Chemical Physics 143 (1990) 281-296
North-Holland
VIBRATIONAL RELAXATION OF FO(o= 1) RADICALS STUDIED BY
FAST-MAGNETIC-FIELD-JUMP
TIME-BESOLVED LMR EXPERIMENT AND THEORY
A.I. CHICHININ and L.N. KRASNOPEROV
Institute of Chemical Kinetics and Combustion, Novosibirsk State University, Novosibirsk 630090, USSR
Received 30 March 1989; in final form 15 January I990
The method of fast magnetic field jump combined with the time-resolved LMR technique has been employed to measure the
rate constants of vibrational mlaxation of FO( u= 1) at T= 320 K by SiF,, CHsF, Os, NF,, PHs, SF,, CF,, NO and NO*: 6.4 x 1O- “,
1.4x lo-“, 1.4x 10-t’, 7.2x 10-t*, 1.5x lo-r’, 1.2x 10-r’, 2.0x 10-r’, 4.4x 10-r’, 9.3x lo-r2cm3/s, respectively. These rate
constants have been compared with those calculated in terms of the Sharma and Brau theory. All the earlier reported results of
calculations by this theory have been tabulated. The intensities of FO LMR spectral lines have been calculated. The technique
based on measurin8 LMR signal saturation value has been applied to estimating the dipole moment of vibrational transition of
FO. The value obtained, 0.084f0.012 D is 19%lower than that calculated quantum-chemically by La&off, Bauschlicher, and
Partridge.
1. Introduction
The present paper is concerned with the study of
vibrational relaxation of FO radicals by the fast-magnetic-field-jump technique in combination with detection of the radicals by time-resolved laser magnetic resonance (LMR). This method has been
applied to investigation of vibrational relaxation
of ND2( 0, 1, 0) [ 1 ] and spin-orbit relaxation of
Cl ( ‘PI ,*) atoms [ 21. The method consists in detection of LMR signal saturation kinetics under fast adjustment to the LMR spectral line by a magnetic field
jump. This method has a number of advantages. It
offers no difficulties in the preparation of vibrationally exited radicals. Besides, it is highly sensitive (e.g.,
[OH]>lo8, [HOz]>109cm-3
[3], [CHz]>3x108
cm-3 [4] in steady-state detection) and relatively
universal (more than 60 radicals and atoms have been
detected by LMR, see reviews [ 3,5,6] ). Another, the
most widely used, method for studying the vibrational relaxation of radicals in the electronic ground
state is laser-induced fluorescence (OH [ 7-9 1, OD
[8], CF2 [lo], NH2 [ll-131, NC0 [14]). The
methods of IR chemiluminescence ( CH3 [ 15 ] ), intracavity laser spectroscopy (NH2 [ 16-181, HCO
[16-19]),EPR
(OH [20-223) andlaserresonance
0301-0104/90/$03.50
(North-Holland)
0 Elsevier Science Publishers B.V.
absorption (HCO, DC0 [ 231) have also been
employed.
In this work, we deal mainly with V-V processes of
relaxation of FO radicals by stable molecules. For
such processes the influence of open-shell nature of
the radicals on V-V energy transfer probability has
been little studied. For stable molecules these processes are described semiquantitatively in terms of the
Sharma and Brau (SB ) theory [ 24 ] which supposes
vibrational energy exchange to occur due to longrange multipole interaction. This theory is applicable
to near-resonant processes involving molecules with
large moments of vibrational transitions. Some of the
collision partners used in this work satisfy these requirements. Pronounced discrepancies between the
theory and experiment might point to the influence
of the open-shell nature of the radical on V-V process rate.
Vibrational relaxation of free radicals by the molecules involving unpaired electrons can proceed via
collisional complex formation and, hence, present
some special interest. Few data have been reported
on such processes. Therefore, in this work, we have
measured the rate constants of FO ( u= 1) relaxation
by NO and NO*.
The other aim of the present work was the follow-
282
A.I. Chichinin. L.N. Krasnoperov / Vibrational relaxation ofF0
ing. The method of fast magnetic field jump not only
yields information on relaxation rates, but also allows us to measure absorption cross sections of rovibrational transitions in the radicals under study. Dipole moment function for FO has been calculated
quantum-chemically by Langhoff et al. [ 25 1. It is in
good agreement with the experimentally determined
dipole moment of the radical in its ground and first
vibrationally exited states [ 26 1. This allows the authors [ 251 to consider that the vibrational transition
dipole moment ,ulo also has been calculated quite accurately. A comparison of the calculated [25] ,ulo
values and those we obtained experimentally would
make it possible to estimate the accuracy of our
method for measuring absorption cross sections.
2. The LMR spectra of FO radicals
The LMR spectra of FO radicals in 2IIs,2 electronic ground state in El B polarization in the range
1025 to 1043 cm- ’ have been detected by McKellar
[ 27 1. In that work the positions of spectral lines have
been determined, their assignment has been performed, and radical parameters have been calculated. In later studies [28-301 the rovibrational
spectra of FO radicals have been analyzed in detail,
the radical parameters have been determined more
precisely. It has been found out [ 301 that the lower
electron-exited state 2II1,2 is 193.8 cm-’ higher than
the ground state 2IIS,2.
In the present work, it was necessary to know the
values of absorption cross sections corresponding to
LMR spectral lines. The Hamiltonian we used coincides with that employed by McKellar [ 27 1. It involves the operators of spin-orbit interaction, rotational energy, first-order centrifugal distortion
correction and nuclear magnetic hyperfine interaction, characterized by the parameters A, B, D, and
h, respectively. The operator of the interaction of
electron orbital and spin momenta with external
magnetic field was also employed. We used the
expressions for matrix elements employed by Carrington et al. [ 3 11. The expressions for centrifugal
distortion correction were taken from the paper reported by Zare and co-workers [ 321, different signs
of matrix elements in these two papers being taken
into account. The Hamiltonian was constructed in the
radicals
(J, Z,F, Q, MF) basis set. To calculate the absorption
cross sections, transformation to the (J, I, Q, A& M,)
basis set was performed. The vibrational transition
dipole moment was calculated from radiative lifetime of the vibrationally excited radical (266 ms)
[ 25 1. In our calculations we used the radical parameters from the work of McKelIar [ 27 ] since application of more precise parameters reported elsewhere
[ 28-301 needs, in any case, recalculation of ho and
hi. Calculating the wavefunction of a state with rotational quantum number J, we took into account the
J- 1, J, J+ 1, J+2 states, that required numerical
diagonalization of a 16 x 16 matrix. Rovibrational
wavefunctions of FO radical coincide with those of a
symmetric top, where J projection on the top axis
equals s2 for a *II0 state. The rovibrational spectrum
of symmetric top is well known. Selection rules correspond to a parallel band, AQ= 0.
