1472
MICHAEL J. HAUCIH AND KYLED. BAYES
Predissociation and Dissociation Energy of HBr+ by Michael J. Haugh and Kgle D . Bages” Department of Chemistry, University o j Calijornia, Los Angeles, Calijornia 90024
(Receiued January 18,2971)
Publication costs assisted by the U.S. A i r Force Ofice of Scientific Research
A predissociation in the A22+ state of HBr+ and DBr+ is described. The electronic state responsible for the predissociation is a stable 4~ state. The dissociation limit of 2180 i 20 cm-l above the A22+ (v = 0) level of HBr+ corresponds to dissociation into H(%) and Br+(3Pa/,)atoms. This results in a dissociation energy of HBr+(X*ra/,),Doo(HBr+) = 3.893 f 0.003 eV, which is compatible with current thermodynamic
data.
Introduction The electronic spectrum of HBr+ was first described by Norling,l and additional work has been reported by Barrow and CauntS2 Emission has been observed from the lowest two vibrational levels of the upper A22+ state. Although no emission has been observed from higher vibrational levels of the A22+ state, the possibility of predissociation has not been mentioned. Recently emission from the lo\+est vibrational level of DBr+(A22+)has been r e p ~ r t e d . ~ While recording the emission spectrum from the charge exchange reaction Ar+
+ HBr +HBr+ + Ar
(1)
we observed a breakoff in the rotational structure of the 1,0 band of the A22+ X2r,system. The high rotational excitation created in this reaction aided in the recognition of this predissociation. This paper \Till attempt to use this predissociation to establish an accurate dissociation limit for the HBr+ molecule. -+
Experimental Section and Results The excited HBr+ was formed by colliding a beam of 2500-eV Ar+ with HBr at room temperature and a pressure of a few milliTorr. The apparatus has been described p r e v i ~ u s l y . ~Spectra were recorded on a l-m Ebert spectrometer with a cooled EM1 62565 photomultiplier. Lines were identified by using previously measured wavelengths along with occasional atomic argon or bromine lines that also appeared in the spectrum. A photoelectric trace of the 1,0 band is shown in Figure 1. Several branches are indicated above the spectrum, with the first missing lines indicated by dashed lines. The predissociation appears to be essentially complete in all of the observed branches, with the first missing lines being a t most 5% as intense as the preceding line. The breakoff occurs in both the %+ 2 ~ 3 / ,and 22+ + 2 ~ 1 , , bands. I n order to use a predissociation limit to establish a bond energy, it is necessary to find breakoffs in more than one vibrational band. A search in the 0,O bands
-+
The Journal of Physical Chemistry, Vol. 76,A’o. 10, 1972
of HBr+ indicated a predissociation, but not with the sharp cutoff observed in the 1,O bands. The effect can be seen in a Boltemann plot, as shown in Figure 2. For most diatomic emission spectra, a plot of eq 2 In ( I / & = -I?”’(”
+ 1)/kT
(2)
gives a simple straight line, indicating a Boltemann distribution among the rotational levels of the emitting state. Here I is the emission intensity of an individual rotational line, X is a line strength factor5 that depends on the particular branch and the rotational quantum number N ’ , B’ is the rotational constant for the emitting state, k is the Boltzmann constant, and T is a “rotational temperature,” which need not be the same as the average temperature of the emitting gas. When the intensities of lines within the 0,O band are placed on a Boltzmann plot (Figure 2) the lines of low rotational quantum number give a straight line corresponding to a rotational temperature of about 3000°K. At high values of N‘, the intensities fall below the expected line, and the effect becomes larger for higher N‘. The first significant drop in intensity occurs for N ’ = 21, for which the R&21 line was 25% less intense than expected. Unfortunately, the corresponding R1 line was overlapped. By N ’ = 23, the R1 line was less than 20% of the expected intensity. Other branches could not be identified due to overlapping and background emission. The abrupt change in slope observed in Figure 2 will be taken as the onset of predissociation. This change occurs for N ’ = 21, with a possible uncertainty of 1. Due to the unusual method of ionizing and exciting the HBr+, it is possible that these breakoff s are due to a collision-induced predissociation, caused by the departing neutral Ar. Additional spectra of the 1,0 bands
*
(1) F. Norling, 2.Phys., 95, 179 (1935). ( 2 ) R. F. Barrow and A . D. Gaunt, Proc. Phys. Soc., Ser. A , 66,617 (1953). (3) L. Marsigny, J. Lebreton, and Y. Petit, C. R. Acad. Sei. Paris, Ser. C , 270, 1632 (1970). (4) M.J. Haugh and K. D. Bayes, Phys. Rev. A , 2, 1778 (1970). (5) L. T. Earls, Phys. Rev., 48, 423 (1935).
