J. Phys. Chem. 1994,98, 9723-9734
9723
Radiative Lifetime and Quenching Rate Constants of PF(bW) and Tests for an Electronic to Vibrational Energy Transfer Quenching Mechanism Yao Zhao and D. W. Setser* Department of Chemistry, Kansas State University, Manhattan, Kansas 66506 Received: March 8, 1994; In Final Form: July 5, 1994@
A dc discharge in a dilute flow of PF3 in He was used as a source of P F ( b ' P ) molecules in a flow reactor to measure the radiative lifetime and quenching rate constants for 38 reagent molecules at 300 K. The concentration of P F ( b ' F ) in the reactor was about 2 x lo8 molecule ~ m - ~The . decay rate of the P F ( b ' F ) concentration was monitored from the intensity of the PF(b-X) transition, and the radiative lifetime was measured to be 9.7 f 1.2 ms. The quenching rate constants are small, except for 0 2 and Cl2, and in the range 10-'2-10-14 cm3 molecule-' s-'. The dependence of the other rate constants on properties of the reagent is consistent with an electronic-to-vibrational (E-V) quenching mechanism, and this was confirmed by studying several isotopic pairs of molecules, such as H2/D2, H20/D20, and CH3CN/CD3CN. The quenching rate constants are compared to predictions of a model for E-V energy transfer. The reaction with 0 2 proceeds by electronic energy transfer to give 02(b12+).
1. Introduction There has been continued interest in the metastable alA and b'Z+ states of the monohalide molecules of the group VA elements, such as NF, PF, NC1, and PCl, because these molecules, which are isoelectronic with 02, are potential candidates for chemical energy storage systems.1-4 The success of the 02/I chemical laser5 has stimulated interest in the possibility of other chemically pumped electronic-transition laser systems. Since the NF molecule has no suitable upper laser states, the energy stored in the NF(a,b) system must be coupled to another chemical system. In this respect, the PF molecule is a more attractive candidate for laser applications, since it not only has the same X3Z-, a'A, and b'Z+ states as 0 2 and NF but it also has bound A311 and d'll states.6 The PF(A311) and PF(d'II) states have the intrinsic potential to serve as upper laser states, since their transitions terminate on high v" levels of the lower triplet and singlet states, respectively. The radiative lifetimes and the rate constants for quenching reactions of the metastable states of the monohalide molecules are needed for evaluation of their potential utility in laser applications. In the present work, a source of PF(b'Z+; 1.6 eV) molecules was developed, and the lifetime and quenching rate constants were systematically measured in a flow reactor at 300 K. Development of chemical sources for these singlet metastable molecules also is important for the study of energy-pooling reactions between various a'A and b'X+ metastable states. The quenching mechanisms for the a'A and b'Z+ states are of fundamental importance for understanding the energy transfer between collision partners. The quenching reactions of 02(a1A) and 02(b1X+) have been comprehensively studied by several research groups, and the electronic-to-vibrational (E-V) energy if there transfer is the accepted mechanism for are no low electronic energy acceptor states in the reagent. The quenching rate constants are small, ranging from to lo-'* cm3 molecule-' s-l for 02(a1A) and to cm3 molecule-' s-l for 02(b1Z+). For the NF molecule, which has the highest energy singlet states of this group, the quenching of NF(alA) mainly proceeds by chemical r e a ~ t i o n ,but ~ the deactivation of NF(b'F) occurs mainly by E-V energy @Abstractpublished in Advance ACS Abstracts, August 15, 1994.
transfer.'O The quenching rate constants for NF(blZ+) are generally smaller than, but comparable to, those for 02(b1Z+). The magnitude of the rate constant for the E-V energy transfer process depends on the energy gap between the electronic transition energy of the target molecule and the vibrational energy state of the reagent. A strong correlation also exists with the highest vibrational frequency and the number of chemical bonds associated with the highest frequency of the A more quantitative model for E-V energy transfer was proposed and applied successfully to the 02(b1Z+)8and NF(b'Z+)" quenching rate constants by Schmidt. The model has several empirical parameters, and we have used the PF(b) data to further examine this model for E-V transfer processes; comparisons of the experimental results and predictions of the model for PF(blZ+) and for NF(blZ+) are given. The spectroscopy of the electronic transitions of PF has been studied,6 and the energy levels for the electronic excited states are known. The To values for the a'A and b'Z+ states are 7096 and 13 364 cm-', respectively. The radiative lifetime for the PF(alA) state is not known, but it is expected to be slightly smaller than 1 s, by comparison to the lifetime of NF(alA). The lifetime of the PF(b'Z+) state was measured as 6.2 ms by Burden et al.12 with a pulsed microwave discharge in a slow flow of Ar containing a trace of PF3. Since this is the only measurement, a re-examination of the lifetime of PF(b'Z+) is desirable; our value of 9.7 & 1.2 ms is in substantial agreement. A long term goal is to explore the chemistry of the PF molecule in order to evaluate its utility for energy storage, and a systematic study of the reactions of the PF(X3Z-, a'A, blZ+, A3H, and d ' n ) states is currently under way in our laboratory. The results for the PF(A3n) and PF(d'II) states are reported in a separate paper.13 The reaction rate constants of PF(X3Z-) and PF(alA) will be reported in the future.14
2. Experimental Techniques PF(b) molecules were generated in a fast-flow reactor using a dc discharge in a He flow containing a small amount of added PF3. The experimental apparatus was similar to that used previously to generate NF(b),'" SiC12(3B1),15aand PF2(B2B2).15b3cThe pre-reactor containing the discharge was made
0022-3654/94/2098-9723$04.50/0 ~... . 0 1994 American Chemical Society
Zhao and Setser
9724 J. Phys. Chem., Vol. 98, No. 39, 1994 from a Pyrex glass tube, 2.2 cm in diameter and 10 cm in length. The discharge consisted of a rolled Ta foil cathode and a pin anode. The load resistor for the discharge was 9000 S2, and the typical applied voltage was 300-400 V. The main flow reactor was a Pyrex tube, 3.1 cm in diameter and 80 cm in length. The pre-reactor was connected to the main flow reactor by an O-ring joint, and the discharged PF3 flow was admitted axially to the main flow reactor. A perforated glass loop injector was placed after the PF(b) injection tube, -17 cm downstream from the discharge, for admission of quenching reagents. The scattered light from the discharge was reduced by a Wood's horn light trap connecting the discharge pre-reactor to the main reactor with a right-angle bend. The pressure in the flow reactor was monitored by a pressure transducer (MKS Baratron, 0- 10 Torr) at the middle of the main flow reactor, and the typical operating pressure was 2.0 Torr. The bulk flow rate of the He metered into the reactor was measured by a floating-ball type flow meter that was calibrated by a wet-test flow meter. The flow speed was -60 m s-l, corresponding to a time scale of 0.17 ms cm-'. The flow reactor was coated with halocarbon wax (Halocarbon Products Co.) to reduce the quenching of PF(b) at the wall and to reduce the deposition rate of a solid brown film on the wall. Without the