Cross sections a:” for the absorption maximum
of Doppler-broadened LMR spectrum lines were calculated by the standard formula (see, e.g., ref. [ 33 ] ):
G’= =8n3~:o(cos Y):&($)
XFvJm,/2rkT
h
06)
(1)
’
= (E?/~~T)FE,
X
exp [ -@J(
Fv= [ 1 -exp(
J+ 1)//CT] ,
FE”= [ 1 +exp(A,/kT)]-’
Plo=I(~v,Irl%o)I
,
-hvIo/kT)]*
,
>
Here the subscripts V= 0 and V= 1 denote the ground
and vibrationally exited states of the radical. &,= (J,
I, 0, M,, M,), is the set of quantum numbers characterizing a magnetic rotational sublevel; !&, and !&,
are the rotational and vibrational wavefimctions; y is
the angle between the electric field vector of absorbed radiation and molecular axis: c is the dipole
moment operator; fo( $) is the probability to find
v= 0) radical in the state with 6, quantum
Fo(*n3,2,
numbers; via= 1033.4812, Ao= - 177.3, Bf=
1.046565 cm-i [ 271 are the vibrational frequency,
spin-orbit interaction constant and effective rotational constant, respectively; ,uio= 0.104 D [ 25 ] ; m,
A.I. Chichinin, L.N. kkwwperov / Vibrational relaxation of FO radicals
is the radical mass; T is the temperature; k, h are the
Boltzmann and Planck constants. The difference in
populations of vibrational states as well as vibra-
283
tional partition function are involved in Fv factor,
‘l-l1,* state effect on 211s,2state population being involved in FEWThe factor 2 in the denominator of eq.
Table 1
Resonances, cross sections, and linewidths in the fundamental band of FO. The calculated LMR spectra of FO radicals at T= 300 K are
presented. The lineshapes are described by the Gaussian function o,(E) =uy
exp[ - (B-&J2/AB2].
The symbols of this formula are
used in the table. The lines whose positions have been measured in the present work are marked with asterisks. Experimentally measured
values for B0 are listed. If there is no measured value, a calculated value of B0 is given, the figure in the co1unm “ohs -talc” beii absent.
TheselectionrulesAMp=O,AMF=+l
correspondto~landEIBpolarizations,rltspectiveWMF=M,+M,)
.L.inesforwhichB0<14.6
kG are listed
& W)
M;tM,
cu.“” (cm*)
Mi+M,
AB (G)
obs-talc
(MHz)
36 ‘) R( 10) 1025.778270 b,
P(3.5) =)
9.733
-2.5
-1.5
9.868
-2.5
-1.5
10.083
-2.5
-1.5
13.344
-1.5
-0.5
13.403
-1.5
-0.5
13.626
-1.5
-0.5
0.5
0.5
-0.5
0.5
0.5
-0.5
-0.5
0.5
-0.5
-0.5
0.5
-0.5
4.67( -23) d,
1.26(-18)
1.26(-18)
7.81(-23)
8.54( - 19)
1.13(-18)
43.8
43.7
43.7
59.1
58.9
59.0
36R(14)
P(2.5)
6.032
6.272
6.307
12.224
12.346
12.453
0.5
0.5
0.5
-0.5
0.5
-0.5
0.5
-0.5
-0.5
0.5
0.5
-0.5
0.5
-0.5
0.5
0.5
-0.5
-0.5
7.65(-19)
7.67( - 19)
2.62( -22)
3.56(-19)
1.84( -22)
3.56(-19)
28.4
28.4
28.5
65.3
65.2
64.4
1.5
1.5
0.5
0.5
0.5
0.5
-0.5
0.5
0.5
-0.5
0.5
-0.5
0.5
-0.5
-0.5
1.08(-18)
1.08(-18)
1.32(-18)
4.68( -22)
1.32(-18)
32.5
32.5
35.0
34.9
35.0
-11
-1.5
-0.5
-1.5
0.5
-0.5
-0.5
-1.5
-1.5
-0.5
0.5
0.5
-0.5
-0.5
-0.5
0.5
-0.5
0.5
0.5
-0.5
-0.5
-0.5
-0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
-0.5
-0.5
-0.5
0.5
2.25( -20)
7.98( -20)
P.OO(-20)
1.08(-18)
1.27(-19)
1.63(-18)
1.26( - 18)
1.22( - 18)
l.65(-18)
1.28( - 18)
1.06(-19)
21.0
23.8
39.1
40.1
41.1
33.6
33.4
35.5
35.2
34.5
38.9
+4
+9
+7*
+8
+8*
+8
+10
+12
+12
+11
+13*
38 R(8)
Q(l.5)
13.832
14.080
14.347
14.419
14.582
26 P(34)
Q(1.5)
0.269
0.354
0.525
0.668
0.723
0.751
0.772
0.963
0.972
0.990
0.995
+13
+6
+4
+I
1028.511931
1.5
1.5
1.5
0.5
-0.5
0.5
0
+5
-3
+3
1032.910232
0.5
0.5
-0.5
-0.5
-0.5
-1
-5
-8
1033.487999
0.5
1.5
-0.5
1.5
0.5
0.5
-0.5
-0.5
0.5
1.5
1.5
(continued on next page)
284
A.I. Chichinin, L.N. Krasnoperov / Vibrational relaxation o$FO radicals
Table 1 (continued)
Bo (kG)
M&M,
lu;clu,
a,”
(cd)
D(G)
ohs-CaJc
(MHz)
~(2.5)
5.377
5.672
5.753
5.833
5.930
5.989
5.998
6.047
6.069
6.167
6.200
6.288
6.363
6.439
6.785
-2.5
-1.5
-2.5
-1.5
-0.5
-2.5
-0.5
0.5
-1.5
-0.5
1.5
0.5
0.5
1.5
1.5
-0.5
-0.5
0.5
0.5
0.5
-0.5
-0.5
0.5
-0.5
-0.5
0.5
-0.5
-0.5
-0.5
-0.5
0.5
0.5
0.5
0.5
0.5
-0.5
0.5
0.5
-0.5
-0.5
0.5
-0.5
0.5
-0.5
0.5
5.42( -22)
8.90( -22)
3.90( - 19)
6.01(-19)
6.59(-19)
3.89(-19)
1.02( -21)
5.76(-19)
6.00(-19)
6.59(-19)
3.98(-19)
5.77( - 19)
8.92( -22)
3.99(-19)
5.50( -22)
74.5
76.5
74.0
75.9
78.4
74.3
78.9
81.6
76.0
78.3
86.2
81.4
82.1
85.9
86.7
-0.5
1.5
0.5
-0.5
0.5
1.5
0.5
1.5
-0.5
-1.5
0.5
-0.5
-1.5
-0.5
0.5
-0.5
0.5
-1.5
-0.5
0.5
0.5
0.5
-0.5
-0.5
-0.5
-0.5
-0.5
0.5
0.5
0.5
0.5
0.5
-0.5
-0.5
0.5
-0.5
2.94(-21)
1.36(-18)
1.76(-18)
1.29(-18)
4.41(-21)
1.37( - 18)
1.76( - 18)
3.76( -21)
1.29(-18)
35.3
33.8
34.5
35.2
34.6
33.7
34.5
33.7
35.3
38 R( 18) 1039.074229
R( 1.5)
8.871
-0.5
8.918
-0.5
9.157
-0.5
14.336
0.5
14.399
0.5
14.575
0.5
- 1.5
-1.5
-1.5
