6104
J. Phys. Chem. 1991, 95,6104-61 11
The activation energy of viscosity of the present nonpolar solvents is about 1380 cm-l (ref 47) and very close to that of polar ethanol.” Similarly, the quantum yield at 23 OC for Rh3B in polar (methanol, vu = 0.55 cP) and nonpolar (chloronaphthalene, 723 = 2.94 cP) solvent are comparable, Le., 39% and 54%. respectively, and a simple mechanism of viscositydependent internal conversion has to bc discarded. Recent experiments using a highly diluted solution of Rh3B in chloronaphthalene, actually revealed the presence of two activation energies.48 Clues as to the mechanism of internal conversion, operating in nonpolar solution and displaying such small activation energies, can be drawn from a polarity-dependent activation barrier for IC in xanthene” and oxazine dyes49and the assumption of direct IC (no twist) and indirect IC (after twist). An equilibrium between loose and tight ion pairM”’ might further complicate matters, and electron (47) AI-Mahdi, A. A. K.; Ubbelohde, A. R. Trans. Faraday. Sa.1955, 51, 361. (48) Kemnitz, K.; Yoshihara, K., manuscript in preparation. (49) Vogel, M.; Rettig, W.; Fiedeldei, U.; Baumgartel, H. Chem. Phys. Lett. 1988, 148, 347. (50) Mishra, A. K.; Shizuka, H. Chem. Phys. Lett. 1988, 151, 379. (51) Vandereecken, P.; Soumillion, J. P.; Van Der Auweraer, M.; DeSchryver, F. C. Chem. Phys. Lett. 1987, 136,441.
transfer, in analogy to the dimer case discussed above, may also play a role in the monomer nonradiative decay. (IV) Conclusions We studied a series of novel monomer-dimer systems of xanthene dyes in nonpolar solution. The main driving force for dimerization results from the interaction of the solvent molecules with the ion-pair dimers, as derived from a strong positive entropy of dimerization. The above systems allowed a direct determination of dimer fluorence lifetime and activation energy of nonradiative dimer decay. We tentatively proposed a novel mechanism of nonradiative dimer decay, based on electron transfer from the counteranion to the excited chromophore. An investigation of a series of counteranions with varying ionization potentials might verify this assumption.
Acknowledgment. The fluorescence spectra were acquired during a stay at the laboratory of Prof. A. Penzkofer (University of Regensburg, FRG), whose hospitality K.K. acknowledges. These studies were, in the early stage, supported by DFG (Ke 372/1-1). (52) Barigelleti, F. Chem. Phys. Lett. 1987, 140, 603. (53) Karstens, T.; Kobs, K. J . Phys. Chem. 1980,84, 1871.
HN,(AIA”) Hypersurface at Excltation Energies of 4.0-5.0 eV Karl-Heinz Cericke, Tobias Haas, Michael Lock, Robert Theinl, and Franz Josef Comes* Institut fiir Physikalische und Theoretische Chemie, Universitat Frankfurt, Niederurseler Hang, D 6000 Frankfurt am Main 50, Federal Republic of Germany (Received: November 27, 1990; In Final Form: January 14, 1991)
The dynamics of the photofragmentation of hydrazoic acid from its lowest excited electronic state, A’A”, has been investigated at various excitation energies in the range 4.0-5.0 eV in order to probe a comparatively wide range of the upper potential energy surface (PES). The NH product has completely been analyzed by high-resolution Doppler spectroscopy. The ji(HN,)-ii(NH)-J(NH) vector correlations and the population correlation between the N2and NH product pair have been determined by detailed line profile measurements. While the NH fragment shows only a moderate rotational excitation which is essentially independent of the deposited energy in the parent, the N2 product is highly rotationally excited. The N2 rotation increases with increasing available energy for the fragments. Low NH rotation correlates with very high N2 partner rotation. The wealth of information that was obtained in the exprimental investigation of the dissociation process provides a qualitative piclure of the PES. The dependence of the HN3(A’A”) potential on the NNH bending angle must be similar to that of the X’A’ ground state which is not the case for the in-plane and out-of-plane NNN bending angles. For both angles the upper PES exhibits a strong gradient toward a bent configuration. The gradient of the A’A” potential along the N-NNH distance is comparable to that of the ground state, since the N2products are formed essentially without vibrational excitation. On the other hand, the NH products are vibrationally excited which indicates a strong change of the upper potential along the NNN-H coordinate during the dissociation of HN3. Ab initio calculations support this picture of the dissociation process.
I. Introduction One of the most interesting topics in physical chemistry is the understanding of an elementary chemical reaction proceeding from reactants to products in two, more or less separate step according to ABC
+ -
+D
ABCD
step I
hu
stop I
stop 2
[A**B-*C-D]# AB(qAB#AB)
+ CD(qcDiPcD)
-
(1
step 2
ABCD#(A,k..) AB(~AB,PAB) + CD(~CD,PCD) (2) where we assume a four-atom transition state ABCD# with only one fragmentation channel AB + CD. Here, (q,p) specifies not only the internal (vibrational, rotational) state distribution of the products but also the vectorial character of the chemical process, like the spatial distribution, the orientation of the rotational vector 0022-3654/91/2095-6104$02.50/0
(m, distribution), and correlations between the products. The transition state or activated complex is reached either by a collision of two reaction partners where wide ranges of orbital angular momentum and of the potential energy surface (PES)are involved or by depositing a certain-but sufficient-energy in a stable molecule, where the initial positions of the nuclei are known and only a certain and well-known range of the upper potential surface is probed. There has been tremendous progress in developing new methods, like supersonic molecular beams, high-resolution lasers (in time or in frequency), or sophisticated spectroscopic techniques in order to obtain information about the multidimensional potential energy surface governing nuclear motion during a chemical process.’*2 (1) Levine, R. D.; Bernstein, R. 8. Molecular Reaction Dynamics and Chemical Reactiuity; Oxford University Press: New York, 1987. ( 2 ) Zewail, A. H.; Bernstein, R. B. Chem. Eng. News 1988, 66, 24.
