The phosphorescence excitation spectrum of biacetyl

The phosphorescence excitation spectrum of biacetyl: An analysis of the acetyl and methyl torsional mode structure D. C. Moulea) and A. C. Sharp Department of Chemistry, Brock University, St. Catherines, Ontario L2S3A1, Canada

R. H. Judge Department of Chemistry, University of Wisconsin–Parkside, Kenosha, Wisconsin 53141-2000

H. Liu and E. C. Limb) Knight Chemical Laboratory, University of Akron, Akron, Ohio 44325-3601

~Received 14 July 1997; accepted 7 October 1997! The T 1 (n, p * )←S 0 laser-induced phosphorescence excitation spectrum of biacetyl has been recorded with a rotating slit nozzle excitation apparatus. The 0 00 system origin was observed for the first time as a weak band at 19 529 cm21. Built on this band were the activities of the three large amplitude modes: y 16(a u ) acetyl torsion, y 15(a u ) gearing methyl torsion, and y 21(b g ), the antigearing methyl torsion. The potential surface for methyl internal rotation extracted from fitting the observed levels yielded a barrier to methyl torsion of 359.6 cm21. © 1998 American Institute of Physics. @S0021-9606~98!00803-4#

INTRODUCTION

As one of the few substances that phosphoresce efficiently in both gas and solution phases, biacetyl has played a key role in the study of the photophysics and photochemistry of intermolecular energy transfer. The sensitization or quenching of biacetyl phosphorescence, through triplet– triplet energy transfer, is now a commonly used technique for the characterization of triplet T 1 electronic states.1 It is because of the importance of the first triplet electronic state that the characterization of the emission from biacetyl has been the subject of great interest.2 The spectrum of biacetyl vapor under room temperature conditions has a broad structureless appearance. This diffuseness under bulb conditions has been attributed to the density and complexity of the underlying band structure. The first detailed view of the vibronic band structure contained in the visible absorption and emission spectra came from the solid crystalline phase at 4 K. In that early study, Sidman and McClure3 observed that under very low temperatures, the visible fluorescence and phosphorescence systems could be resolved into a sharp but complex pattern of vibronic bands. They established that two electronic transitions were responsible for the absorption, 3 A u ← 1 A g and 1 A u ← 1 A g , that came from the electronic excitation of an electron from the nonbonding n orbital located principally on the oxygen atoms to the p * antibonding orbital of the carbonyl groups. More recently, these same visible spectra were recorded by Brand and Mau4 under somewhat the same conditions. As well as confirming much of the earlier vibronic analysis, these authors measured the fluorescence and phosphorescence lifetimes of the two transitions to be 12 ns and 2.5 ms, respectively. a!

Author to whom correspondence should be addressed; electronic mail: [email protected] b! Holder of the Goodyear Chair in Chemistry. 1874

J. Chem. Phys. 108 (5), 1 February 1998

The coupling of laser-induced fluorescence excitation spectroscopy ~LIF! to a supersonic molecular beam has proven to be an ideal technique for studying diffuse spectra that result from vibronic band congestion. The 1 A u ← 1 A g , singlet–singlet, system in biacetyl is an excellent example of the simplification that can be obtained by the jet-cooled fluorescence technique. In contrast to the straightforward analysis of the low temperature crystal spectrum, the assignment of the 0 00 singlet–singlet origin band in the expansion cooled gas-phase fluorescence excitation spectrum has proven to be a nontrivial problem. Campargue and Soep,5 McDonald and co-workers,6 and Ito et al.7 all have reported that the band patterns in the region of the origin were extremely complex. For this reason they assigned the first band that was encountered in the cold jet spectrum, at 22 336 cm21, to the 0 00 origin. Under warm and cold jet conditions, Saenger, Barnwell and Herschbach8 observed three weaker bands further to the red of this band that clearly indicated the position of the origin needed to be reassigned. To distinguish between these conflicting assignments, Senent et al.9 synthesized the vibronic profiles at the red end of the spectrum from ab initio unrestricted Hartree–Fock/restricted Hartree–Fock ~UHF/ RHF! calculations. The band patterns predicted in their work were found to match the experimental jet-cooled LIF spectrum of Saenger et al.,8 who placed the origin the furthest to the red of the existing assignments. These authors also recorded the ‘‘hot jet’’ LIF spectrum of biacetyl. Many of the intervals connecting the hot bands at the red end of the spectrum were found to lock in with band positions in the single vibronic level dispersed fluorescence spectra recorded by Ito and co-workers.7 The corresponding jet-cooled spectrum of the triplet– singlet companion transition, 3 A u ← 1 A g , as a LIP ~laserinduced phosphorescence excitation! spectrum falls into the category of a difficult experiment for two reasons. First, because of the spin-forbidden nature of the process, the system has a low absorption cross section and as a result, the carrier

