reactions 
 in which a cyano ( cn ) radical abstracts a hydrogen atom 
 from an organic molecule present an unusual opportunity to contrast 
 chemical reaction dynamics under isolated conditions and in the presence 
 of a liquid solvent .
these reactions are exothermic , 
 typically releasing more than 100 kj mol ; in contrast 
 to the liquid phase where this energy rapidly transfers to the surrounding 
 solvent , the energy in low - pressure gas - phase reactions can only be 
 distributed among the translational and internal degrees of freedom 
 of the two products .
the potential energy surfaces for reactions of 
 the type summarized by eq 1 , with r = h , ch3 , or other alkyl groups,1have early and low energy barriers , with a 
 flat angular dependence at the transition state .
consequently , the energy released by the reaction excites 
 the hcn product mode - specifically in the c 
h stretching ( v3 ) and bending ( v2 ) vibrations , as confirmed by infrared ( ir ) emission and absorption 
 spectroscopy measurements , as well as trajectory calculations .
the 
 rates and mechanisms of reactions of cyano radicals with hydrocarbons 
 have been extensively studied at low pressures and temperatures because 
 of their importance in the chemistry of the atmospheres of titan , 
 triton , and pluto . crossed molecular 
 beam studies of cn + alkane reactions ,
in which the alkyl radical 
 products were ionized without quantum - state specificity , showed that 
 approximately 8085% of the energy of reaction is deposited 
 in internal modes of the products , which are scattered with angular 
 distributions that indicate direct dynamics .
the energy deposited in 
 hcn bending and c  h stretching vibrations 
 persists for reactions in liquid solvents such as chloroform and dichloromethane , 
 although the degree of vibrational excitation is somewhat reduced .
the reaction mechanism in solution 
 may be modified by factors such as formation of complexes between 
 the cn radical and a solvent molecule , or coupling 
 of the reaction degrees of freedom with the solvent bath .
nevertheless , any shifts in the position of 
 the transition state must be modest , and any solute 
solvent 
 couplings must be weak for the gas - phase - like dynamics to persist 
 to such an extent in solution  at 
 least , for these types of organic solvent .
velocity map imaging 
 studies of various exothermic bimolecular 
 reactions in the gas phase have shown that measurement of the energy 
 disposal to both products of reaction carries additional insights 
 beyond what can be learned by studying only one of the products .
these experiments used molecular beam techniques 
 to ensure isolated collisions , and under favorable circumstances could 
 map out the correlated vibrational energy content of both reaction 
 products .
the correlations were deduced 
 from measurement of kinetic energy release distributions of one product 
 in a specific vibrational quantum state , and application of momentum 
 and energy conservation arguments .
no corresponding methodology has 
 yet been developed to observe correlated product energies for reactions 
 in solution , but both products can be independently probed to determine 
 their internal energy content .
we illustrate this idea in the current 
 report for the case of the reaction of cn radicals with acetone , eq 2,2 in deuterated chloroform ( cdcl3 ) solutions .
we used time - resolved vibrational absorption 
 spectroscopy 
 ( tvas ) in the infrared region with picosecond time resolution to observe 
 absorption features of the hcn and 2-oxopropyl ( or acetonyl ) radical 
 ( ch3c(o)ch2 ) products and present evidence that 
 both are vibrationally excited at their point of formation .
this excess 
 vibrational energy couples to the solvent bath , flowing from the product 
 molecules on time scales of tens to hundreds of picoseconds .
time - resolved 
 electronic absorption spectroscopy ( teas ) provides complementary information 
 on the interactions of the cn radicals with the solvent and their 
 rates of reactive loss .
building on pioneering work by hochstrasser 
 and co - workers , crowther et al .
studied 
 the rates of cn radical 
 reactions in solution by teas and tvas .
their experiments 
 were conducted in ch2cl2 and chcl3 solutions , and the proposal was made that cn forms linear and bridged 
 complexes with these chlorinated solvents . in these complexes , the 
 maximum in the cn ( b  x ) absorption band shifts to shorter wavelength 
 and the band broadens compared to the gas phase .
the reactions of 
 cn radicals with organic cosolutes were determined to have bimolecular 
 rate coefficients smaller than the corresponding gas - phase reactions 
 because of the stabilizing effect of the cn 
we introduce acetone to an icn / cdcl3 solution , and advances in vibrational probing highlight additional 
 intermolecular interactions between the cn radical and the carbonyl 
 group in the ketone .
the results presented here provide evidence for 
 contributions to the observed reactions in solution from both cn  cdcl3 and cn  acetone complexes .
the time - resolved transient - absorption experiments 
 were performed 
 using the ultra facility at the rutherford appleton laboratory . the instrumentation has been described previously , and a brief summary is provided here of the 
 details of particular relevance to the current study .
samples 
 were prepared with 0.36 m icn ( acros scientific , > 97.5% ) 
 in anhydrous cdcl3 ( sigma - aldrich , 99.96 atom % ) or chcl3 ( sigma - aldrich , > 99.8% ) with acetone ( sigma - aldrich , 
  
 99.9% ) concentrations up to 1.5 m. solutions were kept at room temperature 
 ( 294 k ) in brown - glass volumetric flasks .
all glassware was stored 
 in a drying oven when not in use , and water contamination was minimized 
 by drying the acetone and chloroform over 3  molecular sieves . 

the flow cells used for the experiment were assembled with 0.2 mm 
 ptfe spacers between caf2 windows and sealed using kalrez 
 o - rings , which are chemically compatible with acetone and chloroform . 

