7346
J. Phys. Chem. 1989, 93, 7346-7351
perturbed. A partial rotational analysis for 35C1CN+was possible but not for the 37ClCN+speciesz3 With the B,’ value of 35C1CN+ and the ones of 35C1’3CN+,37C1’3CN+,35ClC’5N+,and 37ClC1SN+ determined in this work (see Table 111), the distances of the atoms to the center of gravity were then calculated. This turns out to be 1.038 (12) A for the chlorine atom, which agrees with the Franck-Condon study (1.05 (4) A).37 However, the deduced distances for the carbon and the nitrogen atoms from the center of gravity do not lead to physically meaningful bond lengths and differ from the values obtained from the Franck-Condon factors. In the evaluation of the C and N position, the Bo’value of the 3SCICN+had to be used. The above results suggest that the Bo’ value of the 35ClCN+obtained earlier is considerably affected by
the perturbations in contrast to Bo’values of 35*37Cl’3CN+ and of 35,37C1C15N+ (Table 111). Acknowledgment. This work is part of Project No. 2.221-0.86 of the “Schweizerischer Nationalfonds zur Forderung der wissenschaftlichen Forschung.” Ciba-Geigy SA, Sandoz SA, F. Hoffman-la Roche, and Cie SA, Basel, are also thanked for financial support. We thank Dr. F. G. Celii for recording part of the 1; band of the two isotopic species of the chlorocyanides and J. Lecoultre for their syntheses. Registry No. ClCN+, 37612-72-9; 35Cl, 13981-72-1; I3C, 14762-74-4; 37CI, 13981-73-2; IsN, 14390-96-6.
Photodissociation of ClCN between 190 and 213 nm Samuel A. Barts and Joshua B. Halpern* Department of Chemistry, Howard University, Washington, DC 20059 (Received: February 15. 1989; In Final Form: May 18, 1989)
ClCN was photolyzed at several wavelengths between 190 and 213 nm. Quantum-state distributions of nascent CN photofragments were measured. The distributions are well matched by applying the rotational reflection principle of Schinke and Engel’ to Waite and Dunlap’s excited-state potential energy surface.2
Introduction Photodissociation is a unimolecular reaction. The “transition state” is formed by absorption of a photon, promoting the dissociating molecule from a stable, well-characterized ground state to an unstable excited state. Theoretical models of dissociation are limited by the lack of excited-state potential energy surfaces. Experimental studies are limited by the lack of appropriate excitation sources or product characterization methods. Laser methods have come to dominate experimental photodissociation studies. The practical effect of this is that experimentalists have studied molecules that were accessible to the lasers available to them. These molecules have not been necessarily those to which theoretical methods could be easily or sensibly applied. Ling and Wilson were the first to use laser photodissociation when they studied the 266-nm photolysis of ICN.3 Since that time, lasers have become much easier to use and we have learned how to shift their frequencies into photochemically important areas of the spectrum. In this regard, it is important to note the work by Andresen and co-workers on the photolysis of water.e6 One cannot neglect the important role that studies of cyanogen halide molecules have played and continue to play. The experimental emphasis has remained on IC”-” perhaps unfortunately (1) Schinke, R.;Engel, V. Faraday Discuss. Chem. SOC.1986, 82, 11 1. (2) Waite, B. A.; Dunlap, B. I. J . Chem. Phys. 