Structural and electronic properties of a carbon monoxide monolayer

~

Solid State Cormnunications, Vol.59,No.2, pp.57-60, |986. Printed in Great Britain.

S T ~

AI~ ~N~CTRCNIC Iq~I~ITIES OF A CARBON ~ K ~ I I ~ I R. V. ~

0038-1098/86 $3.00 + .00 Pergamon Journals Ltd.

~

i

E. I. du Pont de Nee~m-s and Company Central Research and Development Department ~rimental Station Wilmin~,

Delaware

M. -H. Tsai, T. N. l ~ i n

19899

and D. D. C ~ i s s

Cornell University School of Applied and Engineering Physics Ithaca, New York 14853 (Received ~

5, 1986, by R. H. Silsbee)

A new ab i n i t i o pseudofunction method based on s o l i d s t a t e theoretical approaches has been developed which is designed to accurately calculate the e l e c t r o n i c properties and t o t a l energy of molecules on surfaces and other i n t e r r a c i a l systems. This method is used here t o investigate c r i t i c a l bonding information of an isolated carbon monoxide layer in the C(2x2)-Ni(001) configuration c h a r a c t e r i s t i c of ~ i s o r p t i o n on a Ni(001) surface. Results f o r a tw~-dimensic~al array of CO molecules give an equilibrium bond length of 1.138 ~ versus 1.128 (experimental), derivative of dipole moment of 3.16 D/~vereus 3.14 D/~ 1 (experimental), and a v i t E a t i ~ a l frequency of 2157 c~ * versus 2170 c~-* (experh~ental), where the experimental values correslx~d to free CO. ~ u s , the C-O bond length and derivative of dipole ,~ment and v i b r a t i o n a l frequency are p r a c t i c a l l y unaltered from that of free CO. We found, however, the dipole mmaent, 1.0 Debyes, and the 1~-4~ level separation, --2.4 eV, are s u b s t a n t i a l l y changed due t o C0-CO coupling.

1.138JI whereas free _~ i s 1.128~[ and_¥ibretional frequency i s 2157 ~a * versus 217(h=m * of free CO. The dipole moment i s p c s i t i v e (1,~)) indicating a negative O, an ~=parent r e s u l t of the ~ coupling as shown by the s u b i t s ~ t i a l electronic hsndwidths. A free CO dipole mcment is -0.121) indicating the 0 is s l i g h t l y p o s i t i v e . Hm~ver, the d e r i v a t i v e of the dipole marent with stretch is close to t h a t of free CO. The method used for these calculations, called the p ~ o f o n c t i o n (PSF) method , uses a r e l a t i v e l y small basis s e t (typically 6-12 functions per atom) t o solve the effective c~e-electrcn I ~ l t ~ m i s n and compute t o t a l energy s e l f - c o n s i s t s n t l y for the valence electrons of a t h i n - l a y e r system. The besis s e t is defined by a s e t of smcoth pseu~ofm~cticns specified by a f i n i t e Fourier s e r i e s which are used to compute the n c r ~ r i c a l t e n m in the I~ltoaian. The large spherical terms within muffin-tin s ~ r e s about each atom are computed using true r a d i a l solutions. Within the local-density approximation and the small basis, the pr~udof~cticn and p o t s ~ t i a l are i t e r a t e d t o s e l f consistency. The PSP~ are expanded in plane

~ , i s o r p t i o n of CO molecules on t r a n s i t i o n metal surfaces is widely studied experimentally and t h e o r e t i c a l l y . Thus far, ab i n i t i o t h e o r e t i c a l studi~s have been limited to non-self c o r a i s t e n t ~ n ~ studies of ordered surface s t ~ . ~ b - ~ and to c l u s t e r calculations ' ' " . Recefltly Wim,wr et a l . 5 have electronic s t r u c t u r e calculations for a C(2x2) CO overlayer c~ Ni(001) using the FLAPW method. In t h i s ~ r k the adsorbed layers were put on both sides of a 3-layer Ni film required by the r e f l e c t i o n sl~metry used in t h i s method. Total energy calculatic~ had not been attempted. Interpreteti~}ns of e~p~rimental investigations such as ~m.~" and ~ indicate that CO c/w~isorhs at the top s i t e f o r a number of transit~o~ metals. Theoretical c l u s t e r s t u d i e s " for (30 on Ru and Cu indicate that the che~isorptic~ s i t e is a t a 3 or 4-fold s i t e contrary to e ~ e r i m e n t a l i n t e r p r e t a t i o n . I t has been suggested that the absence of long range order in the c l u s t e r calculetions could acommt for the d~screpancy with experiment. I t is also suggested that experimental interpretation is incorrect. To f u l l y ~ d e r s t a n d the chemisorption of CO on t r a n s i t i o n metals, i t will be important to distinguish the e f f e c t of C0-C0 interaction frcm C0-metal interaction on properties such as dipole n~ment and v i b r a t i o n a l frequency. As a first step, we have performed the f i r s t at) i n i t i o calculations for a t ~ dimensional monolayer array of (33 molecules and compared the r e s u l t s t o that of free CO. The equilibrium bond length is

