14
This content has been downloaded from IOPscience. Please scroll down to see the full text. Download details: IP Address: 157.92.4.71 This content was downloaded on 20/10/2014 at 19:46 Please note that terms and conditions apply. On the nature of crystalline bonding: extension of statistical population analysis to two- and three-dimensional crystalline systems View the table of contents for this issue, or go to the journal homepage for more 1993 J. Phys. B: At. Mol. Opt. Phys. 26 4871 (http://iopscience.iop.org/0953-4075/26/24/018) Home Search Collections Journals About Contact us My IOPscience

On the nature of crystalline bonding: extension of ... · 4872 R C Bochicchio and H F Reale As we have shown in a previous collection of papers (Bochicchio and Medrano 1989, Bochicchio

  • Upload
    vunhan

  • View
    214

  • Download
    0

Embed Size (px)

Citation preview

This content has been downloaded from IOPscience. Please scroll down to see the full text.

Download details:

IP Address: 157.92.4.71

This content was downloaded on 20/10/2014 at 19:46

Please note that terms and conditions apply.

On the nature of crystalline bonding: extension of statistical population analysis to two- and

three-dimensional crystalline systems

View the table of contents for this issue, or go to the journal homepage for more

1993 J. Phys. B: At. Mol. Opt. Phys. 26 4871

(http://iopscience.iop.org/0953-4075/26/24/018)

Home Search Collections Journals About Contact us My IOPscience

J. Phys. B: At. Mol. Opt. Phys. 26 (1993) 4871-4883. Printed in the UK

On the nature of crystalline bonding: extension of statistical population analysis to two- and three-dimensional crystalline systems

Roberto C Bochicchio? and HCctor F Reale Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aim. Ciudad Universitaria, 1428, Buenos Aires, Argentina

Received I October 199?, in h a l form 30 July 1993

Abstract. In a previous publication, the socalled statistical population analysis (SPA) has been developed and applied to ID periodic systems (polymers). The goal of the present work is to implement the formalism extended to higher dimensional cases and to perform its application to ZD layers (graphite and hexagonal boron nitride), TD crystals (diamond and cubic boron nitride) and two cases of atomic adsorption on surface (carbon+ graphite: oxygen+graphite), in the framework of the semiempirical MNDO-CO-LCAO state function approach. Rather than attempting to improve the band structures our goal is to give com- plete detail of the electronic distribution in atoms and bonds by means of population analysis algorithms for the above-mentioned systems. SPA results permit the showing of striking and novel effects on chemical bonding arising from the cooperative contribution of the whole crystalline environment. Different kmds of effective chemisorption bonds are detected for the absorption cases on a surface which is characterized by binding energies of opposite signs. The partitioning scheme of SPA shows that the proposed population analysis is a suitable tool for describing the electronic distribution ofisolated and interacting crystalline systems even encouraging its application to the study of more complex situations in which catalysis phenomena are present.

1. Introduction

Band theory provides a delocalized picture of electron states in an extended system (del Re et a1 1967, Andrk and Delhalle 1978, Kertbsz 1982, Ladik 1975, AndrC 1975, Calais 1987). On the other hand crystalline structures are built up by atoms and bonds (Phillips 1970) which imply a localized distribution; hence the bonding information contained in the electron states is not immediately available from that band concept.

The linkage between these two views is supported by the use of some methods for picking up bonding information from electron states. One way of doing it is applying electronic distribution techniques which provide a localized picture by means of atomic and bonding electron populations (Bochicchio and Medrano 1989, Bochicchio 1991a, b, Reale and Bochicchio 1991). Also in this way we are able to detect which is the leading component of the bonds, i.e. covalent, ionic, coordinate, etc, or any kind of intermediate bond mixtures. Hence it is also possible to determine the physical nature of chemical bonding (Bochicchio 1991a, b).

7 Caner Member ofthe Consejo Nacional de lnvestigaciones Cientificas y Tknicas de la Republica Argentina (CONICET). Author to whom correspondence should be addressed.

