- Email: [email protected]
Rotational coupling of the β 1 and E 0+ ion-pair states of lodine bromide
JOURNAL OF MOLECULAR SPEmROSCOPY
113, 47-53 (1985)
Rotational Coupling of the 6 1 and E O+ Ion-Pair States of iodine Bromide’ J. C. D. BRAND, A. R. HOY, AND A. C. RISBUD Department
ofChemistry,University of Western
Ontario, London, Ontario N6A 5B7. Canada
The E(Q = O+) and B(B(n= 1) ion-pair states of IBr are coupled by an electronic Coriolis interaction. A nonlinear, least-squares fit of term values for both states yields a set of potential and rotational constants purged of the effects of this interaction. The magnitude of the coupling constant, 1W,Ol = 2.41 cm-‘, is 98% of the value predicted for pure precession. Principal constants of the previously unreported @state of 179Brare T, = 39507.76. wp = 122.09. w& = 0.2546, B, = 0.02937, and (Y,= 8.2 X 10m4cm-‘. 0 198sAcademic press. IIIC. INTRODUCTION
Because the bond distance in ion-pair states of halogens and interhalogens is considerably longer than in the ground state, a one-photon transition between low vibrational levels is practically forbidden by the Franck-Condon shift. A two-step transition avoids this difficulty, since the intermediate state in double resonance can nearly always be chosen so as to match the vibrational functions of the initial and final states. However, insertion of a third state into the reaction sequence, besides changing the selection rules to those of a two-photon process, may introduce new constraints. Thus, in all known examples drawn from the halogen series the intermediate-to-final (i.e., ion-pair) state transitions show a strong preference for parallel as opposed to perpendicular selection rules: consequently, in order to probe, say, a case c Q = O+ ion-pair state the intermediate state must be O+ also, otherwise the electronic transition moment will be small. Among homonuclear halogens the well-known B O+ state fills this prescription very well, but for the interhalogens ICI (1-4) and IBr (5, 6) the B, B' adiabatic states are predissociated (7, 8) so that only a few rotational levels in each band are sufficiently long-lived for sequential spectroscopy. The accessible J states of the ion-pair states are, of course, similarly restricted. Among the heavier interhalogens the first tier of ion-pair states is a triad of states E O+,p 1, and 0’2, which correlate diabatically with the ground states of separated ions. As mentioned, E O+ can be probed sporadically through B, B' (4). Access to P 1 by the sequence /3 - A - X is unencumbered, but entry to D' is difficult because the step A’2 - X Of is a forbidden transition. In the case of ICI an electronic-Coriolis resonance between /3 and D' renders D' accessible from A (9), so that transitions to all three ion-pair states of the first tier are observable by double ’ Publication no. 334 from the Photochemistry Unit. This work was supported by the Natural Sciences and Engineering Council of Canada. 47
0022-2852185 $3.00 Copyright Q 1985 by Academic Press. Inc. All rights of reproduck,”
I” any form resewed.
BRAND,
48
HOY,
AND RISBUD
resonance. The spectroscopy of IBr is less developed, though the constants of E O+ are now quite well determined (5, 6). The present work was undertaken in order to define the largely unknown ,0 1 state and to characterize its J-dependent coupling with E. Although we have not been able to identify the third member of the triad, D’, the possible D’-A’ emission reported by Diegelmann and others (10) gives an indication of the relative energies of these states. States of IBr discussed in this paper, identified by their case c signatures and dissociation limit, are listed below. Valence states
x o+ Al A’ 2 B, B 0+
Ion-pair states +
I + Br I + Br I + Br I + Br*
D’ 2
EXPERIMENTAL
I’(3PZ) + Br-(‘S) I’(3PZ) + Bra I’(3P2) + Br-( ‘S)
DETAILS
Double resonance transitions fi - A - X were recorded by polarization labeling. Transitions of the far-red A - X system (11) were pumped using NB690 or oxazine 725 as lasing media, while the probe laser was operated in the near uv using BBQ or QUI. The pump bandwidth was ca 0.2 cm-‘. Signals were recorded with a 3.4m spectrograph operated in the 15th order at a dispersion of about 2.5 mm A-‘. A commercial sample of IBr was used directly. Steps to suppress I2 or Br, are unnecessary since both are unresponsive to the pump-probe combination used for IBr. A 6-cm cell was filled with IBr vapor in equilibrium with the solid at 20°C. Spectra of 18’Br and 179Br are easily distinguished in these sparse spectra, which stand to gain little from isotopic enrichment. A catalog of pumped transitions is given in Table I. As expected, transitions of 179Brand I*‘Br are observed in roughly equal numbers. Since the probe transitions are parallel, tuning the pump laser to a PR or Q branch of A - X gives access to e or f sublevels, respectively, of the degenerate A and ,8 states. RESULTS
The data were marshalled by computing term values for the /3 state, each term being the sum of the pump frequency, our measured probe frequency, and a ground state term value. The first of these quantities was normally taken from Selin’s measurements (II) while the last was calculated from merged ground state constants given by Weinstock and Preston (12). Dunham coefficients for the p state were then calculated by a least-squares fit of the term values, combining isotopic data by the relationshin (1) where p = CL/#) is the ratio of reduced masses. The results of this empirical refinement are in Table II, which also gives the effective constants for E O+ (6) in order to draw attention to the remarkable similarity between these ion-pair states.
