Langmuir 1988, 4 , 917-920 Table VI. Values of Y~ and 7%Calculated According to Eq AI and A2, Respectively, for the Values of n from the Interval (0,3) with the Step 0.05 n YA Y X n YA Yx 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
0.3712 0.4950 0.5748 0.6323 0.6760 0.7105 0.7368 0.7617 0.7813 0.7979 0.8122 0.8248 0.8357 0.8454 0.8541 0.8619 0.8689 0.8753 0.8810 0.8862 0.8909 0.8954 0.8996 0.9033 0.9070 0.9102 0.9132 0.9161 0.9188 0.9213
0.8909 0.8954 0.8996 0.9033 0.9070 0.9102 0.9132 0.9161 0.9188 0.9213 0.9239 0.9259 0.9280 0.9300 0.9319 0.9337 0.9354 0.9370 0.9385 0.9400 0.9413 0.9427 0.9440 0.9452 0.9464 0.9475 0.9485 0.9496 0.9506 0.9516
1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00
0.9239 0.9259 0.9280 0.9300 0.9319 0.9337 0.9354 0.6370 0.9385 0.9400 0.9413 0.9427 0.9440 0.9452 0.9464 0.9457 0.9485 0.9496 0.9506 0.9516 0.9525 0.9534 0.9542 0.9550 0.9558 0.9565 0.9573 0.9580 0.9587 0.9594
0.9525 0.9534 0.9542 0.9550 0.9558 0.9565 0.9573 9.9580 0.9587 0.9594 0.9598 0.9606 0.9613 0.9618 0.9624 0.9630 0.9635 0.9640 0.9645 0.9650 0.9657 0.9660 0.9664 0.9669 0.9673 0.9677 0.9681 0.9685 0.9689 0.9693
the mean values and the dispersion for these differential distributions are simple and useful for characterizing activated carbons. The mean values of the adsorption potential and the micropore dimension as well as the dispersions of these quantities are recommended for char-
917
acterizing the energetic and structural heterogeneities of microporous activated carbons. This paper shows also that the JC equation generates simple equations for the differential and integral distributions of the adsorption potential and the micropore dimension. The differential enthalpy and the differential entropy of adsorption predicted by the JC equation were discussed in a previous paper.33 These theoretical studies indicate that the JC equation has many advantages in comparison to other equations (e.g., the DR equation); these advantages indicate a favorable forecast for its use in describing physical adsorption of vapors on microporous activated carbons and other heterogeneous microporous solids.
Acknowledgment. This work was supported in part by the Division of Chemical Sciences, Office of Basic Energy Sciences, Department of Energy. Appendix According to Table I the quantities yA and y x depend on the parameter n and are defined as follows: YA
= r(n+f/2)/[n1/2r(n)l
(AI)
Table VI contains the values of YA and y x calculated for values of n from 0 to 3 with a step of 0.05. Registry No. Carbon, 7440-44-0. ~~
(33) Jaroniec, M. Langnuir 1987, 3, 673.
Bonding Studies of Chromium-Nitrogen Molecules E. E. Mola,* E. Corone1,t Y. Joly,t and J. L. Vicente Divisibn Qulmica Tebrica, INIFTA, Sucursal4, Casilla de Correo 16, 1900 La Plata, Argentina Received September 9, 1987. I n Final Form: March 9, 2988 The Cr(lOO)-(lXl)N superstructure is naturally formed during the cleaning cycles of a Cr(100) sample. According to the annealing temperature the nitrogen present in the bulk of the substrate segregates to form the (1x1) structure. The analysis of a low-energy electron diffraction spectrum of such a surface remains unsatisfactory, and more sophisticated model calculations are required to describe properly the bonding strength and, eventually, charge transfer between nitrogen and the chromium cluster, in order to improve the agreement between experiment and theory. For those reasons, we present in this paper a theoretical study of NCr, Cr2,NCr2, Cr5, and NCr6 molecules. For this purpose we have employed the modified neglect of diatomic overlap (MNDO) method. From the present calculations it may be concluded that nitrogen binds very strongly to the chromium cluster with a net charge transfer to the metal. A metal work function reduction upon nitrogen chemisorption may be expected. This calculation also predicts a slight increase in the distance between chromium atoms induced by the adsorbate and larger values of the phase shifts than those obtained from the muffin tin approximation.