1986, 84, 1391. (3) Ling, J. H.; Wilson, K. R. J . Chem. Phys. 1975, 52, 1975. (4) Andresen, P.; Rothe, E. W. J. Chem. Phys. 1983, 78, 989. ( 5 ) Schinke, R.; Engel, V.; Andresen, P.; Hausler, D.; Baht-Kurti, G. Phys. Rev. Lett. 1985, 55, 1180. (6) Haeusler, D.; Andresen, P.;Schinke, R.J . Chem. Phys. 1987,87,3949. (7) Baronavski, A. P.; McDonald, J. R. Chem. Phys. Lett. 1977,45, 172. (8) Sabety-Dzvonik, M. J.; Cody, R. J. J . Chem. Phys. 1977, 66, 125. (9) Amimoto, S. T.; Wiesenfeld, J. R.; Young, R. H. Chem. Phys. Lett. 1979, 65, 402. (IO) Pitts, W. M.; Baronavski, A. P. Chem. Phys. Lett. 1980, 71, 395. ( 1 1 ) Baronavski, A. P. Chem. Phys. 1982, 66, 217. (12) Dekoven, B. M.; Baronavski, A. P.Chem. Phys. Lett. 1982,86,392. (13) Nadler, I.; Reisler, H.; Wittig, C. Chem. Phys. Lett. 1982, 103, 451. (14) Fisher, W. H.; Carrington, T.; Filseth, S. V.; Sadowski, C. M.; Dugan, C. H. Chem. Phvs. 1983.82. 443. (15) Fisher, W. H.; Eng, R.; Carrington, T.; Dugan, C. H.; Filseth, S. V.; Sadowski, C. M. Chem. Phys. 1984,89,457. (16) Shokoohi, F.; Hay, S.; Wittig, C. Chem. Phys. Lett. 1984, 110, 1. (17) Marinelli, W. J.; Sivakumar, N.; Houston, P. L. J . Phys. Chem. 1984, 88, 6685.
0022-365418912093-7346$01.50/0
as it may never be possible to calculate an a b initio surface for this molecule. Moreover, during dissociation of ICN, the separating fragments appear to undergo a complicated final state interaction, which indicates that the excited-state potential energy surface (PES) is complex and makes interpretation of the results difficult. Such behavior may be interesting or even important, yet exemplary systems should be simple. It is easier to work on ICN and BrCN because their absorption spectra are shifted to the red as compared to that of ClCN. However, ClCN is more tractable theoretically than either ICN or BrCN. Experimental results show that the dissociation of ClCN and BrCN is less complicated than that of ICN. At the time that this study was started, Waite and Dunlap had calculated an a b initio excited-state PES2 for ClCN, although they found it necessary to freeze the C-N bond length in order to carry out the calculation. However, this is a reasonable assumption as the bond is very stiff, so there will not be much vibrational excitation of the C N fragments. They parameterized the excited PES as
Vex= A exp[-a(r)R] exp[-P(R)r2] 4 0 ) = (yo
+ ai(r)
P(R) = Po + PiR
(la) (1b)
where A is 235.9 hartrees, a. is 1.88 bohr-’, Po is 3.38255 rad-2, and PI is 0.6541 rad-2 bohr-I. On this surface, al is zero. The ab initio surface, the absorption spectrum, and the nascent C N fragment rotational distributions give a consistent picture of the excited PES and the dynamics of dissociation. The dissociation of ClCN can be understood by examining the schematic drawing (18) Waite, B. A.; Haljavian, H.; Dunlap, B. I.; Baronavski, A. P. Chem. Phys. Lett. 1984, 1 1 1 , 544. (19) Nadler, I.; Mahgerefteh, D.; Reisler, H.; Wittig, C. J . Chem. Phys. 1985. --, 82. -3885. --(20) Scherer, N. F.; Knee, J. L.; Smith, D. D.; Zewail, A. H. J . Phys. Chem. 1985,89, 5141. (21) Hall, G . E.; Sivakumar, N.; Houston, P. L. J. Chem. Phys. 1986,84, ~
--.
71x1
(22) Josweg, H.; OHalloran, M. A.; Child, M. S.; Zare, R. N. Faraday Discuss. Chem. SOC.1986, 82, 79. (23) Hess, W. P.; Leone, S. R. J. Chem. Phys. 1987, 86, 3773. (24) O’Halloran, M. A.; Josweg, H.; Zare, R. N. J. Chem. Phys. 1987, 87, 303.
