GARDINER, MCFARLAND, MORINAGA, TAKEYAMA, AND WALKER
1504
C6HeOzand the latter C6H502 as an intermediate species. However, at higher temperatures as in the present experiment, these intermediates are considered to be very unstable. Thus, the following mechanism assuming C6H5as a chain carrier is considered as one possibility.
+ 0, +CeHjO + O CeH5O + CeHe +C6HeOH + CeH6 O + C6H6 +CeH5 + OH OH + CsH+3 HzO + CeH5 C6Hs
---f
(1) (11) (111)
(IW
If the stationary-state method is applied to this scheme on an assumption that reaction I is rate determining, a linear relationship between log 7[02]and 1/T may be derived as in the case of Hz-02 reaction.8 If a similar mechanism is applied to other aromatics, these aromatics having different substituents may give different radicals such as (CBH5)CH2,(CHaCaH5)CHz,
( C ~ H ~ C Z(CeH5)C3H7, H~, and (CH3)z(CeH6)CHzjwhich shorn different reactivity in each reaction corresponding to (I). However, we could not find any reasonable correlation between the above described experimental activation energies and reactivities of different aromatic radicals. I n order to explain the difference of activation energies of oxidation among varipus aromatic hydrocarbons, a more detailed mechanism is desired. The present results are not sufficient for this purpose and further accumulation of experimental evidence is required.
Acknowledgment. The author wishes to express his thanks to Messrs. E(. Sugiyama and Y. Oyama for their help in the experiment and to Professor G. B. Kistiakowsky, who initiated the author into the field of combustion kinetics. (8) H. Miyama and T . Takeyama, J . Chem. Phys., 41, 2287 (1964).
Initiation Rate for Shock-Heated Hydrogen-Oxygen-Carbon Monoxide-Argon Mixtures as Determined by OH Induction Time Measurements by W . C. Gardiner, Jr.,* M. McFarland, K. Morinaga, T. Takeyama, and B. F. Walker Department of Chemistry, The University of Texas, Austin, Texas 78718 (Received January 8, 1971) Publication costs assisted by the Robert A . Welch Foundation
Induction times for OH mere determined in incident shock wave experiments with H2:02: C0:Ar = 1:5:3:91 mixtures over the temperature range 1400-2500°K. The data are compared to similar experiments with H2:02:Ar= 1:5:94 andused to derive arate constant for the chain initiation reaction CO 02 = COZ 0. The resulting Arrhenius expression IC = 3.1 X 108 exp(-38,000 kcal/RT) 1. mol-l sec-l is compared to previous measurements.
+
Hz
I. Introduction Finding the identity and rate of the homogeneous chain initiation step in the hydrogen-oxygen reaction has proved to be a difficult experimental problem.' In mixtures of hydrogen and oxygen containing carbon monoxide, however, some direct experiments on the chain initiation rate can be done.2-6 It is assumed that the atom transfer reaction co 0 2 = coz 0 (10)
+
+
provides an alternative t o the pathways usually assumed for chain initiation in absence of CO
Hz
+
0 2
=
OH
+ OH
or The Journal of Physical Chemistry, Vo2. 76,
10, I971
+
0 2
= HOz
+
+H
or (1) C. B. Wakefield, Dissertation, University of Texas, 1969. (2) B. F. Walker, Dissertation, University of Texas, 1970.