using deuterated chloroform helps isolate any observed hcn as a product 
 of hydrogen abstraction by cn from acetone .
the ir spectrum of cdcl3 does not contain any strong spectral features in the c = o 
 and c = n stretching regions that might interfere with transient 
 ir spectroscopy measurements .
icn was photodissociated at a 
 wavelength of 267 nm by a 1 j 
 laser pulse of 50 fs duration and products were probed over time delays 
 of 12500 ps by teas using a white light continuum ( 310700 
 nm ) and by tvas using tunable broadband ( 500 cm bandwidth ) mid - ir light pulses . in both cases ,
the transmitted probe 
 pulses were dispersed by a grating onto an array detector ( 512 pixel 
 for teas , 128 pixel for tvas ) to measure changes in optical density 
 induced by the uv excitation pulse .
experiments were also conducted 
 on solutions of acetone in cdcl3 without addition of icn 
 to identify transient features associated with acetone photochemistry 
 that we attribute to triplet states .
samples of cdcl3 without 
 icn and acetone showed only a weak response in teas under our experimental 
 conditions .
irradiation of a solution of icn and acetone in cdcl3 at 267 nm induces both icn dissociation and acetone photochemistry , 
 followed by various possible radical reactions .
multiple intermediate 
 and product species might therefore contribute to the teas and tvas 
 spectra .
hence , calculations were carried out to characterize the 
 harmonic vibrational frequencies and electronic excitations of possible 
 reaction intermediates , reaction products , and acetone photofragments 
 to guide the assignments of bands in the teas and tvas spectra .
dft calculations of harmonic vibrational frequencies were performed 
 in gaussian 09 using the b3lyp functional with the 6 - 311++g(d , p ) basis 
 set .
this method was chosen for its computational 
 efficiency and because of its reliability of calculation of energetics 
 of first row compounds .
the diffuse functions were necessary to capture 
 the interactions between -orbitals in cn radicals and acetone . 

a polarizable continuum model was applied to mimic chloroform solvent 
 effects , as implemented in gaussian 09 .
the calculated vibrational band frequencies were offset from their 
 experimental values , so an empirical linear correction factor , fitted 
 to be 0.948 from comparison with an ftir spectrum of 1.0 m acetone 
 in cdcl3 , was applied to all computed frequencies .
the 
 calculated wavenumbers of bands that might contribute to the tvas 
 spectra in the carbonyl stretching region are used as a guide to assignment 
 of spectral features , with the caveat that the continuum model may 
 not capture all solvent effects , such as formation of solute 
the enthalpy changes ( rh0k ) associated with h - abstraction from acetone reaction 2 were also computed in gaussian 
 using various theoretical methods to quantify the reaction exothermicity 
 and to benchmark more computationally efficient techniques against 
 cbs - qb3 calculations .
the cbs - qb3 calculations 
 predict rh0k = 125.0 
 kj mol for the gas - phase reaction , and mimicking 
 the effects of a chloroform solvent using a polarizable continuum 
 model modifies this computed enthalpy change to 134.7 kj mol . for comparison , dft calculations at the b3lyp/6 - 31++g(d , p ) 
 level incorporating the same treatment of the chloroform give rh0k = 153.5 kj mol for reaction 2 .
the similarly exothermic h atom abstraction reactions of 
 cn with propane and cyclohexane were previously shown to be barrierless , and we therefore expect facile reaction of cn 
 with acetone to make hcn . our group has recently shown that 
 molecular dynamics simulations 
 of cn reactions are helpful as we build atomistic interpretations 
 of the liquid - phase reaction mechanisms . in a computational study of the dynamics of cn radical 
 reactions with propane and cyclohexane in the gas phase and in solution , 
 glowacki et al . computed structures and energies using dft with the 
 bb1k functional , modified to have 56% hartree  fock exchange .
trajectory calculations presented in the current study for the cn 
 + acetone reaction , however , sought only qualitative mechanistic insights , 
 so a simpler treatment of the energetics was used .
direct dynamics 
 trajectory calculations for isolated collisions were performed using 
 the venus program with local gradients extracted from nwchem electronic 
 structure calculations .
trajectories were propagated 
 using potential energy gradients computed by the dft / b3lyp method 
 with a 6 - 31++g(d , p ) basis set .
the cn radicals were initially provided 
 with 2.4 kj mol of translational energy ( corresponding 
 to kbt ) and were directed 
 at the acetone with randomly selected initial orientations and with 
 zero - point vibrational energy but no rotational energy .
impact parameters 
 were fixed to values of 0 , 1 , 2 , 4 , and 5  .
time - step sizes 
 of 0.2 fs were used , and propagation was maintained for up to 1 ps .
the focus of this study is the reaction of 
 cn radicals with acetone 
 in solution in cdcl3 .
acetone was chosen as the coreagent 
 because the strong infrared absorption from the c = o stretching 
 mode facilitates detection of possible organic radical reaction products 
 such as 2-oxopropyl , ch3c(o)ch2 .
ultraviolet 
 photolysis of icn dissolved in a solution of acetone in cdcl3 was used to initiate the reaction .
the 267 nm wavelength photolysis 
 liberates cn radicals in less than 50 fs , and teas in the near - uv and visible regions revealed the production 
 of cn radicals , their association with solvent molecules , and their 
 reactive removal .
the hcn and 2-oxopropyl products were monitored 
 by trvs using broadband ultrafast ir pulses .
acetone absorbs 
 weakly at 267 nm ( contributing an absorbance a  
 1 for most of our samples ) and the photoexcited 
 acetone can undergo norrish type i photochemistry by cleavage of a 
 c  c bond , or vibrational quenching of the photoexcited state 
 can populate low vibrational levels of the s1 and t1 states of acetone with long lifetimes .
teas and tvas of acetone / cdcl3 solutions were therefore used to characterize any contributions 
 by acetone photochemistry to the spectra obtained for icn / acetone / cdcl3 solutions .
ultraviolet photolysis of icn in organic solvents 
 and geminate recombination to icn and inc have been the subject of 
 several previous experimental and computational studies ; these processes are not discussed here , but both icn and inc bands 
 appear in our tvas spectra , as shown below .
this section considers 
 the information obtained from the teas experiments 
 and then turns to the tvas results .
spectral assignments and dynamical 
 deductions are guided by electronic structure calculations of electronic 
 and vibrational band frequencies .
we turn first , however , to discuss 
 the outcomes of the trajectory calculations because the insights they 
 provide influence the interpretation of the teas and tvas data .
the results of 
 our trajectory simulations , which do not include solvent 
 effects , can be separated into the two classes of reaction pathways 
 represented pictorially in figure 1 .
direct abstraction of a hydrogen atom ( figure 1a ) appears to be favored by 
 approach of the cn from the side opposite to the carbonyl group .
this 
 orientation prevents the cn radical from experiencing an attractive 
 interaction with the carbonyl orbitals .
on the other hand , approach 
 of the cn toward the carbonyl group ( figure 1b ) results in three types of trajectories ; 
 in all cases , the cn is first attracted toward a potential well corresponding 
 to a cn 
the trajectory may then redistribute 
 the energy of the collision among the internal modes of acetone so 
 that the complex survives longer than the 1 ps simulation time .
alternatively , 
 the cn radical can experience large - amplitude motions on a flat area 
 of the potential surrounding the carbonyl group , after which the two 
 species separate or the cn abstracts a hydrogen atom . the competition 
 between direct abstraction and this addition 
elimination pathways 
 is reminiscent of the mechanisms for reactions of gas - phase cl atoms 
 with propene and other alkenes .
the direct - abstraction mechanism 
 generates simulated hcn products that are internally hot , with up 
 to 3 quanta of excitation in the c 
h stretching mode and 8 
 quanta in the bending vibration . in our measurements ,
the solvent 
 may quench the energy required to escape from potential energy wells 
 associated with structures like the cn 
acetone complex , trapping 
 these solute  solvent adducts and slowing , or preventing further 
 reaction
. schematic diagram of the classes of trajectories observed in simulations 
 of isolated collisions of cn radicals with acetone .
( b ) pathways initiated by c = n  carbonyl 
 group interactions , leading to a cn  acetone complex , or large 
 amplitude cn radical motion followed by cn separation from acetone 
 or h atom abstraction .
the b  x electronic 
 band of the cn radical centered at 389 nm provides a distinctive signature 
 of this species in teas spectra .
this band evolves with time as the 
 cn radicals form complexes with solvent molecules , and the intensities 
 of transient bands associated with these solvent complexes decay with 
 increasing time delay because of reactive loss of cn radicals .
figure 2 illustrates this 
 behavior following 267 nm excitation of a 0.36 m icn/1.0 m acetone 
 solution in cdcl3 .
decomposition of one illustrative transient 
 spectrum , at a time delay of 2.5 ps , shows the constituent absorptions 
 assigned to uncomplexed (  free  ) cn radicals and solvent - complexed 
 (  solvated  ) cn radicals , and a long - wavelength feature 
 attributed to i*(p1/2)-solvent charge transfer 
 ( ct ) .
the corresponding ct band of ground - state 
 i(p3/2 ) atoms underlies the cn 
radical 
 features and can not be distinguished from them but will grow as i * 
 atoms electronically quench to ground - state i. teas spectra of separate 
 solutions of acetone in cdcl3 and icn in cdcl3 are shown in supporting information . 
 the spectra support these assignments and identify other contributors ; 

