- Email: [email protected]
Coupling between intramolecular and intermolecular nuclear motion in a large van der waals complex
Volume
117, number
6
CHEMICAL
PHYSICS
COUPLlNG BETWEEN INTRAMOLECULAR IN A LARGE VAN DER WAALS COMPLEX Dar BAHATT, Department
Recewed
Uzi EVEN
t# Cfremrrtsy, Tel-Auru
19 March 1985;
and Joshua Unroersiiy,
5 July 1985
LE?ITERs
AND
INTERMOLECULAR
NUCLEAR
MOTION
JORTNER
69978
Tel Auru. Israel
m final form 27 April 1985
The vibralronal level swucture of the S, --+ S, transtlton of lrans-slilbene-Ar, was inierrogaled by mass-resolved resonance kvtFpholon ionization speclroscopy in supersonic beams. CombinaGon bands provide evidence for inxermode couphng between rhe vibrational excilation of the relative molion of Ar and trans-rrilbene (TS) m TS Ar and an inlramolerxlar vibration of 7% which is manifesled by the linear dependence of the intermolecular wbralional energy on the vIbrational quanlum number of Ihe innamolecular motion.
Electronic-vrbrational spectra of large van der Waals (vdW) complexes [ 1,2], consisting of aromatic molecules bound to atomic or molecular ligands, reveal two major types of vibrational modes. (A) Intramolecular vlbration~ modes of the aromatic molecule in the complex [l-7], and (9) intermolecular vibrational modes, which mvolve the motion of the ligand relative to the large molecule [ 1,2,7,8]. The intermolecular modes can be segregated further into: (Bl) perpendicular intermolecular modes involving out-of-plane motion of the ligand relative to the organic molecule [2,7-l I] _ Typical vibrational frequenaes for rare-gas aromatic-molecule complexes were documented experimentally to lie in the range 0 zs 3050 cm-1 [ 1,2,7-l 01. (B2) Parallel mtermolecular modes involving in-plane motion of the ligand with respect to the organic molecule 181. Vibrational frequencies of these modes were calculated to lie in the range 0 = l-1 0 cm-l [9]. These intermoIecuIar modes are of considerable interest in providing an analog for surface vibrational motion in a finite system and in constituting the precursors of phonon modes in condensed phases--A reasonable starting point for the undirstanding of the nuclear motion within large vdW complexes is based on the segregation between intramolecular and intermolecular vibrational modes [7,8J. A heuristic lustfication for such an approach rests on the separation of time scales 0 GG9-2614/85/S 03.30 0 ELsevier Science Publishers B-V. (North-Holland Physics Publishing Division)
for the two distinct types of motion, which are characterzed by a small frequency ratio u(intermolecular)/ u(intramolecular) = 0.001-0.05. Nevertheless, the coupling between mtermolecular and intramolecular motion in large vdW complexes is pertinent for the elucidation of the energetics, i.e the vlbrationaf level structure, and the dynamics, e.g., vibratIonal energy redistribution, in these systems. In this note, we report on the observation of the manifestations of the couplmg between intramolecuIar and intermolecular nuclear motion in 2 large vdW complex. We have explored the elec~o~c-~bration~ spectroscopy of the S, + S, transitxon of the trans-stilbene (TS)-Ar complex interrogated by mass-resolved resonance twophoton ionization (R2Pl) [7,1 l-131. The vibrational level structure of TSsAr, in its S, state exhibits intramolecular vibrations of TS and pe~endicular mtermoleuclar At-TS modes The combination bands, which involve both types of vibration, reveal systematic deviations from additivity, exhibiting the manifestations of the coupling between intermolecular and intramolecular motion in the large vdW complex. The TS-Are-vdW ions were produced by R2PI of the corresponding vdW molecules in supersonic beams and interrogated_ by tune-of-flight mass sptctrometry. TS was heated in the nozzle chamber to 150°C (partial vapour pressure 7 Torr) [ 143, seeded into Ar (stagna527
CHEMICAL PHYSICS IXITERS
Volume 117, number6
