theoretical study of structural and electronic properties of sodium in zeolitic cage

phys. stat. sol. (b) 207, 357 (1998)

Subject classification: 61.46.+w; 68.45.Da; 71.20.Ps; S10.15

Theoretical Study of Structural and Electronic Propertiesof Sodium in Zeolitic Cage

Qiang Sun, Ling Ye, and Xide Xie

Surface Physics Laboratory and Department of Physics, Fudan University,Shanghai 200433, People's Republic of China

(Received September 8, 1997; in revised form December 8, 1997)

The structural and electronic properties of sodium adsorbed in the b-cage of zeolite A havebeen studied by using the extended HuÈ ckel method and cluster model. The b-cage, which con-sists of Si12Al12O48, is one of the structural units of zeolite A. The site preference for a Naadatom and several stable configurations for Na adatoms in the b-cage have been determinedand the electronic structures of the systems are investigated. It is found that instead of formingmetal clusters the Na adatoms prefer to be adsorbed separately at adsorption sites I or II whichare located near the center of the hexagonal face (site I) and on the square face (site II) in theb-cage, respectively. The result is reasonable from the fact that the adsorbed Na atoms are al-most ionized so that the Coulomb repulsion prevents them from forming clusters at short dis-tances. The electronic structures show that the peak near the Fermi level increases obviouslyafter the incorporation of sodium atoms into the b-cage. A new peak which is near the firstionization energy (5.14 eV) of Na atom appears when the numbers of Na atoms adsorbed bythe b-cage are larger than twelve.

1. Introduction

The search for new solid materials with well specified electronic and magnetic proper-ties has been one of the major driving forces of the development of solid state scienceand technology. Up to now two approaches complementary to each other have beenidentified, the first one is through exploratory studies focussing on previously non-exist-ing combinations of elements in the periodic table which might lead to certain spectacu-lar and unpredicted consequences, such as the discovery of high-Tc superconductors [1].The second approach is performed by deliberate modification of the existing host mate-rials which might give rise to new solid state compounds having interesting and specificelectronic and magnetic properties.

Although the application of zeolites as shape and size selective catalysts and molecu-lar sieves has been recognized for a long time [2,3], however, the possibilities of usingthese materials as hosts for the synthesis of new materials is an area that has onlyrecently attracted much attentions [4]. Among the most well known and promising ex-amples of such systems are the inclusion compounds of alkali metals in zeolites. In mostrecent research [4 to 8], it was discovered that the zeolite host can modify the proper-ties of a guest material through the so called ``quantum confinementº by incorporatingextremely small nanoscale clusters into the zeolite pores. After making contact with thedehydrated zeolite, the incorporated alkali atoms are ionized by the strong electric fieldof the host matrix. By carefully control the content of alkali metals and the zeolitestructure, it is possible to inject more atoms (and hence electrons) into the resulting

Qiang Sun et al.: Structural and Electronic Properties of Sodium in Zeolitic Cage 357

compounds. As a consequence, the goal of obtaining a new solid with a high degree ofcontrollable electronic and magnetic properties can be possibly achieved.

In 1966 it was first reported by Rabo et al. [9] that a bright color was observed byexposing the sodium zeolite Y(Na±Y) to sodium vapor under vacuum. Following elec-tron spin resonance (ESR) investigations this was attributed to the formation of para-magnetic Na3�

4 centers, each of which consisting of an electron delocalized among foursodium cations, which had previously been observed on g-irradiation of the same zeo-lite [10]. Similarly, the sodium zeolite X (Na±X) was found to give a blue color onexposure to sodium vapor which was interpreted as arising from Na5�

6 centers [11].Subsequently, several other paramagnetic M�nÿ1��

n species have been discovered by ESRin zeolite X, Y, A and sodalite [12 to 14]. However, the actual positions of these catio-nic clusters within the zeolites remained unknown. Furthermore, there still exists thequestion of whether there are other species which are not paramagnetic (and henceundetectable in the ESR experiment) existing in the zeolite.

As the optical and magnetic properties of the adsorption system are greatly affectedby the size, location and charge transfers of the sodium clusters in the zeolite, it isimportant to determine the location and configurations of the sodium clusters in thezeolite. However, due to the large unit cell and the sophisticated structure of zeolite,there are comparatively few theoretical studies on sodium-doped zeolites and their in-teresting physical properties. By using ab-initio molecular dynamics methods, Ursen-bach et al. [15] have studied sodium atoms adsorbed by a zeolite (Na±Y) pertinent to awide range of sodium doping levels. They found that, at low doping levels, highly io-nized molecular species (predominantly Na3�

4 ) are formed in the sodalite cages. In thispaper, by using the extended HuÈ ckel method and cluster model we have studied theadsorption of sodium atoms in the b-cage of zeolite A.