-0.5
-0.5
-0.5
-0.5
0.5
-0.5
0.5
-0.5
-0.5
0.5
0.5
-0.5
0.5
0.5
-0.5
4.99( -23)
1.14(-19)
1.14(-19)
3.38( - 19)
6.78( -23)
3.38( - 19)
25.2
25.2
25.2
36.7
36.3
36.7
3.5
3.5
3.5
2.5
2.5
2.5
1.5
1.5
1.5
0.5
0.5
0.5
-0.5
0.5
0.5
-0.5
0.5
0.5
-0.5
0.5
0.5
-0.5
0.5
-0.5
-0.5
0.5
-0.5
-0.5
0.5
-0.5
-0.5
0.5
-0.5
5.42( -20)
5.56( -20)
1.86( -23)
1.64(-19)
1.66(-19)
6.93( -23)
3.28( - 19)
3.30( - 19)
1.33(-21)
5.47(-19)
5.48(-19)
78.2
77.8
78.5
94.5
94.4
95.3
119.8
119.8
120.9
163.7
163.8
36 R(22)
Q(l.5)
4.435
4.479
4.539
4.591
4.620
4.726
4,778
4.811
4.829
38 R(24)
R(3.5)
4.295
4.578
4.735
5.287
5.544
5.646
6.825
7.057
7.081
9.542
9.764
-1.5
-0.5
-1.5
-0.5
0.5
-1.5
0.5
1.5
-0.5
0.5
2.5
1.5
1.5
2.5
2.5
-8
-8
-7
-7
-5
-6
-7
-5
-7
-7
1033.630806
+6
0
+1
+4
+4
-5
+2
+11
+15
1042.517640
2.5
2.5
2.5
1.5
1.5
1.5
0.5
0.5
0.5
-0.5
-0.5
0
+4
+2
+2
+3
0
+1
0
A.I. Chichinin,L.N. Krasnoperov/ VibrationalrekzxationofF0 radical
( la) takes into account the complete splitting of
magnetic sublevels over nuclear spin projections
(I= l/2).
Table 1 contains the LMR spectra of FO radicals
in both polarizations. The table shows that (i) the
largest absorption cross section belongs to the line
near 1 kG, consisting of the three transitions:
(M;tM,),forall
-0.S
- l&0.5+ -0.5,1.5+0.5
of them Q( 1.5), A+ -0.5, 9P(34) 12C’602 laser
line. The absorption cross section of this line in LMR
signal maximum (0.947 kG) is t7,=2.28~ lo-l8 cm2.
(ii) The lines in El B polarization are orders of magnitude stronger than the lines in El,Fl polarization.
This is attributed to the fact that all transitions in the
parallel polarization occur despite the approximate
selection rule A&=0. This rule is approximate because A4,is not rigorous quantum number, MF being
rigorous.
There are insignificant discrepancies between our
calculation of the line positions and that reported by
McKellar [27]. The largest discrepancy is 3 mHz.
This may be determined by two factors: ( 1) the C02laser frequencies we used (see ref. [ 34 ] ) were more
precise than those employed by McKellar (see ref.
[ 35 ] ), (2) McKellar’s radical parameters were
rounded off. In fact, the discrepancies could be readily accounted for solely by the second factor.
Fig. 1 shows the LMR spectra of FO radicals de-
tected on our spectrometer. Note that the spectra in
polarization have been obtained in this work for
the first time since McKellar [ 27 ] used only El B
polarization. The positions of the three lines in parallel polarization depicted in fig. 1 were measured by
an NMR Gaussmeter. The error of the magnetic field
measurements, caused by magnetic field inhomogeneity, was less than 3 G. The line positions measured
are in good agreement with calculated ones (see table
1).
EllB
3. Theoretical foundations of the fast-magnetic-fieldjump technique
In this section we shall consider the theoretical
foundations of the magnetic-field-jump technique.
Some results of such consideration have been presented [ 11. Detailed description of the theory of the
method is rather cumbersome whilst its essence is very
simple. Therefore, in the present paper, we shall restrict ourselves to a simplified analysis of the method
and give the results of a more detailed consideration.
The initial equations are as follows:
n,+n,
0.2
0.4
MAGNETIC
0.6
a8
FIELD
M
12
(kGs)
Fis. 1. LA4Rspectraof FO radicalsat the 9P(34) line of the
12C1%2 her
(1033.48800
cm-‘).
The magnetic fieldjumpis
shownwithanarrow.P,=O.5 Ton; doubledmodulation
amplitude= 6.6G.
285
=N,
ncJ(0)=N,
n,(O)=O.
(2)
Here h(t), nl (t) are the concentrations of the radicals under study in the ground and vibrationally excited states; 1 1is the pseudcArst*rder relaxation rate
constant of the exited state; Wis the photon flux density;& andyi are the equilibrium fractions of the radicals in the magnetic sublevels involved in a transition, calculated by formula ( la) wherein, in the case
off,, Jo and Br must be submitted with J, and B$;
o is the cross section of a radiation-induced transition between these sublevels, assuming the population of the initial sublevel to be unity. We neglect the
upper level population at the instant of magnetic field
jump ( t = 0), collisional excitation, diffusion and
chemical decay of radicals. We assume also rotational relaxation to be very fast, that makes it possible to employ the two-level model. The constant d 1is
related to concentrations of relaxators Ri as follows:
A.I. Chichinin.L.N. Krasnoperov/ Vibrationalrelaxationof FO radicals
286
where ku, is the rate constant of the relaxation of radical by Ri molecules.