(3) B. F. Myers, E. R. Bartle, and K. G. P. Sulzmann, J . Chem. Phys., 42, 3969 (1965); 43, 1220 (1965). (4) R. 5. Brokaw, Symp. Combust., l l t h , Berkeley, Calif., 1966, 1063 (1967) (5) A . M . Dean and G. B. Kistiakowsky, J. Chem. Phys., 53, 830 (1970). (6) T. A. Brabbs, F. E. Belles, and R. 8 . Brokaw, S y m p . Combust., 18th, Salt Lake City, 1970, to be published. I
1505
INITIATION RATEFOR SHOCK-HEATED GASMIXTURES impurities
=
+
atoms or radicals
Shock tube experiments on other systems also yield information on the rate of reaction 10 or its reverse (- 10).7--10 Several measurements of the rate constant of reaction 10 have been reported. They are not at all in agreement with one another in the temperature range in which the oxidation of CO in the presence of hydrogen can be studied by shock tube methods, about 12002500°K. For a temperature of 1600”K, the Arrhenius expressions recommended give, in 1. mol-’ sec-’ units: k10 = 410 (ref 3) ; 740 (ref 4); 540 (ref 5) ; 43,000 (ref 6) ; 12,000 (ref 7, from kl = 30 X value of ref 3); 300,000 (ref 8) ; 280 (ref 9) ; 820 (ref 10) ; and 990 or 1400 (ref 11). It is clear that the available data do not permit any definite conclusions about the chain initiation rate to be drawn and that additional experiments are needed.
11. Experimental Section We investigated induction times for appearance of
OH radical in mixtures with nominal compositions H2:02:Ar = 1:5:94 and Hz:02:CO:Ar = 1:5:3:91 heated in incident shock waves to temperatures in the range 1400 < T < 2500°K and pressures in the range 0.15 < p < 0.3 atm. The apparatus and procedures have been described previously.12 As in previous experiments with H2-02-Ar mixtures, the induction time was defined by attainment of [OH] = 2.5 X lo-’ mol/l.13 To compensate for random run-to-run variations in the Bi lamp source, the extinction coefficient E in I = IOexp( - E [OH]) was calculated from the formula E i , N = E O . ~ ~ ( E ~ / E ) . Here €0 25 is the average extinction coefficient of the lamp for [OH] < M found by Ripley,13 ~i is the extinction coefficient found from applying Beer’s law to the measured transmission and computed post-combustion value of [OH] in a given experiment, is the average extinction coefficient for the range of [OH] in which the post-combustion value of [OH] falls, and E ~ , Nis the normalized extinction coefficient used to determine the transmission at [OH] = 2.5 X lo-’ M . The time between arrival of the shock wave, as detected by a laser-schlieren station, and ignition was multiplied by the shock density ratio u to convert from laboratory to gas time14 and by the initial post-shock oxygen concentration [ 0 2 ] 0 to scale the ignition rate according to reactant concentration.15 The results are shown in Figure 1. The induction time data were subjected to a conventional regression analysis in the log (. [ 0 2 ] 0 t i ) , 104/T plane16 using a locally modified version of a standard least-squares routine.17 An “F” test showed that there was not a significant difference between the variances of the two data sets. Both the H2:02:Ar = 1:5:94 and the H2:OZ:CO:Ar = 1:5:3:91 data sets proved t o have virtually identical variances when fit with quadratic [log (u[Oz]otl) = a b(104/T) c.
+
+
(10*/T2)]rather than linear [log ( ~ [ 0 2 ] 0 t i ) = a b e (104/T)] regression lines. Linear regressions were therefore adopted for comparing the two sets of data with one another. The two straight lines generated by the regressions are shown in Figure 1. Their equations are log
(~[02]oti)
=
-8.150
f
0.0078
+
(0.3401 f 0.0075)(104/T - 5.213) for 33 data points with HzO: O2: Ar log