Zeolite A, which is a type of zeolite, has a framework structure which consists ofsilicon and aluminum oxides. In zeolite A the b-cages with a diameter of 6.5 �A, which isshown in Fig. 1, are connected by square prisms and form a cubic lattice (zeolite Y or X,

358 Qiang Sun, Ling Ye, and Xide Xie

Fig. 1. The schematic plot of a b-cage. A Naatom adsorbing in the b-cage by two differ-ent paths are also presented. The small solidballs at the vertices represent Al atoms andthe bigger solid balls Si. The O atoms con-nected Al and Si are not shown

in contrast, have a diamond lattice of b-cages connected by hexagonal faces andprisms). The Si and Al atoms are located at the cage vertices and are joined by Oatoms (not shown in Fig. 1). Each vertex occupied by Al atom is neighbored bySi-occupied vertices (Loewenstein's rules [16]). In ideal Na formed zeolite A, twelveNa� are distributed in the unit cell for charge compensation. The chemical formula isgiven as Na12Al12Si12O48.

By using the cluster model, the binding sites for a Na atom and several stable forma-tions for sodium adatoms in the b-cage are studied, and the electronic structures ofadsorption systems are also investigated.

The paper is organized as follows. First, the extended HuÈ ckel theory and parametersadopted are presented in Section 2. Then, in Section 3, the calculation results are dis-cussed, and a summary is given in Section 4.

2. Computational Method

The configuration of sodium atoms and the electronic structures of the investigatedsystems are studied by using the self-consistent extended HuÈ ckel method, which takesinto consideration the charge redistribution. The method has been used to calculate thegeometric and electronic structures for a variety of systems [17,18], here only a briefdescription of the method will be given.

In the framework of the linear combinations of the atomic orbital (LCAO) method,the wave function of the system is expanded as

Y i �Pmj

Cij�m� fj�m� ; �1�

where fj�m� is the j-th orbital pertaining to the m-th atom. Slater type atomic orbitalsare used [17]

fj�m� ��2x�n�1=2��2n!�p rn eÿxr Ylm ; �2�

where x is the orbital exponent. The energy levels are determined by solving the secu-lar equationsP

mj�Hjk�mn� ÿ EiSjk�mn�� Cij�m� � 0 ; �3�

where Hjk and Sjk are the Hamiltonian and the overlap matrix element of the j-th andk-th orbitals. The elements of those matrices are expressed as following in the HuÈ ckelapproximation:

Hjk�mn� � hfj�m� jHj fk�n�i

� ÿIj; j � k;

ÿ0:5Kjk�Ij � Ik� Sjk�mn�; j 6� k;

�(4)

Sjk�mn� � hfj�m� j fk�n�i ; �5�Ij � I0

j ÿ a�Q0 ÿQ� ; �6�Kjk � 0:5�Kj �Kk� : �7�

Structural and Electronic Properties of Sodium in Zeolitic Cage 359

In the above expressions, I0j is the ionization energy of the j-th orbital of a neutral

atom, Ij is the modified ionization energy of the j-th orbital due to the charge transfer,while Q is the Mulliken charge population of the atom obtained in the process of self-consistent calculation. a is the modification factor of the ionization energy and Kj is theorbital interaction constant which has been obtained by fitting the bond length andbinding energy. For atoms with large charge transfer, an empirical modified ionizationenergy is used [18]

Ij � I0j 1� 2b

nx� b2

n2x2

!; �8�

where n is the main quantum number, b is a parameter related to the transferredcharge. The parameters x and the orbital ionization energies of isolated atoms I0

j for allthe considered atoms are taken from [19,20]. The parameters used in the present calcu-lation are listed in Table 1.

