Resonance Raman Spectroscopy of Small Metal Clusters - ACS

11 Resonance Raman Spectroscopy of Small Metal

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Clusters M. MOSKOVITS and D. P. DI LELLA University of Toronto, Department of Chemistry and Erindale College, Toronto, Ontario, Canada M5S 1A1

The resonance Raman spectra of F e , NiFe, V , Ti and Ni in s o l i d , rare-gas matrices are reviewed. Spectro scopic constants for these were (ω , ω x , cm ): Fe (300.26, 1.45), NiFe (320.0, 1.32), V (508.0, 3.3) and Ti (407.9, 1.08). A Bernstein-LeRoy analysis was performed on the data for Fe , yielding a bond dissocia tion energy of 1.2 eV, close to that reported by Kant. All of the transition metal diatomics studied showed an inordinate ability to remain vibrationally excited when the first few vibrational levels were populated radiatively. This gave rise to intense antistokes emissions. 2

2

2

3

-1

e

e

e

2

2

2

2

I n t e r e s t i n the e l e c t r o n i c p r o p e r t i e s and s t r u c t u r e s o f small t r a n s i t i o n metal diatomics and c l u s t e r s has increased r a p i d l y during the past decade, l a r g e l y as a r e s u l t of the connection, r e a l or suggested, that e x i s t s between these e n t i t i e s and surface chemistry. In t h i s paper we w i l l present some examples of the a p p l i c a t i o n of resonance Raman spectroscopy to the study o f t r a n s i t i o n metal diatomics. The a p p l i c a t i o n of Raman spectroscopy to m a t r i x - i s o l a t e d metal c l u s t e r s was f i r s t reported by Schulze e t a l . ( 1 ) . Having observed only a s i n g l e l i n e i n the Raman spectrum of A g , Schulze concluded that the molecule was l i n e a r s i n c e a bent t r i a t o m i c and an e q u i l a t e r a l t r i a n g u l a r geometry would have, i n p r i n c i p l e , 3 and 2 Raman-active modes. The evidence, however, i s not c o n c l u s i v e s i n c e many C 2 molecules have very weak asymm e t r i c s t r e t c h e s i n the Raman (2) ( f o r example, the V 3 mode o f O3 i s undetectable i n the Raman ( 3 ) ) . Moreover, the bend ( v ) of Ag3 i s expected to be a very low-frequency mode, perhaps lower than one can f e a s i b l y detect i n a matrix Raman experiment. Resonance Raman (RR) spectroscopy has two advantages and a disadvantage over ordinary Raman. The disadvantage i s the unequal enhancement of a l l the fundamentals of a molecule i n i t s RR spec3

V

2

0097-6156/82/0179-0153$05.00/0 ©

1982 A m e r i c a n Chemical Society

Gole and Stwalley,; Metal Bonding and Interactions in High Temperature Systems ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

154

METAL

BONDING A N D INTERACTIONS


trum. Normally i t i s t o t a l l y symmetric modes which are enhanced (4). One advantage l i e s i n the f a c t that s e v e r a l members of a progression are o f t e n seen i n RR spectroscopy. Hence the anharmonicity and an estimate of the bond d i s s o c i a t i o n energy ( a t l e a s t i n the case of diatomics) may be obtained. Secondly, the i s o t o p i c f i n e s t r u c t u r e , i f any e x i s t s , may be resolved q u i t e e a s i l y i n the high harmonics, making the i d e n t i f i c a t i o n and, i n the case of polyatomics, the s t r u c t u r e of the c a r r i e r determinable. Experimental The apparatus has been described i n d e t a i l elsewhere ( 5 ) . B r i e f l y , metal atoms vaporized by e l e c t r i c a l l y heating a metal ribbon filament d i r e c t l y were cocondensed with r a r e gas on a p o l i s h e d aluminum surface cooled to 11°K by means of an A i r Products Displex r e f r i g e r a t o r . The aluminum substrate which was contained i n a vacuum chamber whose l o c a l pressure with the r e f r i g e r a t o r on was approximately 1 0 t o r r could be viewed through a Pyrex or quartz b e l l surrounding i t . The metal vapor stream was p a r t i a l l y c o l l i m a t e d by t r a n s i t through the c y l i n d r i c a l neck of the f l a n g e which connected the metal vapor source to the sample area. Only the upper h a l f of the s u b s t r a t e i n t e r cepted the m e t a l stream and the matrix deposited there was c o l o r e d . There was a d i s t i n c t boundary between the colored part of the sample and the lower p a r t , which was white. The thickness of the r a r e gas d e p o s i t i o n was n e a r l y constant over the substrate. Tor a p a r t i c u l a r sample, the concentration of the colored p a r t was n e a r l y constant, judging from the s p e c t r a obtained when the l a s e r sampled various parts of i t . The s p e c t r a obtained when the l a s e r was focused on the white part of the sample showed that i t a l s o r e c e i v e d some metal f l u x . RR s p e c t r a obtained when the l a s e r was focused on the white p a r t of the sample near the c o l o r boundary were n e a r l y as strong as that on the colored p a r t proper. This c h a r a c t e r i s t i c r e s u l t s from reabsorption of some o f the emitted l i g h t by the colored p a r t of the matrix. The i n t e n s i t y of the features i n the RR s p e c t r a obtained from the white p a r t of the sample q u i c k l y and s t e a d i l y decreased as the l a s e r was moved away from the c o l o r boundary. Parts of the sample with widely v a r y i n g metal concentrations could therefore be studied i n the same experiment. Mixed Fe/Ni deposits were generated by s t r i n g i n g two f i l a m e n t s , one of each metal, s i d e by s i d e across the watercooled e l e c t r o d e s of the metal vapor furnace. An Fe/Ni sample had the same c o l o r as a sample with Fe alone. Emission spectra were e x c i t e d using e i t h e r a C o n t r o l model 554A or a Spectraphysics model 165 argon i o n l a s e r . A Spectraphysics model 375 dye l a s e r (Rhodamine 6G) was a l s o used. The emitted l i g h t was dispersed with a Spex 1401B double monochromator with 1800 lines/mm holographic g r a t i n g s . A cooled Hamamatsu R955 m u l t i a l k a l i p h o t o m u l t i p l i e r detected the s i g n a l , followed by conv e n t i o n a l photon counting. - 8


11.

