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ITALIAN PHYSICAL SOCIETY

PROCEEDINGS OF THE INTERNATIONAL SCHOOL OF «ENRICO FERMI»

COURSE CVII

edited by G. SCOLES Director of the Course VARENNA ON LAKE COMO VILLA MONASTERO 28 June - 7 July 1988

The Chemical Physics of Atomic and Molecular Clusters

1990

NORTH-HOLLAND AMSTERDAM - OXFORD - NEW YORK - TOKYO INDICE

G. SCOLES and S. STRINGARI - Preface pag. xvn

Gruppo fotografico dei partecipanti al Corso fuori testo

PART I. - THEORY

R. S. BERRY - Structure and of Clusters: an introduction.

1. What are Clusters? pag. 3 2. Simulations and diagnostics » 8 21 » 8 2*2 T... » 15

R. S. BERRY - Structure and dynamics of Clusters: phase equilibrium and phase change.

1. Solid and liquid Clusters: their equilibrium » 23 ri » 25 1*2 » 27 2. Simulations » 32 2*1 » 32 2*2 » 37 3. The future » 39

J. JORTNER, D. SCHARF, N. BEN-HORIN, U. EVEN and U. LANDMAN - Size effects in Clusters.

Prologue » 43 1. Energetic and thermodynamic size effects » 44 1' 1. Energetic size effects » 44 1*1.1. From to Clusters » 44 1*1.2. From Cluster to bulk Condensed matter » 45 1*2. Isomerization and melting of Clusters » 50 1*3. Experimental interrogation of Cluster isomerization » 58

v VI INDICE

2. Dynamic size effects in electronically excited rare- Clusters pag. 64 2"1. Reactive and nonreactive relaxation » 64 2'2. Application of classical molecular-dynamics method » 67 2'3. Analysis of the molecular-dynamics data » 71 2'3.1. Size analysis » 71 2'3.2. Energetics » 72 2'3.3. Configurational relaxation » 72 2'3.4. Mass transport of electronic excitations » 73 2'4. Computational results » 73 2'4.1. Atomic-impurity excitations in Xe*Ar12 and Xe*Ar54 Clusters » 73 2'4.2. Excimer excitations in Xe|Arn and XefAr53 Clusters ... » 81 2'5. Discussion » 91 2'5.1. Dynamics of atomic-impurity excitations » 91 2'5.2. Dynamics of excimer excitations » 92

F. G. AMAR - A structural approach to the analysis of Cluster dynamics.

PART I - Introduction » 99 PART II - Melting and isomerization of argon Clusters » 100 1. Background » 100 2. Melting loops » 101 3. Isomers of Ar7 » 103 4. and quenching » 104 5. Residence times » 107 6. Lifetime distributions » 111 7. Ar7 melting: summary » 113

PART III - Cooling and dynamic quenching of Ar13 » 113 1. Introduction » 113 2. Brownian dynamics » 114 3. Other quenching techniques » 115 4. Results » 115 5. Conclusions » 119

PART IV - dynamics of Br^ in (C02)TC and Ar„ Clusters » 119 1. Background » 119 2. A model for negative- photodissociation » 120 3. Variable-charge calculation » 123 4. Minimum-energy structures » 124 5. Photoexcitation dynamics of minimum-energy structures » 125 6. Thermal averages » 129 7. Caging fraction » 130 8. Discussion » 131

PART V - Summary » 132 INDICE VII

R. J. LE ROY - Spectra, phase transitions and «dynamical isomeriza- tions» of mixed Van der Waals Clusters.

1. Introduction pag. 137 2. Methodology, potential-energy surface and equilibrium structures .... » 138 3. Simulating the Cluster spectra » 141 4. Dynamical simulations and phase change behaviour » 146 5. Spontaneously reversing isomerization of an isolated SF6-(Ar)9 Cluster » 150 6. Discussion and speculations » 154