The total density of states (TDOS), r�E�, is defined as

r�E� �Pmj

rmj�E�

�Pmj

Pi

Pnk

C�ij�m� Cik�n� Sjk�mn� d�Eÿ Ei�h i

; �9�

where rmj�E� is the local density of states for the j-th orbital pertaining to the m-thatom. The adsorption energy can be calculated by

DE � ENa=cage ÿ ENa ÿ Ecage : �10�

3. Results and Discussion

Fig. 1 shows the schematic plot of the b-cage, in which O atoms and the saturationatoms for Si and Al at the boundary are not drawn for simplicity. In our calculation,the b-cage cluster consists of Si12Al12O36H012. H0 is the saturation atom. The coordinatesof Si, Al and O are deduced from [21]. The nearest distance between neighboring Siand Al is a0 � 3:22 �A.

Firstly, in order to investigate the site preference of a sodium atom in the b-cage,energy minimization processes are carried out to find some stable adsorbing sites for aNa atom in the b-cage. For this purpose, a sodium atom adsorption in the b-cage


Ta b l e 1Parameters used in the calculation: atomic orbital exponent (x), orbital ionization poten-tial (I0

j ), constant of interaction (K) and modified ionization potential parameter (b)

atom orbital x I0j (at. units) K b

Na 3s 0.8356 0.1889 1.1 0.533p 0.6432 0.1128 1.0 0.53

O 2s 2.2458 1.0471 2.42p 2.2266 0.5007 2.2

Al 3s 1.3724 0.3904 1.43p 1.3552 0.2201 1.2

Si 3s 1.6344 0.4947 1.63p 1.4284 0.2997 1.4

through different pathways is considered and Fig. 1 shows the two adsorption paths tobe chosen. One is for a sodium atom entering the cage along the line perpendicular toa hexagonal face passing through the center of the hexagon, and the other one is alongthe line perpendicular to a square face passing through its center. The adsorption en-


Fig. 2. The chemisorption energy curve (labelled a1) of a Na atom with respect to the distance d ofthe Na atom from the center of the b-cage. The chemisorption path is along a hexagonal pore. Curvesa2 and a3 are the average chemisorption energy of one Na atom for configuration Na4(I) and Na8(I),respectively, with respect to the distance d of the Na atom from the center of the b-cage

Fig. 3. The chemisorption energy curve (labelled b1) of a Na atom with respect to the distance dof the Na atom from the center of b-cage. The chemisorption path is along a square pore. Curveb2 is the average chemisorption energy of one Na atom for configuration Na6(II) with respect tothe distance d of the Na atom from the center of the b-cage

ergy of the Na atom adsorbed in the b-cage with respect to the distance d from thecenter of the b-cage calculated for the two cases are shown in Figs. 2 (curve a1) and 3(curve b1). The minimum of the curve corresponds to a stable or quasi-stable position.From curve a1 in Fig. 2, we can see that the sodium atom can easily enter the b-cagethrough the hexagonal pore and finally incorporated into the oxide hexagonal site Iwhich is near the center of the hexagonal pore and the distance of the Na atom fromthe hexagonal face is only 0.24 �A. The distance between neighboring Na and O atomsis 2.53 �A, which is slightly larger than the sum of the ionic radii of these two atoms(2.30 �A). The Cartesian coordinates of the adsorption site I and the calculated chemi-sorption energy of the Na atom adsorbed at the site I are given in Table 2, with theorigin of the coordinate system shown in Fig. 1. The calculated charge transfer of theNa atom for sites I and II are also listed in Table 2. From Table 2 it can be seen thatthe chemisorption energy of the Na atom at site I is ÿ4:27 eV and the Na atom isalmost completely ionized and becomes a Na� ion. The strong electric field near theoxide sites in the b-cage should be responsible for the strong binding and the ioniza-tion. From curve b1 in Fig. 3, it can be seen that there is another adsorption site IIwhich locates near the inside of the square face of the b-cage. The distance of the site IIto the square face is 0.32 �A and the equilibrium bond length of Na±O is only 2.2 �A.The Cartesian coordinates of the site II, the chemisorption energy and the charge trans-fer of Na atom adsorbed at site II are given in Table 2. The calculated results in Table 2show that the chemisorption energy of a Na atom at the adsorption site II is ÿ5:87 eV,which is lower than that of one single Na atom adsorbed at the site I. The lower chemi-sorption energy means that the site II might be a more stable adsorption site for a Naadatom. However, according to the structure of zeolite A, adsorption site I might bemore easily accessed by a Na atom. Since the number of adsorption sites I available inthe b-cage (eight) is more than that of sites II (six). Moreover, it is difficult for a Naatom to enter the cage through the square face (4-ring) and occupy the sites II becauseof the small radius of the 4-ring (about 1 �A in diameter). It is only possible that a Naatom occupied the site I firstly, then adsorbed at the site II.

