The effect of an external electric field on the vibrational frequency of CO

Vohme 118. numbu 3

CHEMICAL PHYSICS

LETTERS

26 July 1985

THEEFFECI’OFAN IZXTEFWAL ELECT’RIC iFIELD ON THE VIBRATIONAL FREQUENCY OF CO Charles W BAUSCHLICHER NASA Ames Research

Jr.

Cenrer. Mojfeen Aeld,

CA 94035. USA

Received 21 March 1985; in foal form 1 May 19BS

Ab initio cakulatioos. using a CAS SCF wavef~ction and extended basis set, show a change in the vibationaI Irequency xvi& ektnc Iield strengthfor the ground’L+ state of CO of one third that observedfor CO/Ni(llO). This result soppon_sthe view of Lamben

1. Introduction The investigation of chemisorbed molecules with conventional spectroscopic techniques has revealed many interesting features of molecules at metal sur-

faces Such techniques have shown that the CO vibrational frequency changes between the gas phase and

that in chemisorbed systems, and that the frequency dofferswidely between different metals. This has been interpreted as indicating the size of the metal to CO 2~’ donation. This metal to CO donation is into an antibondmg orbital on CO and results in a weakening of the bond and a reduction in the CO vibrational frequency, we. More recently, an electric field has been applied to the metal surface and the chemisorbed molecules investigated [l--4]. The addition of such an electric field causes an additional shift in the CO ue. This has been interpreted by Beden et al. [l] along the traditional $nes, that is, the electric field changes the metal to CO s donation, which changes the number of an&bonding x elections on CO end results in the observed shift in we. Holloway and Norskov [5] have performed a series of model calculations for CO on R with an applied electric field. They find that results are in agreement with the work of Beden et al. [1] and Kunimatsu [2] _ The important physical effect that these calculations show is the change in CO W, is related to the metal to CO a donation. Unfortuare for CO on Pt in a vacuum, while the experiments are for solution. Using

nately, the model calculations

the experimental values for the change in dipole moment with r, dp/dr and d2p/dr2, and potential energy curves, d2E/dr2 and d3E/dr3= Lambert [3,6] has estimated the change in we due to the duect interaction of the applied field with the CO, which has been onented parallel to the field due to its chemisorption on the metal surface. He finds a Stark tuning rate of 4.3 X IO-’ cm-’ (V/cm)-I, or I/3 of the measured value for CO/Ni( 1 IO) (I.12 0.4) X 10V6 cm-l ~~crn)-l~~s large direct interaction of CO with

the electric field is different from alternative view, and seems surprisingly large when one considers the polarizabiliv of the metal. Using similar arguments, Lambert [6] has also considered the additional effect on the Stark tunmg rate associated with CO on the Ni surface and finds that the sum of the direct and Ni induced shift in we to be quite close to experiment. ‘Ihe fact that tbe sum of the two effects is in agreement with experiment adds support to Lambert’s surprisingIy large direct shift. However, his estimate for &e Stark tuning rate for free CO does not include relaxation of the CO in the electric field. The SCF calculations, using a large ba& set, of Gready et al. [7] suggest this relaxation effect could be q&z tiFrts_nt, since their Stark tuning rate for free CO aligned with an electric field is about 6 bmes smaller, 7.2 X lo- 8 cm-l (V/cm)-l. This suggests that Lambert’s assr.ssment of the relative importance of the &ect and indirect contributions to the shift may be incorrect. It should also be noted that Angell and Schaffer 307

CHEhl-IcALPHYsrcsLErrERS

VohmellS,numbcr3

[%I considered CO adsorbed on zeolites and found a linear relationship between the sbrft in CO vibrational frequency and the local electnc field caused by ions of the zeolite; this is similar to Lambert’s view. However Beran [9] and Metier and Geerlings [lo] using the CNDO method considered CO on zeolites and discussed the shift m CO frequency based upon the magnitude to the CO u donation to ‘he zeohte, i.e. bonding arguments not electic field considerations. To resolve the magnitude to direct electric field and bonding contributions to the observed shift, ideally one could consider CO on a metal surface similar to Holloway and Norakov [S] using the hrghest levels of theory, compute a total shift in agreement with experiment, and then decompose the shift into direct and indirect contributions. While ab initio cluster calculations have been used to help understand the bonding of CO to a metal surface, none of the calculations have been definitive. Thus, an accurate calculation to determine the direct effect has been carried out; free CO ahgned in a field is considered using a CAS SCF [ 1 l] wavefunction. It is well known [ 123 that the SCF treatment, such as that used by Gready et al., yreld a p four times larger than, and in the opposite direction to, expenment. Also dp/dr is 50% too large. The CAS SCF treatment used here, adds the needed correlation to correct the description of CO, and a Stark tunmg rate of 3.8 X 10-7 cm-1 (V/cm)-1 is

26July1985

computed; in rather good agreement with the drrect contribution computed by Lambert [3,6].

