J. Phys. Chem. 1995,99, 12925-12932
Modeling of
N2
12925
and 0 2 Adsorption in Zeolites
Imre Phpai: Annick Goursot," and Franqois Fajula URA 418 CNRS, Ecole Nationale SupCrieure de Chimie de Montpellier, 8 Rue de 1'Ecole Nomale, 34053 Montpellier Cedex 1, France
Dominique Plee Groupement de Recherche de Lucq, BP 34, 641 70 Lacq, France
Jacques Weber DCpartement de Chimie Physique, UniversitC de Genkve, 30, Quai Emest-Ansemet, 1211 Genkve 4, Switzerland Received: March 23, 1995; In Final Form: June 15, 1995@
The fundamental aspects of N2 and 0 2 adsorption in zeolites have been investigated by density functional calculations on different models. Simple systems where these molecules interact with a positive point charge or with isolated Li+ and Na+ cations have led to a qualitative explanation for the N2/02 separation process. A classical description involving electrostatic and induction energies is adequate to explain the basic reason for a stronger N2 adsorption. At short distances (bonding interaction), the electronic structure of the cation has to be taken into account. The presence of core electrons in large cations limits the stabilizing contribution of the electrostatic and induction terms to the total energy, implying that Li+ is more efficient than Na+ in the adsorption process. The presence of zeolite clusters decreases the binding energies for both N2 and 0 2 , but the main trends remain valid. Moreover, due to a larger screening of 0 2 adsorption, it improves the efficiency of Li+ with respect to Na+ for the N2/02 separation.
1. Introduction Since the first application achieved by Barrer in 1945,' crystalline zeolites have been popularly used as highly selective adsorbents for gases and vapors. Besides the simple sieving effect, separation processes for gas mixtures are founded upon the differences in adsorption properties of their components.2 An important example is the pressure swing adsorption separation of oxygen from air.3 This process exploits the fact that, at room temperature, dehydrated A or X zeolites adsorb nitrogen when a gas mixture containing N2 and 0 2 circulates through their large pores. These zeolites have a concentrating effect on nitrogen which has been attributed to the interaction between the zeolite cations and the nitrogen q ~ a d r u p o l e . ~Several .~ investigations indicate that separation of N2 from gas mixtures strongly depends on the nature of the counter ion^.^.^.^ Improved A or X zeolites exchanged with lithium or calcium have been reported as much more efficient for N2 adsorption than Na ~eolites.4.~ In spite of numerous experimental results, there has been no attempt to study the fundamental aspects of the N20 2 separation in zeolites. The aim of the present work is thus to investigate the basic grounds for the different adsorption properties of N2 and 0 2 in zeolites, including the reasons for different efficiencies of various counterions. To delineate how large is the role of a purely electrostatic effect in the adsorption process, N:! and 0 2 have first been studied as interacting with a single positive point charge. This simple model has then been compared with systems where N2 or 0 2 interacts with a Na' or a Li+ cation. Finally, the interaction of these molecules with zeolite model
* To whom correspondence should be addressed. Permanent address: Institute of Isotopes of the Hungarian Academy of Sciences, H-1525 Budapest, P.O.B. 7 7 , Hungary. Abstract published in Advance ACS Abstracts, August 1, 1995. +
@
clusters has been studied, when the counterion present in the model is a sodium or a lithium cation. All these calculations are first-principle calculations based on density functional theory (Dfl). The use of rather small clusters to model a zeolite is necessarily an approximation which has to be analyzed according to the property being studied. Combined quantum mechanical and force field calculations on clusters .and extended systems have shown that relaxation is a local property, justifying the use of a relaxed cluster as a good model for this cluster embedded in the zeolite.6 The interaction between a small organic molecule, as NH3 or CH4, and a zeolite proton seems also to be mostly a local process since quantum chemical results obtained with small zeolite clusters reproduce well the experimental data.'%* It is certain, however, that long-range effects also play a role in the weak interactions of N:, or 0 2 with the zeolite. Embedded cluster and periodic calculations are needed to clarify this role and lead to further improvements.
2. Models and Calculations As a general notation for the investigated systems, the two diatomic molecules (N2 and 02) and the two cations (Li+ and Na+) will be generally referred to as Y2 and X+, respectively. The systems which correspond to the interaction of Yz molecules with a single positive point charge (q+) and with X+ will be denoted as q+Y2 and X+Y2. Those including zeolite clusters, Le. a pentameric Al(SiOH3)G model (Figure la) or a sixmembered ring A1&306(0H)12X model (Figure lb), will be denoted as mP(X+)Y2 and m6R(X+)Y2, respectively. The energy of the interaction of the Y2 molecules with a point charge (or with several point charges) is calculated by including the related electrostatic terms in the Hamiltonian and performing self-consistent Kohn-Sham (KS) calculations for the Y2
0022-3654/95/2099-12925$09.0010 0 1995 American Chemical Society
12926 J. Phys. Chem., Vol. 99, No. 34, 1995
D
Figure 1. The mP(X+)Y2 model cluster (a) and the m6R(X+)Y2 model cluster (b), with X = Li, Na and Y2 N2, 0 2 .