tion pressure p = l-2 atm) and expanded by a magnetic pulsed valve (gas pulse length of 200 ps, pulse frequency 10 Hz) through a conical nozzle (nozzle diameter D = 0.3 mm, nozzle opening angle B = 300)_ The use of conical nozzles considerably enhances clustering in the supersonrc expansion [ 153 - The central core of the jet was skimmed by a nickel electroplated copper skimmer (diameter 1 r-run).Light from a frequen~y-doubled N2 laser pumped dye laser (spectral range 2800-3200 Isi, puise duration 4 ns, peak power output 2 pJ/puXse, spectral wdth 03 cm-l) was focused by anf= 7 cm lens onto the molecular beam at the ian source of the t~e~f-~~t mass spectrometer (TOFMS). The total ion accelerating voltages employed in these experiments were 800 V_ The accelerated eons were passed through the drrft tube (length 249 mm) and interrogated by a fast ion detection scheme. This consists of a large-aperture highvoltage (30 kV) detector generatrng free electrons, which are detected by a plastic scint.iUator (Light pulse wzdth 2-S its in the range 4ICIO-4300 ii, in ~o~ju~ctio~ with a photomultiplier Phillips XP2020)- The photomultiplier signal was fed to a boxcar integrator (Brookdeal), which recorded the appropriate mass (TS+, m/e = 180 or TS-AZ+; m/e = 220). The R2PI ion signal was averaged by a signal averager (PAR) and
I
5 July 1985
diplayed after normalization to the square of the incadent laser intensity. The mass-resolved R2PI spectrum for the low-energy regime (excess vibratronal energy EV = O-500 cm-l) of the Sg 4 S1 transition of TS is portrayed in fig. 1. The electronic origin of So + SI is located at 3102.8 jsi (32229 cm-l), which is in accord with the original fluorescence excitation spectra [ 161. The bare-molecule spectrum exhibits weak hot bands at 25 and 38 cm-l and low-frequency vibrations at SO and 89 cmWX, which 1sin good agreement with the previous laser-induced fluorescence (LIF) spectra [ 163 _ The 8G and 89 cm-I modes correspond, according to Warshei f 173, to out-of-plane C--@ bending and C-C--@ bending, respectively. The prominent vibrational mode in the S, state of TS involves the well known [ 163 o. = 200 cm-1 progression, which corresponds to the C-C-4 k-plane bending [ 171. The mass-resolved FZ2PI spectrum of TS -AX (fig- 2) reveals the electronic origm of the So + S, transition at 3 108 4 w (3217 1 cm-l)_ The red dxspersxve spectraI shift Av = -58 + 5 cm-l of the SO -+ SI electronic origm of TS mduced by the binding of an Ar atom is similar to those observed for the ori@ of intense spur-allowed transrtions in other aromatic molecules, e.g., ana.line [ZJ, fl uorene 13J, anthracene [18] and
I
I
I
TRANS-STILBENE
I
0
d 110 WAVELENGTH
6,
Fig i. Ion murent versuswavelengthin the range 3060-3110 A for tmns-Mbene”. X%ans-stilbeneat 150°C wti seeded info Ar at p = 2 atm and expanded through a pulsed co&al nozzle (D = 0.3 mm, B = 30”). The electronic orI& is marked O--Oand the ntibers labe&ngthe spectralfeatures mark the excess vibrationalenewes ahve the [email protected](in cm-l). 528
Volume 117, numbex6
CHEMiCAL
PHYSICS
5 July 1985
LEZ’J-l%=
37 cm-1 -
27 cm- 1 TRANS-STILBENE
Ar
3 WAVELENGTH& Fig. 2. Ion currentversuswavelengthm the range 3060-3110 A for trans-stilbene*Ar?Upenmental conditionsand labeling of spectralfeaturesasin f=. 1_ tetracene [ 1 ] _ The vibrational level structure of TS-AI reveals two types of vrbrations’ (A) Intramolecular vibrations. An mtense progression wrth the frequency W. = 194 cm-1 is exhibited (fig. 2), which is attributed to the intramolecular symmetric C-C-+ in-plane bendmg of TS in the TS-Ar complex. (B) Intermolecular vibrations. The spectra.l feature -l in TS-Ar (fig. 2) is absent in the bare atEV=27cm TS molecule. The intensity of this spectral feature relative to the electronic origin of TS -Ar is independent of the A.r stagnation pressure, whereupon it does not correspond to a hot band of TS in the complex. The spectrdi feature is attributed to an interrnolecul;tr vibrational frequency of Gt = 27 cm-l _Model calculations [2,10] for the benzene -AI vdW complex reveal that the frequency of the perpendicular vibrational motion of Arrelative to the benzene ring is ~30 cm-l_ Accordingly, we attribute the ZJ = 27 cm-1 mode in TS-Ar to the out-of-plane perpendicular motion of the Ar atom with respect to the benzene ring of TS. (C) Combination bands. The vibrational excitations at 227 and 423 cm- 1 (fig- 2) are assigned to combmation (uGO + Gl) bands of Go and &I modes, which corre~ond to Go + 33 em-l (+l cm-L) and to 20~ + 37 cm-l (+l cm-l), respectively.