Introduction Low-energy electron diffraction (LEED) is a well-established method for studying well-ordered surfaces.l To determine adatom positions or first layer relaxations, the
analysis of diffracted beam intensities is indispensable.2 For this a theory-experiment comparison technique is necessary. Then we have to presume various geometries and make the diffracted beam intensity calculation for each geometry. The best agreement between experiment
* Author to whom correspondence should be addressed. 'On leave of absence from Universidad Mayor de San AndrBs, La Paz, Bolivia. *Onleave of absence from Laboratoire de Spectrometrie Physique de Grenoble, France.
(1) Pendry, J. B. Low Energy Electron Diffraction; Academic: London, 1974. (2) Van Hove, M. A.; Tong, S. Y. Surface Cristallography by L E E D Springer: Berlin, 1979.
0743-1463f 88f 240~-0911$01.50 f 0 0 1988 American Chemical Society
918 Langmuir, Vol. 4, No. 4, 1988
Mola et al.
Table I. Heat of Formation P H I and Heat of Reaction AH in kcal/mol for Different Nitrogen-Chromium Moleculesa molecules Lmf Lm d(Cr) d(N) Ll s(N) s(Cr) s(Cr*) CrN Cr2 CrzN cr5 Cr5N
135.24 -48.85 111.15 -2048.14 -2221.00
72.76 -47.00
1.65 1.67
1.30
8.92
-1.379
1.379
1.27
1.00 3.51 0.03
-0.226
0.113 -0.613 -1.105
1.84 285.86
1.92
0.79
2.054
2.450 2.368
'd(Cr) and d(N), see Figure 1, are in angstroms. Dipole moment p is in debyes, and net atomic charges q are in atomic units.
and the model calculation will provide the real geometry of the surface. Each calculation is divided into two steps: (i) the calculation of the scattering by any type of atom present in the sample and (ii) the calculation of the elastic scattering by all the samples with the geometry presumed. For some Cr(loo)-( 1Xl)N surfaces, the agreement between experiment and theory remains unsatisfactory for any presumed ge~metry.~ Auger spectroscopy reveals that nitrogen structures are like a nitride showing that chemical bonding between nitrogen atoms and first-layer chromium atoms is strong. LEED is essentially a core-scattering effect, so it is possible to use the muffin tin approximation, even for surface atoms, and generally to make atomicscattering calculations with simple non-self-consistent models. However, for some structures, as nitrogen on chromium, the bonding strength and eventual charge transfer seem to oblige the use of a more sophisticated model. This is the only way to improve the experimenttheory agreement and thus to give a good description of this surface. Such a calculation has already been succesfully done for nontransition metala4 The Cr(100)-( 1Xl)N superstructure is naturally formed during the cleaning cycles of a Cr(100) sample. According to the annealing temperature the nitrogen present in the bulk of the substrate segregates to form the (1x1)structure. This nitrogen monolayer can be pulled out by ion bombardment, but it will reappear at the next annealing. A large number of cleaning cycles are necessary to eliminate all the nitrogen and thus to get a clean chromium surface. The effect of an adsorbate on the first layers of a substrate is an interesting problem already described for some structures as Ni(ll0)-~(2X2)S.~However, the general behavior is not already known, and for this behavior to be understood theoretically more surfaces with and without adsorbates must be conclusively analyzed. The Cr(loo)-( 1 X l ) N superstructure is a good representation of a bcc (100) surface and will be useful for such a goal. For these reasons, we present in this paper a theoretical study of NCr, Crz, Cr5, and NCr5 molecules. We hope to be able to give a good description of the electronic surrounding of each atom as well as of the interatomic bond lengths and thus to better understand the nitrogen adsorption on chromium.
MNDO Method The justification for the cluster approach, which we are going to use, rests on the assumption that the interaction of a molecule with a surface is largely localized to a small number of metal atoms. This molecule may be treated as a surface compound independently of the rest of the extended surface. Another "local" picture of chemisorption is provided by the surface molecule concept. Using this approach, one (3)Joly, Y. Ph.D. Thesis, UniversitC Scientifique et Medicale de Grenoble, 1984. (4)Neve, J.; Rundgren, J.; Westrin, P. J. Phys. C. 1982, 15,4391. Lindgren, S.A.;Wallden, L.; Rundgren, J.; Westrin, P.; Neve, J. Phys. Reu. E . 1983,28,6707. ( 5 ) Baudoing, R.; Gauthier, Y.; Joly, Y. J. Phys. C. 1985,18,4061.