0 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 21, 1989 7347
Photodissociation of ClCN between 190 and 213 nm 10
I
I
kx
/ , L , . , g o $
0
-30
-10
10
30
BENDING ANGLE (Degrees) Figure 1. Schematic representation of the excited-state PES for BrCN and CICN. The center of mass of the CN fragment is collinear with the ridge of the potential. The numbers on the lines of constant potential show the energy in hartrees.
of the PES shown in Figure 1. This is a representation of the surface calculated by Waite and Dunlap. Following Franck-Condon excitation, the molecular trajectory combines rapid motion along both the bending and C1-C stretching coordinates. The motion in the bending direction leads to significant rotational excitation of the C N fragment. Thus, energy is partitioned between rotation and translation. In 1982, Halpern and Jackson measured the quantum-state distributions of C N fragments from the 193-nm photolysis of BrCN and ClCN.25 Both Waite and Dunlap2 and Schinke and Engell modeled the 193-nm ClCN photolysis using semiclassical trajectory calculation. The former group picked trajectory starting points at random; the latter used a method, that they named the rotational reflection principle, to systematically vary and weight the initial conditions. Waite and Dunlap were able to match the general form and maximum of the fragment quantum-state distributions but predicted too large a population at low rotational quantum numbers. Schinke and Engel were able to almost exactly match the experimental result with significantly less computational effort. In 1984, Fisher et al. measured the quantum-state distribution from the photolysis of BrCN at 308, 248,222, and 193 nm.I5 Lu et al. measured the quantum-state distributions of C N following the 193-nm photolysis of BrCN and ClCN dynamically cooled in a supersonic expansion.26 In 1987, Russell et al. measured quantum-state distributions of C N following the photolysis of BrCN at several wavelengths between 193 and 266 The C N rotational-state distributions following the photolysis of BrCN and ClCN at 193 nm are quite similar. They are rotationally inverted, with about 40% of the available energy distributed to rotation and 50-60% to translation. Of the C N radicals, 10-20% are vibrationally excited following the photolysis of ClCN. In the photolysis of BrCN, less than a few percent of the C N fragments are vibrationally excited. From the analysis of the C N rotational quantum-state distributions in 27, it appeared that the Br atom fragments were produced in both the 2P3/2and 2P,12levels at 248 nm and in the excited 2Pl12level below 230 nm. Recent improved measurements of the quantum-state distributions by Paul show that the Br electronic states are roughly equally populated at 248 nm and that Br is produced in the zP312state at 260 nm.28 Using the reflection principle we have made fits to the absorption spectrum of BrCN shown in 27. These fits show that the absorption can be decomposed into two Gaussian curves. One might associate the longer wavelength and smaller absorption component with dissociation to Br(2P312)and the shorter wave(25) Halpern, J. B.; Jackson, W. M. J . Phys. Chem. 1982, 86, 3528. (26) Lu, R.; McCrary, V.; Halpern, J. B.; Jackson, W. M. J . Phys. Chem. 1984,88, 3419. (27) Russell, J. A.; McLaren, I. A,; Jackson, W. M.; Halpern, J. B. J . Phys. Chem. 1987, 91, 3248. (28) Paul, A. Thesis, Howard University, 1988.
190
200
210
220
230
WAVELENGTH (nm) Figure 2. Absorption spectrum of ClCN between 190 and 240 nm.
