An Electronic Structural Analysis of O₂-Binding Dicopper Complex: Insights from Spin Magnetism and Molecular Orbitals

Abstract

We investigated the geometry and electronic structure of the oxygen-bridged dicopper complex [Cu^II₂(NH₃)₄O₂]²⁺ and discussed how different DFT methods and basis sets, including dispersion corrections and dielectric media, affect the predicted structure and spin state. Our results showed that pure functionals yielded the closed-shell singlet character, whereas hybrid functionals presented a partial diradical character that coincided with increased spin contamination. Incorporating a polarizable continuum model further enhanced the diradical character and more closely reproduced the measured Cu–Cu distance with a bent Cu₂O₂ core. Analysis of the molecular orbitals and computed absorption spectra revealed how orbitals produce the key transition from ligand-to-metal charge transfer. These findings underscore how environmental effects influence the description of Cu₂O₂ chemistry.

1. Introduction

Dicopper–dioxygen (Cu₂O₂) complexes are versatile catalysts in various chemical reactions. A prominent example is found in the protein oxyhemocyanin (OxyHc), where two copper ions reversibly bind O₂ and play a pivotal role in biological oxygen transport [1,2]. In OxyHc, two Cu atoms are bridged by a peroxo ligand (μ-η²:η²) to create a [Cu₂O₂]²⁺ center (side-on) [3,4]. Another example is copper-exchanged chabazite (Cu-CHA), a zeolite-based material employed in the selective catalytic reduction of NO_x with ammonia (NH₃-SCR) [5,6]. Recent studies have identified a μ-η²:η²-peroxo diamino dicopper(II) ([Cu^II₂O₂]²⁺; Figure 1) within Cu-CHA during NH₃-SCR [7], featuring the [Cu₂O₂]²⁺ core coordinated by four ammonia ligands—an arrangement similar to that of OxyHc.

In both OxyHc and Cu-CHA, each Cu atom formally carries a +2 oxidation state with a d⁹ electron configuration. Each of the two Cu sites have an unpaired spin, and these spins are antiferromagnetically coupled through the bridging O₂ ligand, resulting in an overall singlet state verified by the absence of EPR signals [8]. This interaction between two Cu atoms across O₂ ligand is often explained as superexchange mechanism, involving a spin crossover from a triplet to a singlet upon O₂ binding [9]. It is known that to describe such complicated electronic states, it is necessary to incorporate both static and dynamic electron correlations appropriately.

Beyond the complexity of the ground-state electronic structure, the side-on complex [Cu^II₂(NH₃)₄O₂]²⁺ and its bis(μ-oxo) isomer [Cu^III₂(NH₃)₄O₂]²⁺ draw attention due to their close energetic proximity and a small isomerization barrier [10,11,12,13]. Capturing this delicate balance in calculations is challenging and often serves as a benchmark for theoretical methods. Accordingly, numerous computational studies have been performed using density functional theory (DFT) with a range of pure and hybrid functionals [9,14,15,16,17,18,19], as well as molecular orbital (MO) theory, such as the projected Hartree–Fock (HF) method [20], the Møller–Plesset second-order perturbation theory (MP2) [14], the coupled-cluster (CC) method [14,19], and multireference approaches (CASSCF, DMRG-CASPT2, etc.) [21,22,23,24,25,26,27,28,29]. Most of these studies have focused on reproducing isomerization energies. For example, Liakos and Nesse systematically investigated the potential energy profile between the side-on complex and bis(μ-oxo) isomer using CC and DFT methods in conjunction with the relativistic correction and implicit solvent model [19]. It was found that both the relativistic and solvent effects stabilized the bis(μ-oxo) isomer. In addition, among density functionals tested, B3LYP hybrid functional with dispersion corrections best reproduced the high-level LPNO-CCSD results, though quantitative agreement was not obtained. The reaction mechanism of NH₃-SCR in Cu-CHA has been investigated using pure functions such as PBE, mainly due to the requirement to keep computational costs low for periodic systems [30,31,32,33], and further careful verification is needed. Although the high-level MO theory should, in principle, be used to analyze the reaction mechanism, the high computational cost prohibits large-scale reaction path analysis. A method capturing the electronic and spin structures of side-on complex with relatively low computational cost is desirable.