wews

(where Pint is the ~ d i u s o f t ~ muffi~ t i n mt spheres), i . e . , with 3751 plane waves for t h i s system. ~ne potential is expanded to double t h i s set of GmeXs, with 26,901 plane waves.

Currently, LaP~ and p s e ~ t e n t i a l 9 calculations follow criterion similar to ours in 57

58

Vol, 59, NO. 2

PROPERTIES OF A CARBON MONOXIDE MONOLAYER

choosing t h e number o f p l a n e waves f o r t h e i r c a l c u l a t i c r a on s u r f a c e s o f m e t a l s and smaicor~hr~cors. We v i i i show t h a t t h e same rigourous c r i t e r i o n should be followed f o r molecules. However, t h e computer c o s t becomes p r o h i b i t i v e f o r p l a n e wave methods when t h e number o f p l a n e waves b e g i n s t o exceed s e v e r a l hundred. ~ monolsyer O f ~ has been s t u d i e d by the ~ and t h e SCiO"'metbods. However, the

-9

m ~ o l a y e r CO w i l l be more d i f f i c u l t s i n c e CO does n o t have r e f l e c t i o n symmetry. Besides, t h e t o t a l energy was n o t c a l c u l a t e d i n t h e s e two s t u d i e s .

Tne PSF-method improvesl~n t h e e a r l i e r exter~d~uffin-tin o r b i t a l method " m s t l y in i t s choice o f b a s i s . Here t h e PSFs t h e ~ e l v e s incorporate radial solutions to the spherical part of the potential extending to R~,, well belm~ ~. This s e l f - c o n s i s t e n t be~Te more accuretelJ~ r e f l e c t s t h e t r u e e l e c t r o n s t a t e s in the region outside the muffin-tin spheres which is of critical importance in molecules such as CD. I t also r ~ e s greatly the d e ~ of r e s u l t s un tbze v a l u e s o f R.+ and o f t h e decay paremeters x f o r t h e t a i l " ~ l m ~ d R . . , . Another f e a t u r e o f t h e PSF method i s t h a t t ~ ' c o m p u t a t i c ~ can handle any s u f f i c i e n t l y smooth f u n c t i o n a s a PSF. For e x a , p l e , Gaussiar~, S l a t e r o r b i t a l s and even f t m c t i o ~ not b a s e d on s p h e r i c a l l y - s l m m e t r i c potentials ~ be used a s t a i l s . The b a s i s s e t c o n s i s t e d o f 14 f u n c t i o n s , seven c e n t e r e d a t each atom¢ (a) f o u r sp radial solut}cr~ with half in-tin orbital (MrO) t a i l s o f x - - 4 . 0 8 eV and energy ~ s e n t o r e ~ r e s e n t t h e f i l l e d o r b i t a l s 2 a n d , (b) p - r a d i a l s o l u t i o n s w i t h MIX) t a i l s o f K - 2.04 eV and energy ~ to represent the unfilled orbitals. The frozen core approximation is used so that basis states representative of core states are not i n c h g ~ _ . I n c u r computations, t h e CO molecules were a r r a n g e d in a square p a t t e r n (a 3.520 ~) i d e n t i c a l t o t h e s p a c i n g found f o r CO chemdsorbed on Ni(001). The i n t e r m o l e c u l a r d i s t a n c e i s kept f i x e d b u t t h e CO bond l e n g t h i s v a r i e d . The s ~ e v a l u e of P ~ i s used a t b o t h the carbon and oxl~jen sites. ''~ Energy hands for the CO system are shown in Figure I for a bond length of 1.13~. The widtb.~ o f t h e bends t h a t c o n t r i b u t e t o t h e (CO-CO) bending a r e 1.2 eV f o r t h e 5 m bend and 0.5 eV f o r t h e 1~ bends. The 17 - 4~ s e p a r a t i o n is about 2.4 eV substantially ~ frum the free CO value of 2.8 eV. A binding energy curve for CO is shown in Figure 2. The predicted bond length i~ 1.138~ with a vibrational frequency of 2157 cm -. The Coulomb potential at infinity above the O is 0.23 Ry. relative to the potential being 0.0 above the C. Taking ~(V)- 37.TP(D)/A, where ~ is the difference in Coulomb potentials at infinity, P(D) is the dipole moment in Deb~e, and A is the surface area of a unit cell in ~z, we o b t a i n a d i p o l e mcnw.nt o f 1.0 Debye. Such a mm~nt i m p l i e s O i s n e g a t i v e r e l a t i v e t o C. F r e e CO i s s l i g h t l y n e g a t i v e (-0.12D) i n d i c a t i n g O i s p o s i t i v e . The d e r i v a t i v e o f t h e f i l m d i p o l e ~ moment i s 3.16 D/~, w h i l e f r e e CO i s 3.14 D / ~ " . We have f o ~ d that when we do not have enough number of plane waves, the dipole moment is smaller and even changes sign to that of free co when the number is reduced further. We have also tested double layers of CO with the two carbon atoms facing each other and separated by 4.2~ and 7.12~. This is a z reflection symmetric