coating, the reactor would become dirty and unusable in few days and the cleanup was difficult. The coated reactor, however, could be used for several weeks before it had to be cleaned. The brown film and the wax were easily removed with acetone or CCL, and the reactor could be recoated by melting the wax placed in the reactor. Tank grade He carrier gas was purified by passage through three liquid-N2-cooled traps filled with 5 8, molecular sieves and pumped through the flow reactor by a rotatory pump and a blower. The PF3 sample (purchased from Ozark-Mahoning) was degassed by pumping at liquid-Nz temperature; the gas was then loaded by passage through a solid-C02/acetone-slunycooled trap to the Pyrex glass storage reservoir. The PF3 was added to the carrier gas either 10 cm before or 2 cm after the discharge, using a stainless needle valve to control the flow. The flow rate of the PF3 was measured by the pressure rise in a known volume, and the typical PF3 concentration in the flow reactor was -5 x 10l2 molecule ~ m - ~Most . of the reagent gases were purchased from Matheson Co.; the liquid reagents were from Aldrich or Fisher. The reagents were degassed, distilled, and stored in Pyrex glass reservoirs. The photomultiplier tube (PMT, Hamamatsu R943-02) maintained at -20 "C in a rf-shielded housing (Products for Research, Inc.) was used to monitor the PF(b, v' = 0 X, v" = 0) emission at 748.3 nm. The PMT was attached to a 0.5 m monochromator (Minuteman) fitted with a 1200 grooves mm-' grating blazed at 500 nm. The PMT/monochromator could be moved on a track parallel to the axis of the reactor. The signal from the PMT was processed by an amplifier/discriminator (EG&G 1120) and a photon counter (SSR 1105) and then sent to a PC computer for storage and subsequent analysis. A spectrum of the PF(b-X) emission with 3 8, resolution taken 20 cm after the discharge showed a single band at 748.3 nm, corresponding to the 0-0 band of the PF(b-X) transition. The 1-1, 2-2, and higher v' bands at 747.2 and 746.2 nm, etc., were absent. The same result was obtained when Ar was used as carrier gas, which is known to be less effective for vibrational relaxation than He. This indicated that the PF(b) molecules generated by the dc discharge from the PF3/He mixture were mainly in the v' = 0 level. This simplified the study of quenching reactions, since vibrational relaxation cannot
-
cause complications in the relative intensity measurements. A low resolution PF(b-X) spectrum is presented later; see Figure 7. The concentration of the PF(b) in the flow reactor was estimated by comparing the PF(b-X) intensity with the intensity of NO2* emission from the 0 f NO f M reference reaction16 using the following relation:
Signals from both N02* and PF(b) emissions, and SA~02*, were viewed with the same experimental configuration. A slit width of 0.16 mm was used for the monochromator, which gives a spectral resolution of 2.7 A, to ensure that the ratio SAp~(b)/ sAN02* was not distorted by the difference in the band shapes of the two emissions; a large slit width could artificially make the ratio too low, since the PF(b) emission is a narrow band while the N02* emission is a broad continuum. The S A p p ( b j SAN02*ratio was independent of slit width when the slit width was 5 0.16 mm. The absolute emission rate constant16 for N02* is KA = 1 x molecule-1 cm3 s-l at 1 = 748 nm, and the emission intensity is independent of 1 for the small spectral region of the PF(b) emission. A known [O] was obtained by titrating the N atoms from a microwave discharge in N2 with NO. The integration was done over the range of the PF(b) 0-0 band from 745 to 750 nm. Results of several measurements were averaged to give [PF(b)] 2 x lo8 molecule cm-3 at 20 cm downstream from the discharge; the concentration is estimated to be accurate within a factor of 2. The [PF(b)] would increase as the discharge voltage was raised from 250 to 400 V, and the [PF(b)] was higher when PF3 was added before the discharge than when it was added after the discharge, but the difference was less than a factor of 2. This behavior is quite different from the NF(b) case, because adding NFz through the discharge increased the NF(b) emission intensity 20-50-fold and the NF(b) concentration was -5 x 10" molecule cm-3.lOd The intensity of PF(b) emission serves as a measure of the relative concentration of PF(b) in the reactor. The PF(b) decay follows a pseudo-fist-order differential rate law:
-
where t - l is the radiative lifetime; k,/P is the rate constant for quenching at the wall, which is diffusion limited if the quenching probability is large and, therefore, inversely proportional to the total pressure P; k~ is the quenching rate constant by added reagent [Q]; kq[q] is the term that accounts for quenching by other species in the reactor, such as impurities in the He carrier and products generated by the discharge. In eq 2 we have assumed that quenching by He is negligible, which was proven to be the case. The quenching represented by the kq[q] term is expected to be small and constant, since the concentrations of impurity species are low. This term can be ignored for all experiments except for the lifetime measurements. Integrating eq 2 gives the integrated rate law:
Equation 3 was the working equation used to obtain rate constants from the fist-order decay curves of the [PF(b)], which were obtained by observing the relative PF(b) emission intensity. The lifetime of PF(b) was obtained by measuring the decay of the PF(b) emission intensity along the flow reactor in the
Quenching Rate Constants of PF(b'Z+)
J. Phys. Chem., Vol. 98, No. 39, 1994 9725
absence of added reagents. However, caution must be exercised in equating the measured decay time with the radiative lifetime, since the k,[q] term cannot be explicitly controlled, nor completely eliminated, and the k,/P term must be considered. The effect of the wall-quenching term, k,/P, was diminished in most experiments by coating the wall with chemically inert wax. In another experiment k,/P and r-' were separated by measuring the dependence of the decay constant on the total pressure (with [Q] = 0). Both methods were used to select the best value of the radiative lifetime. The quenching rate constants by added reagents can be obtained in two ways. The first way is to acquire several firstorder decay curves of PF(b) at different fixed [Q] and to plot the decay rate constants as a function of [Q]. The plot of kto& versus [Q] should be linear according to eq 2b, and the slope gives the quenching rate constant. The second way is to monitor the PF(b) intensity at a fixed distance (therefore, fixed decay time) after the admission of the reagent and measure the decay of PF(b) as a function of [Q]. Equation 3 then can be written as
0.18 b
0.1 4
0.12
-
0.10
'e B Y
0.00
0.06
0.04
ln([PF(b)l[QI/[PF(b)l[Q1=0)= -kQ[QlAt
(4)
Therefore, the semilogarithm plot of the relative intensity versus [Q] directly yields the quenching rate constant. Notice that measuring the rate constants by either method does not require the elimination of the wall quenching or other quenching not related to the addition of [Q], but such processes need to be independent of [Q]. The second method was used to acquire quenching rate constants of PF(b) in this work. The time scale of 0.17 ms cm-' obtained from the bulk flow rate of He was used to convert the distance between the reagent inlet and the viewing point to the reaction time, At, assuming a plug flow profile.