In this work, we employ DFT to calibrate the computational level for the side-on complex—assessing geometry, spin configurations, and spectral properties—to seek a desired computational condition. In addition, the environmental effect surrounding the side-on complex is investigated using PCM. We intend to deepen the understanding of Cu₂O₂-based catalysis by studying electronic structure of the side-on complex.

2. Methods

Electronic structure calculations of the side-on complex were performed using Gaussian 16 [34]. After geometry optimizations, frequency calculations were also performed to verify that the optimized geometries are stationary points. All calculations were performed using the unrestricted broken-symmetry (BS) description. We employed two pure functionals (BLYP [35,36] and PBE [37]) and eight hybrid functionals: TPSSh [38], B3LYP [39], HSE06 [40], PBE0 [41], B(38HF)P86 [42], B(38HF)LYP [43], BHandHLYP [44], and M06-HF [45,46], incorporating HF exchange 10% (TPSSh), 20% (B3LYP), 20% (HSE06), 25% (PBE0), 38% (B(38HF)P86), 38% (B(38HF)LYP), 50% (BHandHLYP), and 100% (M06-HF), respectively. The electronic structures were treated as singlet states, and the wave functions were optimized with options (stable = opt).

Thirteen different basis sets were examined. Among them, only the BLYP and B3LYP results with def2-TZVP and those with the combination of 6-31G(d) for H, N, O atoms and s6-31G* [47] for Cu atoms (simply referred to as s6-31G*) are shown in the main text. Results obtained with the other functionals and basis sets are provided in the Supporting Information (Table S1). The effect of dispersion corrections was considered using Grimme’s D3(BJ) version [48]. The UV–vis spectra were calculated with the time-dependent DFT (TD-DFT) method considering the lowest 30 excited states. CAM-B3LYP [49], as well as B3LYP functionals, were employed for TD-DFT calculations. The orbital compositions were analyzed using the natural atomic orbital (NAO) approach [50]. The NAOs matrix was generated by converting natural bond orbital (NBO) obtained by the NBO 7.0 program package [51]. The PCM was also applied to consider the effects of the zeolites framework, in which the dielectric constant was set to the value of CHA (2.85) [52]. It was noted that the relativistic effects change the energy difference between the side-on complex and bis(μ-oxo) isomer [19]. However, our preliminary calculations showed no significant changes in the electronic properties of the side-on complex, such as the spin-coupling constant and absorption spectra. Therefore, the relativistic effects were not considered for simplicity in this study.

The spin-coupling constant $-2J$ was calculated using the approximate spin projection method introduced by Yamaguchi et al. [53,54]. Assuming negligible spin contamination in the high-spin (HS) state, the effective exchange integral $J$ is given by

$$J={\displaystyle \frac{E^{BS}-E^{HS}}{{〈{\widehat{S}}^2〉}^{HS}-{〈{\widehat{S}}^2〉}^{BS}}}$$

where $E^{BS}$ and $E^{HS}$ are the total energy of BS singlet (S₀) and HS triplet (T₁) states, respectively, and ${〈{\widehat{S}}^2〉}^{HS}$ and ${〈{\widehat{S}}^2〉}^{BS}$ are their corresponding total spin expectation value. Natural orbitals were calculated to evaluate the spin projected diradical character $y$ from the occupation numbers of HONO and LUNO, where HONO denotes the highest occupied natural orbital and LUNO the lowest unoccupied natural orbital [53,54]. In this scheme, $y=0$ corresponds to a closed-shell system, whereas $y=1$ represents a pure diradical. The approximate spin projection approach was incorporated to remove the spin contamination effects from spin-unrestricted single-determinant methods [54].

3. Results and Discussion

3.1. Geometry

In the first step, we compared the optimized structures of the side-on complex obtained by various computational methods.

Table 1. Optimized structure.