2. Method of caiculation The C and 0 basis sets start with lls6p primitive sets of van Duijneveldt [ 13]_ end adds a set of diffuse p functions [ 141 (those optimized for the negative ions) and four sets of polarization functions The polarization functions are three sets of d functions (a(O) = 3.0, 1.0, and 0.3 and a(C) = 2.0,0.6, and 0.2) and one set off functions (a(O) = l-0 and Q(C) = 0.6). The 3s components of the d functions and the 4p components of the 4f functions were deleted. The fmal basis set is of the form (1 ls7p3dlf/6s4p3dlf). It is well known (see discussion in ref. [ 121) that the dipole moment of CO does not have the correct sign if correlation is not included in the wavefunction. In this work, an MC SCF approach is used to include correlation, specifically a CAS SCF wavefunction is used. For CO the 140 orbitals were not correlated, while the six electrons, nominally arising from the 50 and 1~ orbrtals were drstributed in all ways among the Sa, 60, lrr and 27r’ orbit&, leading to 55 configuration state functions m the CI expanson. This CAS SCF treatment leads tore = 1.138 A, AG1_-, = 2 146.6 cm-l- P = 0.30 D, dp/dr = 3.039 D/A and

Table 1 Theeffectofanelectricfieldonr, AG1_e with inncreasedfxld Property ‘e

Nofield

@oW

AG~_~

andAGl_o.Theelec~cfiedIsinatomic~tg

Can-')

0.005

2.151 2146.64

-

A or (au) dr/* (au)

0.1124 0.63

Stark tuningrate,th~work d~G~_~/dEfieeCO<0.0-0.005)=3.8X d~G~_&EfreeCO (O-O-O.OlO)=

lau=5.16

2.149 2156.26 9.62 0.1855 0.61

lo-' cm-' 3 6 X lo-' cm-'

W/cm)-' (v/cm)-'

Stark txUngrate,previous work dwJdEfrceCOa)(SCF) (O.O-0.010)=7_2 x lo-* cm-' W/cm)-' dw$dEexpb) CO/Ni(llO)(l.l t 0.4)X 10d an-' W/cm)-l dw,ldEfreeCOb)=43 X lo-' cm-l (v/cm)+ a) Ref. 171.

308

b)Ref.

131.

X 10' V/m

Aisthechangein

0.010

0.015

2.147 2164.75 18.11

2.145 2172.00 25.36

CHEMICAL PHYSICS LEl-l-ERS

Vohune118,numIx.r3 Table2 ~JIIIII~oftotalene~smhmtree. dipole R(C-0)

moments

26 July 1985

andelectricfieldiuau

Energy no field

0.005

0.010

0.015

1.8

-112.798008

-112.799889

-112.801982

-112.804371

2.0 2.1 2.15 26 2.3 2.5 3.0

-112.894296 -112.907481 -112.908386 -112.906328 -112.895288 -112.855679 -112.729174

-112.895501 -112.908381 -112.909132 -112.906923 -112.906923 -112.8554U -112.727872

-112.897041 -112.909640 -112.910252 -112.907905 -112.896298 -112.855632 -112.727238

-112.898920 -112.911263 -112.911749 -112.909277 -112.897430 -112.856333 -112.727276

g

2.0 2.1 2.15 2.2 2.3

no field

0.005

-0.2076 -01440 -0.1122 -0.0807 -0.0180

-0.2742 -0.2157 -0.1865 -0.1575 -0.1008

d2p/dr2 = -0.22 D/A2 compared to the experimental values of re = 1.128 A, AG,_, = 2143.3 cm-l [lS],p= 0.1222 D [16], dw/dr= 3.093 D/W and d2p/dr2 = -0 193 D/A2 [17] (see tables 1 and 2). This is quite good agreement. Ln addition to the denvatives of the dipole moment, the denvatives of the potential are also used by Lambert [3,6] and it is therefore of interest to compare those with experiment as well. Using the five points closest to r, and a fiveterm polynomral, a Dunham analysis yields, with experiment in parentheses [ 161, w, = 2 186.8 (2169.8), wexe = 16.30 (13.29), B, = 1.919 (1.931), and a, = 0.0163 (0.0175). The fit yields second and third denvatives of the potential which are in good agreement with those used by Lambert. which were derived from experiment, 9.59 X 16 versus 9.51 X 16 erg/cm2 and -2257 X 1013 versus -22.74 X 1013 erglcm3. The electric field is added to the Hamiltonian and a fully relaxed solution is obtained. (This is different from the approach of Lambert where the potential energy curve and the dp/dr are assumed to be unchanged by the electric field.) The vibrational energy

levels are computed using the ftite tiference technique of Tobin and Hinze [ 181 as programmed by Lengsfield

and Bauschlicher

[ 191.