length and larger absorption component with dissociation to the excited Br(ZPl12). Thus, it appeared sensible to investigate the wavelength dependence of C N quantum-state distributions from the photolysis of ClCN. Much recent work on photodissociation has concentrated on measurement of correlation among the several modes of motion of the fragments and the polarization of the dissociating light.29 In the case of CICN, it shall be shown that a great deal of information about the dissociation process can be obtained from the combination of measured fragment quantum-state distributions, PES calculations, and the rotational reflection principle. Experimental Section The apparatus was similar to that described in ref 27. ClCN from Matheson was purified by freeze-thaw cycling. The gas flow from a 5-L reservoir was controlled by a Granville-Phillips fine-metering value and introduced into the cell through a hypodermic needle. The ClCN pressure was monitored by a MKS Model 200 capacitance manometer and was maintained at about 200 mTorr. The photolysis source was a Spectra Physics PDL-2 dye laser pumped by a DCR- 11 Nd:YAG system. Light from the dye laser was frequency doubled in a KDP crystal and Raman shifted in about 10 atm of hydrogen gas. For this experiment, the third and the fourth anti-Stokes-shifted beams were used. Since the doubled light is 100% polarized, all of the Raman-shifted beams will be 100% polarized. The intensity of the dye laser beam ranged between 25 and 60 mJ, depending on the dye gain curve and dye used. The energy contained in each pulse of the photolysis beam ranged from a few to perhaps 100 pJ. C N fragments were detected by laser-induced fluorescence (LIF) excited by a Molectron Model DL-I1 dye laser pumped by a UV400 nitrogen laser. The roughly 200-115 beam was expanded, attenuated by neutral density glass filters, and passed through a thin film glass polarizer to eliminate any elliptical character. Care was taken that the LIF signal was unsaturated. The electric vector of this dye laser beam was parallel to that of the photolysis laser. In a few experiments, the polarization of the probing dye laser beam was rotated by the insertion of a thin half-wave plate. No displacement of the beam could be observed when the halfwave plate was inserted. No change in the results was observed when the plate was removed and then reinserted. The overlapping laser beams passed through the experimental cell in opposite directions. LIF was monitored by an EM1 Model 9258 photomultiplier tube looking through a 388-nm band-pass filter. The photomultiplier was placed perpendicular to the plane of the laser beams and the electric vector of the photolyzing light. The experiment was controlled by an IBM PC/XT microcomputer-based data acquisition system constructed in our laboratory. The nitrogen laser was fired about 100 ns after the (29) See, for example: Greene, C. H.; Zare, R. N. Annu. Rev. Phys. Chem. 1982,33,119. Dixon, R. N. J. Chem. Phys. 1986,85, 1866. Vasudev, R.; Zare, R.N.; Dixon, R. N. J . Chem. Phys. 1984, 80, 4863.
1348 The Journal of Physical Chemistry, Vol. 93, No. 21, 1989 I 15
I I 1 1
11
a
I I I I I I I~I i I i i i i l n Bo
70
Barts and Halpern I
104
+
+
I
Q
0.51
t + +
++
++
...., +
i
50
..,.. '
.
+ a99+
+++
1
i
.
0 1
386
387
0
388
WAVELENGTH nm Figure 3. LIF spectrum of nascent C N fragments from the photolysis of ClCN at 195 nm.
2000
4000
N(N+l)
. .. ...+ .
I
b
Nd:YAG Q-switch. The fluorescence signal was integrated in one channel of a PAR Model 162 boxcar analyzer. Another channel monitored the signal from a photomultiplier looking a t the central fringe from a 1-cm-' etalon. This was used to measure the frequency displacement of the scanning dye laser. The intensity of the dye laser beam was measured by picking off a reflection and sending it into a photodiode. Dye laser scanning was controlled by the microcomputer.
