Kinetics of excited-state depletion by simpleCr(a 5S2, a 5D

J, a 5G

J)

hydrocarbons

Kenji Honma*

Department of Material Science, Himeji Institute of T echnology, 1475-2 Kanaji, Kamigori,Hyogo 678-1297, Japan

Received 12th April 1999, Accepted 24th May 1999

The depletion kinetics of excited states of upon interaction with simple hydrocarbonsCr(a 5S2 , a 5DJ, a 5G

J)

cyclopropane, and propene) are studied in a discharged Ñow reactor at He(CH4 , C2H6 , C3H8 , C2H2 , C2H4 ,pressures of 0.7 Torr. On interaction with alkanes, show no depletion but an increase in theirCr(a 5S2 , a 5D

J)

populations. The higher excited state, shows depletion upon interaction with alkanes. GoodCr(a 5GJ),

correlation was observed between the depletion rate constants for and the formation rate constantsCr(a5GJ)

for and it is suggested that collisional relaxation from to isCr(a 5S2 , a 5DJ), Cr(a 5G

J) Cr(a 5S2 , a 5D

J)

important for the interaction with alkanes. On the other hand, all excited states show depletion upon theinteraction with unsaturated hydrocarbons. Among the three states, shows the most efficientCr(a 5G

J)

depletion. Rate constants were almost the same as the gas kinetics ones, which suggest no or very small energybarriers for the interaction of this state with alkenes and acetylene. More efficient depletion of byCr(a 5G

J)

alkenes and acetylene compared with alkanes is consistent with the presence of stable p-complexes oninteraction potential surfaces of the former systems.

Introduction

The interactions of transition metal atoms with hydrocarbons,especially alkenes, have drawn much attention inorganometallic chemistry, and a considerable amount ofstudies has been carried out to clarify the structure and stabil-ity of metalÈalkene adducts by using low temperaturematrices.1 Gas-phase studies have also been performed for ter-molecular association reactions between the 3d series tran-sition metal atoms and hydrocarbons.2h6 Compared withthese association type reactions, a limited number of experi-mental studies have been carried out in gas-phase bimolecularreactions for the 3d metals.7,8

Ritter, Carroll and Weisshaar (RCW) presented a broadsurvey of the reactivity of ground-state, neutral transitionmetal atoms from the 3d series with alkanes and alkenes.7Their results showed that none of the ground electronic statesof the 3d-series neutral transition metal atoms react withlinear alkanes at 300 K. Only Sc, Ti, V, and Ni react withalkenes, and the other atoms are inert with alkenes. Thechemical interaction between a transition metal atom and analkene is characterized by a stable p-complex and the forma-tion of the p-complex has been described in terms of theDewarÈChattÈDuncanson (DCD) donorÈacceptor model.9 Inthe DCD model, bonding consists of the simultaneous forma-tion of two donorÈacceptor bonds, i.e. the Ðrst bond involvesdonation of electrons from the alkene 2pp orbital to the metal4s orbital and the second bond involves back-donation fromthe metal 3d orbital to the empty alkene 2pp* orbital. Becausethe electronic ground states of the 3d-series transition metalatoms have a Ðlled 4s orbital except for Cr and Cu in the pureatomic orbital limit, RCW proposed the DCD model with sdor sp hybridization to explain the reactivities of Sc, Ti, V, andNi.

In order to clarify the interaction of the transition metalswith alkenes more clearly, useful information is obtained bythe kinetic study of excited states which have di†erent electron

conÐgurations and spin multiplicities. For Ti and V, Ñow tubeexperiments combined with laser-induced Ñuorescence haveprovided this information The high spin excited states of Tiand V, Ti(a 5F) and V(a 6D), have been studied in our labor-atory and very efficient depletion by (propene),C2H4 , C3H6and has been observed.8 Although these excited statesC2H2could not correlate with the stable p-complex having a lowspin multiplicity, the efficient depletion by alkenes implies thatthese 4s1 states have some attractive interactions followed byintersystem crossing to the p-complex. For a low spin 4s1state which is expected to correlate with the p-complex, Wenet al. have studied the kinetics of V(a 4D), and observed highlyefficient depletion by Qualitatively, the interaction ofC2H4 .10Ti and V with alkenes is now reasonably well understood.

In order to extend such knowledge to other transitionmetals, it is important to obtain a set of kinetic data forseveral electronic states of a particular transition metal atom.In this paper, we have determined bimolecular rate constantsfor reactions of the three excited states of Cr, Cr(a 5S2 , a 5D

J,

with simple hydrocarbons,a 5GJ), CH4 , C2H2 , C2H4 , C2H6 ,

propene, cyclopropane and The electron conÐgu-C3H8 .rations and energies of these states are summarized in Table 1as well as the ground state, The ground state of CrCr(a 7S3).has the 3d54s1 conÐguration which is unique as the groundstate of the 3d metals. Although this conÐguration is expectedto be less repulsive than the 4s2 conÐguration, the groundstate of Cr has been observed to be inert upon interactionwith hydrocarbons.7 Even at high reactant pressure condi-tions where termolecular association is possible, no signiÐcantreactivity has been observed for the interaction with andCH4and termolecular association rate constants areC2H4 ,expected to be very small.11 This small reactivity could beascribed to high spin multiplicity of Cr(a 7S). By analogy tothe theoretical works of the 4d series metals with hydrocar-bons,12h18 the high spin multiplicity, the ground state of Mo,is unfavorable because some loss of exchange energy isrequired to access low spin reactive surfaces.

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Table 1 ConÐgurations and energies of the low-lying states of chro-miuma

Term ConÐguration J Energy/cm~1

a 7S 3d5 4s 3 0.00a 5S 3d5 4s 2 7593.16a 5D 3d4 4s2 0 7750.78

1 7810.822 7927.473 8095.214 8307.57

a 5G 3d5 4s 2 20517.406 20519.603 20520.924 20523.695 20523.94

a Data taken from ref. 12.