MOSKOVITS AND DI LELLA

Resonance

Raman

155

Spectroscopy

Diatomics Fe?. P o r t i o n s of the RR spectrum of Fe2 (6) are shown i n Figure 1. A n a l y s i s of the v i b r a t i o n a l f i n e s t r u c t u r e , employing the r e l a t i o n G(V)

2

= 03 v - oj X (v +v) e e e

(1) 1

y i e l d s the constants u> = 300.26 and u) X = 1.45 cm" . These data were obtained from the p r o g r e s s i o n of the more abundant species Fe . In a d d i t i o n , f i v e members of a second p r o g r e s s i o n belongi n g to F e F e were observed. The v i b r a t i o n a l constants imply a d i s s o c i a t i o n energy of 1.9 eV i f the formula p e r t i n e n t to a Morse o s c i l l a t o r , D = o) /(4u) Xe) , i s used. This value i s l a r g e r than the q u a n t i t y reported by Kant (7), 1.3 eV, and much l a r g e r than that reported by G i n g e r i c h (8), 0.5 eV, obtained by r e - e v a l u a t i n g Kant's data on the assumption that F e possesses a l a r g e number of l o w - l y i n g , e l e c t r o n i c a l l y e x c i t e d s t a t e s w i t h i n one-half an eV of the ground s t a t e . A lower value i s obtained on using an a n a l y s i s due to LeRoy and Bernstein (9). By taking the c o n t r i b u t i o n to the i n t e r a t o m i c p o t e n t i a l to be a s i n g l e i n v e r s e power near the d i s s o c i a t i o n l i m i t , one obtains an expression f o r the v i b r a t i o n a l terms of the form


e

e

e

5 6

2

5 1 +

5 6

2

e

e

e

2

G(v)

= D

2 n

e

n

2

- Xo(n)(v -v) /( ~ )

(2)

D

In eqn. 2 D i s the d i s s o c i a t i o n energy, n the power of the a s y m p t o t i c a l l y dominant inverse-power term i n the p o t e n t i a l , vrj the e f f e c t i v e , non-integer value of the v i b r a t i o n a l quantum number at d i s s o c i a t i o n and X()(n) i s a constant of the form e

X(n)

2

1

= XoCn)/^^ ) ^

1 1

2

- )

(3)

In eqn. 3, y and Cn are, r e s p e c t i v e l y , the reduced mass of the diatomic and the c o e f f i c i e n t of the r ~ term i n the n e a r - d i s s o c i a tion potential. X ( n ) i s a constant tabulated by LeRoy (10). LeRoy has r e c e n t l y enlarged the a n a l y s i s to allow lower v i b r a t i o n a l terms to be used (10). Among the v a r i o u s " c o r r e c t i o n s " to eqn. 3 proposed i s one of the form n

0

G(v)

= D

e

- X (n)(v -v) 0

D

2 n

n

2

/ ( - ) { l + a!(v -v) + a ( v - v ) D

2

D

2

+

...} (4)

The constants i n eqn. 4 have been p r e v i o u s l y defined except f o r a i , a , e t c . , which are a r b i t r a r y , a d j u s t a b l e parameters. The ° F e data of F i g . 1 were f i t to eqn. 4 using a F l e t c h e r - P o w e l l program to minimize the sums of r e s i d u a l s . For the D ground s t a t e of the Fe atom the proper choice of n i s 5 (11). C was c a l c u l a t e d to be -3.1775 x 10** cm A using the formulas and 2

5

2

5

i+

5

-1

5


156


METAL BONDING AND INTERACTIONS

J

0

1

I

1000

i

I

i

2000

^

cm

I -I

3000

i

I

4000

i

I

5000

Figure 1. Spectra obtained from the red-orange part of the sample with three laser excitations for Fe codeposited with Ar at 11 K. The resonance Raman progression is assigned to Fe and all fluorescence features to FeO (6). 2


11.


Resonance

Raman

157

Spectroscopy

data tabulated by Chang (11) and assuming a mean square radius f o r Fe of 1.4948 A (12). The ground s t a t e of F e was taken to be E g as reported by Montano (13) on the b a s i s of a MSssbauer study. The parameters i n eqn. 4 were thereby determined to be: D = 9735.97 cm" , v = 63.83, a = -0.017367 and a = 9.1583 x 10" . The value f o r the d i s s o c i a t i o n energy (1.2 eV) obtained i n the a n a l y s i s i s i n much b e t t e r agreement with that reported by Kant than that based on the Morse o s c i l l a t o r . One should s t i l l regard t h i s r e s u l t as somewhat t e n t a t i v e as may be gauged from F i g . 2 which shows that the a v a i l a b l e v i b r a t i o n a l terms are too few to d i s t i n g u i s h between a l i n e a r Birge-Sponer p l o t f o r which D = a)e /(4a) X ) and the AG(v) versus v curve obtained from eqn. 4. However, i t i s c l e a r that G i n g e r i c h s estimate of 0.5 eV f o r D of F e i s too low s i n c e we see s p e c t r a l emissions ( F i g . 1) to v i b r a t i o n a l s t a t e s of ground s t a t e F e which are higher than 4000 cm" above the ground v i b r a t i o n a l s t a t e and which are s t i l l at a rather harmonic p o r t i o n of the ground s t a t e p o t e n t i a l , implying that they are not near the d i s s o c i a t i o n l i m i t . 2