The quantity under observation is the spectrometer signal proportional to the expression
(4)
a(t)=a(nofo-n1fi).
Substituting the solution of eqs. (2) into (4) we
obtain:
+c=(l-S)+Sexp(-f/r&),
(5)
r& =2wa,+L,
(6)
00
S,=Sexp[S/2(1-S)]=
,
s=2wa,r,ff,
(7)
&=cti+fi)/2.
(8)
For the FO radical the difference between fo and fi
values, as well as the difference of the factor Fv in
formula ( 1) from unity, may be neglected. This allows us to consider the saturation cross section to be
equal to the absorption cross section: a,= a,.
Expressions ( 6 ) and ( 7 ) are the working formulae
of our technique. Eq. (6) allows one to determine the
relaxation rate constant kR from the slope of the reciprocal of saturation kinetics time, 72, plotted as a
function of the relaxator concentration [ Ri ] ; eq. ( 7 )
allows determining the product Wo,. Knowing W, one
can obtain 0,.
A more detailed consideration introduces the following corrections.
( 1)’ The experimentally obtained radial distribution of light intensity has the form:
W(r)=
coefficient of radicals in buffer gas, should be added
to the right-hand side of eq. (3). This statement is
rigorously valid if kD < I,.
(3) The cross section 0 was assumed above to be
independent of I I. However, this is not the case since
in our experiments we performed a magnetic field
jump to a maximum of the saturated line of LMR
spectrum. The smaller A,, i.e. the higher the line saturation, the larger the peak-to-peak width of the saturated line and the smaller 0. With due account of
the abovementioned effects and the radial distribution of light intensity (9), expression (7) should be
written as follows:
W,exp( -r’/rf)
,
(9)
where r is the distance from the laser beam axis, r. is
the laser beam radius, W. is the photon flux density
on the beam axis. Solving the problem with such a
distribution leads to the substitution of the factor 2 W
by 4Wo/3 in eq. (6) and by W. in eq. (7). In this
case the saturation kinetics is nonexponential, the exponent being constructed either from the initial slope
of the kinetics, or by using the root-mean-squares
procedure.
(2) With slow radical diffusion taken into account, the term k,, =2D/r& where D is the diffusion
Woasreff.
(10)
The error in eq. ( 10) is less than 3% for ScO.3.
(4) Taking rotational relaxation rate as a finite one,
one should substitute Qfor 0,:
&s=~/(l+Wo~,)
3
(11)
where rR is the pOpdatiOn rehxatiOn the of the rotational Zeeman sublevel introduced by the “fourlevel model” [ 36,371.
(5 ) If chemical reaction between a radical and a
relaxator is possible, eq. ( 6 ) allows one to determine
the sum of the reaction and relaxation rate constants.
This implies that the reaction rate is independent of
the vibrational state of the radical.
Although this section considered the vibrational
relaxation of radicals, all the conclusions of this consideration are applicable, for example, to the electronic relaxation of atoms as well [ 2 1.
4. Experimental
The experimental apparatus realizing magnetic
field jump in combination with LMR detection has
been described in ref. [ 1,2 1. A gaseous mixture containing FO radicals was pumped through a cell ( 14.5
mm inside diameter) located between the poles of an
electromagnet in the cavity of a CO1 laser. Modulation coils and special coils to provide the magnetic
field jump [ 1 ] also were between the electromagnet
poles. The zone of detection was 12 cm long. C02laser radiation went to a Ge-Hg (53 K) photoresistor. The photoresistor signal was digitized with a
transient recorder (256 channels, 6 bits, up to 50 ns/
287
A.I. Chichinin, L.N. Krasnoperov / Vibrational relaxation ofF0 radicals
channel) and then sent to the computer memory.
LMR signal saturation kinetics curves were observed
after a fast adjustment to the absorption line of FO
radicals by a fast magnetic field jump (80 G, 10 us
duration, 100 Hz repetition frequency). The jump
was performed to the line marked with an arrow in
fig. 1.
For quantitative determination of the absorption
cross section we have measured the intracavity light
flux density on the CO,-laser beam axis. It was 79 + 13
W/cm* (in both directions). This value was determined from the zero-order diffraction grating reflection coefficient ( 13.5 + 1.O%at the 9P( 34) line of our
CO2 laser), the outlet power radiation (1.5 kO.2 W)
and radius r. of the laser beam (3.0 f 0.1 mm). The
zero-field diffraction grating reflection coefficient was
measured in two ways: (i) using the procedure described elsewhere [ 11, where the power inside the
laser cavity was determined with the help of a special
NaCl plate inserted into the cavity and (ii) by direct
measurement of the powers of the incident and reflected beams. In the latter case, the grating was removed from the cavity and located so that an incident beam of another CO* laser coincided with its
reflection from the grating. The radius r. was determined as follows: a NaCl plate was inserted into the
laser cavity, the profile of the beam reflected from
the plate was measured with a narrow slit shielded
powermeter and then approximated using eq. ( 9 ) .
FO radicals were generated via the reaction:
F+03+F0+02,
(12)
k l2=1.3x lo-” cm’/s [38]. Fluorine atoms were
produced by a discharge in the CF,/Ar mixture. The
gaseous mixture passed the distance from the point
of mixing the reactants of reaction ( 12 ) to the detection zone in 2 ms. [O,] =4X 1013, [CR] =2x 10”
cm-3 at the point of mixing, therefore reaction ( 12)
proceeded incompletely (65%). The relaxator was
added to the mixture immediately at the detection
zone entry. The mixture passed the detection zone in
At=5.4 ms, PAr= 1.2 Torr. The cell was overheated
by the coils for magnetic field jump, therefore all the
measurements were performed at T= 320 f 10 K.
Argon was 99.99% pure. The other gases were not
less than 97% pure, which was tested with a massspectrometer. Ozone was generated by an ac discharge in oxygen at 77 K and then condensed. After
switching off the discharge, the oxygen was removed.
For measurements involving NO2 we used (N02+
N,O,)/Ar
mixtures wherein the percentage of
NO2 + N20., was varied from 6 to 100%. Consumption of these mixtures was determined by pressure
drop in the bulb. NO2 concentration in the detection
zone was calculated from the available equilibrium
constant P&,/P,,,
= 0.168 atm at T=298 K [39].
5. Experimental resalts
(a) The vibrational relaxation of FO by R
(R= SiF,, 03, PH3, CH3F, NF3, SF,, CF,, N02) is
much faster than FO reaction with these molecules.