Model	Symmetry	rO-O (Å)	rCu-Cu (Å)	rCu-O (Å)	∠Cu-O-O-Cu (°)
UBLYP/def2-TZVP	D2	1.47	3.64	1.96	180.0
UBLYP/s6-31G*	D2	1.49	3.61	1.95	180.0
UB3LYP/def2-TZVP	D2	1.46	3.59	1.94	180.0
UB3LYP/s6-31G*	C2	1.46	3.58	1.94	169.6
UBLYP-D3(BJ)/def2-TZVP	D2	1.48	3.62	1.95	180.0
UB3LYP-D3(BJ)/def2-TZVP	D2	1.45	3.59	1.94	180.0
UB3LYP-D3(BJ)/s6-31G*	C2	1.46	3.57	1.93	171.9
PCM-UBLYP/def2-TZVP	D2	1.48	3.62	1.95	180.0
PCM-UB3LYP/def2-TZVP	C2	1.45	3.52	1.95	153.5
PCM-UB3LYP/s6-31G*	C2	1.46	3.55	1.94	161.8
PCM-UBLYP-D3(BJ)/def2-TZVP	C2	1.49	3.60	1.94	180.0
PCM-UBLYP-D3(BJ)/s6-31G*	C2	1.51	3.57	1.93	180.0
PCM-UB3LYP-D3(BJ)/def2-TZVP	C2	1.45	3.50	1.94	151.4
PCM-UB3LYP-D3(BJ)/s6-31G*	C2	1.46	3.41	1.94	141.3
Expt. [7]			3.40 ± 0.05	1.911 ± 0.009

summarizes the symmetries, bond lengths (rO-O, rCu-Cu, rCu-O), and dihedral angles (∠Cu-O-O-Cu) of the optimized structures. Results obtained with other functionals are provided in Table S2. UBLYP/def2-TZVP, UBLYP/s6-31G*, and UB3LYP/def2-TZVP yielded a planar Cu₂O₂ core, as evidenced by the ∠Cu-O-O-Cu of 180°. Although structural optimizations were initiated from D_2h symmetry, the final symmetries were D₂ because of the rotation of the NH₃ ligands. By contrast, UB3LYP/s6-31G* yielded a “butterfly” (nonplanar) structure, with ∠Cu-O-O-Cu = 169.6° and C₂ symmetry.

When D3(BJ) was introduced for UBLYP/def2-TZVP and UB3LYP/def2-TZVP, the planar geometry persisted. Even after introducing PCM, the planar structure was maintained in UBLYP/def2-TZVP: The bond lengths showed only modest changes (e.g., up to 0.02 Å in O-O and Cu-O), and the Cu–Cu distance was slightly lengthened up to 0.09 Å. In contrast, PCM-UB3LYP/def2-TZVP and PCM-UB3LYP/s6-31G* converged to butterfly structures, with PCM-UB3LYP/s6-31G* showing an even more pronounced bend than UB3LYP/s6-31G*. Thus, while dispersion corrections alone did not significantly alter the geometry, the presence of PCM favored a bent Cu₂O₂ core. The calculated geometries were compared with experimental data in a zeolite framework [7]. The computed Cu–Cu distances deviated by about 0.01–0.24 Å, and it became closer to the experimental value when PCM was applied. Namely, the results of PCM-UB3LYP-D3(BJ)/s6-31G* were in best agreement with the experimental values. It should be mentioned that, besides the butterfly C₂ structure mentioned above, a planer (D₂) structure was also obtained when using PCM-UB3LYP-D3(BJ)/s6-31G*, but it was 4.9 kJ/mol less stable (Table S3). Solomon et al. reported that the butterfly was less stable compared to its planar counterpart without applying PCM [9]. Although they employed a different condition (UB3LYP/LanL2DZ), the effect from the dielectric environment was crucial in the determination of the stable structure. The bending by PCM may be explained by considering the interaction between the two copper atoms. The electrostatic repulsion between them was weakened in the planar configuration. In PCM, the dipole moment of the complex can contribute to stabilization through interaction with the surrounding media. As shown in Table S3, the butterfly Cu₂O₂ was more stabilized because of the larger dipole moments.

3.2. Spin Structure

Table 2. $⟨S^2⟩$ values and spin-coupling constants.

