0 (Degree)
6. Electronic states of lanthanide oxides
110 K. BALASUBRAMANIAN
alkaline-earth monohalides while the latter group consisted of Ln +3 (4f"-1) and F - and a lone pair ((~6s) 2 localized on the lanthanide atom. Gotkis (1991) found that the energies of the two configurations are close for D y F and TmH. He has predicted the R~
and co e values for the ground state and excited states of these halides. He has discussed the Johnson rule for the variation of properties of lanthanide halides. For the actual tables of molecular constants that Gotkis predicts, the reader is referred to his paper.
Dolg etal. (1991b) has recently used the C A S S C F / M R C I / C P F method in con- junction with quasi-relativistic pseudo-potentials to study both YbF and YbH in- cluding s p i n - o r b i t coupling. For YbF, they computed the molecular constants as R~ = 2.045 ,~, D O = 4.87 eV and (o e = 492 c m - 1, in excellent agreement with the experi- mental values of R~ = 2.016 A, D o = 4.80 eV, or > 5.36 eV, ~o e = 502 cm - 1. The ground state of YbF was found to be a f2=½ state arising from the 4flg(32(sz'g.4(~ 2 (252+) configuration. An excited A 252 + state of YbF was also found by Dolg et al. (1991b) with T e = 0.44 1.51 eV depending on the level of treatment. The predicted ground state of YbF was in accord with the ESR studies of Van Zee et al. (1977).
included in the ligand-field model. We will discuss their results on CeO, P r O and SmO in the individual sections.
In the ensuing sections, we discuss experimental spectra and theoretical studies on individual oxides. We restrict ourselves to those species which were studied extensively in the recent years either experimentally or theoretically.
6.1. LaO
Earlier experimental studies and known electronic states of LaO are summarized in Huber and Herzberg (1979). A recent spectroscopic study is due to Carette (1990). The ground state of LaO is well established as the X2"~+ state with R e = 1.825A, c~ e = 813 c m - x. There are several excited states of A 2A, A 21-I, B 2• + C 21~, D 2~--~ and F 2~ symmetries. Recent experimental studies on LaO and other oxides include the pulsed Fourier-transform microwave spectroscopy of YO, LaO, ZrO and HfO by Suneram et al. (1991). The related YO has also been studied extensively. In particular Steimle and A1-Ramadin (1989) have studied the microwave-optical double-resonance (MODR) spectra of YO. Childs et al. (1988) have obtained the fine and magnetic hyperfine structure in the X zE + and A 21-I states of YO.
There are several theoretical studies on LaO and related lanthanide oxides. We have already mentioned the ligand-field theory model calculations of Field (1982) as well as Carette and Hocquet (1988). More recently, Kotzian et al. (1991a, b) have applied the I N D O technique (Pople et al. (1967) extended to include spin orbit coupling [see also Kotzian et al. (1989a, b)] to lanthanide oxides (LaO, CeO, G d O and LuO). The authors call it I N D O / S - C I method. The I N D O parameters were derived from atomic spectra, model Dirac Fock calculations on lanthanide atoms and ions to derive ionization potentials, S l a t e r - C o n d o n factors and basis sets. The s p i n - o r b i t parameter (~) is derived from atomic spectra in this method.
The I N D O / S - C I computations were made on LaO by Kotzian et al. (1991a, b) at an experimental bond distance of 1.826 A. For LaO, the ground-state configuration is ( l ~ / O 2 s ) z ( l ~ / O 2 p ) 4 (2~/O2p) 2 (3~/La6s) 1 (l~)/La5d) ° (2~/La6p) ° (4~/La6p) ° (3T~/
LaUf)° ( 1 ~/La4f)° ( 5~/La4f )o (28/La4f)° (4~/La5 d) o (6~ / La 5 d) ° .
Table 52, reproduced from Kotzian et al.'s work, compares the I N D O / S C I energy separations with experiment for several electronic states of LaO. It is evident from table 52 that the I N D O / S - C I method predicts the energy separations for these compounds reasonably well. Kotzian et al. also computed the transition moments for the observed A*--~C, B~-~X, C~--~X, D~--,X and F~--~X systems.
6.2. CeO
There are several recent experimental studies on the CeO diatomic molecule. Schall et al. (1986) have studied CeO using the sub-doppler Zeeman spectroscopy. Again, the ligand-field model is so successful in explaining the observed spectra due to the ionic nature of the diatomic lanthanide oxide. Linton et al. (1979, 1981, 1983a, b) as well as Linton and Dulick (1981) have studied the electronic spectrum of CeO using absorp- tion, emission as well as laser spectroscopic method. There are many 0 - 0 bands for
112 K. BALASUBRAMANIAN TABLE 52
Calculated and experimental states of LaO. State energies To are given incm -1. The molecular spin-orbit constant A is defined by the relation (JI2ASEIHso[JI2ASE) = A A S . Reproduced from Kotzian et al. (1991a).
