Description of the ground state electronic structures of Cu2O, Cu2S, Ag2O and Ag2S

Volume 189, number 4,5

CHEMICAL

PHYSICS

I4 February

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I992

Description of the ground state electronic structures of Cu20, CL& Ag,O and Ag,S David

A. Dixon

’

Du Poni Central Research and Development, Experimental Station, P.O. Box 80328. Wilmington, DE 19880-0328,

USA

and James

L. Gole

Department of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA Received

23 August 199 1; in final form 3 1 October

199 1

The electronic structures of the copper and silver oxides CuaO, Cu*S, Ag,O and Ag,S have been calculated in the local density functional approximation. The structures closely resemble an O- or S- bridging an M $ as shown by the geometries and the charge distributions. The symmetric stretch frequency exceeds that of the asymmetric stretch as well as the stretch in the free diatomic. The electronic structures of the oxides and sulfides are similar with the HOMO having most of its density on the oxygen or sulfur. The predicted ionization potentials are also similar.

1. Introduction The structure and resulting behavior of the metal atom and cluster based oxides and sulfides plays a significant role in the development and implementation of many technologies. The coinage metal oxides and sulfides are particularly intriguing. The nature of the bonding in these species can influence the action of catalysts [ 1 ] and the efficiency of photoenvirongraphic processes [ 2 ] #I. The structural ment and the electron density distribution of copper oxide based systems play a role in the action of highT, superconductors [ 41. Recently, in response to their importance and the paucity of information available on these compounds which can be used in the modeling of bulk systems, a number of gas-phase experimental studies [ 51 have been undertaken to characterize the simplest copper and silver based oxides and sulfides. In conjunction with these studies ’ Contribution No. 5890. St The silver sulfides, Ag>, are believed to play an important role through silver-halide interactions, in film emulsion. An elucidation of their properties may be useful in the basic understanding of sulfur sensitization [ 31. 390

0009-2614/92/$

and as part of an effort to apply the local density functional method to the study of chemical systems [ 6 ] we have evaluated the structures and vibrational frequencies of the simplest symmetrical metal oxides and sulfides of copper and silver, CuZO, Cu$, Ag,O, and Ag,S.

2. Methods We describe a series of calculations carried out in the local density functional approximation [ 7 ] by using the program system DMol [S] #2. Here, the atomic basis functions are given numerically on an atom-centered, spherical-polar mesh. The radial portion of the grid is obtained from the solution of the atomic LDF equations by numerical methods. The radial functions are stored as sets of cubic spline coeffkcients so that the radial functions are piece-wise analytic, a necessity for the evaluation of gradients. Some advantages were gained by using exact spher#* Dmol is available commercially

from BIOSYM Technologies,

San Diego, CA. 05.00 0 1992 Elsevier Science Publishers

B.V. All rights reserved.

Volume 189, number 43

CHEMICAL PHYSICS LETTERS

ical atom results. The molecule being described dissociates exactly to its constituent atoms within the LDF framework, although the calculated dissociation energies need not be correct. Furthermore, because of the quality of the atomic basis sets, superposition errors should be minimized and the correct behavior at the nucleus should be obtained. We note, however, that relativistic effects have not been included in these calculations. Because the basis sets are numerical, the various integrals arising from the expression for the energy are evaluated over a grid. The integration points have been generated in terms of angular functions and spherical harmonics. The number of radial points Na is given as NR = 1.2x 14(Z+2)“3,

(1)

where Z is the atomic number. The maximum distance for any function is 12 au. Angular integration points N,, are generated at the NR radial points to form shells around each nucleus. the value of N,, ranges from 14 to 302 depending on the behavior of the density #3. The Coulomb potential corresponding to the electron repulsion is determined directly from the electron density by solving Poisson’s equation. The form for the exchange-correlation energy of the uniform electron gas used in DMol is that derived by von Barth and Hedin [9]. The DMol calculations were done with a double numerical basis set augmented by polarization functions. This corresponds to a basis set of the same size as a polarized double-zeta basis set. However, we use exact numerical solutions for the atom and, thus, this basis set is of significantly higher quality than a normal molecular orbital double-zeta basis set. The titting functions have angular momentum quantum numbers one greater than that of the polarization function. All of the basis sets have d polarization functions so that the value of 1for the fitting function is 3. Geometries have been optimized by using analytic gradient methods [ lo]. Certain difficulties arise in evaluating gradients in the LDF framework associated with the numerical methods used in this description. The energy minimum need not necessarily