This is confirmed by independence of unsaturated
LMR signal value from R concentration. In this situation, the abovementioned analysis of the measuring technique for vibrational relaxation rate constants kR is applicable:
FO(ZJ=~)+R~FO(U=O)+R.
(13)
Fig. 2 shows FO radical LMR signal saturation kinetics at different pressures of relaxator (NF, in this
case). One can note the high saturation ( x 50%) as
well as the decrease in saturation magnitude and in
saturation kinetics time with increasing relaxator
concentration. According to the abovementioned
theory (eq. ( 6 ) ) the reciprocal of saturation kinetics
time, r&J, depends linearly on relaxator concentration. r$ plotted as a function of [R] and of [NO]
is shown in figs. 3-5. The constants kR summarized
t /ms
Fig. 2. LMR signal saturation kinetics at various concentrations
of NFS.
A.I. Chichinin,L.N. Krasnoperov/ VibrationalrelaxationofF0 radicals
288
0
15
10
5-
Fig.3.The reciprocalof saturationkineticstime versusconcentration of daxator R. (0)
R=NFI, (0)
R=SP,, (A)
R=CH3F.
o0
I
5
10
15
F~4.Thereciprocalofsaturationkineticstimeversus [RI. (0)
R=NOZ, (0) R=PH3, (A) R=Ol.
in table 2 have been obtained from the slope of these
lines. It is noteworthy that the reactions F+CH,F,
PH3+HF+ CH2F, PH2 are inessential since the concentration of fluorine atoms is t%voorders of magnitude less than that of CHJF or PH3 and the rate constants kcHsF, ki, are only an order of magnitude less
2
Fig. 5.Thercciprocdof.saturationkincticstimeverws[RI. (0)
R&F,,
(0) R=SiF,, (A) R=NO.
than
I
OO
1
the highest possible ones calculated from gaskinetic cross sections.
Our technique does not allow one to distinguish
between V-V and V-R, T processes. The rate constants given in table 2 are, however, too high (except
for CF4) to be attributed to V-R, T processes. Besides, the vibrational frequencies of most of the relaxators, except for CF.+ NO and NOz, are close
( IA& 1-c90 cm- l) to the vibrational frequency of
FO, which favors the vibrational energy transfer.
Therefore, we suppose V-V processes to be dominant in all the cases except, probably, for CF,.
Near-resonant V-V processes are described by the
SB theory [ 241. Below we shaIl discuss the theory ap
plication to our case and compare the results obtained with our experimental data.
NO and NO* molecules involve unpaired electrons. Hence, the collisions of these molecules with
FO radicals are most likely to lead to the complex
formation. In this case the SB theory is inapplicable.
Our rate constant kNo and kNch are typical of radical-radical vibrational relaxation processes. For instance, the rate constants of the vibrational relaxation of OH, OD, HCO, DCO, NH2, NC0 radicals by
NO at room temperature are within the range (2.6-
A.I. Chichinin, L.N. Krasnoperov/ VibrationalrelaxationofF0 radicals
289
Table 2
Rate constants of vibrational relaxation of FO( v= 1) radicals by R mokcoles
R
kx (cm’/s), experiment
ka (cm3/s), calcolations by SB theory
SiF,
CH3F
(6.4+1.8)(-ll)*’
(1.4kO.4)(-11)
(1.4f0.4)(-11)
(7.2f2.4)(-12)
2.9(-11)
6.5(-12)
7.7(-12)
2.0(-12)
near-resonant exchange,
SB theory is applicable
(1.5*0.4)(-11)
(1.2&0.5)(-11)
(2.0+0.4)(-13)
l.l(-12)
J3.6(-13)
1.2( -15)
nonresonant case
(4.4f0.8)(-11)
b,
(9.3f2.8)( - 12)
3.6( - 19)
1.4( - 16)
rehxator involves an unpaired electron
03
NF3
PH3
SF,
CF,
NO
NOz
‘) a(-b)=axlO-*.
b, The sum of the rate constants of relaxation and reaction ( 14) is given.
3.8)x10-“cm’/s
[8,23,11,14]andourkNoisclose
to this interval.
(b ) The relaxation of FO ( y= 1) by NO molecules
requires a special consideration. In this case, the
reaction
FO+NO+F+N02
(14)
is possible. As far as we know, the rate constant ki4
has not been measured experimentally. It is assumed
to be 2 x lo-” cm3/s [ 401, i.e. the average value of
the
rate
constants
of
the
reactions
ClO+NO-rCl+NO,
(1.8~ 10-i’ cm’/s)
and
BrO+NO+Br+N02
(2.1 x lo-“cm3/s).
Reaction
( 14) causes a decrease in LMR signal with increasing
Fii6.ThedependenceofunsatoratedLMRsignalon
ms.
NO concentration, that was observed experimentally
and is illustrated in fg 6. The [NO] dependence of
the LMR signal magnitude is diffkult to analyze because processes ( 12) and ( 14) form a chain reaction
mechanism. The recombination processes should also
be taken into account:
FO+F0+2F+02,
FOz +F, F2 +O, ,
(15)
k15=3.3~10-1’cm3/s
[41] and&=(8.5+2.8)~
lo-l2 cm3/s [38]. Baulch et al. [40] recommend to
take an average.
Consequently, we can only estimate ki4. If reaction
( 14) is considered as the only process affecting the
concentration of FO radicals, the plot in tig. 6 must
[NO].Thecowecorrespondstoeq.
(16),wh~k~~=l.2~10-~~cm~/s,~=5.4
Ai. Chichinia L.N. Krasnqerov / Vibrational reiaxaiion of FU radicals
290
OV
0
8
SO
I
100
I
1
150
Fig. 7. SaturationfactorS, correctedaccordinsto eq. ( IO) vfmus
saturationkineticstime.
fit the ~uation:
[FO] = 1 -exp( -y),
y=kt4 [NO]At .
(16)
Agreement between this expression and the curve
in fig. 6 is achieved at k,.,= 10-r’ cm3/s. It may be
shown that taking into account reactions ( 12) and
( 15) leads to k,, increase. Our study of the FOf u=
1) + NO process has shown that the rate constant
presented in table 2 is the sum of the rate constants
of relaxation ( 13) and reaction ( 14): kNO-tk14=
4.4x 10-l’ cm3/s. We have estimated that
k,,= lo-” cm3fs
(c) Fig. 7 shows the saturation factor 5’plotted as
a function of time rctr according to formula ( 10).