INDO/S-CI Experiment
State Config. T e A State T e A
12Z~/2 30 100% 0 X 222+ 0
1 zm3/2 15 100~ 8488 353 A' 2A r 7468.9
1 2A5/2 15 100~ 9195 8168.4
1 2FI1/2 2~ 99~ 13856 12635.7
1 z1-I3/2 2V. 100% 14 724 869 A217r 13 497.6
22Z~/2 40 93% 19715 BzE + 17837.8
2217111/2 3~ 94% 22986 22618.9
2 2I~3/2 3'~ 79~ 23 241 255 C 2Flr 22 839.6 2,3 20%
1 2 . lqb 93~ 23310
2 5/2 560
12(I)7/2 lqb 100~ 24990 2 m3/2 25 79~ 24788
3~ 21% 451
2 2A5/2 25 93~ 25 691
3 2E~/2 50 90~ 26007 D2]~ 26959.0
3 21-I 47z 99% 30 180 F 2E 28 049.0
2 1/2 408
3 173/2 4"~ 99% 30588 42]~+/2 6~ 100~ 41616
350.5 862.7
221.4
Ce 2 + CeO
4 0 0 0
E 5 0 0 0 o
w 2 0 0 0 z
I 0 0 0
,Q, =j= ,O,= Jo-I ,.q=%-2 D,= do-3
J
~ 3
T °
2012cm -I
- - 3
- - 4 ~ 0 +
- - I
~ 0 -
Q,=da-4
_ _ , 0 + - - I
~ 0 -
Fig. 36. Energy-level diagram of Ce + 2 arising from the 4f6s configuration and the corresponding states of the diatomic CeO. All states of CeO are arranged by their f2 values. Reproduced from Schall et al. (1986).
C e O arising from electronic transitions between various f~ components of excited states and the ~ states arising from ... (4f)(6s) electronic configurations. The CeO molecule is also the simplest lanthanide oxide containing a single 4f electron.
The electronic states of CeO are best rationalized in terms of the electronic states of Ce + 2 ion since the bonding in CeO is best described as Ce + 2 0 - 2 ionic bond. Figure 36 shows the energy level diagram of Ce + 2 4f6s configuration and the corresponding state of C e O [reproduced from Schall et al. (1986)]. It is evident from fig. 36 that there are 16 f~ states arising from the Ce + 2 4f6s configuration itself.
Table 53 shows the spectroscopic constants of CeO derived by Linton et al.
(1983a, b) from their spectra. As seen from table 53, the X 1 ground state with .(2= 2 and X 2 state with .(2 = 3 are very close to each other. Note that X 3 and X 4 states arise from the same principal 2-s state but the splitting between (X 1, X2) duo with (X3-X4) duo is roughly the atomic Ce +2 splitting between J = 2, 3 and J = 3,4 pairs (see fig. 36). The energy levels in table 53 approximately correspond to the levels in fig. 36.
TABLE 53
C o n s t a n t s for the l o w - l y i n g states of C e O (cm-1). R e p r o d u c e d f r o m L i n t o n et al. (1983a, b).
State Ja Jc To B 0 107 D o AG1/e N o t e
U 3 0 + 3 ~ *4457.7 (30) 0.367 - -
U z 1 4 27 "4133 (5) - - c
T 1 0 4 iv 3821.5 (30) 0.375
V 4 1 3 ~ *3642 (5) - c
V 3 2 4 27 3462.6 (25) 0.355 - 820.7
W,, 2 3 27 2771.7 (15) 0.35999 (1) 2.21 (1) 823.4 d
W 3 3 4 27 2617.3 (21) ~ 0.356 - 824.7 e
X 4 3 3 ~ 2140.6 (15) 0.35658 (2) 2.72 (2) 824.1 f
X 3 4 4 7 2039.8 (21) 0.35327 (1) 2.24 (1) 822.1 g
U 1 0 + 3 ~ ' 1 9 3 1 . 8 (30) 0.377
V 2 1 3 2 s "1869.7(30) 0.343 - -
V1 0 - 2 ~ 1679.4 (25) 0.35788 (1) 2.52 -
W 2 2 3 5 912.2 (15) 0.36139 (6) 7.3 (4) 823.0 h
W 1 ! 2 25 811.6(25) ~ 0.361 - i
X 2 3 3 ~ 80.3 (15) 0.35692 (1) 2.71 (1) 822.8 j
X 1 2 2 ~ 0 0.35454 (1) 2.46 (1) 824.3
* Levels of the c o r r e c t f~, closest to the p r e d i c t e d positions.
N u m b e r s in p a r e n t h e s e s r e p r e s e n t e s t i m a t e s of the s t a n d a r d d e v i a t i o n in the last t w o digits.
b W i t h the e x c e p t i o n s of the X 1 a n d X 2 states, u n c e r t a i n t i e s in AGI/2 are ~ 2 c m 1.
c T h e s e s t a t e s h a v e each been o b s e r v e d o n l y once, in fluorescence, a t J ~ 25: their B values are n o t k n o w n . O r i g i n a l l y l a b e l l e d v (2).
c O r i g i n a l l y l a b e l l e d w (3).
f 103 ~. = 1.4 g 103(~ = 1.27
h O r i g i n a l l y l a b e l l e d u (2).
i O r i g i n a l l y l a b e l l e d y (1).
J 103~t - 1.9
114 K. BALASUBRAMANIAN
A combination of laser-induced fluorescence with classical absorption and emission spectroscopy has yielded a wealth of data on the excited electronic states of CeO.
However, as noted by Linton et al., the spectroscopic data of upper states is less complete and are shown in table 54. Linton et al. (1983a, b) used empirical notation taken from atomic spectroscopy to designate these states.
The vibrational frequencies (Gx/2, e~e) are of the order of 800 c m - 1 for the low-lying states of CeO. Linton et al. (1983a, b) observed several laser-induced fluorescence transitions of CeO. They are shown in fig. 1 of their paper. They have provided a rather detailed and extensive analysis of their fluorescence excitation spectra. The reader is referred to their original paper for further discussion of their spectra.
