K. BALASUBRAMANIAN*
4. Electronic structure.of lanthanide hydrides
In this section, we review the results of calculations and comparison with experi- ments for lanthanide hydrides. Although YH and ScH are strictly not lanthanide or rare-earth compounds, it is important to investigate these compounds as well to compare and contrast these compounds with their periodic analog, namely, LaH. For this reason we include some discussions on Sc and Y compounds. With the intent of demonstrating the effect of the lanthanide contraction, we also include the results of HfH and HfH 2 and compare them with ZrH and ZrH 2. In each section, we briefly describe with acronyms the method of computations. The reader is referred to section 2.1.2 for their meanings. We also include the periodic trends within a group and emphasize any anomalies.
4.1. YH and ScH
Balasubramanian and Wang (1989a, b) carried out CASSCF followed by full second-order CI (SOCI) calculations which included excitations from all CASSCF configurations. They used a (3s3p3dlf) valence Gaussian basis set together with RECPs which retained 4d 1 5s 2 shells of the Y atom in the valence space. For the hydrogen
TABLE 2
Spectroscopic properties of low-lying electronic states of YH.
Reproduced from Balasubramanian and Wang (1989a, b).
State Ro(A) T~(cm - 1) COe(Cm - 1)
1E+(0+) 1.865 0 1510
1E+ 1.865 11 1510
317(0-) 1.907 7884 1488
317(0 +) 1.907 7905 1488
3H(1) 1.907 8187 1489
317(2) 1.907 8458 1489
3H 1.907 8179 1489
3A(3) 1.944 9062 1432
3A(2) 1.944 9000 1431
3A 1.944 9002 1432
3A(1) 1.944 9047 1433
3E +(1) 1.944 10 164 1337
3Z+(0-) 1.944 10 171 1342
3Z+ 1.944 10 175 1334
1A(2) 1.950 10 991 1366
1A 1.950 10992 1366
117(1) 1.944 12687 1380
117 1.944 12 685 1380
1Z +(II)(0 ÷) 2.034 15 049
1Z +(II) 2.034 15 050
3171(11)(2) 1.965 20 226 1418
317 (II)(1) 1.965 20 478 1418
31-I(11)(0-) 1.965 20 789 1417
317(ii)(0 ÷) 1.965 20 789 1417
317 (II) 1.965 20 510 1418
117(II)(1) 1.955 21 990 1386
117(11) 1.955 21991 1386
1F(4) 1.988 30 051 1298
1F 1.988 30 051 1298
atom, van de Duijneveldt's (5slp/3slp) basis set was used. Balasubramanian and Wang studied 29 electronic states of YH. In addition, spin-orbit coupling was included through the RCI method. Langhoff et al. (1987) studied four electronic states of YH using the SCF/MCPF method and the Hay-Wadt ECPs (Hay and Wadt 1985a, b) which included 4s 2 4p64d 1 5s s shells of Y. The spin-orbit coupling was neglected in this work.
Table 2 shows the spectroscopic constants obtained by Balasubramanian and Wang (1989a, b) for the electronic states of YH while fig. 8 shows the computed potential- energy curves.
Both Langhoffet al. and Balasubramanian and Wang predicted the ground state of YH to be 1Z+, in noticeable disagreement with Bernard and Bacis (1977) who had carried out the rotational analysis of a system which they designated as a 3~-3A system.
It now appears that this assignment is incorrect. The most consistent assignment for this system appears to be a 3A-3II system.
54 K. BALASUBRAMANIAN
- r v
1'
W
0 . 0 6 0
0.040
0 . 0 2 0
- 0 . 0 2 0
-0.040
-0.060
- 0 . 0 8 0
-O. IO0
2p +2 S
2D+2 S (Y)(H)
Fig. 8. Potential-energy curves of I I the selected states of YH. Reproduced
2 3 4 5 6 7 8 9
from Balasubramanian and Wang
R ( a , u. ) (1989a).