14 February 1992

correspond exactly to the point with a zero derivative and the sum of the gradients may not always be zero as required for translational invariance. These difftculties introduce errors on the order of 0.00 1 8, in the calculation of the coordinates if both a reasonable grid and basis set are used. Such errors in the coordinates give bond lengths and angles with reasonable error limits. When compared to experiment, the difference of 0.001 A is about an order of magnitude smaller than the accuracy of the LDF geometries. The frequencies have been determined by numerical differentiation of the gradient. A two-point difference formula was used with a displacement of 0.01 au. For CuzO, additional Hartree-Fock and MP-2 calculations were done with the program GRADSCF #4. The geometries and force fields were calculated at the SCF level by using analytic gradients and second derivatives #‘. The MP-2 [ 121 geometry was optimized by grid-fitting methods. The basis set for Cu is from Wachters [ 131 and the basis set for 0 is from Dunning [ 141. The Cu basis set is derived from Wachters’ ( 14s 1 lp, 5d) set for Cu (*S) using contraction scheme 1 and is augmented by a diffuse d function following Hay [ 15 ] to give a [ 8s 6p, 4d] set. The [ 5, 31 contracted set of Dunning for 0 was augmented by two d functions each a two-term fit to STOs [ 161 with effective Slater exponents of 2.1 and 0.7. This results in a [5, 3, 21 set for 0.

3. Results 3.1. Geometries The calculated geometric parameters for Cu20 are summarized in table 1. The SCF geometry corresponds to a bond angle of 135.3” and a bond distance of 1.8 13 A. The linear structure has a similar bond length of 1.810 8, and is only 0.76 kcal/mol higher in energy at the SCF level. The SCF results suggest a structure with significant ionic character similar to that of Li20, with a charge distribution of - 1.36 e on 0 and + 0.68 e on each Cu atom. #4 GRADSCF is an ab initio program system designed and writ-

1(xThis grid can be obtained by using the FINE parameter in DMoI.

ten by A. Komomicki at Polyatomics Research. ” For a discussion of Hartree-Fock methods, see ref. [ I I].

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Volume 189, number Table 1 Structures

CHEMICAL

45

PHYSICS

for CuzO a1 Method

r

I9

SCF MP-2 LDF exp.

1.813

135.3 98.8 86.9 lOOk 10

1.784 I .749

‘) Bond distances

in A. Bond angles in deg.

At the MP-2 level, the optimum geometry for Ct.1~0 has a much smaller bond angle, 98.8”, and a decreased 0.1-0 bond distance, 1.784 A. The correlated result is in much better agreement with the experimental estimate [ 51 of the bond angle ( 100’ f 10’ ), and suggests a structure more like that of H,O than that of Li20. The linear form of CuzO (degenerate imaginary frequency) at the SCF level is 9.7 kcal/mol higher in energy at the MP-2 level. The SCF charge distribution at this geometry corresponds to - 1.17 e on the 0 and + 0.42 e on each cu. At the LDF level (see table 2), both the Cu-0 bond distance and the bond angle are predicted to be smaller. The Cu-0 bond length shortens to 1.75 8, and the CuOCu bond angle is calculated to be 87”. In order to better understand this result, we focus on the Cu-Cu distance, which is 2.41 A. This distance can be compared to that of 2.195 8, calculated for the diatomic (2.22 A, experimental [ 17 ] ) thus suggesting a significant interaction between the two Cu atoms in CuzO. The Cu-Cu interaction distance in Table 2 LDF structures

Diatomics

Molecule

r(M-A)

e

r(M-M)

Molecule

r( talc. )

cu*o AgzD cu*s

1.749 2.019 2.073

86.9 89.6 72.2

2.41 2.84 2.443

Cu2 cu: Ag2

2.196 2.320 2.587

AgzS

2.330

77.8

2.927

Ag: cue cus Ago AgS

2.741 1.688 2.029 1.993 2.306

a) Bond distances

in A. Bond angles in deg.

b, Ref.

[ 17 1.

1992

CuzO is 0.09 A longer than that calculated for Cu: and the overall geometry can be described as an O- bridging a Cu$ .We calculate a charge of - 0.78 e on the 0 and +0.39 e on the Cu at the LDF level. The Cu-0 bond distance is only slightly greater than that of the diatomic. At the LDF level, the linear structure lies 18.1 kcal/mol above the bent structure; the electronic charge distribution for the linear structure is essentially unchanged with -0.80 e on the 0 and +0.40 e on each Cu atom. We note here that relativistic corrections to the bond distance in Cuz are about -0.04 A, based on correlated molecular orbital calculations [ 18,191. We calculate a significantly smaller bond angle for Cu$S. The Cu-Cu bond distance increases by 0.25 A relative to Cu2 (as compared to an increase of 0.22 8, in the oxide). With the sulfur further away, the resulting bond angle in CuzS becomes smaller. The charge separation is less pronounced than in the oxide with only -0.43 e on the S and only 0.21 e on each Cu. The predicted structure of Ag,O is similar to that of CuzO. The increase in the Ag-Ag interaction distance is 0.25 A, similar to the increase of 0.22 A calculated in CuzO. This produces a slight increase in the AgOAg bond angle. The charge distribution is similar to that in CuzO with -0.80 e on the 0 and +0.40 e on each Ag. Relativistic corrections could account for the differences in the calculated and estimated experimental value for Ag,. The relativistic contraction in Ag, has been estimated as - 0.14 A, although this value is probably an upper limit [ 201. There is a larger increase in the Ag-Ag bond dis-

for M2A, M2, M$ and MA ‘)

