Effects of Reaction Atmospheres on Hydrogenation Selectivity of Bicyclic Aromatics on NiMoS Active Sites—Combining DFT Calculation and Experiments

Abstract

During the pre-hydrotreatment process, the hydrogen sulfide and ammonia present in the reaction atmosphere affect the conversion rate of bicyclic aromatics and the retention rate of monocyclic aromatic hydrocarbons (RRMA). In this study, 1-Methylnaphthalene (1-MN) is used to investigate hydrogenation behavior on Ni-Mo-S active sites. The results indicate that at low conversion rates, 1-MN is preferentially converted to 5-methyltetrahydronaphthalene (5-MTHN) on the S-edge, and can be simultaneously converted to 1-methyltetrahydronaphthalene (1-MTHN) and 5- MTHN on the Mo-edge. Additionally, the H₂S in the reaction atmosphere significantly competes with 1-MN for adsorption on the S-edge, limiting the hydrogenation selectivity of 5-MTHN, whereas NH₃ preferentially competes with 1-MN on the Mo-edge. At a high1-MN conversion rate, the competitive adsorption of 1-MN and MTHN is concentrated on the S-edge. Conversely, at a low bicyclic aromatic conversion rate, H₂S increases the RRMA, whereas NH₃ significantly lowers it.

1. Introduction

With the rapid development of new energy technology, the proportion of gasoline and diesel being utilized as vehicle fuel is gradually decreasing [1,2,3]. At present, converting excess fuel into raw chemical materials is an important and economically beneficial task for refineries [4,5]. Hydrocracking, using diesel as the feedstock, has developed rapidly in recent years [6,7,8]. One technical route by which to achieve this is to convert FCC light cycle oil, which is rich in bicyclic aromatic hydrocarbons, into high-value BTX [9,10,11]. However, the hydrogenation process of bicyclic aromatics is inevitably accompanied by the oversaturation of monocyclic aromatic hydrocarbons to cycloalkanes, which is not ideal for direct BTX production [12,13]. In the pretreatment process of diesel hydrocracking, maximum retention of monocyclic aromatics under deep hydrodenitrogenation and of polycyclic aromatics under hydrocarbon saturation is important for improving the economic efficiency of refineries [14].

Similarly to conventional hydrotreatment catalysts, the pretreatment catalyst for diesel hydrocracking uses sulfurized nickel and molybdenum nanoclusters as active sites [15,16,17,18,19]. These active sites have two types of edges: One, based on the nickel-modified (1,0,−1,0) plane of H-MoS₂, is referred to as the S-edge. Under hydrogenation reaction conditions, narrow coordination-unsaturated sites (CUSs) expose the unoccupied d orbitals from two nickel atoms. The other edge, based on the (−1,0,1,0) plane of H-MoS, is referred to as the Mo-edge. At this edge, there are several flat CUSs consisting of multiple exposed Ni/Mo atoms [20,21,22,23]. These two types of CUSs exhibit significant differences in their molecular orbital composition, adsorption selectivity for hydrocarbons, and hydrogenation performance [24,25,26].

In this study, we found that the composition of the reaction atmosphere could affect the reaction behaviors of bicyclic aromatics on the two active sites. Notably, a certain concentration of hydrogen sulfide or ammonia affects the catalytic capacity of the S-edge and Mo-edge in different ways. By combining DFT calculations and hydrogenation experiments, we comparatively investigated the phenomena and mechanisms underlying the influence of H₂S and NH₃ on the hydrogenation of bicyclic aromatics. We hope that the results constitute a valuable reference for R&D and operation condition control for catalysts in diesel hydrocracking pretreatment.

2. Results and Discussion

2.1. Hydrogenation of 1-MN on Ni-Mo-S Active Sites

The hydrogenation products of 1-MN on sulfurized FF-73 between 260 °C and 290 °C are listed in

Table 1. Hydrogenation products of 1-MN under H₂ atmosphere.