W. ANDREONI - The Car-Parrinello method and its application to microclusters.

1. Introduction » 159 2. The Car-Parrinello method » 159 3. Computational procedure » 162 4. Some test examples » 164 5. Some results: structural and finite-7" properties » 167 6. Final remarks » 173

R. KAWAI, I. L. GARZÖN, X. P. LONG and J. H. WEARE - Simulation of metallic and impure van der Waals Clusters.

Introduction » 177 1. Structural and dynamical properties of impure van der Waals Sys­ tems » 178 1" 1. Low-temperature structures » 180 11.1. The A1SB System » 180 1*1.2. The A55B System » 181 1*1.3. The A13B13 system » 182 1*2. The finite-temperature behavior » 182 1*2.1. Heating in the A12B, A1SB and A55ß Systems » 182 1*2.2. Heating in the A1SB13 System » 186 2. Car and Parrinello methods for metallic Clusters » 187

S. STRINGARI - Clusters of quantum liquids.

1. Introduction » 199 2. Bulk and surface properties of 4He and 3He » 200 2*1. Bulk properties » 200 2*2. Surface properties » 203 3. Ground-state properties of helium Clusters » 205 3' 1. The density functional approach » 205 3*2. Ground-state properties of 4He Clusters » 208 VIII INDICE

3'3. Ground-state properties of 3He Clusters pag. 212 3'4. 3He impurities on 4He Clusters » 219 4. Collective excitations in helium Clusters » 223 4' 1. Collective modes in 4He Clusters \ » 223 4' 1.1. Compression modes » 225 4'1.2. Surface excitations » 227 4'2. Collective modes in 3He Clusters » 227 4*2.1. Density excitations » 228 4'2.2. Magnetic excitations » 229 5. Conclusions » 233

X. CAMPI - Fragmentation of Clusters.

1. Introduction » 237 2. Survey of experimental data » 237 2'1. Fragmentation of nuclei » 237 2'2. Fragmentation of atomic Clusters » 244 3. Elements of Cluster fragmentation theory » 248 31. Partitions >» 248 3'2. Geometrical modeis » 250 3'3. Statistical equilibrium » 256 3"4. Rate equation theory » 257 4. Signals of scaling in Cluster fragmentation » 258 4'1. Critical behaviour and critical exponents » 259 4'2. Finite-size scaling » 265 Summary » 266

PART IL - AND PHOTODISSOCIATION

R. 0. WATTS - of large Clusters.

1. Introduction » 271 2. Experimental methods » 272 3. Experimental results » 276 4. Vibrational-spectroscopy theory » 287 5. Semi-classical calculations of band shapes » 299 6. Quantum Simulation » 311 7. Summary » 326

D. J. LEVANDIER, M. MENGEL, J. MCCOMBIE and G. SCOLES - Infrared spectroscopy in and on argon Clusters: matrix and surface spectroscopy in the gas phase.

1. Introduction » 331 2. Experimental background » 332 INDICE IX

3. Clusters as microreactors: complex formation between CH3F and HCl in argon pag. 334 4. The surface of Clusters: a unique environment for spectroscopy and chemical dynamics » 338 5. Clusters and glasses » 345 6. Phase coexistence in Clusters: hot solids and cold liquids » 351 7. Clusters as microsolutions: will the would-be solute be admitted in or left on the surface? » 352

G. DELACRETAZ, P. FAYET, J. P. WOLF and L. WÖSTE - Spectroscopy, reactivity and photodynamics of size-selected metal Clusters.