Bernard and Bacis (1977) observed six electronic systems ascribed to YH. They also carried out the rotational analysis of these systems and identified the transitions as 3(I) ~ 3A, (II-I,1Z)-lY~ and (IE,1A) ~ 1FI. These assignments appear to be incorrect and in any case are not consistent with the theoretically predicted ly, + ground state for YH.
Their B'IZ ÷-A'IE +, when reassigned as B1Z +-1E + system, agrees with the computed T e of the IE+(II) state of Balasubramanian and Wang (1989a, b).
The Voo value of the experimental system is ~ 14300cm -1 while the computed SOCI value for the xE+(II) state is 15 049 cm-1 including s p i n - o r b i t coupling. The BaA-A1FI system of Bernard and Bacis has a v00 value of 11 378 cm-1. This system corresponds to the 1H-XIE ÷ system whose computed transition energy is 12 687 c m - 1 (Balasubramanian and Wang). Likewise, the 3(I)-3A system of Bernard and Bacis should also be reassigned.
The B a l a s u b r a m a n i a n - W a n g computed dissociation energy of YH (3.05 eV) agreed with a value of 2.95 eV obtained by Langhoffet al. (1986). However, the dipole moment computed recently by Balasubramanian (1990) using (4s 2 4p 6 4d a 5s 2) RECPs with a large basis set was found to be 0.3 D lower than the value of Langhoff et al.
Following the theoretical calculations, Simard and co-workers (Simard et al. 1991) have obtained C1E+-X1E + spectroscopic system of YH as well as a system in the
I I
696 700
Y-H
C l Z + - X ' Z+ ( 0 , 0 )
I I I I 1
704 708
Wavelength (nm)
Fig. 9. The C-X system of YH. Reproduced from Simard et al. (1991).
Y-D
i i [ I i I
19900 19800 19700 19600 19500 19400
WAVENUMBER
.... J ti
Y-H
I i I i I i I
19800 19700 19600 19500 19400 19300 19200
WAVENUMBER
Fig. 10. The spectra of YD and YH in the 19 600 cm- 1 region. Reproduced from Simard et al. (1991).
19 600 c m - 1 region. These spectra are shown in figs. 9 and 10. As seen from the assign- ment of the observed spectra, Simard and co-workers confirm the theoretically pre- dicted X1E + ground state of YH.
Figure 11 shows the calculated energy levels of YH and the experimentally observed levels. As seen from fig. 11, the computed values are in excellent agreement with experiment considering the approximations introduced in the theoretical procedures.
Table 3 shows the contributions of important configurations in the SOCI of the electronic states of YH. In table 3, the ~ and b orbitals are non-bonding yttrium orbitals. The contribution from the 5p orbital of Y is very noticeable. Most of the other
251 CALCULATION I
2£
1/T 0 1 3'n 2
1~4-
15
?
o
x
T E L)
1 0 -
5
56 K. B A L A S U B R A M A N I A N
1 A 3E ~.o
3A 1,2,3 / 2
• ,'(~ 3/T
Y - H
EXPERIMENT
-- ]
. . .3~2,3,4
n = O
,43=1 (~'rr?)
",a=2 (3~=?)
;-n=0 ( ~ o ? )
IE+
i - - 1,IT
. . . . 3.rr
. . . 3
CALCULATION qT
3rr
3A
0 'z ÷ I ~Z*(v=O) ~r +
Fig. 11. Predicted and observed energy levels of YH. Calculation I is due to Balasubramanian and Wang (1989a), while calculation II is due to Langhoff et al. (1987). Reproduced from Simard et al. (1991).
electronic states are dominated by a single configuration except the 132 + (II) state which is a mixture of several configurations.
Table 4 shows the MuUiken populations of various electronic states of YH. As one can see from that table, the gross yttrium populations of all the electronic states are considerably smaller than 3.0 indicating the ionic character of the YH bond with the Y + H - polarity. Note that the 5p population is between 0.2 and 0.986 in various states.