0953-4075/93/244871 t 13S07.50 0 1993 IOP Publishing Ltd 4871

4872 R C Bochicchio and H F Reale

As we have shown in a previous collection of papers (Bochicchio and Medrano 1989, Bochicchio 1991a, b, Reale and Bochicchio 1991, Bochicchio et a1 1989, Bochicchio and Reale 1989), electron distributions in extended systems may be described by means of quantum statistical reduced density operators (Coleman 1963, Lowdin 1955, 1982, Davidson 1976). So it becomes the fundamental tool for defining classical chemical concepts from quantum statistical theory (Bochicchio and Medrano 1989, Bochicchio 1991a, b, Bochicchio and Reale 1991).

Electronic distributions may be completely described by magnitudes as multiplicity of the bond, inactive ,and active atomic populations, valence and free valence per atom in the unit cell of a crystalline system.

The electronic population analysis supported by the statistical definition of the mean number of particles in an electron gas spread over the nuclei such as in the case of extended systems (molecules and crystals) is called statistical population analsysis SPA (Bochicchio and Medrano 1989, Bochicchio 1991a, b, Bochicchio and Reale 1991, Bochicchio er ai 1989, Bochicchio and Reale 1989).

In Bochicchio et al(1989) the extension of the formalism (Bochicchio and Medrano 1989, Bochicchio 1991a, b, Bochicchio and Reale 1991) to crystalline electron states or crystalline orbitals (CO) and numerical examples in one-dimensional ( ID) systems were considered.

The goal of this work is to apply this formalism to more complex crystalline systems such as 2~ and 3~ (layers and crystals) and adsorbate-adsorbent supersystems as examples of adsorption on surfaces in order to describe their electronic distributions. Hence it constitutes the first attempt carried out in this field.

Tyo-dimensional ( 2 ~ ) systems such as graphite and hexagonal boron nitride are actual models of 2~ layers because periodic systems with layer structures are charac- terized as having the strongest interaction between atoms within one layer, so in such solid compounds it is a good approximation to use the 2~ approach and to neglect the interactions between layers. Although these two systems as well as three-dimensional diamond and cubic boron nitride have been studied in detail from an experimental point of view and the fact that their band structures have been calculated from several levels of approximation (Ricart et al 1985, Dovesi et a1 1976, 1980a, b, 1981, Ricart et a1 1984), an electronic distribution population analysis of such systems does not exist. Two-dimensional models are not only a useful bridge between the simple I D and the 3~ structure of real solids, but also they are the natural frame for introducing us to the exciting field of the adsorption phenomena. Such processes need electronic distribution details in order to understand the chemisorbed behaviour of atoms and several species. We employ the ?D model of graphite as the adsorbent substrate to perform research of the regular adsorption of atomic carbon and oxygen. So it provides the first results of electronic population distribution in such phenomena.

The organization of this work is as follows. In section 2 we describe the theoretical background to derive the partitioning scheme which gives rise to the SPA definitions (Bochicchio el a1 1989, Bochicchio and Reale 1989). In section 3 we give the description and numerical results for 2~ and 3~ periodic systems and two examples of regular atomic adsorption on a surface. Finally in section 4 some conclusions are drawn.

2. Theoretical background

SPA expressions for 2~ and 3~ systems are similar to those presented for ID systems (Bochicchio et a1 1989, Bochicchio and Reale 1989), the only difference is that the q

Population description of crystalline bonds 4873

cell indices are vectorial ones, because the translation vector now has two and three components respectively. Therefore, the present summations involving cells stand over two ( 2 ~ ) or three ( 3 ~ ) scalars which are the components of the translation vector which place the different cells from the central unit cell in the lattice. Hence, we are only summarizing the definitions of the magnitudes used in this work, namely, mono- and diatomic population expressions.

Our general 30 periodic system is composed of N electrons, M atoms and C2 atomic orbitals (AO) in each unit cell and Li (i= 1, 2, 3) unit cells for each translation direction. Because of such translation symmetry, we only need to work with N electrons in an arbitrarily chosen reference cell, so all the magnitudes are defined per unit cell (del Re et al 1967).

The main tool for our description of the electronic distribution in the system is the statistical operator DN (Coleman 1963, Lowdin 1955, 1982, Davidson 1976). Since we will deal with population analysis for particles, we reduce DN to first-order DI (or simply D ) according to the marginal distribution of N particles (Coleman 1963, Ldwdin 1955, 1982, Davidson 1976).