0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 16, 1991 6105
HN3(A1A”) Hypersurface Molecular beams can be used to cool reactants to low vibrational and rotational temperatures; Le., only a few quantum states of the educts are involved in the chemical event.’ Lasers can be used to deposit a well-defined amount of energy in a molecule in order to dissociate the parent and to analyze the products by spectroscopic methods, like emission spectroscopy, laser-induced fluorescence (LIF), resonance-enhanced multiplephoton ionization (REMPI), or advanced time-of-flight (TOF) techniques.’-5 Especially, the use of polarized laser beams to select parent molecules with the proper alignment and to analyze the degree of alignment of the products is a very useful tool to determine vector correlations in anisotropic processes, for example, the rotational motion of a fragment relative to its recoil direction.69 An extremely accurate measurement of the velocity of one fragment (AB) in a dissociation process, where the energy deposit is well-known, yields the product state distribution of the partner product (CD) generated in the same chemical This microscopic joint reaction probability, P(qAB,qCD), is one of the most detailed pieces of information available for a chemical process.” The unimolecular decomposition of hydrazoic acid has been studied intensively in photodissociation experiments in the UV as well as in ground-state overtone pumped photolysis of HN3(k’A’). The latter expriments involve a spin-forbidden dissociation channel, HN3(X’A’) N2(XlZf) + NH(X’Z-), when overtone and combination levels of HN3 in the range 5ul to 6 ~ 1 are excited.I2 About 97% of the NH(X’Z-) are generated in the symmetric FI and F3spin-orbit states, which can be expected for a planar dissociation process.’’ A very detailed analysis of the fragmentation process of HN3(g’A’) has been performed just recently by Casassa et al. using an IR-visible double-resonance technique.“ When the 7ul band is excited via the sequential vI( 1 4 ) ul(7+l) transitions, the NH products are formed in the a’A state where the population ratio of the A(A? to the A(A”) A doublet state is 4:1 for JNH= 5, which, again, is consistent with a planar process. However, the observed corLelation between the NH recoil velocity and its rotational vector J is slightly positive, indicating a preferentially parallel alignment between these two vectors! In these experiments the dissociation energy of the process NH(’A) was also determined to be HN3(X’A’) N2(X1Z:) ca. 18 750 cm-’.” In the UV photodissociation of HN3 at wavelengths of 248,15 266,I6*l7 and 283 nm,I8 the NH fragments are found exclusively in the aIA state without preference of a A doublet state. The rotational excitation is relatively low, but the vibrational levels were found to be populated up to u = 3 at a photolysis wavelength of 266 nm.I9 At a photolysis wavelength around 283 nm the N2 fragments were directly observed in a (2 2) REMPI study and
-
+
-
+
+
(3) Bernstein, R. B. Chemical Dynamics via Molecular Beam and Loser Techniques:Oxford University Press: New York, 1982. (4) DcmtrBder, W . Laser Spectroscopy; Springer-Verlag: Berlin, 1981. (5) Molecular Photodissociarion Dynomics;Ashfold, M . N. R., Baggott, J. E., Eds.; The Royal Society of Chemistry: London, 1987. (6) Dixon, R. N. J . Chem. Phys. 1986,85, 1866. (7) Docker, M. P. Chem. Phys. 1989, 135, 405. (8) Mons, M.; Dimicoli, 1. J . Chem. Phys. 1989, 90, 4037. (9) Gericke, K.-H.; Klee. S.;Comes, F. J.; Dixon, R. N.J . Chem. Phys. 1986,85,4463. (IO) Gericke, K.-H. Phys. Rev. Lett. 1988, 60, 561. ( I 1) Gericke, K.-H.; GIHeer, H. G.; Maul, C.; Comes,F. J. J. Chem.Phys. 1990, 92,415. (12) Foy, B. R.; Casassa, M. P.; Stephenson, J. C.; King, D. S.J. Chem. Phys. 1988,89,608. Foy, B. R.; Casassa, M. P.; Stephenson, J. C.; King, D. S.J . Chem. Phys. 1989,90.7037. Foy, B. R.; Casassa, M. P.; Stephenson, J. C.; King, D. S. J. Chem. Phys. 1990, 92. 2782. (13) Alexander, M. H.; Werner, H.-J.; Hemmer, T.; Knowles, P. J. J . Chem. Phys.. in press. Alexander, M. H.; Werner, H.-J.; Dagdigian, P. J. J . Chem. Phys. 1908,89, 1388. (14) Casassa, M. P.; Foy, B. R.; Stephenson, J. C.; King, D. S.J . Chem. Phys., in press. (IS) Rohrer, F.; Stuhl, F. J . Chem. Phys. 1988,88, 4788. (16) Gericke, K.-H.; Theinl, R.; Comes. F. J. Chem. Phys. Lerr. 1990,164, 605. (17) Gericke, K.-H.; Theinl, R.; Comes, F. J. Chem. Phys. 1990,92,6548. (18) Chu, J.-J.; Mama, P.; Dagdigian, P. J. J. Chem. Phys. 1990,93, 257. (19) Nelson, H. H.; McDonald, J. R. J . Chem. Phys., in press.
found to be extremely rotationally excited, while no vibrationally excited N2 products were observed.I8 The vector correlation measurements at 266 nmI7 showed that at this excitation wavelength N2 rotation is even more excited and, furthermore, that a strong nonplanar NN-NH bending motion is essential for product rotation. _The equal population of the A doublets as well as the positive (BJ) correlation also indicates that the dissociation process does not occur on a plane. We have investigated the photodissociation dyzamics o,f hydrazoic acid, HN,, from its first absorption band, AIA” X’A’, at different excitation energies to obtain a qualitative mapping of the multidimensional PES. Beside scalar properties, including information about the joint reaction probability, the vector correlations between the transition dipole moment of the parent ( E ) and the rotation (J) as well as the translation (3of the NH product have been analyzed with sub-Doppler resolution.
