Interdiscip Sci Comput Life Sci (2009) 1: 308–314 DOI: 10.1007/s12539-009-0050-9
Study of the Adsorption Step in the Oxidative Dehydrogenation of Propane on V2 O5 (001) Using Calculations of Electronic Density of States 1
Ngoc Ha NGUYEN1∗ , Tran Thanh HUE1 , Minh Tho NGUYEN2 (Department of Chemistry, and Center for Computational Science, Hanoi National University of Education, Hanoi 10000, Vietnam) 2 (Department of Chemistry, and Mathematical Modeling and Computational Science Center (LMCC), University of Leuven, B-3001 Leuven, Belgium)
Received 29 April 2009 / Revised 9 July 2009 / Accepted 9 July 2009
Abstract: The calculations of electronic density of states were applied to obtain insights into the molecular mechanisms of chemical reactions. They are able to predict the active sites and to explain the Mars-van Krevelen redox mechanism of the oxidative dehydrogenation of propane on V2 O5 (001). From the calculated results of this reaction, directions for selecting a reasonable catalyst for other processes can be derived. Key words: density functional theory, density of states, partial density of states, adsorption.
1 Introduction Most of chemical reactions are accompanied by the changes in not only in the internal energy but also in the electronic structure of the starting systems. Therefore a study of the changes in electronic structure versus energy can provide a deep look inside the chemical transformations, and especially in the mechanism of heterogeneous processes. The first important step of any heterogeneous process is the adsorption. The interaction between an adsorbate (as reactants) and the surface of adsorbent (generally the catalysts) is a crucial factor that decides the selectivity and productivity of the whole process. The analysis of the changes in structural parameters allows useful information about the strength of the adsorption to be obtained. An analysis of the charge flow, expressed through calculations of isosurface of differential charges, could be used to describe the character of the bonding and the changes of the electronic density due to adsorption. On the other hand, a decomposition of the density of states (DOS) into the partial density of states (PDOS) can provide with important and detailed information about the electron transfer process between adsorbate and adsorbent. Furthermore, the active sites can also be predicted by the DOS, and therefore this can help in choosing a catalyst for a certain process of interest. The objective of
the present study is to explore the performance of electronic DOS in investigating the redox mechanism of the oxidative dehydrogenation of propane on a V2 O5 (001) surface.
2 Theoretical approach The electronic density of states g(ε) (Yang and Parr, 1985) at energy ε, is defined as: g(ε) =
δ(εi − ε)
(1)
i
Where εi is Kohn-Sham eigenvalue of the corresponding Kohn-Sham orbitals ψi (r), δ(εi − ε) is the delta Dirac function. In solid state, the Fermi-Dirac probability distribution function f (εi − μ) is applied for electrons in the following way: f (εi − μ) =
exp
1 εi −μ kB T
(2) +1
At T = 0, μ is equal to the Fermi energy εF , f (εi − μ) = 1 when εi < μ and f (εi − μ) = 0 when εi > μ and therefore total electrons N in one unit cell can be expressed by:
*Corresponding author. E-mail:
[email protected]
N=
g(ε)f (ε − μ)dε
(3)
Interdiscip Sci Comput Life Sci (2009) 1: 308–314
309
And then μ N=
g(ε)dε
(4)
0
Derivative of Equation (4) with respect to μ, at constant T and V results in: ∂N 1 = = S = g(εF ) (5) ∂μ T,V η From Equation (5), the hardness η and global softness S can be calculated by using g(εF ). The local density of states (LDOS) g(ε, r) is defined as: g(ε, r) = |ψi (r)|2 δ(εi − ε). i
At 0K:
ρ(r) =
μ
g(ε, r)dε 0
(6)
The Fukui function is given by f (r) =
∂ρ(r) ∂N
T,V
.