The reduced density operator D is related to D by D=N D. The definitions of the population contributions to the electronic structure in terms

of the matrix elements of the inter/intra cell density matrix are as follows. Let DFv be the matrix element between the pth orbital on atom A in the reference cell and the vth orbital on atom B in the cell and hence

BFB (1) PEA.VEB

is the bond multiplicity or degree of bonding between atoms A and B in the reference cell,

B S ~ = c’ = C c‘IDF”1I’ (2) < peA.ve6 p

stands for the crystalline bonding contribution that takes into account the crystalline cooperative effect of the periodic lattice by means of the summations of the degrees of bonding between an atom A in the reference cell and all the atoms B in the other cells.

On the other hand, the inactive or unshared charge QA of atom A in the reference cell is defined as follows

(3) 1 M M Q A = $ ETAA- BFB- C Bi’ , [ B=I E - 1

The number of electrons in the unit cell may be written in terms of summation over monatomic magnitudes only. These magnitudes are called atomic gross population N A and are defined by

M M N A = Q A + C BYB+ E:!‘.

E = I B= I (4)

The last two equations allow us to define the active or shared charge QYt of atom A which represents the number of electrons of atom A behaving like bonding ones

4874 R C Bochicchio and H F Reale

Following the same pattern as in molecules (Bochicchio 1991a, b, Bochicchio and Reale 1991) we express the valence VA of atom A in the unit cell within the crystal environment as

vA=2 D p g - 1 I D p v 1 2 . (6) M E A P,"EA

This magnitude means the capacity for bonding of atom A. It should be pointed out that VA is defined in terms of the crystalline reduced density operator D of equation (2) which contains all intra- (q=6) and intercell (4#6) operator D" contributions.

As a way of estimating the atomic reactivity (Bochicchio 1991a, b, Bochicchio and Reale 1991), the free valence FA of atom A is defined as

M M

FA= VA-Qr'= VA- c' BYB- B i T . (7) B - I B - I

FA may be interpreted as the quantity of electrons that atom A would house for further bonding. In other words, FA gives the atomic capacity for bonding which is latent in that particular crystalline arrangement. Unlike closed-shell state functions in molecules in which D satisfies the duodempotency property (D2=2D) (Bochicchio and Medrano 1989, Bochicchio 1991a, b, Bochicchio and Reale 1991, Bochicchio et al 1989, Bochic- chio and Reale 1989) this magnitude is not null and the above development is also valid for closed-shell periodic systems. This is a consequence of the lattice environment which contributes (positively or negatively) as a whole to monatomic population magni- tudes such as FA (Bochicchio et al 1989, Bochicchio and Reale 1989).

3. Numerical results 2nd discussion

The SPA formalism has been implemented in the MOSOL program (Stewart 1984) with the MNDO (Dewar and Thiel 1977a, b) Hamiltonian.

The applications we have used may be considered as being of two different classes: isolated periodic systems and interacting ones. In all the cases the calculations were carried out by considering its respective optimal intra- and inter-cell geometries, obtained by means of DFP (Fletcher and Powell 1963, Fletcher 1965, Davidon 1968) and BFGS (Broyden 1970, Fletcher 1970, Goldfarb 1970, Shanno 1970) algorithms.

In this work we do not present baud structure results explicitly because our goal lies in aaalysing the electronic distribution on atoms and bonds from them.

3.1. Isolated periodic systems

As examples of isolated ZD and 3~ periodic systems we consider four compounds: graphite and hexagonal boron nitride (HBN) (monolayers), and cubic boron nitride (CBN) and diamond (crystals), respectively.

The first two compounds belong to hexagonal lattices and the crystalline structure of the last two is FCC (face-centred cubic).

As we are interested in describing the changes produced at population level when a given reference cell is placed in different crystalline environment, we will discuss two isoelectronic groups: graphite (m-diamond ( 3 ~ ) and ? D - 3 ~ boron nitride separately.

The number of unit cells in the direct lattice and the k points in the employed reciprocal space was large enough to assure stability on the results, specially those very

Population description of crystalline bonds

Table 1 . Lattice parameten (A).