3. Resulk

and discussion

The electric field is parallel to the CO and in such a direction as to increase the P on CO (C-O+), see tables 1 and 2. Associated with the change in ~1is a small rncrease in AC,_,. Also dAGl_O/dEis not hnear, which is observed experimentally [3,4]. This non-linear behavior is either a result of the electric field changmg the CO, for example at a given r, p is increased due to polarization of the CO or the model used. However, this variation from linear is small and, if it is real may not be observed m experiment because of the range of electric fields used is smaller than that considered here. The computed Stark tuning rate for the smallest field used is 3.8 X 1O-7 cm-l (W:m)-l. This value is rather similar to that estiated by Lambert [3,6], but about five tiTles larger than that found by Gready et al. [7]. The difference between the CA5 SCF wave-

function used here and the SCF used by Gready et al. is attributed to the change in dB/dr (and probably the second derivative as well) due to inclusion of correlatron in the CAS SCF procedure. It is not possible to determine if the major difference between the CAS SCF end Lambert’s estimate is due to the relaxa309

Volume 118. number 3

CHEMJCAL PHYSICS LETYYEBS

tion of CO in the field or to the remaining errors in the CAS SCF wavefunction. Since the derivatives of both the dipole moment and energy are in good agreement between this level of theory and experiment and the agreement between this work and the estimate of Lambert is good, it is safe to conclude that relaxation of the CO in the electric field is not large and that Lambert’s esnrnate for the direct contribution is quite good, which adds support to his decomposition of the shift in the vrbrational frequency of CO/Ni(l 10).

References 111 B. Bede- A Bewrck and C. Lamy, J. ElectroauaL Chern 148 (1983) 147. [*I K. Kuminatsl. J. Electroaaal Chem. 145 (1983) 219. r31 D.K. Lambert, Phys. Rev. Letters 50 (1983) 2106; 51 (1983) 2233. 141 R KOQ and E. Yeager, J. Electroaual. Chem. 123 (1981) 335. 151 S. Hollpway and JX. Norskov, J. Etecfzoaual Chem. 161(1984) 193. 161 DX. Lamberf Solid State Commun 5 l(1984) 297. f71 J_E Gready, G.B. Bacskay and N.S. Hush, Chem. Phys. 31 (1978)

4. Conclusions

Acknowledgement This author would like to acknowledge Dave Lambert and Richard E. Teets for many extremely helpful conversations and for pointing out an error in earlier version of this work.

1413.

r91 S. Berau. J. Phys. Chem. 87 (1983) 55. c101 W.J. Mortlsr sod P. Geerliugs, J. Phys Chem. 84 (1980) 1982_

1111 P.E.M. Siegbahn, A He&erg, B-0. Roos aud B. Levy,

Cl21 1131 1141 1151 1161 L171 1181 Cl91

310

467.

WI CL. AngelJ and PC. Schaffer. J. Phys. Chem. 70 (1966)

Using an MC SCF wavefunction, which yields the correct sign for p and accurate values for dp/dr, d*p/dr* and the shape of the potential, results in a Stark tuning rate of 3.8 X 10m7 cm-l (V/cm)-l (about five times that found at the SCF level [7] ) which is in good agreement with the value of 4.3 X 10m7 cm-l (V/cm)--l computed by Lambert [3,6] assuming no field induced changes in CO. This mdicates a full l/3 of the measured Stark tuning rate for CO/Ni( 110) arises by a direct interaction of *e CO with the electric field, as proposed by Lambert.

26 July 1985

Physim Scripta 21(1980) 323; B.O_ Roes. P-R Taylor and P E-M_ Siegbahn, Chem. Phys 48 (1980) 157; P.EM. Siegbshn, J. Almlbf, A. Heiberg and B-0. Roos, J. Chem Phys. 74 (198 1) 238 1. H F. Schaefer HI. The electionic structure of atoms and molecules: a survey of rigorous quantum mechauicalrcz&z