Model	⟨S2⟩		−2J (cm−1)
	S0	T1
UBLYP/def2-TZVP	0.00	2.00	7850
UBLYP/s6-31G*	0.00	2.00	8043
UB3LYP/def2-TZVP	0.54	2.01	5863
UB3LYP/s6-31G*	0.55	2.01	6096
UB3LYP-D3(BJ)/s6-31G*	0.53	2.01	6686
PCM-UB3LYP/s6-31G*	0.63	2.01	5099
PCM-UBLYP-D3(BJ)/def2-TZVP	0.00	2.00	8736
PCM-UBLYP-D3(BJ)/s6-31G*	0.00	2.00	8942
PCM-UB3LYP-D3(BJ)/def2-TZVP	0.74	2.01	2379
PCM-UB3LYP-D3(BJ)/s6-31G*	0.81	2.01	1373
VBCI [24]			2250
CASSCF(12e, 8o) [56]			832
CASSCF(14e, 12o) [57]			1148
CASPT2(12e, 14o) [21]			4288
Expt. [55,58]			≥600

presents $⟨S^2⟩$ values, and spin-coupling constants $-2J$ computed using various approaches. In both cases with and without PCM, UBLYP yielded $⟨S^2⟩=0$ in S₀ states and $⟨S^2⟩=2$ in T₁. In contrast, the results using UB3LYP resulted $⟨S^2⟩\ne 0$ for S₀ and $⟨S^2⟩\ne 2$ for T₁. Table S4 also shows that other pure functionals yielded $⟨S^2⟩=0$ and hybrid functionals yielded $⟨S^2⟩\ne 0$ in S₀ states. These results indicate that the degree of spin contamination was higher in hybrid functionals than in pure functionals. Regardless of whether PCM was applied or not, $-2J$ was larger in UBLYP than in UB3LYP. The spin contamination may have been enhanced because the S₀ and T₁ states were energetically closer in UB3LYP. Due to the limitation of magnetometer, only the lower limit of $-2J$ was determined experimentally [55]. Therefore, the calculated results were compared with other computational studies. The spin-coupling constants computed by UBLYP were larger than a previously reported CASPT2 result [21], whereas those by UB3LYP were comparable. The spin-coupling constant decreased under PCM, which was consistent with the further increase $⟨S^2⟩$.

UBLYP and other pure functionals yielded zero-spin density on Cu atoms (Table S4), whereas UB3LYP and other hybrid functionals gave non-zero-spin densities on both Cu atoms. Note that because the D3(BJ) correction did not affect the electronic structure significantly, the essential differences were attributed to the functional, basis set and the surrounding effect from PCM. As illustrated in Figure 2, the spin density calculated by UB3LYP was delocalized across the Cu₂O₂ core.

By introducing PCM, the spin density was slightly enhanced with both def2-TZVP and s6-31G* basis sets. The Mulliken spin density on each Cu atom increased by ~0.03 relative to the results without PCM (Table S4), and the $⟨S^2⟩$ value rose by 0.20. The increase can be attributed to structural change, namely the spin became more localized on each Cu center when the planar structure transformed into a butterfly-like geometry. A recent study also reported that even in butterfly-like cores with fluctuating spin states, the singlet character can be maximized [59]. It has been argued the significance of the steric effects from ligands such as imidazole [21,59] in the OxyHc, which could be the reason to form the butterfly geometry. However, even the simplified model complex used in this study—lacking such ligand environments—still bent into a butterfly geometry under PCM conditions, thereby stabilizing the antiferromagnetic state.

3.3. Electronic Structure

Table 3. Diradical character y.

Model	y
UBLYP/def2-TZVP	0.00
UB3LYP/def2-TZVP	0.07
UB3LYP/s6-31G*	0.07
PCM-UBLYP-D3(BJ)/def2-TZVP	0.00
PCM-UB3LYP-D3(BJ)/def2-TZVP	0.18
PCM-UB3LYP-D3(BJ)/s6-31G*	0.26

shows that UBLYP/def2-TZVP maintained a strictly closed-shell state $y=0$ under both non-PCM and PCM conditions, in line with its zero-spin density on the copper atoms. By contrast, UB3LYP results displayed a partial diradical character ($y=0.07$) even without PCM. When PCM was introduced, the diradical character $y$ grew more pronounced, indicating that the PCM stabilized a localized electronic structure. This result corresponds to the discussion of spin densities described in Section 3.2. Specifically, in the closed-shell singlet state $y=0$, electrons were delocalized throughout the Cu₂O₂ core, whereas in the pure diradical state $y=1$, each Cu atom was considered to host an unpaired electron. Thus, the butterfly Cu₂O₂ core under PCM was accompanied by an increase in diradical character, reflecting greater energetic stabilization of the system.

