Volume 51, number 2
RYDBERG
SERIES
IN THE VACUUM
P. CijRTLER II. fnstitut fi V.
15 October 197’7
CHEMICAL PHYSICS LETTERS
IN THE ABSORPTION ULTRAVIOLET
Experimentalphysik.
SPECTRA
OF H20
AND D20
*
Universitcit Hamburg. D-2000
Hamburg 50.Germany
SAILE
Sektion Physik. Universitn”rMiinchen, D-8000 Munich 40. Germany
and E-E. KOCH Deutsches Elektronen-Synchrotroron DESY,
D-2000 Hamburg 52. Germany
Received 4 July 1977
The photoabsorption cross section of molecularHz0 and D20 has been determined in the range from hv = 10 eV to 20 eV with 0.03 A resolution. A refined analysis of the Rydberg series including the rotational line shapes of several bands to locate the band origins and a comparison with recent ab initio calculations is given. In the region of continuous absorption we have assigned a p-type and an s-type Rydberg series leading to the 2At and the *Bz state respectively with quantum defects 6 = 0.75 and 6 = 1.36.
1. Introduction
Water vapour is important because of its nearly universal appearance. Consequently the ground and excited states of the water molecule have been the subject of a large number of detailed investigations. For a discussion of the relevant literature up to 1974 we refer to Herzberg’s [l ] and Robins [2] books. In spite of considerable recent theoretical [3--81 and experimental [g-12] efforts several problems concerning the MC
Hz0
m
ultraviolet
(VUV)
absorption
spectrum
of
and
D20, in particular the nature and assignment of ihe absorption bands in the ionization continuum region, need further clarification. We report in the present paper on new measurements of the absorption cross section of H20 and D20 under high resolution in the VUV range for photon energies hv = 10 to 20 eV. In this range we expect * Work supported by Bundesminsterium fiir Forschung und Technologie BMFT.
386
transitions originating from the uppermost three orbitals: In the ground state the molecular orbital configuration is
where the uppermost three orbit& have vertical ionization energies of 12.62 eV, 14.75 eV and 18.54 eV respectively [13,14]. The aim of our investigation is a detailed assignment of Rydberg series originating from the 1b2, 3a, and lb, orbitals. This is done by comparing our results with high resolution photoelectron spectra [14] and with theoretical calculations [5--81. As odginally suggested by Mulliken [ 151 and corroborated quantitatively by the recent calculations of the orbital sizes by Goddard and Hunt [5] the simplest view of the excited orbitals is to consider each as arising from an n > 3 Rydberg atomic orbital modified by the molecular field [I 6 1.
Volume 51, number 2
2. Experiments and results For our measurements we have exploited the COMbination of intense synchrotron radiation from the DORIS storage ring at DESY [17] with a high resolution 3 m normal incidence scanning monochro~tor with a vertical dispersion plane [ 18,193. fn brief, synchrotron radiation emitted from electrons within the storage ring is focussed onto the entrance slit of the 3 m instrument, which has a resolution of 0.03 a in first order. The light emerging from the exit slit traverses a 60 cm long absorption chamber, is converted into longer wavelength photons by a sodium salicylate screen deposited on a glass window and is detected by a photomultiplier (EM1 9804). The gas pressure in the windowless absorption cell ranged from 1 X IO-’ to 1 X 10m4 torr, as measured by a membrane vacuummeter (Datemetrix model 531). Spectra for the absolute photoabsorption cross section of El20 and D20 are displayed in fig- I. Small
01
600
15 October 1977
CHEMICAL PHYSICS LE’ITERS
I 700
I 800
1 so0
portions of the spectra are shown in the inserts in fig. 1, in fig. 2 and in the insert in fig. 3 on an expanded scaleFrom these, an idea of the resolution and accuracy of our data for determining detailed fine structure may be obtained- The spectra shown in fig. 1 are replotted on a photon energy scale in fig. 3 together with absorption data at lower photon energies [9] and with our assignment (see beIow). The absorption spectrum (fig. I) shows a range of strong structured bands between 1250 a and = 1000 a, the range of the A, B, C and D series first observed by Price [20]. This is followed to shorter wavelengths by a broad continuum with vibrational progressions superimposed. With the exception of additional details displayed here, the main features of the absorption spectrum are in good agreement with previous absoiute cross section measurements as reported by Katayama et al- [12]_ A small part of the spectrum extending from 1220 .a to 1240 a has been studied and analyzed previously by Johns [21] with an even higher resolu-
I Iwo
r
I
I
1100
uoo
I 1300
WAVELENGTH (A 1
Fig. 1. Absolute absorption cross section of molecular Hz0 and D&I in the range 1250 li to 600 A. The range of the lbr -P 3d transitions is shown on an expanded scale in the insert. For the assignments see table I and text. 387
CHEMICAL PHYSICS LETTERS
Volume 51. numbx 2 tion of 0.005
A using photographic
recording_ Within
the limits of our “low” resolution nearly perfect agreement between this study 2nd our measurements was found *. A vibrational analysis of the band systems with origins at 1240 Iiand 1219 A has been given by Bell 1231 (see table 2).