in particular , a transient absorption band assigned to the t1 state of acetone is observed at wavelengths below 400 nm .
this triplet 
 state has a lifetime > 2 ns in solution in cdcl3 but may be more rapidly quenched in the presence 
 of iodine atoms . under the conditions of our experiment
, the acetone 
 t1 band contributes about 20% of the intensity of spectral 
 features attributed to cn radicals and can not reliably be separated 
 from the solvated - cn bands .
inspection of figure 2a shows a weak absorption that remains at 
 the longest measurement time of 1.75 ns .
this feature is absent without 
 acetone , but the band shape is inconsistent with both the t1 absorption band of acetone , and with cn  cdcl3 complexes . 

instead , it may correspond to surviving cn radicals bound to cdcl3 or the carbonyl group of acetone .
the latter interpretation 
 is encouraged by teas spectroscopy of an icn solution in acetone , 
 in which a band similar in shape to the long - time feature in figure 2a was observed .
this band was not separately fitted in our spectral decomposition 
 because of its similarity to the free cn band ; instead , it contributes 
 an apparent growth to the free cn band with a time constant of 263 
  22 ps .
transient electronic absorption spectra of icn/1.0 m acetone / cdcl3 solutions and the spectral decomposition into component absorptions . 

( a ) teas spectra following 267 nm excitation for times delays from 
 0 to 1750 ps .
( b ) example of decomposition of the spectrum obtained 
 at a time delay of 2.5 ps into its constituent parts .
( c ) time dependence 
 of the free and complexed cn and the i * absorption bands obtained 
 from decomposition of teas spectra .
the solid lines are biexponential 
 fits with time constants and amplitudes reported in table 1 .
spectral decomposition produced the time - dependent band intensities 
 for free cn , solvated cn , and i * of the type shown in figure 2 .
this decomposition and others 
 presented in this paper all used the koala software package .
the faster decay time scale 1 of the free 
 cn radicals matches the rise in the solvated cn signal ; the time constants 
 for both these processes are controlled by a combination of the cooling 
 of initially rotationally hot cn photofragments , complexation with cdcl3 or acetone , geminate 
 recombination to icn and inc , and reaction with acetone .
the time 
 constant 2 , and the relative amplitude of the slower 
 free cn decay component indicate that up to about one - third of these 
 cn radicals avoid complexation , reaction and geminate recombination 
 on an approximately 12 ps time scale .
the decay of the solvated cn 
 signal is attributed to reaction with acetone or solvent .
the time 
 dependence of the feature assigned to i * is not considered in detail 
 here , but the rapid initial decay is consistent with geminate recombination 
 with cn radicals and is similar to time constants reported by rivera 
 et al . for i * decay in water and ethanol . the longer - time decay may be associated with spin 
orbit quenching 
 of i * that has separated from its geminate cn photoproduct or is an 
 artifact of a contribution from cn 
similar measurements 
 were made for other solutions with acetone 
 concentrations in the range 01.5 m. the second time constant , 
 2 , from biexponential fits of the type shown in figure 2 for both free and 
 solvated forms of cn shows a dependence on acetone concentration because 
 this decay component is associated with the bimolecular reaction between 
 cn and acetone . under conditions in which the acetone is in excess 
 over cn radicals , the reciprocals of the 2 time 
 constants
correspond to pseudo - first - order rate coefficients for h 
 atom abstraction from acetone reaction 2 by free and solvated cn radicals .
reaction with the 
 cdcl3 may also contribute to cn - radical loss , but it is 
 known to be slow and is unimportant to this analysis.figure 3 shows pseudo - first - order 
 kinetic plots from which bimolecular rate coefficients for h atom 
 abstraction of k2f = ( 8.3  0.6 ) 
  10 m s ( for the free cn + acetone reaction ) and k2c = ( 2.5  1.1 )  10 m s ( for the solvent - complexed cn + acetone reaction ) 
 are determined .
uncertainties are 2 sd from the linear fits . the greater 
 uncertainty in the data for the solvated cn loss may be a consequence 
 of overlapping absorption by the i(p3/2)-solvent 
 ct band or by acetone ( t1 ) produced by the 267 nm excitation . 

