DFT Study of Catalytic Styrene Oxidation Using a Bis-Semicarbazide Hexaazamacrocyclic Cu Complex I—Preliminary Calculations

Martin Breza

doi:10.20944/preprints202506.2108.v1

Submitted:

25 June 2025

Posted:

26 June 2025

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Abstract

The catalytic styrene Ph-CH=CH2 oxidation is assumed to be a simple reaction procedure, but its details require further systematic research. Using quantum-chemical treatment, relevant intermediates in various charge and spin states of three reaction pathways of styrene oxidation by hydroperoxyl were investigated. The reaction pathway A without any catalyst most probably proceeds by non-radical mechanism and 1[Ph-CH(O)-CH2OH]- is formed. The alternative formation of epoxide is energetically less advantageous. The reaction pathways B and C are based on the [CuL]- catalyst where H2L = trans-2,9-dibutyl-7,14-dimethyl-5,12-di(4-methoxyphenyl)-1,2,4,8,9,11-hexaazacyclotetradeca-7,14-diene-3,10-dione. Within reaction pathway B the neutral hydroperoxyl radical is bonded to Cu to form 2[CuL(OOH)]-. Subsequent addition of neutral styrene results in 2{[CuL(OH)](Ph-CH2-CHO)}- formation. The reaction pathway C starts with the initial non-radical formation of the π-complex 1[CuL(Ph-CH=CH2)]- which is problematic due to its endothermic character. Subsequent addition of a hydroperoxyl radical leads to 2{CuL[Ph-CH(OOH)-CH2]}-. Its oxidation leads to the separation of Ph-CH(OOH)-CH2.

Keywords:

B3LYP hybrid functional

;

broken symmetry treatment

;

geometry optimization

;

electronic structure

;

Cu oxidation state

Subject:

Chemistry and Materials Science - Theoretical Chemistry

1. Introduction

The catalytic oxidation of styrene is an environmentally friendly path for the production of benzaldehyde, which is an important intermediate for the production of many fine compounds and commodity chemicals [1]. Various catalysts differ in the conversion and selectivity of benzaldehyde, styrene epoxide, phenylacetaldehyde, 1-phenylethane-1,2-diol, benzoic acid, phenylacetaldehyde and other oxidation products. The development of sustainable and effective catalytic systems for the production of benzaldehyde using green oxidants, such as hydrogen peroxide, is highly significant. For the rational design of efficient catalysts, we must know the corresponding reaction mechanisms. Redox-active ligands can contribute to it by storing and providing electrons, modifying the Lewis acidity of the metal, and assisting the formation/breaking of substrate bonding.

The catalytic styrene oxidation is assumed to be a simple reaction procedure, but its details require further systematic research. Knowledge of its important details is crucial for the development of new catalytic systems. Despite intense studies of the catalyzed oxidation of alkenes with hydrogen peroxide, no generally accepted mechanism of these reactions is known.

The Wacker process [2] is an industrial homogeneous catalytic oxidation of ethylene to acetaldehyde in the presence of PdCl₂ and CuCl₂ that was considered to be well understood. Its mechanism is based on an active intermediate [PdCl₂(C₂H₄)(H₂O)], with π-bonded ethylene to Pd(II) central atom.

However, other catalytic studies using transition metal complexes with multidentate ligands suppose that the intermediate M-O-O-H (M is the metal center) is formed and the O-O bond is activated so that the alkene can react with it [3,4,5,6,7,8,9,10,11,12]

In our previous study [13], the CuL complex (Figure 1) with trans-2,9-dibutyl-7,14-dimethyl-5,12-di(4-methoxyphenyl)-1,2,4,8,9,11-hexaazacyclotetradeca-7,14-diene-3,10-dione (H₂L), a 14-membered bis-semicarbazide hexaazamacrocycle (see Figure S1 in Supplementary Information), was synthesized and characterized by analytical and spectroscopic techniques (IR, UV−vis, ¹H and ¹³C NMR, ESI mass spectrometry, single-crystal X-ray diffraction, and spectroelectrochemistry). This complex selectively catalyzes the microwave-assisted oxidation of neat styrene to benzaldehyde using hydrogen peroxide (30% aqueous solution) as the oxidizing agent, under low microwave irradiation (25 W) and in the absence of any added solvent. Under optimized conditions (40 min of irradiation at 80 °C), the catalytic system provided benzaldehyde in a yield of up to 81% (turnover frequency up to 2.4 × 10³ h 1) as the only product. The CuL catalyst can be very simply separated by cooling to room temperature.

