Structure and dynamics of nitrite sodalite. An ab initio study (*)
E. FOIS(1), A. GAMBA(1) and D. MARIC(2)
(1) Istituto di Scienze Matematiche, Fisiche e Chimiche, Università di Milano, Sede di Como Via Lucini 3, I-22100 Como, Italy
(2) CSCS, Centro Svizzero di Calcolo Scientifico - Via Cantonale, 6928 Manno, Switzerland
(ricevuto il 28 Febbraio 1997; approvato l’8 Maggio 1997)
Summary. — We present a first-principles study of nitrite sodalite, a synthetic
zeolite. The NO22anions are hosted in octahedral cavities typical of such crystals, and
each anion is surrounded by four Na cations in a tetrahedral geometry. We found that NO22 is in a rotational state inside the zeolite’s cages. This rotational state
explains the orientational disorder experimentally detected in nitrite sodalite. PACS 36.20 – Macromolecules and polymer molecules.
PACS 01.30.Cc – Conference proceedings.
1. – Introduction
Sodalites are aluminosilicates of chemical formula Mx[Al6Si6O24]Xy[1], where M stands for a metal cation and X is an anion, frequently a halogen anion. Sodalites are well-known zeolites [2], framework crystals formed by corner sharing SiO4 and AlO4 tetrahedra with perfect Si-O-Al alternance. Its structure is characterized by the presence of octahedral cages that host both the cations and the anions (extra framework ions). In proper sodalite, Na8[Al6Si6O24]Cl2, each octahedral cavity (the
b-cage) contains a ClNa413cluster, with the Cl2anion in the center of the cage, and the four Na cations at the vertices of a tetrahedron [1]. In this case, both symmetry and electrostatics favour the central position for a Cl2, however the same considerations do not apply for an asymmetric top like the nitrite anion NO22 or other anion with non-spherical symmetry. This generally gives rise to disorder in the atomic positions of the guest anions. In most cases atoms occupy crystallographic sites, close to the cavity center, of lower symmetry and higher degeneracy. Such symmetry lowering causes a decrease in the resolution of scattering experiments and a lower definition in the position and structure of such anions. X-ray diffraction (XRD) studies on the nitrite sodalite [3] reveal that the nitrite anion is disordered and two different structures are
(*) Paper presented at the “First International Workshop on Reactivity of Oxide Materials. Theory and Experiment”, Como, 8, 9 November 1996.
compatible with the same scattering data. We present a computer simulation study of the sodalite Na8[Al6Si6O24](NO2)2at room temperature. This paper will mainly focus on the structural and dynamical properties of the hosted NO22, and is preliminary to the study of the intracage oxidation of NO22 to NO32[4]. Our work is carried on with the first-principle molecular dynamics method due to Car and Parrinello (CP) [5].
2. – Method of calculation
In the CP method, the wave functions’ coefficients ]f( form a set of classical
coordinates and the time evolution of the real ionic coordinates ]R( and that of the fake coordinates ]f( is generated via an extended Lagrangian formalism [5]. In this
method the forces acting on the ions are calculated ab initio within the density functional approximation. The combined classical equations of motion for ]R( and ]f( are integrated numerically with the standard molecular dynamics techniques [6]. A basic requisite for the motion of the ions to have physical meaning is that the ]f(’s stay as close as possible to the instantaneous ground-state wave functions pertinent to the given ]R(’s.
In our calculations of the nitrite sodalide we have adopted the experimental lattice parameter and symmetry, a cubic cell of 8.923 Å with period boundary conditions. The
0
1
2
3
r / A
0
1
2
3
4
5
N(r)
Fig. 1. – Calculated distances distributions of nitrogen (thin continuous line), oxygen (thin dashed) and sodium (thin dot-dashed) atoms from the b-cages centers. The thick lines represent the coordination numbers N(r) around the same position: thick continuous lines refer to nitrogen, thick dashed to oxygen, thick dot-dashed to sodium. Only NO22’s oxygens are considered here. The b-cages centers correspond to the (0, 0, 0) and (1/2, 1/2, 1/2) crystallographic positions.
simulated cell contains 8 Na1, 6 Al3 1, 6 Si4 1, 28 O6 1 and 2 N5 1 ions and 228 electrons (we consider valence electrons only). Electron-electron interaction is calculated within a gradient corrected density functional approximation [7]. Norm-conserving non-local pseudopotentials [8] were used for the ions electrons interactions. Wave functions ]f( were expanded in plane waves with a cut-off of 60 Ry. We have used a time step of 0.12 femtoseconds for the numerical integration of the equation of motion and assigned a fictitious mass of 500 a.u. for the wave functions coefficients. The initial configuration for our sample was taken from ref. [3], where two possible geometries for the NO22ions were quoted, referenced as model I and model II. As the unit cell contains two of such anions, we started our simulation with one ion in the configuration of model I, and the other in the configuration II. We assigned random velocities to the atoms in our cell and equilibrated the system at 300 K. We have followed the dynamics for about 1.2 picoseconds, with a conservation of the total energy within 1 31025 a.u.