2

7

e

1

5

l


D

2

e

2

e

e

1

e

2

1

2

In a d d i t i o n to the p r o g r e s s i o n observed on the Stokes s i d e of the spectrum, an i n o r d i n a t e l y intense a n t i s t o k e s p r o g r e s s i o n was obtained w i t h F e , as with the other diatomics discussed below. The a n t i s t o k e s l i n e s were too intense f o r them to a r i s e simply from t r a n s i t i o n s from thermally populated v" = 1, 2, 3, etc., l e v e l s . We propose that these s t a t e s are populated r a d i a t i v e l y by the Stokes resonance Raman process. Thus the a n t i s t o k e s spectrum a r i s e s only from consecutive, two-photon (or m u l t i p l e photon) absorption processes, while the Stokes spectrum has cont r i b u t i o n s from both s i n g l e - and two-photon absorptions. In the l i m i t of very low l a s e r powers the r a t i o of the i n t e n s i t y of an a n t i s t o k e s to a Stokes l i n e should be p r o p o r t i o n a l to the l a s e r power. Moreover f o r the i n t e n s i t y of the a n t i s t o k e s spectrum to be so l a r g e , r a d i a t i v e depopulation of e x c i t e d ground s t a t e v i b r a t i o n a l s t a t e s must compete e f f e c t i v e l y with thermal r e l a x a t i o n to the ground s t a t e . This implies very long l i f e t i m e s f o r the f i r s t few v i b r a t i o n a l l y e x c i t e d s t a t e s of the ground s t a t e of F e i s o l a t e d i n s o l i d argon. Very long v i b r a t i o n a l l i f e t i m e s have been p r e v i o u s l y reported f o r a number of m a t r i x - i s o l a t e d diatomics (14). 2

2

The dependence of the Stokes and a n t i s t o k e s i n t e n s i t i e s on i n c i d e n t l a s e r power was considered i n r e f . 6 where i t was shown that the i n t e n s i t y , S j , of the component corresponding to the transition j «- o depends on the l a s e r power, I, as 0

al S

. = k O J

while for antistokes

. °

J

+ b I 2

2

+ c I °_

a + bi + c l

3

( 5 )

2

j -«- i t r a n s i t i o n s where i ^ 0 ( t h i s i n c l u d e s a l l t r a n s i t i o n s when j < i ) the i n t e n s i t y S i j i s given


by


158


Figure 2. G(v + 1) — G(v) vs. v for the Fe data of Fig. 1. Key: a, Birge-Sponer extrapolation using AGfvJ = 300.26 — 2.90(v + 1) cm' ; and b, AG(v) obtained from Eq. 4. 2

1


11.


Resonance

b.I

2

+ c.I

1

l j

In (5) and

159

Spectroscopy

3

I

(6)

a + bi + c l

2

(6) b

and b. < b and c and c. < c. o 1 o 1 The three terms i n the denominators of (5) and (6) (and the numerator of (1)) come about, r e s p e c t i v e l y , from the p o p u l a t i o n (or depopulation) of a o or i l e v e l f o l l o w i n g the absorption of one, two and three s u c c e s s i v e photons. The termination of the numerators of (5) and (6) at the t h i r d order a r i s e s from the f a c t that i n reference 6 the authors considered only the f i r s t three v i b r a t i o n a l l e v e l s of the e l e c t r o n i c ground s t a t e to be s i g n i f i c a n t l y populated and truncated the s o l u t i o n with the v" = 2 l e v e l . Since three or fewer members of the a n t i s t o k e s p r o g r e s s i o n are seen t h i s assumption seems to s u f f i c e . When more v i b r a t i o n a l l e v e l s are s i g n i f i c a n t l y populated, equations (5) and (6) must be enlarged to c o n t a i n terms of higher order. Equations (5) and (6) i n d i c a t e , however, that the i n t e n s i t i e s a s s o c i a t e d with j

15

Figure 4. a: Intensity of S (528). b: Intensity of S (521). c: Ratio of intensity S (521) to S (528). d: Ratio of intensity S 'i'(501) to S (528). a-d: Excited with 496.5 nm; e: Ratio of intensity of the first antistokes line S (—528) to first Stokes S i(528) line excited with 514.5 nm. All as a function of incident laser power. The points are experimental. The lines drawn for c, d and e are best fits to Eq. 4. Parameters A, B, C and D equal to: 20.95, 3.71, 0, and 0 for c; for d, A = 16.44, B = 6.31, C = 0.0706, and D = 0.0936; for e, A = 0.791, B = 2.64, C = 0.169, and D = 0.420 (16). 01

12

01

12

0

01

10

0


11.