molecules. Since the linear geometry was proven to be the most stable (cf. Figure 4), the potential energy curves for qfN2 and q+02 were obtained by varying the q-Y distance in the linear q+***Y-Yarrangement with a Y-Y bond length fixed at the equilibrium value of the free Y2 molecules. The geometries of the X+Y2 systems were optimized, and the X+-Y2 interaction energies were calculated as De = E(X+Y2) - E(X+) - E(Y2), where E(X+Y2), E(X+), and E(Y2) are the total energies of these systems at their equilibrium geometries. The potential energy curves for X+Y2 were derived in the same way as for q+Y2. These curves were all fully corrected for basis set superposition error (BSSE). Since the equilibrium Y-Y bond lengths in X+Y2 hardly differ from those in the free Y2 molecules, the BSSE corrected interaction energies for a given X-Y are simply obtained D,‘ = E(X+Y2) - E‘(X+) - E‘(Y2), where the primed total energies are evaluated within the full X+Y2 basis sets. Two different clusters, illustrated in Figure 1, have been chosen to model a small piece of zeolite. The first one is a pentameric Al(OSiH3)4X cluster (denoted as mP(X+)), in which the X+ counterion is bonded to two 0 atoms of the A104 tetrahedron and the Y2 molecule is assumed to be bonded to the counterion. The dangling bonds of the four Si atoms are saturated with H atoms with a fixed SiH bond distance of 1.50 A, and the SiH bonds are aligned with the corresponding S i 0 bonds of the X-ray structure of zeolite X.9 Since all T sites are equivalent in this framework, any A104
Pipai et al. tetrahedron can be chosen to construct the model. This cluster does not represent any specific site of zeolite X. It is simply the smallest possible model for a zeolite cation structure. As a first step, the structure of the negatively charged cluster has been optimized, allowing all atoms to relax, except the border SiH3 groups. The relaxation effects were very similar to those obtained in our previous studylo and will not be discussed here. Molecular electrostatic potentials (MEP’s) have then been calculated at the optimized geometry as described in ref 11. The counterions (Li+ or Na+) were placed at the position of the deepest MEP minimum, and the geometry of the A104X part in the mP(X+) clusters was then optimized. Finally, Y2 was made to approach in the OXO plane toward the mP(Li+) and mP(Na+) clusters in a linear B-X.**Y-Y arrangement, where B is the midpoint of the two oxygen atoms bonded to X+ (Figure la). Varying only the X-Y distance (r(X-Y)), Le., fixing the geometry of the mP(X+) clusters and the Y2 molecules at their equilibrium structure, the interaction energy, defined as E(r(X-Y)) = E[mP(X+)Y2} - E{m P(X+> - E{Y2} (where E[mP(X+)Y2}, E{mP(X+), and E{Y2} are the total energies of the mP(X+)Y2 and mP(X+) clusters and Y2 molecules, respectively), has been evaluated as a function of r(X-Y). The BSSE corrections were calculated in the same way as for the X+Y2 systems. The second model (denoted m6R(Xf)) has been chosen to represent a six-ring facet connecting a sodalite cage and the supercage. It consists of three Al, three Si, and six 0 atoms that form the ring and 12 OH groups attached to the A1 and Si atoms according to the X-ray structure (see Figure lb). Only one counterion, that corresponding to site I1 (sitting above the six-membered ring in the supercage), has been considered explicitly in this model, the additional negative charges (-2) were balanced by placing three +2/3 point charges at the positions of site I’ which seem to be occupied in dehydrated zeolite X. With all atoms fixed at their experimental positions (the OH’S were aligned properly with r(0H) = 1.0 A), the position of the X+ counterion was varied in the direction perpendicular to the ring. The energy minimum was found at d = 0.36 A for X+ = Li+ and d = 0.74 A for X+ = Na+ , where d is the distance from the center of the six-membered ring. These values correspond to the three equal r(Li0) = 2.25 A and r(Na0) = 2.35 A distances, and the latter compares very well with the experimentally obtained value of 2.30 A . Then the counterions were fixed at their equilibrium positions, and the Y2 molecules (with fixed r(Y -Y) distances) were brought up to the counterions in the linear X***Y-Y arrangement perpendicularly to the six-membered ring. The density functional calculations were performed within the LCGTO-DF forma1i~m~I-l~ using the deMon program package. l6-I8 All the calculations, except for the geometry optimization of the Al(OSiH&-, mP(Li+), and mP(Na+) clusters, was carried out at a nonlocal level, using Becke’s exchange19 and Perdew’s correlation20functionals. Geometry optimization was performed at the local level of theory using the Dirac-Slater exchange term2’ and the Vosko- Wilk-Nusair (VWN) parametrization22for the correlation energy. The basis sets used for the Al, Si, 0, and H atoms are described in ref 10. For Li and Na, (621/1/1) and (6321/411/1) orbital basis sets with corresponding (4,3;4,3) and (5,4;5,4) auxiliary bases were employed, while (521 1/41111) orbital and (5,2;5,2) auxiliary basis sets were used for N and 0 in the diatomic molecules.