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Moule et al.: Excitation spectrum of biacetyl

of the emission is difficult to excite. Second, with a 2.5 ms lifetime for the T 1 state, it is difficult to capture a significant fraction of the emission that emanates sideways from the supersonic molecular beam. Spangler and Pratt10 were able to overcome this latter difficulty by inserting a large parabolic reflector around the beam that concentrated the phosphorescence emission into the photomultiplier. With this technique they were able to record a jet-cooled excitation spectrum consisting of a complex series of bands that lay to the red of the singlet–singlet system that they attributed to the 3 A u ← 1 A g system. In their analysis of the torsional band progressions they employed a two-dimensional model Hamiltonian with decoupled methyl rotors and established the assignments of the stronger prominent bands in terms of the methyl torsional modes, v 15(a u ) and v 21(b g ). Their analysis also indicated that the 0 00 origin of the system was extremely weak relative to the higher members of the torsional band progressions and they were forced to conclude that the calculated location of the 0 00 origin did not correspond to any of the features that were weakly observed in the LIP excitation spectrum. In an attempt to settle the question of the couplings between the two methyl torsional modes as well as that of the origin position, we performed a series of ab initio calculations that were designed to simulate the band progressions in the low frequency region of the spectrum.11 This work confirmed the assignments of Spangler and Pratt10 for the stronger bands. A number of weak features at the red end of their observed LIP spectrum, however, could not be reproduced by our calculations. Thus it was concluded that the starting point for the dominant progressions was not the true origin of the system, but rather a pseudo-origin attached to the true origin that was too weak to be observed. The aim of the present work is primarily to determine if it is possible to record an improved jet-cooled LIP spectrum that would lead to the direct observation of the origin band. An experimental value for the 0 00 transition would secure the intervals in the spectrum and the frequencies of the torsional modes in the upper T 1 state. The high luminescence intensity that can be obtained from the pulsed slit molecular jet makes it an ideal source for detecting weak signals. It could provide the answer to the problem of the vibronic analysis of the origin region of biacetyl. EXPERIMENT

The LIP excitation spectrum was recorded with a pulsed linear nozzle that has been described by Amirav et al.12 for absorption studies but also has proven to be effective in detecting weak luminescence.13 The He–sample mixture was expanded through a rotating slit nozzle of dimension 0.22 346 mm that generated pulsed planar jets with repetition rates of 10 Hz and a pulse duration of roughly 200 ms. The carrier gas, at 200 Torr, was premixed with the sample by bubbling it through liquid biacetyl. To achieve maximum phosphorescence intensity, but with somewhat less cooling, in some experiments the biacetyl was used neat without dilution by the carrier gas. Biacetyl from Aldrich Chemicals

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was used without further purification. The excitation source was a dye laser ~Lamda Physik, FL3002E!, that operated with Coumarin 307 laser dye, with 0.2 cm21 spectral resolution. The dye laser was pumped by an excimer laser ~Lamda Physik, LPX 110i! at a wavelength of 308 nm and an energy of 50–60 mJ/pulse. The laser beam crossed the molecular jet 10 mm downstream from the slit jet. A lens of 40 mm focal length was mounted perpendicular to the axes of the laser and molecular beams and a concave reflector mounted opposite to the focus lens increased the signal intensity. To detect the weak phosphorescence, the lens was focused at a point 15–17 mm downstream from the point of excitation to avoid scattering and fluorescence. The light emitting from the first focus was focused to the second focus of the focus lens where a photomultiplier tube ~PMT! ~Hamamatsu 1527P! was mounted. A cutoff filter and slit aperture oriented parallel to the laser beam was mounted in front of the PMT to further reduce the scattered and fluorescent light. The phosphorescence signals from the PMT were averaged by a homemade boxcar integrator, with gate width of 500 ms and a gate delay of about 5 ms. Thirty to one-hundred laser shots were averaged for each data point in the spectrum.