fitting of the sharper free - cn absorption band is relatively immune 
 to these interferences from broad underlying features .
the solvent - complexed 
 cn reaction rate coefficient value must be 
 treated with some caution because of possible spectral interferences 
 but is similar in value to bimolecular rate coefficients reported 
 by crowther et al . for cn radical reactions with various organic solutes 
 in chlorinated solvents .
the lower reaction 
 rate for solvated compared to free cn is consistent with both its 
 stabilization by complexation , and unfavorable orientation of the 
 cn radical for h - abstraction from neighboring molecules .
the large 
 value of k2f for the facile bimolecular 
 reaction of free cn with acetone can exceed the diffusion limit expected 
 for a homogeneous solution if the acetone solvates the icn precursor 
 preferentially over cdcl3
. the estimated rate of 
 growth of the weak , broad absorption band 
 centered just below 400 nm ( figure 2a ) , and most clearly observable at longer time delays , 
 is similar to the rate of loss of cn  cdcl3 complexes . 

the band is not observed in the absence of acetone , but a similar 
 feature appears following uv photolysis of icn in neat acetone ( supporting information ) .
this evidence suggest 
 assignment to a cn  acetone complex , which can form by transfer 
 of a cn radical from cn  cdcl3 .
dependence of the pseudo - first - order 
 rate coefficients on acetone 
 concentration for loss of ( a ) free cn and ( b ) solvated and complexed 
 cn radicals .
pseudo - first - order rate coefficients were obtained as 
 the reciprocals of the time constants 2 from biexponential 
 fits to time - dependent band intensities .
nonzero intercept values 
 indicate reactive loss of cn radicals with species other than acetone , 
 such as the solvent .
the teas data provide quantitative information on the rates 
 of 
 removal of cn radicals , and distinguish solvated and unsolvated forms . 

consequently , 
 tvas spectra were obtained and analyzed for spectroscopic signatures 
 of reaction products .
transient ir absorption 
 spectra were obtained with the probe laser spanning 14501850 
 cm to observe carbonyl ( c = o ) , and 20002200 
 cm to observe nitrile ( c = n ) stretching 
 modes . in the nitrile region ,
the spectral resolution was improved 
 to 1.5 cm per pixel by changing the order 
 of the spectrometer grating to resolve better some overlapping spectroscopic 
 features . in the carbonyl region ,
the acetone band centered near 1690 
 cm strongly attenuated the probe light and masked 
 the region from 16701720 cm .
the tvas spectra 
 measured in the 20002200 cm region showed 
 numerous , partially overlapping bands , which were 
 assigned on the basis of previous studies of icn photolysis and cn 
a sample set of spectra is shown in figure 4 together with the band assignments .
typical 
 data sets contained spectra at 50 or more time delays from 0 to 2500 
 ps , only a few of which are shown in figure 4 for clarity .
the band centered at 2162 cm is assigned to 
 the c = n stretching mode of icn and appears in the transient 
 spectra as a negative - going  bleach  feature because 
 the icn is depleted by the 267 nm photolysis laser .
spectral decomposition 
 suggests there is a broad positive - going feature with a center displaced 
 to higher wavenumber than the icn bleach ; this feature decays rapidly 
 and is tentatively attributed to vibrationally hot icn formed by i 
 + cn geminate recombination on the ground electronic state . on the 
 basis of this assignment , its decay ( with a time constant of 5.5  
 0.6 ps ) is indicative of vibrational cooling by coupling to the solvent 
 bath .
our caution in the assignment stems from the absence of similar 
 signatures of vibrationally hot icn from i + cn geminate recombination 
 in other solvents .
the interpretation 
 of this feature is not critical to the main themes of this paper . a band centered at 2067 cm
is assigned to the 
 inc product of in - cage geminate recombination ; although a minor channel , 
 it is observed in our spectra because of the large transition dipole 
 moment of the isocyanide group .
evidence 
 from our laboratory indicates that the inc also forms vibrationally 
 excited and that the growth rate of the band at 2067 cm is controlled by vibrational relaxation .
time - resolved 
 vibrational spectra of 267 nm excited icn / acetone / cdcl3 solutions in the 20202180 cm range . 