3. Results and Discussion A. Interaction of N2 and 0 2 with a Point Charge. The interaction energies of N2 and 0 2 with a single positive point
N2 and
0 2
J. Phys. Chem., Vol. 99, No. 34, 1995 12921
Adsorption in Zeolites 0 001
10
-
-
0.000
0-10
7i!
-
lz
-20-
5 -0003-
-
-40 -
+ 0
-0.004-
-a
-
-50
-
-0.00,:
m
-30
-60
-0.001-
h
............
'
,
2
,
,
4
,
6
,
,
8
,
,
,
10
...........
b
-0005
,
12
I
Yaws)
Figure 2. Potential energy curves of q+N? (a) and q+O2 (b) in the linear arrangement, as a function of distance ( R ) between the point charge 'and the midpoint of the diatomic molecules.
charge in the linear arrangement are shown in Figure 2 as a function of the distance between the point charge and the midpoint of the diatomic molecules. Although this model is an ememe simplification of the real Y2-zeolite interaction, the fundamental principle of oxygen separation is clearly seen: the interaction energy of N2 is significantly larger than that of 02, for the entire range of R. This trend can be easily related to the difference in the physical properties of N2 and 0 2 molecules. Indeed, it follows from the general theory of long-range interaction^^^ that the two leading terms in the interaction energy of a point charge and a homonuclear diatomic molecule are those associated with the quadrupole moment (0)and the dipole polarizability (a)of the diatomics. For a linear q+***Y-Y arrangement, these terms are given by and ( l / 2 ) ~ i q ~ R - ~ (referred to as electrostatic and induction term hereafter), where QI is the parallel component of the polarizability tensor, q is the charge value, and R is the distance between the point charge and the origin of the molecule. Considering the experimental values of 0 and QI (O(N2) = -1.093, 0(02)= -0.299, ql(N2) = 14.75, and cq(O2) = 15.73 from ref 24, where both 0 and u.1 are in atomic units), one would expect the induction terms to be quite similar for N2 and 02, whereas the quadrupole moments suggest that the electrostatic term is considerably larger for N2. resulting in favorable interaction energies for this molecule. If, at large distances, the quantum chemical potential energy curves (Figure 2) can be adequately approximated with the - ( 1 / 2 ) ~ 1 q ~expression, R-~ one should be able classical to derive a E ( q ) = alq a2q2 curve for both NZ and 0 2 , by calculating the interaction energies as a function of a charge q at a fixed distance Ro. Then providing that al = OR,-3 and a2 = -( l / 2 ) ~ @ , - ~0, and cq can be determined and compared to the experimental values. The calculated E(q) curves for R, = 4.5 8, and -1.2 Iq I+1.2 are shown in Figure 3. It tumed out that, indeed, both curves can be accurately fitted with the quadratic expression with U I = -0.001 992 and a2 = -0.001 598 for N2 and al = -0.000 485 and a2 = -0.001 552 for 0 2 . The approximate quadrupole moments and dipole polarizabilities derived from these coefficients are listed in Table 1. They are compared with the experimental values and with the theoretical predictions, obtained from a complete quantum treatment. Quadrupole moments and polarizabilities are very much sensitive to the size of the basis set, and an accurate description would certainly need the use of more extended basis sets. However, comparison of these numbers shows that the overall agreement is good enough to guide qualitative interpretations, showing that the quantum chemical results can be approximated with a
+
-a
-
J
-1.5
.
,
-1.0
b
,
,
-0.5
, 0.0, . 0.5 , . , , I 1.0
1.5
Charge
Figure 3. Potential energies curves for the interaction of N2 (a) and 02 (b) with a single q point charge in the linear arrangement, as a function of the amount of charge ( R = 4.5 A).
TABLE 1: Approximate (Classical Expression), Theoretical, and Experimental Quadrupole Moments (e)and Dipole Polarizabilities (ail) of N2 and 0 2 (in auY N2
0 Ql
a
approximate theoretical experimental approximate theoretical experimental
- 1.225 -1.142 - 1.093 16.71 14.32 14.75
O?
-0.298 -0.385 -0.299 16.23 14.52 15.73
From ref 2 1.