3. Experimental Results A. Radiative Lifetime of PF(b). The lifetime of PF(b) was first measured from the pressure dependence of the first-order decay constant in an uncoated reactor. In this experiment the reactor was pumped by the rotatory pump alone and a large diameter plastic pipe was inserted between the far end of the reactor and the pump, which served as a buffer to ensure that the flow speed remained constant at different total pressure. Measurements of the He flow rate were done up to 10 Torr, and the flow speed was -31 m s-l and constant in the 2-10 Torr range. Measurements of the decay curves were started 15 cm downstream from the bend of the reactor to ensure that the results were not distorted by the turbulence introduced into the flow by turning the comer. The decay constants of [PF(b)] were measured for several pressures and fitted to eq 5 . ktod = z-l
+ kJP
(5)
Figure 1 shows the plot of ktod versus [UP]. The intercept of the straight line resulting from the least-squares fit gives the radiative lifetime of PF(b), and the slope gives the wallquenching rate constant, k,. The plot includes four independent sets of data from different days. The intercept is 0.038 f 0.005 cm-', which gives z = 8.5 & 1.2 ms for the lifetime of PF(b). The wall-quenching rate constant is 0.18 cm-' Torr or 558.0 s-l Torr. The diffusion coefficient, DO,is related to k, by the equation DO = kWA2No, where ,I2 = [ ( x / L ) ~-t- (4.82/1)2]-1 is the characteristic diffusion length in the flow reactor, with L being the length and I the diameter, and A2 = 0.387 cm2for our reactor. NO= 3.27 x 10l6 molecule Torr-' cm-3 is the number density
0.02
UP [Torr'']
Figure 1. Decay constants of PF(b) versus reciprocal of He pressure in the uncoated reactor. The straight line is a least-squares fit to k = t-l kJP.
+
at 300 K. Using these numbers, the diffusion coefficient of PF(b) in He was calculated to be 7.0 x 1OI8 cm-' s-'. In the experiment described above, a plug flow profile was assumed to convert the flow distance to flow time. For a fully developed parabolic flow profile with unit probability for wall quenching of PF(b), which is likely to be the case in this experiment since a He flow and an uncoated reactor were used, the measured decay constants should be increased by a factor of 1.6. Therefore, the lifetime of PF(b) obtained from the pressure dependence measurements is 5.3 f 1.2 ms and k, is 891 s-l Torr, which corresponds to a DOof 1.1 x 1019 cm-' s-l. These values probably are lower limits to both z and DO, because quenching due to impurities in the He could contribute significantly to kto& at higher He pressure, thus giving a shorter apparent lifetime. The lifetime of PF(b) was also obtained by measuring the decay time in a wax-coated reactor. The wax coating was effective in reducing wall quenching, and the decay time in a freshly coated reactor was -9 ms compared to -3 ms in an uncoated reactor at 2 Torr. In a freshly coated reactor, the decay time was independent of pressure. The decay time would decrease as the reactor became dirty; the decay time also depended on the discharge voltage, with a shorter decay time at 400 than at 300 V for a slightly dirty tube. Changes in the decay time with discharge voltage were larger if PF3 was added before the discharge than if it was added after the discharge. Figure 2 shows two typical plots of PF(b) decay acquired at two different discharge voltages with PF3 added after the discharge. The decay time is 10.1 & 1.0 ms for 300 V and 7.7 f 1.O ms for 400 V, respectively; the reasons for the difference are not known. To obtain the best value for the radiative lifetime of PF(b), several measurements were made, each with a fresh wax coating on the wall and a discharge voltage of 300 V. The final average value for the lifetime of PF(b) is 9.7 & 1.2 ms. Notice that the correction for the parabolic profile is not
Zhao and Setser
9726 J. Phys. Chem., Vol. 98, No. 39, 1994 0.0
0.0
-0.2
-0.5 -0.4
-1.0 -0.6
-
2
2 -0.8
-1.5
-1.0
\o C H 4
-2.0 -1.2
V = 400V
-2.5
0
10
20
30
40
50
0
the coated flow reactor at different discharge voltage.
20
30
40
!
Concentration [molecule cm-'1
Distance [cml
Figure 2. Semilogarithmplots of the PF(b-X) emission intensity along
10
Figure 3. Semilogarithm plots of the PF(b-X) emission intensity observed at 10 ms reaction time versus added reagent concentration. The slopes of the lines give the quenching rate constants for each reagent.
applicable here because freshly coated reactors were used and the wall-quenching rate was greatly reduced, if not eliminated. 0.0 B. Quenching Rate Constants of PF(b). The quenching rate constants of PF(b) by more than 30 diatomic and small polyatomic molecules were measured in a coated reactor using the fixed point method with a reaction time of 10 ms. The PF3 concentration, which was -5 x 1OI2 molecule ~ m - was ~ , added -0.5 to the He flow before the discharge. For many reagents, especially for HZand D2, methane, ethane, and their halogensubstituted derivatives, two decay components for the [PF(b)] could be observed. The first component had a fast decay and -1.0 a small amplitude, -10% of the total intensity, and occurred from [Q] = 0 to [Q] x 1-5 x 10" molecule ~ m - ~The . second component had a slow, well-behaved, single-exponential decay. E The same phenomenon was observed by Cha and SetserIobin studying the NF(b) quenching reactions. It was suggested that -1.5 F atoms, which are generated by the discharge through N F 2 , were indirectly responsible for the fast-decay component. The situation is likely to be similar for PF3. Therefore, C 2 h . which is known to be an effective F atom scavenger, was added 2 cm after the discharge and 18 cm before the admission of quenching -2.0 reagent to remove the fast-decay component. The concentration CH4 of CZH6 used with all reagents was -5 x 10l2molecule ~ m - ~ , which suppressed -20% of the total PF(b) intensity and C2H5CI removed the fast-decay component from the quenching plots. -2.5 Figures 3-5 show typical plots of the [PF(b)] decay versus 10 20 30 40 50 reagent concentration for a fixed reaction time of 10 ms. The Concentration [molecule cmJ] quality of the data is good for the majority of the reagents, as judged by the excellent linearity of the semilogarithm plots of Figure 4. Semilogarithm plots of the PF(b-X) emission intensity observed at 10 ms reaction time versus added reagent Concentration. the experimental data and their reproducibility. The standard The slopes of the lines give the quenching rate constants for each deviations given by least-squares fits are less than &5%. reagent. Considering the uncertainties in the flow speed calibration and the concentration measurements, the uncertainty of the rate constants is partly due to the possibility of a quenching constants is estimated to be f15% for rate constants 2 1 x contribution from the wall. Very high concentrations of reagent cm3 molecule-' s-'. The uncertainty for rate constants are required to induce an observable intensity decrease for cases smaller than cm3 molecule-' s-' is probably as large as with small rate constants, but such concentrations could change &20%. The limitation on measuring small quenching rate the characteristics of the flow in the reactor and possibly change
s
Quenching Rate Constants of PF(blC+)
J. Phys. Chem., Vol. 98, No. 39, 1994 9727 TABLE 1: Comparison of Quenching Rate Constants for W b ) , W b ) , and Odb)
0.0
rate constants reagent -0.5
-1.0
2
z
D2
-1.5
-2.0
-2.5 0
io
30
20
40
50
Concentration [molecule cmJ]
Figure 5. Semilogarithm plots of the PF(b-X) emission intensity observed at 10 ms reaction time versus added reagent concentration. The slopes of the lines give the quenching rate constants for each reagent.