ROTATIONAL
COUPLING
49
IN IBr
TABLE I Catalog of Pump and Probe Transitions
1’9BT
ll-1,QSl
0
I’lEw
11-1.449
0
12-l,R30
0
12-l,P22
0
12-l,Q35
0
12-1.926
0
12-l,R37
0
12-1.R28
0
12-l,R42
0
12-l,P30
0
12-1.452
0
12-l,R39
0
1s1.R59
1
12-1.450
0
13-l,P61
0.1
12-l,Q55
0
13-l,P67
0
13-l,P54
Or1
13-1.P70
I
14-0,QZl
0.1
14-O.P38
1
14-0.R37
0.1
14-2.R44
0.1.3
14-2.Q44
0.1,2,3
14-2.R47
lr3
15-2,Q39
1.2
15-2.916
2
15-2.940
1.2
15-2,RU
1.2
16-2.P29
2.3
15-2.P34
1.2
16-2.R34
2,3
l5-2.R37
1.2
16-2.P39
2.3
1%2.P39
1.2
16-2.R42
2.3
16-2.P29
2.3
16-2,QSO
2.3
16-2.P31
2.3
16-2.R54
2.3
16-2.P33
2,3
la-l,P21
2t3.4.5
16-2,P52
2.3
18-1.422
3.4
16-2.P54
3
la-1.R30
2.3.4
16-2.R55
2.3
18-1.R36
2.4.5
la-1.P25
2.3,4,5
18-l,R37
2.4.5
M-1,926
2.3,4.5
19-1.R27
3.4
M-l,R33
2.3,4.5
19-l.R40
3r4.5.6
H-1.937
2.3c4.5
19-l,R52
3t4.6
1sl,P37
2,3,4.5
19-l,P56
3,4.6 3.6
la-l,Q12
3,4
19-1.957
19-1.R30
3.4.6
19-l,R59
3.4.6
19-l,R42
2.3.4.6
20-l,P38
5 3.4,5
19-1.P45
2.3.4.6
20-l,P42
19-1,PSl
2.3.6
20-l,P49
5
19-l,P57
2.3,4.6
24-2.R35
6.7
19-1.Q58
4.6
26-2,P25
7
50
BRAND, HOY, AND RISBUD TABLE I-Continued Probe
pump AtX
Probe
PumP AcX
VB
“8
zo-l,R42
5,6
27-O,R6
7,9
24-l,P54
2.3.4.6
27-O,Q19
7.9
24-2.R12
4.5.6.7
27-O,R21
7
24-2.925
4.5.6.7
27-O,P37
7
24-2.P30
7
28-0.428
7.9
24-2.R31
4.5.6
28-O.P33
7.8.9
26-O,R29
6.7.8
28-0.R34
7
27-O.Pl2
7.9
27-O.RlS
7
27-0.422
7.8.9
27-O,R23
7.0.9
27-0.940
7
28-0,430
7.9
28-O,P30
i.9
28-O,Q35
7.9
Q-Doubling in the /3 state is large at low 2) though it falls off progressively as 2) increases. The sense of the splitting is consistent with an electronic-Coriolis interaction between ,8 and E, similar to the coupling recently analyzed for ICI (9). A preliminary calculation confirms this impression. Assuming pure precession, the Q-doubling parameter, q, in the 0 state is given by (4) TABLE II
EffectiveSpectroscopic Constants (cm-‘) for PBr from One-State Fits EO+(‘P,)+”
Yo,.(-Tel
39487.32(U)
39507.652(37)
119.518(21)
yl,o(-%)
122.098(15)
-0.2109(12)
Y,,.(-wk)
-0.2546(14) substatee e
10’
Y,,,(-8.)