.-
11. Experimental Section The experiments were performed using different laser photolysis sources and subDoppler laser-induced fluorescence measurements of nascent NH(a’ A) prod~cts.~’~’~.’’ Briefly, hydrazoic acid was generated in a vacuum line with NaN, in excess of stearic acid. At 75-85 “C sufficient HN3 evolved exclusively and was pumped directly into the observation cell. Typical pressures were 0.5-1 .O Pa controlled by a capacitance manometer. Hydrazoic acid was cooled in seeded supersonic beams with helium or argon as diluent gases. The pulsed nozzle (orifice diameter 0.5 mm) operated with a pulse length of less than 300 ps. The interaction region of the photolyzing and probing laser beams was more than 40 orifice diameters downstream from the nozzle. The photolysis pukes at the long and short wavelength ends of the HN3(A’A’’+XIA’) first absorption band were delivered by an excimer laser (Lambda Physik, EMG 102) operating with KrF (5.0eV) or XeCl (4.0 eV). To excite HN3 at the maximum of its absorption near 265 nm, a frequency-quadrupled Nd:YAG laser (Quanta Ray, DCR 1) was used at an excitation energy of 4.6 eV.I7 The pulse energy inside of the observation cell was about 5-10 mJ at a beam diameter of 2-4 mm. The NH products were probed by two different dye laser systems. For medium-resolution measurements (Av, N 0.1 cm-I) a Nd:YAG pumped dye laser (Lambda Physik, FL 2002 E) with an intracavity etalon was used. The bandwidth of this laser system is sufficient to resolve the shape of the NH(c’n+a’A) rctational transitions of the (0,O)band in order to analyze the (ji-3-J) vector correlations. The N2 partner product distribution was determined with a single-mode ring dye laser (Coherent CR 699-21) whose radiation was amplified in a three-stage dye amplifier (Lambda Physik, FL 2003) pumped by a XeCl excimer laser. The pulse duration of the amplified light was ca. 25 ns, and the spectral width was determined to be 30 MHz with an external confocal Fabry-Perot interferometer (300-MHz free spectral range, finesse 150). A BBO crystal doubled the frequency of the dye laser beam at a nearly constant efficiency of 10%within the UV tuning range of 60 GHz. The delay time between the photolyzing and the analyzing laser was 20-40 ns. The pulse energies of both laser beams were monitored by two Si detectors and stored in a microcomputer (Siemens AT 386) after A/D conversion. For measurements of the vector correlations the laser beams were both linearly polarized. The plane of polarization of the dye laser was rotated by h/2 plates. The polarization plane of the photolysis laser beam was modulated by a photoelastic modulator (Hinds Intzmational, PEM 80) on a shot-to-shot basis switching the electric E vector between being parallel or being perpendicular to the direction of the analyzing dye beam. This laser beam arrangement allowed experiments at four different probe geometries where small differences between geometry I1 and V and between geometry IV and VI9 can be detected. The LIF signal was viewed perpendicular (and unpolarized) to the laser beams with a photomultiplier tube (Valvo) equipped withfl.O imaging optics and an interference filter (327 f 5 nm
-
6106 The Journal of Physical Chemistry, Vol. 95, No. 16, 1991
-
corresponding to the c l n alA emission). The photomultiplier output was registered with a boxcar integrator (Stanford, SRS 250) and stored in the micrmmputer after A/D conversion. The dye laser scanning was also performed by the computer and controlled by spectrum analyzers. All time events in the experiments were controlled by a four-channel trigger device (Stanford, DG 535) and a homc-built variable delay unit which synchronized the photolysis laser with the photoelastic modulator. 111. Results The correlated vector properties of a molecular photofragment provide a pictorial view of the dissociation process and, hence, of the upper PES. Here, the analyzed vectors are the transition dipole moment ji of the HN, parent, the NH alA) product recoil velocity 8, and the NH rotational motion . This dynamical information can be extracted from the shape of the NH absorption lines. If the fragments are formed with a velocity distribution flu), then the Doppler profile D(uk) of the nonisotropic recoil velocity distribution induced by a linearly polarized photolysis laser is given by
s
0.9
0.8 h
-3 v
n z
0.7 0.6
-
7 I
2
0.5
3
5
0.4
-
0
3.3
-
o.2 0.1
1LI-l-
a
0
Gericke et al.
1 t 248 nm
iI,
,, ,, , ,,
2
4 6 8 10 ROTATIONAL QIJANTUM NUMBER J
12
Figure 1. NH(alA) rotational product state distribution in the photodissociation of HN3 at 308, 266,I6.l7 and 248 nm.Is
The contribution of the second term in this expression is of minor importance for Auf I( u ) . The width of the internal energy of the N2 fragment can be calculated (eq 7) according to where uk is the velocity component in the direction of the analyzing dye laser beam and P2(x) is the second Legendre polynomial. The parameter Ben contains the information about the anisotropic character of the dissociation process. In principle, Bertcan also be a function of the velocity u, but in general one assumes u and BCrrto be uncorrelated. The expression (3) has to be convoluted with the line shape of the analyzing dye laser (line width AuJ and the translational motion of the parent at temperature T ( A U=~ uo/c(8kT In 2/ M ) ’ / ~ ) . For jet-cooled molecules the contribution of thermal motion is negligible. If the recoil velocity distributionflu)/u of the fragment is small or can be approximated by a Gaussian function centered around a mean velocity with a width of Auf,then the observed line intensity I(u,) can be described by
where ua is the frequency of the probing dye laser. Aua is the fwhm of the Gaussian convolution function containing contributions from the analyzing dye laser, thermal parent motion, and velocity distribution. A least-squares fit of eq 4 to the observed Doppler profile yields the background B, the amplitude A, the anisotropy parameter the mean Dopper width AUD,and the width Auf of the recoil velocity distribution of the fragment:
sew,
A$ = Au?