k,. In extreme cases, the PF(b-X) intensity actually would increase upon admission of a large amount of reagent. The quenching rate constants were too small to be determined in the existing apparatus for CDC13 and CF31, and an upper limit of 1 x cm3 molecule-' s-' is given to their kQ. Difficulty was encountered with PF3. Apart from the complications associated with the small rate constant, the tendency of PF3 to absorb on the wall caused a further problem. The decay plots of PF(b) with added PF3 were poorly behaved and not reproducible if the wax coating on the wall was not fresh. The best value of the quenching rate constant for PF3, 4.0 x cm3 molecule-' s-', which was measured with a freshly coated reactor, should be considered as an upper limit. Since quenching of PF(b) by PF3 is slow, the effect of a PF3 concentration of 5 x loL2molecule cmw3on the PF(b) lifetime measurements is negligible. The quenching rate constants for PF(b) are listed in Table 1 together with those for NF(b) and 02(b); the reagents are listed in order of increasing kQ for PF(b). The magnitudes of kQ for PF(b) are in the range 10-12-10-14 cm3 molecule-' s-', which actually is the same range as for NF(b) and 02(b). The rate constant for H2 is small, 4.0 x cm3 molecule-' s-', and similar to that for NF(b). The rate constants for CO and C02 also are small, 1.0 x and 1.5 x cm3 molecule-' s-', but somewhat larger than those for NF(b). The rate constant for PH3 is modest, 1.2 x cm3 molecule-' s-', which is of practical interest because the F PH3 reaction could be a chemical source of PF(b). A general trend that can be seen from Table 1 is that molecules with more C-H bonds have larger rate constants. The rate constants for C& and C2H6 are 5.5 x and 7.4 x cm3 molecule-' s-', respectively, which are larger than, but comparable to, those for NF(b). The rate constant for C2H4,2.1 x 10-l2 cm3 molecule-' s-', is about 3 times larger than for C2H6. However, the rate constant for C2F4 is very small, S l O - l 5 cm3 molecule-' s-', and that for
+
PF(b) 50.01 (0.05) 50.01 0.02 (5.5) 0.08 (2.9) 0.10 (0.04) 0.15 (0.019) 0.40 0.40 (0.06) 0.90 (1.4) 1.1 (0.27) 1.2 (0.14) 1.2 (5.9) 1.5 1.6 (0.39) 2.1 (5.8) 2.5 (6.4) 2.8 (0.16) 3.2 3.6 (0.35) 4.3 (8.4) 4.5 (13.6) 5.0 (7.3) 5.3 (10.1) 5.5 (9.7) 5.6 (1.8) 7.2 (12.5) 7.4 (15.1) 8.6 (11.0) 9.1 (12.7) 9.4 (5.3) 13.6 (6.9) 15.2 (11.1) 15.3 (1.1) 21.0 (16.7) 21.0 (0.81) 60.8 (6.9) 80.7 210.0
cm3 molecule-'
SKI)
Wb) 0.03 0.05 1.1 (0.19)
Odb)
0.021 (0.003) 0.014 (0.001)
0.04 4.4
0.25 (0.13) 0.18 (0.05) 0.035 (0.052)
9.3 0.4
0.64 (0.21) 0.25 (0.86) 2.1 (0.20) 8.6 (8.7) 0.025 (0.11) 2.2 (0.30)
2.1 (0.27) 2.1 (0.35) 1.6 (0.34) 0.42 (1.1)
2.0 50 0.12
8.0 0.73 3.8
1.4 (0.53) 1.9 (0.38)
4.5
6.8 (6.4) 3.6 (0.39) 0.88 (3.6) 1.1 (0.58) 0.22 (0.085) 3.7 (2.0) 160.0 0.24
40 3.0 6.5 4.4 6.8 0.004
Values in parentheses are from the model calculation discussed in the text. Experimental values for NF(b) are from ref 10; those for Oz(b) are from refs 10b and ref 8b.
CD3CD-CD2 is modest, 1.5 x cm3 molecule-' s-', indicating that the C=C double bond is not important in the quenching process for C2&. The same conclusion was reached cm3 molecule-' for NF(b). The rate constant of 5.6 x s-l for C2H2 indicates that the C r C triple bond also is not important for the PF(b) quenching; the same was found for NF(b). The methyl and ethyl halides, RX (X = F, C1, Br, and I), have rate constants in the range (2.1-15.2) x cm3 molecule-' s-*, which are in accord with an E-V energy transfer mechanism to the C-H bonds. The systematic increase in rate constants for CH3X and C2HsX (X = F, C1, Br, and I) is quite clear in Table 1 and in Figures 3 and 4. Substitution of F only slightly decreased the rate constant relative to C& and C&, taking into account the smaller number of C-H bonds; but, substitution of C1, Br, and I increases kQ by about a factor of 2 for each member of the CH3X series and by about a factor of 1.5 for the C2H5X series. The increase of rate constant from F to I is unlikely to be caused by chemical interaction, since CF3I caused no observable quenching. The halogen substituent effect in the CHX3 (X = F, C1, and Br) series also exists, as shown in Figure 4; the rate constant for CHF3 is 2 orders of magnitude smaller than that for CHCl3. The dependence of kQ on the halogen substituent was much less pronounced for NF(b), but iodine substituents may have caused some enhancement.
Zhao and Setser
9728 J. Phys. Chem., Vol. 98, No. 39, 1994 350
100 CH3NH2
I
30
h
YI
-3
D2
'0
a
I
I
D20 NH3
CHBOH
10
300
250 CH3ND2
3 200 8
CH30D
I
.-P
3
e"
H20
n
$ v $
I
$
150
I
ND3 1
0.3
1
i
100
CDBCN
H2
50
0.1
i 1 ,
0
740
745
750
Quenching Reagent
Figure 6. Comparison of the quenching rate constants for several isotopic pairs of reagents. The comparison is in a logarithm scale.
Another striking feature is the big difference in the rate constants between H and D isotopic pairs, as demonstrated in Figure 6. Interestingly, some pairs have opposite kinetic isotopic ratios. For instance, k(Dz)/k(Hz) = 9; k(DzO)/k(H20) = 8; k(ND3)/k(NH3) = 0.1; k(CDC13)/k(CHCl3) < 0.01; etc. Analysis in the next section shows that variations in the rate constant ratios are due to changes in the vibrational frequencies, which alter the energy defects for E-V energy transfer. Large kinetic isotopic effects were also observed for the quenching constants of NF(b). lob The quenching rate of PF(b) by 0 2 is fast, and the rate constant is 2.1 x lo-" cm3 molecule-' s-l, which suggests a totally different quenching mechanism, as discussed in the next section. Despite its low vibrational frequency, C12 was found to be an effective quencher for PF(b), and the rate constant is 8.1 x cm3 molecule-' s-l. Chemical reactions are responsible for the quenching with Cl2, and PCl(b) was identified as one product from the PF(b) C12 reaction. A more detailed discussion for the C12 and Br2 reactions will be published separately. l7
+
4. Discussion A. Radiative Lifetime of PF(b) and Comparison with 02(b) and NF(b). The radiative lifetime of PF(b) obtained in the present work, 9.7 f 1.2 ms, is somewhat longer than the 6 ms value measured by Burden et al.12 The longer value for the lifetime of PF(b) obtained in the coated reactor should be more reliable, because a decay time measurement is likely to be a lower limit to the true radiative lifetime, since quenching by impurities and residual wall quenching would tend to shorten the decay time. Consequently,the longest value of the measured decay time for metastable species is usually closer to the true radiative lifetime. The radiative lifetimes for 02(b)18and NF(b)'O are 12 s and 19 f 2 ms, respectively. The lifetime for PF(b) is about half of that for NF(b). The blZ+ X3Z- transition is a spin- and electronic-dipole-forbidden but electronic-quadrupole-and mag-
-.
