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Communications to the Editor
be positive. If intramolecular Coulomb repulsions are assumed to be greater than intermolecular terms, i.e. (#)#) I$$)
("WW
> ($6)"1 > (#)$")
(A.8) (A.9)
then one must conclude that ( \ k o l H J + < ~ ~0.) The treatment of the matrix element (IC/CTIHIIC/pL) is formally analagous to the case just treated. The final expression one has, in analogy to eq A7 is ( $ CT I HI J/pL) =
(- 3/@ IS#)* , N {E"
'/2("I")
-t
'/2("I$*$*)
1/2(#)@1#)*$*)
+
'/2(9$1"))
-
+ E$,#)*(A.10)
Using the same arguments employed earlier, one is here > 0. led to the conclusion that (IC/CTIHI#)PL) The final matrix element to be examined is (+oJ;HJ\kpL) this may be written as
(#)$~aapI~AH(k)Sk,/M,II$$"NX
($OI;HIJ/PL)=
(Baa0- 0aa - a @ a ) / f l l ) =
(2/~%)(#) IA HI#) *)
(A.11) (A.12)
Employing the orbital signs of eq A.l, this will clearly be a positive number.
References and Notes (1) (a) Department of Chemistry, University of Rochester, Rochester, N.Y. 14627; (b) Instkute for Molecular Science, Okazaki, Japan 444. (2) (a) J. Jortner and N. R. Kestner, "Electrons in Fluids, the Nature of Metal Ammonia Solutions", Springer Verlag, New York, N.Y., 1973; (b) W. L. Jolly, "Metal Ammonia Solutions", Dowden, Hutchlnson and Ross, Stroudsberg, Pa., 1972; (c) R. F. Gould, Adv. Chem. Ser.,
No. 50 (1965); (d) G. Lepoutre and M. J. Slenko, "Metal Ammonia Solutions", W. A. Benjamln, New York, N.Y., 1963. (3) M. Natori and T. Watanabe, J . Phys. SOC.Jpn., 21, 1573 (1966). (4) K. Kawabata, J . Chem. Phys., 85, 2235 (1976). (5) (a) B. L. Bales, M. K. Bowman, L. Kevan, and R. W. Schwartz, J . Chem. Phys., 83, 3008 (1975); (b) P. A. Narayana, M. K. Bowman, L. Kevan, V. F. Yudanov, and Yu. D. Tsvetkov, ibM., 83,3365 (1975); (c) S. Schick, P. A. Narayana, and L. Kevan, ibid., 84, 3153 (1976); (d) L. Kevan. J . Phvs. Chem.. 79. 2846 (1975). (6) (ai M. D. Newton, J. b w m . phys., 58,5833 (1973i (b) M. D. Newton, J . Phys. Chem., 79, 2795 (1975). (7) (a) J. Jortner, J . Chem. Phys., 30, 839 (1959); (b) Mol. Phys., 5, 257 (1962); (c) K. Fuekl, D. Fena, and L. Kevan, Chem. Phvs. Left., 4,313 (1969)i (d) K. Fuekl, 0. F G , L. Kevan, and R. E. Chrisiofferscil, J . Phys. Chem., 75, 2297 (1971). (8) (a) J. 0. Noell and K. Morokuma, Chem. Phys. Left., 38, 465 (1975); (b) J. 0. Noell and K. Morokuma, J. Phys. Chem., 80, 2675 (1976). (9) G. Herzberg, "Electronic Spectra of Polyatomlc Molecules", Van Nostrand, Princeton, N.J., 1966. (10) R. Ditchfield, M. D. Newton, W. J. Hehre, and J. A. Pople, J . Chem. Phys., 54, 724 (1971). (11) J. A. Pople and R. K. Nesbet, J . Chem. Phys., 21, 571 (1953). (12) W.J. Hehre, W.A. Lathan, R. Ditchfield, M. D. Newton, and J. A. Pople, WUSSIAN 70, Program No. 236, Quantum Chemistry Program Exchange, Indiana University, Bloomlngton, Ind., 1973. (13) The surface tension term was calculated as EST= 4ry(r,2 - rJ2), where rcis the distance from the cavity center to the outer surface of the first hydration shell. r,' is the analogous distance assuming the water molecules to be close packed spheres. The water molecules were assumed to be spheres of radlus 1.5 A. This yields r: = 3.337 A and r,' = 3.621 A for a tetrahedraland an octahedral model, res ectlvely. y was assumed to be 72 erg/cm2 (0.104 kcal/mol Ag). (14) R. A. Horne, "Water and Aqueous Solutions, Structure Thermodynamics and Transport Processes", Wiley-Interscience,New York, N.Y., 1972. (15) T. R. Dyke and J. S. Muenter, J . Chem. Phys., 60, 2929 (1974). (16) (a) T. R. Hughes, Jr., J . Chem. Phys., 38, 202 (1963); (b) B. B. Wayland and W. L. Rice, ibid., 45, 3150 (1966). (17) M. D. Newton, personal communicatlon. (18) H. M. McConnell, J . Chem. Phys., 24, 764 (1956). (19) M. J. S. Dewar, "The Molecular Orbital Theory of Organic Chemistry", McGraw-Hill, New York, N.Y., 1969, p 82.