Products	1−MN	5−MTHN	1−MTHN	IBAs	1−MDHN	Liquid Yield wt%	RRMA %
Structural Formula
Temperature/°C	Content/wt.%
260	91.5	6.2	2.3	0	0	100.4	100.0
270	55.6	32.5	11.9	0	0	100.6	100.0
280	31.9	47.6	16.8	0.9	2.8	100.3	94.6
290	5.5	56.7	23.8	2.5	11.5	100.4	85.2

. At 260–270 °C, the conversion rate of 1-MN is lower than 50%. The major products are monoaromatic saturated products, namely 5-MTHN and 1-MTHN. As the conversion rate rises with reaction temperature, double-saturated-ring products such as 1-Methyldecahydronaphthalene (abbreviated as 1-MDHN) and other isomeric bicyclic alkanes (abbreviated as IBAs) can be detected. The retention rate of monocyclic aromatic hydrocarbons (abbreviated as RRMA) is used to compare the hydrogenation selectivity of the reactions. The method for calculating the RRMA is as follows:

RRMA = (PT1 + PT5)/(PT1 + PT5 + PI + PD1) × 100%

where PT1 stands for the mass fraction of 1-MTHN in the product;

PT5 is the mass fraction of 5-MTHN;

PI represents the mass fraction of IBAs;

PD1 denotes the mass fraction of 1−MDHN.

It was found that when the reaction temperature is 270 °C or lower, the RRMA is 100%, indicating that the conversion of bicyclic aromatics stops at monocyclic aromatics. Additionally, the RRMA decreases as the reaction temperature increases, with the RRMA being only 85.2% at a reaction temperature of 290 °C.

Notably, under a pure H₂ atmosphere, the content of 5-MTHN in the product is approximately three times that of 1-MTHN across all conversion rates, indicating that on the Ni-Mo-S active sites, the aromatic ring without a methyl group is easier to saturate. The calculations outlined below focus on the conversion of 1-MN on the S-edge and Mo-edge of Ni-Mo-S active sites. The catalytic reaction cycle of 1-MN on two active centers of Ni-Mo-S is shown in Figure 1. According to the calculation results, the hydrogenation saturation of the aromatics comprises two reaction pathways. In each reaction pathway, endothermic and exothermic elementary reactions occur alternately. Endothermic reactions occur when the hydrocarbon contains an odd number of hydrogen atoms and one free radical, whereas exothermic reactions occur when the hydrocarbon molecule contains an even number of hydrogen atoms and no free radicals. The activation energy of the endothermic reaction is higher, while that of the exothermic reaction is lower. In comparing the hydrogenation process of 1-MN on two different reaction active centers, the main differences lie in the first step, which involves breaking of the conjugated aromatic structures and an increase in the system energy.

In Figure 1, RE stands for the reaction energy of each elementary reaction and AE stands for the activation energy.

Several stable adsorption states of 1-MN on the Ni-Mo-S active sites have been calculated and are listed in

Table 2. Adsorption of 1-MN on Ni-Mo-S active sites.

Adsorption Location	Morphology	Adsorption Enthalpy/kJ·mol−1	Charge Transfer/e
Ni-S-edge		−84.68	0.092
		−73.48	0.075
		−54.52	0.061
Ni-Mo-edge		−146.36	0.167
		−81.05	0.081

. On the S-edge, the major adsorption form of 1-MN constitutes being upright and inserted into the narrow CUS. The main interaction involves the two exposed Ni atoms and the hydrocarbons. The adsorption and charge transfer change as the functional groups come into contact with the exposed Ni atoms. When the aromatic ring comes into contact with the Ni atoms, the adsorption enthalpy and charge transfer reach their maximum values. On the Mo-edge, there are two 1-MN adsorption forms. When the two aromatic rings of 1-MN adsorb parallel to the Mo-edge, their centers can both be attached to Ni atoms, resulting in a high adsorption enthalpy and charge transfer capacity. On the contrary, when the two aromatic rings adsorb perpendicularly to the Mo-edge, only the bridge bond can come into full contact with the active sites, leading to comparatively weaker adsorption. The changes in hydrogenation behavior caused by competitive adsorption between 1-MN and other reactants or additives on these two edges will be discussed later.

The breaking of the double-aromatic-ring structure of 1-MN by the active hydrogen on the S-edge, which is the key rate control step in 1-MN hydrogenation, was observed, with the results listed in

Table 3. Hydrogenation saturation of 1-MN on Ni-S-edge.