"truncated" classical expression in which the higher order terms (associated with the higher order multipole moments and static polarizabilities) have been neglected. This means that the calculated quadrupole moments and polarizabilities should slightly depend on R,. It is worthwhile to retum to Figure 3 and to take a closer look at the shape of the E(q) curves. One can observe that (i) the stability order between NZ and 0 2 is reversed for negative charges and (ii) the larger the charge, the larger the difference between the interaction energies of N2 and 0 2 . Both observations are trivial if we consider that the linear term in alq a2q2 becomes positive for q < 0, thus destabilizing the interaction, and that the absolute value of al(N2) is notably larger than al(O2) (whereas a2(N2) and a2(02) are fairly similar). Although it is hazardous to extrapolate any conclusion from this simple model to the zeolite-Y2 interaction, one might expect from above that bivalent counterions should be more efficient in the oxygen separation than univalent cations and also that the relative position of the counterions and the 0 atoms in the zeolite framework could play an important role. So far, only the linear point charge-Y;! (qf-Y2) geometry has been considered. Figure 4 illustrates how the interaction energies vary with respect to the angle (4) between the molecular axis of Y2 and the vector R pointing from the center of mass of Y2 to the point charge. The interaction energies decrease monotonically in absolute value for both N2 and 0 2 going from the linear (4 = 0') to the perpendicular (9 = 90') case, reducing the stability difference between N2 and 0 2 . The order of stability is even reversed for 4 < e60'. However, the interaction energies for the perpendicular geometry are much smaller as compared to those for the linear geometry. Again, these results can be easily rationalized in terms of the classical picture. The angle-dependent formulas for the electrostatic and induction energies (from ref 20) are given by
+
OqRp3((3/2) cos2 r$ - 1/2)
12928 J. Phys. Chem., Vol. 99, No. 34, 1995
0
$0
io
EO
60
angle Figure 4. Potential energy curves of q+N2 (a) and q+OZ, as a function of the angle between the molecular axis of Y? and the vector pointing from the midpoint of the Y2 distance to the point charge ( R = 4.0 A). and -(l/2)q2K4 ( a
+ (1/3)(q, + aJ3
c o s 2~ 1))
where R = IRI, a1 is the perpendicular component of the polarizability tensor, and a = (1/3)(q1 2 a ~ ) .Consequently, the electrostatic term decreases continuously with increasing 4; it becomes zero at 4 = 54.7" and positive for 4 < 54.7". On the other hand, the induction term decreases as well from 4 = 0" to 4 = 90", first because of the angular dependence and second because the ai values are generally smaller than Q'S (ai(N2) = 10.23 au and ~ ~ ( 0 = 2 )8.30 au from ref 21). We will consider now the interaction of N2 and 0 2 with two q = + I point charges placed symmetrically on the molecular axis on both ends of the molecules, with varying R . The calculated interaction energies for 3.0 5 R 5 4.6 A are depicted in Figure 5, where the interaction of a single point charge with N2 and 0 2 is also shown for comparison. It appears that the presence of the second point charge, at least for this particular geometrical arrangement, has a stabilizing effect for N2, whereas the interaction is destabilized in the case of 0 2 . The destabilization is a consequence of the fact that the induced dipole for symmetrically placed charges is zero; therefore, the induction energy vanishes for both molecules. This effect is counterbalanced, and even exceeded, when the additive electrostatic term is doubled for N2, which is not the case for 0 2 , due to its small quadrupole moment. Extrapolating again to zeolites, this might be an indication that variations in the relative positions of the counterions in the main cavities, caused for example by partial or complete ion exchange, could influence the relative adsorption energies of N2 and 0 2 . B. Interaction of NZ and 0 2 with Li+ and Na+ Cations. The calculated equilibrium properties of the X+Y2 systems are listed in Table 2. As expected from the results presented in the previous section, the geometry optimization yields linear structures for all four molecules. A recent Hartree-Fock and MP2 study of Na+N2 concludes also to a linear geometry, in contrast with a perpendicular orientation for Na+H2.25 However, the corresponding Na-N distance (2.49 or 2.50 A) is substantially shorter than the value given in Table 2, which is to be related with an MP2 interaction energy being 1.1 kcal mol-' larger (without BSSE corrections).
+
Piipai et al.
Wangs)
Figure 5. Potential energy curves for the interaction of N? (a) and 02 (b) with two q = + I point charges placed symmetrically on both sides of the molecular axis, as a function of R. A few points on the potential energy curves of q+N2 (full squares) and q+O?(open squares) are also shown for comparison. TABLE 2: Calculated Equilibrium Properties of X+Y2 Molecules (X+ = Li+, Na+; Y2 = N2 , 0 2 ) r(X-Y)a Rb
r(Y-Y)"' Ded D:e q(X+)f
Li'N2
Li+02
Na+N?
Na+0?
2.188 2.747 1.115 12.4 10.4 f0.95
2.111 2.727 1.222 8.0 6.4 $0.95
2.615 3.174 1.114 8.4 6.7 f0.93
2.559 3.175 1.223 5.3 3.9 +0.94
Bond lengths in A. Distance between the center of X+ and the center of mass of Yz, in A. The calculated values for the free Nz and 0 2 are 1.1 18 and 1.232 A, respectively. Dissociation energies in kcal mol-', noncorrected for BSSE. e Dissociation energies in kcal mol-', corrected for BSSE. /Net atomic charges on X+. Similarly, Li+N2 is more stable than Li+O2 and Na+N2 is more stable than Na+02. In addition, it is seen that the dissociation energies of the Li+Y2 systems are always larger than the corresponding Na+Y2 values. To clarify these results, potential energy curves have been evaluated for each system by calculating the BSSE corrected binding energies as a function of r(X-Y), which is the distance between the center of X+ and the closer end of the Y2 molecule. The r(Y-Y) distance in these calculations was fixed at the equilibrium value of the free Y2 molecules (1.118 A for N2 and 1.232 A for 02), which are very similar to those in the X+Y2 systems (see Table 2). The potential energy curves for Li+N2 and Na+N2 are displayed in Figure 6, while those of Li+02 and Na'02 are depicted in Figure 7. The relevant parts of the q+N2 and q+02 curves are also given for comparison. We see that, for a given Y2, the Li+Y2 and Na+Y2 curves become identical for large distances (R =- 4 A) and that, in this region, they fall very close to the q+Y2 curves. The X+-Y2 interaction is thus very well represented by the point charge model, for distances sufficiently larger than the equilibrium distance, which illustrates the expected result that the 1/R electrostatic component is predominant at large R values. Moreover, it appears that the reason the Li+Y2 systems are thermodynamically more stable than the corresponding Na+Y2 systems is that the repulsive short-range forces become significant at much shorter distances for Li+ than for Na+, introducing larger electrostatic and induction energies in the total interaction energy. This explains the fact that replacing Na+
\
N2 and
0 2
J. Phys. Chem., Vol. 99, No. 34, 1995 12929
Adsorption in Zeolites 5
.
