Single-factor analysis of Ni–B–AC-catalyzed β-pinene hydrogenation based on hierarchical analysis

Abstract

In the choice of catalysts for the hydrogenation of pinene, nickel-based catalysts show intriguing activity. Here, a Ni–B catalyst supported on activated carbon with Ni as an active component was synthesized by the titration reduction co-impregnation method. The mechanism of such heterogeneous systems has not yet been articulated, and the industrial applications of the potassium borohydride reduction of nickel-based catalysts are limited by their easy agglomeration and poor stability. The materials were analyzed by hierarchical and DFT studies, in situ XPS, BET, XRD, and SEM, which provided insights into the kind of signals in Ni²⁺ reduction to Ni⁰. The hierarchical analysis indicated that Ni/AC (0.4876) and reaction pressure (0.6066) influenced the catalyst preparation and process efficiency changes, respectively. Activated carbon was shown to provide a favorable basis for the stability of the Ni–B activity. In addition, the hierarchical analysis method provides new insights into the data analysis for chemical experiments.

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1. Introduction

With the continuous development of new synthetic substances in recent years, cis-pinane is now being engineered to manufacture a wide range of chemicals, pesticides, flavorings, drugs, and fuels,^1–4 which is accessible by the transformation of α-pinene and β-pinene under hydrogen partial pressure. The preparation of cis-pinane presents a lucrative economy, well-balanced structure, and has profound utility to research as a key intermediate.^5–7 Turpentine is dominated by α-pinene and β-pinene, and consequently, the further hydrogenation of pinene is favored and requires an enhanced hydrogenation ability of a heterogeneous catalyst. Here, heterogeneous catalysts offer advantages over single metals in terms of their post-use recycling and reuse.^8,9 Other than the existing published catalysts, a latent avenue to boost the selectivity and conversion of the process is to bring in an efficient and stable catalyst carrier,^10–13 and again, activated carbon-loaded rhodium,^14,15 platinum,^16,17 and rubidium^18,19 are among the more studied catalysts, showing equally fine results. Nevertheless, hydrogenation catalysts, such as Ni–B, can affect the process efficiency. For this reason, the use of stable and efficient hydrogenation catalysts for the preparation of cis-pinane allows for high quality to be achieved. Overall, the biggest problems in catalyst production are the production cost, reaction efficiency, and the stability of the catalyst itself.^20–22 The study of hydrogenation catalysts is thus of great practical importance.

The choice of catalyst should be predicated on high catalyst efficiency, stable catalyst performance, and a steady catalyst structure.^23–25 Furthermore, if the catalyst consists of an enriched pore volume and pore size,^26–28 there would be more active ingredient adsorption sites, which would help to improve the overall performance of the catalyst. For the sake of investigating the efficiency of pinene catalysts, including the catalyst and catalyst carrier, to understand the active ingredient sites, it was necessary to explore and develop new catalysts for hydrogenation. Furthermore, Ni–B catalysts have some key limitations, including feeble stability, arbitrary oxidation, and active site deficiency, and hence, a stable matrix material needs to be selected to overcome these disadvantages.^29,30

In the present study, a Ni–B–AC catalyst was used for the first time for the hydrogenation of β-pinene. The single factors affecting the catalyst preparation were experimentally investigated and the weights of each factor were determined using hierarchical analysis, followed by an analysis of the catalysts by BET, XRD, and XPS, and verification of the morphology of the catalysts by density functional theory (DFT) calculations performed in Gaussian 16.

2. Materials and methods

2.1 Catalyst preparation and hydrogenation process

The catalyst was prepared by a static reduction in a low-temperature alcohol bath. Activated carbon (1.4 g), NiCl₆·6H₂O (0.9 g, 0.2 mol L⁻¹), and 50.00 mL of ethanol solution were stirred in a three-necked round-bottom flask under nitrogen protection and placed in an alcohol bath 0 °C, with magnetic stirring at speed 7 for 30 min. Next, KBH₄ (1.00 g, 0.3 mol L⁻¹) solution was prepared, and 0.2 mol L⁻¹ sodium hydroxide was added to adjust the pH to 13. The KBH₄ solution was then dropped into the above three-necked round-bottom flask through an infusion tube and a one-pot reaction occurred for 4 h. After completion of the reaction, repeated washing steps with water were performed to remove the solution, and a final wash with ethanol was used to remove the water. The remaining solid catalyst in the filter paper was dried in a vacuum drying oven for 6 h at 60 °C.

