Optical absorption spectroscopy of sodium clusters as measured by collinear molecular beam photodepletion

P.

 

Foster

,

R.

 

Leckenby

, and

E.

 

Robbins

,  , ();

A.

 

Herrmann

,

S.

 

Leutwyler

,

E.

 

Schumacher

, and

L.

 

Wöste

,  , ();

K.

 

Sattler

,

J.

 

Mühlbach

, and

E.

 

Recknagel

,  , ();

T.

 

Dietz

,

M.

 

Duncan

,

D.

 

Powers

, and

R.

 

Smalley

,  , ();

S.

Riley

,

E.

Parks

,

L.

Pobo

, and

S.

Wexler

, , ().

See, for example,

M.

Kappes

,

M.

Schär

,

P.

Radi

, and

E.

Schumacher

, , ().

See, for example,

A.

Kaldor

,

D.

Cox

, and

M.

Zakin

, , ,

See, for example,

M.

 

Kappes

,

R.

 

Kunz

, and

E.

 

Schumacher

,  , ();

W.

Knight

,

K.

Clemenger

,

W.

de Heer

,

W.

Saunders

,

M.

Chou

, and

M.

Cohen

, , ().

W.

Knight

,

K.

Clemenger

,

W.

de Heer

, and

W.

Saunders

, , ().

J.

 

Gole

,

G.

 

Green

,

S.

 

Pace

, and

D.

 

Preuss

,  , () $(Na3);$

E.

 

Rohlfing

and

J.

 

Valentini

,  , () $(Cu3);$

W.

 

Crumley

,

J.

 

Hayden

, and

J.

 

Gole

,  , () $lpar;Cu3);$

J.

Woodward

,

S.

Cobb

, and

J.

Gole

, , (). $(Ni3).$

P.

 

Cheng

and

M.

 

Duncan

,  , () $(Ag3);$

M.

 

Morse

,

J.

 

Hopkins

,

P.

 

Langridge‐Smith

, and

R.

 

Smalley

,  , (). $(Cu3);$

P. Radi, M. Schär, E. Schumacher, and M. Kappes (to be published) (⁠$LiNa2,$ $Li2Na$⁠);

Z.

 

Fu

,

G.

 

Lemire

,

Y.

 

Hanrick

,

S.

 

Taylor

,

J.

 

Shui

, and

M.

 

Morse

,  , () $(Al3);$

G.

Delacretaz

,

E.

Grant

,

R.

Whetten

,

L.

Wöste

, and

J.

Zwanziger

, () $(Na3).$

D.

 

Leopold

,

J.

 

Ho

, and

W.

 

Lineberger

,  , ();

O. Cheshnovsky, P. Brucat, S. Yang, C. Petiette, M. Craycraft, and R. Smalley, in Physics and Chemistry of Small Clusters, Proceedings of the NATO Advanced Research Workshop, Richmond, 1986, edited by P. Jena, B. Rao, and S. Khanna (Plenum, New York, 1987).

M.

Jarrold

and

K.

Creegan

, , ().

C.

Petiette

,

S.

Yang

,

M.

Craycraft

,

J.

Conceicao

,

R.

Laaksonen

,

O.

Cheshnovsky

, and

R.

Smalley

, , ().

O.

Cheshnovsky

,

K.

Taylor

,

J.

Conceicao

, and

R.

Smalley

, , ().

W.

de Heer

,

K.

Selby

,

V.

Kresin

,

J.

Masui

,

M.

Vollmer

,

A.

Chatelain

, and

W.

Knight

, , ().

K.

Selby

,

M.

Vollmer

,

J.

Masui

,

V.

Kresin

,

W.

de Heer

, and

W.

Knight

, , ().

K.

Selby

,

M.

Vollmer

,

J.

Masui

,

V.

Kresin

,

W.

de Heer

, and

W.

Knight

, , ().

C.

Brechignac

and

P.

Cahuzac

, , ().

K.

McHugh

,

J.

Eaton

,

G.

Lee

,

H.

Sarkas

,

L.

Kider

,

J.

Snodgrass

,

M.

Manaa

, and

K.

Bowen

, , ().

G. Ganteför, M. Gausa, K. Meiwes‐Broer, and H. Lutz, J. Chem. Soc. Faraday Trans. (in press).

M. Jarrold and K. Creegan, J. Chem. Soc. Faraday, Trans. (in press); Int. J. Mass Spec. Ion Phys. (in press).

M. Broyer et al. (to be published).

H.

Fallgren

and

T.

Martin

, , ().

W.

 

Ekardt

,  , ();

W.

Ekardt

, , ().

M.

Puska

,

R.

Nieminen

, and

M.

Manninen

, , ().

C.

Yannouleas

,

R.

Broglia

,

M.

Brack

, and

P.

Bortignon

, , ().

V.

Bonacic‐Koutecky

,

P.

Fantucci

, and

J.

Koutecky

, , ().

