Complete Active Space Self-consistent Field Research Articles

Dihydropyrene/Cyclophanediene Photoswitching Mechanism Revisited with Spin-Flip Time-Dependent Density Functional Theory: Nature of the Photoisomerization Funnel at Stake!

The complex photoisomerization mechanism of the dihydropyrene (DHP) photochromic system is revisited using spin-flip time-dependent density functional theory (SF-TD-DFT). The photoinduced ring-opening reaction of DHP into its cyclophanediene isomer involves multiple coupled electronic states of different character. A balanced treatment of both static and dynamic electron correlations is required to determine both the photophysical and photochemical paths in this system. The present results provide a refinement of the mechanistic picture provided in a previous complete active space self-consistent field plus second-order perturbation theory (CASPT2//CASSCF) study based on geometry optimizations at the CASSCF level. In particular, the nature of the conical intersection playing the central role of the photochemical funnel is different. While at the CASSCF level, the crossing with the ground state involves a covalent doubly excited state leading to a three-electron/three-center bond conical intersection, SF-TD-DFT predicts a crossing between the ground state and a zwitterionic state. These results are supported by multi-state CASPT2 calculations. This study illustrates the importance of optimizing conical intersections at a sufficiently correlated level of theory to describe a photochemical path involving crossings between covalent and ionic states.

Origin of the Distinctive Electronic Structure of Co- and Fe-Porphyrin-Nitrene and Its Effect on Their Nitrene Transfer Reactivity

Metal-bound nitrene species are the crucial intermediate in catalytic nitrene transfer reactions exhibited by engineered enzymes and molecular catalysts. The electronic structure of such species and its correlation with nitrene transfer reactivity have not been fully understood yet. This work presents an in-depth electronic structure analysis and nitrene transfer reactivity of two prototypical metal-nitrene species derived from CoII(TPP) and FeII(TPP) (TPP = meso-tetraphenylporphyrin) complexes and tosyl azide nitrene precursor. Parallel to the well-known "cobalt(III)-imidyl" electronic structure of the Co-porphyrin-nitrene species, the formation mechanism and electronic structure of the elusive Fe-porphyrin-nitrene have been established using density functional theory (DFT) and multiconfigurational complete active-space self-consistent field (CASSCF) calculations. Electronic structure evolution analysis for the metal-nitrene formation step and CASSCF-derived natural orbitals advocates that the electronic nature of the metal-nitrene (M-N) core of Fe(TPP) is strikingly different from that of the Co(TPP). Specifically, the "imidyl" nature of the Co-porphyrin-nitrene [(TPP)CoIII-•NTos] (Tos = tosyl) (I1Co) is contrasted by the "imido-like" character of the Fe-porphyrin-nitrene [(TPP)FeIV[Formula: see text]NTos] (I1Fe). This difference between Co- and Fe-nitrene has been attributed to the additional interactions between Fe-dπ and N-pπ orbitals in Fe-nitrene, which is further complemented by the shortened Fe-N bond length of 1.71 Å. This stronger M-N bond in Fe-nitrene compared to the Co-nitrene is also reflected in the higher exothermicity (ΔΔH = 16 kcal/mol) of the Fe-nitrene formation step. The "imido-like" character renders a relatively lower spin population on the nitrene nitrogen (+0.42) in the Fe-nitrene complex I1Fe, which undergoes the nitrene transfer to the C═C bond of styrene with a considerably higher enthalpy barrier (ΔH‡ = 10.0 kcal/mol) compared to the Co congener I1Co (ΔH‡ = 5.6 kcal/mol) possessing a higher nitrogen spin population (+0.88) and a relatively weaker M-N bond (Co-N = 1.80 Å).

Quadripartite bond length rule applied to two prototypical aromatic and antiaromatic molecules

ContextIn 2000, a remarkably simple relationship was introduced, which connected the calculated geometries of isomolecular states of three different multiplicities. These encompass a ground single state, the first excited triplet state, as well as related radical anion and radical cation. The rule allows the prediction of the geometry of one of the species if the three remaining ones are known. Here, we verify the applicability of this bond length rule for two small planar cyclic organic molecules, i.e., benzene and cyclobutadiene, which stand as prototypical examples of, respectively, aromatic and antiaromatic systems. We see that the rule works fairly well to benzene, and it works independently for quinoid as well as for anti-quinoid minima, despite the fact that radical anion species poses challenges for correct theoretical description.MethodsTo obtain chosen electronic state equilibrium geometries, three types of computational approaches were utilized: fast and efficient density functional theory DFT, the coupled cluster method CC2, the complete active space self-consistent field (CASSCF) approach, and the most accurate but also resource-consuming perturbation theory with multireference wavefunction (CASPT2) with a default value and without IPEA-shift. Dunning and co-workers correlation-consistent basis sets (aug-)cc-pVXZ (X = D, T, Q) were employed. Gaussian 16 revision A.03, Turbomole 7.1, and Molcas 8.0 computational software were used.