Figure 3 and

Table 4. The α orbital compositions of selected frontier orbitals of obtained from PCM-UB3LYP-D3(BJ)/s6-31G* calculations. Values of β orbital were the same as that of α orbital with the atom indices swapped.

Orbital	Energy (eV)	Cu1 d (%)	Cu2 d (%)	O1 p (%)	O2 p (%)
LUMO	1.74	1.6	48.1	18.2	18.0
HOMO	−1.74	13.3	1.9	37.2	37.2
HOMO−1	−2.65	13.8	18.5	20.0	20.5
HOMO−2	−3.87	6.5	75.9	4.5	4.5
HOMO−3	−4.01	14.8	62.1	7.6	7.4
HOMO−4	−4.13	16.0	56.1	7.0	6.8

show the isosurface plots of frontier orbitals and their compositions calculated with PCM-UB3LYP-D3(BJ)/s6-31G*. As represented in Figure 3 and Table 4, the HOMO contained d_yz + d_xy and π_ν* characters, as indicated by the 13.3% and 1.9% d orbital composition along with 37.2% p orbital composition. LUMO contained d_xy + d_xy and π_σ* orbitals as indicated in 1.6% and 48.1% d orbital composition and 18.2% and 18.0% p orbital composition, and the overall d orbital composition in LUMO was about 49.7%. This value is in good agreement with the X-ray absorption experimental result, 52 ± 4% d orbital character in the LUMO [60].

The compositions were essentially the same when using a larger basis set def2-TZVP, with only minor differences in the relative orbital energies (see Table S5 for details). Despite having fewer basis functions than def2-TZVP, the s6-31G* basis set adequately described the system’s geometry and electronic structure.

As shown in Figure 3, the HOMO−1 orbital calculated with PCM-UB3LYP-D3(BJ)/s6-31G* exhibited 2Cu²⁺(d_xy − d_xy) + O₂²⁻ π*_σ character. In this orbital, one Cu atom formed a bonding interaction with O₂²⁻ π*_σ orbital, wherein electron density was directed toward Cu center, while the other Cu atom engaged in an antibonding interaction with the same O₂²⁻ π*_σ orbital. As a result, the phases on the two Cu centers in HOMO−1 were reversed. Although HOMO−1 was designated as 2Cu²⁺(d_xy − d_xy) + O₂²⁻π*_σ (with 2p_x contributions of 8.52% at O1 and 7.11% at O2), it also had π*_ν character as indicated by 2p_z contributions of 11.45% at O1 and 11.52% at O2 (Tables S6 and S7). Similar molecular orbital was also reported as HOMO in a previous study calculated using the cluster DMFT method [59]. The detailed discussion, including the effect of PCM, is summarized in Supporting Information (Table S8, Figures S1 and S2).