The electronic states studied here have low spin multiplicity,quintet, and two of them, and have the 4s1Cr(a 5S2 a 5G

J),

conÐguration and they are expected to be accessible to thereactive surfaces without intersystem crossing. From an ener-getic point of view, and have similar energies,Cr(a 5S2 a 5D

J)

21.7 and 22.2 kcal mol~1, respectively, and hasCr(a 5GJ)

about twice as large an energy as and 58.6Cr(a 5S2 a 5DJ),

kcal mol~1. Therefore, systematic measurements will providea good opportunity to study e†ects of electron conÐgurationand energy on the interaction of Cr with hydrocarbons.

ExperimentalGeneral

The Ñow tube/LIF instrument used in these studies has beendiscussed in detail previously.19 BrieÑy, metal atoms werecreated in a DC-discharge source where a chromium rod wasused as a cathode. The atoms are carried downstream in theHe bu†er gas (300 K). Less than 5% Ar was added to the Ñowto stabilize the discharge. The density of unreacted metalatoms was measured by laser-induced Ñuoresence (LIF) atknown atomic transitions. He(99.9999%), Ar(99.999%),

cyclo-CH4(99.999%), C2H6(99.9%), C3H8(99.9%),propane(99.0%), andC2H2(99.9999%), C2H4(99.999%),propene(99.8%) gases were obtained from NIHON SANSOand used without further puriÐcation. A capacitance manome-ter (MKS Baratron, Type 122A) was used to measure the totalpressure inside the Ñow tube. Thermal mass Ñow meters(KOFLOC Model 3710) were used to measure the Ñow ratesof the reactant gas and He.

The transitions and energies used for detecting the elec-tronic states of chromium are summarized in Table 2. A fre-quency doubled output of a tunable titanium sapphire laser(Continuum TS-60) pumped by a pulsed Nd : YAG laser

Table 2 LIF transitions used to probe Cr(a 5S, a 5D, a 5G)a

Species Transition Energy/cm~1 Wavelength/nm

Cr(a 5D) z 5D1Èa 5D0 25763.01 389.51z 5D2Èa 5D1 25731.29 388.63z 5D3Èa 5D2 25744.08 388.44z 5D3Èa 5D3 25576.34 390.99z 5D4Èa 5D4 25508.49 392.03

Cr(a 5S) y 5P3Èa 5S2 22231.59 449.81Cr(a 5G) z 5G3Èa 5G2 22021.41 454.10

z 5G6Èa 5G6 22086.21 452.77z 5G3Èa 5G3 22017.89 454.18z 5G3Èa 5G4 22015.12 454.23z 5G6Èa 5G5 22081.87 452.86

a Energies and wavelengths are derived from data in ref. 11.

(Continuum NY-82) was used to measure the density ofA tunable dye laser (Lambda Physik SCANMATECr(a 5DJ).2) pumped by a XeCl excimer laser (Lambda Physik

Complex 102) was used with a dye of Courmarin 460 for mea-surements of Spectrally unresolved Ñuores-Cr(a 5G

J, a 5S2).cence was collected by a lens system and focused through a

2.0 mm slit into a photomultiplier tube (PMT)(HAMAMATSU Photonics R-928). The PMT current wasampliÐed by a wide band preampliÐer (NF Electronics, modelBX-31) and the ampliÐed voltage pulse was integrated by aboxcar integrator (SRS, Model SR-250).

Rate constant determination

The following three processes are possible for the interactionof excited state Cr atoms, Cr*, with reactant molecule, X.

Cr* ] X] products (1)

Cr* ] X] Crj] X@ (2)

Cr* ] X] He] CrX ] He (3)

is the Cr atom in the electronic state formed by electronicCrjenergy transfer. The time-integrated rate expressions for thesimple bimolecular processes, eqns. (1) and (2), are given byeqn. (4).

ln[Cr*(nX)/Cr*(0)]\ [(krxm] kq)qrxn nx (4)

is the time-integrated Cr* atom concentration, Cr*(0)Cr*(nX)is the Cr* atom concentration when no reactant gas is present,

is the mean reaction time, is the reactant numberqrxn nXdensity, and and are the rate constants of the bimolecu-krxn kqlar reaction and electronic energy transfer, respectively.The termolecular association reaction, eqn. (3), can be

described by the following mechanism

Cr* ] X A8B

kd

kc[CrÉ É ÉX]* ÈÈÈÕks*He+

CrX (5)

[CrÉ É ÉX]* formed at the total collision rate constant may(kc)be stabilized by collision with He (at or unimolecularlyks)dissociate back to reactants (at Phenomenologically, thekd).depletion rate constant, is given by eqn. (6)kphen ,

kphen\ kc ks[He]/(kd ] ks[He]) (6)

Under constant He pressure, the time-integrated rate expres-sion including processes (1)È(3) is given by eqn. (7)

ln[Cr*(nX)/Cr*(0)]\ [(krxn] kq] kphen)qrxn nX (7)

Laser-induced Ñuorescence intensities with reactant concen-tration and without reactant gas, and I(0), are pro-nX I(nX)portional to and Cr*(0), respectively. Therefore, theCr*(nX)rate constants, were derived by Ðtting semi-(krxn] kq] kphen),logarithmic plots of vs. using a least squareI(nX)/I(0) nXroutine. Because the depletion signal that we measure couldbe a†ected by processes (1)È(3), we refer to these values ase†ective rate constants rather than absolute values.