Adsorption Location	S-Edge
Hydrogen transfer position	Ring without methyl groups	Ring with methyl groups
Reaction
Pre-hydrogen transfer
Transition state
Post-hydrogen transfer
Reaction energy kJ/mol	+56.26	+103.09
Activation energy kJ/mol	+116.98	+158.32

. When the active hydrogen approaches the aromatic ring, the hybridization of the carbon atom transitions from sp² to sp³, resulting in bending of the aromatic ring and an exclusion effect on the CUS of the S-edge. This situation becomes more serious when the aromatic ring has a methyl substituent, because the methyl groups will stick out with the bends in the aromatic ring. The bending constitutes a shift from the original two-dimensional molecular configuration to a three-dimensional configuration that requires more space. The reaction energy and activation energy for the hydrogenation of the aromatic ring with methyl groups are much higher than for that without methyl groups. This is a likely explanation for why 1-MN is easier to convert into 5-MTHN than 1-MTHN on the Ni-Mo-S-based hydrotreatment catalyst, as observed in the experiments.

Based on the most stable adsorption form of 1-MN, namely flat adsorption in parallel, the rate control step of the conversion of 1-MN on the Mo-edge is calculated, with the results listed in

Table 4. Hydrogenation saturation process of 1-MN on Ni-Mo-edge.

Adsorption Location	Mo-Edge
Hydrogen transfer position	Ring without methyl groups	Ring with methyl groups
Reaction
Pre-hydrogen transfer
Transition state
Post-hydrogen transfer
Reaction energy kJ/mol	+57.90	+68.54
Activation energy kJ/mol	+113.09	+129.48

. On the Mo-edge, the active hydrogen could approach 1-MN from both exposed metal atoms. As the aromatic carbon receives the active hydrogen, the adjacent carbon atom simultaneously bonds with or approaches the exposed Ni atom. The newly generated chemical bond or the enhanced adsorption could lower the system energy of the transition state, which determines the activation energy of the hydrogenation saturation of the bicyclic aromatics. Moreover, the CUS on the Mo-edge is a relatively more open space than that on the S-edge. Even if the methyl groups increase the space volume of the aromatic ring after bending, the space above the Mo-edge could accommodate the three-dimensional hydrocarbon in the transition state to avoid squeezing with atoms on the active sites. Therefore, on the Mo-edge, the activation energy increase brought about by the substituent group of the bicyclic aromatics is quite limited, meaning that the 1-MN could be converted into both 5-MTHN and 1-MTHN with similar selectivity.

According to the 1-MN hydrogenation experiments conducted under a H₂ atmosphere, it can be concluded that the major product of 1-MN at a low conversion rate is 5-MTHN, with the content of 1-MTHN being only about one-third that of 5-MTHN. The calculation results indicate that 5-MTHN could be generated on both the narrow S-edge and the open Mo-edge, whereas 1-MTHN could only be generated on the latter.

2.2. Effects of Additives in Atmosphere on 1-MN Conversion

Some polar additive gas molecules in the H₂ atmosphere could also adsorb on the CUS of the Ni-Mo-S active sites, leading to competitive adsorption with the aromatic hydrocarbons. H₂S is a common component in a circulating hydrogen atmosphere. The adsorption of H₂S on the S-edge and Mo-edge was calculated, with the results listed in

Table 5. Adsorption of H₂S on S-edge and Mo-edge.

HOMO of H2S	Location	Number of Adsorption Molecules	Adsorption Morphology	Adsorption Enthalpy kJ/mol
	S-edge	1		−78.85
	Mo-edge	1		−54.68
	Mo-edge	2		−89.14

. The sulfur atoms are relatively large, and the HOMO is distributed symmetrically on both sides of the H₂S molecule. The HOMO space extension of the H₂S molecule could effectively cover the two Ni atoms on both sides of the CUS on the S-edge. When the H₂S molecule adsorbs on the S-edge, the S atom of the H₂S could bond with two Ni atoms of the S-edge simultaneously, leading to a high adsorption enthalpy close to that of 1-MN. However, on the Mo-edge, the H₂S molecule could only bond with a single exposed Ni atom. The adsorption enthalpy of H₂S is only approximately −55 kJ/mol. Even when two H₂S molecules adsorb on adjacent nickel atoms, the total adsorption enthalpy is only approximately −90 kJ/mol, still much lower than the flat adsorption enthalpy of one 1-MN molecule on the Mo-edge (approximately −150 kJ/mol). Based on the adsorption enthalpy difference, it could be predicted that a certain concentration of H₂S will preferentially compete with 1-MN for adsorption, whereas on the S-edge, the adsorption of 1-MN will be favored.