3. Discussion In the discussion we confine ourselves to the Rydberg transitions originating from the 1b,, 3a I and 1 b, orbitals. The analysis of rotational line shapes using model calculations based on the asymmetric rotator [22] enables us to locate precisely the band heads of several Rydberg transitions originating from the uppermost 1 b, orbital. The results of such an analysis are presented for the lb1 --f 3pal(OOO) transition in fig. 2. The fit has been obtained with the rotational constants as determined by Johns [21], namely for the ground state: A = 27.88, C= 9.29 and K = -0.44 and for the excited lB, state A = 25.67, C= 8.55 and K = -0.53. The agreement of this simple model calculation assuming the same geometry for the ground and excited state with the experiment is excellent_ A summary of our assignment is given in table 1 * A detailed presentation and discussion of the results is given inref. 1221. _ 1
1
;s, -
3Pq
I
I
I
I
I
1
. ‘a
52
-LOO
ENERGY
300
(cm41
Fig. 2. Comparison of the experimentally determined band pr@ file for the lb1 -+ 3pal (000) transition (solid curve) with a band profile calculated for an asymmetric rotator (dashed curve). 388
15 October 1977
where we also make comparison with the results of recent theoretical investigations [5-S]. The absorption bands above the first ionization potential are superimposed on a strong continuous background. They are hitherto unassigned, although it has been conjectured [2,12], that the structured bands and progressions belong to Rydberg transitions originating from the 3al and lb, orbital. We have been guided for our assignment by the close correspondence of a vibrational progression associated with a particular Rydberg transition with the vibrational structure observed for the ionic states [ 13,14]_ Since it is difficult to identify the O-O transitions both in the photoelectron and the optical absorption spectrum we have used for the discussion of term values vertical ionization potentials (II?,) as derived from the photoelectron spectra [13,14] _ Furthermore, as recently pointed out by Schwarz [24], the vertical energy difference of two eiectronic states is more suitable in many cases for a comparison of experiment with theory. 3. I. s-like series As regards the s-like Rydberg series in H,O, Robin [2] has noted already a remarkable consistency of the term values regardless from which orbital they originate. The broad absorption bands at around 7.44 eV and 9.85eV have been assigned by him as lb1 --f 3s and 3a, + 3s respectively. This yields together with the IP,‘s at 12.62 eV and 14.87 eV term values of 5.18 eV and 5.02 eV respectively_ Robin’s assignment is also in accord with the most recent ab initio calculations for these transitions (see table 1). Taking the third IP, at 18.86 eV and assuming a term value of roughly 5.0 eV, we expect the 1 b, + 3s transition at around 13.8 eV. In this range strong continuous absorption and p-like states are observed. The 1 b2 + 3s transition, which is expected to be broad and diffuse, may well additionally contribute to the cross section in this region. We assign the absorption bands at around I6 eV to 17 eV to the 1 b, + 4s transition_ This assignment is corroborated by the one to one correspondence between the structure in the absorption cross section and the photoelectron spectrum as determined by Karlsson et al. [ 141. Furthermore, the resulting term value of 2.0 eV for the 4s transition is consistent with this interpretation. On the basis of this term value one would expect 4s transitions originating from lb, and
Volume 51, number 2 Tabie 1 A~ig~en~
15 October 1977
CHEMICAL PHYSICS LETTERS
of Rydberg ~f~~sjt~oRsin the abso~tion spectrum of Xi20 and 020. All energiesare in eV. Subscript VI verticalenergies
Orbital, ionization energy, binding properties% b) H20 D20
Transitions assignment
experiment
tiE0rY
H20
lbr + 3s 4s 5s
lb1 12.62 12.62 (1st band) non bonding perpendicularto molecularplane
13.897 13.988 (1st band) 14.87, 14.96, weakly O-H bonding parallelto molecularplane lbz 17.22 17.26 stronglyO-H bonding parallelto molecularplane a) Ref. 1131.