The reaction time, was determined by laserqrxn ,vaporization-chemiluminescence measurements.6 BrieÑy,second harmonic radiation of the pulsed YAG laser wasfocused on a metal rod to generate electronically excited metalatoms. The metal atoms were carried by He and reacted withreactant molecules introduced from one of the inlets. Chemilu-minescence from the products was measured at the LIFviewing region as a function of time after the laser pulse. TheÑow tube length from metal source to the LIF viewing regionis 40 cm in most measurements. In this study, we used 0.7Torr of He pressure, and two inlet ports, i.e. 20 and 30 cmdownstream of the discharge, in order to change the reactiontime. The reaction time was 1.00 ms at 0.7 Torr for the inletport located 30 cm downstream of the discharge, i.e. 10 cmbetween the inlet and the observation point.

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One possible error of the depletion rate constants maycome from Ñuorescence quenching. Collisions of reactantsduring lifetimes of the excited states of the LIF transitionquench the Ñuorescence and cause phenomenological deple-tion of metal atoms. It is possible to estimate collision fre-quencies during the lifetimes. Maximum partial pressure ofreactants is typically 0.01 Torr. By using hard-sphere rate con-stants, the estimated collision rate is around 1 ] 105kHS,20s~1. Fluorescence rates of the excited states are 1] 107 to2 ] 108 s~1.21 Since they are two to three orders of magni-tude larger than the collision frequencies, we conclude thatÑuorescence quenching is negligible for our experimental con-dition.

We report one standard deviation as the uncertainty in theprecision of the Ðts to multiple data sets. The accuracies arelimited mainly by the atom production source. Other smallercontributions to our absolute uncertainty are from the mea-surement of incomplete mixing of the reagent gases, andqrxn ,the accuracy of the Ñow rate and pressure measurements. Weestimate the absolute sensitivity of our instrument to beD5 ] 10~14 cm3 s~1 based on our ability to easily observe a5% decrease in our signal at a reagent gas Ñow rate of 100sccm, which corresponds to about 5] 1014 cm~3 of reactantnumber density.

Chromium atom reactant conditions

According to eqn. (7), the normalized LIF intensity, I(nX)/I(0),should be a single exponential function of the reactant density,

However, in some measurements, showed posi-nX . I(nX)/I(0)tive or negative curvature in semilogarithmic plots. These fea-tures can be interpreted by the occurrence of formationprocesses of Cr* as well as the depletion processes, eqns. (1)È(3). One inherent characteristic with DC discharge sources isthat a wide distribution of electronic states are produced. Ifhigher excited states are entirely lost by chemical reaction, thisis not a problem in our experiments because we use knownatomic transitions to probe the electronic states of Cr.However, if the higher lying excited states relax (cascade) tolower lying states, Cr*, by collision with reactants, the decayof Cr* shows rise-decay (positive curvature) or multi-exponential decay (negative curvature) features.22

These features are expected to depend on the Ñow tube con-dition ; we carried out all measurements very carefully to seewhether decay features are changed by various conditions. AtÐrst, the measurements were carried out under two di†erentreaction times. One of the ring inlets, inlet 2, was used formost of the measurements and the length from discharge tothe inlet is 30 cm. The other inlet, inlet 1, located 10 cmupstream was also used to double the reaction time. Bothinlets were used separately to check the consistency of ourrate constants. The distance from discharge to the inlets wasalso changed by inserting a tube extension to increase thenumber of collisions with He/Ar prior to the reaction. Sec-ondly, a quencher gas was introduced from the inlet upstreamand the e†ect on the decay proÐle was studied. In the previousstudy of with oxidants,23 was added fromCr(a 5S2 , a 5D

J) N2inlet 1 and depletion measured by introducing a reactant from

inlet 2. The same procedure was applied for the depletion ofHowever, this could not be applied toCr(a 5S2 , a 5D

J).

because this state is depleted by very effi-Cr(a 5GJ), N2ciently.24

Results and discussionA General

Experimental results for the interaction of Cr(a 5S2 , a 5DJ,

with cyclopropane and propene are summarized ina 5GJ)

Figs. 1 and 2. Among Ðve spinÈorbit levels of andCr(a 5DJ)

only the data for and are shownCr(a 5GJ), Cr(a 5D2) Cr(a 5G6)in these Ðgures. The other spinÈorbit levels in these two states

Fig. 1 Semilogarithmic plots of normalized LIF intensities, I(nX)I(0),for three excited states of Cr vs. number density of cyclopropane.Open squares, solid circles, and open circles correspond to Cr(a 5D2),and respectively. The reaction time of these mea-Cr(a 5S2), Cr(a 5G6)surements is 1.0 ms. The solid lines are optimized least-squares Ðts ofeqn. (7) or (9) to the data.

show identical behavior to and respec-Cr(a 5D2) Cr(a 5G6),tively. In the interactions with all hydrocarbons studied here,no di†erent behavior was observed among the spinÈorbitlevels. These results indicate that either the depletion or for-mation behavior of the di†erent spinÈorbit levels are the samewithin the experimental sensitivity or the depletion or forma-tion rate is much slower than interconversion of the levelsfrom collisions with He or Ar. Recent measurements by Wenet al. suggested that equilibrium population of J levels in

is achieved within 80 ls after formation of a certain JV(a 4DJ)

level at 1.2 Torr of He Ñow.10 Because the energy levels spac-ings of are much smaller than those of itCr(a 5G

J) V(a 4D

J),25

is concluded that the interconversion rate is much faster thanthe depletion rate under our experimental condition (0.7 Torrof He).