The distribution of 1-MN hydrogenation products under a mixed H₂S and H₂ atmosphere at different temperatures is presented in

Table 6. Hydrogenation products of 1-MN under mixed H₂S and H₂ atmosphere.

Products		1-MN	5-MTHN	1-MTHN	IBAs	1-MDHN	Liquid Yield wt%	RRMA %
Structural Formula
Reaction Temperature/°C	H2S Partial Pressure/MPa	Content/wt.%
270	0	55.6	32.5	11.9	-	-	100.5	100.0
	0.1	71.8	16.9	11.3	-	-	100.5	100.0
	0.2	77.7	12.6	9.7	-	-	100.6	100.0
280	0	31.9	47.6	16.8	0.9	2.8	100.3	94.6
	0.1	38.2	34.8	25.2	0.3	1.5	100.2	97.1
	0.2	48.5	27.4	23.5	0.1	0.5	100.4	98.8
290	0	7.5	55.7	22.8	2.5	11.5	100.4	84.9
	0.1	14.6	41.1	36.4	1.1	6.8	100.1	90.7
	0.2	20.3	38.9	35.7	0.9	4.2	100.2	93.6

. Compared with a pure H₂ atmosphere, the conversion rate of 1-MN decreases. At low concentrations of H₂S, the selectivity of 5-MTHN reduces remarkably, while the conversion path of 1-MTHN is less affected. As the concentration of H₂S rises, the content of 5-MTHN becomes close to that of 1-MTHN, indicating more severe inhibition of the conversion route to 5-MTHN. The experimental results verified the calculations indicating that competitive adsorption of H₂S and 1-MN is mainly concentrated on the S-edge over the Mo-edge. Meanwhile, the H₂S also hinders the further conversion of methyl-tetrahydronaphthalene (abbreviated as MTHN) to methyl-decahydronaphthalene (abbreviated as MDHN). The reason for this will be discussed in the next section.

The calculation results for NH₃ adsorption on the Ni-Mo-S active sites are listed in

Table 7. Adsorption of NH₃ on S-edge and Mo-edge.

HOMO of NH3	Location	Number of Adsorption Molecules	Adsorption Morphology	Adsorption Enthalpy kJ/mol
	S-edge	1		−90.35
	Mo-edge	1		−114.42
	Mo-edge	2		−205.37

. Despite the polarity of the NH₃ molecule being stronger than that of H₂S, the NH₃ molecule can only bond with one Ni atom on the S-edge. Owing to the adsorption morphology, the hydrogen atoms of NH₃ will repel the Ni atoms on the S-edge, leading to slight deformation of the CUS, increasing the system energy. Therefore, the adsorption enthalpy of NH₃ is close to that of H₂S and 1-MN. On the Mo-edge, the adsorption of NH₃ is free from the influence of steric hindrance, and the contribution of strong polarity to the adsorption enthalpy can be fully reflected. The adsorption enthalpy of a single NH₃ molecule can exceed −110 kJ/mol, while the total adsorption enthalpy of two adjacent NH₃ molecules can reach over −200 kJ/mol, which is much higher than the flat adsorption of one 1-MN molecule on the Mo-edge (approximately −140 kJ/mol). It can be predicted that the NH₃ molecules in the reaction atmosphere will engage in more severe competitive adsorption with 1-MN on the Mo-edge than on the S-edge.

The distribution of 1-MN hydrogenation products under a mixed NH₃ and H₂ atmosphere at different temperatures is provided in

Table 8. Hydrogenation products of 1-MN under mixed NH₃ and H₂ atmosphere.

Products		1-MN	5-MTHN	1-MTHN	IBAs	1-MDHN	Liquid Yield wt%	RRMA %
Structural Formula
Reaction Temperature/°C	NH3 Partial Pressure/MPa	Content/wt.%
270	0	55.6	32.5	11.9	0	0	100.6	100.0
	0.02	68.4	25.1	6.5	0	0	100.4	100.0
	0.04	76.0	20.6	3.4	0	0	100.9	100.0
	0.1	88.3	8.6	3.1	0	0	101.1	100.0
280	0	31.9	47.6	16.8	0.9	2.8	100.3	94.6
	0.02	45.4	40.3	11.9	0.3	2.1	100.6	95.6
	0.04	55.3	36.0	6.9	0.2	1.6	100.8	96.0
	0.1	68.4	28.2	2.7	0.1	0.9	101.4	96.9
290	0	7.5	55.7	22.8	2.5	11.5	100.4	84.9
	0.02	21.5	50.4	17.5	2	8.6	100.5	86.5
	0.04	34.8	44.2	12.5	1.4	6.1	100.7	88.3
	0.1	52.2	37.1	6.2	0.8	3.7	101.2	90.6