3^

d

Resonance

Raman

Spectroscopy

Stokes

1

f: 2cm

0->3

s r

163

Stokes

-1


NT*

Figure 5. Portions of a high-resolution spectrum of V isolated in an Ar matrix excited with 496.5-nm Ar laser radiation, showing the effect of laser power on the first and third members of the Stokes GSRR and RRES progressions. Stokes RRES are indicated with primes (16). 2

+


164

METAL

BONDING

A N D INTERACTIONS

of the quantum mechanical c a l c u l a t i o n may a l t e r the o r d e r i n g of these l o w - l y i n g s t a t e s , causing another s t a t e to be the ground state. H a r r i s and Jones suggest that f o r V a A s t a t e (sa|da^d 7 r d 6 | d 6 d 6 s 6 ) i s another l i k e l y candidate as the ground s t a t e . C l e a r l y , the symmetry of the c o r r e c t ground s t a t e cannot be stated with confidence. I t appears, however, that a s t a t e of high, odd s p i n m u l t i p l i c i t y i s most l i k e l y . Focusing on a p o s s i b l e A ground s t a t e , we note that i n t e r a c t i o n s w i t h the matrix would remove the s p a t i a l degeneracy, y i e l d ing two s t a t e s . We t h e r e f o r e hazard to guess that the ground s t a t e of V i s a A ~ s t a t e whose s p a t i a l degeneracy was removed through the aforementioned i n t e r a c t i o n w i t h the matrix while the e x c i t e d s t a t e A i s a s t a t e of symmetry E " ~ . The E ~ A ~ t r a n s i t i o n i s , of course, Raman-allowed s i n c e they are of the same p a r i t y and t h e i r d i r e c t product transforms as the product of two displacements. 9

2

U

2

u

u

u


9

9

2

U

9

9

U

U

9

U

Ti . With t i t a n i u m (16) i n s o l i d argon one obtains i n t e n s e progressions only when e x c i t i n g with red or orange l a s e r l i g h t . As with the previous molecules both Stokes and a n t i s t o k e s progressions were observed and assigned to T i , whose v i b r a t i o n a l constants were determined to be to = 407.9 and oJgXe = 1.08 cm . With f i v e abundant isotopes each of the Stokes and a n t i s t o k e s v i b r a t i o n a l components s p l i t i n t o a bouquet of l i n e s . Superimposed on these were the sequence components a r i s i n g from the r a d i a t i v e p o p u l a t i o n of e x c i t e d v i b r a t i o n a l s t a t e s each with i t s i s o t o p i c companions. This i s shown i n F i g . 7. 2

2

-1

e

Bonding i n First-Row T r a n s i t i o n Metal Dimers. In t r a n s i t i o n metal dimers of low s p i n c o n f i g u r a t i o n , formal bond orders up to s i x ( f o r Cr) are p o s s i b l e while i n high s p i n , bond orders up to three are p o s s i b l e . These c o n s i s t of an sa bond (even when h i g h s p i n l e v e l f i l l i n g i s assumed the sag o r b i t a l i s g e n e r a l l y taken to l i e s u f f i c i e n t l y below the d-manifold so as to be doubly f i l l e d f i r s t ) and one a, two TT and two 6 bonds a r i s i n g from the dorbitals. The m u l t i p l e bonds of d - o r i g i n do not always c o n t r i b u t e s i g n i f i c a n t l y to e i t h e r the M-M force constant or i t s bond d i s s o c i a t i o n energy. Anderson (20) showed, f o r example, that although Ni i s f o r m a l l y double-bonded i n h i s scheme, promoting one e l e c tron from the s a to the s a o r b i t a l , thereby r u p t u r i n g only the so bond, r e s u l t e d i n a molecule which was almost unbound. This f a c t i s also r e f l e c t e d i n the force constants observed to date f o r the f i r s t - r o w t r a n s i t i o n metals. E s t i m a t i n g the sa c o n t r i b u t i o n to the f o r c e constant by means of S i e b e r t ' s formula (21; the f o r mula k(mdyn/A) = 7.2ZAZB/(n^ng) was used f o r the s i n g l e bond force constant of a diatomic molecule AB i n which Z and n refer, r e s p e c t i v e l y , to the atomic number and the p r i n c i p a l quantum number appropriate f o r atoms A and B) we see (Table I) that the observed f o r c e constant f o r Cu , which contains only one sa bond, i s w e l l reproduced by the formula, that of F e i s only s l i g h t l y 2

g

u

2

2


Gole and Stwalley,; Metal Bonding and Interactions in High Temperature Systems ACS Symposium Series; American Chemical Society: Washington, DC, 1982. 1

2

1

1

Figure 6. Resonance Raman scattering (O) of Ti in Ar matrix at 15 K obtained with the three following excitations: 6328 nm (30 mW) He-Ne laser (6-cm slits); 588.1 nm (10 mW) 6G dye laser excited with Ar* (6-cm' slits); 514.5 nm (10 mW) Ar* ion laser (5-cm' slits) (16).


166


M E T A L BONDING A N D INTERACTIONS

OBSERVED

CALCULATED

Figure 7. Experimental and calculated Stokes and antistokes overtones of Ti in Ar matrix at 15 K recorded under high resolution (1-cm slits) with 632.8-nm laser excitation. Frequencies shown on calculated lines indicate the location of each component used in the calculations, to reproduce the observed spectrum best (16). 2

1



2

2

2

Co

Ni

Cu

A

5

iz

A

7

?z

+

g

g

u

u

u

u

u

u

g

U

U

+

+

state

a

e

a

280

320

360

390

210

220

220

230

630

220

200

03

Calculated

(b)

(b)

266.1

380.9 (14)

~

300.3 (26)

—

—

537.5

407.9

—

co ( r e f . ) e

Observed

e

1.31

2.48

—

1.48

—

—

4.34

2.35

—

k(mdyn/A)