2.9701(U)
2.9925(20)
101
Y1,1(-%)
-5.43(59)
-21.4(16)
10'
Y1,,(-r.)
-6.8(16)
134(44) -4.7(36)
10' Y,,l
Wncertainties
quoted
bu o,l constrained CRange
vg-O-9
are
30
to -4B:/w:
f 2.9453(M) -8.52(41)
ROTATIONAL
COUPLING
q = B(e) - B(f)
N
IN IBr
12B2/AT f
51
(.?I
where AT, = T&?) - T&E). Numerically, the right side of Eq. (2) is G5 X IO-” cm-’ for B = 0.029 and AT, = 20 cm-‘. The parameters B’,“, a$“, etc., obtained from separate, one-state fits are effective constants because the coupling is between e sublevels; but, in the presence of a perturbation the isotope relation, Eq. (l), is not strictly valid and this must lead to some contamination of the other constants also. While this statement of the E, p coupling is inexact it nevertheless gives a correct qualitative account of the problem. A more rigorous analysis is developed in the next section. DISCUSSION
The theory of the E, & D’ coupling develops along lines described recently for the related interhalogen ICI (9). The rotational Hamiltonian can be written (13), H,,Jhc = (h/8r2cpr2){J2
- J: + L2 - L; + S2 - S: - J+(L_ + S_) - J_(L+ + S,) + L+S_ + L-S,}.
(3)
Using case c basis functions IJQuM) = ]Q)lQu)lJQM), the J-dependent electronicrotation coupling between states of different Q develops from the cross-terms on the second line of Eq. (3), i.e., (JQ -1-lv’MIH,,JhclJQuM)
= (n f l]L, + S&) x (u’n + ljh/87r2c~r2JvR)[J(J + 1) - Q(Q + I)]“’
(4)
For E, p coupling the third factor on the right side of Eq. (4) reduces to [J(J + 1)]“2. The second factor is an off-diagonal rotational constant which, provided the potential functions for E and fi are available, is calculable by numerical integration using numerical forms of the appropriate vibrational wavefunctions. However, the first factor is not easily calculable uniess one introduces pure precession (14) which, although it proves a good approximation in the long run, would not be desirable at this stage. Treating this factor as a parameter, Wi,O, the form of Eq. (4) becomes (Jlu’M]H,,,/hclJOuM) = W,,&[J(J + l)]“‘. (5) Furthermore, symmetry allows us to reduce the basic 3 X 3 problem to a quadratic factor for the e sublevels, and a linear factor for the f sublevels of ,& After symmetrizing the Q = f 1 functions, however, the matrix element on the right side of Eq. (5) is multipled by &?. E-state term values used in the two-state refinement were those given in Ref. (6) supplemented by some new observations for uE = 1. Preliminary trials indicated that matrix elements off-diagonal in u could safely be dropped from the global fit in the range of uB and uE covered by our data. An iterative, nonlinear, least-squares refinement led to the set of “deperturbed” constants given in Table III. The isotope relationships (1) were assumed in this refinement. Since the interaction element W 1,0 is reasonably well-determined by the least-
52
BRAND, HOY, AND RISBUD TABLE III Deperturbed Constants (cm-‘) for the E O+ and /3 1 States of PBr E
0ta.b.c
gla,b,d
39507.761(36)
39487.811(90)
122.091(14)
119.430(18) -0.2055(12)
-0.2546(12)
-0.333(23) f
e 2.9852(52)
2.9321(60)
-7.40(66)
-7.63(81)
2.9372(M) -8.24(42)
-2.1(18) 2.41(X) 32500
32480
3.407(3)
aUncertaintles
by,,,
quoted
constrained
are
3.4344(U)
30
to -4B:/w:
cv~=1,3-15.24-31 d "g-O-9 eFor
dlssoc1atlo"
to
I+(‘P,)
+Br-C’S)
squares fit it is interesting to compare its value with that predicted for the pure precession hypothesis, incorporated in the analysis of the previous section. Pure precession assumes that L + S (=J,) is a good quantum number. As E and /3 correlate with 3P2 + ‘S states (J, = 2) of the separated ions, the pure precession value is IV,,0 = (HIL,
+ S,[O) = [J,(J, + 1)]“2 = ti
(6)