4875

System Experimental MNDO‘

Graphite 2.46 2.48 NBN 2.51 2.52 Diamond 3.57 3.63 CBN 3.62 3.68

a Optimized geometry in our work.

sensitive to the size of the sample (Delhalle 1975, Kertksz et al 1980, K e r t k 1982), i.e. the top and bottom of valence and conduction bands, respectively. As a reference it may be noted that an increment of 10% in the size of the sample affects the value of the gap energy only by 0.005 eV and the electron populations magnitudes by 0.0001,

Optimized geometries fit well with experimental results (Pease 1952, Wentrof 1957, West 1976) as shown in table 1.

Table 2 summarizes the SPA monatomic magnitude results. In the graphite structure carbon electron population indicates that all valence electrons are active, hence the gross charge is exactly six and it is in agreement with its valence. Also, the promotion charge is zero as expected for this system.

The change of the ZD carbon lattice to the ;D structure of diamond produces little increment in its active charge due to the decrement of its inactive one. Once again the gross charge is six, as it corresponds to a covalent compound, and its valence is slightly less than in graphite. The bonding capacity of the C atom is lower in diamond than in graphse, which is predicted to be more stable by 0.16 eV, in good agreement with experience (0.2 ev) (Zunger 1978, Kiel et a1 1982).

For HBN both atomic active charges are approximately equal (Q”B”=QR”); the nitrogen atom is underpopulated and the boron inactive population indicates that the inner atomic Is shell participates in bonding (QB<2.0). Gross charges indicate that a charge transfer takes place from boron to nitrogen, which implies a partially ionic character for the compound. Both valences are similar and of intermediate value regard- ing the free atom models.

In the same way that in the case of change from graphite to diamond, when HBN (ZD) becomes CBN (;D), there is an electronic promotion from inactive populations to active ones for both atoms.

Note that valences of N and B atoms are reduced in the 3~ structure. Let us also note an important feature in the transition from the ZD to ;D structure (graphite to diamond and HBN and CBN); atomic active populations are increased in the transition while inactive populations are decreased. This change only means that atoms provide

Table 2. SPA monatomic magnitudes for ZD and 3 0 systems

Svstem Atom 0. N& G? V& Graphite C 2.061 6.000 3.939 4.000 Diamond C 2.032 6.000 3.968 3.961 HBN N 3.639 7.141 3.502 3.643

B 1.361 4.859 3.498 3.624 CBN N 3.305 7.017 3.712 3.506

B 1.405 4.983 3.578 3.484

4816 R C Bochicchio and H F Reale

Table 3. SPA degrees of bonding for 2~ and JD systems.

S W t m Bond (Ill")' ("22) in3d ~~~ ~

Graphite cc 1.234 (&53b, O.27Ic) 0.007 0.042 Diamond cc 0.954 0.005 - NBN BN 1.087(0.891', 0.196) NNd 0.031 0.009

BB 0.027

BB 0.018 CBN BN 0.844 "d 0.025 -

(nxn) indicates bonding betwecn the nearest x neighbour atoms. b o contribution to the degree of bonding. ' z contribution to the degree of bonding.

elements (N-N) or (B-B). For HBN and CBN the snand nearest neighbour atoms correspond to atoms of the same

a greater amount ofcharge for bonding. It does not necessarily indicate a larger popula- tion for each bonding, as we will see below, because in a 3~ structure there are a greater number of neighbouring atoms attached together than in a ZD periodic arrangement.

Table 3 shows SPA degrees of bonding for the four periodic systems. Since CC bonds for graphite have some conjugation degree (0.96 U electrons and 0.27 n electrons for first neighbours) an effect of enhancement of electronic density between atoms which are not translationally equivalent, not connected by lattice parameters, is slightly marked. This can be noticed from the three B, values: third-nearest neighbour atoms are placed at a distance (2.865 A) which is greater than the distance between second- nearest neighbours (2.481 A), however, the degrees of bonding of those, although very small, are higher by one order of magnitude. This effect is less evident that in the case of conjugated polymers (Bochicchio et a1 1989) because here the charge is not simply distributed along an inhite chain, but is spread over an extense surface.

In all the three remaining systems this effect does not arise because: for 3~ systems the symmetry orbital identification in o and n contributions is lost and for the CBN its unit cell is heteroatomic which implies a source of ionic character.

In the case of diamond, the bonds between first-nearest neighbours is 22% less than for graphite. The degrees of bonding vanisb beyond the second neighbouring atoms.