d)
0.72 0.65 0.12 0.07 0.05 0.00
7.30 10.64 11.66 LO.04 10.16 11.07 11.17 Il.17
7.44” c) 10.64 9.998 10.171 10.990 11.041 11,057 fl.122
0.72 0.67 0.11 0.06 0.04 -0.02
10.011 10.171 10.966 11.055 11.070 11.130
4PaI 4ph 4dar 4dbl
il.374 11.432 il.729 11.770
0.69 0.60 0.08 -0.01
Il.385 0.71 i 1.427 0.65 11.752 0.08 11.793 -0.0X
5P 5d
11.890 12.061
0.66 0.05
11.901 12.075
0.70 0.08
6~ 6d
12.120 12.235
0.74 0.02
12.155 12.254
0.69 0.04
7P 7d
12.288 12.337
0.52 0.01
12.300 12.365
0.65 -0.07
8P 8d
12.361 12.399
0.63 0.07
12.386 12.423
0.65 0.03
9P 9d
12.411 12.448
0.7‘7 -0.03
X2.438 12.468
0.75 0.03
-P -d
12.612 12.612
0.67 0‘03
12.637 12.638
0.70 0.01
9.85 C) 212.9
4P
13.5,
0.83
13.9,
0.75
5P
14sv
0.74
14.2v
0.70
m
lb2 --c3s
b, Ref. [14].
6
3Pal 3Pbr 3dal 3da2 3dbt 3dar
3at -, 3s 4s
3%
DzO
6
H2O
4s
a14.9,
00
c) Ref. [2]_
1.38
18.9” d, Ref. ISI.
el3.8” 17.0”
7.22
10.06 10.16
9.93 10.32
9.02 9.48 9.61
9.82
9.80
9.54
11.47 11.92 12.08
11.21 11.72
11.42 11.48
135
f) ReL [6].
g) 7.30
19.0” e, Ref. [ Sl_
9
‘7.61
*115.0v
=13.8v 169,
e)
8) Ref. [75.
Volume S 1, number 2
CHEMlCAL PHYSICS LETTERS
PHOTON ENERGY
(eV)
Fig. 3. Rydberg assignments for the absorption bands in the spectra of H20. For the range below 10 eV the spectra as determined by Watanabe et al. [9] are shown. The dashed curves are the vibrational bands observed in the photoelectron spectra [lb]. The insert shows the observed fme structure for some of the bands in more detail.
3al at around 11 .O eV and 12.87 eV respectively. This expectation for the 1b z + 4s assignment is in good
agreement with the excitation energy cal+ated by Goddard and Hunt [S]. For the 3al -+ 4s transition it
Table 2 Vibrational energies for the ul and v2 mode observed in the present work for various states of Hz0 and D20 as compared to the energies of the same modes in the ground and ionic states. All energies are in meV
is not possible tp give a unique assignment. Nevertheless a contribution of 3a, + 4s to the absorption at around 12.9 eV_is not unlikely. 3.2. p and d-like series Our assignments for the p- and d-like Rydberg transitions originating from the I b 1 orbital are given in table 1. All the sharp and structured bands at around 1 I-.0 eV can be assigned satisfactorily on the basis of their rotational contours to the four optically allowed lb, + 3d transitions [22] (see aIso the insert in fig, 1). Further, we note that for the lower members of the pand d-like series there is excellent agreement between our assignment and the excitation energies as calculated by Goddard and Hunt IS]. The 3al + 4p and + 5p trmSitiOn5 are indicated in fig_ 3. Although here is a strong overlap of vibrational bands belonging to
390
H2O
D20
State
r&eV,
(meV)
Vl (mev)
ground state a) ionic state 2Bt b) 3pbl this work BeU C) 3pal tbii work Bell c) 3d+ 3daz, 3db, 3da; ionic state 2 Al b) 3al -+ 4p
453 402 399
198 177 204
331 293 298
405
203
295
395 394 381
173 174 -
407 400
-
287 290 286 315 300
“2
3a, - Sp ionic state 2~2 h) lb2 + 4sal a) Ref. [l].
