ROTATIONAL ANALYSIS OF THE RYDBERG SPECTRUM OF WATER

Two techniques for rotational analysis ofthe nd --lbl Rydberg spectra of H20 and D20 are discussed--a Coriolis coupled asymmetric top model for the room temperature 3d lbl cluster, and an extension of multichannel quantum defect theory to asymmetric tops, which is applied to recent jet cooled photoionization spectra of the nd lbl series converging to the (100) vibrational levels of H2 O+ and D2 O+. The quantum defects obtained by the two methods are in good agreement and new ionization limits to the (100) series are derived: IP(100) 104985(2) cm -1 for H20 and 104262(1) cm -1 for D20.


INTRODUCTION
This paper summarises recent work 1'2 on the rotational analysis of asymmetric top spectra in the Rydberg region, with particular reference to the strong nd lbl series of H20 and D203. The problems concern collapse of the electronic energy spacings as n increases, leading to a transition from Hund's angular momentum coupling case (b) to Hund's case (d). Even at n 3 the room temperature absorption spectra 3"4 show distinct rotational profiles for only three of the four allowed electronic states, while the fifth )"lA2(3db2 +--lbl) dark component has been observed by 3 + 1MPI. 5 At higher energies the five electronic origins ultimately all lie within the span of the rotational constants and recent jet-cooled photoionization spectra 6 of the series converging to the (100) vibrational levels ofH20 + and D20 + show just two strong rotational lines which merge towards each other as n increases.
Two methods of analysis are adopted. The first is a conventional Coriolis coupled asymmetric top treatment of the room temperature 3d lbl complex, 2 which was observed at high resolution in 19634 but subsequently only partially analysed. 7 Secondly the multichannel quantum defect theory of rotational channel interactions 8 is extended to asymmetric tops and applied to analysis of the photoionization series. Notice that a similar quantum defect theory analysis of the 3d complex, with separate rotational constants for the five electronic components would require an elaborate coupled vibrational-rotational channel treatment, of the kind so far attempted only for H2 .9 254 M.S. CHILD ET AL.

A CORIOLIS COUPLED ASYMMETRIC TOP MODEL FOR THE 3d COMPLEX
To the extent that the dominant interactions occur within a given nl complex the rotational structure may be modelled in terms of an upper state Hamiltonian of the form H A(Ja la) 2 + B(Jb lb) 2 + C(Jc-Ic) 2 + X (1) plus centrifugal stretching terms, where A, B, C and X are (2/+ 1) (2/ + 1) diagonal matrices representing the rotational constants and electronic origins of the different Z components of the complex. Written in this way, H is diagonal in j2 and/2, the total and electronic angular momenta respectively, and diagonalization with respect to the body fixed projections Ja and la is conveniently performed in a basis of parity adapted symmetric top states IZK;pePr) where Pe and Pr are parity labels with values 0 or 1.
The forward calculation of a spectrum by means of Eq. (1) is quite straightforward, but problems of assignment of the 3d -lbl complexes of H20 and D20, required for the reverse calculation, are complicated by strong Coriolis coupling, particularly between the 1A1 and aB1/Tstate components whose origins lie within only 16 cm -1 for both H20 and D20. As a consequence the upper level of any asymmetry doublet in say the/(1A1) component is so strongly coupled to the lower level of the/(1B1) component that the resultant mixed states concentrate spectroscopic intensity into two of the four possible transitions. At the same time the effects of any asymmetry terms involving (B C) are quenched, so that the upper rotational states with K' 4:0 behave like symmetric tops, while those with K' 0 (which are unaffected by the Coriolis terms) retain their asymmetric top character.
Another complication to the analysis is selective predissociation, which allows only K' 0, I branches in the/ and/' bands but K' up to 4 in the/7 bands. There is Figure 1 Assignment and simulation of the ff bands of H20. RYDBERG SPECTRUM OF WATER 255 also a strong perturbation (=150 cm -a) of the K' 0 levels of the/' state by a nearby linear 3pb2 -3al state. Figure 1 gives a reconstruction of the/ band of H20 and Table 1 contains the derived spectroscopic parameters. 2 Entries in brackets could not be determined by least squares optimisation, but values have been chosen to be consistent with reasonable geometries and inertial defects. Several of the latter are however sufficiently large to indicate the presence of interactions (perhaps with nearby 4p states) that cannot be assessed without inclusion of additional data.  Lew and Groleaua3; d assuming core stretching frequencies va 3213.0 cm -a and 2342 cm -a for H20 +14 and D20 +5 respectively; assumed common for H20 and D20.
The resulting ordering of the five components confirms that first suggested by the Hartree-Fock calculations of Goddard but make X non-diagonal. Given these ingredients, the quantum defect equations, which determine the energy eigenvalues for a set of interacting closed channels, may be expressed as 8 where [Ki + tan fij(E)]Z 0 (5) K a= (ilo) tan fi(E) r{Ry/(E E) } '/- (6) in which andj denote N+K + combinations and ois a short for ZK. Each half cycle of the term tan fl.(E) in Eq. (5) corresponds roughly to a new principal quantum number n and the increasing rate of change of fi.(E) as E approaches is responsible for the convergence of the various series. The coefficients Zj relate to amplitudes of different case (d) states iN+K +) in the wavefunction.
Optimised quantum defects and ionization energies, consistent with the simulation are listed in Table 1. Both the magnitudes of the defects and their orbital assignments are in good agreement with those derived from the 3d complex.