To a high-pressure vessel equipped with a thermocouple was added β-pinene (10 g) and the catalysts (5 wt%) and ethanol solvent (10 mL). The overall reaction was carried out at 130 °C for 2 h, and at 3.0 MPa and 800 r per min. After the hydrogenation reaction was complete, the reactor was naturally cooled down to room temperature, and the reaction solution was filtered to remove the catalysts, and the organic liquid to be tested was diluted with ethanol.

2.2 β-Pinene test conditions

The single-factor values affecting the catalysts were determined by gas chromatography (GC 2014). The test conditions for the GC were: DB-5 capillary column (size 30 m × 0.32 mm × 0.5 m), flame ionization detector (FID), high purity nitrogen as the carrier gas, high purity hydrogen as the fuel gas, air as the auxiliary gas, gasification chamber temperature of 250 °C, detector temperature of 250 °C, pressure of 62 KPa, split ratio of 1 : 50, injection volume of 0.5 μL, and temperature program comprising . The experimental data could be well analyzed by the area normalization method, which was normalized by dividing the individual peak area by the total peak area of all peaks for that sample.

2.3 Catalyst characterization

The materials were characterized by N₂ adsorption–desorption isotherms, XRD, XPS, and SEM. The specific surface area was measured using a NOVA 4200e automatic system with a degassing temperature of 80 °C, degassing time of 12 h, and an adsorbent of N₂. XPS was performed on an Escalab 250 Xi-phi-Ves probe 5000 Thermo-Fischer (USA) instrument, employing Al Kα radiation (hv = 1486.6 eV, 14.6 kV, 13.5 mA, 20 cycles), with charge correction performed by passing energy of 20 eV in steps of 0.1 eV, using the binding energy of C 1s = 284.8 eV as the energy standard. X-Ray diffractometer (XRD) measurements were carried out on a Nishiko Ltd model D/max2200 system (Japan), using Cu-K radiation and scanning powder samples at a wide angle of 10° per min in the range 5°–90°. DFT-assisted Ni-B calculations were performed using Gaussian 16 and Multiwfn 3.8 software.

2.4 Analysis methods

2.4.1 Preparation of the catalysts and processing the experimental data for the hydrogenation processes.

2.4.2 Data reliability analysis methods: the hierarchical analysis process (AHP). Hierarchical analysis is an analytical approach for making decisions on a number of complex and single-factor problems. It is chiefly applied for the quantitative analysis of qualitative indicators by constructing a multi-level evaluation index system, which is suitable for problems that are difficult to analyze completely quantitatively. The method was used here for the single-factor analysis of the catalyst preparation and for parametric analysis of the hydrogenation process, using the yield as a judgment indicator for the analysis. The analysis steps were as follows (Fig. 1).

Fig. 1 AHP analysis step-by-step process.

3. Results and discussion

3.1 Single-factor examination of the catalyst preparation

During the preparation of the Ni–B–AC catalysts, the stability of the catalysts slightly varied based on the preparation conditions.^31,32 The optimum preparation conditions were determined by varying the pH value, reaction time, drop acceleration, Ni/AC mass ratio, and the ratio of the reducing agent to the active component Ni. The highest β-pinene conversion and pinane selectivity of the Ni–B–AC catalysts occurred at 130 °C, 3.0 MPa, 5 wt%, 800 r per min, and 120 min. The following data are from a study of the conditions under which the catalysts were prepared.