The most interesting feature of the vibrational level structure of TS-Ar in the S, state is the appearance of the (perpendicular) intermolecular vibration, which exhibits a systematic dependence on the intramolecular vrbrational excitation @GO), being &J = 27 cm-l foru=O,O=l = 33 cm-l for u = 1, and is, = 37 cm-l for IJ= 2. We attribute this nearly linear dependence of GJ for u to rhe effects of inter-mode coupling in a vdW complex. This experimental result IS in accord with the recent theoretical calculations of Sage and Jortner [ 191, who considered the coupling between intermolecular and intramolecular vibrations in alarge vdW complex. This treatment rests on the ~n~deration of the coupled equations restdtmg from the expansion of the t&I vrbrationai wavefunction in terms of the “free”-molecule wavefunctions. Application of van Vleck’s perturbation theory results in explicit Grstorder and secondsrder kinetic energy and potential energy corrections, which incorporate the energetic shift of the intramolecular vibration, as well as the intermolecular vibrational energies, which depend on the vibra-tional quantum numbers OF the intramolecular modes. Consideration of intermode coupling h a simple model system consisting of a single harmonic ~~o~ecul~ mode coupled to an ~termolec~~ mode results in the energy levels [I9 1. 529
Volume
E “,
=
ufiwO
+ Irrq
PHYSICS
CHEMICAL
117, number 6
(1 + u6) )
(1)
u and I are the vIbrationa quantum numbers for the intramolecular and intermolecular modes, respectively. +, is the mtramolecular vibrational frequency in the complex, which is related to the “free” molecule vibrational energy w. via tjo = o. (1 + a), where the “solvent shift” a origrnates from kinetrc energy and potential energy contributions, which are due to the modrficatron of the mtramolecular force field by vdW binding. Wr is the vibrational frequency of the rntermolecular motion for u = 0, while 6 = with 7 being the potential energy (~fi ~O/g&-,~l), contribution for the inter-mode coupling and k, the force constant for the intramolecular vibration From eq. (1) it 1s apparent that the spectral shift of the intramolecular vrbrational frequency relative to that of the “free” molecule is constant, while the energy shiFt of the combination band ~2, involving the intermolecular mode relative to ~0, is linear in u. From the apphcation of eq. (1) for the analysis of our experimental data (fig. 2), we conclude that:
where
(1)
The intramolecular
bending
vibration
the “free” plex.
molecule
Accordingly,
symmetric
is reduced to W.
from
C-C+
w.