Linton et al. (1983a, b) noted that the 4f6s configuration of Ce +2 exhibits a j - j rather than l-s coupling. This is expected in view of the fact that the 4f orbital spin-orbit coupling is larger than the 1F3-3F 3 energy separation. Hence, they con- clude that lanthanide oxide confgurations including 4f electrons would tend towards Case (c) coupling.
It should be noted that although Ce +2 ion has a 4f 2 configuration, the ligand-field calculations of Linton et al. (1983a, b) predict reordering of free ion configurations for the oxides:
4f6s << 46 2 < 4f5d < 4f6p.
Hence, Linton et al. conclude that for all lanthanide oxides, except EuO and YbO, the lowest states should arise from (4f)"6s configuration rather than (40" ÷ 1.
Schall et al. (1986) have deduced the electronic G value for four lower states of CeO and compared them with the values derived from the ligand-field theory. The agree- ment was found to be very good.
Kotzian et al. (1991a, b) as well as Kotzian and R6sch (1991a, b) have applied the INDO/S-CI method extended to include spin-orbit coupling on the diatomic CeO.
They have studied 16 electronic states of CeO arising from the 4f6s configuration of Ce ÷ 2 at the experimental R e of 1.820 A. The results of their computations are shown in table 55. Note that Kotzian et al. have also compared the INDO/S-CI results with ligand-field theories LFT1 and LFT2. As seen from table 55, the agreement between the experimental values and the INDO/S-CI as well as ligand-field models is quite good.
Kotzian et al. (1991a, b) also find that low-lying states of CeO arise from the 4f6s configuration. The charge-transfer excitations O--* Ce were omitted in the Kotzian et al.'s INDO/S-CI since the energy for this excitation is > 55 000 c m - 1. Overall, the experimental trend is reproduced by the INDO/S-CI except that two pairs of states (U10 +, and V21; U/1 and U 3 0 +) have reverse order in the INDO/S-CI calcula- tion compared to the experiment. Mulliken-population analyses of Kotzian et al.
(1991a, b) revealed that the oxygen atom has O(2S 1"923 2pa 1"731 2p~ 3'046) population in the ground state. The corresponding Ce population is Ce 4f, T M 4f~ °'329 4f~ °'284 4fq~ o.286 6S 0.920 5d 0.308 5d~ 0-882-
6.3. PrO
PrO was first studied at complete low resolution by Shenyavskaya et al. (1973).
These authors reported vibrational analyses of 22 electronic transitions of PrO in the
S t a t e a T o B0 107 D O AG1/2 Transitions b [28.6] 1 28 596.1 (e) 0.36122 3.04 - [28.6] 1 - V 1 0 -
(f) 0.36079
[26.7] 4 E a 26715.2 0.35294 4.9 795.5 [26.7] 4 X 3 4
[26.2] 3 H 2 26200.0 0.3514 2.2 732.54 [26.2] 3 - X z 3
[26.1] 2 F 1 26067.5 0.3522 3.75 - [26.1] 2 X 1 2
[25.3] 3 G e 25 292.3 0.3502 3.03 733.90 [25.3] 3 ~ X 2 3 [25.0] 2 E 1 25011.5 0.34863 2.81 744.3 [25.0] 2 - X 1 2
[23.7] 0 23 674.3 0.35348 0.48 - [23.7] 0 - - V 1 0 -
[22.7] 0 - 22 722.8 0.35407 2.63 [22.7] 0 - - V 1 0 -
[22.6] 5 D 3 22 556.0 0.35069 2.61 786.0 [22.6] 5 - X 3 4
[22.5] 1 22 505.8 (f) 0.3576 6.2 - [22.5] 1 ~ V 10-
[22.5] 3 h 2 22498.4 0.3568 5.0 792.3 [22.5] 3--*W z 2
F.-Xa 3, -X 4 3, -W 2 2, -W~ 2 [22.0] 4 A 4 22012.3 0.35443 2.81 768.0 [22.0] 4 - X 4 3
[21.7] 4 21 713.2 0.35353 2.14 [2L7] 4 - X z 3
[21.4] 1 D~ 21 379.2 0.35241 2.75 - [21.4] 1 - X 1 2
0.35203 2.59
[21.1] 2 g2 21 061.9 0.35662 3.98 - [21.1] 2 - X 2 3; [ 2 1 . 1 1 2 - W 2 2 F.-X 2 3, -X 4 3, -W z 2, -W 4 2
[20.9] 4 F 2 20914.5 0.35294 2.97 - [20.9] 4 - X 2 3
[20.3] 3 C 1 20273.8 0.34988 2.99 783.6 [20.3] 3 - X 1 2
[19.9] 1 19926 - - - [19.9] l - X 1 2
[19.313 19 287.5 0.3485 0.4
[18.4] 4 C 3 18 386.2 0.34176 2.3 [17.2] 3 e 2 17 169.5 0.35037 2.44
[16.7] 1 16 714.8 (e) 0.35616 4.28 (f) 0.35643 3.45
[16.5] 2 B 1 16 524.2 0.3436
[16.5] 4 E 2 16495.4 0.35363 5.1
[16.0] 3 D 2 16039.2 0.35953 5.3
[15.8] 4 C z 15813.8 0.35216 3.03