The study of the optimum pH of the catalyst preparation process is shown in Fig. 2a. In a weakly alkaline environment, the pH contributed to the formation of Ni–B–AC.^21,33,34 The pH range was 9–14. When the pH was minimal, the whole system may be free of Ni²⁺. As the pH increased, the reduction efficiency of Ni²⁺ increased, with a consequent increase in the conversion and selectivity. At pH 13, as the alkalinity increases, Ni²⁺ was reduced to Ni⁰, contributing to Ni⁰ loading on the activated carbon. At this point the conversion and selectivity reached a maximum.^35,36 The reduction time of the catalysts prepared by impregnation was also a pivotal factor, whereby when the stirring rate and alcohol bath temperature were fixed, the conversion and selectivity of the impregnation reaction changed gradually as the reaction time increased or decreased. The study of the reaction times during the catalyst preparation is shown in Fig. 2b and c. When the first drop of reducing agent was dropped into the nickel-containing solution, the reaction was violent and produced a significant amount of bubbles, with bubbles continuing to be generated for 20 min. When the reaction time was more than 4 h, the conversion and selectivity of β-pinene hydrogenation decreased. The drop in acceleration rate of the reducing agent was crucial for the preparation of the Ni–B activated carbon, whereby too fast or uneven stirring was not conducive to the reduction of nickel hexachloride H₂O, while too slow had issues reaching saturation, and so 50 drops per min was found to be the optimal rate. It has been reported that the reduction of Ni⁰ can reach saturation with a rapid rate of decline, at which point some unreacted Ni may be encapsulated within Ni⁰.^37,38

Fig. 2 Determination of the single factors affecting the catalyst preparation.

The stability of the loaded catalysts was also related to the properties of the loaded substrate, pore volume, pore size, and specific surface area.^39–42 It can be seen from the analysis of Fig. 2d and e, at a mass ratio of 1 : 4, the conversion and selectivity may be low due to the small amount of Ni loaded on the activated carbon; whereas when at a mass ratio of 1 : 7, both conversion and selectivity reached a maximum. The active component Ni in the catalyst preparation was closely related to the addition of the reducing agent B, wherein the best ratio of Ni to B was 1 : 4. Whereas, as the ratio of Ni to B increased, saturation, encapsulation, and the agglomeration of Ni may occur during the dropwise addition of the reductant B, resulting in a gradual decrease or even leveling off of the selectivity and conversion.^21,43,44,45

3.2 Exploring the hydrogenation process

The hydrogenation catalysts were prepared under the optimum preparation conditions described above. The effects of the stirring speed, temperature, pressure, and catalyst amount on the hydrogenation process were investigated. The fixed factors were 2 h and 10 g β-pinene, with the range of catalyst amount set at 3–7 wt%, temperature 90–140 °C, pressure of 2.0–5.0 MPa, and stirring speeds of 500–850 r per min. The following data were examined for the catalyst preparation conditions.

As can be seen from Fig. 3a, there was a trend toward the increasing conversion and selectivity of the hydrogenation reaction with increasing the magnetic rotor stirring speed. At speeds of 500–750 r per min, the reaction was probably designed to eliminate external diffusion, while at a speed of 800 r per min, the material was stirred to push toward the kettle wall, leading to a reduced catalyst amount. As can be seen from Fig. 3b, as the amount of catalyst increased, the conversion tended to become more stable and the selectivity gradually increased, with the optimum mass ratio being 5 wt%. The reaction pressure also played a major role in the catalytic reaction. As can be seen from Fig. 3c, as the pressure increased to 3.0 MPa, there was an inflection point for the conversion and selectivity, with a decreasing trend and an optimum reaction pressure of 3.0 MPa. Temperature also promoted the catalytic reaction to be carried out. Hydrogenation belongs to an exothermic reaction, and so the conversion and selectivity incrementally increased as the temperature increased, as can be seen from Fig. 3d, and then sluggishly decreased when the temperature rose to 120 °C. These changes may be due to the effect of the partial catalysts properties of the kettle at high temperature.^46,47,48

Fig. 3 Single-factor examinations of the hydrogenation process.