1.48

1.38

1.28

1.19

1.10

1.01

0.93

0.85

0.78

k(mdyn/A)^

1

2

2

3

1

1

1

2

d

3

2

order

Bond 3

1.9

2.37

1.72

1.3

0.33,

1.90

2.48

1.40

1.13

D

T r a n s i t i o n Metal Dimers

S i n g l e bond

Selected P r o p e r t i e s of the F i r s t --Row

0.56

0.94

—

0.33

—

1.20

—

—

(eV)

dd^

*f

3.5

3.0

—

2.9

—

2.7

2.5

2.0

1.9

(eV)

a-a

Taken from or based on the work of H a r r i s and Jones (21). Ref. 16. ^ C a l c u l a t e d from the formula of S i e b e r t (21) which assumes only a s i n g l e sa bond. ^The c o n f i g u r a t i o n was not reported f o r t h i s s t a t e , hence the bond order could not be determined. As r e p o r t e d by Cooper and Hare (17) based l a r g e l y on the experimental work of Kant (7). fc a l c u l a t e d as described i n the t e x t from data given i n the r e f e r e n c e , dd r e f e r s to the^span of the l e v e l s i n the diatomic d e r i v e d mainly from atomic d - o r b i t a l s w h i l e a-a i s the observed a-K7 t r a n s i t i o n energy.

a

2

2

2

Fe

Mn

Cr

2

2

Ti

V

2

Sc

ground

Calculated

TABLE I.


J

ON --J

I 3

§


168

g r e a t e r than the " s i n g l e bond" f o r c e constant, those o f N i and Ti are greater than the s i n g l e bond value w h i l e that o f V lies higher s t i l l above the " s i n g l e bond" v a l u e . This trend m i r r o r s that o f the observed bond d i s s o c i a t i o n energies f o r the s e r i e s . (A summary of the bond d i s s o c i a t i o n energies o f f i r s t - r o w t r a n s i t i o n metal dimers i s given by Cooper e t a l . i n r e f . 17, based mainly on the work of A. Kant (7). A more up-to-date summary has been prepared by K.A. G i n g e r i c h and i s r e f e r r e d to i n h i s c o n t r i b u t i o n to t h i s volume.) The s t r e n g t h of a bond depends, among other f a c t o r s , on the d i f f e r e n c e i n energy between the bonding and antibonding o r b i t a l s a r i s i n g from the same atomic o r b i t a l s . Our observations are cons i s t e n t w i t h thg known f a c t that the energy d i f f e r e n c e between the sag and s a o r b i t a l i s c o n s i d e r a b l y greater than the span o f the m a n i f o l d o f l e v e l s a r i s i n g from the d - o r b i t a l s . They suggest, moreover, that the width of the d-manifold i s g r e a t e r i n V than i n T i or N i whose d-manifolds are broader, i n t u r n , than that of Fe . This i s corroborated by the U V - v i s i b l e a b s o r p t i o n s p e c t r a o f three of these dimers. Moskovits and Hulse (22) r e p o r t that i n the a b s o r p t i o n spectrum of N i two s t r u c t u r a l absorptions at 528 and 377 nm a r i s e r e s p e c t i v e l y from a d 7 r p 7 r and a dag -* pir transition. Since the di\g l i e s near the top of the d-manifold w h i l e the dag l i e s near the bottom, the d i f f e r e n c e i n frequency (0.94 eV) between the v frequencies o f these two absorptions should give a measure of the width of the d-manifold. Both t r a n s i t i o n s end on the same l e v e l . A f e a t u r e l e s s band at 410 nm (3.0 eV) was assigned to the sa -> s a * t r a n s i t i o n . A s i m i l a r procedure f o r F e (23) and V (using the a b s o r p t i o n spectrum reported i n r e f . 18 and i d e n t i f y i n g the high-energy d -> IT t r a n s i t i o n with the s t r u c t u r e d band p a r t i a l l y obscured by the 368 nm atomic l i n e ; i n the case o f V the high-energy d -> TT t r a n s i t i o n which comes a t 370 nm i s p a r t l y obscured by an atomic absorption at 368 nm) y i e l d s estimates of the d-manifold widths of 0.33 eV and 1.2 eV r e s p e c t ively. The d-manifold widths o f V , F e and N i c a l c u l a t e d above c o r r e l a t e w e l l with the extent to which t h e i r f o r c e constants are g r e a t e r than those due to the sa s i n g l e bond alone. There i s , i n a d d i t i o n , an e x c e l l e n t c o r r e l a t i o n between the sa -> sa energy i n t e r v a l s and the " s i n g l e bond" f o r c e constants of the seven f i r s t t r a n s i t i o n row dimers f o r which data were a v a i l a b l e (Table I ) . I t i s c l e a r , however, that the formal bond order i s not a good i n d i c a t o r of bond s t r e n g t h i n t r a n s i t i o n metal systems w i t h out concurrent knowledge of the width of the d-manifold. The ground s t a t e v i b r a t i o n a l f r e q u e n c i e s of the known t r a n s i t i o n metal diatomics are not c a l c u l a t e d with uniform accuracy by any o f the aforementioned groups (17, 19)• This i s e s p e c i a l l y true of V , which has been underestimated i n the c a l c u l a t i o n s of both Cooper and Hare (17) and H a r r i s and Jones (19). 2


2

2

u

2

2

2

2

2

g

u

u

0 0

2

2

2

2

2

2

2


11.