The degrees of bonding between first neighbours in HBN are larger than one and lower than those which correspond to CC bonds in graphite; second-nearest neighbours are equal and translationaUy equivalent atoms and they possess similar and very small degrees of bonding.

Multiplicities of hexagonal HBN and cubic CBN are similar in nature to those of graphite and diamond. The only relevant difference resides in the fact that no enhance- ment of electronic density appears in far neighbours but degrees of bonding decrease u n i f o d y as may be noted from table 3.

Once the ZD-UD change is invoked and the crystalline environment is changed from the hexagonal lattice of HBN to the cubic latiice of CBN, a decrease in bonding may be noted between first-nearest neighbours in the same amount (22%) as that of CC bonds where the graphite-diamond change occurs.

3.2. Adsorption on a s u ~ a c e

In this section we describe the clectronic distribution in two examples of atomic adsorp- tion (carbon and oxygen) on a graphite basal plane [OOOI]. The adsorption described

Population description of crystalline bonds 4811

Table 4. SPA degree of bonding for graphite/Ca. C means carbon atom belonging to graphite (ADE). C' means adsorbed carbon atoms (ADO). ~ ~~~~~ ~ ~ ~~~~~

Bond (nln) (8%) ( n 3 4 (n44

cc 0.968 0.004 0.003 0.002 C C 0.925 0.023 0.002 0.014 C'C 0.049 0.001 - -

a Only magnitudes greater than IO(-3) are listed

by means of crystalline orbitals (del Re et a1 1967) (periodicity included) simulates a regular phase and not an isolated one as cluster model theories based on molecular orbitals do. In this way, the adsorbate atoms or adatoms (ADO) and adsorbent surface (ADE) conform to a ZD periodic system or supersystem, with two interacting parallel monolayer lattices.

Simulation of the substrate AD& was performed without taking into account relaxa- tion effects induced by the presence of the adatom ADO, namely the geometry of that is fixed at its optimized values for graphite in the previous section. Since the localization of the ADE active sites for each supersystem is the most important parameter, we optimized the relative positions of the adsorbate over the adsorbent substrate of graphite.

For both supersystems studied the atomic adsorption relation is 1:2; one ADO atom (carbon or oxygen) and two ADE atoms (carbons) per unit cell. From geometry optimization active sites for the two adsorptions are found to be located at the middle point of the carbon-carbon ADE distance and hence perpendicular distances between ADO and the adsorbent surface of 1.44 8, and 1.27 8, for the graphite/C and graphite/ 0 systems respectively are found.

In order to describe properly e1ec:ron populations among atoms for the supersystem we will refer to the (n x n) neighbouring populations as being of different bond classes; intralayer ADE-ADE, interlayer ADO-ADE, and intralayer ADO-ADO. The first two classes may link atoms of the same or different unit cells. Because of the adsorption relation chosen, 1:2, the third class of bonding, i.e., intralayer ADO-ADO, necessarily occurs between atoms belonging to different cells.

Table 4 shows the bond multiplicities or degrees of bonding for the graphite/C supersystem. The (nln) carbon-carbon bond multiplicity (C-C) on the ADE is the same as that of the CT contribution to the bonding between the same atoms for isolated graphite. Adsorption can clearly be detected by means of SPA in ADE-ADO bonds (C- C') as it may be noted from the value of multiplicities close to one for the first neigh- bours. The effect of reinforcement of electronic density between carbons belonging to adsorbent which are not connected by simple lattice translations disappears and this population is transferred to the ADO-ADE (C-C) bonds formation. It may be be noted by inspection of the second row of table 4 that despite the fact that multiplicities show a uniformly decreasing behaviour with a distance increase, the bond multiplicities of the fourth neighbours are enhanced by one order of magnitude with respect to (n3n) degrees of bonding, and are predicted to be about half as large as the (n2n).

Bond multiplicities between ADO a t o m (e-@) within different unit cells quickly fall OB but the value for the interactions between first neighbours in the adsorbed monolayer is one order of magnitude greater than those belonging to adsorbent atoms separated by a same distance (2.48 A) and corresponding to (n2n) interactions.

4878 R C Bochicchio and H F Reale

Table 5. SPA monatomic magnitudes for p.phite/C. Symbols C and Care dehed as in table 4.