V.

Bonacic‐Koutecky

,

P.

Fantucci

, and

J.

Koutecky

, , ().

V. Bonacic‐Koutecky, P. Fantucci, and J. Koutecky, J. Chem. Phys. (this issue).

V. Bonacic‐Koutecky, M. Kappes, G. Fantucci, and J. Koutecky, Chem. Phys. Lett. (in press).

G.

Mie

, , ().

R.

Gans

, , ().

V.

Bonacic‐Koutecky

,

P.

Fantucci

, and

J.

Koutecky

, , ().

C.

Wang

,

S.

Pollack

, and

M.

Kappes

, , ().

Depletion spectroscopy has been extensively applied to cluster studies; see, for example,

M.

 

Vernon

,

J.

 

Lisy

,

H.

 

Kwok

,

D.

 

Krajnovich

,

A.

 

Tramer

,

Y.

 

Shen

, and

Y.

 

Lee

,  , ();

D.

Michael

and

J.

Lisy

, , ().

S.

Pollack

,

C.

Wang

, and

M.

Kappes

, , ().

M.

Kappes

, , ().

M.

Kappes

,

M.

Schär

,

E.

Schumacher

, and

A.

Vayloyan

, , ().

Calculations were performed using the SIMION package. We thank D. Dahl of EG&G Idaho Inc. for providing the software.

This is likely only a poor approximation as cluster densities in monomer expansions are known to be strongly peaked along the beam center line. See, for example, M. Kappes and S. Leutwyler, in Atomic and Molecular Beam Methods, edited by G. Scoles (Oxford University, Oxford, 1989).

Five experiments had to be performed without intermediate window cleaning in order to generate a visible film (⁠$<1016 cm2 s−1$ total atom flux incident on a 250°C sapphire surface for a total of 10 h).

C. Wang, S. Pollack, and M. Kappes (to be published).

M.

Vollmer

,

K.

Selby

,

V.

Kresin

,

J.

Masui

,

M.

Kruger

, and

W.

Knight

, , ().

Collinear irradiation can give rise to a major perturbation of formation processes thus complicating velocity analysis.

D. Miller, in Atomic and Molecular Beam Methods, edited by G. Scoles (Oxford University, Oxford, 1988).

As in the case of depletion measurements, $Na3$ R2PI probes were carried out in a laser fluence range which ensured linearity [i.e., $S(Na3+)αI2].$

V.

Bonacic‐Koutecky

,

P.

Fantucci

, and

J.

Koutecky

, , ().

C.

 

Brechnignac

,

P.

 

Cahuzac

,

J.

 

Roux

,

D.

 

Pavolini

, and

F.

 

Spiegelmann

,  , ();

C.

Brechnignac

,

P.

Cahuzac

, and

J.

Roux

, , ().,

M.

Kappes

,

M.

Schär

,

U.

Röthlisberger

,

C.

Yeretzian

, and

E.

Schumacher

, , ().

J. Steinfeld, J. Francisco, and W. Hase, Chemical Kinetics and Dynamics (Prentice Hall, Englewood Cliffs, 1989).

M.

 

Jarrold

and

J.

 

Bower

,  , ();

U.

 

Ray

,

M.

 

Jarrold

,

J.

 

Bower

, and

J.

 

Kraus

,  , ();

U.

Ray

,

M.

Jarrold

,

J.

Bower

, and

J.

Kraus

, , ().

Temperature sources: $Na3$ from R2PI spectroscopic assignment, see Ref. 52; $Na4$ from Ref. 88, which for similar beam conditions contains a parameterization procedure and analysis for the onset region of photoionization efficiency curves and $Na8$ by comparison to Ref. 64 (see also Ref. 84). The $Na8$ number is also in good agreement with that obtained from Ref. 88. The selection is admittedly somewhat arbitrary but comprises the only methods presently available to obtain temperature information on sodium cluster beams.

C.

Brechignac

,

P.

Cahuzac

,

R.

Pflaum

, and

J.

Roux

, , ().

D.

Lindsay

,

Y.

Wang

, and

T.

George

, , ().

A.

Herrmann

,

M.

Hofmann

,

S.

Leutwyler

,

E.

Schumacher

, and

L.

Wöste

, , ().

M.

 

Broyer

,

G.

 

Delacretaz

,

G.

 

Ni

,

R.

 

Whetten

,

J.

 

Wolf

, and

L.

 

Wöste

,  , ();

M.

Broyer

,

G.

Delacretaz

,

N.

Guoquan

,

J.

Wolf

, and

L.

Wöste

, , ().

M.

Broyer

,

G.

Delacretaz

,

P.

Labastie

,

J.

Wolf

, and

L.

Wöste

, , ().

The $Na3$ C‐state one‐color R2PI measurement appears to show vibrational structure. This is an ion cross‐talk artifact arising from the underlying $Na2$ $X→B$ transition.

G.