= 194 cm-l
the contribution
in-plane
= 200 cm-1
and
10e2_ The spectral shift (G,-, - w,,) is ind ependent of u, as IS expected(2) The linear dependence of the experimental intermolecular frequency on u is in accord with the relation fZ1 = O,(l + OS), eq. (1). The inter-mode coupling term is 6 = 0.2. This large value of 6 crigmates from the low vaIue of o. (or rather ko) and presumably
potential
energy
terms
IS a = -3.1
X
also from the effective inter-mode coupling for that particular intramolecular mode. A cursory examination of the R2PI spectra of TS and TS - AI reveals that the 80 and 89 cm-1 vibrational frequencies of TS (fig_ 1) are missing in the TS -Ar spectrum (fig. 2). This behaviour is in sharp contrast with the prominence of the Wo mode (fig. 2) The “disappearance” of the S, 80 and 89 cm-1 vibrational excitations in the R2PI spectrum can be blamed on one of the following reactive processes: (i) Vibrational predissociation (VP) of TS-Ar in the SI intermediate state. (ii) VP of the vibrational excited positive vdW TS -AI+ ion. Mechanism (i) is inapplicable for the problem at hand as the vibrational excrtations (8090 cm-l) in the S, state are considerably lower than 530
S.July 1985
the dissociation energy of the TS - Ar vdW complex, which is estimated [ZJO] to be D x 400 cm-l, whereupon the VP channel is closed in the intermediate S, state. On the other hand, the VP channel is open in the final ionic state. The adiabatic ronization potential of TS is 7.75 eV [20], whereupon the excess vibrational energy of TS - Ar+ produced vra R2PL by two 3095 A photons 1s 2250 cm-l, being sufficient for dissociation The “disappearance” of the 80 and 89 cm-l modes (which will heremafter be referred to as the Q modes) together with persistence of the iugher energy w. = 194 cm-l mode in the R2PI spectrum, raises the distinct possibility of mode selective VP of the TS.Ar+ ion, which was excited photoselectively to an cyvibrational state from an Sl(cr) intermediate level. Further work is bemg conducted for a cntical scrutmy of this conjecture_
This research was supported in part by the United States Army through its European Research Office.
References
in
in the com-
of the kinetic
LETTERS
111 A. Amirav. U. Even and J. Joriner, J. Chem. Phys 75 (1981)
2489.
I21 U. Even, k Ambav, S. Leutwyler. M.L On&e&en, PI 141
ISI I61 [71 PI 191 1101 1111 1121 [W [ 141
Z. Berkovitch-Yelbn and J. Jortner, Faraday Discussions Chem. Sot. 73 (1982) 153_ A. Amirav, U. Even and J. Jortner, Chem. Phys_ 67 (1982) 1. A. Amirav, U. Even and J. Jortner, J. Phys Chem. 85 (1981) 309. A. Amirav. U. Even and J. Jortner, J_ Chem. Phys. 74 (1981) 3475. U. Even and J. Jortuer. J. Chem. Phys_ 78 (1983) 3445. S. Leutwyler. U. Even and J_ Jorfner, J Chem. Phyr 79 (1983) 5769. U. Even and J. Jomer, Faraday Discusnons Chem. sot. 73 (1982) 175. S Leutwyler, k Schmelzer and N Meyer, J. Chem. Phys 79 (1983) 5769. M J. Ondrechen. Z. Berkovitch-YelLin and J. Jortner, J. Am. Chem. Sot. 103 (1981) 6586. J.B. Hopkins, D-E. Powers and R.E. Smalley, J. Phyr Chem. 85 (1981) 3739. F-H. Fug. W-E. He&e. T.R Hays, H-L. Selzle and E-W- Schlag. J. Phys. Che+ 85 (1981) 3560: S. Leutwyler, U. Even and J. Jortner, Chem. Phyg Letters 86 (1982) 439. RC. Weast, ed, Handbook of chemisky and physics (CRC Press. Cleveland; 1976)..
Volume 117. number 6
CHEMICAL’PHYSICS
[ 151 D. Bahatt. U. Even and J. Jortner, to be pubkbeb 1161 J. Synge, W. Lambert, P. Felker, A&f. Zewail and R&L Hochstrasser. Chem. Phys Letters 88 (1982) 266; A. Amirav and J. Jorlner. Chem. Phyr Letters 95 (1983) 295; T-S. Zwier, E. CarrasquiJlo and D.H. Levy, J. Chem. Phys. 78 (1983) 5493;
LETTERS
[17] [la] [19] [20]
5 July 19Bs
TJ. Majors, U. Even and J. Jotier, J. Chern. Phys. 81 (1984) 2330. A Warshel, J. Chem. Phys. 62 (1975) 214. k Amkav, M. Sonnenschem and J. Jortner, Chem. Phyr 8B (1984) 199. M. Sage and J. Jorbxr, to be published_ W-C Hemdon, J. Am. Chern Sot. 98 (1976) 687.