In [13] we proposed a free radical mechanism for the catalytic oxidation of styrene. It should be initiated by the Cu-assisted formation of the hydroxyl or hydroperoxyl radicals.

Now we plan to investigate possible mechanisms of styrene oxidation by hydrogen peroxide under CuL catalysis by quantum-chemical treatment. In this part of our study we will investigate structure, energy, and electron structure of relevant intermediates within three reaction pathways.

i): Reaction pathway A is a simple reaction of neutral styrene Ph-CH=CH₂ with hydroperoxyl (O-OH)^q .
ii): Reaction pathway B starts with the formation of a [CuL(OOH)]^q complex followed by styrene addition.
iii): Reaction pathway C starts with the formation of the π-complex [CuL(Ph-CH=CH₂)]^q and subsequent addition of hydroperoxyl.

All intermediates will be studied in various charge q and spin states to account for the noninnocent character of the ligand L^2- and possible Cu(II)/Cu(I) equilibria. The obtained results should enable one to propose a realistic reaction pathway which will be studied in more detail in the next parts of this study.

2. Results and Discussion

2.1. Reaction Pathway A

Selected energy and structure parameters of DFT optimized styrene, hydroperoxyl, and their reaction products in various charge and spin states are presented in Tables 1 and S1 – S3 of Supplementary Information; their pictures are in Figure 2, Figure 3 and Figure S2 – S4 of Supplementary Information. The addition of the O – O_H bond

\ /

O

(C – black, O – red, H – gray).

Table 1. Relative DFT energies, ΔE_DFT, and Gibbs energies at 298 K, ΔG₂₉₈, of the compounds under study with charges q and spin multiplicities M_s. The energy values are related to the most stable systems (in bold) of the same composition.

	q	M_s	ΔE_DFT [kJ/mol]	ΔG₂₉₈ [kJ/mol]
Reaction path A
(OOH)^q	0	2	94.99	97.20
	-1	1	0.00	0.00
	-1	3	67.03	53.90
[Ph-CH(O)-CH₂OH]^q	0	2	251.65	252.31
	-1	1	0.00	0.00
	-1	3	321.52	307.97
[Ph - CH – CH₂(OH)]^q \ / O	0	2	379.46	365.86
	-1	1	139.13	128.78
	-1	3	277.67	245.69
Reaction path B
[CuL]^q	0	2	127.26	148.50
	-1	1	0.00	0.00
	-1	3	90.95	97.98
	+1	1	748.24	776.49
	+1	3	778.22	799.62
[CuL(OOH)]^q	0	1	224.48	232.30
	0	3	224.43	226.92
	-1	2	0.00	0.00
{[CuL(OH)](Ph-CH₂-CHO)}^q	0	1	322.18	341.47
	0	3	323.41	333.39
	-1	2	0.00	0.00
Reaction path C
[CuL(Ph-CH=CH₂)]^q	-1	1	0.00	0.00
	-1	3	37.81	20.01
	0	2	85.46	74.80
{CuL[Ph-CH(OOH)-CH₂]}^q	0	1	184.97	182.87
	0	3	197.46	188.30
	-1	2	0.00	0.00

of hydroperoxyl parallel to the C_α - C_β bond of styrene (with C – O distances of about 1.7 – 1.9 Å) leads after geometry optimization to [Ph-CH(O)-CH₂OH]^q , whereas the analogous perpendicular position leads to epoxides. Independent of the charge and spin states, these epoxides are energetically so high that their formation will not be considered in further studies. According to our results, the most stable structures of (OOH)^q and [Ph-CH(O)-CH₂OH]^q correspond to the charge q = -1 in the singlet ground spin state. This finding makes the radical mechanism of styrene oxidation improbable. The O – O_H bond in the (OOH)^- in triplet spin state is split. The hydroxyl group in epoxides is bonded by hydrogen bonding, its charge is negative in [Ph-CH(O)-CH₂OH]^- in singlet state, whereas in other systems hydroperoxyl is nearly neutral with one unpaired electron (Tables 2 – 3). The oxygen bond to C_α/β weakens the C_α – C_β bond in all the systems under study (Table 4).