,
-10
,
.
,
'
3jO
.
,
,
A
\
-1.5
0
-2 0
-3 0 -2 5
-5
e
2 -35-
{
-10
ti
-40:
$ -45: -15
- a
-20
b C
-5 0
-
-5 5
-
8.0
-
-6 5
-
-25 1'5
2'0
2'5
3'0
3'5
4'0
4'5
5'0
2Io
55
2'5
r(X-Y) (angs)
3l5
r(X-Y) (angs)
Figure 6. Potential energy curves of Na+N2 (a), Li+N2 (b), and q+N2
Figure 8. Potential energy curves of mP(Li+)Nz (a), mP(Li+)Oz (b),
(c), as a function of R.
mP(Na+)N2 (c), and mP(Na+)Oz (d), as a function of R.
TABLE 3: Structural Parameters of the Geometry Optimiied mP(Li+),mP(Na+k and AI(OSiH+- Model Clusters (Bond Distances in , Bond Angles m deg)
'1
mP(Li+)
0
-10
-12
]
1
___________. b C
,
,
1'5
,
2'0
2'5
. , . , 30
35
I
,
40
. ,
45
I
,
50
. ,
55
r(X-Y) (angs)
Figure 7. Potential energy curves of Na+02 (a), Li+Oz (b), and q'O2 (c), as a function of R.
mP(Na+)
Al(OSiH3)d-
4x04)
1.87 1.89
2.17 2.19
r(A1Ol) r(A102) 4~103) r(~104)
1.82 1.70 1.71 1.80
1.79 1.71 1.71 1.79
1.75 1.75 1.76 1.74
r(Si0') r(Si02) 4si03) 4si04)
1.69 1.63 1.63 1.69
1.66 1.64 1.63 1.66
1.61 1.62 1.62 1.60
a(01A102) a ( O A103) a(OiA104)
a(03~104)
110.7 110.7 95.1 113.1 110.1 115.8
111.3 107.2 98.9 114.2 110.6 113.6
110.0 108.2 108.8 110.3 108.3 111.0
a(SiOlA1) a(Si02Al) a(Si03Al) a(Si04A1)
123.7 142.6 134.7 133.2
127.3 139.5 138.6 135.3
133.1 138.2 137.0 145.3
r(XO1)
a(02~103) ~1402~104)
by Li+ increases the binding energy with N2 (3.7 kcal mol-') more than the binding energy with 0 2 (2.5 kcal mol-'), favoring the N2-02 separation. One would expect from this that there should exist a simple relation between the selectivity of the N2/ 0 2 separation and the size of the applied counterion. Although experimental data are consistent with this e~pectation?.~ we will see in the next section that additional effects tum out to be important, when the zeolite framework is taken into account. C. Interaction of NZ and 0 2 with mP(Li+), mP(Na+), m6R(Li+), and m6R(Na+). The structural parameters of the partially relaxed mP(Li+), mP(Na+), and Al(OSiH3)4- clusters
sites and the adsorption of N2 and 0 2 molecules. For the pentameric optimized model, the cation-(zeo1ite)O interaction is stronger in mP(Li+) than in mP(Na+), due to the 0.3 8, shorter distances between Li+ and the zeolite oxygens. The same trend holds for the m6R models with Li+-zeolite (0)bonds of 2.25 8, and Na+-zeolite (0)bonds of 2.35 8,. The potential energy curves for the mP(X+)Y2 and m6R(X+)Y2 clusters are depicted in Figures 8 and 9, respectively. In contrast with Figures 6 and 7, they are not corrected for BSSE, since evaluation of the counterpoise corrections for all curves involved
are listed in Table 3. Although the initial position of the
a too large computational effort. However, for the purpose
counterions in mP(Li+) and mP(Na+) was in the vicinity of the 0' atom, both Li+ and Na+ moved to form two XO bonds (with 0' and 04)in the geometry optimization. It is known from X-ray and neutron diffraction s t ~ d i e s ~ .that ~ ~ the . ~ ' counterions in zeolite X bind to at least three framework 0 atoms, as it is the case in the m6R(X+) models. In spite of the fact that the mP(X+) models are not sufficiently large, comparison with the more realistic m6R(X+) systems provides information on possible relations between the local geometry around the cationic
explained below, one curve has been corrected completely (Figure 10). Moreover, to obtain reasonable estimates of binding energies for N2 and 0 2 , BSSE corrections have been performed at the minimum of each curve. Both Figures 8 and 9 show that the binding energies for N2 is larger than that for 0 2 and that Li+-Y2 is still preferred to Na+-Y2, just as was found for q+-Y2 and X+-Y2 models. It is worth underlining that these trends do not depend on the model chosen for the zeolite, although the four curves related to the six-ring model
12930 J. Phys. Chem., Vol. 99,No. 34, I995
Ptipai et al.