The least-squares W,,0 is 98% of this value. Comparing Tables II and III, the deficiencies of the one-state analyses are all too apparent; the potential constants Y,,, in Table II differ from values in Table III by considerably more than a 3a uncertainty, and the f-substate rotational constants are shifted significantly from their deperturbed values in spite of the fact that fsubstates do not participate in the coupling. These defects are due in part to the fact that the one-state fits to perturbed bands are coerced into obeying the isotope relations, and in part to the state-selective feature of the data themselves, which samples the J distribution in a random rather that a systematic manner. On the other hand, it is reassuring that the p state constants B’,e)and B’pf’ of Table III fall within 2.5~ and so are not distinguished by the present data. In the pure precession limit the only 0’ state to which p is coupled is the state E, so that the residual effect of coupling with other 0’ states of the manifold is expected to be small. Likewise, the deperturbed (Y,are consistent with values calculated for a Morse potential,
ROTATIONAL
W+we) ‘I2 -
B;]/oe
COUPLING
=
IN IBr
53
7.3X IO-$5 state) 8.2 X 10-‘(/3 state)
as expected for low vibrational levels of a strongly bound state. The chief uncertainty in this analysis is our complete lack of knowledge concerning the third state of the triad, D’ (2). No transitions of the P-A system were observed in course of this work. While this indicates that the electronic-rotational D', li,' interaction is small we cannot be sure that it leaves no imprint on the /3 state constants. We also draw attention to a curious though minor anomaly in the properties of E and p; namely, that E has the smaller o,, yet is actually the deeper of the two states. Similar anomalies occur in the ion-pair states of ICI where all three members of the triad have been characterized (9) so that our lack of knowledge regarding D' is probably not responsible. The explanation is obscure. CONCLUSION
A previously unknown ion-pair state of IBr, p(Q = I), has been characterized in the range vB = O-9 by measurements of the /3-A band system. Irrational fl-doubling splittings observed in the lower vibrational levels of /I are due to electronicrotational coupling to a second ion-pair state, E O+,lying close to p. The constant describing this interaction is determined by a simultaneous, nonlinear, least-squares fit of term values for both E and /3. Because these two states converge to the same dissociation limit, namely, the ground states of the ions I+ and Bra, this coupling is expected to correspond with Van Vleck’s conditions for “pure precession.” and this proves to be the case. RECEIVED:
February
1 I, 1985 REFERENCES
I. R. G. GORDON AND K. K. INNES, J. Chem. Phys. 71, 2824-2839
(1979).
2. S. G. HANSEN, J. D. THOMPSON, R. A. KENNEDY, AND B. J. HOWARD, J. Chem.
3. 4.
5. 6. 7. 8. 9. 10. 11. I-7. IS. 14.
SOC. Farudu~~ Trans. II 78, 1293-1310 (1982); S. G. HANSEN, J. D. THOMPSON. C. M. WESTERN, AND B. J. HOWARD, Mol. Phys. 49, 1217-1229 (1983). G. W. KING. I. M. LITTLEWOOD, R. G. MCFADDEN, AND J. R. ROBINS, Chem. Phys. 41, 379-386 (1979). J. C. D. BRAND, U. D. DESHPANDE, A. R. HOY, AND S. M. JAYWANT. J. Mol. Specfrosc. 100,416428 (1983); J. C. D. BRAND, A. R. HOY, AND S. M. JAYWANT, J. Mol. Speetrosc. 106, 388-394 ( 1984). G. W. KING, I. M. LITTLEWOOD, AND J. R. ROBINS, Chem. Phys. 62, 359-367 (1981). J. C. D. BRAND, U. D. DESHPANDE, A. R. HOY, S. M. JAYWANT, AND E. J. WOODS, J. dfol. Spectrosc. 99, 339-347 (1983). M. S. CHILD, Mol. Phys. 32, 1495-1510 (1976). H. KNOCKEL, E. TIEMANN, AND D. ZOGLOWEK, J. Mol. Specfrosc. 85, 225-231 (1981). D. BUSSIERESAND A. R. HOY, Canad. J. Phys. 62, 1941-1946 (1984). M. DIEGELMANN, K. HOHLA, F. REBENSTROST,AND K. L. KOMPA, J. Chem. Phys. 76, 1233-1247 (1982). L. E. SELIN, Ark. Fys. 21, 479-525 (1962). E. M. WEINST~CK AND M. PRESTON, J. Mol. Spectrosc. 70, 188-196 (1978). J. T. HOUGEN, “NBS Monograph 115,” U. S. Govt. Printing Office, Washington. D. C.. 1970. J. H. VAN VLECK, Phys. Rev. 33, 467-506 (1929).