1. Introduction » 359 2. Spectroscopic approaches to metal Clusters » 359 2' 1. Cluster beam sources for performing spectroscopy » 359 2'2. Eesonant two- ionization and depletion spectroscopy » 363 2'3. As an example: spectroscopy of Na3 » 372 2*3.1. The ground State of Na3 » 372 2'3.2. The 675 nm System (A-state) » 372 2'3.3. The510nmSystem(ß-state) » 373 2'3.4. The560nmSystem(ß'-state) » 374 2'3.5. The 475nm System (C-state) »> 375 2'3.6. The predissociated 420 nm System (D-at&te) » 376 3. Chemical reactions of metal Clusters » 378 3'1. Production of size-selected metal Cluster » 378 3'2. Experimental set-up » 381 3'3. Cluster- reactions » 384 4. Photodynamics of metal Clusters » 389

M. MOSKOVITS - Size-dependent properties in small metal and semiconductor Clusters » 397

W. D. KNIGHT - Structures of metal Clusters.

1. Introduction » 413 2. Shell structure » 414 3. Experimental properties » 419 3'1. Abundance and stability » 419 3'2. Ionization potential » 420 3'3. Static electric polarizability » 422 3'4. Giant dipole resonance » 422 4. Conclusions and future directions » 424

1. X INDICE

T. D. MARK, A. STAMATOVIC, F. HOWORKA, P. SCHEIER and G. WALDER - Interaction between visible laser light and expanding van der Waals Cluster beams.

1. Introduction pag. 427 2. Experimental technique » 428 3. Results » 429 4. Experimental tests » 440 4' 1. Laser power dependence » 440 4'2. Laser wavelength dependence » 443 4'3. Laser focus dependence » 443 4'4. Dependence on irradiation geometry » 444 4'5. Various further tests and observations » 444 5. Analysis (cross-section) and Interpretation (dissociation mechanism) .. » 445

D. RAY, N. E. LEVINGER and W. C. LINEBERGER - Spectroscopy and dynamics of «van der Waals» Cluster ions.

1. Introduction » 451 2. Discussion » 452 2' 1. Experimental method » 452 2'2. Optical absorption in «van der Waals» Cluster ions » 454 2'3. Photodissociation dynamics of «van der Waals» Cluster ions ..... » 457 2'4. in Cluster ions » 461 3. Conclusion » 463

S. T. ARNOLD, J. V. COE, J. G. EATON, C. B. FREIDHOFF, L. KIDDER, G. H. LEE, M. R. MANAA, K. M. MCHUGH, D. PATEL- MISRA, H. W. SARKAS, J. T. SNODGRASS and K. H. BOWEN - Photodetachment spectroscopy of negative Cluster ions.

1. Introduction » 467 2. Experimental » 469 3. Results and discussion » 470 3*1. Ion-molecule complexes: Cluster anions with localized excess negative charges » 470 3'2. More complicated cases: Cluster anions with excess Charge dispersal » 479 3'3. Alkali metal Cluster anions » 484 3'4. Water Cluster anions » 486

C. BRECHIGNAC and PH. CAHUZAC - Excitation of free metal Clusters.

1. Introduction » 491 2. Photoexcitation of alkali Cluster ions » 491 INDICE KI

2*1. Unimolecular dissoeiation following electronic excitation pag. 491 2'1.1. Experimental procedure » 493 2'1.2. Energetic of the unimolecular dissoeiation » 494 2'1.3. Dynamics ofthe unimolecular dissoeiation » 496 2'2. Photoinduced dissoeiation: a probe to follow electronic excitation » 500 3. Photoionization of metal Clusters » 502 3'1. Direct ionization » 503 3'1.1. Charge exchange between Na^" Cluster and Cs : generation of neutral mass-selected Cluster beam » 503 3' 1.2. Photoionization of mass-selected neutral Clusters » 506 3'2. Autoionization process » 507