- Aut - Pup2
(5)
The mean fragment velocity ( u ) is given by (0)
CAUD/UO
(6)
Since the recoil velocity of one NH fragment is directly connected with the internal energy of the partner product formed in the same dissociation (simply because of conservation of energy and linear momentum), the mean internal energy (Eint(N2))of the N2 partner fragment is given by (Eint(N2))
Ea
- Eint(NH) - 72mNH2(u2)/@
(7)
where cc represents the reduced mass of the N2-NH system and E, is the available energy for the products. For a Gaussian velocity distribution I(u)/u
-
exp[-4 In 2(u - ( U ) ) ~ / A U + ]
(8)
one obtains
(9)
mint(N2) = mNH2(u)AUf/@
(10)
We have measured the values of Be,,.(JNH)at four different geometries (266-308-nm photolysis) and for all P, Q,and R transitions. The bipolar moments (By, &, &), which quantitatively describe the vector correlation between the transition dipole moment ,of the parent (ji), the recoil velocity (3, and the rotational vector (4 of the NH product have been determined for each rotational state in the usual manner described in the literat~re.~ The rotational alignment &, and the rotational product distribution P(JNH) of the N H fragment were determined by the integrated line intensities
s,,,
j’I(ua) dva
-
P(JNH)[~O+ b 1 / 3 ~
(1 1)
where the geometry- and branch-dependent multipliers bo and b were calculated for observation of undispersed fluorescence.’ J NH Rotational State Distribution. The product state distribution of NH(a’A,u=O,J) at three photolysis wavelengths (308, 266, and 248 nm) is shown in Figure 1. The experimental data for each wavelength can essentially be represented by a Gaussian distribution. Obviously, the most likely NH rotation is nearly independent of the excitation energy. Only the width of the rotational distribution increases slightly with increasing HN, photolysis energy. In the analysis of NH products, the lowest tweelecton IA state is excited to a state. Each rotational transition consists of a pair of lines. The origin of one line is a state of A(A’) symmetry, while the initial level of the other line is the asymmetric A(A”) An unequal population of the two A doublet states contains information about the planarity of the fragmentation process. Within the experimental uncertainty of 10% no preferred population of any A doublet level was observed, neither in the bulk experiments nor in the dissociation of jet-cooled HN,. Therefore, the product state distribution in Figure 1 is given as the average of the ‘A(A’) and lA(A”) state populations. N2 Product State Distribution. The internal energy of the N2 product can be probed by (2 2) REMPI around 283 nm.I* In the case of HN3,radiation at this wavelength will not only excite the N2 fragment but also photolyze the parent molecule. D a g digian and co-workers have studied the N2product distribution in a onecolor photolysis-ionization study of HN,.’* They observed highly rotationally excited N2 photofragments with a Gaussian-like distribution. The population peaks at 4N2)= 56 and the spread is AJ z 14 (fwhm). We analyzed the N2 partner distribution by an accurate measurement of the Doppler width of the NH product according to eqs 4-10. High-rtsolution experiments (Au,
+
(20) Alexander,
M.H.; et ai. J . Chcm. Phys. 1988,89, 1749.
The Journal of Physical Chemistry, Vol. 95, NO. 16, 1991 6107
HN3(A1A”) Hypersurface
r - I 1
A
A
h
v 3
h
701 6o
248 nm
b
h b
m
.
8
.
’
I
t?PJ
I
0.8
1
266 nm
0.6 0.4
.
266 nm
0.2
i
0 -0.2 -0.4
4 O b - j 2
1
4 6 8 10 ROTATINONAL CIUANTUM NUMBER J
12
f%J
Figwe 2. Mean N2 product partner rotation, (J(N2)),for different NH rotations. At the photolysis wavelength of 283 nm,” the N2rotation is given as an average over all NH partner rotations. 1
&J
0.8
o.6 0.4 0.2
0.8 0.6
0.4
.
1
0.2
1
0
0
248 nm Beam
1.
0 0
0
0
-
0
0
0
248 nm Bulk
-0.2
1 -0.4
ROTATIONAL OUANTUM NUMBER J
-o.: -0.4
Figure 4. Vector correlation between the transitio! dipole of the parent ji and the rotational motion of the NH fragment J as a function of NH product rotation in the photodissociation of HN3at 266 and 308 nm.
2
4
6 8 10 ROTATIONAL QUANTUM NUMBER J
12
Figure 3, Correlation between the translational (5) and rotational (3 motion of the NH(IA) product generated in the photodissociation of room temperature and jet-cooled hydrazoic acid at 248 nm. The initial parent motion about the NNN chain does not influence the fragment rotation. H- 50 MHz in the UV region) of jet-cooled HN, at a photodissociation wavelength of 248 nm show no structure in the Doppler profile which may be interpreted as N2 vibrational energy. Therefore, we conclude that the N2 fragments are generated essentially with rotational excitation and the mean N2 partner rotation, (J(N2)),can be calculated from the N2 internal energy (Eint(N2)),when the available energy for the products, E,, is known (eq 7). the Since E, is determined by E, = hv Eint(HN3)dissociation energy EDb(is the quantity in question. Unfortunately, a very precise value of the bond dissociation energy, ED^,, to generate fragments in their lowest quantum state is not known. A discussion of the values appearing in the literature is given by Meier.*’ Most recently, Casassa et al.14 determined a narrow range for the fragmentation of HN,(k’A’) into N2(’2+)+ NH(IA). E h should lie between 18 190 and 18755 cm-I. however, the most likely value is very close to the upper limit.“ Thus, we use a value of Eoi, = 18 750 cm-’ in all calculations. The lower limit of Em, would reduce the calculated N2 rotation only by 2h, which has no important influence on the discussion of the fragmentation process. Figure 2 shows the obtained mean N2 rotation as a function of the NH partner rotation for different photolysis wavelengths. The dash indicates the observed mean N2 rotation at 283 nm, which was monitored only as an average over all NH partner rotations. In contrast to the observed N H product state distribution, the N2 fragment shows a strong de-
+
-
(21) Meier, U. Dissertation, Fakultit For Bochum, 1988.