Table 2. Natural charges of C_α, C_β, O, O_H and H_O atoms in (O-O_H-H_O) and (Ph-C_αH=C_βH₂) units with charges q and spin multiplicities M_s.

	q	M_s	C_α	C_β	O	O_H	H_O
Reaction path A
(OOH)^q	0	2	-	-	-0.145	-0.305	0.450
	-1	1	-	-	-0.767	-0.630	0.396
	-1	3	-	-	-0.511	-0.890	0.401
Ph-CH=CH₂	0	1	-0.191	-0.346	-	-	-
[Ph-CH(O)-CH₂OH]^q	0	2	0.052	0.012	-0.350	-0.691	0.565
	-1	1	0.106	-0.036	-0.945	-0.795	0.477
	-1	3	-0.025	-0.345	-0.360	-0.763	0.388
Ph - CH – CH₂(OH)]^q \ / O	0	2	0.090	-0.044	-0.586	-0.434	0.416
	-1	1	0.042	-0.056	-0.587	-1.319	0.390
	-1	3	-0.025	-0.345	-0.763	-0.360	0.388
Reaction path B
[CuL(OOH)]^q	0	1	-	-	-0.167	-0.317	0.484
	0	3	-	-	-0.167	-0.317	0.484
	-1	2	-	-	-0.614	-0.514	0.437
{[CuL(OH)](Ph-CH₂-CHO)}^q	0	1	-0.488	0.446	-0.566	-0.925	0.433
	0	3	-0.488	0.448	-0.561	-0.856	0.437
	-1	2	-0.491	0.436	-0.584	-1.188	0.424
Reaction path C
[CuL(Ph-CH=CH₂)]^q	-1	1	-0.277	-0.472	-	-	-
	-1	3	-0.240	-0.452	-	-	-
	0	2	-0.192	-0.356	-	-	-
{CuL[Ph-CH(OOH)-CH₂]}^q	0	1	0.019	-0.251	-0.327	-0.452	0.461
	0	3	0.012	-0.228	-0.319	-0.452	0.457
	-1	2	0.081	-0.785	-0.347	-0.454	0.440

Table 3. Natural spin populations at C_α, C_β, O, O_H and H_O atoms in (O-O_H-H_O) and (Ph-C_αH=C_βH₂) units with charges q and spin multiplicities M_s.

	q	M_s	C_α	C_β	O	O_H	H_O
Reaction path A
(OOH)^q	0	2	-	-	0.742	0.268	-0.010
	-1	1	-	-	0.000	0.000	0.000
	-1	3	-	-	1.479	0.535	-0.014
Ph-CH=CH₂	0	1	0.000	0.000	0.000	0.000	0.000
[Ph-CH(O)-CH₂OH]^q	0	2	-0.029	0.116	0.820	0.033	0.000
	-1	1	0.000	0.000	0.000	0.000	0.000
	-1	3	0.050	0.346	0.862	0.032	0.074
[Ph - CH – CH₂(OH)]^q \ / O	0	2	0.000	0.000	0.001	1.021	-0.023
	-1	1	0.000	0.000	0.000	0.000	0.000
	-1	3	0.568	-0.025	0.211	0.967	-0.018
Reaction path B
[CuL(OOH)]^q	0	1	-	-	0.701	0.310	-0.008
	0	3	-	-	0.702	0.309	-0.008
	-1	2	-	-	0.097	0.007	0.001
{[CuL(OH)](Ph-CH₂-CHO)}^q	0	1	-0.002	-0.004	-0.005	-0.343	0.008
	0	3	0.002	0.004	0.005	0.435	-0.011
	-1	2	0.000	0.000	0.000	0.035	-0.001
Reaction path C
[CuL(Ph-CH=CH₂)]^q	-1	1	0.000	0.000	-	-	-
	-1	3	0.042	0.174	-	-	-
	0	2	0.000	0.000	-	-	-
{CuL[Ph-CH(OOH)-CH₂]}^q	0	1	0.035	-0.998	-0.021	-0.006	0.000
	0	3	-0.029	0.982	0.065	0.000	0.000
	-1	2	-0.001	0.254	0.022	-0.001	0.000

Our results indicate that the most probable non-radical styrene oxidation in singlet spin state

Ph-CH=CH2 + (OOH)- → [Ph-CH(O)-CH2OH]- (1)

is highly exotermic (Gibbs reaction energy at normal condition Δ_rG₂₉₈ = -307.84 kJ/mol, compare Table S1 in Supplementary Information).