we attributed the weak feature 
 at 2040 cm , 
 discernible to the low - wavenumber side of the inc band , to solvated 
 cn radicals in previous work .
it grows 
 with an initial ( few picoseconds ) spurt followed by a slower component 
 with a time constant of 27  7 ps ( for a solution with 1.0 m 
 acetone ) .
the initial rise can be accounted for by direct complexation 
 of free cn radicals with either cdcl3 or acetone because 
 it is consistent with the 2.3 ps rise of the solvated cn band in the 
 teas spectra .
the slower time constant for growth of the 2040 cm band depends linearly on the concentration of acetone , 
 and a pseudo - first - order kinetic analysis gives a bimolecular rate 
 coefficient of ( 2.6  0.8 )  10 m s ( 2 sd uncertainties ) .
acetone complexes of the 
 type discussed earlier , and the observed time constants indicate an 
 indirect route in addition to the direct formation from free cn .
we 
 suggest that some fraction of the cn first complexes to the more abundant 
 cdcl3 molecules , then transforms into the more strongly 
 bound acetone complexes . if this interpretation is correct , 
 we must invoke an intermediate 
 denoted cn 
cdcl3 * to reconcile the rate coefficient 
 value above with the k2c = ( 2.5  
 1.1 )  10 m s value for the loss of cn 
cdcl3 such as an isomer or an internally hot complex , in which case it 
 will also contribute to the observed teas band .
acetone complex , or by vibrational 
 energy transfer to the solvent to form thermalized cn
the proposed 
 assignment of the broad uv / visible band centered below 400 nm in teas 
 data ( figure 2a ) to 
 a cn 
cdcl3 complexes by cdcl3/acetone exchange on a time scale of a few hundred picoseconds . 

these various processes are summarized in scheme 1 , with time constants appropriate for 1.0 
 m acetone solutions and the associated up and down arrows indicating 
 growth and decay , respectively .
acetone complexes 
 comes from the carbonyl region 
 tvas data discussed in section iv.c.ii , where some of the time constants incorporated in scheme 1 are explained . however
, 
 we must consider a second possible explanation based on recent work 
 from our group on icn photolysis in various solvents : as was noted earlier , some fraction of the in - cage geminate 
 recombination of cn + i produces inc , and the nascent molecules are 
 vibrationally excited .
hot bands of the inc are shifted to lower wavenumber 
 than the fundamental n = c stretching band at 2067 cm , and their decay rates may be enhanced by vibrational energy transfer 
 to acetone , giving the observed concentration dependence .
because 
 this interpretation requires population to feed from higher vibrational 
 levels into the levels observed via the 2040 cm absorption band to maintain a spectroscopic feature over several 
 hundred picoseconds , we consider it unlikely .
( a ) time dependence of the hcn band 
 shown in figure 4 , 
 with the inset showing an expanded view of the first 500 ps .
( b ) a 
 pseudo - first - order plot of the dependence of first - order rate coefficients 
 ( obtained as reciprocals of exponential time constants for hcn growth ) 
 on acetone concentration .
the band of most interest to the current study is centered 
 at 2097 
 cm and corresponds to the fundamental c = n 
 stretching v1 = 1  v1 = 0 absorption of hcn reaction products .
the time dependence 
 of the growth of this feature is shown in figure 5a .
an exponential rise in intensity is preceded 
 by an initial decay with time constant of 5.9  0.6 ps that is 
 associated with imperfect separation of the hcn feature from the broad 
 band observed at early times to higher wavenumber ( tentatively icn * ) . 

we therefore concentrate on times after 10 ps when this interfering 
 feature has a negligible influence .
the spectral decomposition 
 indicates that the hcn band has a negative 
 intensity from 10 to 100 ps .
the precise zero of intensity is difficult 
 to identify because of neighboring features , but various different 
 fitting procedures consistently returned negative intensities at early 
 times and a delayed growth of the hcn fundamental band .
we have observed 
 these characteristics before : our prior studies of cn radical reactions 
 in solution showed them to be signatures of an initial population 
 inversion in the vibrational levels of hcn .
greater population in vibrationally excited 
 levels than in the vibrational ground state is a consequence of the 
 dynamics of these exothermic reactions with early transition states and has also been reported for gas - phase reactions 
 of cn radicals .
we therefore conclude that the cn + acetone reaction produces vibrationally 
 hot hcn , and past precedent suggests that this excitation will be 
 localized in the c  h stretching and bending modes . the rate of rise in the intensity of the 
 hcn fundamental band at 
 2097 cm depends linearly on acetone concentration 
 ( figure 5b ) and a pseudo - first - order 
 analysis gives a bimolecular rate coefficient of khcn = ( 2.0  0.9 )  10 m s ( 2 sd uncertainties ) that is consistent with 
 the rate coefficient for loss of solvent - complexed cn of k2c = ( 2.5  1.1 )  10 m s deduced from the teas spectra presented in figure 2 .
this correspondence 
 indicates that the chemical reaction step is rate determining for 
 production of hcn from solvated cn radicals . in some of our prior 
 studies of cn radical reactions in chlorinated solvents , vibrational 
 relaxation of the internally excited hcn instead controlled the rate 
 of increasing intensity of the fundamental band .
the two different limiting behaviors depend on whether this vibrational 
 relaxation is faster or slower than the chemical production of hcn . in the current case ,
the coupling of vibrationally 
 hot hcn to cdcl3 is weak , but 
 acetone appears to be an efficient alternative quencher .
vibrationally 
 hot hcn from reactions of free cn radicals should 
 give rise to transient absorption bands observable at short time delays 
 to lower wavenumber than the 2097 cm fundamental 
 band .
however , we are unable to observe these hot bands directly in 
 the current experiments because the small anharmonicity of the c = n 
 stretch ( x11 = 10 cm ) and weak anharmonic couplings between the c = n stretching 
 mode and the bending ( x12 = 3 
 cm ) and c  h stretching ( x13 = 15 cm ) vibrations , shift the absorptions to regions overlapped 
 by the inc band and the low - wavenumber side of the hcn fundamental 
 band
. there are two important features in the c = o stretching region 
 following icn photodissociation in acetone / cdcl3 solutions . 