( ~ [ 0 2 ] o t i )=
-8.122
f
0.0064
(0.3392
f
=
1:5 : 94 and
+
0.0065)(104/T - 5.518)
for 46 data points with Ha:02:CO:Ar = 1:5:3:91. The indicated errors are standard deviations. A “t” test was first performed to test for a significant difference in slope in the two sets of data. The value t = 0.0069, with 75 degrees of freedom, is insignificant. Accordingly, a common slope was computed, giving 2, = 0.3395. A second “t” test was performed to see if the lines might be identical within the scatter of the data. The computed value t = 7.5, with 76 degrees of freedom, is significant at the 99.9% confidence level ( t = 3.2). The lines are therefore not identical: the least-squares regression through the Hz :02 : CO : Ar = 1:5 :3 : 91 data is statistically different from the leastsquares regression through the H2 :0 2 : Ar = 1: 5 :94 (7) S. H. Garnett, G. B. Kistiakowsky, and B. V. O’Grady, J . Chem. Phys., 51, 84 (1969). (8) T. C. Clark, S. H. Garnett, and G. B. Kistiakowsky, ibid., 51, 2885 (1969). (9) E. R . Bartle and B. F. Myers, presented a t the 157th National Meeting of the American Chemical Society, Minneapolis, Minn., April 1969; Division of Physical Chemistry Abstract 152. (10) S. S. Penner, K . G. P. Sulzmann, A. Boni, and L. Leibowitz, Astronaut. Acta, 15, 473 (1970); K . G. P. Sulzmann, L. Leibowitz, and S. S. Penner, Symp. Combust., 13th, Salt Lake City, 1970, to be published. (11) Unpublished work of E . R . Bartle and B. F. Myers (B. F. Myers, private communication) The lower value is obtained from the Os-COz-Ar results of these authors when the value of k ( C 0 z M = CO 0 M) of Fishburne, et al. (E. S.Fishburne, K. R . Bilwakesh, and R. Edse, J . Chem. Phys., 45, 160 (1966), is used in the data analysis, while the higher value is obtained with k(C0z M = CO 0 M) from K . W. Michel, H. A . Olschewski, H. Richterling, and H. G. Wagner, 2. Phys. Chem. (Frankfurt am Main), 39, 9 (1964); 44, 160 (1966). (12) W.C. Gardiner, Jr., K . Morinaga, D. L. Ripley, and T. Takeyama, J . Chem. Phys., 48, 1665 (1968). (13) D. L. Ripley, Dissertation, University of Texas, 1967. (14) Boundary layer growth restricts the validity of this procedure. Cf.R. L. Belford and R. A. Strehlow, Ann. Rev. Phys. Chem., 20, 247 (1969). (15) G. L. Schott and J. L. Kinsey, J . Chem. PhUs., 29, 1177 (1958). The actual test gas compositions varied slightly from the nominal 1: ti : 94 and 1:5 : 3 :91 compositions. The actual compositions were used for computing u, [ O Z ] ~and , the postcombustion steady value of [OH]. All other computed results were dane assuming the nominal compositions. (16) K . A . Brownlee, “Statistical Theory and Methodology in Science and Engineering,” 2nd ed, Wiley, New York, K.Y., 1965, Section 11.6. (17) Los Alamos “LEAST” least-squares package. Los Alamos Scientific Laboratory Publication LA2367. I
+ +
+ +
+
+
The Journal of Physical Chemistry, Vol. 76, N o . 10, 1971
1506
GARDINER, MCFARLAND, MORINAGA, TAKEYAMA, AND WALKER
EXPERIIIENTRL INDUCTION T I I I E O R T R
Figure 1. Induction times. The solid symbols are data taken with various mixtures of the nominal composition H2:Op:Ar = 1:5: 94. The open symbols are data taken with various mixtures of the nominal composition H2:Ot:CO:Ar = 1:5:3:91. The solid lines are the computer-generated least-squares lines through the two sets of data. The three dotted lines were computed using the rate constant set of Table I, except that for the middle dotted line klo had the value given by Brokaw (ref 4). For the upper dotted line the gas composition was H ~ : 0 2 : Ar = 1:5: 94, while the other two dotted lines were computed for H2:02:CO:Ar = 1:5:3:91.