[15.5] 5 B 3 15489.4 0.34534 2.45
[14.7] 3 14701.6 0.35255 2.51
F.-X 1 2, -W 4 2, -V 1 0 - , -V 2 1,-V 3 2 , - U 10 +, -U 3 0 +, -T 1 0 - a
- [ 1 9 . 3 ] 3 ~ X 4 3
750.7 [18.4] 4 ~ X 3 4
F.-X 3 4, -X 2 3, -X 4 3, -W 3 3 765.0 [17.2] 3 ~ X / 3
F. -X l 2, -X 2 3, -X 3 4, -X 4 3, -W 2 2, -W 4 2
- [ 1 6 . 7 ] I ~ V 1 0
F. -X 1 2, -W 1 1, -W 2 2, -W4 2, V 1 0 - , -V 2 1, -V 3 2, -U 1 0 +, -U 3 0 +, -T 1 0 - 720.7 [16.5] 2 , - X ~ 2
F. -X 1 2, -X 2 3, -X 4 3, -W 1 l, -W 2 2, -W 3 3, - W 4 2 753.9 [16.5] 4 ' - X 2 3
F. -X2 3, -X 3 4, -X 4 3, -W2 2 , -W 3 3
[16.0] 3 ~--- X 2 3
[14.2] 3 A a 14 201.8 0.36024 4.48 -
[14.2] 0 - 14 197.0 0.35216 7.8 -
[13.9] 4 B 2 13 884.3 0.34711 2.86 747.39
[15.8] 4~--X 2 3 [15.5] 5 ~ X a 4 [14.7] 3 * - W 2 2, [14.7] 3 *-- W 2 2 [14.2] 3 ~ X a 4 [14.2] 0 - *--V 1 0 [13.9] 4,--- X 2 3, [13.9] 4 ~ X 4 3 0.35974 4.97
[13.2] 1 a 1 13201.6 0.35921 5.51 - [13.2] l~--~X 1 2
[12.8] 2 A 2 12768.0 0.3535 4.5 [12.8] 2,--~X 2 3
[12.6] 3 A 1 12595.8 0.34672 2.90 1-12.6] 3,--,X1 2
a Designations of states prior to Linton et al. (1983a, b) are given in the second column.
b F. indicates a transition observed in fluorescence.
116 K. BALASUBRAMANIAN TABLE 55
Calculated and experimental states of CeO of the configuration 4f6s [reproduced from Kotzian et al.
(199 la)]. Energies are given in cm- 1. In the first column the experimental labeling is given. A is the projection of the total orbital angular momentum, .O the projection of the total angular momentum in the molecular system, and J~ the value of the atomic total angular momentum from which the molecular state originates.
The values of A and Ja, are taken from the leading determinant. Ligand-field (LFT1, LFT2) and experimental values are taken from Dulick et al. (1986), Carette and Hocquet (1988), and Linton et al. (1983a, b),
respectively. Reproduced from Kotzian et al. (199 la).
INDO/S-CI State A .Q J~ Exp. LFT1 LFT2 E n e r g y Configuration
X 1 3 2 2 0.0 0.0 0 0 lqb40 91Vo
X 2 3 3 3 80.3 121.6 197 71 lqb40 90~o
W I 2 1 2 811.6 805.6 1026 857 184o 84~
W 2 2 2 3 912.2 910.8 1160 918 1840 82~o 2~40 17~
V 1 1 0- 2 1679.4 1777.7 1756 1812 2~40 73~o 3040 25~o
V 2 1 1 3 1869.7 1878.4 1919 1937 2"~40 70~o 3040 27~o
U 1 1 0 + 3 1931.8 1866.3 1978 1850 2~t40 75~ 304o 22~o
X 3 3 4 4 2039.8 2021.8 2495 2084 lqb 40 99Vo
X 4 3 3 3 2 1 4 0 . 6 2185.4 2146 2154 lqb40 98~
W 3 2 3 4 2617.3 2632.2 3268 2726 lg)40 84~
W 4 2 2 3 2771.7 2762.7 2994 2791 1~40 84~
V 3 1 2 4 3462.6 3501.5 3944 3453 2~40 80~ 1~40 17~o
V 4 1 1 3 3642. 3600.9 3724 3562 2~40 81~ 1840 14~o
T 1 0 0- 4 3821.5 4035.2 4109 4176 3o4o 72~o 2~40 25~o
U 2 0 1 4 4133. 4101.9 4391 4234 304o 68~ 2~40 29~o
U 3 0 0 + 3 4457.7 4262.8 4476 4217 3o40 70~o 2"~40 23~/o
500 l l 2 0 n m region. S h e n y a v s k a y a et al. (1973) d e s i g n a t e d the observed systems I t h r o u g h XXII. D e l a v a l et al. (1977) studied the systems VII a n d X, b u t n o definitive a s s i g n m e n t of the observed electronic t r a n s i t i o n s came forth. Beaufils et al. (1979) observed the first lines in A,Q = + 1 XVII a n d XX transitions. This led to the assign- m e n t for X V I I / 2 " = 3.5 a n d -Q' = 4.5, a n d .Q" = 4.5 a n d .Q' = 5.5 for system XX. As p o i n t e d o u t by D u l i c k a n d Field (1985), some of the earlier a s s i g n m e n t s of the observed spectra of P r O were either incorrect or speculative.
D u l i c k a n d Field (1985) p r o v i d e d extensive analyses of the observed systems. T h e y s~tudied the (0, 0) b a n d s of n i n e p r o m i n e n t systems in the 5 0 0 - 8 0 0 n m region. F o r the first time definitive ~ a s s i g n m e n t s for the u p p e r a n d lower electronic states participa- ting in these t r a n s i t i o n s were p r o v i d e d by D u l i c k a n d Field.