This indicates considerable
dsp
hybridization. This hybridization is the smallest for the 1F state (0.126) and the largest for the ll-I(II) (0.986), 311(1I) (0.61), 3~+ (0.751), 311TABLE 3
The contributions of important configurations in the SOCI wavefunctions of YH. Reproduced from Balasubramanian and Wang (1989a, b).
State Percentage of contributions
ly+ 162 202 (86), 162 lrt z (8), 31/ 162 201 1~1 (94) 3A 102 261 161 (96) 3E+ 162261 361 (81) XA 162 261 161 (81) 11I 162261 1"~ 1 (80)
IE+(II) 162 261 361 (58), 162 l'rt 2~ (7), 162 182 (6), 162 2o 4o (5), 162 302 (5) 317(11) 162 llz 1 161 (89)
117(II) 162261 2~ 1 (85) 1F 162 1~) 2 (89)
TABLE 4
Mulliken-population analyses of electronic states of YH. Reproduced from Balasubramanian and Wang (1989 a, b).
Gross Overlap
State Y Y(s) Y(p) Y(d) H H(s) H(p) Y-H
12; + 2.694 1.550 0.454 0.690 1.306 1.296 0.010 0.639
31I 2.696 0.947 0.663 1.086 1.304 1.295 0.009 0.690
3A 2.709 0.962 0.368 1.380 1.291 1.283 0.008 0.672
32;+ 0.735 1.025 0.751 0.959 1.265 1.258 0.007 0.700
1A 2.700 0.791 0.610 1.300 1.300 1.292 0.008 0.680
117 2.769 0.918 0.350 1.500 1.231 1.224 0.007 0.653
12;+(11) 2.782 0.900 0.522 1.361 1.218 1.211 0.006 0.670
317(11) 2.730 0.293 0.681 1.757 1.270 1.262 0.007 0.680
117(11) 2.827 0.632 0.986 1.209 1.173 1.168 0.005 0.652
1F 2.758 0.345 0.126 2.287 1.242 1.235 0.007 0.664
(0.603), a n d 1A (0.610) states. T h e d p o p u l a t i o n of the g r o u n d state is 0.690, a n d the d p o p u l a t i o n s o f m a n y o t h e r states are b e t w e e n 0.96 a n d 1.5 with the e x c e p t i o n of the 1F a n d 3I-I(I1) states.
B a u s c h l i c h e r a n d W a l c h (1982) h a v e c o n s i d e r e d full valence M C S C F / C I calcula- tions o n the l o w e s t six e l e c t r o n i c states of ScH. S u b s e q u e n t l y , C h o n g et al. (1986) h a v e s t u d i e d the d i p o l e m o m e n t s o f the first-row h y d r i d e s using the M C P F a n d C A S S C F / M R C I techniques.
T a b l e 5 shows the C A S S C F a n d F O C I results for S c H o b t a i n e d b y B a u s c h l i c h e r a n d W a l c h . W e n o t e t h a t t h e y t o o o b t a i n a 1E+ g r o u n d state for S c H a n a l o g o u s to YH. A n initial c o m p a r i s o n of t a b l e 5 with t a b l e 2 reveals t h a t the e n e r g y s e p a r a t i o n s of the excited states o f S c H are b e l o w the c o r r e s p o n d i n g values o f YH.
T h e g r o u n d state of ScH was f o u n d to be m a i n l y c o m p o s e d o f Sc(d) a n d H(s) o b o n d while the excited states of S c H e x h i b i t e d sp h y b r i d b o n d s . T h e d i p o l e m o m e n t o f S c H in
58 K. B A L A S U B R A M A N I A N
T A B L E 5
S u m m a r y of F V - M C S C F and first-order CI for ScH (Ro is in bohr and T~ in c m - 1). Reproduced from Bauschlicher and Walch
(1982).
M C S C F F O C I
State R e T e R e T e
1E+ 3.39 0 3.37 0
3A 3.67 1412 3.65 2328
3Aa 3.67 2098 3.65 3023
3Ha 3.68 4502 3.61 4995
3Z+" 3.91 5875 3.90 6317
a Core taken from 1]~+ SCF.
its 1Z + state was computed as 1.374 D using the MCPF method if four electrons are correlated and 1.641 D if twelve electrons are correlated.