Chemic, Ruhr-Universitit
pendenccon the HN, excitation energy. (p-74)Vector Comlatioas. Figure 3 shows the correlation between the translational and the rotational motion of the N H product in beam_and bulk experiments. In both cases we observe an increasing (ZJ)correlation with increasing NH rotation. Since a positive PUJparametzr indicates a preferentially parallel alignment between 3 and J, this rotational NH motion can only be generated by an out-of-plane motion of the N2-N_H system due to conservation of angular momentum.” Both (&J)correlations are similar, and therefore initial parent motion does not influence the alignment of the product rotations. The fraction of rotational energy induced by a torsional motion,fmion = (Etonion)/Emt, is given by fbmion = (1 2&,)/3, In the high-J limit, we calculate a fraction of up to 60% of the rotational energy being generated by torsional motion. It should be mentioned that the A doublets A(A’) and A(A”) show slightly different vector correlations. However, the general behavior is the same and therefore only the average value between both A states is shown. The vector correlation between the transition di le moment of HN3,ji(IA”-IA’), and the rotational vector, r o f the N H = +1 product is shown in Figure 4. The limiting values of or = -0.5 coqespond to a parallel or a perpendicular alignment between ji and J . Only at the photolysis wavelength of 266 nm and at low JNHis a small positive P,,, parameter observed. In general, the fragmentation process does not prefer an alignment between ji(HN3) and I(NH). However, a strong correlation between ji(NH,) and the N H recoil velocity U’(NH) is observed (Figure 5). For low NH rotations 0 is negative, indicating a preferentially perpendicular alignment Gtween 0’ and 2. With increasing NH product rotation the value of 8, increases and becomes positive for high fragment rotations. The value of the observed bipolar moment 0 which describes the three-vector correlation between ji(HN3), &H), and j(NH), is close to zero. If all three vectors are parallel to one another, then will reach the limiting value of -1; if two vectors are parallel to one another, but the third one is perpendicular to these
+
6108 The Journal of Physical Chemistry, Vol. 95, No. Jb, 1991
0.6 0.4
0.2
i
LJ j4 0.8
266 nm
j
0.4
-
0.2
I
W
-
W
-
-o.2 -0.4
W
0
308 nm
0.6
i
o.6 0.4
1 0
0
.
-
1
i
0
0
4 6 a 10 ROTATIONAL PUANTUM NUMBER J
12
*
308 nm
*.I
0
-0.2
0
w
I
- 0 . 4 1 , , 2
m
7
0 0
4
0
W
W
0.2 OS4
4 W
W
-0.4
I
266 nm
4
0 -0.2
Gericke et al.
2
,
,
,
,
I
,
,
4 6 8 10 ROTATIONAL PUANTUM NUMBER J
,
,
1
12
Figure 5. Spatial anisotropy of NH products as a function of NH r e tation. The values of 9,, are the average Over the A(A') and A(A") states.
Figure6. Thrce-vector correlation between ji(HN,), C(NH), and j(NH) as a function of NH product rotation. The valua of ,9@ are the average over both A states.
TABLE I: serhr P m p r h in tbe Pbetodirroc&tioD of HN3from Its First Ekctrollie Abmption Band" 248 nm 266 nm 283 nm 308 nm NH N2 NH N2 NH N2 NH N2 14100 19210 16970 4 21950 E b 6800 3640 7040 3770 6430 3440 6950 3720 Em 700 10810 700 7700 -700 6400 690 2740 fg,, 0.31 0.17 0.37 0.20 0.38 0.20 0.49 0.26 0.03 0.49 0.04 0.40 0.04 0.38 0.05 0.20 (u) 3100 1660 3320 1770 3200 1700 3310 1780 A u ~ 660 710 690 (J) 6 73 6 62 -5 56 5 37 hJ 7 18 6 15 -5 14 5 15 Av, 0.067 0.136 0.135 0.100 Au, 0.002 0.100 0.058 Aup 0.010 0.058 A u ~ 0.066 0.072 0.070
rotational excitation whereas that of the N2 fragment is extremely high. Another unexpected behavior is found in the variation of the Nz internal energy with the HN3 excitation energy. Since the kinetic energy and the NH rotational energy do not vary with the photolysis wavelength, the N2 fragment carries the surplus of the HN3 excitation energy. For dynamical calculations it is of advantage to use Jacobian coordinates to describe a photodissociation processz2because the separation coordinate R between the center of mass of the two fragments is directly related to the linear momentum p (dR/dt = p / p ) and the angle 6, between R and the transition dipole moment ii of the (nonrotating) parent is related to the anisotropy parameter 8,
-
-
=Unitsare wavenumbcrs for energy and bandwidth and m/s for velocities. The available energy, E, E(hu) + ELal(HN3) - Emu, is determined by the photon energy, E(hv), the internal energy of the parent, Eh,(HN3)= 380 cm-l in bulk and Ehl(HN3)= 30 cm-'in beam experiments, and the dissociation energy EDI, z I8 750 cm-l." vectors, then PwJ will reach the positive limit of BwJ = +'/*. A very weak tendency for @,+ is observed for changing from positive values at low J to negative values at high J (Figure 6).