From the above discussion, it can be seen that there exit many adsorption sites avail-able for Na adatoms in the b-cage. Since it is difficult to consider all the geometricconfigurations of Na atoms in the b-cage, only a few cases with high symmetry will beconsidered.

At first, the case in which the chemisorption of Na atom at the sites I in the b-cagewill be considered. In this case the stable configurations of the sodium atoms are deter-mined as follows: first Na atoms are located outside the hexagonal faces of the b-cage,then they enter the b-cage through the ``hexagonal pathº. By reducing the distances ofsodium atoms from the center of the b-cage, the total energy of the systems can beminimized and several stable geometric configurations can be obtained. In the present


Ta b l e 2The Cartesian coordinates of adsorption sites I and II, the calculated chemisorption en-ergies DE, and charge transfers of Na atom adsorbed at the sites I and II

site x (�A) y (�A) z (�A) DE (eV) DQNa (e)

I 2.47 ÿ2.47 2.47 ÿ4.27 0.97II 4.06 0 0 ÿ5.87 1.00

work, four and eight Na atoms entering through the hexagonal faces are consideredand the stable configurations obtained are named Na4(I) and Na8(I), respectively. Tobe more specific Na4(I) is obtained by atoms entering along directions �111� ��1�11� ��11�1�and �1�1�1� whereas for Na8(I), the configuration is obtained by atoms entering along�111� ��111� �1�11� ��1�11� �11�1� ��11�1� �1�1�1� and ��1�1�1� directions. The average chemisorptionenergy curves of a Na atom for configuration Na4(I) and Na8(I) with respect to thedistances d of the Na atom from the center of the b-cage are calculated and shown inFig. 2 (curves a2 and a3, respectively). For the stable configuration Na4(I) the four Naatoms are located in the interior of the b-cage inside the four hexagonal face forming atetrahedron. The curve a2 in Fig. 2 shows that the distance of each Na atom from thecenter of the b-cage is 3.90 �A, which is slightly smaller than that of one Na atom chemi-sorbed at the site I (4.20 �A). The Cartesian coordinates of the four Na atoms are givenin Table 3. The calculated chemisorption energy of a Na atom and charge transfers foratoms Na, O, Al and Si are also listed in Table 3. From Table 3 it can be seen that thechemisorption energy of each Na atom for configuration Na4(I) is ÿ4:64 eV, which islower than that of a Na atom chemisorbed at the site I (ÿ4:27 eV). The calculatedresults show that the strong electric field near the oxide sites in the b-cage makes eachNa atom losing charge about 1e. The distance between neighboring Na cations is6.30 �A, which is much larger than the sum of ionic radii of two Na atoms (1.98 �A). Theresult indicates that the four Na� cations are almost separately adsorbed at the fouradsorption sites I with very weak interaction between themselves. Another configura-tion of four Na adatoms (named as Na4�I�±s) are also considered, in which the four Naatoms are seated near sites I forming a square in the middle of the b-cage. In this casethe calculated chemisorption energy of each Na atom is ÿ4:54 eV, which is a little bithigher than that of the previous case (tetrahedron). This indicates that the tetrahedralconfiguration of the Na4(I) in the b-cage is more stable.

For the case of eight Na atoms adsorbed by the b-cage, they occupy all eight hexago-nal sites I forming a cube. From curve a3 in Fig. 2 it can be seen that the distance ofeach Na atom from the center of the b-cage is 4.15 �A for the stable Na8(I) configura-tion. In Table 4 the Cartesian coordinates of the eight Na atoms for the stable config-uration Na8(I), the calculated chemisorption energy of a Na atom and the charge trans-fers for atoms Na, O, Al and Si are given. From Table 4 it can be seen that thechemisorption energy of a Na atom for this case is ÿ4:39 eV, which is lower than thatof one Na atom chemisorption at the site I (ÿ4:27 eV) and slightly higher than that inthe case of four Na atoms (ÿ4:64 eV). As a strong electric field exists in the b-cage,each Na atom almost loses its valence electron completely. The large distance of neigh-


Ta b l e 3The Cartesian coordinates of four Na atoms, the calculated average chemisorption en-ergy of a Na atom DE, and the calculated average charge transfers of Na, O, Al and Si.Four Na atoms are adsorbed near the sites I in the b-cage

x ��A� y ��A� z ��A� DE �eV� DQNa�I� �e� DQO �e� DQAl �e� DQSi �e�

2.25 2.25 2.25 ÿ4.64 0.95 ÿ0.85 0.79 1.04ÿ2.25 ÿ2.25 2.25ÿ2.25 2.25 ÿ2.25

2.25 ÿ2.25 ÿ2.25

boring Na� cations (4.72 �A) for the configuration implies that the interaction betweenNa atoms is weak and the eight Na atoms are also separately adsorbed near the eighthexagonal sites I. They cannot form a metal cluster.