Figure 12 shows the contour plots of the highest-occupied ~ and ~t orbitals of the 1E+ ground state of ScH obtained by Bauschlicher and Walch (1982). As for fig. 12, the 7~ orbital is mainly Sc(4s) but is polarized outward perpendicular to the bond axis.
The 3~ orbital is a non-bonding Sc(4p) orbital. The 6~ bonding orbital is mainly Sc(3d~) + H(ls) orbital.
Following the Bauschlicher-Walch calculation, Balasubramanian (1987) studied ScH using RECPs and a CASSCF/FOCI method. Table 6 compares the all-electrons result with the ECP result. As seen from table 6, the agreement between the ECP and all-electron result is good.
,I
-5
(a) THE 60" ORBITAL (b) THE 70 ORBITAL 5
(c) THE 80 ORBITAL
5 / f--J
- 4
Z
(d) THE 3tr ORBITAL
i: ii> \-/1
Fig. 12. The highest-occupied natural or- bitals of the g r o u n d state of ScH. Repro- duced from Bauschlicher and Walch (1982).10 -4 10
Z
TABLE 6
C o m p a r i s o n of E C P and all-electron results for ScH. Repro- duced from B a l a s u b r a m a n i a n (1987).
R e (A) T~ (cm - 1)
State E C P All-electron a E C P All-electron
1Z + 1.744 1.78 0 0
3A 1.884 1.93 2050 2328
Bauschlicber and Walch (1982).
TABLE 7
Energies and equilibrium structures for the low-lying states of YH z.
Reproduced from B a l a s u b r a m a n i a n and R a v i m o h a n (1988).
State
CASSCF M R S D C I
g (A) 0 (deg) E (eV) g (A) 0 (deg) E (eV)
ZA 1 1.95 123 0.0 a 1.94 123 0.0 a
2 + Z g 2.02 180 0.37 2.01 180 0.36
2B 1 2.04 133 1.11 2.02 132 1.04
2Fig 2.10 180 1.18 2.08 180 1.16
2A 2 2.04 130 1.66 2.02 126 1.56
2A~ 2.10 180 1.74 2.08 180 1.71
a The absolute C A S S C F valence energy of 2A 1 is - 2 . 5 5 0 5 7 8 Hartree and the M R S D C I valence energy of 2A1 is - 2 . 5 7 3 9 8 4 Hartree.
4.2. Y H 2 and S c H 2
Balasubramanian and Ravimohan (1988) have computed the potential energy surfaces of three electronic states of YH 2 of 2A1, 2B x and 2A 2 symmetries. They em- ployed a (3s2p4d/3s2p3d) valence Gaussian basis set in conjunction with RECPs which retained the outer 4d 1 5s 2 shells of the Y atom in the valence space. A full CASSCF followed by M R S D C I calculations which retained all configurations in the CASSCF with coefficients > 0.05 as reference configurations were made.
Table 7 shows the computed equilibrium geometries and energy separations of the electronic states of YH 2, while fig. 13 shows the potential energy surfaces of three electronic states of YH 2 obtained by Balasubramanian and Ravimohan (1988).
It is evident from table 7 and fig. 13 that 2A 1 is the ground state of YH 2 with a bent equilibrium geometry (Ro = 1.94 ~, 0 e = 123°). This state is more stable than 2Z~- by 0.36eV. Balasubramanian and Ravimohan (1988) found that the equilibrium struc- tures in all the cases are bent rather than linear. However, unlike in the 2A:t state, 2A 2 and 2B1 are very close to the linear states in energy. The stability of the 2A1 ground state with respect to Y + H 2 dissociation was found to be 31 kcal/mol at the CASSCF level of theory. It should be mentioned that Balasubramanian and Ravimohan inadvertently compared their computed dissociation energy with the enthalpy of the solid Y + H 2 reaction.