THEORY

In systems containing two methyl groups attached to the same carbon atom, the dynamics of the torsional motions can be studied as a two-dimensional problem in which the dynamical variables are the two torsional angles of the methyl groups. The low frequency vibrations that arise from such rotations may be regarded as a set of gearing and antigearing motions in which the groups rotate in the reverse or same sense with respect to each other, somewhat like a pair of intermeshing gears. In the case of acetone,14 the methyl groups interact directly with each other as a result of their proximity. When the two groups rotate with a gearing-type motion ~clockwise–counterclockwise!, the hydrogen atoms come, on average, into their positions of closest approach, which maximizes the steric repulsions between the interacting hydrogens. On the other hand, when the two groups move in the antigearing direction ~rotation in the same direction!, the hydrogens move away from each other into a position of minimum steric hinderance. The interference between the two groups lifts the degeneracy between the two modes. For the case of acetone, the gearing and antigearing fundamental modes have widely separated frequencies. In biacetyl, (CH3CO) 2 , the two methyl groups attach to the planar a-dicarbonyl frame in a trans conformation. Thus the rigid molecule has a center of inversion and a C 2h symmetry. As the two rotors are attached to different carbon atoms and are directed away from each other at opposite ends of the molecule, it would be anticipated that the methyl–methyl coupling would be very small. The low frequency methyl torsion dynamics thus would be close to two independent rotors coupled only through their kinetic energies. The internal coordinates of interest are given in Fig. 1, where u 1 and u 2 represent the torsional coordinates of the

J. Chem. Phys., Vol. 108, No. 5, 1 February 1998



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V ~ u 1 , u 2 ! 5337.212169.01@ cos~ 3 u 1 ! 1cos~ 3 u 2 !# 12.77 cos~ 3 u 1 ! cos~ 3 u 2 ! 21.12@ cos~ 6 u 1 ! 1cos~ 6 u 2 !# 10.15@ cos~ 3 u 1 ! cos~ 6 u 2 ! 1cos~ 6 u 1 ! cos~ 3 u 2 !# 20.03 cos~ 6 u 1 ! 3cos~ 6 u 2 ! 10.05 sin~ 3 u 1 ! sin~ 3 u 2 ! .

FIG. 1. The three large amplitude coordinates in biacetyl. u 1 and u 2 are the methyl torsion coordinates and a is the coordinate for acetyl torsion.

two methyl groups and a the torsion of the acetyl groups about the central carbon bond. In this initial treatment it is necessary to assume that the methyl and acetyl torsions can be separated from each other. The Hamiltonian operator for a system bearing two equivalent methyl rotors attached to a rigid COCO frame can be written as n

ˆ5 H

n

(i (j

S

2B i j

D

]2 ]Bij ] 2 1Vˆ , ] q i] q j ] q i ] q j

~1!

where the q’s represent the torsional coordinates, u 1 and u 2 and the B i j are the kinetic energy expansion coefficients ~reduced internal rotation constants!. The summation is over the two methyl torsion coordinates, n52. The potential energy for a methyl group undergoing hindered internal rotation can be represented by a cosine function that is three-fold periodic in the torsional angle. For the case of coupled rotors this potential is represented as the double Fourier series n

NV

V5

(k )j V 0k

f kj ,

~2!

where the V 0k are the potential energy expansion coefficients and the f k j are the sine and cosine terms in the expansion. N v is the number of terms in the expansion for the potential energy. A surface is generated when the torsional potential energy is plotted against u 1 and u 2 . For complete 360° revolutions of the methyl groups this surface contains nine wells and for this reason it is often referred to as the ‘‘egg box’’ potential. In our previous study9 of the S 0 ground state, the potential energy was calculated at the MP2/6-31G(d,p) level of ab initio approximation as a series of grid points in u 1 and u 2 . These data points were converted into the analytical form of Eq. ~3! through a least-squares fitting procedure and resulted in the double Fourier series of Eq. ~3!. The energy barrier separating the minimum u 1 5 u 2 50° and maximum u 1 5 u 2 560° points on the potential surface was 675.4 cm21,

~3!