From the previous discussion we have found that the sites II are more stable for aNa adatom than the sites I. Hence when Na atoms are located near the octahedral sitesII, stable configuration Na adatoms may also be formed. Let six Na atoms be seated atthe six sites II firstly, and then by moving the atoms along the �100� ��100� �010� �0�10��001� �00�1� directions, the total energy of the system can be minimized and the stableconfiguration Na6(II) can be obtained inside the b-cage. The curve b2 in Fig. 3 showsthe calculated average chemisorption energy of a Na atom respective to the distance dof the Na atom to the center of the b-cage. From the curve b2 in Fig. 3, it can be seenthat for the stable Na6(II) configuration the distance of each Na atom from the centerof the b-cage is 3.95 �A, which is smaller than that of one Na atom adsorption at thesite II (4.06 �A). The distance of nearest Na atoms is 5.58 �A, which is also mucher largerthan the sum of the radii of two Na cations. The result indicates that in that case theNa adatoms do not form the metal cluster. The Cartesian coordinates of the six Naatoms for the stable Na6(II), the calculated average chemisorption energy of a Na atomand the charge transfers for Na, O, Al and Si atoms are listed in Table 5. The calcu-lated results in Table 5 show that for the stable configuration Na6(II), the averagechemisorption energy of a Na atom is ÿ6:12 eV, which is lower than that of one Na


Ta b l e 4The Cartesian coordinates of eight Na atoms, the calculated average chemisorption en-ergy of a Na atom DE, and the calculated average charge transfers of Na, O, Al and Si.Eight Na atoms are adsorbed near sites I in the b-cage

x ��A� y ��A� z ��A� DE �eV� DQNa�I� �e� DQO �e� DQAl �e� DQSi �e�

2.36 2.36 2.36 ÿ4.39 0.91 ÿ0.87 0.77 1.02ÿ2.36 2.36 2.36

2.36 ÿ2.36 2.36ÿ2.36 ÿ2.36 2.36

2.36 2.36 ÿ2.362.36 ÿ2.36 ÿ2.36ÿ2.36 2.36 ÿ2.36ÿ2.36 ÿ2.36 ÿ2.36

Ta b l e 5The Cartesian coordinates of six Na atoms, the calculated average chemisorption energyof a Na atom DE, and the calculated average charge transfers of Na, O, Al and Si. SixNa atoms are located near the sites II in the b-cage

x ��A� y ��A� z ��A� DE (eV) DQNa�II� (e) DQO (e) DQAl (e) DQSi (e)

3.95 0.00 0.00 ÿ6.12 1.00 ÿ0.86 0.78 0.98ÿ3.95 0.00 0.00

0.00 3.95 0.000.00 ÿ3.95 0.000.00 0.00 3.950.00 0.00 ÿ3.95

atom chemisorption at the site II (ÿ5:87 eV). The charge transfer of each Na atomto the b-cage is about 1e.

When sodium atoms are adsorbed in the b-cage, both sites I and II may be occupied.A stable configuration in which fourteen Na atoms occupy all the adsorption sites I and IIcan be obtained. In this configuration, six Na atoms are located near the octahedralsites II inside the b-cage and the other eight Na atoms near the hexagonal sites I out-side the b-cage. In Table 6, the Cartesian coordinates of the six Na atoms which arelocated in the b-cage are presented. The average chemisorption energy of the fourteenNa atoms and the average charge transfers of Na(II), O, Al and Si are also listed inTable 6. From Table 6 it can be seen that the six Na atoms inside the b-cage are closerto the center of the b-cage. The distance of nearest Na atoms is 3.49 �A. However, thelarger distance between Na atoms implies that alkali metal clusters are not formedthough fourteen Na atoms are adsorbed.