113, 47-53 (1985)
Rotational Coupling of the 6 1 and E O+ Ion-Pair States of iodine Bromide’ J. C. D. BRAND, A. R. HOY, AND A. C. RISBUD Department
ofChemistry,University of Western
Ontario, London, Ontario N6A 5B7. Canada
The E(Q = O+) and B(B(n= 1) ion-pair states of IBr are coupled by an electronic Coriolis interaction. A nonlinear, least-squares fit of term values for both states yields a set of potential and rotational constants purged of the effects of this interaction. The magnitude of the coupling constant, 1W,Ol = 2.41 cm-‘, is 98% of the value predicted for pure precession. Principal constants of the previously unreported @state of 179Brare T, = 39507.76. wp = 122.09. w& = 0.2546, B, = 0.02937, and (Y,= 8.2 X 10m4cm-‘. 0 198sAcademic press. IIIC. INTRODUCTION
Because the bond distance in ion-pair states of halogens and interhalogens is considerably longer than in the ground state, a one-photon transition between low vibrational levels is practically forbidden by the Franck-Condon shift. A two-step transition avoids this difficulty, since the intermediate state in double resonance can nearly always be chosen so as to match the vibrational functions of the initial and final states. However, insertion of a third state into the reaction sequence, besides changing the selection rules to those of a two-photon process, may introduce new constraints. Thus, in all known examples drawn from the halogen series the intermediate-to-final (i.e., ion-pair) state transitions show a strong preference for parallel as opposed to perpendicular selection rules: consequently, in order to probe, say, a case c Q = O+ ion-pair state the intermediate state must be O+ also, otherwise the electronic transition moment will be small. Among homonuclear halogens the well-known B O+ state fills this prescription very well, but for the interhalogens ICI (1-4) and IBr (5, 6) the B, B' adiabatic states are predissociated (7, 8) so that only a few rotational levels in each band are sufficiently long-lived for sequential spectroscopy. The accessible J states of the ion-pair states are, of course, similarly restricted. Among the heavier interhalogens the first tier of ion-pair states is a triad of states E O+,p 1, and 0’2, which correlate diabatically with the ground states of separated ions. As mentioned, E O+ can be probed sporadically through B, B' (4). Access to P 1 by the sequence /3 - A - X is unencumbered, but entry to D' is difficult because the step A’2 - X Of is a forbidden transition. In the case of ICI an electronic-Coriolis resonance between /3 and D' renders D' accessible from A (9), so that transitions to all three ion-pair states of the first tier are observable by double ’ Publication no. 334 from the Photochemistry Unit. This work was supported by the Natural Sciences and Engineering Council of Canada. 47
0022-2852185 $3.00 Copyright Q 1985 by Academic Press. Inc. All rights of reproduck,”
I” any form resewed.
BRAND,
48
HOY,
AND RISBUD
resonance. The spectroscopy of IBr is less developed, though the constants of E O+ are now quite well determined (5, 6). The present work was undertaken in order to define the largely unknown ,0 1 state and to characterize its J-dependent coupling with E. Although we have not been able to identify the third member of the triad, D’, the possible D’-A’ emission reported by Diegelmann and others (10) gives an indication of the relative energies of these states. States of IBr discussed in this paper, identified by their case c signatures and dissociation limit, are listed below. Valence states
x o+ Al A’ 2 B, B 0+
Ion-pair states +
I + Br I + Br I + Br I + Br*
D’ 2
EXPERIMENTAL
I’(3PZ) + Br-(‘S) I’(3PZ) + Bra I’(3P2) + Br-( ‘S)
DETAILS
Double resonance transitions fi - A - X were recorded by polarization labeling. Transitions of the far-red A - X system (11) were pumped using NB690 or oxazine 725 as lasing media, while the probe laser was operated in the near uv using BBQ or QUI. The pump bandwidth was ca 0.2 cm-‘. Signals were recorded with a 3.4m spectrograph operated in the 15th order at a dispersion of about 2.5 mm A-‘. A commercial sample of IBr was used directly. Steps to suppress I2 or Br, are unnecessary since both are unresponsive to the pump-probe combination used for IBr. A 6-cm cell was filled with IBr vapor in equilibrium with the solid at 20°C. Spectra of 18’Br and 179Br are easily distinguished in these sparse spectra, which stand to gain little from isotopic enrichment. A catalog of pumped transitions is given in Table I. As expected, transitions of 179Brand I*‘Br are observed in roughly equal numbers. Since the probe transitions are parallel, tuning the pump laser to a PR or Q branch of A - X gives access to e or f sublevels, respectively, of the degenerate A and ,8 states. RESULTS
The data were marshalled by computing term values for the /3 state, each term being the sum of the pump frequency, our measured probe frequency, and a ground state term value. The first of these quantities was normally taken from Selin’s measurements (II) while the last was calculated from merged ground state constants given by Weinstock and Preston (12). Dunham coefficients for the p state were then calculated by a least-squares fit of the term values, combining isotopic data by the relationshin (1) where p = CL/#) is the ratio of reduced masses. The results of this empirical refinement are in Table II, which also gives the effective constants for E O+ (6) in order to draw attention to the remarkable similarity between these ion-pair states.