60 K. BALASUBRAMANIAN 0 . 0 9
0 . 0 7
0 . 0 5
I'
0 . 0 3
-0.01 Y(2D) +H2 ~ ~ - - 2rig
\ 2.
-0.03 ~ 1 2 ,
- O . 0 5 ~ i i l i ~ - - ~ - - - n S I I
0 ZO 4 0 60 80 I00 120 140 160 leO
e ( D e g r e e s ) --~
Fig. 13. Potential-energy surfaces of Y H 2. Reproduced from Balasubramanian and Ravimohan (1988).
In fig. 13 for each 0 = H / Y \ H bond angle, Y - H bond lengths were optimized. All the three states have barriers for the insertion of the yttrium a t o m into H 2 to form YH 2.
The saddle points occur near 28, 37 and 40 ° for ZA1, 2B 1 and 2A 2 states, respectively.
The saddle points were obtained as the superposition of the surfaces obtained by starting from the CASSCF wavefunction of the linear structure and the CASSCF wavefunction of the dissociated structure (Y + H2). The barrier height of the 2A 1 surface (0.98eV) is lower than the corresponding values of 2B 1 (2.09eV) and 2A z (1.41 eV) states.
Table 8 shows the dipole m o m e n t s of the 2A1, 2B 1 and 2A 2 s t a t e s at their bent equilibrium geometries obtained from the M R S D C I density matrices. All three states have Y + H - polarities. The dipole m o m e n t of the 2A 1 s t a t e is the smallest, while that of 2A 2 state is the largest. The large dipole m o m e n t s of these states reveal the ionic character of Y - H bonds.
TABLE 8
Dipole moments for the low-lying states of Y H 2. Reproduced from Balasubramanian and Ravimohan (1988).
State p (D)"
2A 1 1.41
2B 1 3.81
2A 2 6.01
" Polarity Y+H-.
TABLE 9
Mulliken-population analysis for the low-lying states of YH 2. Reproduced from Balasubramanian and Ravimohan (1988). Populations of the two H atoms are combined together.
Gross populations Y H
State Y (total) H (total) Y (s) Y (d) Y (p) overlaps
2A x 2.36 2.64 0.83 1.01 0.52 1.35
2]~ + 2.40 2.60 0.98 0.92 0.50 1.36
2 B 1 g 2.34 2.66 0.41 1.47 0.45 1.34
2Fig 2.38 2.62 0.44 1.46 0.48 1.34
2A z 2.47 2.53 0.54 1.55 0.38 1.33
2Ag 2.51 2.49 0.53 1.42 0.56 1.34
The analyses of the leading configurations near equilibrium geometries of the three states of YH 2 revealed that they are dominated by their leading configuration with coefficients > 0.98. The 2A 1 ground state is composed of the la 2 2a I l b 2 con- figuration, wherein the l a l and 2a I orbitals are mixtures of Y(5s)+ H ( l s ) + H2(ls ) and Y(4d) + Ha(ls) + H2(ls), respectively. The lb 2 orbital is composed of Y(5py) + Ha(iS ) - H2(ls ).
Table 9 shows the Mulliken-population analyses of the electronic states of YH 2. The Y population strongly deviates from its neutral 3.0 population suggesting transfer of up to 0.6 electrons to the hydrogen atoms. We also note significant deviation from the neutral 4d 1 5s 2 electronic configuration near the equilibrium geometries. T h e Y - H overlaps are also quite significant.
Balasubramanian (1987) studied the insertion of Sc(2D) into H 2 in the 2A 1 state. In addition, the linear 2Z~, 2Fig and 2Ag states of the ScH 2 molecule were studied. He used a complete active space M C S C F method followed by full second-order CI (SOCI). F o r the Sc atom, R E C P s which retained the outer 3d 1 4s 2 shells were retained in the valence space. The (4s5d/3s3d) valence Gaussian basis set augmented by two sets o f p functions suggested by Wachters was used for the Sc atom.