a representative set of tvas spectra is shown in figure 6 . in this section ,
we describe 
 our assignment of the weaker feature at 1640 cm to the cn  acetone complex and the stronger feature at 1550 
 cm to the 2-oxopropyl reaction product .
both bands 
 are only present in the transient spectra when both acetone and icn 
 are dissolved in cdcl3 , indicating both features involve 
 cn interaction with acetone . calculated vibrational frequencies and 
 steady - state infrared spectra guided the interpretations we make , 
 and relevant computed frequencies and relative band intensities of 
 candidate species are presented in table 2 alongside the measured frequencies of the 
 observed absorption bands .
our trajectory calculations indicate 
 that the cn radical can form 
 transiently stable complexes with acetone .
( an addition reaction at 
 the carbonyl group may also be possible but was not observed in the 
 trajectory calculations and would lead to a product with a significantly 
 shifted c  o stretching frequency . ) the transient complexes were suggested 
 to contribute a band centered just below 400 nm in the teas spectra 
 of figure 2 and a weak 
 feature at 2040 cm that is evident in the c = n 
 stretching region spectra shown in figure 4 .
they are stabilized by approximately 3600 
 cm compared to separated cn and acetone , according 
 to our calculations .
furthermore , these stabilized structures are 
 dynamically decoupled from the h - abstraction pathway , which inhibits 
 further reaction .
the cn shifts the acetone c = o stretch down 
 in wavenumber in both our calculations and the spectrum .
the calculations 
 predict the band to occur at 16081618 cm , with the range encompassing two isomers in which the c or n end 
 of the cyano radical is oriented toward the acetone , as shown in figure 6b .
other potential absorbers 
 in this region include acetaldehyde , ch3cho , a stable product 
 of the possible radical chemistry .
its fundamental c = o stretch , 
 calculated to be at 1717 cm , lies to the higher 
 wavenumber side of the acetone carbonyl band .
similarly , acetyl radical 
 photoproducts of acetone fragmentation have computed ir bands at 1833 
 cm and are not responsible for the features of 
 interest in figure 6a .
the other features in the spectrum that lie close to the strong 
 acetone fundamental band must be interpreted with caution , but there 
 are indications of time - dependent bands at 1740 and 1770 cm ; both are observed with and without icn .
we suspect they are associated 
 with the uv photochemistry of acetone and with different solvation 
 environments of acetone in cdcl3 .
( a ) time - resolved vibrational spectra spanning 14701755 
 cm after 267 nm excitation of icn / acetone / cdcl3 solutions .
( b ) time 
 dependence of the weak feature at 1640 cm and 
 computed structures of the cn  acetone complexes
negative intensities are a consequence of baseline fluctuations 
 at early times because of the neighboring acetone band . the weak , time - dependent feature at 1640 cm assigned to the cn 
acetone complex sits upon 
 a shifting baseline 
 because of proximity to the strong acetone band .
nevertheless , it 
 can be fitted to extract time - dependent band intensities , as shown 
 in figure 6b .
its growth 
 fits to a biexponential rise with time constants of 1 = 3.0  0.3 ps and 2 = 55  25 ps ( both 
 for 0.5 m acetone solutions ; 2 sd uncertainties ) .
it then undergoes 
 a slow decay ( with 3 = 800  400 ps ) .
the two 
 rise times are consistent with the formation of the complexes directly 
 from unsolvated free cn , which teas data show decays on a 2.3  
 0.2 ps time scale , and from cn 
a time constant of 27  7 ps was suggested 
 from the c = n stretching region tvas feature at 2040 cm , which is approximately half that for the 0.5 m solution 
 but was measured for twice the acetone concentration .
cdcl3 complexes because the former are more strongly bound ( we 
 estimate 3600 cm versus 1800 cm for cn  acetone and cn  cdcl3 from our calculations ) . 

the remainder of this analysis describes 
 our assignment and interpretation 
 of the temporal evolution of the stronger transient feature at 15051575 
 cm .
we attribute this band to the 2-oxopropyl 
 product of the h - abstraction reaction of cn with acetone , on the basis 
 of our calculations that place the band center at 1545 cm .
several alternative assignments can be quickly discounted because 
 the band lies 150 cm below the carbonyl 
 band of acetone .
for example , the c = o stretching band of 1-iodoacetone 
 from recombination of i atoms with 2-oxopropyl is expected near 1700 
 cm ( on the basis of the known gas - phase ir spectrum 
 of 1-chloroacetone , and our observed 
 solvent shifts in chloroform solutions ) and will be masked by the 
 acetone feature .
the band assigned to 2-oxopropyl develops in 
 the tvas spectra with 
 a center at 1552 cm at late time delays . however , 
 at early times , this feature is broadened to lower wavenumber and 
 coalesces into the sharp 2-oxopropyl feature over a time scale of 
 50 ps .
this behavior is suggestive of vibrational cooling 
 of an initially internally hot radical , with broadening and shifting 
 of the absorption to lower wavenumber , because of either vibrational 
 anharmonicity in the c = o stretch or anharmonic coupling to 
 other excited modes .
it is less likely to be a consequence of an equilibrating 
 solvent environment around the newly formed radical , which we expect 
 to shift the vibrational frequencies from higher to lower wavenumber 
 with time .
energy flow from the hot hcn 
 to the 2-oxopropyl radical , an effect we first noted in the reaction 
 of cn radicals with cyclohexane , can 
 be ruled out as the cause of the narrowing feature because the vibrationally 
 hot 2-oxopropyl radicals are formed more promptly than the likely 
 time scale for vibrational relaxation of the hcn .
the time dependence 
 of the 2-oxopropyl band was analyzed by fitting 
 to two gaussian functions with centers x0i and widths i ( both specified in cm ) : x0 g = 1552 and g = 14 for absorptions by ground - state 
 molecules ( as determined from fitting the late - time spectra ) , and x0e = 1533 and e = 35 for vibrationally excited molecules . 