ROTATIONAL
COUPLING
49
IN IBr
TABLE I Catalog of Pump and Probe Transitions
1’9BT
ll-1,QSl
0
I’lEw
11-1.449
0
12-l,R30
0
12-l,P22
0
12-l,Q35
0
12-1.926
0
12-l,R37
0
12-1.R28
0
12-l,R42
0
12-l,P30
0
12-1.452
0
12-l,R39
0
1s1.R59
1
12-1.450
0
13-l,P61
0.1
12-l,Q55
0
13-l,P67
0
13-l,P54
Or1
13-1.P70
I
14-0,QZl
0.1
14-O.P38
1
14-0.R37
0.1
14-2.R44
0.1.3
14-2.Q44
0.1,2,3
14-2.R47
lr3
15-2,Q39
1.2
15-2.916
2
15-2.940
1.2
15-2,RU
1.2
16-2.P29
2.3
15-2.P34
1.2
16-2.R34
2,3
l5-2.R37
1.2
16-2.P39
2.3
1%2.P39
1.2
16-2.R42
2.3
16-2.P29
2.3
16-2,QSO
2.3
16-2.P31
2.3
16-2.R54
2.3
16-2.P33
2,3
la-l,P21
2t3.4.5
16-2,P52
2.3
18-1.422
3.4
16-2.P54
3
la-1.R30
2.3.4
16-2.R55
2.3
18-1.R36
2.4.5
la-1.P25
2.3,4,5
18-l,R37
2.4.5
M-1,926
2.3,4.5
19-1.R27
3.4
M-l,R33
2.3,4.5
19-l.R40
3r4.5.6
H-1.937
2.3c4.5
19-l,R52
3t4.6
1sl,P37
2,3,4.5
19-l,P56
3,4.6 3.6
la-l,Q12
3,4
19-1.957
19-1.R30
3.4.6
19-l,R59
3.4.6
19-l,R42
2.3.4.6
20-l,P38
5 3.4,5
19-1.P45
2.3.4.6
20-l,P42
19-1,PSl
2.3.6
20-l,P49
5
19-l,P57
2.3,4.6
24-2.R35
6.7
19-1.Q58
4.6
26-2,P25
7
50
BRAND, HOY, AND RISBUD TABLE I-Continued Probe
pump AtX
Probe
PumP AcX
VB
“8
zo-l,R42
5,6
27-O,R6
7,9
24-l,P54
2.3.4.6
27-O,Q19
7.9
24-2.R12
4.5.6.7
27-O,R21
7
24-2.925
4.5.6.7
27-O,P37
7
24-2.P30
7
28-0.428
7.9
24-2.R31
4.5.6
28-O.P33
7.8.9
26-O,R29
6.7.8
28-0.R34
7
27-O.Pl2
7.9
27-O.RlS
7
27-0.422
7.8.9
27-O,R23
7.0.9
27-0.940
7
28-0,430
7.9
28-O,P30
i.9
28-O,Q35
7.9
Q-Doubling in the /3 state is large at low 2) though it falls off progressively as 2) increases. The sense of the splitting is consistent with an electronic-Coriolis interaction between ,8 and E, similar to the coupling recently analyzed for ICI (9). A preliminary calculation confirms this impression. Assuming pure precession, the Q-doubling parameter, q, in the 0 state is given by (4) TABLE II
EffectiveSpectroscopic Constants (cm-‘) for PBr from One-State Fits EO+(‘P,)+”
Yo,.(-Tel
39487.32(U)
39507.652(37)
119.518(21)
yl,o(-%)
122.098(15)
-0.2109(12)
Y,,.(-wk)
-0.2546(14) substatee e
10’
Y,,,(-8.)