data. At 1800°K, the difference between the regression lines corresponds to a difference in induction time of 19% or 8 psec laboratory time. There is a significant decrease in induction time when CO is added to the experimental gas. The difference is too large to be attributable to an error in the temperature assigned to the gas caused by ignoring the vibrational relaxation of CO, which proceeds on a time scale comparable to the time scale of ignition. It must therefore be due to changes in the chemistry of the induction zone when reactions involving CO are added to the induction zone reactions of the Hz-OZ system. Two kinds of reactions are possible. In the induction zone itself, the reaction of CO with OH CO
+ OH = COz + H
(9)
can accelerate the conversion of OH into H by supplementing the reaction responsible for this in the H2-02 system Hz
+ OH = HzO + H
I n the initiation zone, reaction 10 can supplement the Hz-02 initiation reactions. I n order to see which of The Journal of Physical Chemistry,Vol. 76,No. 10,1971
these reactions of CO is responsible for the observed decrease in induction time, a number of computer simulations of the shock-initiated combustion of these mixtures were made. The simulations were accomplished by numerical integration of the kinetic equations for the mechanism shown in Table I under the constraint of steady shock flow. The rate constant expressions used for reactions 01 to 8 in Table I were chosen as a set which gives optimum reproduction of induction times in H2-02-Ar shocks over wide ranges of temperature and composition. The fit to the induction times of H2 :0 2 :Ar = 1:5 :94 obtained with this set, assuming ideal shock flow, is very good. We experimented with the rate constant parameters for reactions 9 and 10 to determine whether the induction time decreases were occurring in the initiation zone or in the exponential growth region of the induction zone and to deduce a value of the appropriate rate constant. A complication of the numerical integrations arises due to the effects of the wall boundary layer on incident shock propagation.6i14 Extensive computer investigations of these effects were carried out in the course of this study;2 they will be reported elsewhere. For the purpose at hand it turns out that as long as a consistent treatment of the shock propagation is made, the results will not be dependent upon whether the shock propagation is assumed to be ideal, or whether the boundary layer flow is laminar or turbulent. This is so because the reaction primarily responsible for the induction time decrease is indeed reaction 10, which participates to a significant extent only in the chemistry immediately behind the shock wave. The calculations reported here are based on the assumption of ideal steady shock flow. The calculations done for the case of steady boundary layer flow, both laminar and turbulent, confirm that the rate constants deduced for the Hz-02 system would change wjth the flow models, while the rate constant for reaction 10 would not. The calculated times between shock heating and attainment of [OH] = 2.5 X lo-' M were scaled as the experimental data and plotted us. inverse temperature for comparison between calculation and experiment, A number of such calculated induction times are shown in Figure 2, and three of these are compared with the data in Figure 1.
111. Results The goal of the computer simulations was to explain the difference in induction times between the Hz-02 experiments and the H2-O2-CO experiments, the magnitude of which is the separation of the solid lines in Figure 1. Such B difference could be computed in various ways, and it was necessary to decide which of the several possibilities is the proper one. First it was required to discover whether the thermal effects of changing the gas composition affect the induction time apprecjably. To this end the mechanism of
1507
INITIATION RATEFOR SHOCK-HEATED GASMIXTURES Table I: Mechanism and Rate Constant Expressions for ti Calculations Reaotion
Hz+M=2H+M OZ+M=20+M Hz M = Hz* M Hz* 02 = 2OH H 0 2 = OH 0 0 Hz = OH H OK Hz = HzO H H 02 M = HOz M H 0 2 HzO HOz HzO H OH M = HzO M OH = HzO 0 OH Hz HOz HzO OH CO OH = COz H co On = coz 0 CO 0 M = COz M
