**Comparison of the contour for the band illustrated in Fig. 1.9 **
**with that of the origin band of BTD [Christoffersen, Hollas and Wright **

**1969] shows a close similarity in the gross features present in both the **
**high and low wavenumber series. ** **The transition in BTD is 1B**2** which is **

**the same as that predicted for IBF by the molecular orbital **
**considerations of Section 1.2. ** **Moreover, the alternation in the **

**intensity of successive R branch features strongly suggests that these **
**are groups of transitions each of which may be labelled by successive **
**values of the (pseudo-) quantum number K " .** **The intensity alternation is**

**cl**

(even K M : odd K" = 7:9). These maxima c o n f o r m to the predicted energies

cl cl

of R s u b b r a n c h transitions in a prolate symmetric top. F r o m Eq. (1.1), and the a p p r o p r i a t e selection rules,

AE = ABJ"(J" + 1) + 2 B ’ (J" + 1) + A(A - B ) K " 2 + 2 ( A ’ - B ’)K" + A' - B' , (1.5)

w h e r e A implies the difference between an excited and ground state quantity, and B = ^ (B + C). Therefore

2ABJ + 2B' + B .

**(****1****.****6****)**

Tu r n i n g points in the function AE(J), w h i c h c orrespond to reversals in the R subbranches (subbranch h e a d s ) , are a c h ieved whe n

AB = **2Bf**

2 J + 1

v «/

(1.7)

and so AB must clearly be negative in the present case. The w avenumbers of the subbranch heads are given by Eq. (1.8), where

v = v 0 + 2 (A* - B ?)k" + A ( A - B ) K " (1.8)

a a

Vn is the w a v e number of the K " = 0 band.

u a

The wave n u m b e r s of the observed series were fitted by least squares to a quadratic w h i c h returned the coefficient of the squared ter m in Eq. (1.8); this coefficient is independent; of the n u m b ering of the series members. The v a lue obtained w a s 0.00195 cm - 1 . This figure should, if these bands are R subbranch heads, provide a reasonable trial v a l u e for the quantity A ( A - B ) . The ground state infertial constants wer e c alculated from the geometry illustrated in Fig. 1.5, so yielding a

trial v a l u e for A ? - B f. The numbering of the series w a s then adjusted to force the coefficient of the linear t e r m in Eq. (1.8) to the value of 2 (A 1 - B ’). This gave K = 1 8 for the first observed band. (In BTD

**cl**

[Christoffersen 1969a] the first observed R head has K ~ 9 . ) a

1.6.7 The P Branch

The long series of line-like features to low wavenumber of the main pea k was expected to result from the commonly o c c urring high J, low K s t r u cture [Mcllugh 196obj. ide kinds of m o l e cules w h i c h show this type of structure have been reviewed by Ross [1971] and Brown [1969] and the

reason for its formation is now outlined. Gora [1965] obtained a formula for the energy levels of an oblate top w h i c h have high J values and low K values. This is roughly the region to the right of the upward running d i a gonal in Fig. 1.6. Brown [1969] obtained similar expressions for pr o l a t e tops. For planar molecules, M c Hugh [1968b] showed that G o r a ’s equation may be considerably simplified to

E = C(n + 1 ) 2 - S (1.9) w h e r e m = J - K c n = J + m = 2 J - K c S = %U2(A-!-B) m2 = 2 m 2 + 2m + 1 .

In terms of m and n the selection rules for the r^P and subbranches
of a type B band, w h i c h are degenerate in the *oblate* top region, become:

Am = AJ - AK = 0

**c**

An = -1

A p p l y i n g these rules to Eq. (1.9) yields, for these transitions,

AE = A C n 2 -- (2n + 1)C" - AS , w h e r e

AS = ^ 2 (a a + a b ) •

**(**

**1**

**.**

**10**

**)**

**(**

**1**

**.**

**11**

**)**

The v a l u e of AS, for a fixed value of n and various ra, is small in

comp a r i s o n wit h the n C M terms. So the transitions wit h the same value of n = 2 J - are almost coincident in energy. For example, the transitions

75 74 73 1,75 2,73 3,71 ■*- 76 <- 75 74 0,76 ; 1,74 ; 2,72 ’ 0,75 1,73 73 2,71 76 •*- 75 74 1,76 2,74 3,72 e t c .

are all ver y nearly coincident; the transitions wit h initial and final J values because they have the usual oblate top d e g e neracy for low K , and those w i t h different sets of J values b e c ause they have the same n value.

**The members of the high wavenumber series were thus fitted by **
**least squares to a quadratic, and yielded -0.000523 cm 1 for the **

**coefficient of the squared term. ** **This was equated with AC from Eq.**
**(1.11). ** **Not all the series members were included in the fit, for the **
**region towards the end of the band becomes irregular in both the spacing **
**and the intensities of the peaks, as will be discussed in a later section.**