122 117
r;eV] 146 132 153 152 131 129 89
365
128 185
267
FE 134
342
180
259
133
b, Ref. [14].
c) Ref.
(231.
Volume 51, number
2
15 October 1977
CHEMICAL PHYSICS LE-lTERS
different p-like transitions as well as to the s-like states, as discussed above, our assignment is supported by the close correspondence of the structures in the absorption and photoelectron spectra as well as by the resulting term values. The detailed fine structure observed for several vibrational bands belonging to these Rydberg transitions (see the insert in fig. 3) is still a problem. Aside from rotational structure the deviation of the molecular potential from spherical symmetry results in Liehr splitting effects [16] of the p-like final states_ At the same time a Renner-Teller splitting [25] in the nearly linear geometry of the excited states is expected. Without detailed calculations it is at present premature to give a more elaborate discussion of this point. Finally we turn to the vibrational analysis for several of the observed transitions. We have summarized the main points in table 2, where we give the frequencies of the ground state and the ionic states for comparison [22].
References [ 11 G. Herzberg,Molecularspectraand molecularstructure, Vol. 3. Electronic spectra and electronic structure Jf polyatomicmotecules(Van Nostrand,Princeton,1966). [ 21 M.B. Robin,Higherexcited statesof polyatomicmolecules,Vol. 1 (AcademicPress,NewYork, 1974). [3] R.P. Hosteney, A.R. Hinds, A.C. Wahl and M. Krauss, Chem. Phys. Letters 23 (1973) 9. [4] J.A. Horsley and W.H. Fink, J. Chem. Phys. 50 (1969) 750. (51 W.A. Goddard III and W.J. Hunt, Chem. Phys. Letters 24 (1974) 464.
[6] R.J. Buenker and S.D. Peyerimhoff, Chem. Phys. Letters 29 (1974) 253. [7 ] D. Yeager, V. McKay and G.A. Segal, J. Chem. Phys. 61 (1974) 755. 18) N-W. Winter, W.A. Goddard III and F.W. Bobrowicz, J. Chem. phys. 62 (1975) 4325, and references therein. [9] K. Watanabe and M. Zelikoff,J. Opt. Sot. Am. 43 (1953) 753. [ 10) A. Skerbele, M. DilIon and EM. Lassettre, J. Chem. Phys. 49 (1968) 5042; E.N. Lassettre, A. Skerbele, M. Dill&x and K. Ross,
J. Chem. Phys. 48 (1968) 5066. [I I J S. Trajmar, W. WiUiams and A. Kuppermann, J. Chem. Phys. 54 (1971) 2274. [12] D.H. Katayama, R.E. Huffman and C.L. O’Bryan, J. Chem. Phys. 59 (1973) 4309. [ 131 D.W. Turner, C. Baker, A.D. Baker and CR. Brundle, Molecular photoelectron spectroscopy (Wiley, New York, 1970). [ 141 L. Karlsson, K. Mattsson, R. Jadmy, R.G. Albridge, S. Pinchas, T. Bergmark and K. Siegbahn, J. Chem. Phys. 62 (1975) 4745. [ 151 R.S. Mulliken, J. Chem. Phys. 3 (1935) 506. [16] A.D. Liehr, Z. Naturforsch. 11A (1956) 752. 1171 E-E. Koch, C. Kunz and E.W. Weiner, Optik 45 (1976) 395. [ 181 V. SaiIe, P. Giirtler, E.E. Koch, A. Kozevnikov, M. Skibowski and W. Steinmann, Appl. Opt. 15 (1976) 2559. [ 191 P. Giirtler, V. Saile and E.E. Koch, Chem. Phys. Letters 48 (1977) 245. [20] WC. price, J. Chem. Phys. 4 (1936) 147. [21] J.W.C. Johns, Can. J. Phys. 41 (1963) 209.
[22] [231 [24) 1251
P. Giirtler, Diplomarbeit, UniversitZt Hamburg (1976). S. Bell, J. Mol. Spectry. 16 (1965) 205. W.H.E. Schwarz, J. Electron Spectry. 6 (1975) 377. J-A. Pople and H.C. Longuet-Higgins, Mol. Phys. 1 (1958)
372.
391
