Rotational Relaxation of Benzophenone in the Vapour Phase

The excited singlet state lifetimes of benzophenone vapour have been measured at 
shorter wavelengths than previous studies and with picosecond time resolution. 
Excitation was at a series of wavelengths from 313.5 nm to 284 nm, which gave S2( Π Π *) 
decay times of tens of picoseconds. We also report measurements of the polarisation 
anisotropy decay due to free rotation of excited state benzophenone. Time-dependent 
anisotropies calculated by both quantum mechanical and classical formulae are in good 
agreement with the experimental data and demonstrate benzophenone to behave as a 
rigid rotor. From the residual anisotropy, at long times, it is concluded that no rotation 
to vibrational energy transfer occurs during the excited state lifetime.


INTRODUCTION
Benzophenone has been the subject of many experimental studies, both in the gas phase and in solution.In solution the photophysics is governed by a rapid (8 30 ps-1) $1 --T intersystem crossing rate and almost complete lack of fluorescence from the nr* $1 state.In the isolated molecule limit, gas phase benzophenone has a long lumine- scence lifetime, of some hundreds of nanoseconds, and which depends upon excitation wavelength.Because of this long lifetime, the excited molecules can collide with the cell walls or drift out of the detection region unless special precautions are taken, and these effects have led to the observation of complex 2'3 and biexponential decay profiles. 4The longest of these decays yielded lifetimes greatly in excess of the natural radiative lifetime of the state excited, and this was explained by extensive singlet-triplet mixing. 4Naaman et al. 5 used an experimental arrangement which removed the possibility of wall collisions or drift out of the detector region.They generated an effusive beam of benzophenone, detected the emission by observing along and perpendicularly to the beam direction, and measured only single exponential decays when the benzophenone was isolated in its excited state.The $1 lifetimes measured varied with excitation energy from 470 ns at 337 nm to 690 ns at 367 nm, and a very large collision cross section was claimed to be responsible for the longer lifetimes previously reported.Besides the early work of Borisevich et al., 6 who measured a 6.5 ns duration emission exciting into the rr* absorption, no other similar experiments have been reported exciting into $2.In an effort to understand the excited state properties of benzophenone we have extended the range of measurements to shorter wavelengths than used previously and also down to the picosecond region.

EXPERIMENTAL
Excited state decays were measured using a pump/probe technique with multiphoton ionisation detection. 7Subpicosecond pulses (0.8 ps fwhm autocorrelation) originate from a synchronously pumped and mode-locked dye laser with an intracavity saturable absorber. 8The pulses were amplified to 800/xJ per pulse in a four stage dye laser amplifier pumped by a Nd:YAG laser operating at 10 Hz.The experi- mental arrangement is as shown in Figure 1.The amplified pulse was split, 60% telescoped, frequency-doubled and the fundamental fil- tered out.The U.V. was passed through a calcite polariser.The visible beam, transmitted by the beam splitter, was passed along a delay line and its polarisation rotated either parallel or perpendicular to the pump beam.The U.V. and visible beams were recombined at the sample by a Pellin-Broca prism and focussed with the same 300 mm fl lens.A photodiode after the cell monitored the U.V. and visible reference signal levels.The ion signal was measured by a charge sensitive pre-amplifier and further amplified (Ortec 575) before being digitised by a fast track and hold and ADC circuit.Ion signals were Benzophenone energy levels.A set of rotational levels in the S2 vibrational manifold are coherently excited by the pump pulse and are ionised by the probe pulse.An intermediate set of rotational levels is also shown.normalised for laser intensity fluctuations and poor pulses discrimi- nated against by passing the reference signal through a narrow window of a single channel analyser.The cell contained benzophenone vapour in equilibrium with the solid which was contained in a side arm.
Measurements were made at 294 K, and at this temperature the vapour pressure was estimated to be 4 x 10 -4 torr, 9 which ensured isolated molecule conditions during the time-scale of the experiment.
Laser wavelengths were calibrated against optogalvanic lines in a neon discharge.
The ionisation energy of benzophenone is 75802 cm-1.1 Using only fundamental (O)1) and frequency doubled (0)2) light, photons of wave- length shorter than 659.6 nm are required to ionise the al state in a four photon (0)2 + 30)1) scheme, Figure 2. The ion signal diminishes in proportion to the number of excited molecules present, and thus measures the excited state decay. 7The intensity of both the excitation and ionising beams was carefully controlled so as to prevent ionisation from either beam alone.Some ionisation from the excitation beam alone is, however, unavoidable and contributes a constant background signal.A five to eight times ion signal enhancement is observed when both beams are present compared to the excitation beam alone, Figure 3a.