Substituting the Equation (6) into the Fukui function gives the following expression: f (r) =
∂ρ(r) ∂N
T,V
= g(εF , r)
=
∂ρ(r) ∂μ
∂μ T,V
∂N
T,V
1 S
(7)
Thus: g(εF , r) = f (r).S = s(r)
(8)
Where s(r) is local softness. The partial density of states (PDOS) is a useful construct to introduce at this point; as they are obtained from decomposition of the total density of states. The PDOS is defined through: gj (ε, r) = |χj |ψi (r)|2 δ(εi − ε) (9) i
Using (5), (8) and the principle of hard and soft acid and base (HSAB) (W. Yang and R. G. Parr, 1985; L. T. Nguyen et al., 1999), the active sites of reactants can be predicted. Moreover, the changes of the LDOS and PDOS during a chemical process provide the information about: (i) the adsorption type: only chemical adsorptions lead to the significant changes of DOS. (ii) an analysis of orbital contributions into PDOS allow details to be obtained about the right direction of molecules before reaction (which state being more important).
3 Result and discussion All calculations were performed by using the SIESTA program code (Soler et al., 2002). The exchangecorrelation functional proposed by Perdew, Burke, and Ernzerhof (PBE) has been used, in conjunction with a double-zeta basis plus polarization (DZP) basis set for valence electrons. The core electrons are “frozen” in their atomic state by using norm-conserving pseudopotentials in its fully nonlocal (Kleinman-Bylander) Troullier-Martins form with mesh-cutoff (real energy) as defined to be the equivalent plane wave cutoff for the grid of 680 eV. The 2×4×1 k-grids for Brillouin zone integrations and 2×7×6 for finding cell parameters were used. The vibrational modes were calculated from a finite difference approximation of the energy for the Hessian matrix (Frederiksen et al., 2007). Some results listed in the Tables 1, 2 and 3 are calibration for the methods chosen. The calculated results are reliable as they are in good agreement with experimental data. Table 1
Selected structural parameters and dipole moment of C3 H8 . Distances (r) are given in ˚ A, bond angles (a) in degrees and dipole moment in Debye. r(C-C)
a(CCC)
Dipole moment
Present work
1.53
112.9
0.068
Experiment
1.54a
112.4b
0.084c
a M.
Mondellon, 1995; b M. Moseler, 2000; c R. Merz and F Linder, 2003
into contributions due to different angular momentum components χj (s or px , py , pz , · · · ).
Table 2
Vibrational frequencies of C3 H8 (in cm−1 ).
Present work
3115.6
3109.0
3098.5
3094.4
3054.9
3019.1
3015.6
3008.9
Experimenta
2977.0
2973.0
2968.0
2968.0
2967.0
2962.0
2887.0
2887.0
Present work
1476.7
1462.6
1459.5
1450.6
1442.8
1395.5
1387.0
1342.1
Experiment
1476.0
1472.0
1464.0
1462.0
1451.0
1392.0
1378.0
1338.0
Present work
1289.1
1185.7
1165.7
1107.4
940.8
928.5
906.5
758.9
Experiment
1278.0
1192.0
1158.0
1054.0
940.0
922.0
869.0
748.0
a http://webbook.nist.gov/
310 Table 3
Interdiscip Sci Comput Life Sci (2009) 1: 308–314 Lattice parameters of V2 O5 (orthorhombic), cell vector modules in ˚ A and cell angles in degrees a
b
c
α
β
γ
Present work
11.510
3.563
4.183
90
90
90
Experimenta
11.522
3.566
4.375
90
90
90
a reaction is occurred between C3 H8 and V2 O5 follows the oxidation-reduction mechanism but not acid-base reaction because C3 H8 is “soft”, and on the contrary V2 O5 (001) is “hard”. This result agrees with available experimental results (Late et al., 2002), that is, the oxidative dehydrogenation of propane on V2 O5 (001) is proceeded via the Mars-van Krevelen redox mechanism.
a Fachinformationszentrum
Karlsruhe, and the U.S. Secretary of Commerce on behalf of the United States, Data 99808-ICSD, 2006
3.1
Prediction of active sites of the oxidative dehydrogenation of propane on V2 O5 (001) Bulk V2 O5 forms a layer-type orthorhombic lattice with space group P mmn (D2H-13). Its unit cell, V4 O10 , comprises two formula units. In the crystal structure (Fig. 1), the layers are stacked in such a way that distorted VO6 octahedra are formed with V-O bond distances varying between rather small (1.59 ˚ A) and quite large (2.79 ˚ A) value. This large value is indicative of a weak van der Waals bond, which explains why V2 O5 presents an easy cleavage parallel to the (001) plane. The (001) surface is therefore chosen for modeling of the catalytic dehydrogenation of propane, as it is the most representative and stable one in the vanadia catalyst. Fig. 2
System C3 H8 + V2 O5 (001)
1.8 1.6
εF
Fig. 1
Crystal structure of V2 O5 .