Table 4. Overlap weighted bond orders between C_α, C_β, O, O_H and H_O atoms in (O-O_H-H_O) and (Ph-C_αH=C_βH₂) units with charges q and spin multiplicities M_s.

	q	M_s	C_α-C_β	C_α-O	C_α-O_H	C_β-O	C_β-O_H	O-O_H
Reaction path A
(OOH)^q	0	2	-	-	-	-	-	0.679
	-1	1	-	-	-	-	-	0.417
	-1	3	-	-	-	-	-	0.090
Ph-CH=CH₂	0	1	1.380	-	-	-	-	-
[Ph-CH(O)-CH₂OH]^q	0	2	0.756	0.930	-0.026	0.010	0.823	-0.006
	-1	1	0.800	0.944	-0.023	-0.020	0.787	-0.022
	-1	3	0.935	0.834	-0.015	-0.048	0.699	0.010
[Ph - CH – CH₂(OH)]^q \ / O	0	2	0.817	0.674	0.001	0.669	0.001	-0.010
	-1	1	0.814	0.656	-0.020	0.685	-0.001	0.000
	-1	3	0.902	0.026	0.001	0.877	-0.002	-0.011
Reaction path B
[CuL(OOH)]^q	0	1	-	-	-	-	-	0.720
	0	3	-	-	-	-	-	0.719
	-1	2	-	-	-	-		0.505
{[CuL(OH)](Ph-CH₂-CHO)}^q	0	1	0.868	-0.027	0.000	1.292	-0.012	0.001
	0	3	0.869	-0.026	0.000	1.294	-0.007	0.001
	-1	2	0.855	-0.027	0.001	1.282	-0.017	0.001
Reaction path C
[CuL(Ph-CH=CH₂)]^q	-1	1	1.279	-	-	-	-	-
	-1	3	1.279	-	-	-	-	-
	0	2	1.379	-	-	-	-	-
{CuL[Ph-CH(OOH)-CH₂]}^q	0	1	0.949	0.722	-0.025	-0.025	0.000	0.530
	0	3	0.958	0.690	-0.024	-0.019	-0.001	0.529
	-1	2	0.975	0.668	-0.027	-0.043	-0.005	0.524

2.2. Reaction Pathway B

We optimized the geometry of [CuL]^q starting from its X-ray structure [13] and subsequently with added hydroperoxyl (starting from the Cu – O distance of ca 2.2 Å) in various charge and spin states (the spin multiplicity is denoted as the left superscript where necessary). After geometry optimization, the original square-planar [CuL]^q complex changed its coordination to square-pyramidal only in the case of anionic doublet ²[CuL(OOH)]^- (Tables S2 and S3 in Supplementary Information, Figures 4 - 5 and S5 – S6 in Supplementary Information) while its neutral analogues contain the neutral hydroperoxyl radical (O-O_H-H_O)⁰ (see atomic charges in Table 2 and spin populations in Table 3) attached by hydrogen bonding H_O…N3 (N3 has the highest negative charge and spin population among nitrogen atoms, see Table 5 and Table 6) without any Cu-O bond (see Table 7, Figure S6 and Tables S2 – S3 in Supplementary Information). The anionic complexes ¹[CuL]^- and ²[CuL(OOH)]^- are more stable than their neutral analogues (Tables 1 and S1 in Supplementary Information). It can be deduced that they are related by the exothermic reaction

¹[CuL]^- + ²(OOH)⁰ → ²[CuL(OOH)]^- (2)

as indicated by the reaction Gibbs energy under normal conditions Δ_rG₂₉₈ = -56.37 kJ/mol (Table S1 in Supplementary Information).