+ + + + + + + + + + + + + + + + + + + + + + + + + + + +
Ref
k
2.23 X 10gT’/2exp(-92,600)/RT 3.60 X 10l6 T-l exp( - 118,00O/RT) (Calculated) 6.5 x 1 0 W 2 2.34 X 1O1O exp(-10,000/RT) 6.28 X 1O1O exp(-10,900/RT) 2.30 X 1Olo exp(-5150/RT) 2 X lo8 exp(+870/RT) 6 X 1O1O exp(+870/RT) 2 X 101O exp(+87O/RT) 7.59 x 108 exp( - 1000/RT) 2 x 108exp(-24,000/RT) 3 . 1 X 108exp(-600/RT) 3.14 X lo8 exp(-37,600/RT) 3.16 X lo6 exp(+23,400/RT)
a
b C
C C C
d e
f B h
i d j k
C. B. Wakea A. L. Myerson and W. S. Watt, J . Chem. Phys., 49,425 (1968). * RI. Camac and A. Vaughan, ibid., 34,460 (1961). field, Dissertation, The University of Texas, 1969. The rate of reaction 03 was adapted for the composition of these mixtures from J. H.Kiefer and R. W. Lutz, J . Chem. Phys., 44, 668 (1966). The rates of reactions 04, 1, and 2 were adjusted for optimal fit of Hz-Os-Ar induction times. It should be noted that the initiation mechanism of the Hz-Oz explosion is not of importance for the purposes of the present paper. All that is necessary is a correct accounting for the length of the induction period in the one Hz-02 mixture with which we are comparing the H2-02-C0 mixture. Any other combination of elementary reactions and rate constants which would give the correct induction times would also be satisfactory. d G. Dixon-Lewis, W. E. Wilson, and A. A. Westenberg, J . Chem. The efficiency Phys., 44, 2877 (1966). e D . Gutman, E. A. Hardwidge, F. A. Dougherty, and R. W. Lutz, ibid., 47, 4400 (1967). The ratio k& was suggested by G. L. Schott and P. F. Bird, J . Chem. Phys., of HzOwas taken to be 30 times that of Ar; cf. ref g. 41,2869 (1964); R. W. Getzinger and G. L. Schott, ibid., 43,3237 (1965); and R. W. Getzinger, Symp. Combust., I l l h , Berkeley, 1966, 117 (1967). F. Kaufman and F. P. Del Greco, Symp. Combust., Qth,Zthaca, 1969, 659 (1963); EA = 1000 cal was assumed. Recent high-temperature measurements of the reverse rate (E. A. Albers, K. Hoyermann, H . Gg. Wagner, and J. Wolfrum, paper presented a t the 13th Symposium (International) on Combustion, Salt Lake City, Aug 1970) confirm that this expression is a suitable extrapolation to shock tube temperatures. a V. V. Voevodsky, Symp. Combust., 7th, London, 1958, 34 (1959). ’ B. F. Walker, Dissertation, The University of Texas, 1970. M. C. Lin and S. H. Bauer, J . Chem. Phys., 50, 3377 (1969).
’
Table I was used to calculate the induction times of a Hz:O2:CO :Ar = 1: 5 : 3 : 91 mixture in which all chemical effects of CO were suppressed by setting the rates of reactions 9 and 10 equal to zero. (The termolecular reaction 11 was found to be too slow to affect any part of the profiles at the low pressures used in these experiments.) The induction times were almost the same as in a mixture in which [CO] = 0 (Figure 2). Next we tested the effect of reaction 9 alone on the chemistry of the induction period. Including reaction 9 with a rate constant expression that was proposed as a consensus of several measurements a t high temperatures,ls while still holding klo = 0, gave about half of the necessary correction at 1600°K but had no effect at 2000°K. In order to calculate an acceleration of the right magnitude from reaction 9 alone, it was necessary to increase its rate to about 4 times the consensus value, well beyond the range of the scatter of the measured values of this rate constantlg(Figure 2 ) . With the rate constant for reaction 9 set at the consensus value, the rate constant for reaction 10 was varied until good agreement with the experimental values was obtained. It can be seen in Figure 2 that this rate had t o be taken somewhat faster than the slower rates assigned by previous authors ( e . g . , ref 5
and lo), but far slower than the fast rate assigned by other previous authors (ref 6). Finally, a check was made to see if the assumed nature of the shocked gas flow had an effect upon the results. The absolute value of the effect itself is large (Figure 2 again), but if the rate constants for the Hz-O? system alone were adjusted to give proper agreement once more with Hz-02 induction times, either for laminar or for turbulent boundary layers, the relative change in induction time when CO is added to the mixture is almost the same as in the case when ideal shock propagation is assumed.