D u l i c k et al. (1986), as well as C a r e t t e a n d H o c q u e t (1988), have used the ligand- field t h e o r y to c o m p u t e the energy levels of P r O . M o r e recently, K o t z i a n a n d Rosch (1991a, b) used the I N D O / S - C I m e t h o d to investigate the electronic states of P r O a n d T m O . T h e y c o m p u t e d the properties of 33 electronic states of P r O a n d c o m p a r e d their c o m p u t e d energies with e x p e r i m e n t a n d ligand-field theory. All of these studies have p r o v i d e d significant insight into the low-lying electronic states of PrO.
T a b l e 56 shows the D u l i c k Field a s s i g n m e n t of the observed systems of P r O d e s i g n a t e d b y their .Q q u a n t u m n u m b e r s . N o t e that D u l i c k a n d Field suggest that the
TABLE 56
Twelve observed electronic transitions of P r O and their sug- gested assignments by Dulick and Field (1985). Reproduced from
Dulick and Field (1985).
System .(2' T' ° ( c m - 1) .O" T O ( c m - 1)
VI 5.5 11 102 4.5 2157
IX 4.5 16597 3.5 3887
X 5.5 13 259 4.5 220
XI 5.5 13 865 4.5 220
XIV 5.5 16595 4.5 2157
XVI 5.5 19 169 4.5 3720
XVII 4.5 16597 3.5 0
XVIII 7.5 21 321 6.5 3965
XIX 6.5 19687 5.5 2111
XX 5.5 18 069 4.5 220
XXI 4.5 18 885 4.5 220
XXII 5.5 19 169 4.5 220
lowest state has a .Q quantum number of 3.5. A diagrammatic interpretation of the observed systems and the energy levels of P r O was provided by these authors. We reproduce this in fig. 37. Figure 37 nicely summarizes the electronic states of PrO and the observed transitions. Table 57 shows the comprehensive assignment of systems I - X X I I for PrO observed by Shenyavskaya et al. (1973). Tables 56 and 57 together yield the experimentally known states of PrO. We now proceed to theoretical calcula- tions and insight into the nature of electronic states of PrO.
As mentioned before, there are INDO/S-CI as well as ligand-field theoretical studies on PrO. The recent work of Kotzian and R6sch (1991 b) provides a beautiful summary of all known information on PrO up to now. We will use this work and the paper of Dulick and Field as basis for discussion of the electronic states of PrO. Table 58 shows the ~ v a l u e s of several electronic states of PrO, their energy separations obtained using the INDO/S-CI method by Kotzian and R6sch (1991b) as well as the ligand-field theoretical values of Dulick et al. (1986) and Carette and Hocquet (1988). Figure 38 shows schematically the computed energy levels of PrO using various methods together with known experimental data up to now.
The electronic states of PrO are best rationalized using the energy levels of the Pr + 2 ion which has the configuration 4f 2 6s. Figure 39 shows the energy levels arising from 4fZ(3H)6s and 4f2(3H)6pl/z configurations of the Pr +. As seen from fig. 39, the coupling i s i S . The s p i n - o r b i t coupling of the 4f 2 shell (3H) is roughly 2000 cm - 1. The PrO diatomic states are rationalized as arising from P r + 2 0 -2. The I N D O / S C I yields a ground state electronic configuration of (10"/02s) 2 ( l T r / O 2 p ) 4(2c~/O2p) 2- (1 qb/Pr4f) 4/7 (18/Pr4f) 4/7 (27r/Pr4f) 4/7 (3o/Pr4f) 2Iv (4cy/Pr6s) 1. This configuration is, of course, consistent with P r + 2 0 -2 picture. The I N D O calculations revealed that the 4f 2 4cy configuration is the lowest while 4f 2 28 and 4f 3 configurations are 8200 and 18 300cm 1 above the 4f 2 4 o configuration. Other configurations are much higher (energy > 41 850 c m - 1). Hence, the INDO-SCI studies were focused on the electronic
118 K. BALASUBRAMANIAN
i
2 2 0 0 0
2 0 0 0 0
1 8 0 0 0
1 6 0 0 0
1 4 0 0 0
1 2 0 0 0
¢..)
>- (.9
" '
t
0 0 0 0Z uJ
800C
600C
4 o o c
2 o o c
P r O E N E R G Y L E V E L S
~- 75
\l
\ \
\
\ \
\ __L_.._ 5,5 , 45
m 5 5
- . v
Fig. 37. Energy-level diagram and the electronic transitions of PrO. The full line designates electronic transition examined under high resolution. Reproduced from Dulick and Field (1985).
states arising from 4f 2 40. As seen from table 58, the INDO-SCI model as well as ligand-field models reproduce the energies of the experimentally known states (O>_ 3.5).
6.4. SmO
The spectra of samarium monoxide (SmO) have been studied by Dekock and Weltner (1971), Hannigan (1983), Dickson and Zare (1975), Linton et al. (1987), Bujin and Linton (1989) and recently by Bujin and Linton (1991). The recent work of
TABLE 57
Electronic assignments of Pro for systems I - X X I I of Shenyavskaya et al. (1973) suggested by Dulick and Field (1985).
Bandhead a
System v (cm- 1) g2,/b .(2"
I 9233 ? ?
II 9996 ? ?
IlI 10 205 ? ?
IV 10438 5.5 4.5 (XX) c
V 10976 ? ?