1473
PREDISSOCIATION AND DISSOCIATION ENERGY OF HBr +
5
1 II
I12
I IO
Q,
I! I 3
I I I
112
f13
PQ12
I12
I II
I IO
III
I9
1 I 3640
3620
Wavelength,
I
I
3600
-
Figure 1. Spectrum of the HBr +(A%+(v’ = 1 ) -+ X2m/2(zf’ = 0)) band in emission. The breakoffs in three of the branches are indicated. The numbers shown are N ’ , rather than the usual J”.
5
’I A I
100
200
I
i
I
300 400 “ ( N ‘ + I).
500
600
Figure 2. Boltzmann plot for the HBr +(A28+(d = 0) -+ X27ra/2(u’’= 0)) band. The RQ21 lines are indicated by circles, the RI lines by triangles.
were taken using a microwave discharge (2450 MHz) in pure HBr at a total pressure of 7 mTorr. The same breaking-off points were observed, showing that the predissociation is not collisionally induced. The emission spectrum of DBr+ was also observed in the charge-exchange reaction of Ar+ with DBr. In addition to the expected emission from the 0 and 1 vibrational levels of the A2Z+state, strong bands from v’ = 2 were present. This additional vibrational level is the result of the lowering of vibrational levels within the potential energy curve due to the isotope effect.6
Break-off s in the rotational structure of the 2,O bands of DBr+ were very evident, as can be seen in Figure 3. There is some uncertainty in assigning rotational quantum numbers to the 2,O band since a complete rotational analysis has not been carried out. The numbers shown in Figure 3 are derived by using the spectroscopic constants for HBr+ and applying the appropriate isotopic factors to calculate the constants for DBr+.’ Due to the uncertainties in some of these factors, the rotational assignments shown in Figure 3 should be considered tentative. The break-off in the 2,O band of DBr+ is not as complete as that observed for the 1,O band of HBr+. For example within the P1 branch, emission from N ‘ = 13 is about 3001, as intense as the N ’ = 12 line, while the N’ = 14 line is very weak. (A comparable decrease in intensity can be observed in the QP21,&I, and ”Q21 branches.) The observed predissociations are summarized in Table I. When the break-offs in the various branches are compared, it can be seen that the break comes between the doublet splitting of the N’ = 12 level of HBr+(A2Z+,v = l), defining the predissociation t o within that 25-cm-’ interval. Similarly, the break in (6) G. Hersberg, “Molecular Spectra and Molecular Structure. I. Spectra of Diatomic Molecules,” Van Nostrand, Princeton, N. J., 1950, p 162. (7) M. J. Haugh, Ph.D. Thesis, University of California, Los Angeles, Calif., 1968.
The Journal of Physical Chemistry, Vol. 76, No. 10,1971
1474
MICHAEL J. HAUGH AND KYLED. BAYES
I 3225
3235
3215
3205
Wavelength, Figure 3. Spectrum of the D B r f ( A 2 2 + ( d = 2) + Xans/2(v’f= 0)) band in emission. The weak lines are indicated by dashed lines. The numbers shown are N‘.