Atom QA E' NA V* F* C 2.174 3.944 6.118 3.962 0.018 c 3.588 2176 5.764 1.858 -0.318

Results concerning the monatomic quantities are reported in table 5 which shows that active charges of the ADE carbons (C) remain at almost the same value as that for isolated graphife. The excess of electrons over each carbon (N ,>6) is produced by the increment in its unshared charge as it should from symmetry considerations of the arrangement.

Valences for ADO atoms are approximately four as expected for a carbon atom which is placed in an organic environment. Moreover, a small and positive free valence is observed.

The 'behaviour of the adsorbed atom (C) is entirely different: it transfers 0.24 electrons to the ADE and houses more than 3.5 nnshared electrons. Its active charge is more than two and shows an uncommon valence value of approximately two. Free valence is perhaps too much negative; this fact is not altogether unreasonable keeping in mind the use of valence basis set of atomic orbitals. Nevertheless, it should be emphasized the fact that for the adsorption, which is endothermic (Ead.= 19.5 kcal mol-'), to occur the ADO atoms must be forced to be linked to the layer.

Some features of the electronic distribution inferred by means of SPA for graphite/ C still remain valid for graphite/O, even though the last supersystem houses more electrons within the unit c e U and leads to an heteroatomic interaction between ADO and ADE. In this connection we may note from table 6 the following results.

(i) Once again an increased multiplicity of the ADE-ADO bonds (CO), is observed for the (n4n) interactions, after a monotonic decrement of bonding from first to third neighbours.

(ii) Degrees of bonding between oxygen atoms on the one hand and carbon atoms on the other hand vanish when the interactions among neighbouring atoms reach the second or more distant ones.

(ii) C C bond multiplicities for first neighbours remain the same value as U contri- bution of the bondings between carbons for isolated graphite (table 3).

The (nln) carbon-carbon and carbon-oxygen bondings are predicted to have similar values, but the composition for the CC is as follows: 0.76 electrons placed in the graphite plane, 0.07 arising from p: orbitals (out of periodic plane) and 0.1 3 belonging to the (s, p,)-p, orbital density matrix component. Whereas the contributions to ADS

Table 6. SPA degrees of bonding for graphitej0'.

Bond (n ln ) (n2n) h 3 n ) (n4n) CC 0.961 0.007 ' 0.003 0.003 CO 0.964 0.016 - . 0.007 00 O.02lb - - -

0.003

'Only magnitudes greater than 10(-3) arc listed. See text.

Populalion descriprion of crysfalline bonds 4819

w Figme 1. Active sites (0) for adsorption of oxygen on graphite surface.

ADO bonds are as follows, 0.37 arising from pz0 - pZc orbitals and 0.59 of the remaining carbon-oxygen interactions. There is another feature in table 6 that deserves some attention: oxygen-oxygen bonds betwen first neighbours have two values depending on their relative dispositions over the adsorbent (see figure 1). This suggests that an effect associated with the directionality of the ADO-ADO intercell bonds is present. The difference in the multiplicities between 0 atoms (table 6) is due to the electronic environmental C-C bonds. The 0 pair which exhibits a 0.021 degree of bonding is separated by a C-C bond of a character which reinforces the linkage between these atoms. The other pair considered as having a 0.003 multiplicity is separated by a C- C bond of a o character which as it was expected can not reinforce the 00 bond because of its rigidity. Hence the high delocalization of the n cloud produces the difference and two different values are quoted in table 6 for 00 bonding.

In figure I we show three ( n l n ) active sites (x ,y , z) for adsorption which are occup- ied by adsorbate atoms which are equidistant (2.48 A) and translationally equivalent. Oxygen-oxygen bonds established between atoms placed over the opposite sides (x-z) of the same hexagon of the adsorbent are very small whereas those built between oxygen atoms adsorbed in adjacent hexagons (x-y) increase by roughly one order of magnitude (0.02). This difference may be attributed to the fact that for the second kind of inter- actions the ( A n ) C-C degrees of bonding of the adsorbent (0.96) interfere in a construc- tive way, reinforcing them. The same is not true for the first case where the bonds are underpopulated because between 0 atoms located at x and z there is no strong inter- actions among carbon second or third neighbours.