. Although in some experiments, the partial pressure of NH₃ is lower than that of H₂S, the inhibition of 1-MN hydrogenation is even stronger. When the reaction atmosphere contains NH₃, conversions to 5-MTHN and 1-MTHN are both hindered, with conversion from 1-MN to 1-MTHN more severely inhibited. These results support the calculated prediction that the competitive adsorption of NH₃ is more likely to occur on the Mo-edge, the primary location of 1-MTHN generation. In addition, the inhibition of MTHN-to-MDHN conversion by NH₃ is not as strong as that by H₂S, leading to a lower content of monocyclic aromatics affected by NH₃ at the low 1-MN conversion rate.

2.3. Effects of Additive in Atmosphere on RRMA

Compared to the position of the substituent groups, the RRMA in the hydrogenation of bicyclic aromatics is of greater relevance to pretreatment for diesel hydrocracking. In the deep conversion step of bicyclic aromatic hydrogenation, the competitive adsorption between the intermediate monocyclic aromatics and the unconverted monocyclic aromatics determines the RRMA. The adsorption of 1-NM, 5-MTHN, and 1-MTHN on the Ni-Mo-S active sites was calculated, with the results listed in

Table 9. Adsorption of 1-MN, 1-MTHN, and 5-MTHN on S-edge and Mo-edge.

Hydrocarbons	1-MN	1-MTHN	5-MTHN
Structural formula
HOMO
Eigenvalues/eV	−5.34	−5.55	−5.43
Adsorption morphology on S-edge
Adsorption enthalpy/kJ·mol−1	−84.68	−79.51	−88.75
Charge transfer/e	0.092	0.128	0.142
Adsorption morphology on Mo-edge
Adsorption enthalpy/kJ·mol−1	−146.36	−78.10	−68.20
Charge transfer/e	0.167	0.086	0.061

. 1-MN is a planar-structure molecule with conjugated double aromatic rings. The HOMOs are homogenously distributed on the conjugated-double-ring plane. As both 1-MTHN and 5-MTHN consist of an aromatic ring and a cycloalkane ring, the HOMOs of MTHNs are concentrated on a single aromatic ring. On the S-edge, only one aromatic ring of the hydrocarbons could strongly interact with the narrow CUS, making the effective contact areas and the adsorption energies of 1-NM and MTHNs relatively close. On the Mo-edge, the double aromatic rings of 1-NM could both come into sufficient contact with the exposed Ni atoms of the CUS, whereas the single aromatic ring of MTHNs could not provide matching adsorption capacity alone. Therefore, it can be predicted that competitive adsorption of 1-MN and MTHNs is most likely to occur on the S-edge.

1-MN hydrogenation under different atmospheres at higher temperatures and reaction rates was conducted, and the product distributions are listed in

Table 10. Hydrogenation products of MN at high temperature.

Products			1-MN	5-MTHN	1-MTHN	IBAs	1-MDHN	Liquid Yield %	RRMA %
Structural Formula
Reaction Temperature/°C	Additive	Partial Pressure/MPa	Content/wt.%
290	/	0	7.5	55.7	22.8	2.5	11.5	100.4	84.9
	H2S	0.1	14.6	41.1	36.4	1.1	6.8	100.1	90.7
	H2S	0.2	20.3	38.9	35.7	0.9	4.2	100.2	93.6
	NH3	0.04	34.8	44.2	12.5	1.4	6.1	100.7	88.3
	NH3	0.1	52.2	37.1	6.2	0.8	3.7	101.2	90.6
300	/	0	0.8	40.1	17.3	5.1	36.7	99.7	58.8
	H2S	0.1	3.5	52.9	20.6	3.9	21.1	99.9	74.6
	H2S	0.2	6.2	64.0	23.1	0.3	6.4	100.2	92.9
	NH3	0.04	10.2	45.4	20.5	3.3	20.6	100.5	73.4
	NH3	0.1	18.6	50.7	22.5	1.4	6.8	100.9	89.9