Table 5. Natural charges of the relevant atoms in some compounds under study with charges q and spin multiplicities M_s (see Figure 1 for atom notation).

	q	M_s	Cu	N1	N3	N2
H₂L	0	1	-	-0.357(2×)	-0.680(2×)	-0.383(2×)
Reaction path B
[CuL]^q	0	2	0.927	-0.339(2×)	-0.787(2×)	-0.363(2×)
	-1	1	0.603	-0.356(2×)	-0.784(2×)	-0.404(2×)
	-1	3	0.853	-0.334 -0.504	-0.748 -0.781	-0.373 -0.366
[CuL(OOH)]^q	0	1	0.925	-0.348(2×)	-0.859 -0.793	-0.350 -0.355
	0	3	0.925	-0.348(2×)	-0.859 -0.793	-0.350 -0.355
	-1	2	0.903	-0.315 -0.332	-0.777 -0.750	-0.369(2×)
{[CuL(OH)](Ph-CH₂-CHO)}^q	0	1	0.923	-0.296 -0.303	-0.651 -0.677	-0.350 -0.347
	0	3	0.955	-0.295 -0.307	-0.670 -0.722	-0.337 -0.348
	-1	2	0.956	-0.312 -0.317	-0.751 -0.743	-0.376 -0.356
Reaction path C
[CuL(Ph-CH=CH₂)]^q	-1	1	0.670	-0.326 -0.270	-0.785 -0.782	-0.411 -0.356
	-1	3	0.885	-0.377 -0.396	-0.774 -0.781	-0.372(2×)
	0	2	0.928	-0.340 -0.342	-0.787 -0.783	-0.362(2×)
{CuL[Ph-CH(OOH)-CH₂]}^q	0	1	0.931	-0.340 -0.342	-0.787 -0.784	-0.363 -0.363
	0	3	0.926	-0.341 -0.341	-0.787 -0.780	-0.362 -0.363
	-1	2	0.848	-0.310(2×)	-0.778 -0.759	-0.390 -0.351

Table 6. Natural spin populations of the relevant atoms in some compounds under study with charges q and spin multiplicities M_s (see Figure 1 for atom notation).

	q	M_s	Cu	N1	N3	N2
Reaction path B
[CuL]^q	0	2	0.526	0.115(2×)	0.111(2×)	0.006(2×)
	-1	1	0.000	0.000	0.000	0.000
	-1	3	0.590	0.090 0.345	0.098 0.115	0.001 0.006
[CuL(OOH)]^q	0	1	-0.532	-0.110(2×)	-0.111 -0.116	-0.011 -0.006
	0	3	0.525	0.110(2×)	0.110 0.116	0.011 0.006
	-1	2	0.575	0.054 0.047	0.106(2×)	0.002 0.004
{[CuL(OH)](Ph-CH₂-CHO)}^q	0	1	0.197	0.104(2×)	-0.061 0.022	0.008 0.003
	0	3	0.673	0.138(2×)	0.296 0.186	0.050 0.008
	-1	2	0.610	0.059 0.065	0.109 0.106	0.000 0.002
Reaction path C
[CuL(Ph-CH=CH₂)]^q	-1	1	0.000	0.000	0.000	0.000
	-1	3	0.571	0.153 0.166	0.111 0.108	0.000 0.002
	0	2	0.526	0.115(2×)	0.112 0.110	0.006(2×)
{CuL[Ph-CH(OOH)-CH₂]}^q	0	1	0.527	0.115(2×)	0.112 0.109	0.007(2×)
	0	3	0.527	0.115(2×)	0.111(2×)	0.007(2×)
	-1	2	0.507	0.000 0.023	0.083 0.087	-0.001 0.002

The spin population in ²[CuL(OOH)]^- is located mainly at Cu, unlike the spinless ¹[CuL]^-. Consequently, the spin transfer from neutral hydroperoxyl radical to central Cu atom can be concluded in reaction (2) which is connected with weakening of the O-O_H bond (Table 4 and Table 5).