TABLE 4: Binding Energies of Nz and 0 2 to mP(Li+), mP(Na+), m6R(Li+), and m6R(Na+) Clusters at the Eauilibrium X-Y Distances r(X-Y)" D,b D;C mP(Li+)N2 2.34 6.5 3.7 mP(Li+)02 2.37 3.3 1.2 2.62 4.9 2.6 mP(Na+)N2 mP(Na+)02 2.64 2.7 0.9 2.24 9.6 3 .O m6R(Li+)Nz m6R(Lif)02 2.21 5.5 0.0 m6R(Na+)N2 2.60 8.2 1.3 2.68 5.4 -0.5 m6R(Na+)O? ~~
" In A. Binding energies in kcal mol-', not corrected for BSSE, calculated from D, = E{m(X+)Y2}- E{m(X+)}- E(Y2). Binding energies in kcal mol-', corrected for BSSE, calculated from D,' = E{m(X+)Y2}- E'{m(X+)} - E'{Y2}, where the primed total energies were calculated within the full m(X+)Y2 basis sets.
-lo -11
2.5
20
30
TABLE 5: Binding Energy Differences between Li+ and Na+ Models E[(Li+)N2]E[(Li+)02]system E[(Na+)Nz]" E[(Na+P21" X+ D,b 4.0 3.1 D;b 3.7 2.8 mP(X+) Deb 1.6 0.6 ~~
r(X-Y) (angs)
Figure 9. Potential energy curves of m6R(Li+)N2(a), m6R(Li+)02 (b), m6R(Na+)N?(c), and m6R(Na+)02(d), as a function of R .
m6R(X+)
D;b Deb Dlb
1.1
0.3
1.4 1.7
0.1 zo.0
" In kcal mol-'. Same definition as in Table 4.
-61
20
1
1
"1 ,
~
25
,
, 30
,
, 35
" -;,
-a-
c
40
45
50
r(X-Y) (angs)
Figure 10. Potential energy curve for the interaction of N2 with the Mulliken point charges of the mP(Na+) cluster (a) and the BSSE corrected (b) and uncorrected (c) potential energy curves of mP(Na+)N2.
are more stable than the four curves conceming the mP(X+) models. The same conclusions can be drawn from the Y2 binding energies, which are presented in Table 4 together with the equilibrium X-Y distances. In spite ot the large BSSE values found for the large m6R systems, a valuable qualitative analysis can be performed. Indeed, if we consider De (noncorrected) and D,' (BSSE corrected) differences between binding energies involving the same model but changing N2 for 0 2 or Li+ for Naf, we see that these differences are not much affected by BSSE corrections (Table 5). This result is reasonable since the basis set extension is comparable for N2 and 02 and also for Li+ and Na+, and the error due to the basis set extension of the zeolite model should almost vanish in making energy differences (not comptetely because of the different bond distances for the two counterions and the two Y2 molecules). In fact, the trends we have already underlined are unchanged after BSSE corrections and differences between De or D,' values differ by less than 1 kcal mol-'. Comparison with XfY2 models (Table 2 ) shows that adsorp-
tion energies are smaller in the presence of any zeolite cluster but display the same relative ordering. This indicates that the N2 and 02 adsorption is, to first order, controlled by the Y2cation interaction, whereas the zeolite framework plays a perturbative role, which can however modify the adsorption strength of N2 and 0 2 molecules. N2 and 02 binding energies are strongly correlated with the equilibrium distance between these molecules and the cation. For free cations (Table 2), the available positive net charge is roughly one. The major factor, which induces a larger binding energy for Li+, associated with a shorter equilibrium distance, is the smaller size of this cation with respect to Na+. When the cation is embedded in a zeolite anionic surrounding, a charge transfer occurs, and its net charge is decreased from f l . This decrease depends on the local geometry around the cation but also on the nature of the cation itself. As seen above, Li+ and Na+ are situated at larger distances from the zeolite oxygens in the six-ring model with respect to the pentameric model. The weaker interaction with the zeolite framework explains the larger magnitude of the m6R-Y2 binding energies and also the shorter m6R(Li+)-Y2 bond distance with respect to mP(Li+)-Y*. Due to its larger size, Na+ is more distant from the zeolite oxygens and thus less dependent on the local geometry, which, in turn, induces a smaller dependence of its interaction with N2 and 0 2 . However, in spite of these remarks, the different behaviors of Lif and Naf, with respect to N2 and 0 2 adsorption, remain almost the same for both zeolite models: Li+ is more strongly bonded to N2 than Na+, by around 1 kcal mol-', whereas both cations have comparable binding energies with 0 2 . In all cases, N2 and 0 2 binding energies are increased when Na+ is replaced by Li'. Both De and De' differences give a reasonable estimate of the damping effect produced by the presence of the zeolite cluster (Table 5). This damping factor is roughly 2.6 (4.0A.5) for N2 binding and 6.0 (3.0/0.5) for 0 2 binding. These numbers indicate that the weakening of the bonding interactions due to the zeolite is much more effective for 0 2 than for N2. Moreover, these results show that the presence of any zeolite cluster decreases more the efficiency
N2 and
0 2
Adsorption in Zeolites
J. Phys. Chem., Vol. 99, No. 34, 1995 12931
TABLE 6: Net Mulliken Charges on the Atoms in mP(Li+) and mP(Na+) m(Li+) X AI 0' 0 2
0 3 0 4
Si' Si2 Si3
Si4 H's
+0.79 +0.67 -0.66 -0.38 -0.41 -0.52 +0.64 +0.52 +0.54 1-0.60 -0.14 to -0.16
m(Na+) +0.86 +0.87 -0.65 -0.46 -0.47 -0.56 +0.74
---a
+0.65 +0.66 +0.70 -0.18 to -0.20
-6
-/
' I
2