. Under the pure H₂ atmosphere, the conversion rate of 1-MN reaches 92.5% and the content of bicyclic cycloalkanes (sum of 1-MDHN and IBAs) reaches approximately 14% at 290 °C. When the reaction temperature reaches 300 °C, the conversion rate of 1-MN exceeds 99%, accompanied by approximately 40% of the bicyclic cycloalkanes. The H₂S in the reaction atmosphere hinders the conversion of 1-MN and MTHN simultaneously, whereas the more significant inhibition is reflected in the deep hydrogenation saturation step of MTHN. From another perspective, at a low 1-MN conversion rate, the H₂S increases the RRMA compared to the pure H₂ atmosphere. Although NH₃ could also hinder the entire reaction chain of 1-MN hydrogenation, its inhibition of the deep hydrogenation saturation of MTHN is less effective than that of H₂S. Moreover, multiple NH₃ molecules densely adsorbing on the Ni atoms could weaken the competitive adsorption advantages of bicyclic aromatics over monocyclic aromatics on the Mo-edge. At the same reaction temperature, the products in the NH₃ mixed atmosphere consist mostly of unconverted 1-MN, with the sum of fully hydrogenated saturated cycloalkanes even exceeding that of H₂S. The RRMA under the NH₃ mixed atmosphere is lower than that of H₂S.

Both the experimental and computational results indicate that the addition of H₂S and NH₃ to the reaction atmosphere could affect the product distribution of 1-MN. H₂S preferentially affects the S-edge of the Ni-Mo-S active sites. Although H₂S adsorption will hinder the conversion of 1-MN, the deep hydrogenation saturation of MTHN could also be effectively inhibited. In fact, H₂S slightly increases the RRMA at a low conversion rate of the bicyclic aromatics. The inhibition of NH₃ is stronger than that of H₂S, and it preferentially affects competitive adsorption on the Mo-edge. NH₃ less effectively inhibits the subsequent deep conversion of MTHN, so that the NH₃ in the reaction atmosphere significantly lowers the RRMA relative to H₂S at the low conversion rate.

3. Materials and Methods

3.1. Experimental Section

One commercialized diesel hydrocracking pretreatment catalyst from Sinopec (Beijing, China), branded as FF-73, is used for the hydrogenation experiments in this study. The properties of the catalyst are listed in

Table 11. Properties of hydrocracking pretreatment catalyst FF-73.

Item	Parameter
MoO3 wt.%	13–18
NiO wt.%	3.0–5.0
Supports	γ-Al2O3
Specific surface area/m2·g−1	160–200
Pore volume/cm3·g−1	0.4–0.6

.

The hydrogenation reactions were carried out in a fixed-bed reactor with an inner diameter of 6 mm length of 200 mm, loaded with 5.0 g of the FF-73 catalyst. The catalyst is shaped into small, 20–40-mesh particles. Both ends of the reactor are blocked with inert 20-mesh–40-mesh silicon carbide particles. Firstly, the hydrogenation catalyst needs to be pre-sulfurized. A cyclohexane solution with 5.0 vol% dimethyl disulfide is used as the sulfurizing feedstock. The sulfurization is performed at 650 K with 5.0 MPa of hydrogen and a weight hourly space velocity (WHSV) of 2.0 h⁻¹ for 10 h.

A transmission electron microscopy (TEM) image of the sulfurized FF-73 is shown in Figure 2, while the statistics of the geometric morphology of the Ni-Mo-S active sites according to 25 TEM images are listed in

Table 12. Geometric statistics of Ni-Mo-S active sites.

Length/nm	Proportion/%	Stack Layer	Proportion/%
<5	14.2	1	70.5
5–8	76.4	2	21.1
>8	9.4	≥3	8.4
Average Length/nm	6.6	Average Stack Layer	1.4

. The image and the statistics show that the Ni-Mo-S active sites are mainly composed of single-layer nanoclusters, with their length mostly in the range of 5.0 nm–8.0 nm.

The average length of the active sites is calculated according to the following formula:

$${\mathrm{L}}_{\mathrm{A}} = {\displaystyle \frac{{\sum }_1^{n}Li \times Pi}{{\sum }_1^{n}Pi}}$$

where L_A is the average length of the active sites;

Li is the average length of each stack layer;

Pi is the proportion of each stack layer.