2.9701(U)
2.9925(20)
101
Y1,1(-%)
-5.43(59)
-21.4(16)
10'
Y1,,(-r.)
-6.8(16)
134(44) -4.7(36)
10' Y,,l
Wncertainties
quoted
bu o,l constrained CRange
vg-O-9
are
30
to -4B:/w:
f 2.9453(M) -8.52(41)
ROTATIONAL
COUPLING
q = B(e) - B(f)
N
IN IBr
12B2/AT f
51
(.?I
where AT, = T&?) - T&E). Numerically, the right side of Eq. (2) is G5 X IO-” cm-’ for B = 0.029 and AT, = 20 cm-‘. The parameters B’,“, a$“, etc., obtained from separate, one-state fits are effective constants because the coupling is between e sublevels; but, in the presence of a perturbation the isotope relation, Eq. (l), is not strictly valid and this must lead to some contamination of the other constants also. While this statement of the E, p coupling is inexact it nevertheless gives a correct qualitative account of the problem. A more rigorous analysis is developed in the next section. DISCUSSION
The theory of the E, & D’ coupling develops along lines described recently for the related interhalogen ICI (9). The rotational Hamiltonian can be written (13), H,,Jhc = (h/8r2cpr2){J2
- J: + L2 - L; + S2 - S: - J+(L_ + S_) - J_(L+ + S,) + L+S_ + L-S,}.
(3)
Using case c basis functions IJQuM) = ]Q)lQu)lJQM), the J-dependent electronicrotation coupling between states of different Q develops from the cross-terms on the second line of Eq. (3), i.e., (JQ -1-lv’MIH,,JhclJQuM)
= (n f l]L, + S&) x (u’n + ljh/87r2c~r2JvR)[J(J + 1) - Q(Q + I)]“’
(4)
For E, p coupling the third factor on the right side of Eq. (4) reduces to [J(J + 1)]“2. The second factor is an off-diagonal rotational constant which, provided the potential functions for E and fi are available, is calculable by numerical integration using numerical forms of the appropriate vibrational wavefunctions. However, the first factor is not easily calculable uniess one introduces pure precession (14) which, although it proves a good approximation in the long run, would not be desirable at this stage. Treating this factor as a parameter, Wi,O, the form of Eq. (4) becomes (Jlu’M]H,,,/hclJOuM) = W,,&[J(J + l)]“‘. (5) Furthermore, symmetry allows us to reduce the basic 3 X 3 problem to a quadratic factor for the e sublevels, and a linear factor for the f sublevels of ,& After symmetrizing the Q = f 1 functions, however, the matrix element on the right side of Eq. (5) is multipled by &?. E-state term values used in the two-state refinement were those given in Ref. (6) supplemented by some new observations for uE = 1. Preliminary trials indicated that matrix elements off-diagonal in u could safely be dropped from the global fit in the range of uB and uE covered by our data. An iterative, nonlinear, least-squares refinement led to the set of “deperturbed” constants given in Table III. The isotope relationships (1) were assumed in this refinement. Since the interaction element W 1,0 is reasonably well-determined by the least-
52
BRAND, HOY, AND RISBUD TABLE III Deperturbed Constants (cm-‘) for the E O+ and /3 1 States of PBr E
0ta.b.c
gla,b,d
39507.761(36)
39487.811(90)
122.091(14)
119.430(18) -0.2055(12)
-0.2546(12)
-0.333(23) f
e 2.9852(52)
2.9321(60)
-7.40(66)
-7.63(81)
2.9372(M) -8.24(42)
-2.1(18) 2.41(X) 32500
32480
3.407(3)
aUncertaintles
by,,,
quoted
constrained
are
3.4344(U)
30
to -4B:/w:
cv~=1,3-15.24-31 d "g-O-9 eFor
dlssoc1atlo"
to
I+(‘P,)
+Br-C’S)
squares fit it is interesting to compare its value with that predicted for the pure precession hypothesis, incorporated in the analysis of the previous section. Pure precession assumes that L + S (=J,) is a good quantum number. As E and /3 correlate with 3P2 + ‘S states (J, = 2) of the separated ions, the pure precession value is IV,,0 = (HIL,
+ S,[O) = [J,(J, + 1)]“2 = ti
(6)