RESULTS AND DISCUSSION
The absorption spectrum of benzophenone shows a broad and weak nr* transition centered at 350 nm and more intense and structureless absorption starting at about 300 nm and peaking at 255 nm which is due to :rr* transitions.Excitation into the net* state produces a long lived emission, which decays at a rate of 1.5 x 106 to 2.13 x 104 s-1, depending on excitation energy. 5The radiative rate of this state as measured from the integrated absorption spectrum is 0.5 x 106 s -1.It has been suggested 5 that benzophenone is in the large molecule statistical limit, and that the increase in rate with excess energy in $1 is due to $1 -So internal conversion.'5 The r:r* transitions have been analysed by Yoshino et al. 1 based on reference wavefunctions of a benzene dimer and a carbonyl group.Using polarised absorption in stretched films they identified transitions at 317, 305 and 257 nm.The 257 nm, A B2, transition is about seven times more intense than the other two A -A transitions.The location of these weak transitions must be uncertain, however, as they overlap extensively and generate only small changes in the polarisation &dOIOSINU IIISN31NI ratio of stretched films.In our experiments we excited into the tail of the 257 nm transition and also into the short wavelength end of the nr* transition.Table I lists the decay times observed exciting from 313.5 to 284 nm.At the longest two wavelengths very small signals were observed and we attribute this as due to excitation primarily into the n:r* absorption from which we assume that the overall ionisation cross section is small compared to that of the r* state.At shorter wave- lengths the excited state lifetime was measured as several tens of picoseconds, Table I, and this great shortening compared to the nr* state is probably due to spin-orbit enhanced rr* T,, intersystem crossing.The radiative rate of the rr* state is not known but if we assume that it is similar to that of benzene (2.40 x 10 6 s-1) the reciprocal fluorescence lifetime is effectively the non-radiative rate constant.The decrease in lifetime with increasing energy in the excited state is typical of many aromatic molecules and in general terms is explained by radiationless transition theory as an increase in the Franck-Condon weighted density of states between the two states involved.12 The benzophenone absorption spectrum is very congested, it is unknown which levels are being excited and thus it is unclear how to apply the Golden rule formula directly.The approach of Jacobson et al. 13 in treating high vibrational levels in substituted naphthalenes should be of more use.They show that the non-radiative rate depends on the ratio of the density of states times the square of the average interaction matrix element when many initial levels are excited.Using this approach, calculating the density of states using Raman and i.r.NO ion signal enhancement.b Anisotropy decay assumed exponential in non-linear least squares convolution with instrument profile.frequencies, 14 leads to a 1.7 x increase in rate between 307 and 284 nm which is of the correct order of magnitude increase as shown by the data.The larger non-radiative decay rate from the r:r* than the nr* state could be due to allowed lrr* --3n:rt'* crossing, via a spin-orbit coupling operator with B symmetry (in CEv), compared to the "forbid- den" lnr* --3nr* transfer.
When the polarisation of the pump and probe are parallel a rapidly decaying transient is observed at short times after excitation, Figure 3 and we attribute this transient to the free rotor motion of the excited molecule.Similar transients were observed from 4,4'-dimethoxy and 4,4'-dichlorobenzophenone. Stilbene also exhibits polarisation dependent signals, and our measurements are similar to those of Zewail et al.,7 but in aniline and several substituted naphth- alenes no fast transient on the decay of the ionisation signal was ob- served.
The data in Figure 3a shows the effect of probe polarisation both parallel and perpendicular to the excitation, from this data the aniso- tropy r(t) [Ill(t) I+/-(t)]/[Ill(t) / I+/-(t)] was calculated, Figure 3b where/ll and I' are signals at time for probe polarisation parallel and perpendicular to the pump polarisation respectively.Initially the anisotropy decays on the time scale of (I/kT) 1/2 where I is the moment of inertia, but at longer times does not fall to zero but is a slowly varying function of the moments of inertia. 5At very long times, or increased pressures, collisions will change the angular momentum of the molecule and the anisotropy should tend to zero, as in solution.At short times the free rotor behaviour should still be observable.This transient, which represents the rigid-body rotational motion in a classical picture, is in quantum terms due to interferences between different intermediate J levels that are connected to the same initial and final states, Figure 2. Using a quantum approach Felker et al. 16 have examined fluorescence transients produced from free rotation in isolated molecules, this approach can be extended to describe ioni- sation experiments if we assume that ionisation occurs equally well from any of the intermediate J levels produced, Figure 2.