The average stack layer is calculated according to the following formula:

$${\mathrm{S}}_{\mathrm{A}} = {\displaystyle \frac{{\sum }_1^{n}Si \times Pi}{{\sum }_1^{n}Pi}}$$

where S_A is the average stack layer of the active sites;

Si is the number of each stack layer;

Pi is the proportion of each stack layer.

After sulfurization, the mixture of 20 wt.% 1-MN dissolved in cyclohexane is pumped into the reactor. The reactions are performed with different temperatures and WHSVs, whereas the gas/oil ratio is fixed at 600 (v/v) and the reaction pressure is set at 5.0 MPa. The reaction atmospheres are diverse, including pure H₂, H₂ mixed with H₂S, and H₂ mixed with NH₃, with adjustable partial pressures. The liquid products are collected after a stabilization period of 4.0 h and analyzed offline on an Agilent 4890D gas chromatograph (Santa Clara, CA, USA) with a 60.0 m capillary Rtx-1 column (0.25 mm, RESREK, Bellefonte, PA, USA). A Finnigan TRACE gas chromatography/mass spectrometry (GC/MS) system consisting of a TRACE Ultra gas chromatograph (Thermo Fisher Scientific, Waltham, MA, USA) capillary column and an HP 5973 MS detector (Agilent, Santa Clara, CA, USA) is used to analyze the collected liquid products for further compound identification.

3.2. Computational Section

3.2.1. Modeling

The computational model of the Ni-Mo-S single-layer active nanocluster is derived from our previous research [27,28,29,30]. The atomic structure diagram of the Ni-Mo-S nanocluster model is shown in Figure 3. A sufficient Ni atom concentration on the edges provides an environment that is prone to CUS formation under hydrogenation conditions [31,32].

3.2.2. Calculation Method

The DFT calculation are perfomed using the DMol³ code in Materials Studio 7.0 (Accelrys, San Diego, CA, USA). The calculation method used herein makes reference to relevant prior research conducted by us, though some parameters have been adjusted (as shown in

Table 13. Calculation method.

Items		Parameter
Functions		General gradient approximation–Perdew–Burke–Ernzerhof function (GGA-PBE) [33]
Basis set		Double numerical plus polarization basis (DNP) [34,35]
Electron spin		Open shell
Symmetry		Asymmetry
Self-consistent field density convergence (SCF)		1 × 10−5
Thermal smearing		2 × 10−4 Hartree (Ha)
Orbital cut-off		4.9 angstroms (Å)
Core treatment		Effective core potentials (ECPs)
Dispersion correction		Grimme 06 [36,37]
Exchange–correlation Dependent factor, s6		0.75
Damping coefficient, d		20.0
Grimme 6.0 atomic dispersion parameters [38,39]		Element	Interaction distance R0	Dispersion coefficient C6
		H	1.001	1.451
		C	1.452	18.134
		N	1.397	12.748
		S	1.683	57.729
		Ni	1.562	111.943
		Mo	1.639	255.686
Geometry optimization	Energy tolerance	1 × 10−5 Hartree (Ha)
	Force tolerance	3 × 10−3 Ha/Å
Transition state	Transition state search	Complete linear synchronous transit (LST) and quadratic synchronous transit (QST) methods [40]
	RMS force	0.003 Ha/Å
	Transition state confirmation	Nudged elastic band (NEB) method [41,42]
	Transition state optimization	Eliminating redundant imaginary frequencies

). To simulate adsorption under reaction conditions, the temperature is set at 553 K (280 °C). In addition, the H₂ pressure is set at 5.0 MPa, the partial pressure of H₂S or NH₃ at 0.1 MPa, and the partial pressure of the hydrocarbons at 0.25 MPa.

4. Conclusions

According to the quantum chemistry calculations and experimental results obtained herein, it can be concluded that on the S-edge, 1-MN is more likely to convert to 5-MTHN, whereas on the Mo-edge, 1-MN can convert to 5-MTHN and 1-MTHN synchronously. H₂S molecules and 1-MN preferentially compete for adsorption on the S-edge, while the NH₃ molecules have an advantage on the Mo-edge. At a low 1-MN conversion rate, the H₂S in the reaction atmosphere will reduce the selectivity of 5-MTHN, whereas the NH₃ will reduce that of 1-MTHN. At a high 1-MN conversion rate, the competitive adsorption of 1-MN and MTHN will be concentrated on the S-edge. At a low conversion rate, H₂S slightly increases the RRMA, whereas NH₃ lowers it.