531
117, number
6
CHEMICAL
PHYSICS
COUPLlNG BETWEEN INTRAMOLECULAR IN A LARGE VAN DER WAALS COMPLEX Dar BAHATT, Department
Recewed
Uzi EVEN
t# Cfremrrtsy, Tel-Auru
19 March 1985;
and Joshua Unroersiiy,
5 July 1985
LE?ITERs
AND
INTERMOLECULAR
NUCLEAR
MOTION
JORTNER
69978
Tel Auru. Israel
m final form 27 April 1985
The vibralronal level swucture of the S, --+ S, transtlton of lrans-slilbene-Ar, was inierrogaled by mass-resolved resonance kvtFpholon ionization speclroscopy in supersonic beams. CombinaGon bands provide evidence for inxermode couphng between rhe vibrational excilation of the relative molion of Ar and trans-rrilbene (TS) m TS Ar and an inlramolerxlar vibration of 7% which is manifesled by the linear dependence of the intermolecular wbralional energy on the vIbrational quanlum number of Ihe innamolecular motion.
Electronic-vrbrational spectra of large van der Waals (vdW) complexes [ 1,2], consisting of aromatic molecules bound to atomic or molecular ligands, reveal two major types of vibrational modes. (A) Intramolecular vlbration~ modes of the aromatic molecule in the complex [l-7], and (9) intermolecular vibrational modes, which mvolve the motion of the ligand relative to the large molecule [ 1,2,7,8]. The intermolecular modes can be segregated further into: (Bl) perpendicular intermolecular modes involving out-of-plane motion of the ligand relative to the organic molecule [2,7-l I] _ Typical vibrational frequenaes for rare-gas aromatic-molecule complexes were documented experimentally to lie in the range 0 zs 3050 cm-1 [ 1,2,7-l 01. (B2) Parallel mtermolecular modes involving in-plane motion of the ligand with respect to the organic molecule 181. Vibrational frequencies of these modes were calculated to lie in the range 0 = l-1 0 cm-l [9]. These intermoIecuIar modes are of considerable interest in providing an analog for surface vibrational motion in a finite system and in constituting the precursors of phonon modes in condensed phases--A reasonable starting point for the undirstanding of the nuclear motion within large vdW complexes is based on the segregation between intramolecular and intermolecular vibrational modes [7,8J. A heuristic lustfication for such an approach rests on the separation of time scales 0 GG9-2614/85/S 03.30 0 ELsevier Science Publishers B-V. (North-Holland Physics Publishing Division)
for the two distinct types of motion, which are characterzed by a small frequency ratio u(intermolecular)/ u(intramolecular) = 0.001-0.05. Nevertheless, the coupling between mtermolecular and intramolecular motion in large vdW complexes is pertinent for the elucidation of the energetics, i.e the vlbrationaf level structure, and the dynamics, e.g., vibratIonal energy redistribution, in these systems. In this note, we report on the observation of the manifestations of the couplmg between intramolecuIar and intermolecular nuclear motion in 2 large vdW complex. We have explored the elec~o~c-~bration~ spectroscopy of the S, + S, transitxon of the trans-stilbene (TS)-Ar complex interrogated by mass-resolved resonance twophoton ionization (R2Pl) [7,1 l-131. The vibrational level structure of TSsAr, in its S, state exhibits intramolecular vibrations of TS and pe~endicular mtermoleuclar At-TS modes The combination bands, which involve both types of vibration, reveal systematic deviations from additivity, exhibiting the manifestations of the coupling between intermolecular and intramolecular motion in the large vdW complex. The TS-Are-vdW ions were produced by R2PI of the corresponding vdW molecules in supersonic beams and interrogated_ by tune-of-flight mass sptctrometry. TS was heated in the nozzle chamber to 150°C (partial vapour pressure 7 Torr) [ 143, seeded into Ar (stagna527
CHEMICAL PHYSICS IXITERS
Volume 117, number6