When a particular vibronic state and rotational level (JoKoMo) is excited by a short pulse of polarised light a coherent superposition of rotational levels tp(t), is produced in the excited vibronic manifold.This superposition evolves in time as transitions occur by fluorescence or absorption to the final state dp(JKM)f.The signal intensity with either parallel or perpendicular pump and probe polarisations, can be calculated after averaging over a thermal distribution of J0 and K0, I(J,r) Z ( q(t)lef'llcP(J,K,M)f) z JKM I(t) I(J, K) exp (-EdKbT) JoKo where E B Jo(Jo + 1) + (A B)K and A and B are the usual rotational constants of a prolate symmetric top; er is the detection polarisation and/x the dipole moment operator.Finally l(t) should be multiplied by the population decay probability exp (-t/).
If we assume that the benzophenone although asymmetric, with principal moments of inertia (x 10 -Kgm2) Iz 0.49, Ix 1.93 and Iy 2.42,17 can be represented as a symmetric top and averaging Ix and Iy, Eq. ( 1) may be evaluated with selection rules AJ 4-1, 0 and AK 0 for parallel transitions and AK + 1 for perpendicular transitions, and by summing over M to account for the isotropy of the sample.The unique inertial axis lies perpendicular to the carbonyl bond and in the plane of the molecule.The A B2 (.*) transition is polarised along this axis and the nr* transition is perpendicular to it.In evaluating Eq. (1) the direction-cosines are tabulated by Cross et al. is and polarisation dependent factors for the time independent terms by Loge and Par- menter.19 Time dependent terms arise as cosines with frequencies Vl 2BJo, 112 2B(Jo + 1) and 113 111 q-112 when AK 0. For AK + 1,111 2BJo + v,, v2 2B (Jo + 1) + vk, and v3 vl + v2 + Vk, where Vk (A B)/(2.The factors needed to evaluate these off-diagonal terms are given in the appendix.Interference between the cosine terms generates the initial oscillatory nature of the anisotropy near 0, reoccur- rences may also occur at longer times. 16Figure 4 shows transients calculated using Eq.(1).
As described above no transients attributable to rotational motion were observed in aniline or several naphthalenes for reasons that are unclear.The lack of fast signals could mean that rotational to vib- rational coupling is fast, but we have excited both below and above the energies expected for the onset of IVR with similar results.Another possibility is that the pumping or ionising transition is easily saturated in these molecules where the signals are several hundred times greater than from benzophenones.In saturation the laser would excite most molecules in the cosine squared distribution about the direction of laser polarisation; 21 this would produce a more isotropic distribution and remove the possibility of observing rotational motion.
Because our experiments were done at room temperature many J levels (430) need to be summed over in evaluating Eq. ( 1), and both /l(t) and I+/-(t) calculated to obtain r(t).Alternatively r(t) can be calculated directly [but not I(t)] from the classical formulae of Yang and Bersohn 2 vis, r(t) goo(Doo(t)) + g11(t) (Dl(t)) + g22(D22 (t)) where the g's are sums of products of spherical harmonics, and describe the angle between the absorption, emission (probe) dipole moments and the principal axis.The D's are the correlation functions averaged over reorientation angles.
These functions are simpler to evaluate than the equivalent quantum ones and surprisingly we found that for benzophenone even at as low a temperature as 3K the anisotropy calculated from the classical model is almost indistinguishable from that calculated by the quantum formulae.The reason being the large number of J levels are still populated at this temperature.Convoluting the calculated anisotropy with a Gaussian pulse of the duration of our laser pulse produces similar decay products to those measured experimentally, Figure 5.
The decay of the calculated r(t) gave a lifetime very similar to the 1.5 ps measured experimentally.
The long time value for the anisotropy r() is 0.06 + 0.02 and compares well with the calculated value of 0.067 for a parallel transi- tion.If the transition were perpendicular to the unique inertial axis (i.e.nz* state) r(o) would be 1/4 that of the parallel case. 15 '21 In principle the measured r(o) value could indicate which state the excited singlet decays into.If the 3n*, or another state which is perpendicu- larly polarised is populated, r() should decrease, however, in practice since the ion signals [l(t)] return to close to the background level the cross-section for ionisation from the 3n* state must be small com- pared to that from the initially excited state.The initial anisotropy value r(0) 0.4 + 0.05 is effectively at its maximum value which means that the dipoles for absorption and ionisation are parallel and that little if any rotation to vibrational coupling occurs on the fast time scale i.e. during the laser pulse.Similarly the value of r(o) implies that in benzophenone hundreds of rotational periods are needed before rotational to vibrational energy transfer occurs.If some rotation to IISN+/-NI XilgN+/-NI vibrational coupling were occurring, as is the case in stilbene where r(0) 0.15-0.2and r() 0.05, 22 or pyrimidine 23 the r(0) value for benzophenone would be smaller than measured and the r() could decrease to 0.034 which is the limit for complete statistical behaviour in a parallel transition. 15

Table I
Excited state lifetimes and radiation times of benzophenone vapour