PART III. - MASS SPECTROSCOPY SCATTERING AND CHEMICAL PROP- ERTIES

G. TORCHET, J. FARGES, M. F. DE FERAUDY and B. RAOULT - diffraction studies of Clusters produced in a free jet expansion. 1. Introduction » 513 2. Experimental methods » 514 2' 1. Cluster beam » 514 2'2. Electron diffraction » 515 2'3. Apparatus » 518 3. Diffraction pattern analysis » 520 3'1. Onset of condensation » 520 3'2. Crystallographic methods » 521 3'2.1. Cluster strueture » 522 3'2.2. Cluster size » 522 3'2.3. Lattice parameter » 523 3'2.4. Lattice dynamics » 524 3'3. Calculated diffraction funetions » 526 3'3.1. Homogeneous modeis » 526 3'3.2. Simulation of Cluster dynamics » 527 3'3.3. Molecular dynamics » 531 4. Size effects in Ar Cluster strueture » 532 4' 1. Diffraction patterns » 532 4'2. Polyicosahedral strueture » 532 4'3. Multilayer icosahedral strueture » 533 4'4. Crystalline strueture » 536 5. Temperature effects in SF6 Clusters » 537 5' 1. Cluster temperature » 537 5'2. Temperature effects in SF6 experiments » 539 5'3. MD Simulation ofthe » 540

U. BuCK - Cluster properties from scattering experiments with atoms. 1. Introduction » 543 2. Scattering analysis and size selection » 545 XII INDICE

21. The method pag. 545 2'2. Experimental results » 547 3. Collisional energy transfer » 550 4. Cluster formation in supersonic expansions » 552 5. Fragmentation by electron impact ionization » 555 6. Infrared photodissociation of size-selected Clusters » 565 6' 1. Experimental method » 565 6'2. Results for ethylene » 567 6'3. Results for methanol » 571 7. Conclusions » 573

L. BENEVENTI, P. CASAVECCHIA, L. YU. RUSIN and G. G. VOLPI - Crossed-molecular-beam experiments on nitric oxide Clusters.

1. Introduction » 579 2. Experimental » 581 3. Scattering analysis » 583 4. Results » 585 4'1. Electron energy dependence of dinier fragmentation » 591 4'2. Beam temperature dependence of (NO)TC Clusters » 591 5. Discussion » 593

J. P. TOENNIES - Helium Clusters.

1. Introduction » 597 2. Mass spectrometer and time-of-flight experiments » 600 3. Scattering of monoenergetic » 605 4. Scattering of atoms and molecules » 611 5. Summary » 615

H. HABERLAND - Solvated-electron Clusters.

Introduction » 619 1. Experiment » 621 l'l. The experimental problem and its Solution » 621 2. Mass spectra » 623 3. Field detachment » 629 4. Photodetachment » 631

M. L. MANDICH - of carbon and Silicon Clusters.

1. Introduction » 635 2. Experimental techniques » 636 INDICE XIII

2'1. Ion cyclotron resonance pag. 636 21.1. Basic principles of ICK » 637 2'1.2. Application of FTICR to studies of Cluster chemistry .... » 643 2" 1.2.1. Getting Clusters into the ion cell » 643 2' 1.2.2. Cluster are trapped to allow for reactions » 649 2' 1.2.3. Obtaining reaction rates and product distribu- tions » 651 2'1.2.4. Distinguishing ground-state reactions » 654 2'2. Selected ion flow tube techniques » 655 2-2.1. Basic principles of SIFT » 655 2'2.2. Determination of rate constants and product distribu- tions using SIFT » 657 3. Carbon Cluster chemistry » 658 3'1. Reactions of positive carbon Cluster ions » 659 3'1.1. Reactivity with smallmolecules: 02, D2and CO » 659 3'1.1.1. Primary reactions » 659 3'1.1.2. Secondary reactions » 664 3'1.1.3. Correlations of Qn reactivity with carbene chemistry » 666 3'1.1.4. Comparison of C„ reactivity with theoretical electronic-structure calculations » 669 3'1.1.5. The special reactivity of C7": evidence for multi­ ple isomers » 674 3'2.1. Reactivity with small hydrocarbons: CH4, C2H2 and C2H4 » 677 3'2.1.1. Reactions with CH4 » 677 3'2.1.2. Reactions of Cs+9 with C2H2 » 679 3'2.1.3. Reactions of Cf0+2o with C2H2 » 681 3"2.1.4. Reactions of C + with C2H4 » 682 4. Silicon Cluster chemistry » 684 4'1. Reactions of small positive and negative Silicon Cluster ions » 685 4'1.1. Systematic trends in the reactions of Silicon Cluster ions .. » 685 4'1.2. Silicon Cluster structure and the nature of possible reactive sites » 689 4'1.3. Chemistry of reactive Silicon centers; lessons from organosilicon chemistry » 692 4*1.3.1. Silylenes » 693 4'1.3.2. Silicon centers (silyls) » 695 4'1.4. Reactions of small Silicon Clusters with N02, XeF2 and 02 » 696 4'1.4.1. N02 » 696 4'1.4.2. XeF2 » 703 - 4 1.4.3. 02 » 707 4'1.5. Reactions of small Silicon Clusters with CH3SiH3 and SiD4 » 710 4-1.5.1. CH3SiH3 » 710 4'1.6. Reactions of small Silicon Clusters with D2, C2H2, NH3, H2OandN20 » 714 4'1.7. Dependence of observed reactivity on Cluster size » 717 4'2. Reactions of large positive Silicon Cluster ions » 719 5. Sequential clustering reactions of Silicon ions with SiD4 » 720 5' 1. Observed reaction sequence starting with Si+ » 721 XIV INDICE