Due to the fact that this adsorption process is exothermic adsorption (Eadr= -7.4 kcal mol-') a charge transfer of 0.12 takes place (see table 7) from the unit cell of the adsorbent surface to the adsorbed oxygen, so that this excess of charge on the ADO is disposed to give somewhat more than two active electrons and six inactive ones in 0 atoms. On the other hand each carbon atom is underpopulated and 3.94 electrons are used for bonds formation. The values of valences and free valences of C atoms are

Table 7. SPA monoatomic magnitudes for graphite/O.

Atom QA Q?' N* VA FA

C 2.001 3.939 5.940 3.962 0.022 0 6.080 2.041 8.121 1.984 -0.057

4880 R C Bochicchio and H F Reale

B w o o

0.975

as50

0.9 2 5

0.300 1.23 1.27 1.31 1.35 I

Figure Z (nln) d e g a s of bonding Ea and B , plotted against ADO-ADE distance d for adsorption of oxygen on graphile,

in agreement with the value for active and inactive populations reported. Oxygen atoms show a valence very close to two and a slightly negative free valence, as it would be expected because of its overpopulation.

Further details can be obtained by studying the evolution of the populating magni- tudes into the interval of distances 1.20-1.40A for approaching the oxygen atom to the adsorbent surface. In this way it is possible to point out that the C-0 bonds gain charge whereas the C C loses it (see figure 2). Since during the adsorption, at least in the range of the studied distances the inactive charges of C atoms are fixed, 0 atom may obtain charge for bonding only from two sources: breaking its lone pairs to make its charge active or from C-C bonds because all charge of carbons is active and constant.

This last statement explains the decreasing CC degrees of bonding between first neighbours (see figure 2). If we consider the first mechanism it may be noted that for the 0 atom, QD decreases and Qg' increases in the same magnitude, with a mean velocity of 0.47 electrons per 8, with decreasing distance of the adsorbed atom from the adsorbent layer. Hence, there is no change of the gross charge of the 0 atom during the adsorption. As a consequence of this, for the range of distances ADO-ADE of figure 2 the charge transfer from oxygen to graphite remains at the value of 0.12 electrons corresponding to the position of maximum stability.

Population description of crystalline bonds

“0 2.1 0

2.00

1.90

1.80

1.23 1.27 1.31 1.35

4881

;I

F- 3. Valence of oxygen Vi plotted against ADO-AD€ distance d for adsorption of oxygen on graphite surface.

The behaviour of the valence of 0 atom is represented by figure 3; it shows a near$ linear shape above all in the environment where the adsorption is energetically favoured, which is stated for a perpendicular ADO-ADE distance of 1.268 8, and corresponds to a CO bond distance of 1.456 8,. The free valence of 0 atom becomes less negative and both the valence and free valence of the carbon atoms decrease to an extent satisfying the constant value of QFf (3.94) mentioned above according to equation (1 1).

4. Conclusions

The four isolated periodic systems and the two ADO-ADE supersystems studied here cover a wide range of electronic and structural situations: bi- ( 2 ~ ) and tridimensional ( 3 ~ ) systems, covalent and partially ionic characters and adsorptions on surface. It is possible to uilderstand the behaviour of individual atoms and bonds in the periodic context of systems with translational symmetry as well as to establish if chemisorption is present by means of the evolution of the multiplicities of bonding during the atomic adsorption on surface. Further lines of research in this direction may include the study of formation and breaking of bonds for migration of several chemisorbed species among

4882 R C Bochicchio and H F Reale

active sites, dissociative chemisorption of adsorbed molecules, and even for the investi- gation of the delicate processes of chemical bonding and charge transfer in the hetero- geneous catalysis.

SPA is perfectly suited for setting up interpretative schemes in order to bridge the gap between the description by means of delocalized band theory language and that of local chemical bonds. On the other hand, keeping in mind the fact that the only tool required for SPA is

the reduced density operator D, then the accuracy of results depends exclusively on the quality of the wavefunction attempted, namely, SPA is valid for all quality of state functions and hence the reliability of the description is supported by the density matrix provided for such a function. Besides, SPA does not represent an increment ofcomputa- tional resources because it works with magnitudes already converged in the iterative procedure. This analysis is indistinctly applicable to ab initio or semiempirical closed shell wavefunctions without any change in its actual formulation.