States/eV
1.4
O20
1.2 1.0
V4 O8 O10
0.8 0.6 0.4 0.2 0
–10
Fig. 3
–5 eV
0
LDOS of some atoms in V2 O5 (001)
1.4 1.2 States/eV
The supercell V2 O5 (001)-(1×2×2) is modeled as a slab two layers with vacuum region of 15 ˚ A. LDOS s(r) of some atoms of C3 H8 and V2 O5 (001) present before and after adsorption are calculated via Eq. (8) and displayed in Figures 3, 4 and 5. -System C3 H8 + V2 O5 (001): The total DOS g(ε) of all states of C3 H8 and V2 O5 (001) are shown in Fig. 5. The intersection point between 2 lines, g(ε) and εF , is the global softness S, therefore we can find out a S value of C3 H8 being equal to 1.24, while that of V2 O5 (001) amount to nearly 0. The same method is used to evaluate the local softness s(r) = g(εF , r). The results are presented in Figures 3 and 4. The calculations show the very small s(r) values of 1, 2, 3-fold coordinated O and V (∼zero, Fig. 3), whereas the values for C2, H5 and C1 are quite different, ranging from 0.1 to 0.22. The calculated results of g(εF ) and g(εF , r) lead to the following prediction:
1.0 0.8
LDOS_C1 LDOS_C2 LDOS_H3 LDOS_H5 εF
0.6 0.4 0.2 0
Fig. 4
eV
LDOS of some atoms of C3 H8
Interdiscip Sci Comput Life Sci (2009) 1: 308–314 20
εF(V2O5)=– –6.53 eV
States/eV
3.2
Mechanism of the electron transfer in the adsorption step of C3 H8 on V2 O5 (001) Previous theoretical and experimental results have shown that the adsorption step of C3 H8 is the ratedetermining step (Late et al., 2002). In the present study, we have used the electronic DOS to study the electron transfer process of the adsorption step of C3 H8 with an orientation of CH2 onto V2 O5 (001).
εF(C3H8)=––7.24 eV
15
TotalDOS_V2O5 10 TotalDOS_C3H8
5 0
_
5
Fig. 5
eV
0
Total DOS of C3 H8 and V2 O5 (001)
The HOMO of the electron donor partner and the LUMO of the electron acceptor partner are important in indicating the nature of the interactions. The molecule C3 H8 turns out to be an electron donor, and V2 O5 (001) an electron acceptor. As a consequence, electrons are transferred from the HOMO of C3 H8 to the LUMO of V2 O5 (001). In solid state, the Fermi energy is the energy of the highest occupied state, so the meaning of s(r) or g(εF , r) indicates how many states (atom position vector r) are expected to contribute to the HOMO: the higher the s(r), the higher the possibility of electron transfer. The LDOS at Fermi energy of C2, H5 (Fig. 3) indicates that the CH2 group is more active than the CH3 group, which is in good agreement with the calculated results of activation energy Ea using the Climbing Image-Nudged Elastic Band method, and chemisorption energy Eads listed in the Table 4. Table 4
Ea and Eads of two directions of the adsorption step
Direction
Ea [kJ/mol] (present work)
Ea [kJ/mol] (experiment)
Eads [kJ/mol] (present work)
CH2
96.8997
87a ;110-120b
−6.0133
CH3
141.4714
a R.Grabowski,
311
15.5523
2006; b M. D. Argyle, 2002.
The lower Ea and Eads show that the initial attack at the CH2 site is predominant. The calculated activation energy is qualitative agreement with experimental results. For V2 O5 which is an electron acceptor, only the unoccupied states being above the Fermi level were considered. The results shown in Fig. 3 indicate that unoccupied states of vanadium atoms have the highest contributions, and they contribute the most to the LUMO of V2 O5 (001). A direct interaction between CH2 and V species could not occur because of a steric hindrance, the 1-fold coordinated O (such as O13) should instead interact with CH2 . In essence, there is an electron transfer process between CH2 and V (such as V7) through the 1-fold coordinated O.