755
780
765
7 0
Wavelength [nml
Figure 7. Low-resolution emission spectrum of PF(b-X) and Oz(bX) following the addition of 02 to the flow reactor at a reaction time of -3 ms. The concentrations of PF3 and 0 2 were 4.5 x lo1*and 8.6 x ioi3molecule ~ m - respectively. ~,
netic-dipole-allowed transition. l9 The reduction in lifetime for PF(b) compared to NF(b) is due to relaxation of the spinselection rule caused by increased spin-orbital interaction for heavier atoms. The diffusion coefficient for PF(b) in He, (1.1 & 0.1) x l O I 9 cm-l s-l, can be compared with those for other similar atoms and molecules. The DOvalue for Ar at 273 K is 1.6 x 1019 cm-I which corresponds to 1.9 x 1019 cm-l s-l at 300 K, and the DOvalue at 300 K for Ne(3P2,~)is 2.0 x 1019cm-I s-1.21 Both species probably have smaller collision cross sections than PF(b). The Cl2 molecule should have a cross section similar to PF(b), and the DOvalue at 300 K for Cl2 was calculated as 1.1 x 1019 cm-' which is the same as that for PF(b). These favorable comparisons show that the DOvalue for PF(b) determined in this study is reasonable. B. Reaction of PF(b) with 0 2 . The large quenching constant for 0 2 suggests that the mechanism for the PF(b) quenching by 0 2 is not E-V energy transfer but electronic-toelectronic (E-E) energy transfer via a crossing of potential curves. The following spin-allowed process is a logical choice. PF(b'2')
+ 02(X32-) +
02(b1Z+) PF(X3Z-)
AH;= -243 cm-' (6)
This reaction was proven by observing an emission at 762 nm when 0 2 was used as a reagent; see Figure 7. The emission band was due to the O2(b-X) transition, identified by the spectral location and the band shape showing a P-R branch structure.22 To ensure that the emitting 02(b) was generated by energy transfer from PF(b), rather than from the interaction of He(23S) with 02(X), experiments were carried out with a higher concentration of PF3 to ensure removal of all the He(23S). The O(3p5P-3ssSo) emission at 777.3 nm could be used as a diagnostic test because the He(23S) 0 2 reaction gives the 777.3 nm line.23 When [PF3] = 1.3 x 1013molecule cm-3
+
Quenching Rate Constants of PF(b'P)
J. Phys. Chem., Vol. 98, No. 39, 1994 9729
was added, the 777.3 nm line disappeared completely, indicating that He(23S) was absent. However, the 02(b-X) emission was still present, thus c o n f i i n g that 02(b) was generated by energy transfer from PF(b) to 02(X). The intensity of the 02(b-X) band was consistent with the expectations for the [02(b)] and the ratio of tpp(b) and r02(b). Reaction 6 may be useful as an 02(b) source without concomitant formation of Oz(a). Stuhl and co-workers have used the NH(alA) reaction with 0 2 to advantage for this purpose in a pulsed experiment.8b The rate constant for the reverse process of eq 6, k,, can be calculated from the equilibrium constant and the forward rate constant, kf,for reaction 6:
where the q are vibrational and rotational partition functions. The vibrational and rotational partition functions cancel, since they are virtually the same for PF(X) and PF(b) and for 02(X) and 02(b) at 300 K. The electronic degeneracies also cancel and
k, = kf exp(AH2RT)
(8)
Using AH: = -243 cm-' and kf = 2.1 x lo-" cm3 molecule-' s-', the rate constant for the reverse reaction of eq 6 is assigned as 6.6 x lo-'* cm3 molecule-' s-' at 300 K. The rate constants for the quenching of NCl(b),24NF(b),lob and PCl(b)24by 0 2 are 1.0 x 10-l2, 2.4 x and 51.0 x cm3 molecule-' s-', respectively. The exoergic energy defects for the formation of 02(b) are 1920 and 5786 cm-l, respectively, for NCl(b) and NF(b) quenching, which are much larger than that for the PF(b) case, leading to much smaller rate constants. For the NF(b) case, an alternative process, formation of Oz(a) and NF(a), may become important, as implied by the strong temperature dependence of koz.loc In the PCl(b) case, the formation of 02(b) becomes endothermic by 1020 cm-', which results in a rate constant too small to measure by our technique at 300 K. C. General Evidence for an E-V Energy Transfer Mechanism. The electronic-to-vibrational(E-V) energy transfer with formation of the alA state and release of the energy difference to vibrational energy of the reagent is the accepted mechanism for the quenching of 02(b) and NF(b). In fact, the formation of NF(a) has been observed from the quenching by H20 and CH4.1°d The 'A' entrance channel potential seems to be mainly repulsive, and the interaction with the repulsive 'A" originating from the alA state is not important; that is, the E-V transition is not a process that involves a crossing of potential surfaces. The trends in the rate constants for quenching of PF(b) show that the same mechanism is operative. The energy separation between PF(b) and PF(a) is 6260 cm-', and the stretching frequency of C-H bonds and H-Cl is -3000 cm-'. Consequently, two quanta of vibrational excitation in H-Cl and C-H bonds have a good energy match. This is consistent with the experimental observation that quenching rate constants of PF(b) by H-Cl and by molecules with C-H bonds are large and correlate with the number of C-H bonds in the reagent. In comparison, the NF(b-a) energy difference is 7470 cm-' and two quanta of vibrational excitation in the H-C1 and C-H bonds result in a large energy defect, which explains why the quenching rate constants for H-C1 and molecules with C-H bonds are smaller for NF(b) than for PF(b). The isotopic effects on the rate constants can also be qualitatively explained by energy defect consideration. Take the Hz/Dz pair as an example. The vibrational frequency is 4400 cm-' for H2 and 3 120 cm-' for D2. One quantum of vibrational ,excitation in H2 has a
