First-Principles Investigation of CO Adsorption on h-Fe 7 C 3 Catalyst

: h-Fe 7 C 3 is considered as the main active phase of medium-temperature Fe-based Fischer–Tropsch catalysts. Basic theoretical guidance for the design and preparation of Fe-based Fischer–Tropsch catalysts can be obtained by studying the adsorption and activation behavior of CO on h-Fe 7 C 3 . In this paper, the ﬁrst-principles method based on density functional theory is used to study the crystal structure properties of h-Fe 7 C 3 and the adsorption and activation CO on its low Miller index surfaces (cid:16) 110 (cid:17) , (cid:16) 111 (cid:17) , ( 101 ) , (cid:16) 111 (cid:17) and ( 001 ) . It was found that the low Miller index crystal plane of h-Fe 7 C 3 crystal has multiple equivalent crystal planes and that the maximum adsorption energy of CO at the 3F2 point of the (cid:16) 111 (cid:17) plane is − 2.50 eV, indicating that h-Fe 7 C 3 has a better CO adsorption performance. In addition, the defects generated at the truncated position of the h-Fe 7 C 3 crystal plane have a great impact on the adsorption energy of CO on its surface, that is, the adsorption energy of CO on Fe atoms with C vacancies is higher. The activity of CO after adsorption is greatly a ﬀ ected by the adsorption conﬁguration and less a ﬀ ected by the adsorption energy. The higher the coordination number of Fe atoms after adsorption, the higher the CO activity. At the same time, it was found that the bonding of O and Fe atoms is conducive to the activation of CO. corresponding with the CO orbital at (cid:16) 111 (cid:17) 3F2 has a split nearby E f , while this is not observed on the Fe atom at (cid:16) 111 (cid:17) 4F3 and ( 001 ) 3F1, indicating that back-donation from the Fe atom to the adsorbed CO molecule is relatively tiny at (cid:16) 111 (cid:17) 4F3 and ( 001 ) 3F1. This shows that the electron transfer is a ﬀ ected to some extent by the adsorption conﬁguration.


Introduction
Due to the increasing demand for petroleum in human industrial production and life, the conversion of synthesis gas (CO + H 2 ) into fuel and high-value organic chemicals through Fischer-Tropsch synthesis has been receiving increasing attention [1][2][3]. Owing to their high activity, high selectivity and low cost and the flexible distribution of low H 2 /CO synthesis gas conversion products, iron-based catalysts are widely used in the Fischer-Tropsch synthesis industry [4]. However, the phase types of Fe-based catalysts during Fischer-Tropsch synthesis are very complicated, and the understanding of their catalytic mechanism is not clear. Therefore, the active phase structure type and catalytic mechanism of iron-based catalysts need to be further studied to provide theoretical guidance for the design and preparation of new and efficient Fischer-Tropsch synthesis catalysts.
When an iron-based catalyst is used in the Fischer-Tropsch synthesis reaction, the catalyst precursor (α-Fe 2 O 3 ) is first reduced to magnetite (Fe 3 O 4 ) [5,6] and then converted into a mixture of iron oxide and carbide phases during the reaction, such as ε-Fe 2 C,έ-Fe 2.2 C, χ-Fe 5 C 2 , θ-Fe 3 C and h-Fe 7 C 3 [7,8]. Among them, Hägg carbide (χ-Fe 5 C 2 ) and Fe 2 C are considered as the main active phases [9]. However, in recent research, the catalytic activity of h-Fe 7 C 3 in medium-temperature Fischer-Tropsch synthesis (260-300 • C) was found to be higher than that of χ-Fe 5 C 2 and ε-Fe 2 C by Li Yongwang's team [10]. At present, the research on the catalytic mechanism in the medium-temperature Crystals 2020, 10 Fischer-Tropsch synthesis reaction needs to be deepened, and the adsorption activation behavior of CO on the h-Fe 7 C 3 surface has not been reported. In this paper, the characteristics of the crystal structure of h-Fe 7 C 3 , as well as the adsorption and activation of CO on its low Miller index crystal planes, were studied through the first-principles method of density functional theory to provide basic theoretical guidance for designing, preparing and controlling Fischer-Tropsch synthesis catalysts.