An exotic 3-center/4-electron carbon–carbon pi long-bond: Is it tangible?

Centrosymmetric species with AB2 boding motif where central atom (A) is relatively more electronegative than the end ligands (B atoms) have been predicted to exhibit an unusual form of three-center/four-electron (3c/4e) long-bonding where bonding/antibonding interactions occur between the two end ligands (B–B) bypassing the central atom albeit via sharing the latter’s lone pair. Such a long-bond of sigma- and pi-type has so far been predicted as single bonds and mainly as linear (B–A–B) bonding motifs. This work, through computations based on density-functional theory (DFT) and natural bond orbital (NBO) analysis, reveals pi-type long-bonding between carbon atoms separated by more than 2 angstroms in the gas-phase chain species, namely CnX (X = O,N; n = 2,4,6,8). Notably, this work, through DFT and NBO analysis, not only successfully predicts pi-type long-bonding in linear and nonlinear CnX species (mainly those where X is the central atom) but is also able to reveal multiple pi long-bonds particularly in the triplet-C2O as well as a pi long-bond in an isomer of C8N where N is not the central atom. However, preliminary computations using complete active space self-consistent field (CASSCF) multi-reference method performed in this work could only confirm antibonding pi long-bond orbital, whereas the validity of bonding pi long-bond orbital of the proposed long-bond could not be ascertained through the CASSCF.

Proton Reaction Path in Base Pairs of DNA Molecule According to the Complete Active Space Self-Consistent Field Method

The double proton transfer reaction paths in AT and CG base pairs of DNA molecule are calculated in the Complete Active Space Self-Consistent Field method and compared with the same paths in Density Functional Theory with B3LYP approximation approach. We found that an essential increase of an activation energy, which significantly reduces the probability of spontaneous mutations in DNA via double proton transfer. There exist two transition points on the singlet potential energy surface divided by a flat region for GC base pair. The applicability of various quantum-chemical methods for description of double proton transfer reactions was discussed.

Static and Dynamic Magnetic Properties of a Co(II)‐Complex with N2O2Donor Set – A Theoretical and Experimental Study

AbstractA representative Co(II) based single ion magnet (SIM) with N2O2donor set and distorted pseudo‐tetrahedral geometry has been synthesized and characterized to study the atomic and electronic structure. DC magnetometry results have been evaluated by means of a phenomenological Hamiltonian approach regarding zero field splitting (ZFS) parameters and compared with results from ab‐initio multi‐reference CASSCF (complete active space self‐consistent field) calculations and qualitative ligand field theory (AILFT). Profound investigation of spin‐lattice relaxation with the variation of temperature (from 1.8 to about 8 K) and magnetic field (at 14 different fields from zero up to 1 T) have been performed based on AC magnetometry. Under an applied dc magnetic field, spin‐lattice relaxation occurs via a direct process withT2temperature dependence due to limited heat transfer at very low temperature and above 5 K relaxation by an Orbach process with an energy barrier of≈80 K dominates.

Mechanism of Hydroboration of CO2 Using an Fe Catalyst: What Controls the Reactivity and Product Selectivity?

Using a combination of density functional theory (DFT) and ab initio complete active space self-consistent field (CASSCF) calculations, various elementary steps in the mechanism of the reductive hydroboration of CO2 to two-electron-reduced boryl formate, four-electron-reduced bis(boryl)acetal, and six-electron-reduced methoxy borane by the [Fe(H)2(dmpe)2] catalyst were established. The replacement of hydride by oxygen ligation after the boryl formate insertion step is the rate-determining step. Our work unveils, for the first time, (i) how a substrate steers product selectivity in this reaction and (ii) the importance of configurational mixing in contracting the kinetic barrier heights. Based on the reaction mechanism established, we have further focused on the effect of other metals, such as Mn and Co, on rate-determining steps and on catalyst regeneration.