IV. Discussion The rate constant expression for reaction 10 obtained in the final comparison with the data is compared with earlier results on the Arrhenius plot of Figure 3. It is clear from this representation that our results are in good agreement with the lower values obtained by previous authors, but in disagreement by over an order (18) W. E. Wilson, Report on the Establishment of Chemical Kinetics Tables, Chemical Propulsion Information Agency, 1967. (19) D. L. Baulch, D. D. Drysdale, and A. C. Lloyd, “High Temperature Reaction Rate Data,” No. 1, Leeds University, 1968. The Journal of Physical Chemwtry, Vol. 76,N o . 10,1971
1508
-'I7
GARDINER, MCFARLAND, 1\/IORINAGA, TAKEYAMA, AND WALKER
t
5
10000 /
T
( O K )
1
6
Figure 2. Computed induction times. Except as noted, all computations were done assuming ideal shock propagation, the composition H2:Oz:CO:Ar = 1:5:3:91, and the rate constant set of Table I. The symbols denote the exceptions: klo = 0; SLP, rate constant for klo as given by Sulzmann, Leibowitz, and Penner (ref 10); TV, no exceptions; [CO] = 0; ks, klo = 0 ; DX, rate constant for klo as given by Dean and Kistiakowsky (ref 5 ) ; BBB, rate constant for klo as given by Brabbs, Belles, and Brokaw (ref 6 ) ; TBL, rate constant for klo of Brabbs, Brokaw, and Belles (ref 6) and turbulent boundary layer growth; klo = 0, kg = 4W, rate constant for klo = 0 and rate constant for k~ = 1.24 X I O 9 exp(-600/RT), 4 times the consensus value recommended by Wilson (ref 18 and 19). The symbols are to the right of the corresponding solid lines and to the left of the corresponding dotted lines.
of magnitude with the higher values obtained previously. The discrepancy with the rate constant of Brabbs, Belles, and Brokaw6 is well outside of the error range of our measurements, as can be seen by comparing Figures 1 and 2. Mechanistic complications seem unlikely, as the compositions, temperatures, and pressures used by these authors were similar to ours. If dissociation of impurities is an important initiation mechanism for experiments under these conditions, then a possible explanation of the difference would be that the purity of our experimental mixtures was greater than that of theirs. In view of the fact that many different mixtures, made with gases from different sources, gave induction times that agreed within experimental error, we believe that impurities do not play a controlling role at least in our experiments. An interesting possible reconciliation of the discrepancy between the present results and those of ref 6 lies in the fact that the experimental mixtures used by them contained about 5% COz as a catalyst for assuring vibrational relaxation of CO through the rapid V-V The Journal of Physical Chemistry, Vol. '75, AVO.10,1971
5 10000 / T
3
7
9
( O K )
Figure 3. Rate constants for reaction 10. B = Brokaw, ref 4; BBB = Brabbs, Belles, and Brokaw, ref 6; BllI = Bartle and Myers, ref 9; CGK, Clark, Garnett, and Kistiakowsky, ref 8; D = L. J. Drummond, Aust. J . Chem., 21, 2631 (1968); DK = Dean and Kistiakoursky, ref 5 ; 0 = Garnett, Kistiakowsky, and O'Grady, ref 7 ; SMB = Sulzmann, Myers, and Bartle, ref 3; W = this study.
transfer between the vg mode of Con and the v = 1 state of CO.*O It may be that the rate constant measured in our experiments (and the other low values as well) pertains to vibrationally cold CO, while the higher value of ref 6 pertains to vibrationally relaxed CO. This would be subject to direct experimental test by repeating the experiments reported here with a COZcontaining mixture. The finding of Myers, et U Z . , ~ that addition of He to CO-02-Ar mixtures did not alter the ignition data speaks against the idea, however. It is also possible that the use of the CO flame spectrum emission, as in ref 6, provides a mechanistically different diagnostic of reaction progress than in our case and that the present results are t o be preferred since they were done directly with observations of a ground state reaction intermediate. This appears unlikely to us, since exponential growth constants have been measured quite successfully in reflected shock waves by monitoring the growth of the CO flame spectrum emission intensity in a manner that is spectroscopically very much like the method employed in ref
eaz1 It seems most likely to us that the discrepancy between our value for klo and the value derived in ref 6 (20)
W.A. Rosser,
Jr., R. D. Sharma, and E. T. Gerry, J . Chem.