of Li+ versus Na+ in the case of 0 2 adsorption than it does for N2 adsorption. The long-range interactions between the N2 or 0 2 molecules and the zeolite framework are not negligible, since we have seen above that they decrease as 1/R.To take them into account in a further study, we have thus investigated how accurate is a representation where atoms located at large distances from Y2 are replaced by appropriate point charges. The choice of point charges for the evaluation of the Coulomb potential used either in embedded cluster or in force field calculations is the subject of great debate. The Mulliken population analysis is one of the most popular procedures used to distribute the electronic density among the different atoms. However, charges obtained from a fit of molecular electrostatic potentials are also much used in molecular mechanics simulations. Both methods are strongly dependent on the size of the orbital basis set and also on the level of the t h e ~ r y . ~ Indeed, , ~ ~ . ~correlation ~ effects correct the artificially too ionic character of Hartree-Fock results, which leads to smaller atomic charges obtained from MP2 as well as from DFT calculation^.^^ In a very simple first attempt, net Mulliken charges calculated for the mP(X+) clusters (see Table 6) have been used as point charges fixed at the positions of the corresponding atoms in mP(X+). Including the point charge-Y2 interaction terms in the Hamiltonian, selfconsistent KS calculations have been performed for these embedded Y2 molecules. In other words, the total energy of the diatomic molecules is calculated in the presence of an electric field induced by the atomic point charges of the mP(X+) clusters. Varying the X-Y distance the same way as in the full quantum calculations, potential energy curves have been derived for the Y2 point charges systems. The potential energy curve for X = Na and Y2 = N2 is shown in Figure 10, along with the curve obtained for mP(Na+)N2 in the full quantum chemical treatment and the corresponding BSSE corrected curve. It is clearly seen that the BSSE corrected curve is fairly accurately reproduced with the N2 point charges results for r(X-Y) > 3.2 8, illustrating that the longe-range mP(Na+)-Nz interaction is purely electrostatic. Obviously, the latter curve does not have a minimum at around 2.6 8,since the short-range exchange-repulsion interactions arising from the electron density at the cation are not taken into account in the simpler point charge model. The four curves (for X = Li, Na and Y2 = Nz, 0 2 ) obtained from this point charge model are given in Figure 11. It is interesting to note that the interaction energies for N2 are about 3 times larger than those for 0 2 for the whole range of R, which is fully consistent with the BSSE corrected binding energies listed in Table 4. Moreover, the interaction energies, calculated at the equilibrium X-Y distances (2.3 and 2.6 8, for X = Li and X = Na), exhibit the same trend as the values in Table 4;Le., the Li+-N2 interaction is about 1 kcal/mol more stable than Na+-N2, and the Li+-02 and Na+-02 interaction
+
+
I
3
4
5
6
7
0
r(X-Y) (angs)
Figure 11. Potential energy curves for the interaction of Y2 molecules with the Mulliken point charges of the mP(X+) clusters (a) X = Li, Y2 = N2; (b) X = Li, Y2 = 0 2 ; (c) X = Na, Yz = N?; (d) X = Na, Y2= 02.
energies are almost identical. It is therefore reasonable to suggest that the point charge model is able not only to describe the longe-range (zeolite cation)-Yz interaction accurately but also to provide reliable relative energies for different cations.
+
4. Conclusions These quite simple quantum mechanical calculations have shown that the different N2 and 0 2 adsorption properties in zeolites can be explained by simple electrostatic arguments. Indeed, interaction of these molecules with a positive point charge has demonstrated that a classical description involving electrostatic and induction energies, which depend respectively on their quadrupole moment and dipole polarizability, is adequate to explain the basic reason for a stronger N2 adsorption. However, although this simple electrostatic model is sufficient to give the trends, it is only reliable with enough accuracy for long range interactions between N2 or 0 2 and one (or several) point charges. For a more precise description of the bonding between these molecules and the counterion in the zeolite, the electronic structure of the cation has to be taken into account. This treatment leads to the conclusion that a small cation such as Li+ is a better attractor than a larger cation like Na+, the presence of the core electrons being the factor which limits the stabilizing contribution of the electrostatic and induction terms into the total energy. Simple systems where N2 and 0 2 are bonding with isolated Li+ and Na+ cations have thus allowed the proposal of a qualitative explanation for the N2/02 separation process. The study of models including zeolite clusters has shown that the zeolite framework plays a perturbative role, screening the binding of both N2 and 0 2 while leaving the main trends valid. Moreover, a more detailed analysis has led to the conclusion that, due to a larger screening of 0 2 adsorption, the presence of the zeolite framework improves the efficiency of Li+ with respect to Na+ for the N2/02 separation.