From the slope of this line we obtain lVoa~P = 5.2 4
0.9 ms --I. Knowing the value of W, (measured, see
above), we determine cr:w = (1.36kO.32) x lO_”
cm2. As already mentioned, for our spectral lines
c&c
0% ~c~z2.28~ lo-‘* cm2. Comparing this cross
section value with the experimental one, one should
take into account the cell overheating by 20 K, which
decreases a? by 9%. Hence,
o~Q/a~=0.65+0.15
(17)
and, consequently, @zp/pF ~0.81 If:0.12. Thevalue
of & has been determined from the radiative life-
time of the vibrationally excited FO [ 25 1. Langhoff
et al. [ 25 ] consider that the accuracy of their calculations is within a few per cent. We attribute the discrepancy ( 17) to the saturation of the Zeeman-rotation~-vibmtion~
transition (“bottleneck” effect
[ 36 ] ) in our experiments. Formula ( 11) involves this
effect. Let us assume that the relaxation between the
sublevels within the vibrational FO state occurs in
each gas-kinetic collision of FO with Ar atoms. Hence,
under our conditions rK= 0.13 ps and by formulae
(la),(S),
(ll~~~pap~~to~76%~~erth~
the abovementioned value, that improves noticeably
the agreement between a:xP and a?.
It should be noted that the time rn is determined
by processes of three types:
( 1) Relaxation between Zeeman-rotational sublevels. The cross sections of such processes are typically somewhat larger than gas-kinetic cross sections.
Relaxation of this type determines primarily the CR
value.
(2) Relaxation between 211Q(G?= l/2,3/2) states.
The cross sections of these processes are sufXciently
large. For example, the cross section of the process:
NO(Q=1/2,
N=l)+Ar+NO(Q=3/2)+Ar
(for
NO hE( 211,,2-2113,2)= 120 cm-‘) is w 15 A2 [42],
iVbeing the rotational quantum number.
(3) The relaxation to equal populations of the
states with M I= - l/2 and M1= + l/2 (M; relaxation ) . In our case, noneq~ib~um populations of M1
states appear due to stimulated radiative transitions
between the states in whose wavefunctions the
M,= - l/2 projection is predominant. The radical
wavefunctions of our spectral line were determined
in calculating the absorption cross sections. Employing these wavefunctions we obtain the probabilities
for the radical to be found in the states with M,=
- l/2 and MI= l/2 equal to 94 and 6%, respectively.
It may be shown that this determines the fact that M,
relaxation proceeds about 16 times slower than the
relaxation of the terns-ro~tion~
state populations (see point ( 1) ). Tbe M~relaxation time is equal
to m 16ra, which is much less than the typical times
T=~. Therefore, in our case, the MI relaxation has no
effect on the saturation factor S.
Thus, the assumed ru value is plausible and the
discrepancy ( 17) may be accounted for by the “bottleneck’” effect.
(d) From the intercept of the plots in figs. 3-5 one
A.I. Chichinin. L.N. Krasnoperov / Vibrational relaxation ofF0 radicals
can obtain the upper estimate for the rate constant of
FO relaxation by Ar. If the whole of the intercept is
determined by this process, kAr= 1.5~ lo-i3 cm3/s.
In fact the major part of the intercept is defined by
the fust term of formula (6 ), as well as by the diffusion contribution and relaxation by ozone. Therefore, the abovementioned kA, value is overestimated
at least by several times.
6. The Shama and Brau theory
The SB theory allows one to calculate the rate constants of the near-resonant V-V exchange:
Mt+M*+M,
+M;+L!Cv,
(18)
where AK, is the difference of vibrational energies of
M: and Mt. The main assumptions of the theory are
the following:
( 1) The probability of V-V exchange P is calculated in the first order of perturbation theory, multipole interaction of molecules being the operator of
the perturbation. As a rule, for each molecule only
the multipole moment of the lowest order is taken
into account.
(2) A relative motion of the molecules is considered as classical, determined by the trajectory R ( t ) .
(3) The probability of vibrational energy transfer
( 18 ) is averaged over relative velocity v and impact
parameter b. Averaging over the impact parameter is
realized as follows. A distance d is introduced which
is usually taken as equal to the parameter of the LennardJones potential for interaction between molecules M, and M2. In a reference system involving the
molecule M, at rest, at bad the M2 trajectory is assumed to be rectilinear and at b= 0 the molecule M2
is assumed to be reflected from the molecule M1 in
the direction opposite to the initial one. In both cases
the motion of molecule Mz is taken as uniform:
R(t)=d+vltj,
=dM,
b=O,
bad.
(19)
When 0 < bc d probability of the V-V process is determined by the simple interpolation:
P=P(b=0)+b2/d2[P(b=d)-P(b=O)] .
(20)
Another way of averaging over b was applied by Lev-
291
On and co-workers [ 43 1. For b< d they assumed
PEP(d).
(4) For b> d it is assumed that
P(v, b)=G(v)b-2’,
(21)
1~1, +12, li is the order of the multipole moment of
molecule Mi, for the dipole moment li= 1. This assumption is a purely mathematical approximation
whose applicability region has been analyzed by
Sharma and Brau. It is too rough and is not employed
in further modifications of the SB theory.
( 5 ) The cross section of process ( 18 ) is calculated
by summing over the rotational quantum numbers of
the initial and final states of both colliding molecules.
We believe that the most consistent and mathematically developed modification of the SB theory is
that described by Lozovskii et al. [ 18 1. In terms of
that modification the calculation of the V-V exchange rate constant kw does not require calculating
several special functions. The final formula of the
theory is very simple:
k,=
X
9(21)!d2-2’
27?(21,+1)!(212+1)!
J
8kT
A(W
+m2)
(22)
Xl(W~R(ei)l~,ilWV,(ei)>12.
(23)
Here v- and v/;R are the rovibrational wavefunctions of the initial and final states of the ith molecule,
pii is the multipole moment operator, m=
ml m2/
( ml + m2)
is the equivalent mass,pi( 6,) is the
probability of molecule Mi to be found in the state
with rotational quantum numbers 0,. In the most typical case li= 1, and expression (23) yields the cross
section in the maximum of a Doppler-broadened line
of the rovibrational transition, without taking into
account the difference in the populations of vibrational states. The function q/ is universal and can be
tabulated. The plot and integral expression for this
function have been reported by Lozovskii et al. [ 18 1.