IV. Di~lmsion The applied spoctroscopic method based on sub-Doppler and polarization experiments provides a deep insight into molecular motions on the upper PES. Although the scalar and vector properties are integrated with tesptct to time, the final data reflect the complete reaction path and detailed information on the upper PES can be extracted if on1 one PES is involved. This is expected in the dissociation of HN3(k1A"). All measured scalar properties are summarized in Table 1. There is striking evidence for an extremely uneven distribution of the rotational motion between the two fragments. The NH product exhibits a surprisingly low
6, = arccos (?&,
+ y3)l/2
However, the upper PES can be described easier when normal coordinates are used. In the case of the photodissociation of HN3 the upper potential energy surface v(rN1, r N H , r", (TNNH, OI"N, CY'"") depends on the distance rN, between the two nitrogen atoms of the Nz fragment, on the distance rNH between the hydrogen and the nearest nitrogen atom, on the distance "r between the separating nitrogen atoms, and on the bending anglcs (TNNH, (T"N, and which describe the v4 NNH, the us NNN in-plane, and the Yg NNN out-of-plane bending motions. Since no vibrational excited N2 fragments are observed, the dependence of the upper PES on rN2 is comparable to the ground-state potential surface. Vibrationally excited NH products have been observed at an excitation wavelength of 266 nm.l9 and rNH is an important coordinate in the photodissociation of HN,. However, we have analyzed the fragment distribution at NH(u=O), and therefore only those trajectories probing the PES will be discussed which end in the u = 0 state. Obviously, the PES must be strongly dependent on the separation coordinate " r because the fragments N2 and NH are formed. To obtain a quantitative idea about the range r of the (22) Schinke, R. Annu. Rev. Phys. Chcm. 1988, 39.
The Journal of Physical Chemistry, Vol. 95, No. 16, 1991 6109
HN3(A1A”) Hypersurface separation coordinate, we assume a simple exponential decay V(R) = Vo exp[-(R
- Ro)/r]
(13)
and neglect all other coordinates (R rm). & is the equilibrium distance, and Vo is determined by the final kinetic energy (ELin = Ekn(N2)+ Ekin(NH)in Table I) of the fragments. The Hamiltonian for this simple model is given by
H = (p2/2~) + ELin exp[-(R - RO)/rI
(14)
n 7 W
a
Integration of this equation of motion yields the separation distance R as a function of time. Obviously, the defintion of a dissociation time (i.e., the end of the fragmentation process) is arbitrary to a certain extent, because the range of the potential is, in principle, unlimited. The better the experimental resolution becomes in terms of the forces at long separation distances, the longer the influence on dissociation dynamics will be seen. If the separation R - Ro = r defines the dissociation time tD, then one obtains
r = O.46(2ELin/~tD)’/*
(15)
after integration of the equation of motion. In a previous work17 we estimated an upper limit for the dissociation time of about tD I100 fs. This result was obtained by the deviation of the observed &, parameter at J = 2 from its limiting value (bW= -0.5). Equation 15 implies that all important features of the dissociation process take place within a distance of r I 2.37 A. In general, one expects only a slightly shorter interaction range of about 1-2 A. Thus, we assume that the fragmentation process of HN3 from its first absorption band is essentially a direct repulsion, and no strong potential barrier should be found al_ongr”. The modest modulation on the absorption spectrum, A’A” %A’, is another hint for an insignificant potential The rotational excitation of the products is related to the torque provided by the gradient of the PES with respect to the bending angles CYNNH, CY”N, and CY‘””. A strong NH rotation could be induced by a v4 bending motion of the NNH frame. Since the rotation of the NH fragment is relatively low and independent of the HN3 excitation energy, the a N N H dependence of the electronic excited PES must be similar to that of the ground state, Vex(...,a”H,...) * Vgr(...,a”H,...) Vo. A significant amount of N2 rotation is generated by bending motion of the NNN frame (v5, v6 mode). It has already been shown17 that not only an in-plane bending motion is responsible for N2 rotation but that also a strong dependence of the PES on the out-of-plane bending angle, CY’””, will generate a strong product rotation. Here, the plane is defined by the planar HN3 parent in its ground state. Experimental evidence for an out-of-plane motion are an equal population of the A(A’)_and A(A_II)A doublet levels, a positive (jbij) correlation for a AIA” XIA’ transition, and a positive ( b J ) correlation at high NH product rotations. The rotational product state distribution of the N2 fragment P(JN) can be extracted from the velocity distributionflu) of the NH tragment: P(J) =flu) dv/dJ.
0.6
1
308 nm
0.4
0.2
0 0
20
40 60 ROTATIONAL QUANTUM NUMBER J(N2)
Figure 7. Product state distribution of the N2fragment obtained from the NH velocity distribution (eq 10) for different excitation energies. For a better comparison, the distribution at a photolysis wavelength of 283 nml*is calculated from the most likely N2rotation and the width (fwhm) of the experimentally observed N2 distribution.
-
+
-
P(JN,)
-
I
(UN2+ 1 ) exp -4 In 2
X
b
(16) In Figure 7 P(JN ) is shown for different HN3 excitation energies where the mean k H rotational energy and the mean width of the velocity distribution are taken from Table I. This rotational (23) Okabe, H. J. Chem. Phys. 1968,49,2726. ’McDonald, J. R.; Rahlais, J. w.; McGlynn, S. P. J. Chem. Phys. 1970, 52, 1332. (24) Meier, U.; Staemmler, V. Vertical Excitation Energies of the LowLying Excited States of HN,, to be published.