B Interaction with alkanes

The behaviors of three excited states observed for cyclo-propane (Fig. 1) are qualitatively common for the interactionwith the other alkanes studied here. That is, Cr(a 5S2 , a 5D

J)

Fig. 2 Semilogarithmic plots of normalized LIF intensities,for and vs. number density ofI(nX)/I(0), Cr(a 5D2 , a 5S2 , a 5G6) C3H6(propene). Open squares, solid circles, and open circles correspond to

and respectively. The reaction timeCr(a 5D2), Cr(a 5S2), Cr(a 5G6)of these measurements is 1.0 ms. The solid lines are optimizedleast-squares Ðts of eqn. (7) or, I(nX)/I(0)\ (1[ a)exp([bnX qrxn)]a to the data.exp([cnX qrxn)

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increase their population upon interaction with alkanes, whileshows depletion described by a single exponentialCr(a 5G

J)

function. They are similar to the interaction of the threeexcited states with The single exponential decay ofN2 .23,24

is interpreted as the Ðrst order depletion describedCr(a 5GJ)

in the Experimental section, eqn. (7). E†ective rate constantswere determined by least mean square Ðtting and summarizedin Table 3. The rate constants are around 10 ] 10~12 cm3s~1, which is very similar to that of 16] 10~12 cm3N2 ,s~1.24 Among four alkanes, cyclopropane showed the mostefficient depletion and the least efficient.CH4The most reasonable explanation for the increase of thepopulation of is the occurrence of the energyCr(a 5S2 , a 5D

J)

transfer process, eqn. (8).

Cr** ] alkane] Cr(a 5S2 , a 5DJ)] alkane (8)

In the Ñow tube, there are some populations of higher lyingexcited states which are not quenched completely by collisionswith He or Ar. Some of these excited states proceed the energytransfer, cascading, instead of reactions. As a result of the cas-cading, the population of the state measured, Cr(a 5S2 , a 5D

J)

in this case, increases with the concentration of reactants. Asimilar increase has been observed for andCo(a 4F

J)] N226Because shows noCr(a 5S2 , a 5D

J) ] N2 .23 Cr(a 5S2 , a 5D

J)

depletion, the relative concentrations of these states aredescribed by the depletion rate constant of the original state,Cr**, as the following equation, eqn. (9).

[Cr*(nX)]/[Cr*(0)]\ 1 ] [Cr**(0)/Cr*(0)]

] M1 [ exp([k8 qrxn nX)N (9)

Here Cr**(0) is the concentration of Cr** without reactant atof reaction time. Since there could be two or more higherqrxnexcited states, Cr**, it is not necessary for the increase of

to be characterized by a single rate param-Cr(a 5S2 , a 5DJ)

eter, However, the experimental results were representedk8 .by eqn. (9) reasonably well, and we did not Ðt them by sum-mation of two exponential functions as in the case of the inter-action with The increases observed forN2 . Cr(a 5S2 , a 5D

J)

were analyzed by a least square Ðtting with eqn. (9), and deter-mined rate constants are listed in Table 3. In this table, therate constants for the increase of the electronic state areshown in parentheses. The increase rate constants for

and are almost identical. The quenching isCr(a 5S2) Cr(a 5DJ)

most e†ective upon the interaction with cyclopropane and theother linear alkanes are less efficient.

One interesting comparison can be made between the for-mation rate constants of and the depletionCr(a 5S2 , a 5D

J)

ones of They are of the same order of magnitude.Cr(a 5GJ).

This similarity implies that can be Cr** in eqn. (8).Cr(a 5GJ)

That is, are formed by the quenching ofCr(a 5S2 , a 5DJ)

by collisions with alkanes. Because the formationCr(a 5GJ)

rate constants of are larger than those forCr(a 5S2 , a 5DJ)

depletion of except for the entire increase ofCr(a 5GJ) C2H6 ,

can not be explained by the quenching ofCr(a 5S2 , a 5DJ)

alone and some other higher excited states are alsoCr(a5GJ)

quenched to form The presence of suchCr(a 5S2 , a 5DJ).

higher excited states other than was conÐrmed byCr(a 5GJ)

the following experiment. When was introduced fromCH4inlet 1, upstream of the Ñow, the LIF intensities of Cr(a 5S2 ,were increased as a result of the cascading of highera 5D

J)

excited states. Even though the Ñow rate of was highCH4enough to see no more increase of furtherCr(a 5S2 , a 5DJ),

increases, 10 to 20%, of their LIF signals were observed byadding or cyclopropane from inlet 2. This resultC2H6 , C3H8 ,indicates that some higher excited states can be quenched toform by as well as other alkanes, whileCr(a 5S2 , a 5D

J) CH4other higher excited states can be quenched only by larger

alkanes. Because shows depletion upon thisCr(a 5GJ) CH4 ,

state belongs to the former group.

Product channels. For product channel consideration,almost no experimental information is available for thermo-chemical data, though there have been some theoreticalstudies relevant to the interaction of Cr with alkanes.12,14,15For Cr, only the CÈH activation process has been studied.Theoretical studies of Mo, the same Group 6 metal in the 4dseries, provide useful information for CÈC activation. Onecommon feature of CÈH and CÈC activation is very high acti-vation barriers with respect to the ground state reactants.Because the ground states of Cr and Mo are septet states,CÈH or CÈC insertion requires a large loss of exchange energywhich results in the high activation barriers. The calculatedbarrier heights for CÈH activation of are 37.5 and 37.8CH4kcal mol~1 for Cr and Mo, respectively.12 For CÈC activa-tion, 41.2 kcal mol~1 is reported as the barrier height of Mo

Cyclopropane has a lower barrier for its CÈH and] C2H6 .16CÈC insertion 28.0 and 9.3 kcal mol~1, respectively. Althoughthe electronic energies of and reduce theseCr(a 5S2) Cr(a 5D

J)

barriers by 21.7 and 23.1 kcal mol~1, respectively, thereremains considerable barriers except for the CÈC insertion ofcyclopropane. Thus, CÈH or CÈC insertion is very unlikely for

and this is consistent with the observation ofCr(a 5S2 , a 5DJ),

no depletion of Cr(a 5S2 , a 5DJ).