COMMUNICATIONS TO THE EDITOR Nanosecond Temperature-Jump Technique with an Iodine Laser
Sir: The temperature-jump method is probably the most widely used of all relaxation techniques in the study of very fast reactions in solution. In commercially available instruments a high-voltage capacitor is discharged through an electrolyte solution. It is therefore not possible to achieve heating times shorter than R C / 2 of the measuring ce1l.l Direct optical heating of the solvent, however, is not limited by the electrical resistance of a discharge circuit and the sample especially.2 Here the heating time is governed by the emission time of the pulsed light source and the lifetime of the excited state. In the case of water the relaxation time of the vibrational rotational excited states in the near-IR is about s . ~If an oscillatoramplifier laser chain is used as an energy source heating times shorter than 10-12scan in principle be achieved, but the optical damage thresholds of the sample and the cuvet to normally prohibit heating times shorter than 8.
From the absorption spectrum of water4 it is apparent that a suitable wavelength for direct absorption of enough laser energy to cause a temperature-jump greater than 1 The Journal of Physical Chemktty, Vol. 81, No. 24, 7977
K in a volume of 0.1 cm3 exists above 1.15 pm. An assessment as to which degree of absorption would be the most suitable for producing spatially homogeneous temperature jumps at 50% or more laser energy consumption can be made by examining this dependence theoretically. Inhomogeneities inside the measuring cell causing temperature gradients that are above 10% should be avoided, because they generate locally different relaxation amplitudes as well as unwanted shock waves which may disturb the detection channel. From Figure 1we see that under these conditions such a temperature jump can only be achieved if the product of the absorption coefficient and the thickness of the heated layer lies between 0.15 and 0.2. Thereby the assumption is made that by means of a single reflection the laser beam passes through the sample twice. For an absorption layer thicker than 0.1 cm, which is necessary for the detection beam perpendicular to the heating beam the laser wavelength should be in the range from 1.15 to 1.36 pm. For mixtures of HzO and DzO this interval is shifted to longer wavelengths.6 Taking the above into consideration we have chosen an iodine laser which operates at 1.315 pm where the absorption coefficient of water is 0.76 cm-'. As can easily be seen from Figure 1the inhomogeneity of heating is around
2301
Communications to the Editor '
Absl
'
ao'"t
'
'
'
'
'
'
I
'
In
/
70 '10
inhomogeneity
Flgure 3. Time-resolved iodine laser pulses.
i
30%
o,i
O,Z
0,)
0,s
0.1
_.*
O,E
0.7
o,a
I
0,9
P *
Flgure 1. Dependence of the absorption of initial laser energy and temperature inhomogeneity in the measuring cell on the product of absorption coefficient (p) and thickness of the heated layer ( d ) with the laser beam passing twice through the cell. os 2 , I!(1 t o r
P
"
15 5 e Ie c t 0 I
T
- Jump
Detection
&
4
1 4 ,
'
/
/ Amplifier
1
0
'
8
L
6
8
,
,
10 12
,
, 16
,
, 20
,
, 21
, , 28
,
,
,
,
'-80 2m
,
,
,
680 860
k''
Flgure 4. Relaxation signal of a glycine buffered aqueous solution of phenolphthalein at pH 9.6, temperature 298 K registered with a Bomation 8100. (X) computed points for the relaxation trace.