The least-squares W,,0 is 98% of this value. Comparing Tables II and III, the deficiencies of the one-state analyses are all too apparent; the potential constants Y,,, in Table II differ from values in Table III by considerably more than a 3a uncertainty, and the f-substate rotational constants are shifted significantly from their deperturbed values in spite of the fact that fsubstates do not participate in the coupling. These defects are due in part to the fact that the one-state fits to perturbed bands are coerced into obeying the isotope relations, and in part to the state-selective feature of the data themselves, which samples the J distribution in a random rather that a systematic manner. On the other hand, it is reassuring that the p state constants B’,e)and B’pf’ of Table III fall within 2.5~ and so are not distinguished by the present data. In the pure precession limit the only 0’ state to which p is coupled is the state E, so that the residual effect of coupling with other 0’ states of the manifold is expected to be small. Likewise, the deperturbed (Y,are consistent with values calculated for a Morse potential,
ROTATIONAL
W+we) ‘I2 -
B;]/oe
COUPLING
=
IN IBr
53
7.3X IO-$5 state) 8.2 X 10-‘(/3 state)
as expected for low vibrational levels of a strongly bound state. The chief uncertainty in this analysis is our complete lack of knowledge concerning the third state of the triad, D’ (2). No transitions of the P-A system were observed in course of this work. While this indicates that the electronic-rotational D', li,' interaction is small we cannot be sure that it leaves no imprint on the /3 state constants. We also draw attention to a curious though minor anomaly in the properties of E and p; namely, that E has the smaller o,, yet is actually the deeper of the two states. Similar anomalies occur in the ion-pair states of ICI where all three members of the triad have been characterized (9) so that our lack of knowledge regarding D' is probably not responsible. The explanation is obscure. CONCLUSION
A previously unknown ion-pair state of IBr, p(Q = I), has been characterized in the range vB = O-9 by measurements of the /3-A band system. Irrational fl-doubling splittings observed in the lower vibrational levels of /I are due to electronicrotational coupling to a second ion-pair state, E O+,lying close to p. The constant describing this interaction is determined by a simultaneous, nonlinear, least-squares fit of term values for both E and /3. Because these two states converge to the same dissociation limit, namely, the ground states of the ions I+ and Bra, this coupling is expected to correspond with Van Vleck’s conditions for “pure precession.” and this proves to be the case. RECEIVED:
February
1 I, 1985 REFERENCES
I. R. G. GORDON AND K. K. INNES, J. Chem. Phys. 71, 2824-2839
(1979).
2. S. G. HANSEN, J. D. THOMPSON, R. A. KENNEDY, AND B. J. HOWARD, J. Chem.
3. 4.
5. 6. 7. 8. 9. 10. 11. I-7. IS. 14.
SOC. Farudu~~ Trans. II 78, 1293-1310 (1982); S. G. HANSEN, J. D. THOMPSON. C. M. WESTERN, AND B. J. HOWARD, Mol. Phys. 49, 1217-1229 (1983). G. W. KING. I. M. LITTLEWOOD, R. G. MCFADDEN, AND J. R. ROBINS, Chem. Phys. 41, 379-386 (1979). J. C. D. BRAND, U. D. DESHPANDE, A. R. HOY, AND S. M. JAYWANT. J. Mol. Specfrosc. 100,416428 (1983); J. C. D. BRAND, A. R. HOY, AND S. M. JAYWANT, J. Mol. Speetrosc. 106, 388-394 ( 1984). G. W. KING, I. M. LITTLEWOOD, AND J. R. ROBINS, Chem. Phys. 62, 359-367 (1981). J. C. D. BRAND, U. D. DESHPANDE, A. R. HOY, S. M. JAYWANT, AND E. J. WOODS, J. dfol. Spectrosc. 99, 339-347 (1983). M. S. CHILD, Mol. Phys. 32, 1495-1510 (1976). H. KNOCKEL, E. TIEMANN, AND D. ZOGLOWEK, J. Mol. Specfrosc. 85, 225-231 (1981). D. BUSSIERESAND A. R. HOY, Canad. J. Phys. 62, 1941-1946 (1984). M. DIEGELMANN, K. HOHLA, F. REBENSTROST,AND K. L. KOMPA, J. Chem. Phys. 76, 1233-1247 (1982). L. E. SELIN, Ark. Fys. 21, 479-525 (1962). E. M. WEINST~CK AND M. PRESTON, J. Mol. Spectrosc. 70, 188-196 (1978). J. T. HOUGEN, “NBS Monograph 115,” U. S. Govt. Printing Office, Washington. D. C.. 1970. J. H. VAN VLECK, Phys. Rev. 33, 467-506 (1929).