Triatomics

392

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LETTERS

r(exp.) 2.220 2.50 1.724 [2.051] 2.003

b,

CHEMICAL PHYSICS LETTERS

Volume 189, number 45

I4 February 1992

Table 3 Calculated LDF frequencies (cm- ’ ) Mode

cuzo

A.&O

cuzs

A&S

stretch (s) ‘) stretch (a) ‘) bend

679 583 163

514 458 89

465 353 143

364 278 70

‘) s=symmetric, a=asymmetric.

tance, 0.34 A, when S is substituted for 0. This increase leads to a larger 78” bond angle. The charge distribution indicates a larger ionic contribution to the bonding in Ag$S than found for Cu2S with -0.58 e on the S and +0.29 e on the Ag. 3.2. Frequencies Calculated vibrational frequencies are given in table 3. The symmetric stretch frequency is calculated to be significantly higher than the asymmetric stretch frequency. The bend is, of course, at considerably lower frequency. The frequencies of the corresponding diatomic oxides or sulfides where known are lower than those of the symmetric stretch ( V( Cu0) ~640 cm-‘, v(Ag-0)=490 cm-‘, v(Cu-S) ~415 cm-’ [ 171). Although the following model is simplistic, one could analyze the vibrational spectrum in terms of an atom chemisorbed to a metal surface. Thus the symmetric stretch would correspond to vI, the motion of the chemisorbed atom perpendicular to the surface and the asymmetric stretch to Y,,, the “frustrated translation”. The bend could then be assigned to a metal atom-metal atom stretch (a surface phonon). For example, for Ag,O in this model,

3.3. Electronic structure The molecular orbitals of greatest interest are summarized in table 4. The molecules are oriented such that their twofold axis is the z axis and they lie in the xz plane. The HOMO for all species is the b2 orbital predominantly localized in the out-of-plane pYorbital on the oxygen. The coefficient of the p,, orbital ranges from 0.73 in CuZO to 0.92 in Ag,S. The remaining density comes from the metal d orbitals. The energies of the HOMO are quite similar although the Cu complexes have a slightly higher ionization potential. The NHOMO (next highest occupied molecular orbital) is of b, symmetry with some 0 pX character. The remaining contribution results from s and d character on the metal. In the Cu structures, there is d metal density whereas in the Ag complexes, the orbital is more localized on the oxygen. The s character on the metal for the highest b2 and a, orbitals is similar in all of the structures. In the next occupied orbital (of a, symmetry) we find an increased role for the metal. For the Cu complexes, the metal is clearly dominant whereas in the Ag complexes, the 0 still has the largest coefftcient. For the highest b, and a, orbitals the oxides have a similar ionization potential, whereas the sulfides require a somewhat higher ionization energy. It is useful to note that the Cu d orbitals have significantly lower ionization potentials than do the Ag orbitals. This is most obvious in Cu$ where there are six orbitals close in energy to the a, orbital. This result is consistent with the differences in the atomic structures of Cu and Ag.

Table 4 Calculated LDF orbitals for M2A

HOMO b2 a) HOMO ci b, NHOMO b, ‘) NHOMO c, b, OMO a, a) OMO c, b,

5.07 0.73 py: 0.57 d 5.29 0.47 px: 0.44 s, 0.59 d 5.98 0.4 p.: 0.47 s, 0.60 d

5.11 0.82 p; 0.46 d 5.60 0.51 px: 0.40 s, 0.66 d 6.40 0.33 pz: 0.43 s, 0.69 d

4.84 0.91 p; 0.28x2d 5.34 0.72 px: 0.42 s, 0.42 d 5.77 0.66 p; 0.45 s, 0.36 d

4.93 0.92 p; 0.24 d 5.66 0.73 px: 0.42 s, 0.38 d 6.21 0.63 pz: 0.46 s,. 0.31 d

‘) Orbital energies in eV. b, Orbital coefficients are given. The first atom is the 0 atom and the coefficients on the M are separated from it by a colon.

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Volume 189, number 4,5 Table 5 Calculated

CHEMICAL

PHYSICS

LDF dipoles (D)

Triatomic

/1

Diatomic

p

cu*o

3.60 4.36 3.90 4.96

cue AgG cus

4.25 4.76 3.65 4.40

Ag,G CUzS AgzS

AgS

The oxides and sulfides are quite ionic. The calculated dipole moments (table 5) also demonstrate this ionicity. The Ag complexes have higher dipole moments than do the Cu complexes. Similarly the sulfides have higher dipoles than the oxides, presumably resulting from an increase in the charge separation associated with the differences in atomic size.

4. Conclusion The above results suggest that these simple complexes of the copper and silver oxides and sulfides are strongly bent and are well described as an O- and S- bridging M: .

Acknowledgement

We thank the referee for pointing out the analogy to surface vibrations.

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