Subsequent addition of neutral styrene to the hydroperoxyl group in ²[CuL(OOH)]^- similarly to reaction pathway A (due to sterical reasons C_β must be close to O and C_α close to OH) causes hydrogen and oxygen transfers resulting to ²{[CuL(OH)](Ph-CH₂-CHO)}^- where Ph-CH₂-CH=O is only weakly bonded to [CuL(OH)]^- (Figure 6, Table 7 and S2 – S3 in Supplementary Information). Here, the O atom originally bonded to Cu is moved to C_β simultaneously with H transfer from C_β to C_α and Cu is bonded to O_H of hydroperoxyl. It is interesting that if we remove one electron, analogous neutral complexes are obtained (Figure S7, Tables S2 – S3 in Supplementary Information) with significantly higher energies (Table 1 and S1 in supplementary Information). Consequently, the C_α-C_β bonds are weakened and the double C_β=O bonds are formed (Figure 4). The strengths of Cu-O bonds are comparable with those of Cu-N1/N3 (Figure 7) and the Cu coordination is square-pyramidal (unlike

Table 7. Overlap weighted bond orders of the relevant atoms in some compounds under study with charges q and spin multiplicities M_s (see Figure 1 and Table 2 for atom notation).

	q	M_s	Cu-N1	Cu-N3	Cu-O/O_H	Cu-C_α/β
Reaction path B
[CuL]^q	0	2	0.260(2×)	0.339(2×)	-	-
	-1	1	0.188(2×)	0.298(2×)	-	-
	-1	3	0.272 0.357	0.338 0.346	-	-
[CuL(OOH)]^q	0	1	0.232 0.230	0.311 0.305	0.069 0.015	-
	0	3	0.232 0.230	0.310 0.305	0.070 0.015	-
	-1	2	0.238 0.215	0.305 0.313	0.302 0.023	-
{[CuL(OH)](Ph-CH₂-CHO)}^q	0	1	0.293 0.297	0.384 0.391	0.000 0.333	0.000(2×)
	0	3	0.287 0.295	0.362 0.386	0.000 0.333	0.000(2×)
	-1	2	0.241 0.233	0.308 0.310	-0.001 0.309	0.004 0.009
Reaction path C
[CuL(Ph-CH=CH₂)]^q	-1	1	0.172 0.132	0.220 0.240	-	0.195 0.240
	-1	3	0.287 0.294	0.332(2×)	-	-0.001 0.007
	0	2	0.259(2×)	0.338(2×)	-	0.001(2×)
{CuL[Ph-CH(OOH)-CH₂]}^q	0	1	0.258(2×)	0.337 0.333	0.000(2×)	0.000(2×)
	0	3	0.258 0.260	0.337 0.339	0.000(2×)	0.000(2×)
	-1	2	0.161 0.178	0.277 0.262	0.010 0.003	0.052 0.324

square-planar [CuL]^q, see Tables S2-S3 in Supplementary Information). Non-vanishing spin populations in the compounds within this reaction pathway can be at Cu, N1, N3 and hydro(perox)yl oxygen atoms (Table 3 and Table 6). Cu in ¹[CuL]^- has a less positive charge and no spin population, which implies the oxidation state of Cu(I) (Table 2 and Table 5). More positive Cu charges and nonzero spin populations in other compounds of this reaction pathway correspond to the oxidation state Cu(II).

The most probable styrene oxidation step can be described by the exothermic reaction

²[CuL(OOH)]^- + Ph-CH=CH₂ → ²{[CuL(OH)](Ph-CH₂-CHO)}^- (3)

as indicated by the reaction Gibbs energy under normal conditions Δ_rG₂₉₈ =-266.67 kJ/mol (Table S1 in Supplementary Information).

2.3. Reaction Pathway C

We optimized the structures of [CuL(Ph-CH=CH₂)]^qstarting from the optimized structures of [CuL]^q with added neutral styrene in the form of a π-complex with Cu-C_α/β distances of ca 2.4 Å. Only the optimized structure of ¹[CuL(Ph-CH=CH₂)]^-preserved the original form of a π-complex where the Cu- C_α/β bond lengths are comparable with the Cu-N1/N3 ones and the square-planar Cu coordination lost its planarity (Figure 7, Tables S2 – S3 in supplementary Information). Its ¹[CuL(Ph-CH=CH₂)]⁰and ³[CuL(Ph-CH=CH₂)]^- analogues with separated square-planar [CuL]^q and neutral Ph-CH=CH₂ components are energetically higher (Table 1, S1 – S3, and Figure S8 in Supplementary Information).

Figure 7. DFT optimized structure of [CuL(Ph-C_αH=C_βH₂)]^- in singlet spin state (Cu – green, C – black, N – blue, O – red, H – gray).