For having 58.6 kcal mol~1 of electronic energy,Cr(a 5GJ),

the CÈH and CÈC insertion processes are accessible from athermochemical viewpoint. However, metal inserted products,HÈMÈR or RÈMÈR, are probably not Ðnal products becauseof the high electronic energy of According to theCr(a 5G

J).

theoretical studies for Cr and Mo, inserted adducts havealmost the same energies as the ground state reactants. Thatis, 8.3, [2.6, [4.9, and [21.0 kcal mol~1 for HÈCrÈCH3 ,12

and respec-HÈMoÈC3H5 , H3CÈMoÈCH3 , cyclo-MoC3H6 ,16tively. The exothermicities of around 50 kcal mol~1 withrespect to seem so high that the stabilizedCr(a 5G

J)] alkane

association product is very unlikely. The energetics for H2elimination from the adduct is only determined for Mowhich is 22.9 kcal mol~1 endothermic for the ground] CH4 ,

Table 3 E†ective bimolecular rate constants for the reactions of with hydrocarbons at 300 K (10~12 cm3 s~1)Cr(a 5S2 , a 5DJ, a 5G

J)

kobsState CH4 C2H6 C3H8 cÈC3H6 C2H2 C2H4 C3H6Cr(a 7S3)a NRb È NR NR È NR NRCr(a 5S2) (9.8^ 1.0)c (7.9^ 0.8) (28^ 3) (77^ 8) 94 ^ 23 125^ 27 60^ 6

32 ^ 14Cr(a 5D

J) (11^ 4) (7.5^ 0.8) (32^ 3) (82^ 9) 119 ^ 29 124^ 47 72^ 21d

27 ^ 5 27^ 7Cr(a 5G

J) 6.9^ 1.0 14^ 1 10 ^ 3e 31 ^ 3 268^ 27 156^ 16 146^ 15

a Ref. 7. b NR indicates that no depletion was observed. c Numbers in parentheses are the rate constants for the population rises. d Mostlynon-exponential and only a fast component is listed because a slower component shows poor reproducibility. e Only one measurement wasperformed and 30% of the value was used as the error limit.

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state reactants.16 This product is probably possible even if thedi†erence of metal is taken into account.

An alternative channel is an electronic energy transfer, eqn.(2). The increases of and strongly indicateCr(a 5S2) Cr(a 5D

J)

the occurrence of the energy transfer from higher excitedstates. Typical rate constants for the electronic energy transferare given by the interaction of and withTi(a 5F

J) V(a 6D

J) N2 .

They were determined to be 6.5] 10~12 and 0.5] 10~12 cm3s~1, for and respectively.27Ti(a 5F

J) ] N2 V(a 6D

J) ] N2 ,

Since these systems have no reactive channel, the depletionwas explained entirely by the energy transfer. One order ofmagnitude di†erence between Ti and V was attributed to theoccurrence of the electronic to vibrational energy transfer for

Comparing these values with the rate con-Ti(a 5FJ)] N2 .

stants determined for all rate constants are a littleCr(a 5GJ),

larger than that of This distinction could beTi(a 5FJ) ] N2 .

explained by the number of vibrational modes of the hydro-carbons and the presence of low frequency ones.

One interesting result is the absence of depletion forand As we discussed in the previous para-Cr(a 5S2) Cr(a 5D

J).

graph, the CÈH or CÈC insertion is not accessible for thesestates, and only electronic energy transfer to the ground state,

is energetically possible. Experimentally, it is veryCr(a 7S3),difficult to see an increase of as the product of thisCr(a 7S3)energy transfer because the population of in the ÑowCr(a 7S3)tube is much higher than that of However,Cr(a 5S2 , a 5DJ).

the measurements of showed no sign of deple-Cr(a 5S2 , a 5DJ)

tion up to fairly high concentration of alkanes and we con-cluded that the energy transfer from these states is very slow.A qualitative explanation can be made by repulsive potentialcurves evolved from three low lying states, Cr(a 7S3 , a 5S2 ,and as shown in Fig. 3. Among them, the curve froma 5D

J)becomes repulsive at a longer distance between CrCr(a 5D

J)

and alkane than that from and because ofCr(a 5S2) Cr(a 7S3)the Ðlled 4s orbital of The curve evolved fromCr(a 5DJ).

has the highest energy among the three, and doesCr(a 5DJ)

not cross with the other two lower curves. The curve evolvedfrom is also parallel to that from and noCr(a 5S2) Cr(a 7S3)crossing is available for the collisional energy transfer. Theschematic explanation is useful for the energy transfer of

As shown in Fig. 3, the curve evolved from thisCr(a 5GJ).

state crosses with the curve from Cr(a 5DJ).

Conclusively, in the depletion of an importantCr(a 5GJ),

process is the collisional energy transfer which can beexplained qualitatively by the crossing of repulsive curves. Thelargest rate constant for may beCr(a 5G

J) ] cyclopropane

ascribed to the lower barrier for the CÈC insertion channel

Fig. 3 Schematic potential curves for the interaction of four lowerelectronic states, with alkanes.Cr(a 7S3 , a 5S2 , a 5D

J, a 5G

J),

which makes the interaction potential attractive and leads to alonger lived intermediate.

C Interaction with alkenes and acetylene

Depletion of three excited states, uponCr(a 5S2 , a 5DJ, a 5G

J),

the interaction with is shown in Fig. 2. AmongC3H6(propene)the three excited states, and show singleCr(a 5S2) Cr(a 5G6)exponential depletion features, while the depletion of

is non-exponential. For three unsaturated hydrocar-Cr(a 5D2)bons, and (propene), onlyC2H2 , C2H4 , C3H6 Cr(a 5GJ)

shows single exponential decays consistently. Least squareÐtting of these Ðrst order decays provided very large rate con-stants, (268 ^ 27) ] 10~12, (156 ^ 16) ] 10~12, and(146 ^ 15) ] 10~12 cm3 s~1, for andC2H2 , C2H4 , C3H6(propene), respectively. These values are the same order ofmagnitude as the hard-sphere rate constants, 298, 292, and288 ] 10~12 cm3 s~1 for and (peopene),C2H2 , C2H4 , C3H6respectively,20 and suggest that the depletion of Cr(a 5G

J)

upon the interaction with three unsaturated hydrocarbonshave no or very low energy barriers as summarized in Table 4.