3.4. Absorption Spectrum

The UV–vis absorption spectra of the side-on complex with butterfly and planar structures were computed using TD-DFT at the PCM-UB3LYP-D3(BJ)/s6-31G* level of theory. Figure 4 shows the calculated spectra. In the butterfly structure, one strong absorption band at 336.7 nm and two weak bands at 426.1 nm and 489.3 nm were exhibited. Oda et al. reported that the side-on complex exhibited an intense band around 350–370 nm in both AEI and CHA zeolite cages [61]. Similarly, OxyHc, which had a structurally analogous [Cu^II₂(NH₃)₄O₂]²⁺, showed a strong absorption at 345 nm. This band was attributed to a π_σ* (π anti-bonding orbital parallel to Cu₂O₂ plane) → d transition and was classified as a ligand to metal charge transfer (LMCT) [62]. OxyHc also presented two weaker bands around 425 nm and 570 nm, assigned to a charge transfer transition from protein ligands to metal and π_ν* (π anti-bonding orbital perpendicular to Cu₂O₂ plane) → d transition, respectively. In the butterfly structure, the present results appear to reproduce the characteristic features of these bands. The intense band at 336.7 nm arose mainly from the transition from HOMO−1 to LUMO, involving the 2Cu²⁺(d_xy − d_xy) + O₂²⁻π*_σ (HOMO−1) to 2Cu²⁺(d_xy + d_xy) − O₂²⁻π*_σ (LUMO) transition. Because HOMO−1 and LUMO were mainly distributed on ligands and Cu atoms, respectively (Table 4), this band could be assigned to an LMCT transition involving π*_σ orbital. The weak band at 426.1 nm was mainly due to the transitions from HOMO−7 to LUMO, involving the 2Cu²⁺(d_xz − d_x2-y2)+ O₂²⁻ π*_ν (HOMO−7) to 2Cu²⁺(d_xy + d_xy) − O₂²⁻π*_σ (LUMO) transition. The weak band at 489.3 nm contained the transition mainly from HOMO−4 and HOMO−2 to LUMO, involving the 2Cu²⁺(d_xz − d_z2)+ O₂²⁻ π_ν (HOMO−2) to 2Cu²⁺(d_xy + d_xy) − O₂²⁻π*_σ (LUMO) transition, which could be viewed as a d-d or an MLCT transition related to π_ν orbital. These assignments of absorption are consistent with previous experiments [62] and multireference calculations [24]. Furthermore, the detailed assignments of these bands are shown in Figure S3. The planar structure exhibited absorption bands at 323.9 nm and 486.7 nm with assignments similar to those of the butterfly structure. However, no absorption was observed near 425 nm in the planar structure. Therefore, the experimental peak around 425 nm was considered to arise from the butterfly structure.

In addition, UV–vis spectra were also computed at the PCM-UCAM-B3LYP-D3(BJ)/s6-31G* level. As shown in Figure S4, the spectra obtained using PCM-UB3LYP-D3(BJ) and PCM-UCAM-B3LYP-D3(BJ) were similar; the differences of spectra between the planar and butterfly structures remained consistent. Additional calculations for the butterfly structure were performed using Tamm–Dancoff approximation (TDA). The spectra with TDA were slightly blue-shifted, but the overall shapes were similar (Figure S5). We also examined the influence of the dispersion corrections on the absorption spectra (Figure S6). The results indicate that the spectra were unaffected by the inclusion of the D3(BJ) corrections.

4. Conclusions

Our calculations revealed that while the peroxo Cu₂O₂ species took a planar geometry, introducing PCM induced a pronounced bending into a “butterfly” configuration. This bent structure aligned more closely with the experimental Cu–Cu distance. Among the computational models tested, PCM-UB3LYP-D3(BJ)/s6-31G* showed the best correspondence with experimental observables regarding geometric and spectroscopic features. Fortunately, as noted in Introduction, B3LYP functional with dispersion corrections also reproduced the energy difference between the side-on complex and bis(μ-oxo) isomer (if the relativistic effects were included) [19]. Comparison between the computed orbitals with and without PCM suggested that the bending promotes the copper–copper superexchange interactions due to π*_σ and π*_ν characters.

Spin analyses showed that pure functionals, such as UBLYP, yielded zero-spin density on Cu atoms, whereas hybrid functionals, such as UB3LYP, promoted spin density. The inclusion of PCM further enhanced the magnitude. Based on the index y, the diradical character was shown to be enhanced by introducing the effect from the dielectric media.

In addition to the inherent complicated electronic structure of the side-on [Cu^II₂(NH₃)₄O₂]²⁺ alone, the environment significantly affected and modulated the electronic and geometrical structure. We believe that this work paves the way for more detailed mechanistic studies involving reactive intermediates and transition states in environments such as Cu-CHA and proteins. A detailed analysis of the reaction mechanism of NH₃-SCR in Cu-CHA using the reliable and cost-effective method found in this study is in progress.