tion pressure p = l-2 atm) and expanded by a magnetic pulsed valve (gas pulse length of 200 ps, pulse frequency 10 Hz) through a conical nozzle (nozzle diameter D = 0.3 mm, nozzle opening angle B = 300)_ The use of conical nozzles considerably enhances clustering in the supersonrc expansion [ 153 - The central core of the jet was skimmed by a nickel electroplated copper skimmer (diameter 1 r-run).Light from a frequen~y-doubled N2 laser pumped dye laser (spectral range 2800-3200 Isi, puise duration 4 ns, peak power output 2 pJ/puXse, spectral wdth 03 cm-l) was focused by anf= 7 cm lens onto the molecular beam at the ian source of the t~e~f-~~t mass spectrometer (TOFMS). The total ion accelerating voltages employed in these experiments were 800 V_ The accelerated eons were passed through the drrft tube (length 249 mm) and interrogated by a fast ion detection scheme. This consists of a large-aperture highvoltage (30 kV) detector generatrng free electrons, which are detected by a plastic scint.iUator (Light pulse wzdth 2-S its in the range 4ICIO-4300 ii, in ~o~ju~ctio~ with a photomultiplier Phillips XP2020)- The photomultiplier signal was fed to a boxcar integrator (Brookdeal), which recorded the appropriate mass (TS+, m/e = 180 or TS-AZ+; m/e = 220). The R2PI ion signal was averaged by a signal averager (PAR) and
I
5 July 1985
diplayed after normalization to the square of the incadent laser intensity. The mass-resolved R2PI spectrum for the low-energy regime (excess vibratronal energy EV = O-500 cm-l) of the Sg 4 S1 transition of TS is portrayed in fig. 1. The electronic origin of So + SI is located at 3102.8 jsi (32229 cm-l), which is in accord with the original fluorescence excitation spectra [ 161. The bare-molecule spectrum exhibits weak hot bands at 25 and 38 cm-l and low-frequency vibrations at SO and 89 cmWX, which 1sin good agreement with the previous laser-induced fluorescence (LIF) spectra [ 163 _ The 8G and 89 cm-I modes correspond, according to Warshei f 173, to out-of-plane C--@ bending and C-C--@ bending, respectively. The prominent vibrational mode in the S, state of TS involves the well known [ 163 o. = 200 cm-1 progression, which corresponds to the C-C-4 k-plane bending [ 171. The mass-resolved FZ2PI spectrum of TS -AX (fig- 2) reveals the electronic origm of the So + S, transition at 3 108 4 w (3217 1 cm-l)_ The red dxspersxve spectraI shift Av = -58 + 5 cm-l of the SO -+ SI electronic origm of TS mduced by the binding of an Ar atom is similar to those observed for the ori@ of intense spur-allowed transrtions in other aromatic molecules, e.g., ana.line [ZJ, fl uorene 13J, anthracene [18] and
I
I
I
TRANS-STILBENE
I
0
d 110 WAVELENGTH
6,
Fig i. Ion murent versuswavelengthin the range 3060-3110 A for tmns-Mbene”. X%ans-stilbeneat 150°C wti seeded info Ar at p = 2 atm and expanded through a pulsed co&al nozzle (D = 0.3 mm, B = 30”). The electronic orI& is marked O--Oand the ntibers labe&ngthe spectralfeatures mark the excess vibrationalenewes ahve the [email protected](in cm-l). 528
Volume 117, numbex6
CHEMiCAL
PHYSICS
5 July 1985
LEZ’J-l%=
37 cm-1 -
27 cm- 1 TRANS-STILBENE
Ar
3 WAVELENGTH& Fig. 2. Ion currentversuswavelengthm the range 3060-3110 A for trans-stilbene*Ar?Upenmental conditionsand labeling of spectralfeaturesasin f=. 1_ tetracene [ 1 ] _ The vibrational level structure of TS-AI reveals two types of vrbrations’ (A) Intramolecular vibrations. An mtense progression wrth the frequency W. = 194 cm-1 is exhibited (fig. 2), which is attributed to the intramolecular symmetric C-C-+ in-plane bendmg of TS in the TS-Ar complex. (B) Intermolecular vibrations. The spectra.l feature -l in TS-Ar (fig. 2) is absent in the bare atEV=27cm TS molecule. The intensity of this spectral feature relative to the electronic origin of TS -Ar is independent of the A.r stagnation pressure, whereupon it does not correspond to a hot band of TS in the complex. The spectrdi feature is attributed to an interrnolecul;tr vibrational frequency of Gt = 27 cm-l _Model calculations [2,10] for the benzene -AI vdW complex reveal that the frequency of the perpendicular vibrational motion of Arrelative to the benzene ring is ~30 cm-l_ Accordingly, we attribute the ZJ = 27 cm-1 mode in TS-Ar to the out-of-plane perpendicular motion of the Ar atom with respect to the benzene ring of TS. (C) Combination bands. The vibrational excitations at 227 and 423 cm- 1 (fig- 2) are assigned to combmation (uGO + Gl) bands of Go and &I modes, which corre~ond to Go + 33 em-l (+l cm-L) and to 20~ + 37 cm-l (+l cm-l), respectively.