Developments regarding UHF treatments and extension to electronic pairs descrip- tion of electronic density are being considered in our laboratory and details will be gvien elsewhere in the similar way made for molecular systems (3ochiochio and Medrano 1989).

Acknowledgments

The authors gratefully acknowledge the Physics Department of the Facultad de Ciencias Exactas y Naturales for financial support and Instituto del CBlculo (Buenos Aires University) for computing facilities. Also the authors wish to acknowledge Fundacih Antorchas for financial support.

References

Andd 1 M 1975 Electronic Stnrcrure of Polymers and Molecular Crysruls ed J M AndrC er U / (New York:

AndrC J M and Delhalle J 1978 @"m rheory ojPolymers ed I M AndrC er ol (Holland: Dordrecht) and

Bochicchio R C 1991a J. Mol. Srrucr. (Tlreochem) 228 209 - 1991b J , MO/, Srrucr. (Tkeochem) 228 227 and references therein Bochicchio R C and Mcdrano I A 1989 J . Mol. SInrel. (Tkeochem) 201 177 Bochicchio R C and Reale H F 1989 Proc. Inr. Congr. Theor. Chem. of Lotin Expression (r0 Pldu. Argentina)

Plenum) p I

references therein

ed E A Castro er nl Bochicchio R C, Reale H F and Medrano J A 1989 fhys. Rev. B 40 7186 Broyden C G 1970 J. Inst. Math. Appl. 6 76 Calais 1 L 1987 Winler School of Quunrum ChemMry und Solid Stole Physics (Gainsuille, FL: Florida

University) Coleman A J I963 Rev. Mod. Plivs. 35 668 Davidon W C 1968 Comput. J . 10 406 Davidson E R 1976 Reduced Densirv Murrices in Ouanrum Cltemisrrv (New York: Academic) del Re G, Ladik I and Biczo G 1967 Phys. Rev. 155 997 Delhalle J 1975 Necrronic Srrucrure of Polymers und Molecular Crysruls ed J M AndrC er a/ (New York: . .

Plenum) p 53 Dewar M I Sand Thiel W 1977a J . Am. Qem. Soc. 99 4907 - 1977b J. Am. Cltein. Soc. 99 7822 Dovesi R, Pisani C, Rima F and Roetti C 1976 J . Clrem. Phys. 65 3075

Population description of crystalline bonds 4883

- 1980a Plays. Rev. B 22 4170, 5936 Dovesi R. Pisani C and Roetti C 1980b Inf. J. Quanfum. Chem. 17 517 Fletcher R 1965 Compul. J . 8 33 - 1970 Compuf. J . 13 317 Fletcher Rand Powell M J 1963 Compuf. J. 6 163 Goldfarb D 1970 Murlr. Compuf. 24 23 K e r t k M 1982 Adv. Quunfum. Chem. 15 161 and references therein K e r t k M, Koller J and Arman R 1980 Recent Advances in d e Quanfum Theory of Polymers (Berlin:

Kiel B, Stollhoff G, Weigel C. Fulde P and Stoll H 1982 Z. Phys. B 46 I h d i k J 1975 Electronic Structure of Pdymers und Molecular Crystals ed J M AndrC ef a/ (New York:

Academic) p23 and references therein LBwdin P 0 1955 Rev. Mod. Phys. 97 1474 - 1982 Inf . J . Quunfum. Chem. 16 485 Pease R 1952 A d a Crysf. 5 356 Phillips J C 1970 Rev. Mod. Phys. 42 317 Reale H F and Bochicchio R C 1991 J. Phys, E : Al. Mol. Opt. Phys. 24 2937 and references therein Ricart J M, lllas F, Dovesi R, Pisani C and Roetti C 1985 Chem. Plrys. Lelf. 108 593 and references therein Stewart 1 J P 1984 Quunlum Chem. Progr. Kxclt. 495 MOSOL Program Shanno D F 1970 Mofh. Compuf. 24 647 Wentrof R 1957 J. Chem. Phys. 26 956 West R (ed) 1976 Hundbook of Chemirfry und Physics (Cleveland, OH: Chemical Rubber Company) Zunger A 1978 Phys. Rev. B 17 626

Springer) p 56