Results Figure 2 shows the absorption spectrum of ClCN between 240 and 190 nm. This spectrum was measured on a Beckman Model DU-7 spectrophotometer. Figure 3 shows a typical LIF spectrum of C N fragments following the photolysis of ClCN at 195 nm. Only the P-branch area is shown. The C N fragment distribution is seen to be rotationally inverted. Figure 4 shows the measured population distributions of C N from photolysis at 190.6, 201 S, and 206 nm. Filled squares represent data taken with the polarization of both lasers parallel. Crosses represent data taken with the polarization of the lasers crossed and the electric vector of the dye laser beam pointing at the photomultiplier. Measurements of the distributions with both orientations of the dye laser polarization were only taken at these three photolysis wavelengths. The right-hand sides of Figures 5-14 show, in a reduced format, the ut' = 0 C N rotational quantum-state distributions measured at 190.6, 191.5, 195.0, 196.0, 200.3, 201.5, 206.0, 208.7, 211.6, and 213.0 nm, respectively. Discussion The ClCN absorption spectrum shown in Figure 2 is very similar in shape to the red end of the BrCN absorption spectrum. Absorption by oxygen limits measurement of the spectrum on the blue end to about 190 nm, and this also sets the limit for photolysis with the current apparatus. Because all of the atoms in ClCN are relatively heavy, one approach to the analysis would be to run classical trajectories on the calculated PES, selecting the starting points in a random manner weighted by the ground-state wave function. The calculated results would then be compared to the experimental measurements. Waite and Dunlap followed this procedure using 5000-IO OOO trajectoriesS2 Schinke and Engel have demonstrated a more parsimonious procedure for selecting a set of properly weighted starting points, which they call the rotational reflection principle.' The following discussion is taken directly from Schinke and Engel.' Trajectories are calculated by integrating the equations of motion starting with the classical Hamiltonian H ( R , r , P j ) = p2/2p
+ ~j~ + j2/2pR2 + vex(R,r)(2)
where p is the A-BC reduced mass, B the BC rotational constant, P the radial momentum, R the radial coordinate, and r the angular (bending) coordinate. j is the continuous time-dependent
6000
m
m
m
i
+
+
.+
.
+. ++
i
.A
0
0
2000
4000
6000
N(N+l) C ~
+
:.". . .. +
.
+
.+ m+
+*9
+
+
+
0.51
++++
'8
0 1
0
2000
4000
6000
N(N+l) Figure 4. Measured nascent CN rotational population distributions of CN from photolysis of ClCN as a function of N(N 1). Filled squares represent data taken with the polarization of the lasers parallel to each other. Crosses represent data taken with the polarization of the lasers crossed. The photolysis wavelength for (a) is 190.6 nm, for (b) 201.5 nm, and for (c) 206 nm.
+
molecular angular momentum, and Vexis the excited-state PES. The classical equations of motion are then as follows: dR/dt = P / p
(3)
d r / d t = 2j[B + 1/(2pR2)]
(4)
dP/dt = -(dVex/dR)
+jz/(pR3)
(5)
dj/dt = -(dV,,/dr) (6) The initial angle rois varied systematically between 0 and ?r radians. It is assumed that the angular and linear momenta are initially zero on the excited PES. This allows calculation of a starting value of Ro(r0), which conserves energy. Each set of initial conditions leads to a unique final BC angular momentum,
The Journal of Physical Chemistry, Vol. 93, No. 21, 1989 7349
Photodissociation of ClCN between 190 and 213 nm 90
I
I Rotational Distribution
Excitation Curve
ohtina Weib ....~ Function
I
90
1
I
1 Rotational Distribution
Excitation Curve
/
Function
0 0
5
15
0
ANGLE (degrees)
0.5
1
5
P(N)/Pmax
I Rotational Distribution
Excitation Curve
15
0
ANGLE (degrees)
Figure 5. Photolysis at 190.6 nm. The left-hand side of the figure shows the classical excitation function and the weighting function as calculated by the rotational reflection principle. The excitation function is the upper curve. The right-hand side of the figure shows the calculated fragment rotational-state distributions and the measured ones. 90
0
1 0
0.5
1 0
P(N)/Pmax
Figure 8. ClCN photolysis at 196.0 nm. 90
I
I3
I Rotational Distribution
Excitation Curve
4I-
z
2 3
a I-
8 0
15
5
0
ANQLE (degrees)
0.5
1 0
P(N)/Pmax
Figure 9. ClCN photolysis at 200.3 nm. 0
5
15
0.5
0
ANGLE (degrees)
1.o
P(N)/Pmax
--
I
I Rotational Distribution
Excitation Curve
I
Figure 6. ClCN photolysis at 191.5 nm. 90
1
Excitation Curve
Rotational Distribution
I
60
:/
Weighting
y 0
5
15
0 5
0
ANGLE (degrees)
1 0
P(N)/Pmax
Figure 10. ClCN photolysis at 201.5 nm. 0
5
15
0
ANGLE (degrees)
0 5
1 0
P(N)/Pmax
Figure 7. ClCN photolysis at 195.0 nm.