The lower charge and absence of spin at Cu in ¹[CuL(Ph-CH=CH₂)]^- indicates the formal oxidation state Cu(I) unlike the Cu(II) one in [CuL]^q, ¹[CuL(Ph-CH=CH₂)]⁰ and ³[CuL(Ph-CH=CH₂)]^- (Table 5Tables –Table 6). The Cu-N1/N3 bonds in ¹[CuL(Ph-CH=CH₂)]^- are weaker than in [CuL]^q and comparable with the Cu-C_α/β ones (Table 7). The C_α=C_β bond strength is equal to that of free styrene (Table 4).

According to our results, the only stable π-complex can be obtained by the non-radical endothermic reaction

¹[CuL]^- + Ph-CH=CH₂ → ¹[CuL(Ph-CH=CH₂)]^- (4)

as indicated by the reaction Gibbs energy under normal conditions Δ_rG₂₉₈ = +91.95 kJ/mol (Table S1 in Supplementary Information).

The addition of the hydroperoxyl radical to ¹[CuL(Ph-CH=CH₂)]^- leads to ²{CuL[Ph-CH(OOH)-CH₂]}^- (analogously to the reaction pathway A) with a split Cu-C_α bond and hydroperoxyl bonding to the C_α site (Figure 8, Tables S2-S3 in Supplementary Information). Subsequently, the spin density is moved from hydroperoxyl to Cu with a higher positive charge corresponding to the real oxidation state instead of Cu(I) in ¹[CuL(Ph-CH=CH₂)]^- (Table 2, Table 3, Table 5 and Table 6). The Cu-N1/N3 bonds are weaker than the Cu-C_β one in ¹[CuL(Ph-CH=CH₂)]^- (Table 7).

Figure 8. DFT optimized structure of {CuL[Ph-C_αH(O-O_H-H_O)-C_βH₂]}^- in doublet spin state (Cu – green, C – black, N – blue, O – red, H – gray).

An electron removal from ¹[CuL(Ph-CH=CH₂)]^- should correspond to the formal oxidation state Cu(II) but it causes the Ph-CH(OOH)-CH₂ split from the [CuL]⁰ unit (Tables S2-S3 and Figure S9 in Supplementary Information) with higher energies (Tables 1 and S1 in Supplementary Information). Based on charges and spin populations (Tables 2, 3, 5 and 6), the real Cu(II) oxidation state is preserved in neutral [CuL(Ph-CH=CH₂)]⁰ complexes and the spin density is moved from hydroperoxyl to N1 and N3 atoms.

Our results show that the most advantageous hydroperoxyl addition to the above mentioned π-complex can be described by the endothermic reaction

¹[CuL(Ph-CH=CH₂)]^- + ²(OOH)⁰ → ²{CuL[Ph-CH(OOH)-CH₂]}^- (5)

as indicated by the reaction Gibbs energy under normal conditions Δ_rG₂₉₈ = -35.92 kJ/mol (Table S1 in Supplementary Information).

3. Method

Geometry optimization of the systems under study was performed using B3LYP hybrid functional [14] and 6-311+G* basis sets from the Gaussian library [15]. The optimized structures were tested on the absence of imaginary vibrations using vibrational analysis. Singlet spin states in Cu complexes were treated using an unrestricted formalism and their energies related to triplet spin states were corrected as follows (‘broken symmetry’ treatment, BS) [16].

E_{S} - E_{T} = \frac{{〈S^{2}〉}_{T} (E_{B S} - E_{T})}{{〈S^{2}〉}_{T} - {〈S^{2}〉}_{B S}}

(6)

E_S, E_T and E_BS are singlet, triplet, and ‘broken symmetry’ (unrestricted singlet) energies, respectively. <S²>_T and <S²>_BS are triplet and ‘broken symmetry’ values of spin squares, respectively. Atomic charges, spin populations, and overlap weighted bond orders were evaluated in terms of natural population analysis [17,18]. All quantum-chemical calculations were performed using Gaussian16 software [15]. The MOLDRAW software was used for geometry manipulation and visualization purposes [20].