MOSKOVITS A N D DI L E L L A

Resonance

Raman

Spectroscopy

169


Triatomics With t r i a t o m i c s one has the added dimension o f s t r u c t u r e to contend with. This should, i n p r i n c i p l e , be determinable from the i s o t o p i c f i n e s t r u c t u r e of the resonance p r o g r e s s i o n , assuming o f course that the various i s o t o p i c counterparts of a molecule are simultaneously i n resonance w i t h the l a s e r beam. While the broadening of v i b r a t i o n a l l e v e l s due to i n t e r a c t i o n with the matrix tends to work i n t h i s d i r e c t i o n , one cannot guarantee t h i s c o n d i t i o n i n a l l cases. O c c a s i o n a l l y the magnitude of the frequency may suggest a geometry. So, f o r example, i n a molecule the highest f r e quency i s the t o t a l l y symmetric one and hence the one l i k e l y to form the resonance Raman p r o g r e s s i o n . A frequency higher than that of the diatomic would suggest t h i s s t r u c t u r e . In a l i n e a r t r i a t o m i c , on the other hand, the t o t a l l y symmetric v i b r a t i o n i s the lowest frequency v i b r a t i o n . This f a c t may help guide one i n choosing the c o r r e c t geometry. A l l t h i s depends, of course, on the assumption that the metal-metal f o r c e constant i n the t r i a t o m i c i s not too d i f f e r e n t from that of the diatomic, an assumption which i s not always r e a l i z e d . In a d d i t i o n one may have a t r i atomic which i s J a h n - T e l l e r or Renner-Teller unstable producing a f l u x i o n a l or pseudo-rotating molecule even i n a matrix e n v i r o n ment, as has been suggested f o r L i 3 (24) and K3 (25). In t h i s case the concept of a v i b r a t i o n a l s t a t e i s no longer tenable and one must d i s c u s s the spectroscopy of the trimers i n terms o f vibronic states. N13. Figure 8 shows the RR spectrum a t t r i b u t e d to N i 3 (26). A high r e s o l u t i o n spectrum of the t h i r d Stokes component i s shown i n Figure 9 together with the p r e d i c t e d i s o t o p i c f i n e s t r u c t u r e c a l c u l a t e d f o r various geometries assuming, f i r s t , that a l l i s o t o p i c molecules are e q u a l l y e x c i t e d and hence produce s p e c t r a l components p r o p o r t i o n a l i n height to t h e i r n a t u r a l abundances and, second, that the spacing between adjacent components o f the progression shown i n Figure 8 i s the t o t a l l y symmetric v i b r a t i o n . D e t a i l s of the c a l c u l a t i o n are given i n r e f . 26. The r e s u l t s o f the c a l c u l a t i o n i n d i c a t e that the spectrum c a l c u l a t e d f o r a C £ molecule with an apex angle () between 95° and 95.5° f i t s the observed spectrum best. The c a l c u l a t i o n was repeated w i t h d i f f e r ent r a t i o s o f f / f , f being the Ni-Ni f o r c e constant and f r r the i n t e r a c t i o n f o r c e constant between two Ni-Ni bonds. F o r f approximately equal to zero the best f i t was obtained f o r a C 2 molecule with $ = 90° whereas f o r f = 0.1 f , $ = 111° gave the best f i t . Since f / f r a t i o s i n n e u t r a l t r i a t o m i c s are r a r e l y greater than 10% and even l e s s o f t e n negative (27) , we propose that M 3 i s a C v molecule with an apex angle between 90 and 100°, f a v o r i n g the former v a l u e . (A p o s i t i v e i n t e r a c t i o n s t r e t c h i n g constant f r r implies that s t r e t c h i n g one bond causes the other to s h r i n k i n length and therefore strengthen. In a molecule such as V

r r

r

r

V

r

r r

r

r

r

2


r


170


Figure 8.

Raman spectrum of Ni-containing, solid Ar matrix excited with 4880 A Ar-ion laser radiation (26).


11.


Resonance

Raman

Spectroscopy

I

111


n

e

d c b

a I

I

I

669

675

681

687

Figure 9. a-1 Calculated isotopic fine structure of the v = 3 component of the resonance Raman progression assuming the scatterer to be Ni and that the normal mode is the symmetric stretching vibration and taking frr/fr to be 0.05. Key: a, D geometry; b - i , C geometry; Apex angles, 80°, 90°, 95°, 95.5°, 96°, 96.5°, 100°, 120°, 140°, 160°, and 180°; and n, experimentally obtained fine structure on the v = 3 component excited with 4965-A radiation (26). 3