the areas of the two gaussian components were free parameters in the 
 fits , and figure 7 illustrates 
 the outcomes .
the temporal evolutions of the two bands are both satisfactorily 
 modeled with exponential time constants of 1 = 2.3 
 ps ( fixed to match the faster time constant for loss of free cn radicals 
 from teas data ) and 2 = 34  10 ps ( determined 
 by simultaneous fits to the time - dependent intensities of both bands ; 
 2 sd uncertainty ) .
the analysis is therefore consistent with production 
 of vibrationally hot 2-oxopropyl radicals from cn reaction with acetone 
 with a time constant of 2.3 ps , and vibrational relaxation with a 
 time constant of 34 ps .
this cooling may correspond to loss 
 of multiple quanta of vibrational excitation in different modes and 
 is an average time scale .
more quantitative information on the vibrational 
 energy content of the nascent 2-oxopropyl radical can not be deduced 
 from our tvas data alone .
( b ) tvas spectra ( dots ) and illustrative fits to two gaussian 
 functions ( lines ) for time delays of 2.0 ps ( dark blue ) , 11 ps ( light 
 blue ) , and 1200 ps ( orange ) .
( c ) time dependences of the feature attributed 
 to vibrationally excited ( red ) and ground - state ( blue ) 2-oxopropyl 
 radicals .
the 2-oxopropyl radical and its 
 coproduct hcn have different long - time 
 kinetics . the band attributed to the c = o stretch of ground - state 
 2-oxopropyl radicals reaches a steady - state absorbance at 50 
 ps
but the hcn absorption continues to grow for time scales up to 
 our experimental limit of 2 ns .
the differences in longer time behavior 
 of these two populations hint toward subsequent 2-oxopropyl reactions . 

this radical is therefore an intermediate in a sequence of steps , 
 which result in a balance between its production and loss .
a steady - state 
 ( but low ) concentration will occur if the rate of removal of the 2-oxopropyl 
 radicals is larger than their rate of production .
in addition to the 
 fast reactive production by free cn radicals , a slower contribution 
 to 2-oxopropyl growth will derive from reaction of solvated cn radicals , 
 for which the rate coefficient is 2  10 m s as determined from hcn growth 
 and cn 
the time constants for 
 production of the 2-oxopropyl radicals are therefore several hundred 
 picoseconds under our experimental conditions , and assuming that steady - state 
 behavior leads to the effects we see , indicates a decay lifetime of 
 100 ps .
the analysis 
 of the teas and tvas data obtained for uv - excited 
 icn / acetone / cdcl3 solutions reveals distinguishable reactivity 
 of free and solvent - complexed cn radicals .
the free cn quickly ( cn = 2.3 ps ) decays by geminate recombination ( to icn and inc ) , 
 association with a cdcl3 solvent molecule or acetone cosolute 
 molecule to form complexes , and reaction with acetone to produce hcn . 

the bimolecular rate coefficient for reaction of acetone with free 
 cn radicals , i.e. , for those cn that survive initial loss or complexation 
 to the solvent , is deduced to be k2f = 
 ( 8.0  0.5 )  10 m s. we suspect that this large reaction rate coefficient 
 results in part from microscopic inhomogeneity that develops in these 
 solutions . although the reaction itself is facile , preferential solvation 
 of icn by acetone over cdcl3 will augment the reaction 
 rate .
cdcl3 complexes with acetone are more than 
 an order of magnitude 
 slower and are controlled by both diffusion and activation : we extracted 
 values of k2c = ( 2.5  1.1 )  
 10 m s from the 
 loss of the solvated cn band in the teas spectra and k2c = ( 2.0  0.9 )  10 m s from the rise in the hcn band in tvas experiments 
 ( see sections iv.b and iv.c ) .
reactions of cn  acetone 
 complexes are slower still because of the greater stabilization deriving 
 from cn  carbonyl interactions .
acetone 
 and 1800 cm for cn  cdcl3 complexes , 
 which support this idea .
acetone complexes form both 
 directly from free cn radicals that happen to have a neighboring acetone 
 molecule when photolytically generated , and by exchange of partner 
 following initial complexation to cdcl3 solvent molecules . 
 the driving force for the cn 
figure 8 summarizes 
 the various processes that follow uv excitation of icn in an acetone / cdcl3 solution and the associated time constants ( specified for 
 a 0.5 m acetone solution where dependent on the acetone concentration ) . 

it extends the initial kinetics of solvation of the free cn radicals 
 with cdcl3 and acetone summarized in scheme 1 to include the abstraction reaction pathways . 