Table I : The Predissociations Observed in the A% + + X2ri System of HBr + and DBr +. All Energies Are Relative to the H B r f ( A 2 2 + ,v = 0, N = 0) Level Last normal elve-l-
c
Band
HBr +( 1,0)
Branch
Pe
P1 Qz Q1 ’Qiz
RQzi
HBr+(O,O)
RQzi
DBr +(2,0)
Ri P1 Qi
QPZl RQei
J”
J’
25/2 25/2 23/2 23/2 23/2 23/2 39/2 39/2 27/2 25/2 27/2 25/2
23/2 23/2 23/2 23/2 23/2 23/2 39/2 41/2 25/2 25/2 25/2 25/2
the DBr+(A2Z:+,v = 2) structure occurs between the two N’ = 13 levels, which are only 13.5 cm-’ apart.8
Discussion A predissociation may be used to establish a dissociation limit, but only if the type of predissociation can be established. This usually requires the observation of predissociation in three or more different vibrational levels. The Journal of Physical Chemistry, Vol. 76, No. 10, 1971
N’
12
11 12
11 11 12 20 20 12 12 13 13
7
Level
Energy (om-’)
2213.1 2103.1 2213.1 2103.1 2103.1 2213.1 2433.4 2476.5 2128.7 2128.7 2188.5 2188.5
First level of reduced intensity Energy Level (om-’)
2357.6 2238.5 2357.6 2238.5 2238.5 2357.6 2677.8 2935.1 2202.0 2202.0 2266.5 2266.5
One type of predissociation, called type I11 by Herzbergjgoccurs when the effective potential energy curve (electronic plus vibrational plus rotational) becomes entirely repulsive. For low vibrational levels, this occurs only for high rotational quantum numbers. With more vibrational energy, less rotation is required, but always the total energy must be above the dissociation limit for that particular electronic state. This type of “predissociation by pure rotation” can be eliminated for
1475
PREDISSOCIATION AND DISSOCIATION ENERGY OF HBr + 2700
HBr+, since the dissociation limit for the A22+ state should be well above the observed predissociations. (Compare the corresponding A2X+state of HC1+.lO) Then the predissociation must be caused by another electronic state crossing the A2Z+ state. Herzberg distinguishes three different cases,9 depending on whether the crossing point is above the dissociation limit (case IC),below it (case Ib), or just a t the dissociation limit (case Ia). Case ICcan be most easily distinguished by comparing the breali-off in two different vibrational states. Consider t,he general formula for the effective potential energy U N ( v ) of the predissociating state
)O
N ( N t I) for HBr’ or 05066N(N t I) for Dart.
Figure 4. The limiting curve of dissociation for HBr + and DBr+. The pair of points to the left are for DBr+, the others for HBr +. The energy intercept is 2180 & 20 em-’.
where the first term, U0(r),gives the purely electronic potential, and the second term is the rotational energy a t a particular internuclear distance T . The reduced mass is p , and N represents the nuclear rotation quantum number. If the crossing point for the rotationless curves is above the dissociation limit at an internuclear distance rC, then the maximum in U N ( r ) for values of N > 0 will also occur at approximately rc. Now by considering the energy difference between two observed break-offs, AU, and the two rotational quantum numbers corresponding to the break-offs, N I and Nz, the value of T, can be calculated.