3.3 Hierarchical analysis (AHP) of the data for each factor for β-pinene hydrogenation

3.3.1 Single-factor analysis affecting the catalyst preparation. Hierarchical analysis was carried out to analyze the experimental data on the single factors.^49–52 The stratification structure is shown in Fig. 4 and the main objective was to obtain the best single factor. Five indicators: pH of the reducing agent, reaction time of the catalyst preparation, drop in acceleration of the reducing agent, and Ni/AC and Ni/B ratios were used as the standard layers, with the individualized next-level indicators of each factor used as the sub-standard layers. The differences in β-pinene hydrogenation yields were used to form a judgment matrix on a scale from 1–9 and the results were analyzed.⁵³ The consistency index of the intermediate elements (0.0202 ≠ 0) and the consistency ratio of the five indicators (0.0180 < 0.1) indicated that the consistency of the judgment matrix of the intermediate elements and the inter-pair sorting results were acceptable, and the weighting coefficients obtained were reasonably valid without logical confusion.

Fig. 4 Distribution of weights for each element in the catalyst preparation.

The results covered the sub-target reductant pH concentration index (0.0215 ≠ 0) and the concentration ratio between different gradients of pH (0.0192 < 0.1); the reaction time consistency index (0.2291 ≠ 0) and the consistency ratio (0.0511 < 0.1); the consistency index of the drop rate (0.0213 ≠ 0) and the consistency ratio (0.0190 < 0.1); the index of the mass ratio of Ni/AC (0.0192 ≠ 0) and the consistency ratio (0.0171 < 0.1); and the consistency of the quantity ratio of Ni/B substances (0.0293 ≠ 0) and each substance (0.0262 < 0.1). All the above factors satisfied the consistency, while the weighting factors were all reasonable and valid.

As can be seen from Fig. 4, the Ni/AC ratio (0.4876) was the most important element in the interlayer. A suitable active component Ni/AC ratio can stabilize the catalyst, which was related to the loading of the active component and the specific surface area. The index analysis further indicated the formation of Ni–B–AC-loaded catalysts and showed that the key to the catalyst preparation was to master the Ni/B and Ni/AC ratios.

As per the analysis in Fig. 5, disparate single-factor indicators showed distinct hydrogenation effects during the catalyst preparation. Fig. 5a shows the single-factor weighting ratio of Ni/AC (0.4876) with a relatively large reaction time (0.2961). Fig. 5b depicts the reaction time during the catalyst preparation, with a large proportion at 4 h (0.5617) and 4.5 h (0.1802), indicating that the yield gradually increased with time, but then gradually decreased after a certain time. Fig. 5c shows that for the Ni/AC ratio, 1 : 7 (0.4252), 1 : 8, 1 : 6 (0.2361) accounted for a large proportion of the catalyst preparation. Fig. 5d shows the pH during the catalyst preparation, with pH 13 (0.5411) and 12 (0.2483) accounting for large proportions. Fig. 5e shows the drop in acceleration rate with 50 drops per min (0.4471) and 60 drops per min (0.2311) accounting for large proportions. Fig. 5f shows that during the catalyst preparation, 1 : 4 (0.4794) and 1 : 3 (0.3133) represented relatively large Ni/B ratios. Pursuant to the data analysis, the optimal reaction time was 4 h, the Ni/AC ratio was 1 : 7, the pH was 13, the drop in rate was 50 drops per min, and the Ni/B ratio was 1 : 4, which was consistent with the results of the single-factor examination.

Fig. 5 Graph of the weighting ratios between the two factors of the hydrogenation process.

3.3.2 Single-factor analysis of the hydrogenation process. Hierarchical analysis was used to analyze the single-factor data from the hydrogenation process. The hierarchical structure is shown in Fig. 6. The main objective was to obtain the best single factor for the process. Four indicators, namely the stirring speed, reaction pressure, catalyst dosage, and reaction temperature, are used as criterion layers, and the individual indicators for each factor were used as sub-criteria layers. Using the differences in hydrogenation yields of β-pinene, a judgment matrix was constructed on a scale of 1–9 and the results were analyzed.

Fig. 6 Optimal conditioned hierarchical analysis diagram for the hydrogenation process.