To complete the evaluation of the Hamiltonian, Eq. ~1!, the kinetic energy terms were evaluated by numerical differentiation15 at the same grid points in u 1 and u 2 . A fit to the data points yielded the constant kinetic energy coefficients: B 115B 2255.5826 and B 12520.1668 cm21. The resulting Hamiltonian matrix was constructed and then symmetrized according to the symmetry operations of the nonrigid G 36 point group. Energy levels and eigenvectors were calculated using the variational method with 37 basis functions for each rotor. These were reduced to 16 boxes corresponding to the representation of the G 36 point group; A 1 (49), A 2 (42), A 3 (42), A 4 (36), G(43156), E 1 (2378), E 2 (2366), E 3 (2378), and E 4 (2366). Table I shows the calculated energy levels for the ground state. For the levels that lie at the bottom of the potential surface, the internal rotation is restricted and resembles a torsional oscillation which is best described by the quantum numbers of the harmonic oscillator. Thus, the C 2h rigid biacetyl rather than the fully flexible G 36 model is more useful in classifying the lower quantum levels. Table I shows that each of the levels of the rigid C 2h model contains four microlevels A, E, E, and G for a total degeneracy of 9. The splitting between these levels depends on the degree of restriction of the rotational motion. At the bottom of the well the levels split by torsion are close together, whereas in the region of the top of the barrier they will be widely separated. The correlation between the one-dimensional representations of the two groups are: G 36(nonrigid)→C 2h ~rigid point!; A 1 →a g , A 2 →b g , A 3 →a u , A 4 →b u . A 3 A u ← 1 A g electronic transition that involves the interchange of electron spin direction during the LIP excitation process is forbidden by the selection rule, DS50. The strength of the transition comes from the spin–orbit couplings between the triplet and the adjacent singlet excited states. In the language of perturbation theory, the intensity of a singlet–triplet transition is said to be borrowed or stolen from the allowed singlet–singlet transition, provided the combining electronic states are of the correct symmetry. If it is the 1 B u ← 1 A g valence p → p * transition that provides the strength of the singlet–triplet n→ p * system, then the dominant transition would be B u (x,y) polarized and would be directed in the a/b plane of the molecule. The out-of-plane c-type transitions would require vibronic–spin–orbit coupling and would not be expected to appear in the spectrum. Relative intensities of the bands in the methyl torsional progression were obtained from I a ~ g n 2g m ! m 2nm ,

~4!

where the g’s represent the nuclear statistical weights of the




1877

TABLE I. Torsional energy levels for the S 0 ~ground!a and T 1 ~excited!b electronic states of biacetyl (cm21). v 15c

v 21d

Ge

S0

T1

v 15

v 21

G

S0

T1

0

0

A1 G E1 E3

123.76 123.78 123.81 123.81

107.10 107.24 107.39 107.39

2

0

A1 G E1 E3

330.46 330.49 339.05 339.04

249.65 251.98 262.50 261.79

1

0

A3 G E2 E3

238.55 238.04 237.66 237.66

188.70 187.13 185.80 185.81

1

1

A4 G E2 E4

330.48 339.14 339.26 339.26

256.67 269.74 274.20 275.51

0

1

A2 G E1 E4

241.98 241.60 241.10 241.10

220.30 215.16 217.83 215.20

0

2

A1 G E1 E3

257.62 356.82 356.04 356.04

307.29 303.09 301.97 299.62

From Ref. 11 with parameters of Eq. ~3!. This work and Eq. ~5!. c n 15(a u ) methyl gearing vibrational quanta. d n 21(b g ) methyl antigearing quanta. e G 36 nomenclature. a

b

lower levels of the transition and m nm is obtained from the Franck–Condon overlap of the n and m wave functions of the T 1 and S 0 states.

Figure 3 presents an overall view of the 3 A u ← 1 A g LIP excitation spectrum of biacetyl recorded with the slit-jet molecular beam device, while Fig. 2 gives a detailed view of the origin region. Table III gives the positions of the observed bands. What is perhaps not too surprising, in this expanded and improved view, is the existence of a complex underlying cold band structure in the origin region. All of this band complexity can be related to the activity of the set of three torsional modes, 2a u 1b g , that have fundamental frequencies of less than 100 cm21. Two of the torsional modes result from methyl internal rotation, namely, from the n 21(b g ) an-

tigearing rotations of the two groups and the n 15(a u ) gearing combination. For the sake of convenience, these modes are labeled A and G. The third torsional mode in biacetyl comes from the rotation of the two acetyl groups ends of the molecule against each other, y 16(a u ) and is designated by the letter T. The single quantum additions of all three modes would be forbidden by the vibronic–spin–orbit rules of the rigid C 2h point group. The wave functions of the overtone levels of these modes G 2 , A 2 , and T 2 are totally symmetric and the intensities of the transitions are controlled by the Franck–Condon considerations. As the methyl groups undergo the eclipsed to staggered conformational displacements, the overtones of gearing and antigearing modes are expected to be much stronger than the origin band. The starting point for our assignments came from the 19 794 and 19 825 cm21 bands at the blue end of the spectrum. These are prominent bands in the spectrum and were