Figure 8. Joint reaction probability P ( J N 2 , J N H ) in the photodissociation of jet-cooled HN3 at 248 nm.
distribution reflects the N2 product state distribution without consideration of the NH partner fragment, since all relevant properties were derived from mean values. However, there is a small correlation between the NH rotation, JNH, and the most likely N2 rotation, ( J N I ) which , is shown in Figure 2. This distribution indicates that for a given photolysis wavelength low rotational excitation of NH correlates with high rotational states of the N2 fragment and high JNH correlate with (relatively) low JN
h e joint reaction probability P(JN2,JNH)is depicted in Figure 8. This joint distribution shows the N2 rotational distribution
when the NH partner-generated in the same dissociation event-is formed in a specific JNH state. In this case the NH rotational energy of a specific JNH in eq 16 as well as the measured width of a single distribution (eq 5 ) has to be used. The photolysis energy was 5.0 eV, and the parent was cooled in a molecular beam. For all given JNH the N2 partner distribution P(JNH,JN,)is very similar. Only at high NH rotations the width of the N2 partner distribution becomes slightly broader. The influence of initial parent motion on the N2 partner distribution can be extracted from Figure 9. The mean N2 rotation, J N 2 , as a function of JNH is shown for HN3 at 300 K (bulk) and for jet-cooled parent molecules (beam) where the rotational temperature of the parent is less than 10 K.” The N2 product rotation increases only by 1-2 quantum numbers when “hot” HN3 at 300 K is photolyzed in a bulk experiment. Thus, the initial parent motion prior to dissociation has no significant influence on the scala: properties of the fragmentation process. Since the observed ( 6 J ) correlation is not influenced by parent motion either (see Figure 3 ) , the dynamical features of this dissociation process are essentially independent of parent rotation.
6110 The Journal of Physical Chemistry, Vof. 95, No. 16, 1991
,
82
8
0
4
248 nm Bulk 248 nm Beam
I
4
A
N
5 7
78
0 0
4
-
4
0
2.2
LL
V
1
2.4
-s
4 0
CI
2.6 7
1
-
80
Gericke et al.
2
1.8 1.e 1.4
4
1.2
76
1
4
0.8 74
0.6 0.4
0.2
72
0 ROTATlONAL QUANTUM NUMBER J(NH)
Figure 9. Mean N, product partner rotations, (J(Nz)),as a function of
NH rotation in bulk and beam experiments at an excitation energy of 5 eV. The mean N2 rotation is only slightly affected by initial parent
motion. TABLE II: Derived Panmetem in t k Fng”tatiaa of HN1 from the First Electronic Excited State, AIA”, at Different Excitation Encnles
5.0 eV 4 68 88
J,,,
lmin
Lux
4.6 eV
32 42 37, 0.47 0.43
62 0.78 0.38
0.99 0.39
Ab/A
3
57 67
18
$A
4.0 eV
4
Due to the detailed knowledge of the NH(’A) and N2(’Z:) product pair and vector correlations, the orbital angular momentum f of the N2-NH system, the impact parameter b, and its distribution can be determined. In general, for a nonrotating HN3 parent the orbital angular momentum I is limited to JN*
+ JNH 2 2
IJN, - JNHI
= M l + 28u,)J(J + 1)
Jul:
J(J
+ 1) - J,,llJ2
(18) (19)
Thus, we obtain for the orbital angular momentum f the limited range lJ01XN2) - J”,XNH)I 4 1 5 JUiXN2)
+ JuJNH)
(20)
with JuIIXN2) = JuII,(NH) Jvif(N2) = J ( J + 1 )
- JUIIZ(NH)
N ~
the impact parameters which increase with increasing excitation energies (Table 11) and reach 1 A for a dissociation wavelength of 248 nm. For a simple repulsion between the nitrogen atoms in the N2-NH system the impact parameter has to be less than 0.1 A. Thus, strong bending motions have to be involved in the fragmentation process and the upper PES must be strongly dependent on the v5(a’) and u6(a”) coordinate. The distribution function of the impact parameter, P(b), which gives a quantitativepoint to the range of the forces that act during the fragmentation process, will be calculated in the following. Conservation of energy and linear momentum yields the equation Ea = y2mNH20NH2/p+ BNHJ(J +
(21)
)NH
+ BN,J(J + 1)Nz (24)
Using the relations 20-22 for the orbital angular momentum, one obtains
f(f
+ 1 ) = J(J + l)Nz + J(J + I)NH - 2Juij2(NH)f
(17)
as a consequence of conservation of total angular momentum, where JNzand JNH are the product pair rotations generated in the ?me dissociation event. However, fragment rotation with the J vector being aligned parallel to the recoil velocity 8 cannot be compensated by any orbital angular momentum, but only by a counterrotation of the partner product. This rotation, JUH,,can be calculated by the pUJparameter, Bur = (P2(cose,, )), which describes the alignment of the rotational vector with respect to the recoil velocity: J,,l[,2
Figure 10. Distribution of the impact parameter, P(b), at different excitation energies.
2IJu,XNH) Ju*,(N2)l (25) which is used to replace the term J(J
+1
) in~ eq~ 24:
Ea = f/2mNH2uNH2/p+ (BNH - BN,)J(J + 1)NH + ~ E N , J , , ~ , ~ ( N+HBNJ(f ) 1)(1 f A) (26)
+
whece A measures the uncertainty in the relative orientation of the J vectors: A = 2lJ,,,XNH) Ju,,(N2)1/~(1+ 1)
(27)
The maximum value of A is reached for the minimum value of the orbital angular momentum fw At the excitation wavelength of 266 nm one obtains A = O.17[lmi, = 57, J,,,(NH) = 4.5, 621 which will be neglected in the following. Jul,(N2) Introducing the abbreviation w2 = 2p[Ea - (BNH - BNz)J(J + 1 ) N H - 2BN2JullJ2(NH)1/”H2 (28) and the relation h21(I + I ) = “H2VNH2b2 the impact parameter and the recoil velocity are connected via
(22)
u2
= w2/(1
+ 2pBN,b2)
(29)
The values of JON,in the high-/ limit as well as those for the minimum, lminr and maximum, I,, of the orbital angular momentum are listed in Table 11. The large value of the impact parameter is essentially a consequence of low NH and high N2 rotations. The impact parameter b is calculated from the relation L bpUNH-N2 b“HuNH h[f(\ + 1)]’12 (23)
and the distribution of the impact parameter P(b) =flu) do/db is given by
where p is the reduced mass of the NH-N2 system and U N H - N ~ is the relative velocity between the two fragments. Using the mean velocities for the NH fragments (Table I), we obtain values for
where a Gaussian distribution forf(u)/o is used. The distribution P(b) which is comparable with the classical opacity function,’ is depicted in Figure 10 for different excitation energies. As can
P(b)
-
(1
+ 2&2b2)2
expl-4 In 2[w/(1
+ 2~BNzb2)1/2 (u)12/Au?1 (30)
J. Phys. Chem. 1991,95,6111-6117
Figure 11. Pictorial view of the vs in-plane and v6 out-of-plane bending motions which are responsible for fragment rotation.