Toward more accurate adiabatic connection approach for multireference wavefunctions.

A multiconfigurational adiabatic connection (AC) formalism is an attractive approach to compute the dynamic correlation within the complete active space self-consistent field and density matrix renormalization group (DMRG) models. Practical realizations of AC have been based on two approximations: (i) fixing one- and two-electron reduced density matrices (1- and 2-RDMs) at the zero-coupling constant limit and (ii) extended random phase approximation (ERPA). This work investigates the effect of removing the "fixed-RDM" approximation in AC. The analysis is carried out for two electronic Hamiltonian partitionings: the group product function- and the Dyall Hamiltonians. Exact reference AC integrands are generated from the DMRG full configuration interaction solver. Two AC models are investigated, employing either exact 1- and 2-RDMs or their second-order expansions in the coupling constant in the ERPA equations. Calculations for model molecules indicate that lifting the fixed-RDM approximation is a viable way toward improving the accuracy of existing AC approximations.

Intermolecular-Type Conical Intersections in Benzene Dimer.

The equilibrium and conical intersection geometries of the benzene dimer were computed in the framework of the conventional, linear-response time-dependent and spin-flipped time-dependent density functional theories (known as DFT, TDDFT and SF-TDDFT) as well as using the multiconfigurational complete active space self-consistent field (CASSCF) method considering the minimally augmented def2-TZVPP and the 6-31G(d,p) basis sets. It was found that the stacking distance between the benzene monomers decreases by about 0.5 Å in the first electronic excited state, due to the stronger intermolecular interaction energy, bringing the two monomers closer together. Intermolecular-type conical intersection (CI) geometries can be formed between the two benzene molecules, when (i) both monomer rings show planar deformation and (ii) weaker (approximately 1.6-1.8 Å long) C-C bonds are formed between the two monomers, with parallel and antiparallel orientation with respect to the monomer. These intermolecular-type CIs look energetically more favorable than dimeric CIs containing only one deformed monomer. The validity of the dimer-type CI geometries obtained by SF-TDDFT was confirmed by the CASSCF method. The nudged elastic band method used for finding the optimal relaxation path has confirmed both the accessibility of these intermolecular-type CIs and the possibility of the radiationless deactivation of the electronic excited states through these CI geometries. Although not as energetically favorable as the previous two CI geometries, there are other CI geometries characterized by the relative rotation of monomers at different angles around a vertical C-C axis.

Isolation of an Annulated 1,4-Distibabenzene Diradicaloid.

The first 1,4-distibabenzene-1,4-diide compound [(ADC)Sb]2 (5) based on an anionic dicarbene (ADC) (ADC=PhC{N(Dipp)C}2 , Dipp=2,6-iPr2 C6 H3 ) is reported as a bordeaux-red solid. Compound 5, featuring a central six-membered C4 Sb2 ring with formally SbI atoms may be regarded as a base-stabilized cyclic bis-stibinidene in which each of the Sb atoms bears two lone-pairs of electrons. 5 undergoes 2 e-oxidation with Ph3 C[B(C6 F5 )4 ] to afford [(ADC)Sb]2 [B(C6 F5 )4 ]2 (6) as a brick-red solid. Each of the Sb atoms of 6 has an unpaired electron and a lone-pair. The broken-symmetry open-shell singlet diradical solution for (6)2+ is calculated to be 2.13 kcal mol-1 more stable than the closed-shell singlet. The diradical character of (6)2+ according to SS-CASSCF (state-specific complete active space self-consistent field) and UHF (unrestricted Hartree-Fock) methods amounts to 36 % and 39 %, respectively. Treatments of 6 with (PhE)2 yield [(ADC)Sb(EPh)]2 [B(C6 F5 )4 ]2 (7-E) (E=S or Se). Reaction of 5 with (cod)Mo(CO)4 affords [(ADC)Sb]2 Mo(CO)4 (8).

A Theoretical Account of the Coupling between Metal- and Ligand-centred Spins.