eV.

-I0

-

-12

-

-13

-

-14

--

1Try

/ -15

--

-16

--

-

I'rrx

4o"

-17

P Fig. i .

~

~

P

The energy bands of an isolated CO .~nolayer

-5969

-59p,

~c

-597. I

o

-g I,-- 597.

- 597,

1.06

;

1.08

I

~

1,10 C -0

;

1.12 bond

I.ength

1.14

I

1.16

1.18

in

Fig. 2. Potential energy curve for a CO n~nolayer

System. The sane large dipole m~ment is obtained in both C-C separations when we use a large enough number of plane waves. The double layer tests confim the large dipole m~nent obtained for the monolayer. In Figure 3, a comi:~rison of the no~-spherical (i.e. the non muffin-tin) Coulomb potential along the molecular axis is.made for

Vol. 59, No. 2

PROPERTIES OF A CARBON MONOXIDE MONOLAYER

59

Gymax~6.0/Rmt and GzmaX~3/~,t for t h e double layer with a 7.12~ C-C spacing. As stated

The s i m i l a r bond length, d i p o l e n ~ , e n t ~ s l o p e and v i b r a t i o n a l frequency between f r e e CO and t h e monolayer a r e r e a s o n a b l e a s t h e s e p r o p e r t i e s a r e r e l a t e d t o changes i n t h e normal d i r e c t i o n and would be expected t o depend m o s t l y on s h o r t range bonding. The d i p o l e moment and energy l e v e l s s h o u l d be s e r ~ i t i v e t o long range o r d e r . As 0 i s more e l e c t r o n e g a t i v e than C, i t i s not t o o s u r p r i s i n g t h a t charge i s s h i f t e d t o 0 even b y the relatively weak mol~ztle - molecule i n t e r a c t i o n . I t has been ShOWn'=, the s m a l l dipole moment of a free CO results frcm a detailed bal _ailc~ng between the triple bond CO, which has a C,Oi dipole, and a single bond CO, which has a C O dipole. The latter is favored f o r a l o n g e r bond l ~ w j t h . Our s l i g h t l y l a r g e r CO l e n g t h and a C O d i p o l e a r e c ~ s i s t e n t w i t h t h i s p i c t u r e . B e s i d e s , t h e (X)-CO coupling draw ~ charge fra~ the C-O bonding region; this will make the triple b~-~ less l~s~lated. FL~q4 work o f Wimmer e t a l . " used double l a y e r s o f CO and a f i x e d C-O bond l e n g t h . There a r e no o t h e r c a l c u l a t i o n s f o r s i m i l a r molecular monolayers w i t h which t o compare. There i s a l s o no e x p e r i m e n t a l i n f o r m a t i o n s i n c e experiments can n o t be d e v i s e d which i n c l u d e o n l y t h e CO-(Z) i n t e r a c t i o n a s in an i s o l a t e d monolayer. We w i l l however, in Table I compare our r e s u l t s t o l o c a l densi~][ " for free CO molecule. 'Fne I / ~ " " ~ : ~ U L ~ a calculations obtain too large a bond lengthl7 whereas the Xa computation of Dtmlap et.al. obtains the correct bond length.

previously, t h e G~aX's a r e doubled for expanding the potential. In the former case 4225 plane waves are used to expand the potential. While in the latter case 26901 plane waves are used. The potential is poorly represented in the latter case. Even the larger set is still not sufficient as can be seen by the plateau in between t h e films is wavy like, while it should be completely flat. The depth of this plateau results from the net dipole density of either one o~ _the film. A negative plateau corresponds to a C O dipole. This figure dmnonstrates that a correct film dipole m~nent can not be obtained with insufficient number of plane waves. It is worthy to note that at the center of the CO molecule the potential is about -52.5 eV when the larger set of plane waves is used, while it is only about -6.8 eV for the smaller set.