Figure 14 shows the bending potential energy surface of ScH 2. Again 0 is the H / S C H bond angle, as in fig. 13. F o r each 0, S c - H bond lengths were optimized. Table 10 shows the geometries and energy separations of three linear electronic states of ScH 2 at the CASSCF and S O C I levels of theory.
As seen from both fig. 14 and table 10, the Sc a t o m has to surpass a large barrier of 1.57 eV (SOCI) to insert into H 2 to form the 2Z~- state. The 2Zg+ state thus formed is only 0.22eV more stable than the dissociated Sc + H 2 species. As seen from fig. 14, there exists a shallow obtuse angle bent m i n i m u m for ScH 2. At the CASSCF level, this
o
m i n i m u m has R e = 1.81 A and 0 e = 133.4 °. At this level, this m i n i m u m was found to be 0.04 eV below 2Z~-. The author thus suggested that the possibility of an obtuse angle 2A~ ground state for ScH 2 cannot be ruled out, but such a m i n i m u m formed only a shallow potential well.
Table 11 shows the Mulliken populations of the S O C I natural orbitals of ScH 2 obtained by Balasubramanian (1987). The leading configuration of the 2y,,+ state of
62 K, B A L A S U B R A M A N I A N
0.070 -
0.060 -
0.050 -
0.040 -
t 0
0.030 -
t
I L l 0.020 -
0.010 --
O . O -
Sc+H 2
-0.010 I I I I I I I I
20 40 60 80 100 120 140 160
1 180
2E+g
Fig. 14. Potential-energy surface of the 2A 1 state of ScH 2. Reproduced from B a l a s u b r a m a n i a n (1987).
TABLE 10
Geometries and energies of low-lying states of ScH 2. Reproduced from B a l a s u b r a m a n i a n (1987).
Method State R e (A) 00 (degrees) E (eV)
SOCI zE + 1.84 180.0 0.0 a
SOCI 217~ 1.91 180.0 0.16
SOCI 2Ag 1.91 180.0 0.62
SOCI Sc + H 2 0.22
SOCI 2A~ (barrier) 1.57 b
CASSCF 2E + 1.86 180.0 0.0 c
CASSCF
ZlI~
1.94 180.0 0.19CASSCF zAg 1.94 180.0 0.68
CASSCF ZA 1 1.83 29.0 1.81 a
a SOCI energies reported with respect to the energy of the zE+ state at its equilibrium geometry.
g
b The energy splitting between the linear geometry and the barrier evaluated at the CAS geometries.
c Energies reported with respect to the 2E+ CASSCF energy.
. g
d The energy of the barrier at the estimated CASSCF geometry with respect to the 2]~ + minimum.
g
TABLE 11
Mulliken-population analysis (net and overlap) of the low-lying states ofScH 2 at their equilibrium geometries.
Populations of both the hydrogen atoms are grouped together. Reproduced from Balasubramanian (1987).
Net population
State Sc H Sc (s) Sc (d) Sc(p) H(s) H ( p ) Overlap
2E+ 1.77 1.90 0.75 0.81 0.22 1.89 0.01 1.33
2 g
Hg 1.67 1.99 0.41 1.16 0.21 1.98 0.01 1.35
ZAg 1.74 1.92 0.47 1.14 0.25 1.91 0.01 1.35
S c H 2 is l~ 2 1~ 2 1~ 1 ( - 0.967). The lt~g orbital is primarily a bonding orbital of Sc 4s and H l s (Sc 3d makes non-negligible contributions). The 2gg orbital is dominantly Sc 3d and ls but is slightly anti-bonding with respect to hydrogen ls orbitals, The 1~ u is primarily Sc(4p) + H l ( l s ) - H2(ls ). As seen from table 11, the Sc(4s) net population is smaller but the 4p population is not zero suggesting considerable 4p mixing in the 1~ u orbital.