1
I
Amplifier 2
'
2
e m 150 W o
Flgure 2. Experimental arrangement of the iodine laser T-jump: M, mirrors; AOM, acousto-optical mode locker; G, Glanprism; P, Pockels cell; SG, spark gap, MC, measuring cell; L, lenses; MO, monochromator; PM, photomultiplier: AM, amplifier; OSC, oscilloscope; and REU, registration unit.
6% at an absorption of 49% laser energy if a single reflection is allowed and the water layer is 0.2 cm thick. The experimental arrangement is shown schematically in Figure 2. The laser can be operated in two different ways. As an oscillator-amplifier chain with two amplification stages using acousto-optical mode locking for obtaining a train of short pulses and a Pockels cell for single pulse selection. This system produces 1-3 J in 3 ns. If the amplifiers are operated separately as oscillators in the multimode version they produce 1-30 J in about 3 ps. Higher energies could be achieved if the system is scaled up.6 Figure 3 shows time-resolved measurements of the laser pulses from the oscillator-amplifier chain in the TEM,, mode and from an oscillator in the multimode operation obtained with a valvo XA 1003 vacuum photodiode on a Tektronix 7904 oscilloscope and on a Biomation 8100, respectively. This versatile iodine laser being part of a temperature-jump system has been tested by measuring the protonation of tropaeolin 0 and phenolphthalein in aqueous solution.' As an example Figure 4 shows the relaxation signal obtained from phenolphthalein with a single heating pulse. Three advantages of this kind of laser T-jump technique can be stated from our results. There is enough energy available for T-jumps of some Kelvin with characteristic time constants of 2 ps or 2 ns in a volume of 0.1 mL containing solvents such as H20, D20, and alcohols. No additives are required to assist in heat
transfer. Shock waves and different relaxation amplitudes inside the measuring cell can be avoided so that the observation of relaxation times from nanoseconds to seconds at different temperatures is possible.
Acknowledgment. The authors thank Dr. S. Witkowski and Professor Dr. H. Gerischer for the encouraging support of this work and the Deutsche Forschungsgemeinschaft for a research grant. References and Notes (1) E. F. Caklin, Chem. Br., 11, 4 (1975); G. 0.Hammes in "Techniques of Chemistry", Vol. VI, Part 11, A. Welssberger, Ed., Interscience,
New York, N.Y., 1974. (2) E. M. Eyring and B. C. Bennion, Annu. Rev. Phys. Chem., 19, 129 (1968). (3) D. M. Goodall and R. C. Qeenhow, Chem. Phys. Lett., 9, 583 (1971). (4) J. V. Beitz, G. W. Flynn, D. H. Turner, and N. Sutln, J . Am. Chem. SOC.,92, 4130 (1970). (5) D. H. Turner, G. W. Flynn, N. Sutin, and J. V. Beltz, J . Am. Chem. Soc., 94, 1154 (1972); G. W. Flynn and N. Sutin in "Chemical and Biochemical Appllcations of Lasers", Vol. I, C. B. Moore, Ed., Academic Press, New York, N.Y., 1974, Chapter 10. (6) K. Hohla, 0.Brederlow, W. Fuss, K. L. Kompa, J. Raeder, R. Volk, S. Witkowski, and K.J. Witte, J . Appl. Phys., 46, 808 (1975). (7) M. C. Rose and J. Stuehr, J . Am. Chem. Soc., 90, 7205 (1968). Fritz-Haber-Ins titut der Max-Planck-Gesellschaft D-1000 Berlin 33, West Germany Max-Planck-Institut, fu? Plasmaphysik, 0-8046 Garching Projektgruppe fur Laserforschung D- 1000 Berlin 33, West Germany
J. F. Holzwarth" A. Schmldt H. Wolff R. Volk
Received July 1 1, 1977
Laser Induced Decomposition of Fluoroethanes Pubiication costs assisted by Kansas State Unlversity
Sir: The use of intense infrared radiation to promote selective chemical proce~sesl-~ has led us to examine the high-power, pulsed C 0 2 laser induced unimolecular deThe Journal of Physical Chemistty, Voi. 81, No. 24, 1977