-1900 cm-' energy defect, but two quanta make the energy transfer endoergic by -2500 cm-', which guarantees a small quenching rate constant. On the other hand, two quanta of excitation in D2 give nearly a perfect match with the PF(b-a) energy difference, which results in a large rate constant. The experimental rate constants of HZ and D2 agree with this analysis. The isotopic effect on the rate constants of the H20/ D20 pair is similar to the H2/D2 pair. The vibrational frequency is 2734 cm-' for D20 and 3636 cm-' for H20, and D20 should have a better energy match for double excitation and a larger rate constant than H20, which is in accord with the experimental observations. The same consideration can be applied to the CHCl3/CDCl3 pair; the former has a frequency of 3030 cm-' for the C-H bond and the latter has 2270 cm-' for the C-D bond. The explanation for the NH3/ND3 pair is not so obvious, since two quanta of N-H excitation (2 x 3340 cm-') would lead to an endothermic transition and two quanta of N-D excitation (2 x 2560 cm-l) also would have a large energy defect. However, the model calculation given in the next section indicates that the ratio of rate constants for ND3 and NH3 is consistent with the E-V energy transfer mechanism, although both calculated values are lower than the experimental values. An attempt was made to observe the formation of PF(a) from the E-V energy transfer processes by monitoring PF(a) formation by laser-induced fluorescence (LIF).13 The PF(d-a) transition at 348.3 nm was excited by a laser beam, and the LJF signal of the PF(d-a) transition at 358.2 nm was monitored. In principle, formation of PF(a) could be detected by the increase of the LIF intensity when a quenching reagent was added. Unfortunately, this scheme was not successful because the concentration of PF(a) produced directly from the discharge was large and any PF(a) produced by the E-V energy transfer from PF(b) was a small fraction of the total PF(a). Consequently, the LIF intensity did not show a definitive increase when a reagent was added. D. Model for E-V Rate Constant Calculation. Schmidt has proposed a model that permits calculations of rate constants for reactions proceeding by E-V energy transfer to terminal bonds of a molecule." The basic assumption is that the E-V energy transfer can be regarded as a coupled transition from the (b, v' = 0 a, v" = m) transition of the electronically excited molecule to the (X, v" = 0 v' = n) vibrational transition of the molecule that accepts the energy. The rate constant of this coupled transition is proportional to the product of two Franck-Condon factors, one for the electronic transition and the other for the vibrational transition in the reagent, and an energy defect term, which assumes the form of an exponential gap law. The total rate constant for an individual bond is the sum of the rate constants for all possible elementary transitions, Le., summed over m and n. The Schmidt model does not include excitations of the bending modes nor combination levels involving bending plus stretching modes or two different stretching modes. This model was applied to the 02(a), 02(b), and NF(b) reactions by Schmidt, and the agreement of the calculated k~ with the major trends of the experimental results was encouraging." In the 02(b) and NF(b) cases, an "experimental" rate constant for an individual bond, which also can be called a rate constant for a generic type of bond, was obtained by averaging the rate constants from several reagents with the same type of bond. These generic rate constants can be useful for predicting unmeasured rate constants by summing the generic rate constants for the different bonds in a molecule. We used Schmidt's model to calculate rate constants for the PF(b) reactions. Rate constants for individual reagents, instead of those for generic bonds, were calculated and compared
-
-
9730 J. Phys. Chem., Vol. 98, No. 39, I994 TABLE 2: Calculated Franck-Condon Factors for PF and NF (b, v‘ (a, v’’)
0
1
a, v”) Transition@ 3
5
4
PF
1 2 3 4 5 6 7
1.o 2.1 x 1.3 x 5.7 x 8.9 x 1.6 x 2.8 4.5 x
0 1 2 3 4 5
0.99 9.3 x 10-3 4.7 10-5 1.6 x 7.6 x 5.3 10-9
0
2
-
Zhao and Setser
10-3 10-5 10-7 10-9 10-10
2.1 x 0.99 4.5 4.6 x 2.5 x 4.4 x 9.5 x 2.3 x
10-3
3.2 x 4.5 x 0.99 7.1 x 1.1 x 7.2 x 1.4 x 3.2
10-3 10-5 10-7 10-8
10-7 10-3 10-3 10-4 10-7
10-8 10-7
10-3 10-4 10-5 10-6
3.5 x 7.8 x 4.0 x 1.0 x 0.98 1.3 x 3.5 x 3.0 x
1.4 x 1.3 x 10-4 2.8 x 0.93 3.8 x 4.6 x 10-3
6.5 x 5.9 x 2.6 x 3.8 x 0.91 4.8 x
10-9 10-6 10-4 loW2
1.7 x 1.4 x 7.2 x 0.98 1.0 x 2.0 x 1.6 3.5 x
10-7 10-3
10-2 10-4 10-5
5.4 x 10-9 1.8 x 10-7 1.9 x 9.1 x 1.4 x 0.97 1.6 x 5.6 x 10-4
NF 4.1 x 10-5 1.9 x 0.95 2.8 x 2.8 x 10-4 1.5 x 10-5
9.3 x 10-3 0.97 1.9 x 1.4 10-4 6.1 x 3.7 x 10-7
1.2 x 4.3 x 1.5 x 4.5 x 4.8 x 0.89
10-9 10-8 10-5 10-4
Calculated from RKR potentials of a and b states, which were constructed from the corresponding experimental vibrational and rotational constants. directly with each experimental constant. This was necessary because the idea of a generic bond is not very meaningful in the PF(b) case. For example, the rate constant for the C-H bond changes for different molecules because of halogen substituent effects. For instance, kc-H from CH3I, CH3F, and CHF3 would be 5.1 x 10-13, 0.7 x 10-13, and 0.007 x cm3 molecule-’ s-l, respectively. The equations used in our calculation are the same as given by Schmidt, but we have selected improved spectroscopic constants.
kQ = Ziki = C%iZmnFmF$im
constants.6 Table 2 lists the calculated Franck-Condon factors for transitions involving (b, v’ = 0-5) and (a, v” = 0-7) energy levels, which shows that the value of F, decreases rapidly for transitions of (b, v’ = 0 a, v” = m ) as m increases. Schmidt’s procedure for computing the Franck-Condon factor for the reagents, F,, is based on the Morse potential. It is described here with slightly changed notation for convenience of discussion. G r ~ t and h ~ ~ ~ showed that eqs 17 and 18, which were derived by Timm and Mecke26for the square of IR absorption moment IP,12, could reproduce overtone intensity distributions for isolated C-H chromophores.
-
(9)
ki is the rate constant for each terminal bond, which is the summation of coupled transitions over m and n levels, and the index i refers to the terminal bond under consideration. F, and F, are the Franck-Condon factors for the PF(b, v’ = 0 a, v” = m ) transition and for the Q(X, v” = 0 v’ = n) transition, respectively. Rim, is the factor from the exponential gap law to account for the energy defect.
-
-
AK), = [n(K - 2n - l)]-’(K - 2)!/[(K - 2 - n)!n!]
(13)
In eqs 12 and 13 K = l/x and x is the anharmonicity. E: is the overtone energy, which is E’Q(v”= 0 v’ = n) in eq 11. Since Franck-Condon factors for optical transitions and for the coupled transition involved in E-V energy transfer are equivalent and since the ratio FJFl is proportional to the ratio IPnI2/ IP1I2, F , can be calculated as
-.