The cross section for finding the C N fragment in rotational state J is then aCL(J)= W(I'o)l(dFL/dI'o)l-l
FL(ro) =j(t=-,r0). The probability of starting at any particular rois the weighted probability function
(8)
This procedure will work best for a simple, dissociative potential. The assumption of zero initial momentum will be most valid for surfaces where the molecule experiences large torques in its initial (7a) w(rO) = sin r0 '&,rz[rOl (p,.Rz[RO(rO)l position on the excited PES and where the photoexcitation originates in low vibrational states. where Figures 5-14 are similar to those found in ref 1 and summarize the rotational reflection principle. Both calculations and meaVEr~[Ro(ro)l= exP[-aR(R - Re)*] surements are shown. The left-hand side of each figure shows r0)and the weighting function the classical excitation function ~8r,r[r0l= kxP[-ar(r - re)'] + exP[-ar(r + rJ211/2 (7b) vs initial angle, ro.The right-hand side shows the calculated and For CICN, re= 0' and Re = 4.262 bohr. The fwhm of c~pr,~[I'~] measured CN quantum-state distributions as functions of rotais 19.5' and that of cpgr,R[Ro(r,)] is 0.248 bohr. tional quantum number (spin has been neglected). Note that the angle
sL(
7350 The Journal of Physical Chemistry, Vol. 93, No. 21, 1989 90
1
Barts and Halpern 90
1 Rotational Distribution
Excitation Curve
I
1I Rotational Distribution
Excitation Curve
I
1 60 -
1
i
Weighting Function
-1 a
4
/
L
y
0 0
5
15
1
0 5
0
ANGLE (degrees)
1 0
P(N)/Pmax
I
I
i
I
1
I
0
5
15
0
0 5
ANGLE (degrees)
1 0
P(N)/Pmax
Figure 12. ClCN photolysis at 208.7 nm. 901
1
Excitation Curve
Rotational Distribution
~
/
o ’ , 0
I 5
15
0
ANGLE (degrees)
I
5
15
0
0 5
1 0
P(N)/Pmax
Figure 14. ClCN photolysis at 213.0 nm.
1 Rotational Distribution
Excitation Curve
I
# ’! 0
ANGLE (degrees)
Figure 11. ClCN photolysis at 206.0 nm. 90.
0
I
\
0 5
1 0
P(N)/Pmax
Figure 13. CICN photolysis at 21 1.6 nm.
right-hand side has been rotated 90° from the usual orientation. These figures show in a clear way how the weighting functions are reflected from the classical excitation function to give the quantum-state distribution. In the region below 206 nm, the match between experiment and theory is extraordinary. Above 206 nm, the form matches but the maximum is shifted. We attribute this to ClCN having two parallel PESs. As was the case for BrCN, one of these curves would dominate the absorption at higher wavelengths and the other would do so at lower wavelengths. A vacuum-monochromator system is being set up that will allow measurement of the entire A-system absorption spectrum of ClCN. This should allow a decomposition of the spectrum to separate absorption bands. The most striking feature of the calculated quantum-state distributions is that the maximum does not change as the photolysis wavelength is varied between 47000 and 52500 cm-I. This
corresponds to a change in excess energy of between 13 400 and 18 900 cm-I. Inspection of Figures 5-14 shows that this is a result of the peak of the weighting functions shifting out to higher initial angle with decreasing excitation energy. The shift compensates the expected decrease in the classical excitation function. As the photolysis energy decreases, one also sees a narrowing of the distribution. This is a result of the excitation probability at higher angles sampling a region of the classical excitation function where the slope is small. The reflection of the weighting function off the flat part of the excitation function produces narrow fragment rotational quantum-state distributions. The fragment rotational distributions are a consequence of the strong torques that the ClCN experiences when it is lifted to the upper state by absorption of a photon. An interesting question to be answered is whether the upper state has an equilibrium bent configuration. As discussed in ref 25 the region of Franck-Condon excitation near the ridge of the potential (near r = 0 and R = Re) must be a stationary point of the motion. From the potential as drawn in Figure 1 and from the experimental results, it appears that the component of the gradient parallel to the bending coordinate is large and