 

Jeung

,

M.

 

Broyer

, and

P.

 

Labastie

,  , ().

See, also,

D.

Pavolini

and

F.

Spiegelmann

, , ().

Based on an experimentally determined volume plasmon energy of 5.71 eV. C. Kittel, in Introduction to Solid State Physics, 5th ed. (Wiley, New York, 1976), p. 293. Note that applying the Drude model to measurements of the frequency dependence of the real part of the dielectric constant of bulk sodium gives an $ω0$ of 388 nm. In contrast, using electron densities determined from the Wigner‐Seitz radius, one obtains a Drude $ω0$ of 361 nm.

M.

Broyer

,

G.

Delacretaz

,

P.

Labastie

,

J.

Wolf

, and

L.

Wöste

, , ().

F.

Cocchini

,

T.

Upton

, and

W.

Andreoni

, , ().

T.

Welker

and

T.

Martin

, , ().

M.

Hofmann

,

S.

Leutwyler

, and

W.

Schulze

, , ().

The near‐IR absorption spectrum of sodium vapor is also informative in this regard:

A.

Vasilakis

,

N.

Bhaskar

, and

W.

Happer

, , ().

M. Hoffmann, Ph.D. thesis, University of Bern, Bern, Switzerland, 1980.

J.

Pacheco

and

R.

Broglia

, , ().

This conclusion can also be reached by comparing neutral cluster beam abundance distributions pertaining (Refs. 34, 64, 66, 84, and 88).

W.

de Heer

,

W.

Knight

,

M.

Chou

, and

M.

Cohen

, , ().

R.

 

Martin

and

E.

 

Davidson

,  , ();

J.

Martins

,

R.

Car

, and

J.

Buttet

, , ().

J.

 

Martins

,

J.

 

Buttet

, and

R.

 

Car

,  , ();

J.

Martins

,

J.

Buttet

, and

R.

Car

, , ().

M.

McAdon

, and

W.

Goddard

III, , ().

I.

Boustani

,

W.

Pewestorf

,

P.

Fantucci

,

V.

Bonacic‐Koutecky

, and

J.

Koutecky

, , ().

C.

Gatti

,

P.

Fantucci

, and

G.

Pacchioni

, , ().

B.

Rao

,

S.

Khanna

, and

P.

Jena

, , ().

The same ground state equilibrium topology also results from geometry optimized Car‐Parrinello local density calculations:

U.

Röthlisberger

and

W.

Andreoni

(to be published); see also,

P.

Ballone

,

W.

Andreoni

,

R.

Car

, and

M.

Parrinello

, , ().

J.

Koutecky

and

P.

Fantucci

, , ().

I.

Boustani

, and

J.

Koutecky

, , ().

See, for example,

M.

Smithard

and

M.

Tran

, , ().

W.

Ekardt

and

Z.

Penzar

, , ().

K.

 

Clemenger

,  , ();

K. Clemenger, Ph.D. thesis, University of California at Berkeley, Berkeley, 1986.

J.

Parks

and

S.

McDonald

, , ().

Preliminary photodepletion spectra at about the same signal to noise as those shown here are now being obtained for $Na20.$ It appears that the dominant absorption feature inferred previously to be centered at 490 nm is part of a doublet with the second peak located near 440 nm (Ref. 89).

J.

Osborn

, , ().

J.

Perenboom

,

P.

Wyder

, and

F.

Meier

, , ().

Predicted cross sections are $Na3$ (502 nm: $14.2 Å2;$ 688 nm: $9.7 Å2$⁠); $Na4$ (440 nm: $22.0 Å2;$ 680 nm: $16.9 Å2$⁠) and $Na8$ (478 nm: $30.8 Å2$⁠).

Spheroidally distorted jellium calculations may be used to get a rough potential energy surface (Ref. 78). Spheroidal distortions of metal spheres induce a characteristic surface plasmon splitting (see text). Given the potential surface and assuming a continuous vibrational state density, the thermally averaged optical response may be obtained by integration over the sampling probability (Ref. 64). Resonance widths for $Na8$ have been so determined at temperatures of 50, 150, and 300 K, respectively. Interpolating among these curves, our $Na8$ measurement has a FWHM compatible with an internal temperature of 200 K.

It appears that RPA prediction can be improved by using a potential which is slightly perturbed relative to the jellium mean field. Then the calculation predicts a dominant transition at 2.5 eV, a smaller one at 1.93 eV and a high energy shoulder to the blue of the “surface plasmon” which is similar to that seen in experiment: R. Broglia et al. (to be published).

D.

Mann

and

H.

Broida

, , ().

P.

 

Engelking

,  , ();

P.

Engelking

, , ().,

U. Röthlisberger, Diploma thesis, University of Bern, Bern, 1988;

U.

Röthlisberger

,

M.

Schär

, and

E.

Schumacher

, , ().

C. Wang, S. Pollack, and M. Kappes (to be published).