When this is done with the HBr+ (v’ = 1 and v’ = 0) predissociations, the calculated crossing point is about 3.3 8. Since this internuclear distance is considerably larger than the distances involved in the lower part of the A 2 8 +state, for which T, = 1.688, this type of curve crossing is not compatible with the observations in HBr+. For the same reason it is unlikely that the predissociating state crosses the A22+ state close to the dissociation limit. Therefore, the predissociating state is stable, crossing the A22+curve at a point below the dissociation limit. As will be seen later, this state is almost certainly the 47r state arising from the groundstate atoms H(2S)and Br+(3P2). Even though the predissociation in HBr+ has been established as case Ib, it is still possible that the rotationless predissociating state has a potential maximum a t large internuclear distances. If that were true, any extrapolation of the break-off energies to the rotationless state would not yield a true dissociation limit, but rather the dissociation limit plus the unknown barrier height. Only if there is no potential maximum will an extrapolation to the rotationless state give a true dissociation limit. These two possibilities, case I b with or without a potential maximum, can be distinguished by making a plot of total energy at the observed break-
+
offs as a function of N ‘ ( N ’ 1). If there is a significant potential maximum, the plot will be a straight line, since the critical internuclear distance, rm, at which U,(T) has its maximum, will remain approximately constant as N’ increases. If there is no potential maximum, the rmvalues increase rapidly as N ’ + 0, and the plot of break-off energy vs. N ’ ( N ’ 1) is curved, with a slope that approaches zero as N’ +. 0. Only in this latter case does the energy limit for N’ + 0 correspond to a true dissociation limit. The break-off energy plot of HBr+ is shown in Figure 4. For each breali-off the first rotational level which has a significantly decreased emission is given as a cross, while the last normal level is indicated with a circle. The limiting curve of dissociation has been sketched in so as to pass between each pair. Since there are only two break-offs for HBr+, these cannot distinguish between a straight line and a curve. However, when the breali-off for DBr+ (v’ = 2 ) is added to the plot, a straight line cannot be drawn through the three intervals, but a curved line with zero slope at N ’ = 0 can be drawn. It is concluded that
+
(8) By chance, the energy of the DBrf(A2Z+, 1~ = 2) level, relative t o the HBr +(A22 +, n = 0) level, can be calculated quite accurately, even though the vibrational constants of the A*2+ state are not known accurately. Letting a superscript i denote the heavier molecule, then the vibrational energy difference
G’(v = 2 )
- G(v
=
0)
=
~ ~ ~ ( 2-. 5 )
+
p * w , ~ , ( 2 . 5 )~ ~ ~ ( 0 . 5 )~~~e(0.5)’
where me and wexe refer, to the HBr + molecule, and p2 equals the ratio of reduced masses, f i / f i l . Inserting values for p and p* and simplifying gives
G’(v
=
2)
- G(u = 0 )
1 . 2 7 9 4 1 [ w e - 2 w . ~ e ] - 0.3575weze
Now although neither me nor w e z e is known accurately, the difference ( w e - 2weze)is, since this is just the A G ‘ I / ~measured by Barrow and Caunt2 as 1328.7 cm-1. Thus using their estimated value of wexe E 40 cm-1 gives a value for G’(v = 2) - G(v = 0) of 1685.7 em-’, while an error of 4 ~ 2 0 %in the value of wexc will cause an error of only 1;3 cm-1 in the energy separation. (9) See pages 420-432 of ref 6. (10) F. Norling, 2. Phus., 104, 638 (1935). The Journal of Phwical Chemistru, Vol. 76, N o . 20, 1971
1476
MICHAEL J. HAUGHAND KYLED. BAYES
there is no maximum in the V o ( r )curve and that the extrapolated energy limit, 2180 f 20 cm-’, represents a true dissociation limit.lltlz The error limits on this value represent only the uncertainty in the curve, and not the possible uncertainties in the analysis of the DBr+ spectrum. When a proper rotational analysis has been done, Figure 4 should be redone using the measured parameters for DBr+. The states of the atoms formed by the predissociation cannot be determined from the predissociation alone. However, by using the relationship between ionization potentials, I , and dissociation energies, D I(HBr)
+ Doo(HBr+)= Doo(HBr)+ I(H or Br)
(5)
If the above value for Doo(HBr)is used, the calculated value for I(HBr) becomes 11.677 f 0.004 eV. Since this value agrees well with recent measurements,16p16 the energetics of the HBr system appear to be well established. The combination of a 2S hydrogen atom and a 3P Br+ can result in a total of four molecular states: %-, %, 4Z-, 4r. The resulting 2r state can be identified with the ground state of HBr+, X 2 r i . Since both of the 2 states are 2 - states, they cannot be predissociating the A2Z+ state, due to the rigorous selection rule, -, for perturbation^.'^ Therefore the predissociating state must be 4r,as was previously concluded by Lemka, et a1.16 Since the predissociation is spin forbidden, the break-off may not be complete, which could explain the fact that Korling was able to observe lines photographically beyond the break-off The conclusion that the 4rstate must have a potential minimum is in contrast to the potential energy curves drawn by Lemka, et al.