Phys., 54, 1196 (1971). (21) D. Gutman and G . L. Schott, ibid., 46, 4576 (1967); D. Gutman, E. A. Hardwidge, F. A . Dougherty, and R. W.Lutz, ibid., 4 7 , 4400 (1967).
1509
OPTICALPROPERTIES OF M METHYL URACIL CRYSTAL is attributable to their measurements being affected by scattered light. Downstream scattering of just a small amount of the intense CO flame spectrum radiation from the end of the reaction zone would be sufficient to exaggerate the apparent linear increase of chain center concentrations between the shock front and the exponential growth occurring in the later part of the initiation zone. If this occurs, it would certainly lead to spuriously high values of klo. The lclo values inferred by Dean and Kistiakowsky6 from ir emission growth measurements in the same temperature range, which would be expected to show less disturbance from scattered radiation, are in good agreement with our result sa Extrapolation of our Arrhenius expression to higher temperatures gives rate constants smaller than the
direct m e a s u r e r n e n t ~ ~and ~ ~ l much smaller than the indirect The inaccuracy of the long extrapolation makes the first comparison of doubtful value, but it would seem to be impossible to increase the activation energy obtained in our experiments to such a high value that agreement with the indirect measurements could be obtained. I t has been suggested that the indirect measurements were affected by small concentrations of hydrocarbon impurities. 2 2 Acknowledgment. This research was supported by the U. S. Army Research Office, Durham, and the Robert A. Welch Foundation. (22) T. C. Clark, A. M. Dean, and G. B. Kistiakowsky, J . P h y s . Chem., 54, 1726 (1971).
Calculations of the Optical Properties of 1-Methyluracil Crystal by an All-Order Classical Oscillator Theory
by Howard DeVoe Department of Chemistry, University of Maryland, College Park, Maryland
20742
(Received January 6 , 1972)
Publication costs assisted by Department of Chemistry, Uninersity of Maryland
An all-order classical oscillator model which takes molecular absorption band shapes into account was used to calculate the polarized refractive indices, reflection spectra, and absorption spectra of 1-methyluracil crystal in the near-ultraviolet region. Lattice sums were evaluated from theoretical transition monopoles for the three lowest 7~ + T * molecular transitions and point dipoles for the in-plane components of the background polarizability. At the first crystal band the spectral shapes and intensities agree well with experiment for two directions of the light propagation but are uniformly shifted to higher frequencies. At the second crystal band the calculated frequencies, but not the intensities, are satisfactory. The crucial importance of the background polarizability to the crystal optical properties is demonstrated. It is pointed out that molecular transition moment directions cannot be reliably determined from crystal polarization ratios.
Introduction The optical properties of molecular crystals are usually calculated by tight-binding (Frenkel) exciton theory as originally developed by Davydov.1*2 The frequency shifts and intensity changes of absorption lines are derived by first-order quantum mechanical perturbation theory. The present paper is an application of a classical oscillator model3 which differs from exciton theory in treating intermolecular interactions to all orders and in taking the empirical molecular absorption band shapes into account. In common with exciton theory, the classical oscillator model assumes that intermolecular electron ex-
change and charge transfer are negligible in the ground and excited states so that the crystal differs optically from an oriented gas only because of intermolecular coulomb interactions. The exciton crystal frequency shifts are the same as in the classical theory to first order. Rhodes and Chase4 have shown that the classical oscillator model is equivalent to an all-order quan(1) A . S. Davydov, “Theory of Molecular Excitons,” McGraw-Hill, New York, N. Y., 1962. (2) D. P. Craig and S. H. Walmsley, “Excitons in Molecular Crystals,” W. A . Benjamin, New York, N . Y . , 1968. (3) H . DeVoe, J . Chem. Phys., 43, 3199 (1965). (4) W. Rhodes and M.Chase, Rev. Mod. Phys., 39, 348 (1967).
The Journal of Physical Chemistry, Vol. 76, N o . 10,1971