Fig. 6
C3 H8 adsorbed on V2 O5 (001)
By analysing LDOS of the positions C2, H5, O13 and V7 before and after C3 H8 adsorption (Figures 7 and 8) the possibility of losing/gaining electron for each atom can be estimated. The sum of all states of each atom is constant before and after adsorption; the occupied states of the electron donor atom should be reduced while its unoccupied states are increased after adsorption. Reversely, the occupied states of the electron acceptor atom should be increased while its unoccupied states are reduced after adsorption. the situation is changed, that is, the occupied states of C2 and H5 are depleted while the unoccupied states with higher density appear and approach closer to the Fermi level than corresponding occupied and unoccupied states before adsorption. These results demonstrate that C2 and H5 atoms lost electrons after adsorption. The results shown in Figure 6 indicate that the occupied states of C2 and H5 before adsorption are quite large at Fermi level, while their unoccupied states are far from Fermi level. After adsorption the situation is changed, that is, the occupied states of C2 and H5 are depleted while the unoccupied states with higher density appear and approach closer to the Fermi level than corresponding occupied and unoccupied states before adsorption. These results demonstrate that C2 and H5 atoms lost electrons after adsorption. The results of LDOS for O13 and V7 are shown in Fig. 8. An interesting feature is that a high density of occupied states (nearly 1.4 states/eV) of V7 appears at the Fermi level after adsorption. It can be seen that
Interdiscip Sci Comput Life Sci (2009) 1: 308–314
States/eV
312 LDOS_C2_before LDOS_C2_after LDOS_H5_before LDOS_H5_after εF_before εF_after
1.4 1.2 1.0 0.8 0.6 0.4 0.2 0
–10
–5
0
5
eV
States/eV
Fig. 7
1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0
LDOS of C2, H5 atoms before and after adsorption
LDOS_O13_before LDOS_O13_after εF_after LDOS_V7_before
LDOS_V7_after εF_before
–10
–5
0
eV
Fig. 8
LDOS of O13, V7 atoms before and after adsorption
the occupied density of states of O13 remains almost unchanged, furthermore the shape of LDOS for O13spectrum is only slightly changed before and after adsorption. Accordingly, an electron transfer process effectively occurs from C2 and H5 to V7 via O13. The significant change in spectra intensity of C2, H5, V7 indicates the presence of a typical chemical adsorption. 3.3
Frontier orbitals and further analysis of PDOS
The calculation is performed using the Equation (9) for DOS for each atomic state (atomic orbitals such as s, px, py, pz, · · · ). Analysis of PDOS reveals the contributions of different angular momentum components to the chemical reaction process. The results in Fig. 9
2S_C2_before 2S_C2_after 2pz_C2_before 2pz_C2_after 2py_C2_before 2py_C2_after 2px_C2_before 2px_C2_after εF_before εF_after
0.7 0.6 0.5 States/eV
show the PDOS of 2 s, 2 px, 2 py v` a 2 pz for C2 before and after adsorption. The 2 s states of C2 are almost absent from the adsorption process as pointed out by a very small DOS at the Fermi level before adsorption. A similar observation can be made for the 2 s states of O13 (Fig. 10). The density of occupied states 2py of C2 (2 py C2) before adsorption is quite large (being nearly 0.2 states/eV) at the Fermi level while the density of occupied states of C2 (2 pz and 2 px) is very small (∼0.0 states/eV at the Fermi level). An other interesting result is the appearance of the highest density of unoccupied states 2py C2 near the Fermi level after adsorption. These results demonstrate that the 2 py states of C2 make the largest contribution to the adsorption process.