the figure excludes the photochemistry that results from 267 nm excitation 
 of acetone molecules . under the conditions of our experiments
, we 
 estimate that fewer than 0.02% of the acetone molecules within the 
 volume of the 266 nm laser beam are photoexcited . hence excited - state 
 ( s1 and t1 ) acetone molecules and acetone photoproducts 
 ( e.g. , acetyl radical ) are unlikely to react with cn radicals in sufficient 
 numbers to contribute to our observed time - resolved spectra .
summary of 
 the photochemical processes involving cn radicals and 
 acetone following uv photolysis of icn in an icn / acetone / cdcl3 solution .
the rate coefficient values deduced from this work 
 are k2f = ( 8.0  0.5 )  10 m s for the slower 
 component of the reaction of the free cn radical with acetone , k2c = ( 2.5  1.1 )  10 m s for the solvent - complexed cn 
 reaction , and kcomplex = ( 2.6  0.8 ) 
  10 m s for formation of the cn  acetone complex
. lifetimes ( from 
 decay time constants ) are 1,cn = 2.3 ps for the 
 initial fast - component of the loss of free cn , cn  acetone = 800 ps for the complex , and r * = 34 ps for the 
 cooling of vibrationally excited 2-oxypropyl radicals .
both the hcn and the 2-oxopropyl radical products 
 form with some 
 degree of vibrational excitation greater than expected for thermalized 
 products ( see sections iv.c.i and iv.c.ii ) . in the case of the hcn 
 product
, the evidence from the current and our previous studies of 
 cn radical reactions in solution is that there is a vibrational population inversion , 
 with the majority of the hcn formed both c 
h stretching excitation in the hcn corresponds 
 to an energy of 39 kj mol , and each bending quantum 
 adds approximately 8 kj mol more internal energy . 
 in this regard ,
the reaction dynamics are similar to those for h atom 
 abstraction reactions by cn in the gas phase .
the extent of vibrational excitation of the 2-oxopropyl radical 
 is less clear - cut , but the evolution from its initially broad to its 
 final , narrow c = o stretching spectrum in figure 7 shows that a large fraction of the 2-oxopropyl 
 radicals are vibrationally excited .
a franck  condon type model 
 can be applied to predict a limiting case for the internal excitation 
 of the 2-oxopropyl radical .
sudden abstraction of a hydrogen atom 
 may be a reasonable approximation for the direct dynamics with an 
 early transition state and will leave the 2-oxopropyl radical in a 
 geometry otherwise identical to that of acetone .
electronic structure 
 calculations indicate that relaxation to the equilibrium structure 
 of the 2-oxopropyl radical most significantly involves changes to 
 the c  h bond length in the ch2 group from 
 1.098  ( the c  h bond length in acetone ) to 1.083  , 
 and a change from tetrahedral to trigonal planar coordination .
we 
 estimate from these calculations that the gain in internal energy 
 associated with this structural reorganization is 46 kj mol . the structural changes identified might excite c  h stretching 
 and ch2 wagging and scissoring modes .
these arguments suggest 
 that approximately 70% of the available energy may be channeled into 
 product internal motions , which is similar to the fraction reported 
 for cn reactions in the gas phase .
the 
 fast rise time of a few picoseconds of the vibrationally hot 
 2-oxopropyl radicals , and the concomitant development of the population 
 inversion of vibrational levels of hcn intimate that these products 
 result from reactions of the free cn radicals before they complex 
 to solvent molecules .
acetone 
 complexes react to form hcn more slowly , with time constants on the 
 order of a few hundred picoseconds ( depending on acetone concentration ) .
we are unable to detect vibrationally excited hcn and 2-oxopropyl 
 radicals from the slower reactions of the complexed forms of cn .
this 
 absence may indicate that the complexed reactions exhibit different 
 reaction dynamics , perhaps with later transition states along the 
 reaction pathway , so that the vibrational excitation does not develop 
 in the products .
more likely , given the large exothermicity of the 
 reactions ( 140 kj mol ) and the relatively 
 small stabilization energies of the complexes ( < 45 kj mol ) , is that this product vibrational excitation does develop , but 
 that it relaxes by solvent coupling on faster time scales than the 
 overall buildup of products , so can not be detected in our experiments .
we have previously shown that exothermic reactions in solution 
 have a propensity to form one vibrationally hot product despite the 
 coupling of the solvent bath to nuclear motions along and orthogonal 
 to the reaction coordinate .
this vibrational 
 excitation mostly appears in the new bond formed from the reaction 
 as a consequence of an early transition state , as predicted by the 
 polanyi rules for gas - phase reactions .
the current study demonstrates that the coproduct 
 of a bimolecular reaction in solution can also be formed with significant 
 amounts of internal vibrational excitation .
similar behavior is known 
 from gas - phase studies of exothermic reactions of f atoms with methane and may also occur for cn 
( anti)correlations between 
 the degrees of vibrational excitation of the two products can be established 
 from velocity map imaging measurements .
methodology is lacking to 
 make the corresponding correlated measurements in solution , but our 
 current efforts show that dynamical insights can still be forthcoming 
 from the uncorrelated observations .
time - resolved absorption spectroscopy of the exothermic reaction 
 of cn radicals with acetone in cdcl3 solutions demonstrates 
 that a significant fraction of the energy released enters vibrational 
 modes of the hcn and the 2-oxopropyl radical coproduct .
transfer of 
 this excess energy to the solvent bath occurs on time scales on the 
 order of 10 ps , leading to thermally equilibrated reaction products . 

we have previously reported substantial vibrational excitation of 
 one product of a reaction in solution ( for exothermic reactions of 
 cn radicals , and of f and cl atoms ) , but this is our first observation that both nascent 
 products can be vibrationally hot .
the cn radicals were generated 
 photolytically from icn , and take 2.3 ps to equilibrate with the solvent 
 and form cn  cdcl3 complexes .
distinct spectroscopic 
 signatures of complexed and uncomplexed ( free ) cn radicals allow us 
 to distinguish their reactions . in the reactions with acetone ,
the 
 complexed cn radicals react more than an order of magnitude more slowly , 
 but the kinetics of reactions of the free cn radicals are partly controlled 
 by in - cage geminate recombination with i atoms , and solvent - complex 
 formation .
the cn radicals also complex to acetone molecules , and 
 c = n  carbonyl interactions thermodynamically favor these 
 species over cn 
evidence from our 
 measurements suggests that the cn radicals complexed with acetone 
 have significantly reduced reactivities .
the combination of time - resolved 
 electronic and vibrational spectroscopies allows us to unravel the 
 rates and dynamics of several competing processes that occur following 
 photoinitiation of radical chemistry in solution .
 transient electronic and vibrational 
 absorption spectroscopy unravel 
 the mechanisms and dynamics of bimolecular reactions of cn radicals 
 with acetone in deuterated chloroform solutions . 
 the cn radicals are 
 produced by ultrafast ultraviolet photolysis of dissolved icn . 
 two 
 reactive forms of cn radicals are distinguished by their electronic 
 absorption bands :  free  ( uncomplexed ) cn radicals , 
 and  solvated  cn radicals that are complexed with solvent 
 molecules . 
 the lifetimes of the free cn radicals are limited to a 
 few picoseconds following their photolytic production because of geminate 
 recombination to icn and inc , complexation with cdcl3 molecules , 
 and reaction with acetone . 
 the acetone reaction occurs with a rate 
 coefficient of ( 8.0  0.5 )  1010 m1 s1 and transient vibrational spectra in the c = n 
 and c = o stretching regions reveal that both the nascent hcn and 2-oxopropyl ( ch3c(o)ch2 ) radical products are vibrationally excited . 
 the rate coefficient 
 for the reaction of solvated cn with acetone is 40 times slower than 
 for free cn , with a rate coefficient of ( 2.0  0.9 )  109 m1 s1 obtained from 
 the rise in the hcn product v1(c = n 
 stretch ) ir absorption band . 
 evidence is also presented for cn complexes 
 with acetone that are more strongly bound than the cn  
 cdcl3 complexes because of cn interactions with the carbonyl group 
 . 
 the rates of reactions of these more strongly associated radicals 
 are slower still . 
Introduction
Experimental
Details
Computational
Details
Results
Discussion
Conclusions