VI 11 109 5.5 (X) 4.5 d
VII 11 777 4.5 3.5 (XVII) c'e
VIII 11 922 2.5 3.5 (XVII) c
IX 12 711 4.5 (XVII) 3.5 d
X 13 047 5.5 4.5 (XX) c'e
XI 13 657 5.5 4.5 (XX)
XI1 14006 ? ?
XIII 14 090 ? ?
XIV 14 384 5.5 (XX) 4.5 d
XV 14439 3.5 4.5 (XX) ~
XVI 15 442 5.5 (XXII) 4.5
XVII 16 610 4.5 3.5
XVIII 17 346 7.5 6.5
XIX 17 567 6.5 5.5
XX 17 863 5.5 4.5
XXI 18 680 5.5 4.5 (XX)
XXII 18 961 5.5 4.5 (XX)
Shenyavskaya et al. (1973).
b System designations enclosed in parentheses share the indicated upper or lower electronic state.
AJ2 assignments taken from Shenyavskaya and Kaledin (1982).
a Assignments suggested by Dulick and Field (1985).
Assignments taken from Beaufils et al. (1979).
Bujin and Linton (1991) summarizes the known electronic states of SmO up to now.
Carette and Hocquet (1988) have used the ligand-field theory to calculate the lower electronic energy levels of SmO. These authors found 11 electronic states of SmO below 2280 cm-1. The ground state of SmO was calculated as the X O - electronic state.
Table 59 shows the most recent spectroscopic data on the energy separations of the electronic states of SmO. Both experiment and theory seem to agree on the X O - ground state of SmO. The two ligand-field calculations are in reasonable agreement with the experimental energy separations. Figure 40 shows the energy-level diagram of the electronic states of SmO. The calculation of Dulick et al. (1986) yields more energy levels than known experimentally. As seen from fig. 40, the Carette-Hocquet ligand- field calculation is slightly in better agreement with experiment. Linton et al. (1987) attributes this to differences in the choice of Sm 2 + atomic-orbital basis sets; the Carette-Hocquet eigenfunctions are considered probably more realistic.
TABLE 58
Energies of molecular states of PrO (in cm- 1) arising mainly from the atomic states of Pr. III. Reproduced from Kotzian and R3sch (199ta, b).
INDO/S-CI LFTb LST c
-(2 Energy Composition" Energy Energy
3.5 0 IH 4 3.5)53~ [H 5 4.5)25~ 0 0
IH 4 4.5)11~o
4.5 235 LH 4 4.5) 57~o IH 5 5.5)35~o 233 225
2.5 1678 IH 4 3.5) 71~o IH 4 4.5) 14~o 1867
3.5 1985 IH 4 4.5) 66~o IH 4 3.5) 18~ 2074 1696
5.5 2136 IH 5 5.5)59~ [H 6 6.5)39~o 2094 1995
0.5 2155 IN 6 6.5)30~ IP 2 2.5)23~ 2866
4.5 2197 [H 5 4.5)60~o IH 6 5.5) 30~o 2144 2059
1.5 2395 IH 4 3.5)21~ IH 5 5.5)18~ 2924
IP 2 2.5) 14~ IF 4 4.5) 11~
0.5 2519 IP2 1.5) 17~ IH5 4.5)15~ 3107
I H 6 5.5) 14~
1.5 2774 IH 4 3.5)40~o IU 4 4.5)27~ 3125
2.5 2835 I U 4 4.5 )62~o I G 4 4.5 )1570 3099
Ig 4 3.5) 14~
4.5 3618 [H 5 5.5)47~o IH 4 4.5)41~o 3767 3285
3.5 3753 IH 5 4.5)4870 IH 4 3.5)26~ 3824 3357
[H 5 5.5)11~o
6.5 4033 [H 6 6.5)10O70 396O 3998
0.5 4326 [F 3 2.5) 1970 [H 5 5.5) 17~ 4941
IF3 3.5)17~ IP00.5 ) 1 7 ~ }P 1 0.5)1270
5.5 4329 IH 6 5.5)97~ 4246 4313
1.5 4439 IH 4 4.5)28~ IH6 6.5)21~ 4946
IP 1 1.5)10%
0.5 4456 IH 6 5.5)21~ /H 4 3.5)19~ 5022
IN 4 4.5)15~ bH 6 6.5)14~
[P 2 1.5) 10~
2.5 4508 IH 5 5.5) 59~o [P 2 2.5) 14~ 4853
3.5 4568 IH 5 5.5)72Vo IH 5 4.5)21~ 4786 4195
1.5 4652 IH 5 4.5)32~ IF4 3.5)13~ 5070
IN 5 5.5)11~
2.5 4811 IH 5 4.5)81~ 4992
5.5 5363 [H 6 6.5)57~o IH 5 5.5)41~ 5548 5210
4.5 5779 IH 6 5.5)46~o IH 5 4.5) 28~o 5812 5490
IH 6 6.5) 18~
0.5 6050 ]P 0 0.5)31~ IH4 4.5) 15~ 6560
IF 2 1.5) 13~o
1.5 6213 IH 5 5.5)29~ IP 1 1.5)23~o 6679
IH 6 6.5 ) 12~
2.5 6422 I H 6 6.5) 54~o IF 2 2.5 ) 12~ 6849
0.5 6427 IP 1 0.5)24~ IH 5 4.5)17~o 6866
IF 2 2.5) 12~o IH 5 5.5) 10~o
4.5 6540 [H 6 6.5)68~ IH 6 5.5)23~ 6702 6170
3.5 6576 IH 6 6.5)88~ 6848 6377
1.5 6737 IH 6 5.5)29~ IH 5 4.5)12~0 7069
IP 2 1.5) 10~
3.5 7044 I H 6 5.5 ) 90~o 7085 6781
2.5 7069 IH 6 5.5)73~ 7233
a The atomic states are labeled according to [Lf Jf J~). Only states contributing b Duliek et al. (1986).
c Carette and Hocquet (1988).
more than 10~o are listed.