be seen, the distribution is very sharply centered around the mean impact parameter listed in Table 11. Thus, probably only a small range of the PES is involved in the fragmentation process. S,o far, only information concerning scalar properties and the (8-J) correlation have been used to discuss the dissociation dynamics on the upper PES. The spatial distribution of the fragments is given by the bw parameter, which is a quantitative measure of the (ji-8) correlation. At low NH rotations the bw parameter is close to the limit of -0.5, which indicates a perpendicular alignment between I; and 8. Since for a A“-A‘ transition the dipole moment I; is perpendicular to the symmetry plane of the parent, one would expect this negative value for a planar dissociation geometry. The deviation of Ow from -0.5 is essentially caused by initial parent rotation about the axis that is in the plane of HN3but perpendicular to the N” chain. Since the N2 partner products of those low rotationally excited NH fragments are generated at high JN2(see Figure 2), the PES must be strongly dependent on the in-plane bending angle (Y”N. Therefore, the high N2 rotational motion should take place in the kitial plane of the parent and the alignment of the rotational vector JY2should be parallel to the transition dipole moment E;. Indeed, this alignment at high JN2was observed in the dissociation of HN3 at 283 nm.I8 At high NH rotations, the HN3system behaves diff%ently. The correlations between I; and 8 as well as between 8 and JNH become positive. Thus, a strong out-of-plane motion of the N-N-N chain must be responsible for fragment rotation, and the PES must also depend on the angle (Y’””. For a better visualization a cartoon
6111
of both types of motion is shown in Figure 11. NH products formed at high JNH correlate with N2 fragments at lower N2 rotations. (JN2is still very high, but lower than the mean N2 rotation.) Therefore, one expects that the alignment of lower JN with respect to I; should be less positive than the alignment of higher JN2.Again, this behavior is observed in the experiment.18 Roughly the same amount of NH product rotation is generated either via an @-plane or an out-of-plane motion as can be seen from the ( W ) correlation and Table 11. Thus, the torques d V / ~ 3 a and ” ~ dV/da- should be similar. In order to generate the high N2 rotation, the potential energy difference between the configuration corresponding to the equilibrium geometry (of the ground state) and the minimum of the upper PES with respect to CY”N and CY’”” should be in the order of 1 eV. A “phase shift” in the induced cotational motion should occur for a generation of a positive ( G J ) correlation, i.e., a torsional motion of the NH rotor. Therefore, it seems to be more likely that the upper PES is constantly steep with respect to CY”N for all N2-NH separation distances, while the gradient with respect to CY’”” should be small in the beginning of the dissociation process at R N Ro and increase with increasing R, ~V(CY””N,R=RO)/dd’”N
< C~V((Y””N,R>RO)/~CY””N.
All statements concerning the PES and the dissociation dynamics are derived from detailed experimental data. Ab initio calculations by Meier and Staemmler24*25 which are presented in the accompanying paper are in full agreement with these (sometimes semiquantitative) predictions. Trajectory calculations on the ab initio surface would be a quantitative test of the PES. Since several coordinates are involved in this direct dissociation process, the fragmentation of HN3 from its first absorption band will also be a good test of how far we can simplify the theoretical calculation without missing important features of this unimolecular reaction.
Acknowledgment. Support of this work by the Deutsche Forschungsgemeinschaft is gratefully acknowledged. We also thank Dr. U. Meier and Prof. Dr. V. Staemmler for stimulating discussions. (25)
issue.
Meier, U.; Staemmler, V. J. Phys. Chem., following paper in this
CASSCF and CEPA Calculations for the Photodissociation of HN,. 2. Photodissociation into N2 and NH on the Lowest ’A” Surface of HN, U. Meiert and V. Staemmler* Lehrstuhl fiir Theoretische Chemie, Ruhr- Universitat Bochum, 0-4630 Bochum, Germany (Received: November 21, 1990; In Final Form: March 20, 1991)
Ab initio CASSCF (complete active space SCF) and valence CI calculations have been performed for the lowest electronic states of HN3. The potential energy curves of the five lowest singlet and the five lowest triplet valence states of HN3along the interior N-N distance R show that only the lowest excited singlet state, 1 IAN, is involved in the UV photodissociation of HN3 at long wavelengths (A > 220 nm). The photodissociation products are exclusively N2(X1Z8+)and NH(alA). At shorter wavelengths several higher excited states of HN3can also be involved; this makes the photodissociation process very complex and leads to the production of NH in several different electronic states. Large parts of the potential energy surface of the 1 lA” state have been calculated, in particular in the Franck-Condon region. The dependence of this surface on the NZ-NH distance R and the various valence angles is used to explain the experimentallyobserved rotational state distributions of the photodissociation fragments N2 and NH(a). HN3(X1A’) + hv
I. Introduction The UV photodissOciation of HN3 is currently studied by several groups under different experimental condition~.l-~The reaction
(1)
0022-3654/91/2095-6111$02.50/0
HN3*
-
+
N2(X1?&+) NH*
(1)
is the dominating photodissociation channel at wavelengths longer than about 200 nm and has therefore attracted the most attention.
Present address: CONVEX Computer GmbH, D-4000 Dllsseldorf,
Germany.
+
Rohrer, F.; Stuhl, F. J. Chem. Phys. 1988,88, 4788.
0 1991 American Chemical Society