FIG. 2. The origin region of the 3 A u ← 1 A g singlet–triplet transition in biacetyl recorded as a LIP ~laser-induced phosphorescence! excitation spectrum. Mode T is the n 16(a u ) acetyl torsion; mode G, n 15(a u ) methyl gearing torsion, and mode A the n 21(g g ) methyl antigearing torsion.

FIG. 3. An overall view of the LIP spectrum of biacetyl with assignments given for the bands attached to the T 20 acetyl torsion suborigin.

ASSIGNMENTS AND ANALYSIS



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assigned by Spangler and Pratt to the overtone transitions, G 20 and A 20 . Their assignments are immediately confirmed by the strongest bands in the LIP spectrum at 19 871 and 19 918 cm21 and were assigned to G 20 A 10 and G 20 A 20 . These four bands and their intensities are sufficient to establish the pattern and assignments for the band progressions at the blue end of the spectrum. The identification of the vibronic origin of these four bands has proven to be more elusive. Senent et al.11 derived the T 1 surface for these modes by the UMP2/6231G(d,p) ab initio procedure and fitted the positions of the intense bands. An extrapolation of their model placed the origin at 19 640 cm21. The difficulty with this prediction is that this position is considerably lower than the 19 680 cm21 suggested by Spangler and Pratt.10 Each of these bands could be a candidate for the vibronic origin. The choice between these alternatives was made by forcing a fit to the energy levels of Eq. ~1! and the intervals with each of the two band positions as a starting point. The results of the fitting procedure clearly showed the feature at 19 680 cm21 to be the best starting point. It was taken to be the origin. The next problem concerned the weak cold bands in the region of the origin. As a result of the improved phosphorescence intensity of the slit-jet apparatus, a complex pattern of bands was observed to emerge from the background. It thus follows that the true origin of the 3 A u ← 1 A g electronic transition must lie among the weak bands that are further to the red. The 19 680 cm21 band to which the strong A and G progressions are attached then must be assigned as a vibronic suborigin of the system. To account for this cluster of cold bands, a cardboard template was constructed that took the form of a stick spectrum ~see Fig. 2!. This template was moved 1150 cm21 across the unassigned bands until a match between the two spectra was achieved. In this way, the true origin was located as the sharp band at 19 529 cm21. Figure 2 shows the bands in this region and their assignments in term of the gearing and antigearing mode activity. Table II gives the observed band positions and their displacements from the 0 00 band. In order to complete the assignments in the origin region, it was necessary to find a spectral designation for the 1150 cm21 interval between the vibronic and true origins. Help in this direction comes from the observation of the n 16(a u ) mode in the lower S 0 ground state. During et al.16 have observed a Q branch in the far infrared spectrum of the vapor at 56 cm21, which they attributed to n 16 . As a single quantum, this antisymmetrical mode would not be expected in the LIP excitation spectrum as a consequence of the vibronic–spin–orbit selection rules. However, the 1150 cm21 interval then could be assigned to the double quanta 2 n 16 . Assuming zero anharmonicity, this would place the fundamental at 150/2575 cm21. This assignment is also able to account for the last major problem, namely, the band at 117 cm21. This interval is too small to be a fundamental, but it does lock in as the sequence band n 816 2 n 916 and would bear the assignment, T 11 . The very low ground state frequency of 75 cm21 would account for the

TABLE II. The observed and calculated band positions and intensities for the LIP3A u ← 1 A g LIP excitation spectrum (cm21).

Assign.