3h

2v


METAL

172

BONDING AND INTERACTIONS

M 3 , i n which each i n d i v i d u a l bond i s weaker than that i n N i (as gauged by t h e i r r e l a t i v e f o r c e constants), the i n t e r a c t i o n f o r c e constant i s almost c e r t a i n l y p o s i t i v e . Negative values of f are encountered i n K r F , H 0 and HCN, while unusually l a r g e values of f are found i n t r i a t o m i c anions such as HC1 ~, HF ~, CI3", BrCl and other members of t h i s c l a s s . The geometry of M 3 deduced by the arguments given above i s i n apparent c o n t r a d i c t i o n w i t h that reported by Anderson using a semi-empirical molecular o r b i t a l c a l c u l a t i o n (28) and by Walch and Goddard (29), who suggest that M 3 i s l i n e a r . Anderson f i n d s , however, that the energy r i s e along the bending coordinate i s so s l i g h t that even at $ = 120° i t i s only 0.1 eV higher than that c a l c u l a t e d f o r the l i n e a r molecule (28). This may imply that the i n t e r a c t i o n w i t h the Ar matrix, which i s commonly greater than 0.1 eV, i s a dominant f o r c e i n determining the shape of the molecule. (An attempt to produce t h i s Ni species i n a krypton matrix i n order to t e s t t h i s p o s s i b i l i t y f a i l e d because i t i s considerably more d i f f i c u l t to produce metal c l u s t e r s i n matrices formed from the l a r g e r rare gases.) A l t e r n a t i v e l y the d i s t o r t i o n from a l i n e a r c o n f i g u r a t i o n or conformation may r e s u l t from the RennerT e l l e r e f f e c t (30) . This e f f e c t a r i s e s from the i n t e r a c t i o n between the e l e c t r o n i c angular momentum and the angular momentum a s s o c i a t e d with the bending v i b r a t i o n , causing an e l e c t r o n i c TT or A s t a t e of a l i n e a r t r i a t o m i c to s p l i t i n t o A and B s t a t e s of a C molecule (30). I t has been shown (31) , however, that w h i l e the d i f f e r e n c e i n the p o t e n t i a l energy curves f o r the two new s t a t e s contains both quadratic and q u a r t i c terms i n the bending coordinate when the o r i g i n a l e l e c t r o n i c s t a t e i s TT, only q u a r t i c terms ( i . e . , only the anharmonicity) c o n t r i b u t e i n the case of A states. Consequently the Renner-Teller e f f e c t i s expected to be much more pronounced i n e l e c t r o n i c TT s t a t e s than i n A s t a t e s . And, indeed, Renner-Teller d i s t o r t i o n has been observed i n many t r i a t o m i c molecules formed from a parent TT e l e c t r o n i c s t a t e (30, 32) but only one report has been published of a s u b s t a n t i a l Renner-Teller e f f e c t i n a A s t a t e (33). The e l e c t r o n i c ground s t a t e of Ni3 i s unknown. The united atom formalism allows Zg , ^g"» g> g * g states, while the separated atom method allows e s s e n t i a l l y any e l e c t r o n i c s t a t e with A between 0 and 6 f o r both the d s and d ^ s configurations of each Ni atom. Anderson (28) reports the c o n f i g u r a t i o n of M 3 to be l s a „ l s a l d 7 r l d a l d 6 l d T r l d a l d 6 g 2 d 6 2 d a g 2 d T r , which i s obtained by f i l l i n g the lowest seventeen o r b i t a l s of l i n e a r M 3 with the e l e c t r o n s i n a h i g h - s p i n c o n f i g u r a t i o n . The s m a l l energy spacing between the l e v e l s apparently d i c t a t e s t h i s choice. This ground s t a t e c o n f i g u r a t i o n allows s p i n q u i n t e t s , t r i p l e t s and s i n g l e t s and suggests an e l e c t r o n i c A s t a t e . (Had a low-spin c o n f i g u r a t i o n been chosen, the e l e c t r o n i c ground s t a t e of M 3 would have been ^g-) Although one can rearrange the c a l c u l a t e d l e v e l s somewhat to y i e l d other e l e c t r o n i c ground s t a t e s , no 2

r

2

r

r

2

r

2

2


2

2 v

l

+

3

l7r

3 7 r

a

8

n

d

A

2

1

2

2

u

1 +

u

2

I +

?

u

I +

g

2

1 +

3

u

u

1

2

g

u

1


11.


Resonance

Raman

173

Spectroscopy

reasonable c o n f i g u r a t i o n can be found which leads to a TT ground state. The "parent" ground s t a t e o f M 3 would appear to be a A s t a t e o f unknown s p i n m u l t i p l i c i t y . This s t a t e has the p o s s i b i l i t y of d i s t o r t i n g as a r e s u l t of the Renner-Teller e f f e c t , although the d i s t o r t i o n does not lead to a great d e a l of s t a b i l i z a t i o n . In the gas phase the molecule i s most l i k e l y f l u x i o n a l w i t h a l i n e a r average geometry. The matrix a f f e c t s the s t a b i l i z a t i o n of the molecule i n a bent c o n f i g u r a t i o n . This p o s s i b i l i t y was a l s o suggested i n the context o f the dynamical J a h n - T e l l e r molecule L i 3 (24). I f M 3 occupies three neighboring vacancies (a t r i v a c a n c y ) i n the matrix, assuming the ease o f d i s t o r t i o n suggested both by Anderson's c a l c u l a t i o n s and the Renner-Teller argument, the bent c o n f i g u r a t i o n might come about as a r e s u l t o f the molecule's a d j u s t i n g to the matrix environment i n a manner l e a s t l i k e l y * to cause c r y s t a l l i n e s t r a i n . The four types of t r i v a c a n c y which e x i s t i n a f a c e - c e n t e r - c u b i c c r y s t a l have l i n e a r , 120°-bent, 9 0 ° bent and e q u i l a t e r a l t r i a n g u l a r geometries. T h e i r r e l a t i v e abundances are i n the r a t i o 1:4:2:2 (23). The D3I1 geometry i s u n l i k e l y to be s u f f i c i e n t l y s t a b i l i z e d by the matrix i f the "parent" molecule i s l i n e a r . Consequently one has a six-to-one preponderance of bent molecules with a p i c a l angles o f 90° and 120°, over the l i n e a r conformation. These angles are not too d i s s i m i l a r to the value of determined by the i s o t o p i c f i n e s t r u c ture a n a l y s i s p r e v i o u s l y discussed. I t i s a l s o p o s s i b l e that the matrix s t r u c t u r e around a M 3 may deform s l i g h t l y , compromising between argon c r y s t a l s t r a i n and E 3 s t a b i l i t y . This may allow molecules i n 90° and 120° t r i v a c a n c y to assume a more uniform geometry with an a p i c a l angle between 90° and 120°. L i n e a r molecules, i f present a t a l l , would not be d i s c e r n i b l e i n the spectrum because of t h e i r reduced c o n c e n t r a t i o n . Formally M 3 would be expected to have e i t h e r an A or a B ground s t a t e i n the matrix, these being the s t a t e s to which A r e s o l v e s i n C . The e x c i t e d s t a t e which causes the resonance Raman i s l i k e l y of s i m i l a r symmetry, n a t u r a l l y of the same s p i n , and probably o f opposite p a r i t y i n i t s l i n e a r c o r r e l a t e ( i . e . , a Ag s t a t e ) . These conjectures are based on the s i m i l a r i t y i n the frequency of the v i b r a t i o n i n the two s t a t e s . Moreover, the f a c t that a p r o g r e s s i o n i n v i s not seen suggests that the apex angle i s also s i m i l a r i n the two s t a t e s . The molecule i n i t s e x c i t e d s t a t e i s t h e r e f o r e s u b j e c t to the same d i s t o r t i o n s d i s cussed above. S e v e r a l t r a n s i t i o n s ( r e f e r r e d to the l i n e a r parent molecule) are l i k e l y candidates f o r the e x c i t e d s t a t e , among them dTTg -> p*rr , d a -> p a . In each case n e i t h e r the symmetry of the s t a t e n o r the bond strengths which are p r i m a r i l y d e r i v e d from so r b i t a l i n t e r a c t i o n s are s u b s t a n t i a l l y a f f e c t e d .