The most interesting feature of the vibrational level structure of TS-Ar in the S, state is the appearance of the (perpendicular) intermolecular vibration, which exhibits a systematic dependence on the intramolecular vrbrational excitation @GO), being &J = 27 cm-l foru=O,O=l = 33 cm-l for u = 1, and is, = 37 cm-l for IJ= 2. We attribute this nearly linear dependence of GJ for u to rhe effects of inter-mode coupling in a vdW complex. This experimental result IS in accord with the recent theoretical calculations of Sage and Jortner [ 191, who considered the coupling between intermolecular and intramolecular vibrations in alarge vdW complex. This treatment rests on the ~n~deration of the coupled equations restdtmg from the expansion of the t&I vrbrationai wavefunction in terms of the “free”-molecule wavefunctions. Application of van Vleck’s perturbation theory results in explicit Grstorder and secondsrder kinetic energy and potential energy corrections, which incorporate the energetic shift of the intramolecular vibration, as well as the intermolecular vibrational energies, which depend on the vibra-tional quantum numbers OF the intramolecular modes. Consideration of intermode coupling h a simple model system consisting of a single harmonic ~~o~ecul~ mode coupled to an ~termolec~~ mode results in the energy levels [I9 1. 529
Volume
E “,
=
ufiwO
+ Irrq
PHYSICS
CHEMICAL
117, number 6
(1 + u6) )
(1)
u and I are the vIbrationa quantum numbers for the intramolecular and intermolecular modes, respectively. +, is the mtramolecular vibrational frequency in the complex, which is related to the “free” molecule vibrational energy w. via tjo = o. (1 + a), where the “solvent shift” a origrnates from kinetrc energy and potential energy contributions, which are due to the modrficatron of the mtramolecular force field by vdW binding. Wr is the vibrational frequency of the rntermolecular motion for u = 0, while 6 = with 7 being the potential energy (~fi ~O/g&-,~l), contribution for the inter-mode coupling and k, the force constant for the intramolecular vibration From eq. (1) it 1s apparent that the spectral shift of the intramolecular vrbrational frequency relative to that of the “free” molecule is constant, while the energy shiFt of the combination band ~2, involving the intermolecular mode relative to ~0, is linear in u. From the apphcation of eq. (1) for the analysis of our experimental data (fig. 2), we conclude that:
where
(1)
The intramolecular
bending
vibration
the “free” plex.
molecule
Accordingly,
symmetric
is reduced to W.
from
C-C+
w.