292
A.1, Chichinin, L.N. Krasnoperov I Vibrational relaxation of FO radicals
7. Application of the SB theory
Table 3
Coeficients for expression (24 )
YO
YI
YZ
Y3
Y4
Y5
Y6
I=2
I=3
I=4
1615
1.445
6.988(
1.162(
5.428(
7.552(
60/l
0.9277
4.157( -2)
2.631(-4)
1.737( -6)
1.202( -8)
1612
1344/u
0.6454
2.805( -2)
3.234( -5)
8.211(-7)
3.420( -9)
25/2
912
-2)
-3)
-6)
-8)
a)
.) a(-b)=aXlO-‘.
We have obtained the fitting analytical approximation:
1+YsYsx’
6pI(x)= yo+yIx+y*x*+y3x3+y~x4+y5x5
*
(24)
The maximum error of this approximation is less than
5%, the coefftcients for this expression are listed in
table 3.
It should be noted that if the vibrationally exited
state of molecule M2 is degenerate, the cross section
(23) should be multiplied by the degeneracy factor
g. This is the only asymmetry of the SB formula about
the interchange of molecules M, and M2.
Eq. (22) is the final formula in the SB theory modification proposed by Lozovskii et al. [ 18 1. We have
changed a little the form of this expression. In particular, we prefer the rate constant kw to be expressed
explicitly via IR-absorption cross sections commonly
used in spectroscopy. For dipole-dipole interaction
( 1= 2 ) kw can be calculated as follows:
XV2
2~*md*(v, -v2)*
dv dv
1 2.
kT
>
Here sii(Vi) is the rovibrational spectrum of a molecule Mi in cross section units. Its value can be calculated by eq. (23 ) or obtained experimentally. The
formula (25) allows the calculations to be easily
checked since JF oi( v) dv - the integral IR band intensity - is the analytically calculated and experimentally measured value.
Table 4 summarizes data for calculating the rate
constants of processes ( 13) by the SB theory. The
right columns of tables 2 and 4 present the figures
calculated by formula (25). Table 5 contains all the
V-V processes calculated by the SB theory, available
in the literature. Theoretical and experimental cross
sections of these processes at room temperature are
given in the table and in fig. 8.
An analysis of the data of tables 2 and 5 leads to
the following conclusions:
(i) The SB theory underestimates by 2-3 times the
rate constants for near-resonant processes and we
think this result shows good agreement between theory and experiment. The rate constants for nonresonant processes, calculated in terms of this theory, are
too small.
It is interesting that the rough formula proposed by
Strekalov and Burstein [ 5 1 ] describes our rate constants for near-resonant processes better than the SB
theory. That formula [ 5 1 ] takes into account the effect of van der Waals forces on the relative motion of
molecules and the vibrational transition probabilities and differs by a factor 2-3 from the resonant SB
formula for the molecules without rotational
structure.
(ii) The discrepancies between the theory and experiment, as seen from fig. 8, are almost equal for
( radical* + molecule ) and (molecule* + molecule )
systems. An exception are the processes FO( v=
1) +PH3, SF,+, ND*(y) +ND3+, for which these
discrepancies are somewhat larger than for the processes with close AEv values. In principle, these discrepancies may be indicative of the effect of the collisional complex relaxation mechanism occurrence,
or may be attributed to the limitations of the SB
theory.
8. Conclusions
The absorption cross sections of the LMR spectral
lines of FO radicals have been calculated. The line
intensities in El B polarization are order of magnitude higher than the line intensities in El1B polarization. The most intensive line is observed at the
9P( 34) line of the ‘*C1602laser.
AI. Chichinin.L.N. Krarnoperov/ VibrationalrelaxationofF0 radicals
293
Table 4
Parameters for calculations by the SB theory (eq. (25 ) ) and results of these calculations
M
Rotational
Lennard-Jones
Vibrational
constaots
parameter&
(A) a’
frequency
(cm-‘)
[Ml
(em-‘)
[441
FO
b= 1.05
3.4 lY’
SiF,
b=0.137
4.88 [45]
1031 (F) =)
C&F
bz5.10
c=O.852
3.73 [46]
1050(A)
a=3.55
bE0.455
c=o.395
3.42 ‘)
1042(B)
1103(A)
b=0.359
4.14 [47]
1032(A)
906(E)
3.98 [45]
03
NF,
czO.196
b=4.45
PH,
c=O.196
A&
(cm-‘)
l(1dg
(D)
k,”
b,
(cm’/s)
0.104 [25]
2
0.479 [48]
2.9(-11)”
-17
0.203 [48]
6.5( -,12)
-9
-70
0.178 (491
0.0233
7.7(-12)
4.0( - 14)
1
127
0.107 [48]
0.420
2.0( - 12)
3.5(-14)
992(A)
1122(E)
41
-89
0.0862 [48]
0.0902
7.6(-13)
3.6(-13)
86
0.674 [48]
8.6(-13)
SF,
b=0.091
5.13 [45]
947(F)
CF,
b=0.190
4.66 [45]
1283(F)
-250
0.564 [48]
1.2(-15)
NO
b= 1.70
3.49 [45]
1883
-850
0.0573 [48]
3.6(-19)
NOz
a=8.00
3.42 b,
750(A)
1320(A)
1617(B)
283
-287
-584
0.0434 [ 501
0.0112
0.296
8(-17)
3(-18)
4(-17)
b=0.434
c=410
‘) d= (dM+dpo)/2.
b, fl10is the vibrational transition dipole moment, g is the vibrational state degeneracy.
c) Resultofcalculation.
d)dpoistakenequal (a&+d&/Z.
“)Vibrationalsymmetryisindicatedinparentheses.
‘)a(-b)=gxlO-*.
I) &s = &0z is assumed. b, dNo, wascalculatedfrom parahor and Y-factor, ref. [ 47 1.
Table 5
Experimental and SB calculated cross sections for V-V energy transfkr procewes at T=3OOK
v-v
process
A&
(cm-‘)
1. CO,(~)+SF,+CO,(Y,)+SF~
2. co2(q)+co’*o-eo*+co’~(v3)
3. c02(4)+‘3c02402+‘3c02(v3)
4. CO,(4)+N,O~cO,+N,O(vl)
5. C0~(~)+‘5N20-Co,+‘sNN20(~,)
6.C02(u~)+CO+C0~+CO(u=1)
7.co~(q)+‘~co~co~+‘~co(v=l)
8. COz(y)+N2-+COI+N2(~=1)
9. COl(y)+‘5N-tC02+‘5N2(~=1)
IO. C02(u3)+CH9
CO2(hd+CH3Ws)
T
C02(~1)+CbWti)
13
18
66
125
193
206
256
19
99
16
-87
G#
(AZ)
0%
(AZ)
Ref.