4. Conclusions

Using quantum-chemical treatment, relevant intermediates in various charge and spin states of three reaction pathways of styrene oxidation by hydroperoxyl were investigated. The reaction pathway A without any catalyst probably proceeds by non-radical mechanism when neutral styrene is attacked by a hydroperoxyl anion and ¹[Ph-CH(O)-CH₂OH]^- is formed (Figure 2). The alternative formation of epoxide (Figure 3) is energetically less advantageous.

The alternative reaction pathways B and C are based on the [CuL]^q catalyst (Figure 1), most probably its anionic form in the singlet spin state corresponding to the formal oxidation state Cu(I). Within the reaction pathway B the neutral hydroperoxyl radical is bonded to Cu to form ²[CuL(OOH)]^- (Figure 4) which is unstable in other charge and spin states. The spin density is moved to Cu, which corresponds to the real oxidation state of Cu(II). Subsequent addition of neutral styrene results in ²{[CuL(OH)](Ph-CH₂-CHO)}^- formation after significant O and H atoms rearrangements which contains only weakly bonded ²[CuL(OH)]^- and Ph-CH₂-CH=O units. This reaction pathway seems to be realistic, but in future studies we must solve the Cu-OH split (probably by reaction with hydroperoxyl as in [4,5]) and the formation of benzaldehyde (by interaction with hydroperoxyl [4] or with ²[CuL(OH)^]- [3,7]).

The reaction pathway C starts with the initial non-radical formation of the π-complex ¹[CuL(Ph-CH=CH₂)]^- (Figure 7) with the oxidation state of Cu(I) according to Eq. (4) but this reaction is problematic because of its endothermic character. However, its analogues in other charge and spin states do not allow for such a π-complex formation. Subsequent addition of a hydroperoxyl radical leads to ²{CuL[Ph-CH(OOH)-CH₂]}^- (Figure 8) with Cu-C_β bonding. Its oxidation leads to Ph-CH(OOH)-CH₂ separation.

Our study explains why reaction pathway B of the catalytic oxidation of styrene by hydroperoxylating a bis-semicarbazide hexaazamacrocyclic Cu complex is preferred. Our future studies will provide additional details of its reaction mechanism, including solvent effects.

Supplementary Materials

The following supporting information can be downloaded at the website of this paper posted on Preprints.org, Table S1: DFT energies, E_DFT, and Gibbs energies at 298 K, G₂₉₈, of the compounds under study with charges q, spin multiplicities M_s, and spin squares <S²>; Table S2: Selected bond lengths (in Å) between relevant atoms in the compounds under study with charges q and spin multiplicities M_s; Table S3: Selected bond angles (in degrees) in the compounds under study with charges q and spin multiplicities M_s; Figure S1: X-ray structure of H₂L with atom-labelling scheme and thermal ellipsoids drawn at 20% probability level; Figures S2 – S9: DFT optimized structures of the possible reaction intermediates in various charge q and spin states M_s.

Funding

Slovak Grant Agency VEGA (contract No. 1/0175/23) is acknowledged for financial support.

Data Availability Statement

Data is contained within the article or supplementary material.

Acknowledgments

We thank the HPC center at the Slovak University of Technology in Bratislava, which is a part of the Slovak Infrastructure of High-Performance Computing (SIVVP Project, ITMS code 26230120002, funded by the European Region Development Funds), for computing facilities. .

Conflicts of Interest

The author declares no conflicts of interest.

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Figure 1. X-ray structure of CuL with atom-labeling scheme and thermal ellipsoids drawn at 50% probability level [13].

Figure 2. DFT optimized structure of [Ph-C_αH(O)-C_βH₂OH]^- in singlet spin state (C – black, O – red, H – gray).

Figure 3. DFT optimized structure of [(Ph-C_αH-C_βH2)(OH)]- in singlet spin state.

Figure 4. DFT optimized structure of [CuL]^- in singlet spin state (Cu – green, C – black, N – blue, O – red, H – gray).

Figure 5. DFT optimized structure of [CuL(O-O_H-H_O)]^- in doublet spin state (Cu – green, C – black, N – blue, O – red, H – gray).

Figure 6. DFT optimized structure of {[CuL(O_H-H_O)](Ph-C_αH₂-C_βHO)}^- in doublet spin state (Cu – green, C – black, N – blue, O – red, H – gray).

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