= 194 cm-l
the contribution
in-plane
= 200 cm-1
and
10e2_ The spectral shift (G,-, - w,,) is ind ependent of u, as IS expected(2) The linear dependence of the experimental intermolecular frequency on u is in accord with the relation fZ1 = O,(l + OS), eq. (1). The inter-mode coupling term is 6 = 0.2. This large value of 6 crigmates from the low vaIue of o. (or rather ko) and presumably
potential
energy
terms
IS a = -3.1
X
also from the effective inter-mode coupling for that particular intramolecular mode. A cursory examination of the R2PI spectra of TS and TS - AI reveals that the 80 and 89 cm-1 vibrational frequencies of TS (fig_ 1) are missing in the TS -Ar spectrum (fig. 2). This behaviour is in sharp contrast with the prominence of the Wo mode (fig. 2) The “disappearance” of the S, 80 and 89 cm-1 vibrational excitations in the R2PI spectrum can be blamed on one of the following reactive processes: (i) Vibrational predissociation (VP) of TS-Ar in the SI intermediate state. (ii) VP of the vibrational excited positive vdW TS -AI+ ion. Mechanism (i) is inapplicable for the problem at hand as the vibrational excrtations (8090 cm-l) in the S, state are considerably lower than 530
S.July 1985
the dissociation energy of the TS - Ar vdW complex, which is estimated [ZJO] to be D x 400 cm-l, whereupon the VP channel is closed in the intermediate S, state. On the other hand, the VP channel is open in the final ionic state. The adiabatic ronization potential of TS is 7.75 eV [20], whereupon the excess vibrational energy of TS - Ar+ produced vra R2PL by two 3095 A photons 1s 2250 cm-l, being sufficient for dissociation The “disappearance” of the 80 and 89 cm-l modes (which will heremafter be referred to as the Q modes) together with persistence of the iugher energy w. = 194 cm-l mode in the R2PI spectrum, raises the distinct possibility of mode selective VP of the TS.Ar+ ion, which was excited photoselectively to an cyvibrational state from an Sl(cr) intermediate level. Further work is bemg conducted for a cntical scrutmy of this conjecture_
This research was supported in part by the United States Army through its European Research Office.
References
in
in the com-
of the kinetic
LETTERS
111 A. Amirav. U. Even and J. Joriner, J. Chem. Phys 75 (1981)
2489.
I21 U. Even, k Ambav, S. Leutwyler. M.L On&e&en, PI 141
ISI I61 [71 PI 191 1101 1111 1121 [W [ 141
Z. Berkovitch-Yelbn and J. Jortner, Faraday Discussions Chem. Sot. 73 (1982) 153_ A. Amirav, U. Even and J. Jortner, Chem. Phys_ 67 (1982) 1. A. Amirav, U. Even and J. Jortner, J. Phys Chem. 85 (1981) 309. A. Amirav. U. Even and J. Jortner, J_ Chem. Phys. 74 (1981) 3475. U. Even and J. Jortuer. J. Chem. Phys_ 78 (1983) 3445. S. Leutwyler. U. Even and J_ Jorfner, J Chem. Phyr 79 (1983) 5769. U. Even and J. Jomer, Faraday Discusnons Chem. sot. 73 (1982) 175. S Leutwyler, k Schmelzer and N Meyer, J. Chem. Phys 79 (1983) 5769. M J. Ondrechen. Z. Berkovitch-YelLin and J. Jortner, J. Am. Chem. Sot. 103 (1981) 6586. J.B. Hopkins, D-E. Powers and R.E. Smalley, J. Phyr Chem. 85 (1981) 3739. F-H. Fug. W-E. He&e. T.R Hays, H-L. Selzle and E-W- Schlag. J. Phys. Che+ 85 (1981) 3560: S. Leutwyler, U. Even and J. Jortner, Chem. Phyg Letters 86 (1982) 439. RC. Weast, ed, Handbook of chemisky and physics (CRC Press. Cleveland; 1976)..
Volume 117. number 6
CHEMICAL’PHYSICS
[ 151 D. Bahatt. U. Even and J. Jortner, to be pubkbeb 1161 J. Synge, W. Lambert, P. Felker, A&f. Zewail and R&L Hochstrasser. Chem. Phys Letters 88 (1982) 266; A. Amirav and J. Jorlner. Chem. Phyr Letters 95 (1983) 295; T-S. Zwier, E. CarrasquiJlo and D.H. Levy, J. Chem. Phys. 78 (1983) 5493;
LETTERS
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5 July 19Bs
TJ. Majors, U. Even and J. Jotier, J. Chern. Phys. 81 (1984) 2330. A Warshel, J. Chem. Phys. 62 (1975) 214. k Amkav, M. Sonnenschem and J. Jortner, Chem. Phyr 8B (1984) 199. M. Sage and J. Jorbxr, to be published_ W-C Hemdon, J. Am. Chern Sot. 98 (1976) 687.
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