negative. For fixed R = Re, if the system moved along the bending coordinate, the rotating C N fragment would crash into the C1-C bond. Therefore, the potential must rise to infinity at Oo and 360°, and the potential must have a bent equilibrium configuration for R between 0 and Re and perhaps somewhat beyond. However, the trajectories do not pass through this region but rather they pass through the part of the surface that looks like Figure 1. The trajectories involve rapid motion along both the bond-stretching and bond-bending coordinates. For large values of R >> 4,where one encounters large angles, the potential minimum disappears. For triatomic, A-BC dissociation processes, impulsive models assume that the torque on the diatomic fragment arises from an instantaneous repulsion between atoms A and B that occurs at some quasi-equilibrium angle ABC. It is unnecessary to postulate the existence of such a quasi-equilibrium bent configuration and difficult to understand how the molecule could be brought to this configuration in a momentum-less state.jO The passage of the system through such a configuration would imply that at least some trajectories would be confined for one or more orbits, giving rise to structure in the absorption spectrum to lower angular momentum quantum numbers in the fragment state distributions. Indeed, this may be happening in ICN but is not the case for photolysis of ClCN (and BrCN). The steepness of the grad ( Vex).erat all significantly occurring starting points except for the ridge where r = 0, accounts for the strong torque that the molecule experiences. This force is so strong that in comparison one can neglect the linear and angular momenta of the molecules in the ground state, which is transferred (30) Schinke, R. Rotational Excitation in Direct Photodissociation and Its Relation to the Anisotropy of the Excited State Potential Energy Surface: How Realistic Is the Impulsive Model? To be published in Comments At. Mol. Collisions.
J . Phys. Chem. 1989, 93, 7351-7354
to the excited PES when the system undergoes a Franck-Condon transition. The probability is very low that a molecule will undergo such a transition at coordinates where this assumption is not valid, i.e., on the ridge of the potential or a t very large angles. This justifies the use of the rotational reflection principle to analyze the photodissociation of CICN. The implication of this analysis is that the fragment rotational distributions are determined by the shape of the upper-state potential energy surface and the overlap of the well-known ground-state wave function with the excited PES. On the other hand, because the dissociation is direct with no complicated interactions between two or more PESs or orbiting trajectories, correlations in the orientations of the fragments should be determined by the nature of the spectroscopic transition. The measurements shown in Figure 4 are preliminary. They demonstrate that there is a measurable alignment below 206 nm. At 206 nm, there appears to be no, or at best a small, alignment. Higher order correlations have not been measured. As discussed above, a t 206 nm, the results may be a superposition of mea-
7351
surements from two PESs. Below 206 nm, the distributions are most likely the result of the excitation of a single PES.
Conclusion ClCN was photolyzed at several wavelengths between 190 and 21 3 nm. Rotational-state distributions of nascent C N fragments have been measured. For wavelengths below 206 nm, these measured distributions can be calculated by applying the rotational reflection principle to a calculated a b initio surface. We assume that dissociation above this limit involves a second excited-state PES that is roughly parallel to the first. Acknowledgment. Parts of this work were supported by NASA under Grant NAG-5071 and a grant of money from the Howard University Research Development program. S.A.B. was supported by a Danforth Foundation Fellowship. We thank Dr. R. Schinke for allowing us to read his unpublished m a n ~ s c r i p t .We ~ ~ also acknowledge helpful discussions with Dr. W. M. Jackson. Registry No. ClCN, 506-77-4; CN, 2074-87-5.