-d
ICrl-
dIY1
I..
Cr
i r
d(N1 ..t. Cr
Figure 1. Geometry of five nitrogen-chromium molecules. Cr5 simulates the clean Cr(100) surface. Cr* is just beneath the surface.
of the authors6has studied nitrogen chemisorption on iron. The great strength of the chemical bonding between nitrogen atoms and first-layer chromium atoms revealed by Auger spectroscopy and confirmed by the present calculations suggests a highly localized bonding. Some theoretical justification for using a surface compound model has been given.'-'O For our purposes we have chosen the program AMPAC from the Quantum Chemistry Program Exchange, No. 506. This one contains the semiempirical Hamiltonians MNDO, MIND0 3, and AM1 and a sophisticated set of convergence techniques. We have employed in our calculations the MNDO method, which is described in detail by its auth0rs.l' The MNDO method includes a semiempiricalmodel for the two-center repulsion integrals which permits calculations 1000 times faster and with comparable results than those done with ab initio methods.12 It has already widely been used with success for molecules of all kinds but without transition-metal atoms. Fortunately, a very new version gives the parameters for chromium atom. The complexity introduced by the d-orbitals implies that a very few number of methods work with molecules containing Cr atoms. (6)Mola, E. E. Surf. Sci. 1975,51,290. (7)Messmer, R. P. Semiempirical Methods of Electronic Structure Calculation, Part B Segal, G . A., Ed.; Plenum: New York, 1977. (8)Grimley, T.B. Molecular Processes on Solid Surfaces; Grauglis, E., Gretz, R. D. Jaffee, R. I. Eds.; McGraw-Hill: New York, 1969;p 299. (9)Grimley, T.B.;Mola, E. E. J.Phys. C 1976,9, 3437. (10)Einstein, T.L. Phys. Rev. E 1975,11, 577. (11)Dewar, M. J. S.; Thiel, W. J. Am. Chem. SOC.1977,99,4899. (12)Dewar, M. J. S.; Storch, D. M. J.Am. Chem. SOC.1985,107,3898.
Langmuir, Vol. 4, No. 4, 1988 919
Bonding Studies of Cr-N Molecules
-2000
\
I 1
1
60
I
I
I
I
2 00
180
-
I
2 20
d(Cr) [AI Figure 2. Dependence of the heat of formation AHf (kcal/mol) of a Cr, cluster on the chromium-chromium distance d(Cr).
(AI
Cr5N Cr5
(El I
I
I
l
-8
-10
l
-6
I
l
I
I
-2
-4
l
1
IL,,
Er:O
I
EleVI-
I
Figure 5. Total density of states of Cr5N (A), Cr5 (B),and their difference (C).
1
Table 11. Occupation Numbers of the N Atomic Orbitals at Optimized Position of Cr,N Cluster 2s
-2000
-2200-
free N adsorbed N
I
180 d(Cr)
I 60
-
2 00
2 20
[AI Figure 3. Dependence of the heat of formation A", (kcal/mol) of a Cr5N cluster on the chromium-chromium distance d(Cr).
0 60
0 80
1
00
1 20
Dependence of the heat of formation AHf (kcal/mol) d(N1
[AI
Figure 4. of a Cr5N cluster on the distance d(N).
Results We have done calculations for Cr2,CrN, Cr2N,Cr5, and Cr5N molecules. Principal results are given in Table I at the optimized interatomic distances. Geometry and interatomic distances are shown in Figure 1. We have adopted the body cubic center geometry for the five chromium atom cluster; d(Cr) is the lattice spacing. Figure 2 shows the dependence of the heat of formation, A",, of a Cr, cluster on lattice spacing d(Cr). Figures 3 and 4 show the dependence of the heat of formation of a Cr,N cluster on lattice spacing d(Cr) and on the distance d(N) by keeping the distance d(N) constant at 0.791 A and d(Cr) constant at 1.915 A. In every case a very well-defined minimum is obtained. The total density of states (DOS) curves of Cr5N and Cr, and their difference are shown in Figure 5. A t -8.7 and -4.8 eV below the Fermi level, EF,two strong additional peaks induced by the adsorbed N atom appear. They have a strong nitrogen contribution, (2s,2p) and 2p, respectively.