Ga

Int.b 31022

Calc.c Position

0 00

A1 G E1 E3

0.052 0.027 0.002 0.002

0.00 0.50 1.00 1.00

0

G 10

G E3

0.293 0.047

61.14 59.01

61

A 10

G E1

0.126 0.061

76.59 71.66

77

G 20

A1 G E1 E3

0.711 0.185 0.262 0.063

109.12 108.82 125.59 124.55

109

A 20

A1 G E1 E3

0.076 0.153 0.112 0.434

146.35 128.72 140.86 141.09

G 10 A 10

G

0.158

142.93

G 10 A 20

G

0.060

178.38

G 20 A 10

E3 G E1

0.000 3.441 0.023

179.02 186.82 179.11

A1 G E1 E3

0.691 0.526 1.164 0.621

232.69 212.56 214.27 201.82

G 20 A 20

Obs.d Position

141

186 233

a

Identical G 36 representations for the T 1 and S 0 states. Relative intensities from Eq. ~4!. c From the level data of Table I with 0 00 (A 1 – A 1 ) set to 0.00 cm21. d Intervals measured from the 19 529 cm21, 0 00 band. b

presence of this hot band, albeit weakly, in the cold jet spectrum. There are three torsional modes 2a u 1b g whose fundamental frequencies lie in the first 100 wave numbers of the spectrum. In the C 2h rigid point group, all three modes would be forbidden by the vibronic–spin–orbit selection rules. These modes are labeled T, n 16(a u ) acetyl torsion, G, n 15(a u ) methyl gearing torsion, and A, n 21(b g ), methyl antigearing torsion. The unanswered question in the present analysis concerns the appearance of the single quantum transitions, G 10 , A 10 , and T 10 . The location of T 10 can be arrived at 8 (a u )519 680275519 605 cm21. An inspection as T 20 2 y 16 of this region clearly showed that the T 10 band is absent in the spectrum. If a band does appear, it is below the somewhat noisy background level of the experimental spectra. The question of the possible appearance of the G 10 and A 10 fundamentals required help from computer simulation. While the rigid C 2h selection rules do not allow for the single quantum of G ~methyl gearing! or A ~antigearing torsion!, both of these fundamentals become active under the selection rules of the G 36 nonrigid group. The ab initio calculations of Senent et al.11 predicted that because of the




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DISCUSSIONS AND CONCLUSIONS

FIG. 4. A 120°3120° segment of the V( u 1 , u 2 ) potential surface for the methyl internal rotation.

eclipsed-staggered conformational shifts in the geometry, the G 10 and A 10 bands should have considerable strength relative to the 0 00 band. The overtone transitions of these methyl torsion modes have bands, G 20 and A 20 , that appear very clearly in the spectrum at 1109, 1141 cm21. Other major bands were found as G 20 A 10 at 1186 cm21 and G 20 A 20 at 233 cm21. A fitting of these G and A levels of the T 1 state to the Hamiltonian of Eq. ~1! yielded the torsional energy levels for the joint methyl rotation of Table I. When the data were combined with the intensities calculated by the Franck–Condon overlap factors of Eq. ~4!, the position and intensity data of Table II were generated. Figure 2 compares the observed LIP spectrum in the origin region with a stick representation of the fitted spectrum. It is clear that the G 10 band at 161 cm21 is accounted for. It consists of E 3 – E 3 and G – G components with strengths, 0.047 and 0.293 separated by 2.13 cm21. On the other hand, the two E 1 – E 1 and G – G components of the A 10 transition are weaker with intensities of 0.061 and 0.126. The weakness of these components and their 4.93 cm21 separation mitigates against a firm assignment of this band. The double Fourier expansion with B 115B 2255.5588 and B 12520.2522 cm21 was found to reproduce the observed T 1 level structure,

The true 0 00 origin of the 3 A u ← 1 A g transition appears to be firmly established. Amajor reason for this belief is that all of the weak band features at the red end of the spectrum have been assigned. The other satisfying aspect of the placement of the origin at its current value is that the intervals in the acetyl torsional mode lock in with the ground-state infrared fundamental. Also, it is possible to make a correlation between the singlet–triplet energy difference for the S 1 and T 1 electronic states of the three molecules: biacetyl ~dimethyl glyoxal!, methyl glyoxal, and glyoxal, all of which bear the COCO a- dicarbonyl framework. For glyoxal17 and methyl glyoxal,10,18 the singlet–triplet splittings, E(S 1 ) – E(T 1 ), are observed to be 2776 and 2655 cm21. The effect of methyl substitution is to increase the physical space available for the lone electrons in the n and p * outermost orbitals and thereby reduce the Fermi correlation energy, 2 K. The 2653 cm21 value observed here for biacetyl is in good agreement. The identification of the acetyl torsional mode attached as an interval of 2375 cm21 to the 0 00 origin is the other significant aspect of this analysis. The increase in acetyl torsional frequency from the ground state value of 56 cm21 is completely in keeping with the changes that occur in the structure and bonding in the formation of the np * excited states. The addition of the excited electron to the p * orbital creates an antibonding orbital that is spread out over the COCO network and while antibonding in the CO group is bonding between the two carbon atoms. The net effect is to introduce partial double bond character into the central bond and stiffen the COCO group to torsional flexing. As a result, the height of the acetyl torsional barrier and the frequency of the acetyl torsion mode increases from 56 to 75 cm21. In

TABLE III. The positions of the observed bands in the LIP spectrum of biacetyl (cm21).