~ledgement--t~e o f computing ~ r t add o t I ~ r f a c i l i t i e s o f t h e E. I . ~u P ~ t Company i s g r a t e f u l l y ac]mowle~ged, a s w e l l a s p a r t i a l s t ~ p o r t o f Dr. Min-I~itmg T s a i . Support f o r Dr. TSai i s a l s o acknowledged from NSF I:MR-8303742. David ( ~ l i s s gratefully acknowledges appointment a s an I ~ Fellow a t C o r n e l l . We a r e a l s o t h a n k f u l f o r t h e use o f t h e c e n t r a l computing f a c i l i t i e s o f t h e C o r n e l l M a t e r i a l s Science Center and f o r t h e o p p o r t u n i t y of c r i t i c a l d i s c u s s i o n s w i t h J . W. Wilkins and C. Umrigar. We a l s o thank Dr. A. W. S l e i g h t and Dr. R. H. S t a l e y f o r h e l p f u l d i s c u s s i o n s and a c r i t i c a l review o f t h i s m a n u s c r i p t .

=Curve I

~4225p~"~ A v o

-I0'-20

o

o u -30

f~ m

-40

o 7

1j/

Curve using 2 26901 p*s

-50

-

.,

60

-I0

o c

z (,~)

~o c o

Fig. 3. The non n~ffin-tin Coulomb potential along the molecular axis for a double layer of CO. Curve i is for a smaller set of plane waves, while curve 2 is for a larger set of plenewavas. Arrows mark the position of atoms. Zero potential is set at the v ~ level.

T A r a I. Cumparison with Calculated Bond Lengths, Vibrational Frequencies, dipole moments and their derivatives for CO.

Ze~h (X) Vibrat ional frequency (an-I) dipole mmrent derivative (D/X)

~(1~) ~_mx(15) ~ 1 5 )

~o~To(16) Work~is

1.128

1.127

1.148

1.175

1.138

2170

2160

2300

2299

2090

2157

3.137

3.118

3.137

3.175

3.213

3.16

e~.

dipolemument (D) -0.122

-0.24

1.137

-0.25

-0.19

-0.01

1.0

60

PROPERTIES OF A CARBON MONOXIDE MONOLAYER

1. s. Anderson end J. S. Pendry, ~ .

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Rev.

A. Igrlatlev, F. 3ona, D. W. Jet:sen, and P. M. Marcus, Phlm. I ~ . Left. 43, 360 (1979). 2. Jenet ~ l ~ s o n end .. a. _ ~ , a , n , , Sur~.

~i. ~j~, ~ 3 (i~2)

Phys. Rev. B26, 2790 (1982). 9. I0.

3. Pei-Lm Cat), D. E. Ellis, A. J. Free~an, Qing-Qi ~ n g , and S. D. Bader, Phys. Rev.

11.

~9, 4146 (1~). 4. D. Post and m. J. ~ e r ~ s , 78, 5663 (1983).

12. 13.

J. Ch~. Phys.

5. E. W ~ r , C. L. Fo and A. J. I ~ Phys. 1~L.v.Lett. 55, 2618 (1985) 6. G. E. ~TKX~BS and W. H. Weinberg, J. C2~m.

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Vol. 59, No. 2

14. 15. 16.

H. Krakauer, A. J. Freeman, and E. WL~er, phys. ~ v . s28, 610 (1983). M. T. Yin and M. L. Cohen, Phys. Rev. B24, 2303 (1981). E. WL~mer, H. Krakaur, M. Weinert, and A. J. Freeman, Phys. Rev. ~_44, 864 (1981). F. J. Arlinghaus, J. R. Smith, J. G. Gay, and R. Richter, Phys. Rev. ~_!, 6507 (1983). R. V. Kasowski, Phys. Rev. B25, 4189 (1982). C. Chakerian, Jr., J. Chem. Phys. 654228 (1976). W. M. I~uo, J. Chem. Phys. 43, 624 (1965). E. J. Baerends and P. F~x~, Int. J. Quantum Chem. Symp. 12, 169 (1978). O. GUmlarsson, J. Harris, and R. O. Jones, J.

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