3. – Results and discussion
Room temperature XRD pattern of nitrite sodalite [3] are consistent with the typical sodalite structure of Na8[Al6Si6O24] [1]. The Na ions form two regular tetrahedra encapsulated in the two octahedral b-cages. However XRD does not give a unique answer for the guest anions. There are at least two models that are compatible with the scattering data. In both models, however, the NO22 ion is inside the Na tetrahedra with the nitrogen atom displaced by 0.37 Å from the center of the cage. In fig. 1 the distribution of the calculated center-of-cage N distances are shown. It is clear
0
1
2
3
4
5
r/A
0
2
4
6
8
g(r)
Fig. 2. – Calculated radial distribution functions g(r), that give the probability of finding an atom at a distance r from another atom. The thin dashed line represents the N-Na g(r), while the continuous thin line represents the O-Na g(r). The thick lines represent the calculated coordination numbers vs. distances for N-Na (dashed) and O-Na (continuous). Only NO22’s
–0.50
–0.25
0.00
0.25
0.50
Crystallographyc Coordinates
x
y
z
Fig. 3. – Distributions of the calculated crystallographic coordinates of nitrogen atoms in nitrite sodalite.
that also our calculations predict an off center position for the N atoms. In fig. 2 the radial distribution functions calculated for the N-Na and O-Na distances (oxygens of the NO22) are shown. The peaks positions for Na-N (2.77 Å) are closer to the proposed model II (2.67 Å) than for model I (2.47 Å). Moreover also the calculated geometry for the anions (NO distance 1.25 Å, O-N-O angle 1107) are closer to model II (1.25-1.27 Å, 104-1097) than to model I (1.18 Å, 1047). Figure 3 reports the calculated cystallographic positions of the N atoms. The three (x , y , z) components do not have unimodal distributions around 0. This means that the N atoms have not a unique crystallographic position but are moving around the center of the cage
(
that corresponds to the (0, 0, 0) position)
. Figure 4, where the calculated distances of one N with the four nearest Na as a function of time are shown, confirms this hypothesis: the nearest Na is changing along the trajectory, and every few tens of femtoseconds the coordination of the N atom is different, while the average number of Na atoms around N is practically constant. As nitrogen atoms are covalently bonded to oxygen in NO22, also those oxygen atoms are involved in this motion. In fig. 5 the distances of one of such oxygens with its nearest four Na cations are shown. It appears that also the oxygen is changing its coordination along the trajectory. However the exchanges of first neighbour of both N and O simply means that NO22 is rotating inside the Na tetrahedron. As in our simulation cell both guest anions are in this rotational state, independently of their0
300
600
900
1200
t/fs
2.2
2.5
2.8
3.1
3.4
r
N-Na/A
Fig. 4. – Calculated N-Na distances vs. time in nitrite sodalite. Only the distance of one nitrogen with its four sodium nearest atoms are shown.
0
300
600
900
1200
t/fs
2
3
4
r
Na-O/A
Fig. 5. – Calculated O-Na distances vs. time in nitrite sodalite. Only the distances of one oxygen of NO22with its four nearest Na atoms are shown.
initial configuration (model I or II), we believe that experimental data needs a new interpretation. The orientational disorder [3] of NO22 in nitrite sodalite is actually a rotational state, where the nitrite ion changes the orientation of its molecular axis with
Y X X Y X Y X Y Z Z Z Z
Fig. 6. – Four configurations of nitrite sodalite at different times along the calculated trajectory. Black spheres represent oxygens, grey spheres represent silicon and aluminium atoms. Large white spheres represent sodium and small white spheres nitrogen atoms. The zero of the axis is set in the center of one b-cage.
respect to the crystallographic axis, and that this rotation occurs around the center of the sodalite b-cage. This motion is fast (A100 femtoseconds) compared to typical scattering experiments data collections (A hours), so what experiments actually can see is the averages of all possible orientations of NO22inside the b-cages. In fig. 6 four snapshots of Na8[Al6Si6O24](NO2)2 taken at different times from our trajectory are shown. It is clear that NO22anions are rotating around the b-cages centers.
In summary we have performed a first-principles molecular dynamics simulation of nitrite sodalite at room temperature. Nitrite sodalite is an interesting compound because, in air at high temperature it gives an example of an intracage oxidation of NO22to NO32. Moreover our results explain the orientational disorder of the guest NO22
anion as a rotational state of this C2 v ion inside an octahedral b-cage. A detailed analysis of this rotational states, that required longer simulations of the one presented here, is in progress.
R E F E R E N C E S
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[3] SIEGERP., WIEBCKEM., FELSCHEJ. and BUHLJ.-C., Acta Cryst. C, 47 (1991) 498.
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[5] CARR. and PARRINELLOM., Phys. Rev. Lett., 55 (1985) 2471.
[6] CPMD Version 3.0, HUTTERJ., BALLONEP., BERNASCONIM., FOCHERP., FOISE., GOEDECKER S., PARRINELLO M. and TUCKERMAN M., MPI fur Festkörperforschung and IBM Research 1990-96.
[7] PARR R. G. and YANG W., Density-Functional Theory of Atoms and Molecules (Oxford University Press, Oxford) 1989; BECKEA. D., J. Chem. Phys., 96 (1992) 2155; PERDEWJ. P., Phys. Rev. B, 33 (1986) 8822.