V ~ u 1 , u 2 ! 5151.67190.40@ cos~ 3 u 1 ! 1cos~ 3 u 2 !# 122.50 cos~ 3 u 1 ! cos~ 3 u 2 ! 18.13@ cos~ 6 u 1 ! 1cos~ 6 u 2 !# 20.50@ cos~ 3 u 1 ! cos~ 6 u 2 ! 1cos~ 6 u 1 ! cos~ 3 u 2 !# 210.63 cos~ 6 u 1 ! 3cos~ 6 u 2 ! 215.40 sin~ 3 u 1 ! sin~ 3 u 2 ! .

~5!

A plot of the potential function is given in Fig. 4. This surface has a minimum at u 1 5 u 2 560° and a maximum of 359.6 cm21 at u 1 5 u 2 50°.

a

Relativea position

Assign.

Position

0 00 T 11 G 10 A 10 G 20 A 20 T 20 G 10 A 10 G 10 A 20 G 20 A 10 T 20 G 10 T 20 A 10 T 20 G 20 T 20 A 20 T 20 G 10 A 10 T 20 G 10 A 20 T 20 G 20 A 10 T 20 G 20 A 20

19 529 19 546 19 590 19 606 19 638 19 670 19 680

10 117 161 177 1109 1141

19 715 19 748 19 757 19 794 19 825

1186

19 871 19 918

Relativeb position

10

168 177 1114 1145

1191 1238

Gearing and antigearing bands attached to the 0 00 origin at 19 529 cm21. Attached to the T 20 acetyl torsion suborigin at 19 680 cm21.

b



1880


glyoxal the corresponding y 7 fundamental changes from 127 to 232 cm21 on electronic excitation. The surprising aspect of the spectrum is the strength of the transition in acetyl torsion, T 20 . If the COCO is rigidly planar in the two electronic states, then the transition is directed vertically upwards, D a 50, and the Sponer–Teller theorem19 suggests that I(T 20 )/I(0 00 )50.01. That is, based on the frequency shifts alone, the double quantum of the out-ofplane acetyl torsion mode, T 20 , should have 1% of the intensity of the 0 00 , origin band. This intensity ratio appears to be borne out in the spectrum of glyoxal.10 For methyl glyoxal the rule is observed to break down and Spangler and Pratt report a ratio of 30/70 for the two bands.10 Thus, it is clear that it is the presence of the methyl group that is related to the unusual strength in this mode. Presumably, the source of the intensity is a coupling between three internal coordinates, u 1 , u 2 , and a in the formation of the normal coordinates. As the methyl torsion coordinates, u 1 and u 2 , have large Franck–Condon factors as a result of the eclipsed-staggered conformational changes, mode mixing would introduce strength into the acetyl coordinate, a. That is, the acetyl torsion transition, T 20 , forbidden by the planar–planar vertical nature of the transition, steals intensity from the methyl torsional modes. The other question, the methyl torsion dynamics, has been addressed by Spangler and Pratt10 and by Senent et al.11 With the assignment of the true 0 00 origin of the system, the intervals that define the torsional energy levels are now secure. The strength of the acetyl torsional mode is unexpected and must have its source in a potential energy coupling between a, u 1 , and u 2 . Thus a reliable hypersurface for the torsional modes in T 1 biacetyl will require a treatment of the three large amplitude modes. ACKNOWLEDGMENTS

We are grateful to Y. D. Shin and J. Praeger for their experimental assistance during the early stages of this re-

search. The work at the University of Akron was supported by the Office of Basic Energy Sciences of the Department of Energy. D.C.M. thanks the University of Akron for a visiting fellowship and the National Sciences and Engineering Council of Canada for financial support. R.H.J. gratefully acknowledges the support of the Petroleum Research Fund and the National Science Foundation.

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