2P 3.000 1.116
Table I summarizes the main numerical results. AH represents the heat of reaction corresponding to Cr, + N Cr,N AH. Nitrogen chemisorption seems to be a highly exothermic reaction. There is charge transfer from chromium to nitrogen in CrN. This process is reversed when we consider chemisorption on a chromium cluster due to the fact that the extended states, provided by the cluster, will reduce the Coulomb interactions within it. These states are mainly constituted by the four "surface" atoms. The chromium atom which is just beneath the surface does not participate to a great extent in the chemisorption bond. I t is expected that this charge transfer from nitrogen to the cluster would not be altered by increasing the cluster size. The increasing band width that will be obtained by considering larger clusters will be enough to ensure this charge-transfer direction. The convergence of the electronic structure of the chromium clusters as a function of cluster size will not be discussed here. Suffice it to say that, insofar as the distribution of energy levels and character of orbitals are concerned, the cluster of five atoms represents a reasonable description of the local electronic structure of the substrate. There is a small relaxation of the distance between chromium atoms (-4%) upon nitrogen chemisorption. This type of relaxation has been observed by one of the authors5 when sulfur is chemisorbed upon Ni( 110). The distance between chromium atoms in the five-atom cluster Cr5 is smaller than the lattice spacing in a bulk sample, and this fact might be explained by the ionic character of the cluster due to its reduced extension. Therefore, attention should be placed more on relative changes of the physical quantities quoted in Table I rather than on their absolute values. Another interesting feature that emerges from the present calculations is the reduction of the surface dipole moment upon nitrogen chemisorption. We can conclude from this fact that there should be a noticeable reduction of the chromium work function by nitrogen chemisorption. The occupation of the atomic orbitals of N and Cr at the optimized position of the Cr,N cluster is given in Tables I1 and 111. We found that the atomic orbital occupation of Cr has changed much more than for the other (Cr*) atom. It implies that the interaction between the adsorbed N and the substrate is rather local. The occu-
-
,
2.000 1.830
+
Mola et al.
920 Langmuir, Vol. 4, No. 4, 1988 Table 111. Gross Atomic Charge of C r Atoms of Cr5 and Cr5N Clusters at Optimized Position Cr* Cr cr6 3d 3.548 4.614 4s 0.001 1.205 0.001 0.794 4P Cr,N 3d 3.623 5.105 4s 0.004 1.156 0.005 0.844 4P
1 I:;
I
1.2
--.
‘“1
1
I
n
1
I
I
,
I
I
spectroscopy, a net charge transfer from nitrogen to the four “surface” chromium atoms. This fact will favor a metal work function reduction upon nitrogen chemisorption. There is also a slight relaxation of the distance between chromium atoms upon the chemisorption process. We expect that the present calculation will help to make a good LEED intensity analysis of a Cr(100)-(lxl)N in order to improve the agreement between theory and experiment. Since one of the goals of this work is to provide new data to improve LEED calculations, we have used previous results to calculate the scattering by such a charged nitrogen atom. Since the LEED theory uses the muffin tin approximation, we have spherically symmetrized the electronic density and then calculated the phase shifts in the usual LEED energy range from the Noumerov approximation.13 Figure 6 shows the phase shifts for 1 = 0, 1, 2, and 3 obtained from the cluster approach and those obtained from the simple superposition of atomic den~ities.~ In this later calculation no charge transfer is accounted for. The cluster approach yields larger values characteristic of larger scattering factors.
Acknowledgment. INIFTA is a Research Institute jointly established by the Universidad Nacional 4e La Plata, the Consejo Nacional de Investigaciones Cientificas y TBcnicas, and the Comisidn de Investigaciones Cientificas de la Provincia de Buenos Aires. We are grateful to Dr. R. W. Court (QCPE) for providing a copy of the AMPAC program and to the IFLYSIB computing facilities. Registry No. Cr, 7440-47-3; N2,7727-37-9; CrN, 24094-93-7; Crz, 12184-82-6; CrzN, 12053-27-9; Cr,, 114201-38-6; Cr,N, 114201-39-7. (13) Hartree, D. R. Numerical Analysis; Clarendon: Oxford, 1958.