Calculation Methods
All calculations in this paper were conducted with the CASTEP(Cambridge Sequential Total Energy Package) according to the density functional theory (DFT). The Perdew-Burke-Ernzerh (PBE) functional in the generalized gradient approximation (GGA) was employed in the electron exchange correlation potential [11][12][13]. Spin polarization was included for all calculations on the ferromagnetic h-Fe 7 C 3 system to deal with an accurate description of magnetic properties by fixing the initial number of spins of each iron atom to 4. In order to calculate the plane wave basis set, the cut-off energy, the convergence accuracy of the self-consistent field and the k point were set as 400 eV, 2 × 10 −6 eV/atom and 3 × 3 × 1, respectively. Meanwhile, all atoms were allowed to be fully relaxed for calculating the h-Fe 7 C 3 unit cell structure. Furthermore, 28 iron atoms and 12 carbon atoms were used as crystal planes with the fixation of underlying atoms in order to reduce the calculation quantity while the adsorption of crystal planes and CO on the h-Fe 7 C 3 crystal plane was calculated. Moreover, a vacuum layer of 15 Å was added to the crystal planes to prevent applied forces between crystal planes from interfering calculation results.
We utilized h-Fe 7 C 3 as the unit cell structure, in accordance with a literature report, with the space group of P6 3 mc. Fourteen iron atoms and six carbon atoms were contained in the crystal lattice [10,14]. There were a total of 12 symmetric elements in the P6 3 mc symmetric group, including one threefold rotor, three screw axes, three mirror planes and three glide planes, as well as identity operations. Identical crystal planes were searched in line with the symmetry of h-Fe 7 C 3 , so as to avoid repeated selection of crystal planes. The basic idea is presented as follows: First, a coordinate system is established with three crystal axes; then, the direction vector Since it is difficult to obtain the vector product from a coordinate system that is not an orthogonal coordinate system (α = β = 90 • , γ = 120 • ), the vector product → β is solved by transforming the coordinates into the coordinates → α in the orthogonal coordinate system, and then the vector product is obtained before → β is converted into → β, as shown in Equation (1), Equation (2) and Equation (3): Crystals 2020, 10, 635 3 of 10 2.
→ γ = (a, b, c) and the point B x 2 , y 2 , z 2 are obtained by conducting symmetric operation on → β and the point A x 1 , y 1 , z 1 on the crystal plane based on the general equivalent point system of the P6 3 mc symmetry group (see Table 1).