Depletion of and For the interaction ofCr(a 5S2) Cr(a 5D

J).

and some depletion curves were not ableCr(a 5S2) Cr(a 5DJ),

to be Ðt by a single exponential function with[Cr(a 5S2) C2H4and with and (propene)]. Similar non-Cr(a 5DJ) C2H4 C3H6exponential depletion curves were observed for the interaction

of with and with and bothMo(a 5S2) O228 Cr(a 5DJ) N2O,23

were interpreted by the occurrence of higher lying excitedstates which are quenched to form or AsMo(a 5S2) Cr(a 5D

J).

we discussed in the previous section, our Ñow tube source gen-erates some higher lying excited states of Cr which are stillalive at the observation region. Non-single exponential decayfeatures indicate that a part of these higher lying states arequenched by collisions with reactants to form Cr(a 5S2 , a 5D

J).

In order to get a little more detail of the non-exponentialdecay features, a simple analysis was made based on the two-state model described in the Appendix. As we described in theAppendix, the depletion features of Cr* coupled with higherexcited states could be a double exponential or a rise-decay ifquenching of the higher excited states by He is neglected. Thisassumption of negligible quenching by He could be reasonableif we take into account very large energy di†erences betweenhigher excited states and or i.e. at leastCr(a 5S2) Cr(a 5D

J),

12431 cm~1. Most non-exponential depletion featuresobserved in this study could be characterized by a doubleexponential decay, [Cr*(nx)]/[Cr*(0)]\ (1[ a)exp([bnXqrxn)and the two parameters, b and c, were] aexp([cnXqrxn),reproducible throughout the same reaction system. The tworate constants derived are listed in Table 3. The double expo-nential depletion for and requires that theCr(a 5S2) Cr(a 5D

J)

depletion rate constant for or is largerCr(a 5S2) Cr(a 5DJ), kr ,than the depletion rate constant for a higher excited state, k1Therefore, the larger rate constants in Table 3 could] k2 .

correspond to the depletion rate constants of orCr(a 5S2)Cr(a 5DJ).

Table 4 E†ective bimolecular rate constants for on theCr(a 5G6)interaction with hydrocarbons at 300 K

Hydrocarbons kobs/10~12 cm3 s~1 kHS/kobs Ea/kcal mol~1 a

CH4 6.9^ 1.0 46 2.3C2H6 8.0^ 0.8 37 2.2C3H8 10 ^ 1 33 2.1Cyclopropane 31 ^ 3 10 1.4C2H2 268 ^ 27 1 0.06C2H4 156 ^ 16 2 0.4C3H6 (propene) 146^ 15 2 0.4

were estimated by the equation where Ra Ea s Ea\ 300R ln(kHS/kobs),is the gas constant.

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For the depletion of measurements wereCr(a 5S2 , a 5DJ),

also carried out by introducing a quenching gas from inlet 1located at 10 cm upstream of the inlet for the reactant. Asdescribed in the previous section, alkanes are e†ective forquenching higher excited states to form Cr(a 5S2 , a 5D

J).

Molecular nitrogen is also e†ective. When these quenchinggases were added, enhanced population of Cr(a 5S2 , a 5D

J)

gave better signal-to-noise ratio and the decay proÐles werechanged to a more single-exponential-like one as shown inFig. 4. Unfortunately, the decay proÐle is still non-exponentialand could not be Ðt by a Ðrst-order decay process. The doubleexponential Ðtting for the decay proÐles obtained with quen-ching gas provides identical rate parameters to those from thedecay proÐles obtained without quenching gas. Addingalkanes or increases the relative amount of the faster com-N2ponent which corresponds to the depletion rate of Cr(a 5S2 ,

These results are reasonable because these moleculesa 5DJ).

quench only higher excited states and are inert for Cr(a 5S2 ,a 5D

J).

The rate constants for estimated by theCr(a 5S2 , a 5DJ)

above considerations are about half of those for Cr(a 5GJ),

and no di†erences other than experimental errors were seenbetween rate constants for and However,Cr(a 5S2) Cr(a 5D

J).

it should be noted that these values are derived by assuming avery simple model, and a more reliable measurement isrequired.

Product channels. Since rate constants for Cr(a 5S2 , a 5DJ)

are ambiguous, we will mainly discuss the reaction productand mechanism for As we discussed for the case ofCr(a 5G

J).

alkanes, product channels are possible, i.e. the bimolecularand termolecular chemical reactions as well as quenching. Forbimolecular or termolecular reactions, theoretical studiesprovide insight into product mechanism. Because one charac-teristics of the interaction of transition metal atoms withunsaturated hydrocarbons is p-coordination, CÈH activationand p-coordination must be considered as an entrancechannel. Unfortunately, no theoretical calculation has beenperformed for the interaction of Cr with unsaturated hydro-carbons. However, the CÈH activation and the p-coordinationof Mo with ethylene and acetylene have been studied, andthey are useful for Cr.15,17,18 As for the CÈH insertion, the 4dseries transition metal atoms can insert CÈH bonds of ethyl-ene or acetylene more easily than CÈH bonds of Mo hasCH4 .the highest activation barrier for the CÈH insertion of ethyl-

Fig. 4 Semilogarithmic plots of normalized LIF intensities,for vs. number density of The reactionI(nX)/I(0), Cr(a 5D2) C2H4 .

time of these measurements is 1.0 ms. Solid squares are data withpropane (0.03 Torr) and open squares are those with no quencher.The solid lines are optimized least-squares Ðts of I(nX)/I(0)\ (1

to the data. Details are given[ a)exp([bnX qrxn) ] a exp([cnX qrxn)in the text.

ene and acetylene, 18.216 and 27.3 kcal mol~1,18 respectively.While these barrier heights are comparable to the electronicenergies of and the energy of isCr(a 5S2) Cr(a 5D

J), Cr(a 5G

J)

high enough to surmount these barriers and the CÈH inser-tion is energetically possible as an entrance channel.