~t~
t.l.l 7
6 5 4
3
2
I
4.5 u m
5.5
I ~,.s 3d
4.5
4.5 5.5 3.5
2.5
4 5 0 3.5 k = 0 -I
I N D O t S E x p . I J ' T
3.5 2.5 1.5
11.5 4.5 3.5 ~'~ ~ 11.5
D.5 " ~
2,.5 15
m 1.5 1t.5 3.5 2.5 ~
11.5
2.5
I J . 5
1.5 1.5
M
5.5
5.5 55
I,.5 ~ ~.~ 3.5
3.5 " 6.5 ~
4.5 4.5
4.5 ,15 3.5
5.5 [ ]
3.5 5.5
25
3.5 m25 1.5
m 0.5
35 2.5
4.5 1.5 ils
4.5
5.5 2.5 1.5 I s
2.5 1.5 0 5
m
15 ~%
4.5 .15
m
3"7
-2 -3 -4 -5 -6 0 -I -2 -3 -4 -5 -6
F i g . 38. E n e r g y l e v e l s o f P r O a s c o m p u t e d b y l N D O / S a n d L F T m e t h o d s t o g e t h e r w i t h k n o w n e x p e r i m e n t a l e n e r g i e s . R e p r o d u c e d f r o m K o t z i a n a n d R 6 s c h ( 1 9 9 1 a , b).
The spectra of SmO exhibited significant .(2 doubling for the lowest states. This was anticipated by calculations although calculations were not found to be in accord with the observed values. Bujin and Linton (1991) attribute this to incorrect ordering of the e and f levels in calculations.
The electronic states of SmO can be rationalized from the Sm +2 4f 2 6s(6H) super- multiplet. The overall ordering of the electronic states of SmO closely resembles the low-lying states of Sm + 2 derived from the (4f z 6s)6H electronic supermultiplet. This is further supported by the remarkable agreement of the observed energy levels with the values obtained from ligand-field models.
6.5. EuO
Experimental data on EuO are rather limited at the present time. Dulick et al. (1986) have derived the dissociation energy of EuO as 4.92 ___ 0.1 eV from a thermodyamic study. They have also discussed the electronic structure of EuO using the ligand-field model. The 4 f 7 - 4 f 6 cr (excited) superconfiguration energy separation was found to be 0.60 +0.1 eV from thermodynamical studies and 0.41 eV from ligand-field theory, although Carette and Hocquet (1988) found a different value of 0.98 eV for this energy separation.
Gabelnick et al. (1984) have obtained the vibrational frequency (c%) of Ar-isolated EuO as 672 cm-1. McDonald (1985) obtained a o) e of 688 cm-lo confirming that the ground sta~e arises from a 4f 7 superconfiguration. An R e of 1.891 A was estimated from the rotational constant of 151EuO.
122 K. BALASUBRAMANIAN
"7
o Z I- 6oo(
rr
Q,,.
W O3 ) - (.9 n,-
400C uJ W >
I,- .J lad n,*
2000 de ,~')
(6,~-)
(5, ~-) _ _
(4,~-}
Pr { m )
4 f2(3H)6s
J=Jc+-~ -
5.5
6.5
4.5 5.5
4.5 3.5
Pr (/IT) 4 f 2 [3 H ) 6 P i / 2
I j=jc±_ ~
(Jc ,~-I
'~6,~- ~ 6.5 5.5
( 5 , 2 ) - - 5.~ 4.5
( 4 ~ l ~ 4.5
3.5
Fig. 39. Energy levels of Pr +2 from 4fZ(3H)6s and 4f2(3H)6p. Reproduced from Dulick and Field (1985).
TABLE 59
The energies (in c m - 1) of the observed low-lying states of SmO. Repro- duced from Bujin and Linton (1991).
State Experimental Calculated ( 1 ) a Calculated (2) b
X 0 - 0.0 0.0 0.0
(1) 1 146.98 115.0 130.1
(1) 2 566.77 498.0 549.0
(2) 0 + 582.25 640.0 982.0
(2) 1 879.30 873.0 1167.3
(1)3 1280.49 1189.0 1299.7
(3) 0 - 1546.36 1359.0 2018.4
(2) 2 1604.25 1517.0 1741.6
(4) 0 ÷ 1661.0 1603.0 2030.0
(3) 1 1661.39 1472.0 2182.9
(3) 2 2239.91 1998.0 2839.5
(4) 1 2013.5 1963.0 2317.4
(1) 4 2286.57 2226.0 2417.1
(5) 0 + 2520.0 2603.0 2990.0
(5) 1 2867.3 2718.0 3272.9
a From Carette and Hocquet (1988).
b From Dulick et al. (1986).
3500
3000
2500
2000
1500
i 0 0 0
..qO0
- - ( S ) I . . . (4)Z - - ( S ) I . . . (6)0"
- - ( S ) O ° . . . (S)O ° (2)3 (I)4
- - ( 3 ) 2
- - ( I ) 4
- - ( 4 ) 1 ~ ( 3 ) 2 ,
~ ( 4 ) 1 ( 3 ) 1 1
(4)0*1 (4)0"
( 2 ) 2 (Z)2
(3)0" _ _ (3)1
- - (3)0"
- - ( I ) 3
- - (1)3
- - ( 2 ) 1 - - ( 2 ) 1
~ ( 2 ) 0 ° ~ ( 1 ) 0 "
- - ( ! } 2 - - ( 1 ) 2
. . . (6)0"
(S)t . . . (4)2
"(S)O °
~ 1 3 ) 1
....... . . o .