This study addresses the magnetic interaction between paramagnetic metal ions and the radical ligands taking the [CuII (hfac)2 (imVDZ)] and [MII (hfac)2 (pyDTDA)] (imVDZ=1,5-dimethyl-3-(1-methyl-2-imidazolyl)-6-oxoverdazyl; hfac=(1,1,1,5,5,5)hexafluroacetylacetonate; pyDTDA=4-(2'-pyridyl)-1,2,3,5-dithiadiazolyl), (M=Cu, Ni, Co, Fe, Mn) compounds as reference systems. The coupling between the metal and ligand spins is quantified in terms of the exchange coupling constant (J) in the platform of density functional theory (DFT) and the wave function-based complete active space self-consistent field (CASSCF) method. Application of DFT and broken symmetry (BS) formalism results ferromagnetic coupling for all the transition metal complexes except the Mn(II) complex. This DFT-BS prediction of magnetic nature matches with the experimental finding for all the complexes other than the Fe(II)-pyDTDA complex, for which an antiferromagnetic coupling between high spin iron and the thiazyl ligand has been reported. However, evaluation of spin state energetics through the multiconfigurational wave function-based method produces the S=3/2 ground spin state for the iron-thiazyl in parity with experiment. Electronic structure analyses find the overlap between the metal- and ligand-based singly occupied molecular orbitals (SOMOs) to be one of the major reasons attributing to different extent of exchange coupling in the systems under investigation.

Does the Spin State and Oriented External Electric Field Boost the Efficiency of Fe(II) Pincer Catalyst toward CO2Hydrogenation Reaction?

In this study, we have explored the catalytic reactivities of four PNP-pincer supported Fe(II) complexes, namely, [(iPrPNMeP)FeH2(CO)] (1), [(iPrPNMeP)FeH(CO)(BH4)] (2), [(iPrPNHP)FeH2(CO)] (3), and [(iPrPNMeP)FeH(BH4)] (4) (iPrPNMeP = MeN{CH2CH2(PiPr2)}2 and iPrPNHP = HN{CH2CH2(PiPr2)}2) toward reductive CO2 hydrogenation for formate production. Our density functional theory and ab initio complete active space self-consistent field study have identified three fundamental steps in this catalytic transformation: (i) anchoring of the CO2 molecule in the vicinity of the metal using noncovalent interactions, (ii) catalyst regeneration via H2 cleavage, and (iii) formate rebound step leading to catalytic poisoning. The variations in the catalytic efficiency observed among these catalysts were attributed to either easing of steps (i) and (ii) or the hampering step (iii). This can be achieved in various chemical/non-chemical ways, for instance, (a) incorporation of strong-field ligands such as CO facilitating single-state reactivity and eliminating two-state reactivity that generally enhances the rate and (b) inclusion of Lewis acids such as LiOTf and strong bases found to either avoid catalytic poisoning or ease the H-H cleavages, to enhance the rate of reaction (c) evading mixing of excited open-shell singlet states to the ground closed-shell singlet state that hampers the catalytic regeneration. We have probed the role of oriented external electric fields (OEEFs) in the entire mechanistic profile for the best and worst catalyst, and our study suggests that imposing OEEFs opposite to the reaction axis (z-axis) fastens the catalytic regeneration step and, at the same time, hampers catalytic poisoning. The application of OEEFs is found to regulate the energetics of various spin states and can hamper two-state reactivity, therefore increasing the efficiency. Thus, this study provides insights into the CO2 hydrogenation mechanism where the role of bases/Lewis acid, ligand design, spin states, and electric field in a particular direction has been established and is, therefore, likely to pave the way forward for a new generation of catalysts.

Excited state calculations using variational quantum eigensolver with spin-restricted ansätze and automatically-adjusted constraints

The ground and excited state calculations at key geometries, such as the Frank–Condon (FC) and the conical intersection (CI) geometries, are essential for understanding photophysical properties. To compute these geometries on noisy intermediate-scale quantum devices, we proposed a strategy that combined a chemistry-inspired spin-restricted ansatz and a new excited state calculation method called the variational quantum eigensolver under automatically-adjusted constraints (VQE/AC). Unlike the conventional excited state calculation method, called the variational quantum deflation, the VQE/AC does not require the pre-determination of constraint weights and has the potential to describe smooth potential energy surfaces. To validate this strategy, we performed the excited state calculations at the FC and CI geometries of ethylene and phenol blue at the complete active space self-consistent field (CASSCF) level of theory, and found that the energy errors were at most 2 kcal mol−1 even on the ibm_kawasaki device.

Ab Initio Investigation of the Na3[Ln(ODA)3]·2NaClO4·6H2O (Ln = Ce-Yb; ODA = Oxydiacetate) Series.