u

2

2

u

2 v

2

u

g

u


174

METAL

BONDING A N D INTERACTIONS

Acknowledgements We wish to thank NSERC and Imperial O i l f o r f i n a n c i a l support. Discussions with M i c h e l T r a n q u i l l e , Therese Mejean, Robert Lipson and Kathleen Taylor are a l s o g r a t e f u l l y acknowledged. The a s s i s t a n c e of P r o f e s s o r R. J . LeRoy i n performing the c a l c u l a t i o n of the d i s s o c i a t i o n energy of F e i s noted w i t h thanks. 2


Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

vits, 19. 20. 21. 22. 23.

24. 25. 26. 27. 28. 29.

Schulze, W; Becker, H.U. Chem. Phys. L e t t . 1978, 35, 177. B e a t t i e , I.R.; G a l l , M.J. J . Chem. Soc. A 1971, 3569. S e l i g , H.; Claassen, H.H. I s . J. Chem. 1968, 16, 499. K i e f e r , W. Appl. Spectrosc. 1974, 28, 115. D i L e l l a , D.P.; Gohin, A.; Lipson, R.; McBreen, P; Moskovits, M. J . Chem. Phys. 1980, 73, 4282. Moskovits, M.; D i L e l l a , D.P. J . Chem. Phys. 1980, 73, 4917. Lim, S.S.; Kant, A. J . Phys. Chem. 1969, 73, 2450. G i n g e r i c h , K.A. This volume, Chap. 000. LeRoy, R.J.; B e r n s t e i n , R.B. J . Chem. Phys. 1970, 52, 3869; LeRoy, R.J. I b i d . 1980, 73, 6003. LeRoy, R.J. Chem. Phys. L e t t . 1980, 71, 544. Chang, T.Y. Rev. Mod. Phys. 1967, 39, 911. Clementi, E. "Tables o f Atomic Functions," IBM J . Res. Develop. 1965, 9, 2. Montano, P.A. Farad. Symp. Chem. Soc. 1980, 14. Legay, F. "Chemical and B i o l o g i c a l A p p l i c a t i o n s of L a s e r s , " C.B. Moore, ed., Academic, New York, 1977, 2, 43. Ahmed, F.; Nixon, E.R. J . Chem. Phys. 1979, 71, 3547. Cossé, C.; Fouassier, M.; Mejean, T.; T r a n q u i l l e , M.; D i L e l l a , D.P.; Moskovits, M. J . Chem. Phys. 1980, 73, 6076. Cooper, W.F.; Clarke, G.A.; Hare, C.R. J . Phys. Chem. 1972, Ford, T.A.; Huber, H.; Klotzbücher, W.; Kündig, E.P.; Mosko M; Ozin, G.A. J . Chem. Phys. 1977, 66, 524. H a r r i s , J . ; Jones, R.O. J . Chem. Phys. 1979, 70, 830. Anderson, A.B. J . Chem. Phys. 1977, 66, 5108. S i e b e r t , H. "Anwendungen der Schwingungsspektroscopie in der Anorganischen Chemie"; Springer: B e r l i n , 1966. Moskovits, M.; Hulse, J.E. J . Chem. Phys. 1977, 66, 3988. a) Data of Hulse, J.E. Ph.D. Thesis, U n i v e r s i t y M i c r o f i l m s , Ann Arbor, Michigan, 1978. b) DeVore, T.C.; Ewing, A.; Franzen, H.F.; Calder, V. Chem. Phys. Lett. 1975, 35, 78. Gerber, W.H.; Schumacher, E. J . Chem. Phys. 1978, 69, 1692. Lindsay, D.M. This volume, Chap. 000. Moskovits, M.; D i L e l l a , D.P. J . Chem. Phys. 1980, 72, 2267. Jones, L.H. "Inorganic V i b r a t i o n a l Spectroscopy, V o l . 1"; Marcel Dekker: New York, 1971. Anderson, A.B. J . Chem. Phys. 1977, 66, 5108 and 1976, 64, 4046 and p r i v a t e communication. Walch, S.P.; Goddard I I I , W.A. Surf. S c i . 1978, 72, 645.


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30. Herzberg, G. "Molecular Spectra and S t r u c t u r e , V o l . III"; Van Nostrand Reinhold: New York, 1966. 31. Pople, J.A.; Longuet-Higgins, H.C. Mol. Phys. 1958, 1, 372. 32. D r e s s l e r , K.; Ramsey, O.A. J . Chem. Phys. 1957, 27, 971. 33. Merer, A.J.; T r a v i s , O.N. Canad. J . Chem. 1965, 43, 1795.


R E C E I V E D September 21, 1981.


Resonance Raman Spectroscopy of Small Metal Clusters - ACS

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