A more energetically favorable channel is the p-coordination. The energies of the p-coordinated complexes arecalculated to be [17.3 and [24.2 kcal mol~1 with respect tothe ground state reactants, andMo(a 7S3) ] C2H416respectively. Therefore, it is reasonableMo(a 7S3) ] C2H2 ,18to assume that the interaction potential for Cr with alkene oracetylene is very attractive and it is more likely for the reac-tion system to take this thermodynamically more favorablechannel. One interesting di†erence suggested by the theoreti-cal studies is the binding energies with ethylene and acetylene.Because there is an extra attractive interaction between theout-of-plane p-orbital and an empty 4d-orbital (for Mo) onthe metal, acetylene gives a more stable p-coordinatedcomplex. The occurrence of a potential well is usually helpfulto proceed termolecular association. However, very highexcess energies from a combination of these well depths andthe electronic energy of makes the complexes liveCr(a 5G

J)

very shortly, and the termolecular processes are unlikely forthe three states of Cr.

Only a little information is available for products fromthe attractive interaction, i.e. bimolecular reactions. For theinteraction with theoretical studies again provideC2H4 ,useful information. One possible product is MC2H2] H2 .The energy of this product is calculated to be 12.1 kcal mol~1above the ground state reactant for The elec-Mo ] C2H4 .16tronic energy of is much higher than this energy,Cr(a 5G

J)

and this product must be possible for For acety-Cr] C2H4 .lene, no information is available, although mightCrC2 ] H2be less likely and a H atom elimination may occur.

For all electronically excited states, energy transfer is pos-sible. Compared with typical rate constants for the electronicenergy transfer for 6.5 ] 10~12 cm3 s~1,27 allTi(a 5F

J)] N2 ,

rate constants for are almost two orders of magni-Cr(a 5GJ)

tude larger. In the previous section, the depletion of Cr(a 5GJ)

by alkanes was explained by mostly electronic energy transfer,and their rate constants are again more than one order ofmagnitude smaller than the rate constants for Cr(a 5G

J)]

alkenes or acetylene (Table 4). One important di†erencebetween the systems of unsaturated hydrocarbons and thoseof alkanes is the presence of the stable p-complex on the inter-action potential. The associationÈdissociation mechanism mayprovide a highly efficient electronic energy transfer.

Among three unsaturated hydrocarbons, shows theC2H2largest rate constant upon the depletion of and theCr(a 5GJ),

rate constant for is similar to that for (propene).C2H4 C3H6This advantage of could be ascribed to the entranceC2H2channel of the interaction. From the viewpoint of productchannels, probably has no advantage because hasC2H2 C2H2the smallest number of vibrational modes which can acceptthe electronic energy and elimination from the p-complexH2seems to be less favourable. As we mentioned in the discussionof energetics of the p-coordinated complex, one advantage of

is the stability of the complex. For interaction with Mo,C2H2several kcal mol~1 more stability is suggested for the p-coordinated complex with compared with that withC2H2Thus, it is expected that the interaction ofC2H4 . Cr(a 5G

J)

with leads to the complex with higher probability andC2H2more efficient depletion occurs via this complex than the inter-action with or (propene).C2H4 C3H6

Summary

The kinetics of depletion of three excited states in Cr(a 5S2 ,were studied upon the interaction with simplea 5D

J, a 5G

J)

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hydrocarbons. On interaction with alkanes, Cr(a 5S2 , a 5DJ)

showed an increase of their population, which could beexplained by the cascading of higher lying excited states.

showed depletion described by a Ðrst order process.Cr(a 5GJ)

Discussion based on the energetics from relevant theoreticalstudies suggested that the important process is the electronicenergy transfer governed by repulsive potential curves. Oninteracion with unsaturated hydrocarbons, the depletion of

could not be described by a single exponentialCr(a 5S2 , a 5DJ)

decay because of the cascading of higher lying excited states.Highly efficient depletion of was observed for theCr(a 5G

J)

interaction with unsaturated hydrocarbons. The near gas-kinetic rate constant suggests that the depletion occurs withno or a very low energy barrier which is consistent with theinteraction potential having a stable p-coordinated complex.

Acknowledgementswork is supported by grant (No. 10440177) from the Jap-This

anese Ministry of Education, Science, and Culture.

AppendixThe following simple model is useful to get insight into theprocesses semiquantitatively, though processes in the Ñowtube must be much more complicated. That is, two levels(Cr** and Cr*) participate and Cr*, the state measured here,has depletion, eqn. (A1), and formation, eqns. (A3) and (A4),processes.

Cr** ] X] products k1 (A1)

Cr* ] X] products kr (A2)

Cr** ] X] Cr* ] X k2 (A3)

Cr** ] He] Cr* ] He k3 (A4)

The reverse processes of eqns. (A3) and (A4) were neglectedbecause their rates were expected to be very small from themicroscopic reversibility. Rate equations for these processeswere solved by using the Laplace transformation method,29and time integrated expressions for species Cr** and Cr* weregiven as the following.