In this work, the Na3[Ln(ODA)3]·2NaClO4·6H2O (Ln = Ce-Yb; ODA = oxydiacetate) series was analyzed with the ab initio ligand field theory (AILFT) module of the ORCA computational suite. The results were discussed within the framework of the angular overlap model (AOM) and compared to literature data. We find that the structural changes observed across the series exemplifies the effects of the lanthanide contraction also manifesting in the value of the AOM parameters. It is also shown that the complete active space self-consistent field (CASSCF) methodology is sufficient to describe the ligand field interactions in mononuclear lanthanide complexes, and the effects of dynamic correlation, through n-electron valence state perturbation theory (NEVPT2), are discussed. The calculated ligand field parameters of the present work are compared to the experimentally derived values from the literature.

State averaged CASSCF in AMOEBA polarizable water model for simulating nonadiabatic molecular dynamics with nonequilibrium solvation effects.

This paper presents a state-averaged complete active space self-consistent field (SA-CASSCF) in the atomic multipole optimized energetics for biomolecular application (AMOEBA) polarizable water model, which enables rigorous simulation of non-adiabatic molecular dynamics with nonequilibrium solvation effects. The molecular orbital and configuration interaction coefficients of the solute wavefunction, and the induced dipoles on solvent atoms, are solved by minimizing the state averaged energy variationally. In particular, by formulating AMOEBA water models and the polarizable continuum model (PCM) in a unified way, the algorithms developed for computing SA-CASSCF/PCM energies, analytical gradients, and non-adiabatic couplings in our previous work can be generalized to SA-CASSCF/AMOEBA by properly substituting a specific list of variables. Implementation of this method will be discussed with the emphasis on how the calculations of different terms are partitioned between the quantum chemistry and molecular mechanics codes. We will present and discuss results that demonstrate the accuracy and performance of the implementation. Next, we will discuss results that compare three solvent models that work with SA-CASSCF, i.e., PCM, fixed-charge force fields, and the newly implemented AMOEBA. Finally, the new SA-CASSCF/AMOEBA method has been interfaced with the ab initio multiple spawning method to carry out non-adiabatic molecular dynamics simulations. This method is demonstrated by simulating the photodynamics of the model retinal protonated Schiff base molecule in water.

The ionic and ground states of gamma-pyrone. The photoionization spectrum studied by synchrotron radiation and interpreted by configuration interaction and density functional calculations.

A synchrotron-based photoionization spectrum up to 27eV represents a considerable improvement in resolution over early He(I) and He(II) spectra. Symmetry-adapted coupled cluster calculations of the ionic state sequence give the sequence of state vertical ionization energies (VIE) as 12B2 < 12B1 < 12A2 < 22B1 < 12A1. Generally, these symmetry-adapted cluster configuration interactions VIE match reasonably well with the experimental spectrum over this wide energy range. Density functional calculations of the corresponding adiabatic terms (AIE) were also performed. Higher energy ionic states were determined by complete active space self-consistent field methods; these include all π-ionizations and some σ-ionic states. These were analyzed by Franck-Condon (FC) procedures and compared with an experiment. The spectral onset is complex, where two states, later shown to be the 12B2 and 12B1 states, are strongly overlapping. The superposition of the FC vibrational structure in the 12B2 and 12B1 states accounts for most of the peaks arising at the onset of the photoelectron spectra. However, the small separation between these two ionic states makes vibronic interaction fairly inevitable. In the absence of Herzberg-Teller analyses for ionic states, we have sought and determined a transition state between the 12B2 and 12B1 states, showing that vibronic coupling does occur. The lack of degradation in the vibrational envelope of the higher of the two states contrasts with our previous work on the halogenobenzenes, where overlapping state envelopes led to considerable widening of the line width at half-height of the higher energy states.

Multireference Wavefunction-Based Investigation of the Ground and Excited States of LrF and LrO.