The results demonstrated the consistency index of the middle element (0.0448 ≠ 0) and the consistency ratio of the five indicators (0.0504 < 0.1); the consistency index of the sub-objective stirring speed (0.0224 ≠ 0) and the consistency ratio (0.0200 < 0.1); the consistency index of the reaction pressure (0.0312 ≠ 0) and the consistency ratio (0.0279 < 0.1); the consistency index of the catalyst amount (0.0131 ≠ 0) and the consistency ratio (0.0117 < 0.1); and the consistency index of the reaction temperature (0.0213 ≠ 0) and the consistency ratio (0.0190 < 0.1). All the above data indicate that the judgment matrix of the middle element was consistent, and that acceptable weighting coefficients were obtained that were reasonably valid without logical confusion.

As can be seen from Fig. 6, the reaction pressure (0.6066) and the amount of catalyst (0.2110) were the main factors for the intermediate layer. An appropriate pressure helps to reduce the burden of the reaction; while the importance of choosing the catalyst dosage should not be overlooked. In practical industrial applications, the catalyst dosage will be selected on the basis of low cost and large benefits to help achieving the industrial goals.

As can be seen Fig. 7a, the reaction pressure (0.6066) had the largest share and thus impact by far. Fig. 7b shows the stirring speed, with 750 r per min (0.4144) and 800 r per min (0.3936) having relatively large shares. Fig. 7c shows the reaction pressure, with 3.0 MPa (0.3496) and 2.5 MPa (0.2942) accounting for a relatively large proportion. Fig. 7d shows the amount of catalyst, with 4 wt% (0.3199) and 5 wt% (0.3075) accounting for relatively large amounts, while Fig. 7e shows the reaction temperatures, with 120 °C (0.3545) and 130 °C (0.2833) prominent. In summary, the data analysis showed that a stirring speed of 750 r per min, a reaction pressure of 3.0 MPa, a catalyst dosage of 4 wt% and a reaction temperature of 120 °C were optimal. The single-factor process experiments were highly consistent compared to each other.

Fig. 7 Graph of the weighting ratios between two factors of the hydrogenation process.

3.4 Experimental characterization and computational verification

3.4.1 Characterization of the experimental materials. The Ni–B–AC materials were characterized by nitrogen adsorption–desorption isotherms, XRD, and XPS. The specific surface area, pore volume, and pore size of the material were analyzed by nitrogen adsorption–desorption isotherms, as shown in Fig. 8a and b. The crystalline state of the material was determined by wide-angle XRD, as shown in Fig. 8c. XPS allowed the analysis of the specific elements contained in the material, as shown in Fig. 8d.

Fig. 8 Ni–B–AC-loaded catalyst: (a and b) N₂ adsorption and desorption profiles ((b) is presented as the inset), (c) wide angle XRD, (d) XPS analysis.

According to the characterization data in Fig. 8a above, the specific surface area adsorption and desorption curves at different pH values were consistent with a type-IV isotherm, with a specific surface area of 719.841 m² g⁻¹ at pH 13. The pore structure in Fig. 8b shows that the pore sizes between 5 and 10 were mesoporous. The AC in Fig. 8c (XRD) is a raw material for activated carbon, as can be seen from the graphite peak at 2θ = 28°. A graphite peak was still present in the loaded Ni–B–AC activated carbon sample. When it was in the range of 20°–30°, at 2θ = 45°, both AC and Ni–B–AC showed a large diffraction peak and a small diffraction peak, indicating that the material was amorphous. Fig. 8d shows that the sample contained elements such as C, O, Ni, and B. The element O 1s in the spectrum was probably from the oxygen-containing functional group of the activated carbon loaded on the substrate with a binding energy of 529.41 eV. The element C 1s in the figure was from the carbon-based component of the activated carbon with a binding energy of 282.35 eV. In the spectrum, the active component Ni 2p element was from NiCl₂·6H₂O with a binding energy of 857.65 eV, while B 1s was from the reducing agent KBH₄ solution, with a binding energy of 187.06 eV. The above spectra indicated that the loaded catalyst Ni–B–AC had been successfully loaded with a high specific surface area, good stability, and an abundance of active sites, which contributed to improving the catalytic activity.

