction mechanisms for 1,3-dipole cycloaddition of ozone with ethylene (1) and acrylonitrile (2) are investigated. The stationary points are optimized by using four hybrid R(U)DFT methods. A geometry optimization method based on an approximate spin projection (AP-opt method) is applied to eliminate a spin contamination from the broken-symmetry (BS) solution. The AP-opt method reveals that a diradical intermediate for the stepwise pathway is spurious due to the spin contamination. The revised reaction profile with no diradical intermediate supports the stereospecificity. On the basis of the experimental data, the RCCSD(T) method outperforms AP-UCCSD(T), AP-UBD(T), and MkMRCCSD(4e,4o) for the systems, indicating that the RCCSD(T) method can describe the diradical character of ozone within a framework of single reference wave function. The subsequent single point energy calculations show that the highly synchronous transition state is much more favorable than the asynchronous one for 1. In the case of 2, there is not much difference between two transition states because of its asymmetric structure and charge separations in the transition states.

MkMRCC, APUCC and APUBD approaches to 1,n-didehydropolyene diradicals: the nature of through-bond exchange interactions

Mukherjee-type (Mk) state specific (SS) multi-reference (MR) coupled-cluster (CC) calculations of 1,n-didehydropolyene diradicals were carried out to elucidate singlet-triplet energy gaps via through-bond coupling between terminal radicals. Spin-unrestricted Hartree–Fock (UHF) based coupled-cluster (CC) computations of these diradicals were also performed. Comparison between symmetry-adapted MkMRCC and broken-symmetry (BS) UHF-CC computational results indicated that spin-contamination error of UHF-CC solutions was left at the SD level, although it had been thought that this error was negligible for the CC scheme in general. In order to eliminate the spin contamination error, approximate spin-projection (AP) scheme was applied for UCC, and the AP procedure indeed eliminated the error to yield good agreement with MRCC in energy. The CCD with spin-unrestricted Brueckners orbital (UB) was also employed for these polyene diradicals, showing that large spin-contamination errors at UHF solutions are dramatically improved, and therefore AP scheme for UBD removed easily the rest of spin-contaminations. Pure- and hybrid-density functional theory (DFT) calculations of the species were also performed. Three different computational schemes for total spin angular momentums were examined for the AP correction of the hybrid DFT. The AP DFT calculations yielded the singlet-triplet energy gaps that were in good agreement with those of MRCC, AP UHF-CC and AP UB-CC. Chemical indices such as the diradical character were calculated with all these methods. Implications of the present computational results are discussed in relation to previous RMRCC calculations of diradical species and BS calculations of large exchange coupled systems.

MkMRCC, APUCC, APUBD calculations of didehydronated species: comparison among calculated through-bond effective exchange integrals for diradicals

Mukherjees type of multireference coupled-cluster (MkMRCC), approximate spin-projected spin-unrestricted CC (APUCC), and AP spin-unrestricted Brueckners (APUBD) methods were applied to didehydronated ethylene, allyl cation, cis-butadiene, and naphthalene. The focus is on descriptions of magnetic properties for these diradical species such as S-T gaps and diradical characters. Several types of orbital sets were examined as reference orbitals for MkMRCC calculations, and it was found that the change of orbital sets do not give significant impacts on computational results for these species. Comparison of MkMRCC results with APUCC and APUBD results show that these two types of methods yield similar results. These results show that the quantum spin corrected UCC and UBD methods can effectively account for both nondynamical and dynamical correlation effects that are covered by the MkMRCC methods. It was also shown that appropriately parameterized hybrid density functional theory (DFT) with AP corrections (APUDFT) calculations yielded very accurate data that qualitatively agree with those of MRCC and APUBD methods. This hierarchy of methods, MRCC, APUCC, and APUDFT, is expected to constitute a series of standard ab initio approaches towards radical systems, among which we could choose one of them, depending on the size of the systems and the required accuracy.

Theory of chemical bonds in metalloenzymes - Manganese oxides clusters in the oxygen evolution center -

In early 1980 we have initiated broken-symmetry (BS) MO theoretical calculations of transition-metal oxo species M = O (M = Ti,V,Cr,Mn,Fe,Ni,Cu) to elucidate the nature of dσ-pσ and dπ-pπ bonds. It has been concluded that high-valent M = O species such as [Mn(IV) = O]2+ and [Fe(IV) = O]2+ exhibit electrophilic property in a sharp contrast with nucleophilic character of low-valent M = O bonds: [M(II)O2−]0, and closed-shell dπ-pπ bonds of high-valent M = O species often suffer the triplet-instability, giving rise to open-shell (BS) configurations with significant metal-diradical (MDR) character: •M-O•: note that these bonds are therefore regarded as typical examples of strongly correlated electron systems. Because of the MDR character, 1,4-metal diradical mechanism was indeed preferable to four-centered mechanism in the case of addition reaction of naked Mn(IV) = O to ethylene. Recently the manganese-oxo species have been receiving renewed interest in relation to catalytic cycle of oxygen evolution from wat...