0.4 0.3 0.2 0.1 0
–10
–5
0 eV
Fig. 9
PDOS 2s, 2px, 2py, 2pz of C2 atom before and after adsorption
Interdiscip Sci Comput Life Sci (2009) 1: 308–314
313
εF
0.2 States/eV
2py_O13 2px_O13
0
–5
0 eV
Fig. 10
PDOS 2s, 2px, 2py, 2pz of O13 atom
3dxy 3dyz 3dz2 3dxz 3dx2-y2 εF
0.7
States/eV
0.6 0.5 0.4 0.3 0.2 0.1 0
Fig. 12 –10
Fig. 11
–5 eV
(a) LUMO V2 O5 (001); (b) LUMO V2 O5 (001)
0
PDOS of AOs 3 d of V7 atom
The partial densities of unoccupied states of O13 and V7 atoms before adsorption are shown in Figures 10 and 11. The higher density of unoccupied states belongs to 2py O13 atom, and especially 3dxy V7 atom. The 2py O13 and 3dxy V7 maps can be found in the Cartesian coordination system by seeing the LUMO V2 O5 (001) (contour value of 0.0402 electron/˚ A3 ) in two different directions shown in Figures 12(a) and 12(b). Especially, at a lower contour value of 0.0233 electron/˚ A3 (Fig. 13), the overlap between 2py O13 and 3dxy V7 in the LUMO V2 O5 (001) can be seen with reasonable sign to easily merge with the HOMO C3 H8 to which the 2py C2 contributes the largest. Approximately, the shape of orbitals contains the space allowed for electron moving with the highest probability distribution, and accordingly the 2py C2 merges easily with the 2py O13. That is the reason for why an electron transfer process occurs from C2 to V7 via O13. Moreover, from the principle of maximum overlap in molecular orbital theory, the CH2 group is expected to be more active than the CH3 due to the higher density of states (Fig. 13).
4 Conclusion The calculations based on electronic density of states appear to be useful to probe the chemical interactions, and can be used to follow the adsorption processes. They can be helpful in predicting the active sites, the
Fig. 13
HOMO C3 H8 and LUMO V2 O5 (001)
direction of molecules in reactions and thereby the electronic mechanism of reactions. The properties of the orbitals involved in the process can be explained from the calculated PDOS. In addition, the results of this study for C3 H8 on V2 O5 (001) can be used as a starting point for further studies to select an efficient catalyst to similar processes.
Acknowledgments This research is supported by the project B2008-17-132 “Theoretical studies of nbutane oxidative dehydrogenation on metal oxides” by Hanoi National University of Education. We would like to thank Dr. Le Minh Cam, Faculty of Chemistry, for helpful discussion.
References [1] Argyle, M.D., Chen, K., Bell, A.T., Iglesia E. 2002. Effect of catalyst structure on oxidative dehydrogenation
314
[2]
[3]
[4]
[5]
[6]
Interdiscip Sci Comput Life Sci (2009) 1: 308–314 of ethane and propane on alumina-supported vanadia. Journal of Catalysis 208, 139. Frederiksen, T., Paulsson, M., Brandbyge, M., Jauho, A.P. 2007. Inelastic transport theory from firstprinciples: methodology and applications for nanoscale devices. Phys Rev B 75, 205413.1-205413.22. Grabowski, R. 2006. Kinetics of oxidative dehydrogenation of C2 -C3 alkanes on oxide catalysts. Catylis Reviews 48, 199–268. Late, L., Blekkan, E.A. 2002. Kinetics of the oxidative dehydrogenation of propane over a VMgO catalyst. Journal of Natural Gas Chemistry 11, 33–42. Merz, R., Linder, F. 2003. Elastic and vibrationally inelastic scattering of low-energy electrons from propane. J Phys B: At Mol Opt Phys 36, 2921–2941. Mondellon, M., 1995. Molecular dynamics of linear and branched alkanes. J Chem Phys 103, 7156.
[7] Moseler, M. 2000. Formation, stability, and breakup of nanojets. Science 289, 1165. [8] Nguyen, L.T., Le, T.N., De Proft, F., Chandra, A.K., Langenaeker, W., Nguyen, M.T., Geerlings, P. 1999. Mechanism of [2+1] cycloadditions of hydrogen isocyanide to alkynes: molecular orbital and density functional theory study. J Am Chem Soc 121, 5992–6001. [9] Soler, J.M., Artacho, E., Gale, J.D., Garcia, A., Junquera, J., Ordejon, P., Sanchez-Portal, D. 2002. The Siesta method for ab initio order-N materials simulation. J Phys: Condens Matter 14, 2745–2779. [10] Yang, W., Parr, R.G. 1985. Hardness, softness, and the Fukui function in the electronic theory of metals and catalysis. Proc Nati Acad Sci USA 82, 6723–6726.