3.4.2 DFT calculations of the analytical data.
3.4.2.1 Calculation of the basic information. The Ni–B structure and stability were analyzed by density functional theory (DFT) in Gaussian 16⁵⁴ and Multiwfn 3.8.⁵⁵ In order to consider the effect of Ni–B, the possible configurations of the atomic clusters were optimized at the B3LYP/6-311 + g(d) level using DFT, and at the same time, the single-point energy was calculated under the 6-311++g(d) basis set, which could obtain the high-precision energy, and allow analyzing the electrostatic potential. The binding sites were observed by electrostatic potential diagrams to obtain stable monomers.^34,56

According to Table 1 above, the basic structure of the bond lengths showed that B–B bonds could be found between the NiB₂, Ni₂B₂, and Ni₃B₂ molecules, while there were no chemical bonds between B–B in the Ni₄B₂ molecule. It could also be predicted that Ni₄B₂ clusters would form more readily than NiB₂, Ni₂B₂, and Ni₃B₂ molecules, which was consistent with the experimental results. As the number of Ni atoms increased, the Gibbs free energy of the molecule gradually increased, and the structure of the Ni–B molecule tended to stabilize. Among the four molecules, among which the most stable structure was that for Ni₄B₂, NiB₂ had a weaker binding energy compared to Ni₄B₂, while Ni₂B₂ and Ni₃B₂ were in a sub-stable structure.

Table 1 Key lengths after the structural optimization

Molecular	Key type	Key length/Å	Key type	Key length/Å	G/hartree
NiB2	Ni3–B1	1.883	B–B	1.563	−1559.136
Ni2B2	Ni4–B1	1.909	B–B	1.695	−3066.196
	Ni4–Ni3	2.198
Ni3B2	Ni4–B1	1.914	B1–B2	1.899	−4574.543
	Ni4–Ni3	2.226
	Ni5–B1	1.842
	Ni4–B1	1.915
	Ni3–Ni5	3.025
Ni4B2	Ni4–B6	1.952	—	—	−6082.889
	Ni4–Ni3	2.236

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3.4.2.2 Optimization of the molecular structure of NiB₂, Ni₂B₂, Ni₃B₂, and Ni₄B₂. The optimized structures of NiB₂, Ni₂B₂, Ni₃B₂, and Ni₄B₂ were used to analyze the electrostatic potential spectrum. As demonstrated, the red region represents a negative electrostatic potential value, indicating that it is easier to give electrons and is more nucleophilic than the other regions. Conversely, the blue region represents a positive electrostatic potential and is more likely to give electrons being more electrophilic than the other regions.^57,58

As can be seen in Fig. 9, the blue regions of the molecules NiB₂, Ni₂B₂, Ni₃B₂, and Ni₄B₂ reacted preferentially, and all four molecules had the same atoms with binding sites on the Ni atom. Table 2 shows that in the NiB₂ and Ni₂B₂ structures, the Ni atom was positively charged and the B atom was negatively charged. In the Ni₃B₂ structure, the Ni atom was two positive and one negative, while the B atom was positive. In the Ni₄B₂ structure, the Ni atom was negatively charged and the B atom was positively charged. The Ni₃B₂ and Ni₃B₂ and Ni₄B₂ molecules were globally distributed with both the HOMO and LUMO, both of which were locally excited. The high agreement with the experimental results was indirectly consistent with the claim that Ni–B is an amorphous alloy.^59–63

Fig. 9 Electrostatic potential diagrams for NiB₂, Ni₂B₂, Ni₃B₂, and Ni₄B₂.