The energy defect of the coupled transitions is given by
E,,, = E,,(b, v’ = 0
-
-
a, v” = m) - EQ(X,v“ = 0 v ’ = n ) (11)
The Boltzmann factor, exp(- IEimnl/(RZ‘)),is introduced for endothermic transitions, when Eimn< 0. Schmidt assigned the empirical range parameter, a = 0.0032, by fitting the Oz(a) and 0 2 ( b ) data, and he used the same value for NF(b). We employed the same value for a in our calculation for PF(b). The PF(ba) transition energy was calculated from the experimental energy levels. Only the fundamental and the overtone levels of the strecthing modes of the reagent molecules were considered in our calculations. Transitions involving the bending modes and combination levels were not used because the Franck-Condon factors for these transitions cannot be calculated from the simple model, even though their contributions to the total quenching could be significant in some cases. The Franck-Condon factors for the PF(b-a) transition, F,, were calculated from RKR potentials of the PF(a) and PF(b) states, which were constructed from experimental molecular
Schmidt’smodel is based on the local model (LM) description for stretch vibrations. In Schmidt’s calculation for NF(b), a single value for the LM frequency, U M , and the LM anharmonicity, x = IXM/OJM~, was used for each generic bond. Since we want to treat individual molecules with specific energy levels, a model based on the normal mode (NM) description could be used as well. For polyatomic molecules, the overtone energy levels are frequently mixed through Fenni resonance and the observed overtone transitions often extend over a wide spectral region. Therefore, the observed normal mode energy levels should be better for computing energy defects. Practically, however, the NM approach is difficult to implement. One obstacle is that complete sets of normal mode anharmonicities are not available for most molecules. Another one is that the correct assignment to an experimental band as an overtone transition versus a combination transition is not always obvious. If only the overtone excitations of normal modes are considered and excitations of combination modes are ignored, due to limitations on the available anharmonicity data, numeric dif-
Quenching Rate Constants of PF(blX+)
J. Phys. Chem., Vol. 98, No. 39, 1994 9731
TABLE 3: Vibrational Frequencies and Anhamodcities Used in the Model Calculationa molecule @M x = IXM/OMI bond molecule WM
co D2 CZH4 CHCls cHF3 CDC13 CH3F CH3CI CH3Br CH3I CzHsF CzHsC1 CzHsBr CH3CN CH30H CH3NH2
2170 3116 3167 3226 3214 2334 3040 3132 3146 3148 3098 3084 3087 2278 3101 3855 3088(2) 3013 3538 3046(2) 2941
0.0061 0.0198 0.0183 0.0201 0.0199 0.0146 0.0194 0.0194 0.0192 0.0192 0.0201 0.0203 0.0203 0.0049 0.0191 0.0223 0.0194 0.0204 0.0223 0.019 0.019
c-0
coz
1875
D-D C-H C-H C-H C-D C-H C-H C-H C-H C-H C-H C-H C-N C-H 0-H C-H C-H N-H C-H C-H
Hz CJIZ CHBr3
4401
cZm5 PH3 NH3 ND3 HzO D20 HCl CH4
czH6 CD3CN CH30D (high)
(low) CH3NDz (high) (low)
3435 3242 3111 2384 3577 2594 3796 2778 299 1 3078 3085 2289 2275 2810 3088(2) 3013 2594 3046(2) 294 1
x = IXM/WM~
0.0082 0.0276 0.0153 0.0204 0.021 1 0.0153 0.0208 0.0150 0.0221 0.0159 0.0176 0.0195 0.0203 0.0049 0.0134 0.0159 0.0194 0.0204 0.0151 0.019 0.019
bond
c-0 H-H C-H C-H C-H P-H N-H N-D 0-H 0-D H-Cl C-H C-H C-N C-D 0-D C-H C-H N-D C-H C-H
(high) (low) (high)
(low)
Sources of molecular parameters: for COz, see text; Czm5, ref 25b; C& and CH3X, ref 27; C2H2, ref 31; CzH6 and CZH~X, ref 33; CHX3, ref 34; C h , H20, and NH3, ref 35; CD3CN and CHsCN, ref 36; CH30H, ref 37; CH3NH2, ref 38; PH3, ref 39. ferences in the NM and LM anharmonicity constants would still cause difficulties. This becomes clearer with some examples. The relations between the LM and some NM anharmonicites are XM = k,, = 2xm for XY2 group molecules with symmetry and XM = 3xSs= 2xm for XY3 group molecules with C3” symmetry, where subscript “M” refers to the LM stretch mode, while “s” and “a” refer to the NM symmetric and asymmetric stretch modes. For instance, XM = -84 cm-I and X I ’ = -42 cm-’ for H20, and XM = -60.7 cm-’ and x11 = -20.3 cm-’ for CH3CLZ7 Similar relations exist for molecules of other symmetry groups. Thus, a choice must be made regarding the use of LM or NM in equations 9-14. The Franck-Condon factor, F,,is a rapidly decreasing function of n, since x HkCH3C1 ~ c >~ KCHCI, series and, ~ C H ~ C>I k H C l 3 series were verified for PF(b) and NF(b), respectively. The order of k c 2 > ~ kc2b for PF(b) was also verified; the energy defects are 198 cm-’ for C2H4 and 435 cm-’ for C2H6, and the rate constant for the C-H bond in C2H4 is more than 2 times larger than for the C-H bond in C2H6. The calculated kinetic isotopic effects match the experimental results for both PF(b) and NF(b), as demonstrated by the relative values of the isotopic pairs. The rate constants for D20,Dz, CHCl3, NH3, CH3CN, and CH3NH2 are larger for PF(b), while those for H20, H2, CH30H, and NH3 are larger for NF(b), compared with their corresponding partners. This is expected, since the kinetic isotopic effects are mainly due to changes in the energy defects.
-
Zhao and Setser
9132 J. Phys. Chem., Vol. 98, No. 39, 1994
CH3OHY CH3NHZ
CH3I
-g
cHF3
1
--
I a44
I
CHCI3 I
'b
-P
5
0.1
CZHZ
a,...
B
-
9
I
I co
///
0.001 I 0.001
//
I ND3
ID2 a: CH,OD
b: CH,CN
,
I
I
0.I
0.01
I
1
10
100
16'[10L3 molecule" cm3 d] Figure 8. Comparison of the calculated and experimental quenching rate constants for NF(b) on a logarithm scale. The calculated rC, have been scaled by CNF= 3.0 x lo-'' molecule-' cm3 s-I, which was obtained from the best global fit to the set of experimental rate constants. 100 CH3NHZ DZO t3 NH3
10
m z
-
m 4
CH3I t3
CH3NDZ I I ' I CLHSF
HZO DZ I B ND3 PH3 I
YI
-g
I
1
-$P
I
CD3CN
H2
0
-
5
c02
I
B
C2F5-H
0.1
9 CHF3 I
0.01
0.001 0.001
0.01
0.1 1 [10'3mo1de-l cm3 d l
10
100
Figure 9. Comparison of the calculated and experimental quenching rate constants for PF(b) on a logarithm scale. The calculated rC, have been scaled by CPF = 2.7 x lo-'' molecule-' cm3 s-', which was obtained from the best global fit to the set of experimental rate constants.