Symmetry and Broken-Symmetry in Molecular Orbital Descriptions of Unstable Molecules. 3. The Nature of Chemical Bonds of Spin Frustrated Systems

Symmetry and broken symmetry in the molecular orbital description of spin frustration systems have been investigated in relation to the resonating valence bond (RVB) theory of the spin liquid state and non-BCS superconductivity. Broken symmetry (BS) and resonating BS (RBS) molecular orbital (MO) methods have been employed to obtain resonating valence bond (RVB)-type explanations of spin frustrated systems. RBS MO solutions are expanded using the localized molecular orbitals (LMO) to elucidate a universal MO-VB description. The BS and RBS MO descriptions of triangular spin frustrated systems corresponding to transition structures for exchange-forbidden radical insertions were investigated in comparison with the RVB-type explanations of such systems. The BS and RBS calculations by the use of three different axial (SDW) solutions or three noncollinear GSO (helical SDW) solutions of a triangular hydrogen cluster were performed to obtain potential curves with and without resonance (quantum) effects. The resonating GSO (noncollinear) state responsible for short-range correlation was found to be the most stable for the system. The reliability of the approximate spin projection (AP) procedure to eliminate the high-spin component was also elucidated, comparing with the AP BS and RBS potential curves. The BS GSO (GHF) computations of several triangular systems, N(CH(2))(3), (CH(2))(3), and Mn(II)(3)O(4), were performed to obtain total energies and total spin angular momentums and effective exchange integrals (J) between local spins, which are crucial for construction of effective spin Hamiltonian models. The exact diagonalization of the Heisenberg models was also performed to depict the energy levels and magnetic susceptibility curves for triangular and kagome lattices to elucidate spin frustration effects and related quantum spin behaviors. Implications of the computational results have been discussed in relation to magnetic properties of several triangular and kagome systems synthesized recently and the superconductivity of triangular systems discovered recently.

Locality and nonlocality of electronic structures of molecular systems: Toward QM/MM and QM/QM approaches

We present a simple guideline to inspect the large molecular systems towards QM/MM theory and various types of divide-and-conquer electronic structure theories, in which we utilize on the linear-response function. We present the basic ideas of our approach, simple introduction of the computational method, and some numerical results.

Instability In Chemical Bonds: Uno Cascc, Resonating Ucc And Approximately Projected Ucc Methods To Quasi-Degenerate Electronic Systems

We review several versions of coupled-cluster (CC) methods based on spin-unrestricted Hartree–Fock (UHF) approximation. A multireference (MR) CC theory by the use of UHF natural orbitals (UNO), UNO CASCC, is revisited to elucidate scope and limitation of UHF coupled-cluster (CC) methods and two types of quantum corrections for UHF CC (UCC) solutions: first one is the approximate spin-projected UCC scheme (AP UCC) based on Heisenberg model Hamiltonian, and second one is the recently developed resonating UCC configuration interaction (Res-UCC CI) approach. In this article, we examine these CC-based approaches for quasi-degenerate electronic systems such as dissociation of covalent bonds. The computational results are discussed in comparison with those of the MR-CC theory. Our methods have been applied to exchange-coupled systems and ion-radical systems, which have been accepted current interests.

First principle calculations of effective exchange integrals: Comparison between SR (BS) and MR computational results

First principle calculations of effective exchange integrals (J) in the Heisenberg model for diradical species were performed by both symmetry-adapted (SA) multi-reference (MR) and broken-symmetry (BS) single reference (SR) methods. Mukherjee-type (Mk) state specific (SS) MR coupled-cluster (CC) calculations by the use of natural orbital (NO) references of ROHF, UHF, UDFT and CASSCF solutions were carried out to elucidate J values for di- and poly-radical species. Spin-unrestricted Hartree Fock (UHF) based coupled-cluster (CC) computations were also performed to these species. Comparison between UHF-NO(UNO)-MkMRCC and BS UHF-CC computational results indicated that spin-contamination of UHF-CC solutions still remains at the SD level. In order to eliminate the spin contamination, approximate spin-projection (AP) scheme was applied for UCC, and the AP procedure indeed corrected the error to yield good agreement with MkMRCC in energy. The CC double with spin-unrestricted Brueckners orbital (UBD) was furtherm...