Acknowledgment. This work is part of a project of the European COST-Chemistry D3 action. Financial support from ELF (France) and from the Office Federal de 1'Education et de la Science (acting as Swiss COST partner) are gratefully acknowledged. The authors are grateful to Centro Svizzero di Calcolo Scientific0 for a generous grant of computer time on the NEC-SX3 computer. Finally, I.P. gratefully acknowledges the CNRS for providing him with a temporary position. References and Notes (1) Barrer, R. M. J. SOC. Chem. Ind. 1945, 64, 130.
PBpai et d.
12932 J. Phys. Chem., Vol. 99, No. 34, 1995
-
(2) Breck. D. W. Zeolite Molecular Sieves; R. E. Krieger Publishing: Malabar. FL, 1984. (3) Jasra, R. V.; Choudary, N. V.; Bhat, T. S. G. Sep. Sci. Technol. 1991, 26, 885. (4) Choudary, V. N.; Jasra, R. V.; Bhat, T. S. G. Ind. Eng. Chem. Res. 1993, 32, 548. ( 5 ) Coe, C. G.; Kimer, J. F.; Pierantozzi, R.; White, T. R. U.S. Patent 5,152.813, 1992 and references therein. (6) Kramer, G. J.; Van Santen, R. A. J. Am. Chem. SOC.1993, 115, 2887. (7) Teunissen, E. H.; Van Duijneveldt, F. B.; Van Santen, R. A. J. Phys. Chem. 1992, 96, 366. (8) Kramer, G. J.; Van Santen, R. A.; Emels, C. A,; Novaks, A. K. Nature 1993, 363, 529. (9) Olson, D. H. J. Phys. Chem. 1970, 74, 2758. (10) Pipai, I.; Goursot, A.; Fajula. F.; Weber, J. J. Phys. Chem. 1994, 98, 4654. (11) Salahub, D. R.; Foumier, R.; Mlynarski, P.; PBpai, I.; St-Amant, A.; Ushio, J. In Density Functional Methods in Chemistry; Labanowski. J., Andzelm, J., Eds.; Springer-Verlag: New York, 1991; p 77. (12) Sambe, H.; Felton, R. H. J. Chem. Phys. 1975, 62, 1122. (13) Dunlap, B. I.; Conolly, J. W. D.; Sabin, J. R. J. Chem. Phys. 1979, 71, 3396. (14) Andzelm, J.; Radzio, E.; Salahub, D. R. J. Chem. Phys. 1985, 83, 4573. (15) Foumier, R.; Andzelm, J.; Salahub, D. R. J. Chem. Phys. 1989, 90, 6371.
(16) St-Amant, A.; Salahub, D. R. Chem. Phys. Lett. 1990, 169, 387. (17) St-Amant, A. Ph.D. Thesis, Universiti de Montrial, 1991. (18) Daul, C.; Goursot, A,; Salahub, D. R. In Numerical Grid Methods and Their Application to Schrodinger's Equation; Cerjan, C., Ed.; NATO AS1 Series Vol. 412; Kluwer Academic Press: Dordrecht, 1993; p 153. (19) Becke, A. D. Phys. Rev. A 1988, 38, 3098. (20) Perdew, J. P. Phys. Rev. B 1986, 33, 8822; erratum in Phys. Rev. B 1986, 38, 7406. (21) Slater, J. C. Quantum Theory of Molecules and Solids; McGrawHill: New York, 1994; Vol. 4. (22) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200. (23) Buckingham, A. D. In fntennolecular Interactions: From Diatomics to Biopolymers; Pullman, B., Ed.; John Wiley & Sons: Chichester, 1978. (24) Visser, F.; Wormer, P. E. S.; Jacobs, W. P. J. H. J. Chem. Phys. 1985, 82, 3753. (25) Koubi, L.; Blain, M.; Cohen de Lara, E.; Leclerq, J. M. Chem Phys. Lett. 1994, 217, 544. (26) Mortier, W. J.; Bosmans, H. J. J. Phys. Chem. 1971, 75, 3327. (27) Shepelev, Y. F.; Anderson, A. A,; Smolin, Y. I. Zeolites 1990, 10, 61. (28) Stave, M. S.; Nicholas, J. B. J. Phys. Chem. 1993, 97, 9630. (29) Velders, G. J. M.; Feil, D. J. Phys. Chem. 1992, 96, 10725. (30) Schwerdtfeger, P.; Boyd, P. D. W.; Fisher, T.; Hunt, P.; Liddel, M. J. Am. Chem. SOC. 1994, 116, 9620. JP950843Q