4.3
24
8.5
0.60
0.072
0.030
0.008
0.082
0.076
0.28
3.6
41
3.4
0.006
5(-6)”
1521
3(-5)
3(-7)
0.086
0.058
0.12
[=S31
[5231
[=S41
[52,241
[52,55,56]
1521
[52,24,55,57]
1521
[461
0.005
(continuedon next page)
A.I. Chichinin. L.N. Krasnoperov / Vibrational relaxation ofF0
294
radicals
Table 5 (continued)
A&
(cm-‘)
a=$?#
agr
(A*)
(A*)
11. CO*(u,)+CD,+CO*+CD,(v,)
12. CO*(u*)+CHD,+CO*+CHD,(v*)
13. CO*(v*)+CH*D*
CO*+CH*D*(u6)
90
86
115
0.84
0.66
0.46
T,
CO*+CH*D*(u*)
14. CO*(q)+CH,D+CO*+CH*D(y)
15. co*(u,)+co*(u*)-+co*+co*(v*+v*)
16. CO*(v*)+CH*Cl*-rCO*+CH*Cl*(v,+v7)
17.“‘CO*(y)+CHCl,
co*(rJ,)+CCl,(u*)
147
V-V process
-E
18.b’ CO*(q)+CHCl*
T,
co2(~1)+CC4(u*+u3)
-21
co2(2Y)+ccl.(~3+~4)
CO*CHCl* (2~4 )
-61
CO* (v, ) + CHCl* ( v,--tie )
l9.N*0(v,)+CO-+N*0+CO(v=l)
20. N*O(v,)+N*+N*O+N*(u=
1)
21.N*O(vI)+‘5N*~N*0+‘SN*(v=l)
22. N*0(uI)+N*0+N*0+N*0(Y+v3)
23. N*O(V~)+‘~N*O-+N*O+~~N*O(~,)
24. N*O(vr ) +‘5N’4NO+N*0+‘5N~4NO(
v,)
25. N*O(V,)+“N’~NO+NO*+‘~N’~NO(V,)
26. NH*(u*)+NH*+NH*+NH*(v.,)
27.NH*(q)+0*-+NH2+0*(~=1)
28. HCN(v*+v*)+HCN
HCN(v*)+HCN(q)
-c
HCN(y)+HCN(u*)
29. HCN(v*+v,)+CO*-+HCN(u*,)+CO*(v*)
30. HCN(v*+y)+OCS
HCN(y)+OCS(v,)
II
31.
32.
33.
34.
35.
36.
37.
38.
39.
HCN(v,)+OCS(u*)
HCN(~+v*)+C*H*+HCN(v*)+C*H*(ur)
ND*(y)+ND,+ND*+ND,(v~)
ND*(@)+CF,+ND*+CF,(u*,)
FO(v= l)+SiF,+FO+SiF,(y)
FO(u=l)+O,~FO+O,(v*)
FO(u=l)+CH,F+FO+CH,F(u*)
FO(u=l)+NF*+FO+NF,(v,)
FO(v=l)+SF,-*FO+SF,(v,)
FO(v=l)+PH*
FO+PH,(v*)
r:
FO+PH,(u,)
40. FO(Y=~)+CF,-+FO+CF,(V,)
4l.FO(v=
l)+NO*
FO+NO*(v*)
E
149
12
45
166
6.3( -4)
1.0
0.039
0.046
8.5
3.2
7.9
6.6
1.4
0.019
1.5
0.56
0.032
0.05 1
14
1.9
13
6.5
0.023
6.9( -3)
0.34
[601
5.6( -4)
[61,521
[571
[571
[591
1591
[591
[591
I181
[I81
1621
0.014
1.1
0.21
-173
0.21
2.1(-9)
1621
1621
9(-11)
2.6
3.3
2.9
13
2.5
2.3
1.4
2.5
2.5
-89
0.42
0.014”
0.25 ”
5.9
1.4
1.1
0.38
0.18
0.13
1621
111
[II
d)
d)
d)
d)
d)
d)
0.06
-250
283
0.04
2.4( -4)
1.4( -5)
FO+NO*(v,)
-287
1.6
5.2( -7)
FO+NO*(y)
-584
a( -b)=ax
10mb. ‘) These processes are not shown in fs. 8.
Cl Calculations were performed by formula (25) in this work, dipole transition
earlierdata
[1,18].
‘) This work.
[581
[591
1601
16’31
5.1(-4)
0.19
19
35
-82
-174
2
-9
-17
1
86
41
2.1(-3)
35
0.16
3.5(-4)
5.4( -4)
10
-26
166
[581
[581
[581
1.3(-3)
0.14
21
0.35
0.013
-4
80
-107
-28
14
69
22
46
-129
-58
19
0.30
0.14
8.7( -3)
Ref.
d)
d)
6.9( -6)
‘)
moments
for ND* and ND, were determined
from the
A.I. Chichinin, L.N. Krasnoperov/ VibrationalrelaxationofF0 radicals
1
r”
41
295
FO has been determined by the method of fast magnetic field jump. The value obtained is 19% less than
that calculated quantum-chemically,
that may be ascribed to the “bottleneck” effect. Eiimination of the
effect will, probably, improve the agreement between
theoretical calculations and experimental measurements.
Acknowledgement
The authors are grateful to E.N. Chesnokov and
V.P. Strunin for their valuable discussions and assistance in calculations by the SB theory, to V.P. Strunin
also for his help in analyzing reactant purity.
References
0
.__
wu
Fig. 8. Illustration to table 5. Triangles - the processes involving
participation of FO, NH*, ND*; circles - relaxation of stable molecules. Filled circles -experimental measurements, empty circles
- calculations by the SB theory. The points correspond to AEv of
the main relaxation channel.
A fitting approximation formula for calculations by
the SB theory has been proposed.
The rate constants of the vibrational relaxation of
FO(v= 1) by SiF,, OJ, CHsF, NF3, CF4, PH3, SFs,
NOz, and NO have been measured; the rate constant
of the FO +NO+F+NO*
reaction has been estimated. The first four of the abovementioned relaxators show vibrations, near-resonant to the vibration
of FO radical, in such cases the SB theory is applicable. In these four cases the calculated V-V rate constants are 2-3 times smaller than the experimental
ones.
All previous calculations by the SB theory have
been summarized. One can see that the discrepancy
between the SB-calculated and experimental V-V rate
constants is almost the same for (radical*+ molecule) and (molecule* + molecule) systems.
The dipole moment of the vibrational transition of
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