3.
The intercept of the crystal plane on the coordinate axis is solved by the plane equation in the current coordinate system, as shown in Equations (4) and (5): where C is the transformation matrix of the above-mentioned coordinate. 4.
The Miller index of the symmetric crystal plane can be obtained from calculating the intercept with the plane equation. Besides, the stability of the crystal plane is measured by the surface energy, as shown in Equation (6): where E n is the total energy of the n-layer crystal plane, E bulk is the energy of a single-layer unit cell, n is the number of layers of unit cell and A is the area of the crystal plane. The smaller the surface energy, the more stable the crystal plane will be [15]. The adsorption of CO on h-Fe 7 C 3 is expressed by its adsorption energy: where E CO/slab represents the energy adsorbed by CO on the crystal plane, E slab is the energy of the crystal plane and E CO is the energy of free CO. The more negative the adsorption energy, the more stable the adsorption of CO on the crystal plane will be.
As can be seen from Table 1, the surface energy of a surface with a low Miller index is significantly lower than that of a surface with a high Miller index; furthermore, the 110 plane is the most stable among the surfaces with low Miller indexes. The crystal plane with low surface energy is more stable in thermodynamics, with a higher probability of occurring during crystal formation. In that case, five crystal surfaces with lower surface energy were selected for calculating CO adsorption and activation.
As can be observed from Table 2 Figure 2). Results are shown in Table 3.   A weak CO adsorption can be witnessed in the C position, and CO can barely be absorbed on the C position under a low coverage. With only two vertices and two 2F points, few positions on the 110 plane are suitable for CO absorption, according to By combining Figure 2 and Table 3, it can be seen that the point positions with large adsorption energy are all around a specific Fe atom, such as 2F2 and T2 on (11 0); T3, 3F2 and 4F1 on (11 1); T1 and 2F1 on (101); 2F1 and 4F3 on (11 1 ); and 3F1 on (001). The adsorption energies at these point positions are remarkably higher than other point positions on the same plane. This is because these Fe atoms are in the C-deficient position on the crystal plane, which makes it easier for them to adsorb CO.
The orbital of CO adsorbed on the surfaces is studied by calculating the local density of states (LDOS) of the adsorbed CO molecules. Based on Figure 4, the LDOS was analyzed for CO molecules adsorbed on the five surfaces of h-Fe7C3 with the highest adsorption energy. According to the curves shown in the figure, CO on the (11 0)2F2 and (101)2F1 has the localized 2π* orbital, which means that the back-donation from the surface to the adsorbed CO molecule is relatively tiny. For the CO on the (11 1)3F2, the 2π* orbitals are remarkably delocalized, which indicates the increasing backdonation from the surface to antibonding 2π* orbitals. Although the adsorption energy of CO on (001)3F1 and (11 1 )4F3 is large, the delocalization of the 2π* orbit is not obvious. Based on Figure 5, the d orbital of the Fe atom corresponding with the CO orbital at (11 1)3F2 has a split nearby Ef, It can be seen from Table 3  By combining Figure 2 and Table 3, it can be seen that the point positions with large adsorption energy are all around a specific Fe atom, such as 2F2 and T2 on 110 ; T3, 3F2 and 4F1 on 111 ; T1 and 2F1 on (101); 2F1 and 4F3 on 111 ; and 3F1 on (001). The adsorption energies at these point positions are remarkably higher than other point positions on the same plane. This is because these Fe atoms are in the C-deficient position on the crystal plane, which makes it easier for them to adsorb CO.
The orbital of CO adsorbed on the surfaces is studied by calculating the local density of states (LDOS) of the adsorbed CO molecules. Based on Figure 4, the LDOS was analyzed for CO molecules adsorbed on the five surfaces of h-Fe 7 C 3 with the highest adsorption energy. According to the curves shown in the figure, CO on the 110 2F2 and (101)2F1 has the localized 2π* orbital, which means that the back-donation from the surface to the adsorbed CO molecule is relatively tiny. For the CO on the 111 3F2, the 2π* orbitals are remarkably delocalized, which indicates the increasing back-donation from the surface to antibonding 2π* orbitals. Although the adsorption energy of CO on (001)3F1 and 111 4F3 is large, the delocalization of the 2π* orbit is not obvious. Based on Figure 5, the d orbital of the Fe atom corresponding with the CO orbital at 111 3F2 has a split nearby E f , while this is not observed on the Fe atom at 111 4F3 and (001)3F1, indicating that back-donation from the Fe atom to the adsorbed CO molecule is relatively tiny at 111 4F3 and (001)3F1. This shows that the electron transfer is affected to some extent by the adsorption configuration.
Crystals 2020, 10, x FOR PEER REVIEW 9 of 11 while this is not observed on the Fe atom at (11 1 )4F3 and (001)3F1, indicating that back-donation from the Fe atom to the adsorbed CO molecule is relatively tiny at (11 1 )4F3 and (001)3F1. This shows that the electron transfer is affected to some extent by the adsorption configuration.

Conclusions
In this study, the crystal structure characteristics of h-Fe 7 C 3 , as well as the adsorption and activation of CO on its low Miller index crystal planes, were studied through the first-principles method of density functional theory. The results show that the low Miller index crystal plane of the h-Fe 7 C 3 crystal has multiple equivalent crystal planes; in fact, the maximum adsorption energy of CO on the 111 plane is −2.50 eV, indicating that h-Fe 7 C 3 has better CO adsorption performance. In addition, the defects generated by the cut-off position of the h-Fe 7 C 3 crystal plane have a greater effect on the adsorption energy of CO on its surface, that is, the adsorption energy of CO on Fe atoms with C vacancies is higher. The activity after CO adsorption is greatly affected by the adsorption configuration and is less affected by the adsorption energy. The higher the coordination number of Fe atoms after adsorption, the higher the CO activity. In addition, the bonding of O and Fe atoms is beneficial to the activation of CO.