5'2. Theoretically derived reaction mechanisms of clustering se- quence pag. 723 + 5'2.1. Si + SiD4 » 724 + 5'2.2. Si2D2 + SiD4 » 727 - f 5 2.3. Si3D4 + SiD4 » 729 + 5"2.4. Si4D6 + SiD4 » 731 5'3. Phase space model calculations of transition State energies » 732 5'3.1. Application of phase space theory to the reaction of Si+ with SiD4 » 733 53.1.1. Overview » 733 5*3.1.2. Derivation of various reaction probabilities («;) + for *Si + SiD4 reactions » 733 5'3.1.3. Calculation of experimental observables for + *Si + SiD4 reactions » 735 5'3.1.4. Calculation of experimental observables for + f *Si2D2 and *Si3D4 + SiD4 reactions » 738 5'4. Phase space model calculations of Si5Dto complex energy » 742 5'4.1. mechanism » 742 5'4.2. Phase space calculation of the unimolecular dissociation rate, fcD » 743 5'4.3. Calculation of experimentally observed formation rate for Si5Dto » 744 5'5. Comparison of theory and experiment » 746 5'6. Sequential clustering reactions of Si2+7 with SiD4 » 747 5'7. Implications for prenucleation of hydrogenated Silicon particles » 751

E. K. PARKS and S. J. RILEY - Experimental studies of the chemistry of metal Clusters.

1. Introduction » 761 2. Experimental '. » 762 3. Example of measurements of Cluster chemical properties » 767 4. Conclusion » 776

A. J. ST ACE - The unimolecular fragmentation of ion Clusters.

1. Introduction » 779 2. Experimental considerations » 781 3. Ion Cluster fragmentation processes » 784 3'1. The unimolecular decay of X^ Clusters » 784 3'2. Intermolecular ion-molecule reactions in X£ Clusters » 786 3'3. Unimolecular fragmentation of molecular ions in association with inert-gas Clusters » 788 3'3.1. Excitation » 788 3'3.2. Fragmentation » 790 3'3.3. Position of the molecular ions with respect to the inert­ gas component » 791 4. Conclusion » 794 INDICE XV

N. NiSHl and K. YAMAMOTO - Molecular Clusters isolated from aqueous Solutions by adiabatic expansion of liquid jets: a new approach for molecular association in Solutions.

1. Introduction pag. 797 2. Apparatus >» 798 3. Nozzle to skimmer distance » 800 4. Stochastic solute concentration in Clusters » 801 5. Dissociation and evaporation of molecules on electron impact ionization » 802 6. Association-dissociation equilibriumofhydrate Clusters in Solution .... » 803 7. Ethanol chain formation assisted by water » 806 8. Hydrophobie hydration and hydrophilic hydration » 810 9. Summary » 813