Since there are many adsorption sites available in the b-cage, several different config-urations of adsorbed Na atoms can be formed. In the present study, only configurations


Ta b l e 6The Cartesian coordinates of six Na(II) atoms, the calculated average chemisorption en-ergy of a Na atom DE, and the calculated average charge transfers of Na(II), O, Al andSi. Fourteen Na atoms occupy all the sites I and II of the b-cage

x ��A� y ��A� z ��A� DE (eV) DQNa�II� (e) DQO (e) DQAl (e) DQSi (e)

3.22 0.00 0.00 ÿ3.60 0.84 ÿ0.91 0.71 0.96ÿ3.22 0.00 0.00

0.00 3.22 0.000.00 ÿ3.22 0.000.00 0.00 3.220.00 0.00 ±3.22

Fig. 4. The density of states (DOS) for the Na8/b-cage (solid line) system. The DOS for the b-cageis plotted as dotted line for comparison

of high symmetry have been considered. From the calculated results it can be seen thatthe Na adatoms are adsorbed almost separately at the adsorption sites I and II in theb-cage. Since the nearest Na±Na distances are quite large, one can hardly say that theadsorbed Na atoms form clusters in the b-cage, even the number of adsorbed Na atomsare increased to fourteen. The reason for the adsorbed Na atoms not forming a clusterin the b-cage is obviously associated with the fact that the adsorbed Na atoms are al-most ionized and the Coulomb repulsion prevents them from forming a cluster at shortdistances.

As pointed out in the Introduction, the electronic properties of zeolite can be modi-fied when more and more sodium atoms are incorporated into zeolite cages. When thenumber of Na atoms adsorbed by the b-cage of zeolite A is increased, the total densityof states (DOS) of the systems can be changed drastically. In Fig. 4, the DOS for thesystem Na8/b-cage is plotted as solid line, while the DOS of the b-cage without sodiumis given by the dotted line for comparison. The curves of the DOS are obtained byGaussian broadening. Comparing the DOS of the Na8/b-cage systems with that of theb-cage, it can be seen that the density of states near the Fermi level (EF) (labelled by P)has increased obviously after Na atoms adsorbed by the b-cage. In Fig. 5 the DOS ofthe Na14/b-cage system (curve a) and of the Na13/b-cage is presented (curve b) forcomparison. Here the configuration of thirteen Na atoms is formed by taking away aNa atoms located at the site I from the Na14/b-cage system. From Fig. 5 it can be seenobviously that a new peak (labelled P1) appears near the energy 5 eV, which is near thefirst ionization energy of a Na atom. The partial density of states of Na adatoms showsthat the new peak P1 is mainly contributed by the Na adatoms which are located in theb-cage. The reason for this may be due to the fact that as the number of Na adatoms isincreased, the charge transfer of Na adatoms to the b-cage will be saturated and then anew peak appears in the DOS plot. The calculated results show that when the numberof Na atoms adsorbed by the b-cage is larger than twelve, such as thirteen which meansthat there is an extra Na atom for each b-cage of Na12 ±A (zeolite A), the electronic


Fig. 5. The density of states (DOS) for the systems Na14/b-cage (curve a) and Na13/b-cage (curve b)

properties of the systems can be modified drastically, since the physical and chemicalproperties, such as optical and transport properties are mainly determined by the elec-tronic structure near the Fermi level. The calculated results imply that when more andmore sodium atoms are incorporated into zeolite, some new interesting propertiesmight appear.

4. Conclusions

By using the extended HuÈ ckel method and cluster model, the geometric configurationsof sodium atoms in a zeolitic cage have been studied. The preferable sites for a Naatom in the b-cage have been determined. It is found that there are two sorts of ad-sorption sites I and II in the b-cage. The hexagonal site I is located near the center ofthe hexagonal face, whereas the site II is inside the b-cage near the center of thesquare face. By minimizing the total energy of the systems, high symmetric stable con-figurations are obtained for four, six, eight and fourteen Na atoms adsorbed by theb-cage. Because of the much larger distance between adsorbed Na cations one canhardly say that they form the Na clusters in the b-cage. In fact, they are adsorbed onthe walls of the frameworks of the b-cage. The Coulomb repulsion of the adsorbed Nacations impedes these cations for constructing clusters in the b-cage. The electronicstructures of the chemisorption systems show that the peak of the density of states nearthe Fermi level increases obviously after the sodium atoms are adsorbed inside theb-cage, and a new peak appears near the first ionization energy of a Na atom when thenumber of Na atoms being adsorbed by the b-cage exceeds twelve.

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theoretical study of structural and electronic properties of sodium in zeolitic cage

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