(2)3
( I ) 4
~ ( 4 ) 1 (3)1 (4)0"
(3)1"
(2)2
(1)3
~ ( 2 ) 1
~ ( 2 ) 0 "
~ ( I ) 2
- - ( I ) l - - ( I ) 1 (I}1
XO"
Exp ( : | 1 ( I ) (:al(2)
Fig. 40. Energy-level diagram for the electronic states of SmO. The experimen- tal energies are compared with Cal (1) by Carette and Hocquet (1988) as well as Cal (2) by Dulick et al. (1986). Both calcula- tions are ligand-field calculations. Repro- duced from Bujin and Linton (1991).
Dolg et al. (1990a, b) have studied the s 2 - ground state and the first excited 8Z- state of EuO using ab initio SCF and SDCI methods in conjunction with non- relativistic and quasi-relativistic effective core potentials. They obtained the spectro- scopic constants of these two states and their potential energy curves. They employed the Wood-Boring (WB) quasi-relativistic ECPs as well as ECPs derived from non- relativistic Hartree Fock (HF) calculations. They used an energy optimized GTO basis sets of (7s6p5d2f)/[Ss4p3d2f] and (12sl lp9df)/[9sSp6d5f] types for Eu. For the oxygen atom, (9s5p)/(4s2p) basis set of Dunning was used together with one set of d-functions. They also include the effect of unlinked quadruple clusters using the Davidson method. The spin-orbit effects were estimated using ECPs which included spin-orbit operators. The spin-orbit effects were obtained using the double group CI method of Pitzer and Winter (1988).
Table 60 shows the spectroscopic constants of two electronic states of EuO (X s 2 - and A s2-). The theoretical constants were obtained by Dolg et al. (1990a, b) using CISD, CISD + Q levels of theories. The experimental values are from Dulick et al.
(1986), McDonald (1985) and Gabelnick et al. (1984). As seen from table 60, experi-
124 K. BALASUBRAMANIAN TABLE 60
Spectroscopic constants of two electronic states of EuO. CISD and CISD + Q values from Dolg et al.
(1990a, b). We show only the quasi-relativistic values computed by Dolg et al. (1990a, b)
R o ( A ) D o l T e (eV) ~oo (cm- ')
~e (D)
State CISD + Q Exp. CISD + Q Exp. CISD + Q Exp. CISD
X 8Z- a 1.912 1.919 ~ 1.89 3.573 3.916 4.88 716 702 672 9.175
X BE- b 1.940 1.953 3.56 4.13 - 699 676 - 9.67
A BE- a 1.807 1.814 - 0.002 0.041 0.60 806 834 - 3.987
a 4f orbitals in the valence space.
b 4f orbitals in the core.
mental data on EuO are restricted to the X ground state which arises from the 4f 7 superconfiguration. The A BE- state arises from the 4f6cr 1 superconfigurations and it appears that no experimental spectroscopic data exist on this state with the exception of an estimate of T c. Evidently, this estimate differs significantly from the CISD + Q value of only 0.04 eV and hence further studies are warranted on the A BE- state.
The spin orbit contribution estimated from quasi-relativistic CI is - 0.77 eV for the ground state of EuO. Dolg et al. found that the A BE- excited state of EuO, which is split into £2 = 0.5, 1.5, 2.5 and 3.5 states, is significantly contaminated by the 8II state.
All £2 components of the BE- state were found to be within 1400 c m - 1.
The Mulliken-population analysis of the SCI wavefunction yields that Eu has a positive charge of 1.04 with a population of 4f 7"°4 5d °84 6s °'°4 6p °°4 while the oxygen atom has a O 2s 1"9 2p 5'14 population. Dolg et al. rationalize that the X 8 2 - ground state arises from a 4f 7 supermultiplet while the A 8Z- state arises from the 4 f 6 ~ supermultiplet. Dolg et al. found that 99.3~o of the unpaired electronic population is in the 4f orbital in the X BE- ground state. The doubly occupied cr orbital of EuO is composed of 21~o Eu and 79~o O orbitals. However, in the A 8E- state 99.7~o of the six unpaired electrons are on Eu 4f orbitals while the seventh unpaired electron is 98~o on Eu (6s 80.6~o, 6p 16.6~o, 5d 3.0~o).
6.6. GdO
Carette et al. (1987) have studied the spectra of GdO. From their spectra, energy separations of six electronic states of G d O could be derived. These authors have also used the ligand-field model to derive the energy levels of eight electronic states of GdO. Dolg et al. (1990a, b) have studied the 9N- and r E - states of G d O using ab initio SCF/CISD methods in conjuction with quasi-relativistic ECPs. More recently, Kotzian et al. (1991a, b) have used the INDO/S-CI method to compute the energy separations of 45 .O electronic states of GdO. We use the Kotzian et al. (1991 a, b) and the Dolg et al. (1990a, b) works as the basis for discussion on the electronic states of GdO.
Table 61 shows the Dolg et al. (1990a, b) CISD and CISD + Q results on G d O for two electronic states. As seen from table 61, the agreement between the computed SDCI, SDCI + Q properties with experiment is quite good with the exception of the D e.