Table 2 Molecular charges

Molecular	Electropositive sites (charge)	Electronegative sites (charge)	Electrostatic potential
NiB2	Ni3(0.012)	B1(−0.047)	−4.160e^−2–4.160 × 10^−2
		H4(−0.041)
Ni2B2	Ni3(0.014)	B2(−0.014)	−8.112e^−2–8.112 × 10^−2
Ni3B2	B1(0.117)	Ni3(−0.083)	−6.473e^−2–6.473 × 10^−2
		Ni5(−0.069)
Ni4B2	B5(0.080)	Ni1(−0.040)	−5.190e^−2–5.190 × 10^−2

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As can be seen from Table 3, FED² was the atomic contribution to the orbital. The attack object was guided by the 2FED²_HOMO value; whereby, the larger the value, the more vulnerable the atomic position was to the attack of the electrophile. The Ni₃ atom in NiB₂, the Ni₃ and Ni₄ atoms in Ni₂B₂, and the Ni₄ and Ni₅ atoms in Ni₃B₂ made the largest contributions. The Ni₁ and Ni₄ atoms in Ni₄B₂ making the largest contributions were electrophilic reaction sites. The FED²_HOMO + FED²_LUMO values predict the site of an attack by free radicals; whereby, the higher the value is, the more likely it is to be attacked. The Ni3 atoms in NiB₂, Ni₃ atoms in Ni₂B₂, Ni₃ atoms in Ni₃B₂, and Ni₁ and Ni₄ atoms in Ni₄B₂ contributed the most and were free radical reaction sites.^64–66

Table 3 Atomic contributions to the orbit^a

Symbol		FED^2HOMO	2FED^2HOMO	FED^2LUMO	2FED^2LUMO	FED^2HOMO + FED^2LUMO
a FED^2 is the amount of atomic contribution to the orbital.
NiB2	B1	0.2135	0.42706	0.2456	0.49124	0.4592
	B2	0.2135	0.42706	0.2456	0.49124	0.4592
	Ni3	0.5429	1.08582	0.4661	0.9322	1.0090
	H4	0.0150	0.03004	0.0213	0.04266	0.0364
	H5	0.0150	0.03004	0.0213	0.04266	0.0364
Ni2B2	B1	0.2066	0.41322	0.0881	0.17628	0.2948
	B2	0.2066	0.41316	0.0882	0.1763	0.2947
	Ni3	0.2934	0.5868	0.4119	0.8237	0.7053
	Ni4	0.2934	0.5868	0.4119	0.82372	0.7053
Ni3B2	B1	0.1093	0.21866	0.0313	0.06258	0.1406
	B2	0.1094	0.2187	0.0313	0.06258	0.1406
	Ni3	0.1978	0.39568	0.4878	0.9755	0.6856
	Ni4	0.2917	0.58348	0.2248	0.44968	0.5166
	Ni5	0.2917	0.58348	0.2248	0.44968	0.5166
Ni4B2	Ni1	0.1824	0.36484	0.2370	0.47394	0.4194
	Ni2	0.1822	0.36444	0.2365	0.47304	0.4187
	Ni3	0.1822	0.36444	0.2365	0.47304	0.4187
	Ni4	0.1824	0.36484	0.2370	0.47394	0.4194
	B5	0.1354	0.27072	0.0265	0.05302	0.1619
	B6	0.1354	0.27072	0.0265	0.05302	0.1619

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4. Conclusion

The analysis tools used in the present study feature some general implications for other analysis methods for experimental data. Here, Ni–B–AC catalysts were prepared by an impregnation reduction, and showed good stability and catalytic activity during the hydrogenation of β-pinene. Analyzed for the first time, a detailed analysis of the data of β-pinene hydrogenation single-factors was carried out using hierarchical analysis, which was highly consistent with the experimental results. The factors influence the catalyst stability, the selectivity and conversion of pinene, and the catalyst availability for industrial production. The analysis ideas presented in this study are also instructive for the further design and development of amorphous catalysts in the direction of nickel-based hydrogenation, but need to be further assessed for the preparation of such catalysts.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors wish to acknowledge the support of the Analysis and Testing Foundation of Kunming University of Science and Technology. The authors thank Dr Jiang for her assistance in this matter.

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Footnote

† Electronic supplementary information (ESI) available. See https://doi.org/10.1039/d2ra05632a

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