Despite the general level of agreement, notable deviations exist between experimental and calculated rate constants for a few cases, especially for PF(b). The most serious problem is that the H20/D20 and NH3/ND3 pairs have calculated rate constants that are -10 times and -5 times smaller than the experimental ones for PF(b). However, the ratios of experimental and calculated rate constants for each pair are about the same. The isotopic effects seem to be explained by changes in the energy defects, but the absolute values of the rate constant need to be scaled. For NF(b), the calculated rate constants compare well with experimental values for the H20/D20 pair,
but the rate constants for the N H W 3 pair are overestimated by a factor of 4, although the calculated ratio is nearly correct. The difference between the calculated rate constant and the experimental value is not related to the energy gap term or the F, term of the model, but to some electronic factor(s). The explanation for why the deviations of the NH3/ND3 pair are in opposite directions for PF(b) and NF(b) is not known; however, one possible cause is the role of the larger dipole moment for PF(b).28 The dipole moments for NF(b) and PF(b) are not experimentally known, but theory gives -0.04 and -0.6 D for NF(b)19 and PF(b),28respectively. The dipole moment given
Quenching Rate Constants of PF(blZ+)
J. Phys. Chem., Vol. 98, No. 39, 1994 9733
for PF(b) is actually for PF(X), but the values for the X and b states are similar, as shown by Buenker et al. in their work on A s p 9 and Yarkony on NF.I9 Therefore, the dipole moment for PF(b) should be much larger than that for NF(b). The larger dipole moment would lead to stronger attractive intermolecular interactions for PF(b) than for NF(b). The model also does poorly for other cases with large energy defects, as illustrated by the examples below. The calculated rate constants for CO and C02 are 5 and 10 times smaller than their respective experimental values for both NF(b) and PF(b). One factor that may have contributed to the disagreement is the questionable accuracy of Franck-Condon factors for F,. Because of the low frequencies, the vibrational quantum number must increase by 3, and the k~~ for the Av = 3 transitions are very sensitive to the Franck-Condon factors. Equation 14 may not be universally applicable for obtaining reliable Franck-Condon factors. For C02, another factor may also have contributed to the discrepancy. The vibrational frequencies for the C-0 stretch30 are 01 = 1354 and 0 3 = 2396 cm-', which indicates that the two C-0 bonds are strongly coupled and the uncoupled local mode description is not applicable to C02. The value of W M for C02 is 1875 cm-', as calculated from the relation OM = (01 ~ $ 2 ,which clearly does not give a realistic measure of the energy levels of C02. For the anharmonicity, the local mode theory requires that x11 = x33 = (1/2)xM, but x11 = -2.94 and x33 = -12.47 cm-' for C02. In our calculation, XM = x11 x33 was used to obtain the XM value for C02. Although the terminal bond model cannot be expected to hold for C02, the theory does reproduce the increase in rate constant from NF(b) to PF(b) due to the difference in energy defects. Both CO and C02 have significant positive temperature coefficients for quenching of NF(a) and several off-resonance product channels seem to be likely. lot The C-H stretches in the C2H2 molecule fit the local mode description very well, since the two C-H bonds are well ~ e p a r a t e dbut, ; ~ ~ the calculated rate constant for PF(b) is about 3 times smaller than the experimental value. On the other hand, the calculated rate constant for NF(b) is about 3 times larger than the experimental value, contrary to other molecules with C-H bonds for which the calculated rate constants are underestimated. The deviations may partially arise from the uncertainty in the energy defect; the actual energy defect for C2H2 may be smaller than that calculated from OM for PF(b), but larger for NF(b), because of Fermi resonance with the bending mode.31 The halogen substituent effects observed for the CHX3, CH3X, and C2H5X (X = F, C1, Br, and I) series for PF(b), and to an lesser extent for NF(b) with CH31, cannot be reproduced by the model calculation. The observed changes in the rate constants are not explained by minor changes in energy defects that could be induced by the halogen substitution. The heavier halogen atoms seem to induce a large electronic coupling, Le., a larger CPFvalue. Furthermore, multiple fluorine substitution exhibits a strong reduction in k ~ The . experimental rate constants for CHF3 and C2HF5, 0.02 x and 0.08 x molecule-' cm3 s-l, are disproportionately small compared to CHC13, and the calculated and experimental values for CHF:, and C2HFs differ by 2 orders of magnitude. In addition to the factor that is associated with changing the halogen substituent, other factors reduce the rate constants for multiple fluorine substitution. A similar effect is well-known for H abstraction from fluorinated methanes. The H atoms become more positive with F substitution, and this must adversely affect the interaction with the rather polar PF(b) molecule; that is, an additional electronic effect must be considered for kQc.
+
+
As already discussed by Schmidt," the model consistently underestimates the NF(b) rate constants for molecules with C-H bonds. However, the PF(b) rate constants are generally well reproduced for molecules with CH bonds, except for the aforementioned halogen substituent effects. This difference is related to the energy defects. Two quanta of C-H excitation give a good energy match for PF(b), but a -1400 cm-' energy defect for NF(b). The poor energy match gives a small rate constant, and excitation of bending and stretching combination modes may become important; but, the model does not include such pathways. Furthermore, our calculation shows that contributions from the m = 1 and n = 2 transition are comparable to those from the m = 0 and n = 2 transition for NF(b) quenching by C-H bonds. The NF(b) case with C-H bonds seems to be another example for which the theory underestimates rate constants that have large energy defects. In summary, the E-V transfer model needs to be improved in several aspects. For cases with small energy defects, more accurate energies of the vibrational levels are required and more realistic Franck-Condon factors for the vibrational transitions that are not adequately represented by LM are also needed. The theory seems least adequate for cases with large energy defects or excitation to levels above v = 2, and a formalism to incorporate excitations of bending and stretching combination modes needs to be developed. State-resolved experimental data are needed to identify the favored product states for the offresonance cases where vibrational excitation of the NF(a) and PF(a) or of combination bands is possible.32 The simple theory probably will not adequately reproduce the temperature coefficients of many of the E-V processes.sb,lh Finally, electronic and steric factors probably need to be explicitly incorporated into the model to account for deviations from "pure" E-V energy transfer, as shown by the multiple fluorine substituent effect and the failure to explain the rate constants for the H20/ D20 and NH3/ND3 pairs. 5. Conclusions
The energy of the PF(blC+) state is similar to that of 0 2 (b'C+), and the excitation transfer rate between PF(b'Z+) and 02(X3Z-) to give Oz(blZ+) is fast at 300 K. However, the reaction rates of PF(blZ+) with other molecules were rather slow, and the mechanism seems to be E-V transfer with formation of PF(a'A). The magnitudes and the dependence of the rate constants of PF(blZ+) on energy defects for E-V energy transfer to various molecules resemble the situation for quenching of NF(b'Z+). Treatment of E-V transfer by a model that considers only excitation of a local mode in terminal bonds without a crossing of potential curves explains overall trends of the rate constants for both PF(blZ+) and NF(blZ+); however, large discrepancies exist for several individual cases, which indicates that improvement of the model is needed for quantitative interpretations. The fact that quenching of both PF(blCf) and NF(blZ+) can be modeled without specific consideration of the electronic states is rather remarkable. The radiative lifetime for PF(blX+) is 9.7 & 1.2 ms. The chemically unreactive nature of PF(blZ+) at 300 K offers some promise for the PF molecule as an energy storage system; other molecules that are isoelectronic to PF(b'Z+) may also have this chemical property. In actual applications, the reactivities of the PF(alA and X3Z-) states may be important variables for scaling to high concentration, and these aspects of the PF system remain to be studied. The reaction rate of PF(b'Z+) with Cl2 and Br2 (and probably other halogen molecules) is fast and proceeds by a chemical mechanism. These results will be published separately."
9734 J. Phys. Chem., Vol. 98, No. 39, I994
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