Complete active space self-consistent field (CASSCF) and multireference configuration interaction with Davidson correction (MRCI+Q) calculations have been carried out for lawrencium fluoride (LrF) and lawrencium oxide (LrO) molecules, detailing 19 and 20 electronic states for LrF and LrO, respectively. For LrF, two dissociation channels were considered, Lr(2P)+F(2P) and Lr(2D)+F(2P). However, due to the more complex electronic manifold of LrO, three dissociation channels were computed: Lr(2P)+O(3P), Lr(2D)+O(3P), and Lr(2P)+O(1D). In addition, equilibrium bond lengths, harmonic vibrational frequencies ωe, anharmonicity constants ωeχe, ΔG1/2 values, and excitation energies Te for the ground and several excited electronic states were calculated for both molecules, for the first time. Bond dissociation energies (BDEs) were calculated for LrF and LrO using several different levels of theory: unrestricted coupled-cluster with single, double, and perturbative triple excitations (UCCSD(T)), density functional theory (B3LYP, TPSS, M06-L, and PBE), and the correlation-consistent composite approach developed for f-elements (f-ccCA).

One Bridge, Three Bonds: A Frontier in Multiple Bonding in Heterobimetallic Complexes

A single bridging phosphinoamide ligand was shown to support a metal-metal triple bond in a Zr/Co heterobimetallic complex. The similarity of the bonding in this compound to previously synthesized Zr/Co species, and therefore the assignment of the Zr/Co triple bond, is supported by the structural parameters of the complex, the electronic structure predicted by density functional theory, and complete-active-space self-consistent-field (CASSCF) calculations. This demonstrates that metal-metal multiple bonds can be realized in heterobimetallic complexes without multiple bridging ligands to enforce the proximity of the two metals.

Tweezer-like magnetic tip control of the local spin state in the FeOEP/Pb(111) adsorption system: a preliminary exploration based on first-principles calculations.

The magnetic interactions between the spin-polarized scanning tunnelling microscopy (SP-STM) tip and the localized spin impurities lead to various forms of the Kondo effect. Although these intriguing phenomena enrich Kondo physics, detailed theoretical simulations and explanations are still lacking due to the rather complex formation mechanisms. Here, by combining density functional theory (DFT), complete active space self-consistent field (CASSCF) theory, and hierarchical equations of motion (HEOM) methods, we perform first-principles-based simulation to elaborate the regulation process of the magnetic Co-tip on the spin state and transport behaviour of FeOEP/Pb(111) system. Compared with the non-magnetic tip, the stronger interaction between the magnetic tip and FeOEP molecule results in a more drastic deformation of the molecular structure with more electron transfer from the local environment to Fe-3d orbitals. The magnetic anisotropy of FeOEP changes very drastically from positive values in the tunnelling region to negative values in the contact region. The ferromagnetic electron correlation between the magnetic tip and the molecule induces an asymmetric Kondo line-shape near the Fermi level. This work highlights that the DFT + CASSCF + HEOM approach can not only predict complex quantum phenomena and explain underlying physical mechanisms, but also facilitate the design of more fascinating quantum control experiments.

How does multi-reference computation change the catalysis chemistry? DFT and CASPT2 studies of the Cu-catalysed coupling reactions between aryl iodides and β-diketones.

The molecular mechanism of a Cu-catalysed coupling reaction was theoretically studied using density functional theory (DFT) and the complete active space self-consistent field method followed by the second-order perturbation theory (CASSCF/CASPT2) to investigate the effects of the strong electron correlation of the Cu centre on the reaction profile. Both DFT and CASSCF/CASPT2 calculations showed that the catalytic cycle proceeds via an oxidative addition (OA) reaction, followed by a reductive elimination (RE) reaction, where OA is the rate-determining step. Although the DFT-calculated activation energies of the OA and RE steps are highly dependent on the choice of functionals, the CASSCF/CASPT2 results are less affected by the choice of DFT-optimised geometries. Therefore, with a careful assessment based on the CASSCF/CASPT2 single-point energy evaluation, an optimal choice of the DFT geometry is of good qualitative use for energetics at the CASPT2 level of theory. Based on the changes in the electron populations of the 3d orbitals during the OA and RE steps, the characteristic features of the DFT-calculated electronic structure were qualitatively consistent with those calculated using the CASSCF method. Further electronic structure analysis by the natural orbital occupancy of the CASSCF wavefunction showed that the ground state is almost single-reference in this system and the strong electron correlation effect of the Cu centre can be dealt with using the MP2 or CCSD method, too. However, the slightly smaller occupation numbers of the 3dπ orbital in the course of reactions suggested that the electron correlation effect of the Cu(III) centre appears through the interaction between the 3dπ orbital and the C-I antibonding σ* orbital in the OA step, and between the 3dπ orbital and the Cu-C antibonding σ* orbital in the RE step.