Calculation of the Molecular g Tensor from Data for the Calculation of Rotational Strengths in Vibrational Circular Dichroism W. R . Salzman Department of Chemistry, University of Arizona, Tucson, Arizona 85721 (Received: February 27, 1989; In Final Form: May 23, 1989)
The calculation of the rotational strength in vibrational circular dichroism (VCD) and the calculation of the molecular g tensor in microwave spectroscopy share a common feature, namely that the contribution of the electrons in both c a m vanishes when calculated with adiabatic Born-Oppenheimer (type) wave functions. It is shown that Stephens' method for calculating the electronic contribution to the rotational strength in VCD, using only ground-state electronic properties, can also be applied to calculating the molecular g tensor elements that give the rotational strength in microwave optical activity theory. The same electronic structure calculation that gives the VCD magnetic moment matrix element can be used to calculate the elecronic contribution to the molecular g tensor.
Introduction Optical activity phenomena (by which we mean the rotation of the plane of polarized light, optical rotatory dispersion, and circular dichroism) have been known in the spectral region of visible light-due to the motion of electronssince the early 19th century.' Optical activity in the infrared or vibrational circular dichroism (VCD)-due to molecular vibrations-has been known since about 19742and is being developed into a powerful tool for structural analysis of optically active molec~les.~Optical activity in the microwave-due to molecular rotations-has been predicted but has not yet been ~ b s e r v e d . ~ , ~ ( I ) For an excellent historical introduction, see: Mason, S. F. Q. Reu. Chem. Soc. 1963, 17, 20. For a more recent review of optical activity theory and calculations, see: Hansen, A. E.; Bouman, T. D. Adu. Chem. Phys. 1980, 44, 545. (2) Holzwarth, G.; Hsu, E. C.; Moser, H. S.; Faulkner, T. R.; Moscowitz, A. J. Am. Chem. SOC.1974, 96, 251. (3) Stephens, P. J. In Optical Activity and Chiral Discrimination; Mason, S. F., Ed.; Reidel: Dordrecht, The Netherlands, 1979. Nafie, L. A.; Vidrine, D. W. In Fourier Transform Infrared Spectroscopy; Ferraro, J. R., Basile, L. J., Eds.; Academic Press: New York, 1982; Vol. 3. Polavarapu, P. L.In Fourier Transform Infrared Spectroscopy; Ferraro, J. R., Basile, L. J., Eds.; Academic Press: New York, 1985; Vol. 4. (4) Salzman, W. R. J. Chem. Phys. 1977,67, 291. Polavarapu, P. L. J . Chem. Phys. 1987,86, 1136. ( 5 ) Salzman, W.R. Chem. Phys. Lett. 1987,134,622. Salzman, W. R. Chem. Phys. Lett. 1987, 141, 71. Salzman, W. R. J. Chem. Phys., submitted for publication.
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The theories of optical activity phenomena in the infrared and microwave share a common feature. Namely, the contributions of the electrons to the rotational strengths in each case vanish when calculated with Born-Oppenheimer wave functions for the electronic ground The reason for this is simple and wellknown. The rotational strength is a product (or sum of products) of an electric dipole moment matrix element and a magnetic dipole moment matrix element. In both VCD and microwave optical activity, these matrix elements are calculated for the ground electronic state. The operator for the magnetic moment of the electrons is Hermitian and pure imaginary. Thus, the diagonal elements-in particular the ground-ground element-of this operator must be zero. This means that within the Born-Oppenheimer approximation the electrons do not contribute to the rotational strength in VCD and an analogous statement holds for microwave optical activity. In each case, in order to correctly include the contribution of the electrons to the rotational strength, one must write electron-vibration wave functions (i.e., corrected or nonadiabatic Born-Oppenheimer wave functions) or electron-rotation wave functions that couple the motion of the electrons to the respective molecular motion. In the rotational case, this problem takes the form of the absence of a contribution of the electrons to the molecular g tensor, the (6) Eshbach, J. R.;Strandberg, M. W. P. Phys. Reu. 1952,85, 24. ( 7 ) Stephens, P. J. J. Phys. Chem. 1985, 89, 748.
0 1989 American Chemical Society