[Cr**]\ [Cr**]0 exp([M(k1] k2)nX ] k3nHeNt) (A5)

[Cr*]\ A exp([M(k1 ] k2)nX ] k3 nHeNt)

] ([Cr*]0[ A)exp([kr nX t) (A6)

Here, A\ [Cr**]0 (k2 nX ] k3nHe)/Mkr nX~((k1 ] k2)nXand and are the concen-] k3 nHe)N, [Cr**]0 , [Cr*]0 , nX , nHetrations of species Cr** and Cr* at time 0, the concentrationsof reactant and He, respectively. At Ðxed reaction time (qrxn)and He concentration these equations are the following.(nHe)

[Cr**]\ B expM[(k1 ] k2)nX qrxnN (A7)

[Cr*]\ C expM[(k1] k2)nX qrxnN] ([Cr*]0[ A)

] exp([kr nX qrxn) (A8)

where, C\ AB\ [Cr**]0 exp([k3 nHe qrxn), exp([k3 nHe qrxn).[Cr**] is expected to show single exponential decay, eqn.(A7), while [Cr*] is given by a complicated function of nX ,eqn. (A8).

Probably the most complicated part is the dependentnXcoefficient A. If we assume that the quenching process of Cr**by He, eqn. (A4), is negligible, the coefficient A can be given bya simpler form, and eqn. (A8)A\ [Cr**]0 k2/Mkr [ (k1 ] k2)N,becomes the following form.

[Cr*]\ A expM[(k1 ] k2)nX qrxnN

] ([Cr*]0 [ A)exp([kr nX qrxn). (A9)

In this study, normalized concentration, [Cr*]/[Cr*(0)], ismeasured as a function of the concentration wherenX ,[Cr*(0)] is the concentration of Cr* with no reactant at t \

Under our assumption, the normal-qrxn . [Cr*(0)]\ [Cr*]0 ,ized concentration is then given by

[Cr*]/[Cr*(0)]\ D expM[(k1] k2)nX qrxnN

] (1 [ D)exp([kr nX qrxn), (A10)

where This form canD\ [Cr**]0 k2/M[Cr*]0[kr~(k1 ] k2)]N.be a rise-decay (for D\ 0 or 1\ D) or a biexponential func-tion (for 0 \ D\ 1) of nX .

References1 W. E. Klotzbucher, S. A. Mitchell and G. A. Ozin, Inorg. Chem.,

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106, 5509.11 Upper limits for second-order rate constants are 3 ] 10~15 and

2 ] 10~14 cm3 s~1 for Torr) and Torr),CH4(0È50 C2H4(0È20respectively, in ref. 5.

12 A. M. Christina Wittborn, M. Costas, M. R. A. Blomberg and P.E. M. Siegbahn, J. Chem. Phys., 1997, 107, 4318.

13 M. R. A. Blomberg, P. E. M. Siegbahn and M. Svensso, J. Am.Chem. Soc., 1992, 114, 6095.

14 P. E. M. Siegbahn and M. R. A. Blomberg, J. Am. Chem. Soc.,1992, 114, 10548.

15 M. R. A. Blomberg, P. E. M. Siegbahn and M. Svensson, J. Phys.Chem., 1992, 96, 9794.

16 J. J. Carroll, K. L. Haug, J. C. Weisshaar, M. R. A. Blomberg, P.E. M. Siegbahn and M. Svensson, J. Phys. Chem., 1995, 99,13955.

17 P. E. M. Sigbahn, M. R. A. Blomberg and M. Svensson, J. Am.Chem. Soc., 1993, 115, 1952.

18 P. E. M. Siegbahn, T heor. Chim. Acta, 1994, 87, 277.19 D. E. Clemmer, K. Honma and I. Koyano, J. Phys. Chem., 1993,

97, 11480.20 The hard-sphere rate constant is calculated by kHS \p/4(dCrThe diameters of hydrocarbons are taken from J. O.] dOX)2SlT.

Hirschifelder, C. F. Curtis and R. B. Bird, in Molecular T heory ofGases and L iquids, Wiley, New York, 1954 ; and R. C. Reid, J. M.Prausnitz and B. E. Poling, in T he Properties of Gases andL iquids, McGraw-Hill, New York, 1987. The diameter of Cr istaken to be 3.70 All Cr states are assumed to have the sameÓ.diameter. The mean relative velocity, was used for(8kB T /pk)1@2,SlT, where T , and k are the BoltzmannÏs constant, tem-kB ,perature, and reduced mass, respectively.

21 J. R. Fuhr, G. A. Martin and W. L. Wiese, J. Phys. Chem. Ref.Data, 1988, 17, Suppl. No. 3.

22 One typical example was seen in the depletion of Ti(a 5F) uponthe interaction with where the rise-decay feature wasN2O,observed, ref. 19. This rise-decay feature comes from a fast forma-tion and a slow depletion of the state measured. It can bechanged to a double-exponential feature when the formation ofthe state is slower than the depletion of that.

23 C. L. Hanes and K. Honma, J. Chem. Soc. Faraday T rans., 1998,94, 1171.

24 K. Honma, J. Phys. Chem., 1999, A103, 1809.

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25 The smallest and largest spacings between two adjacent levels are0.25 and 2.77 cm~1 for respectively. They are muchCr(a 5GJ),smaller than 63.2 cm~1 for the smallest spacing between twoadjacent levels for V(a 4D1).26 R. Matsui, K. Senba and K. Honma, Chem. Phys. L ett., 1996,250, 560.

27 K. Honma and D. E. Clemmer, L aser Chem., 1995, 15, 209.

28 M. L. Campbell, R. E. McClean and J. S. S. Harter, Chem. Phys.L ett., 1995, 235, 497.

29 J. I. Steinfeld, J. S. Francisco and W. L. Hase, in ChemicalKinetics and Dynamics, Prentice-Hall, Inc., 1989.

Paper 9/02886B

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