+ +-I+
combined with other measurements it is possible to determine the products. The dissociation energy, Doo(HBr+,X2ra/,), will be just the sum of the voo for the transition A22+ + X2ra/,,which Norling‘ measured as 29,227 cm-’, and the predissociation limit shown in Figure 4; thus Doo(HBr+)is 31,407 f 20 cm-l, or 3.894 f 0.003 eV, where the products of the dissociaAcknowledgments. This paper is offered as an ention are not yet specified. The ionization potential of comium to Dr. G. B. Ilistiakowsky for his gracious help HBr has been measured several times r e ~ e n t l y , ~ ~ - ’ ~ and inspiration during the past 15 years. For finanand the range 11.67 =k 0.05 eV encompasses the meacial support we thank the Air Force Office of Scientific sured values. The dissociation energy for neutral HBr Research (AF-AFOSR 687-64) and the National Aerocan be calculated from thermodynamic tables” as 86.64 nautics and Space Administration for a Predoctoral kcal/mol, or 30,303 cm-l. When the possible atomic Traineeship (to n!t. J. H.). ionization energies are added to this dissociation energy, the possible energy limits are shown in Table 11. Since (11) This reasoning would not be valid if there were a significant the sum of Doo(HBr+)and I(HBr) is 125,500 f 400 maximum in the Uo(r) curve and tunnelling were occurring. Since HBr+ and DBr+ have different reduced masses, their tunnelling cm-’, this energy limit is compatible only with the probabilities are different and the points for HBr+ would lie on a atomic states H(%) and Br+(3P2). curve below those for DBr+ (cf. A H and AID12). However, as was
Table 11: The Lowest Energy States for the System (H Br)+
+
Total energy above HBr
htomio states
+ Br+(aP,) + Br+(SP1) + Br+(3P~) H+(’S) + Br(2Pa;,) H(%) H(%) H(2S)
125,588 cm-l 128,724 cm-’ 129,425 cm-1 139,982 cm-’
Since the ionization potential of the bromine atom has been measured accurately as 95,285 cm-1,18 the spectroscopic measurements now may be combined to provide an accurate relationship between I(HBr) and Doo(HBr).
+ 63,878
I(HBr) = Doo(HBr)
f
30 cm-l
The Journal of Physical Chemistry, Val. 75, No. 10, 1971
(6)
shown earlier, if there is a maximum in Uo(r) then its position occurs at about 3.3 A. It has not been possible t o construct a curve Uo(r) with a maximum at 3.3 A that can give the observed break-offs as sharply as observed, and at essentially the same energy for HBr +(P’ = 1) and DBr+(v’ = 2). Although tunnelling may be responsible for the incomplete break-off observed in HBr+(u’ = 0), there is at present no evidence for a potential maximum in Ua(r). (12) C.Hereberg and L. C. Mundie, J . Chem. Phys., 8, 263 (1940). (13) K.Watanabe, T.Nakayama, and J. T. Mottl, J. Quant. Spectrosc. Radiat. Transfer, 2, 369 (1962). (14) D.C.Frost, C. A. McDowell, and D. A. Vroom, J . Chem. Phys., 46,4255 (1968). (15) J. H. Lemka, T. R. Passmore, and W. C. Price, Proc. R o y . Soc., Ser. A , 304, 53 (1968). (16) D. W. Turner, C. Baker, A. D. Baker, and C. R. Brundle, “Molecular Photoelectron Spectroscopy,” Wiley-Interscience, London, 1970. (17) D. D. Wagman, W.H. Evans, V. B. Parker, I. Halow, S. M. Bailey, and R. H. Schumm, “Selected Values of Chemical Thermodynamic Properties,” National Bureau of Standards (E. s.) Technical Note 270-4, U. S. Government Printing Office, Washington, D. C., 1969. (18) R.E. Huffman, J. C. Larrabee, and Y . Tanaka, J . Chem. Phys., 47, 856 (1967). (19) Seep 416 of ref 6.