N o w we c o m p a r e YH z with ScH 2 while the bending potential-energy surface of the 2A 1 s t a t e of ScH 2 has a shallow bent m i n i m u m (0 e = 133.4 °, R e ~ 1,81 A), the 2A 1 surface Y H 2 has a well-bound m i n i m u m (0 e = 123 °, R e = 1.95A). The 2A1-2Y,+
splitting is very small for ScH 2 while it is somewhat large for Y H 2. The barrier to insert the Sc a t o m into H 2 is a b o u t 36 kcal/mol in the 2A 1 surface, while for the Y a t o m the corresponding barrier is a b o u t 23 kcal/mol, which is much smaller. Thus, the Y a t o m is found to be m o r e reactive with H 2 than Sc. The 2A 1 bent YH 2 state is more stable with respect to Y + H 2 by about 31 kcal/mol while the 2Z+ state of ScH 2 is only 5 kcal/mol more stable than Sc + H 2. Thus, bonding in Y H 2 is much stronger than in ScH/.
The total gross population of Sc in the 2Z+ state of ScH 2 is 2.44 while the corresponding population is 2.40 in Y H 2. This suggests greater charge transfer from Y to H in Y H 2 c o m p a r e d to ScH~. The Y(5p) population of all electronic states o f Y H 2 (cf., table 9) are considerably larger than the corresponding Sc(4p) populations. This suggests greater involvement of the Y (5py) orbital in the l b 2 orbital of YI-][ 2.
4.3. L a H
Das and Balasubramanian (1990) computed the spectroscopic constants and poten- tial energy curves of 20 electronic states of LaH. They used R E C P s with 5s 2 5p 6 5d 1 6s 2 valence shells for the La a t o m together with a (5s5p3dlf) valence Gaussian basis set.
CASSCF followed by the F O C I method of calculation was used to compute the potential-energy curves while the spectroscopic constants were obtained using the S O C I method. In addition, the spin orbit effects were introduced using the R C I method.
Table 12 shows the c o m p u t e d energy separation for the atomic states of La com- pared with experimental values together with the possible molecular states of LaH. As evidenced from table 12, there are several possible low-lying electronic states for LaH.
64 K. B A L A S U B R A M A N I A N TABLE 12
Dissociation relationships for some low-lying electronic states of LaH. Reproduced from Das and Balasubramanian (1990).
Atomic state Energy (cm- 1)
Molecular state (La + H) SOCI Exp. a
iZ+, iFI, 1A, 3Z+, 317, 3A 1Z -, 1Fi ' 1A, l@, 3Z- ' 3FI ' 3A, 3@
1E+ 117I, iA, 3Z+, 3H, 3A
1Z+, 11"I, bX, 1¢, 1r, 3y+, 3II ' 3A, 3@, 3 F
a 2 D ( d l s 2 ) + 2 S 0 0
a 2F (d 2 s 1) + 28 5706 6961
b 2D (d 2 s 1) + 2S 9437 8249
a 2G(d2 s 1) + 2S 11193 9280
"Averaged over J.
T
-'i-
i,,.
l..d
. n
n,"
0 . 0 9 -
0 . 0 6 -
0 . 0 3 "
O-
- 0 . 0 3 -
- 0 . 0 6 -
-0.09
LaH
- i A
19
~-3TI{]]I) - 3 ~ -
~ 3Ac-rr )
oZG+2S
b~D+2S o2F+2S
o2D+2S (LG)(H)
,% z'.o i.o 4'.0 s',o 6'.0 -/.o 8'.o
R(,~) )
Fig. 15. Potential-energy curves for LaH. Reproduced from Das and Balasubramanian (1990).
Figure 15 shows the potential-energy curves for L a H obtained using the C A S S C F / F O C I method while table 13 shows the S O C I spectroscopic constants of LaH. As seen from table 13, the ground state of L a H is a X 1E+ state with R c = 2.08 and ~oc = 1433 c m - 1
Bernard and Bacis (1976) have observed B~--~A, C--*A and b ~ a systems of LaH.
They have made rotational analysis of the observed systems and assign these three systems to XA III, 1E-1FI and 3@-317 systems, respectively.
TABLE 13
Spectroscopic properties of LaH. Reproduced from Das and Balasubramanian (1990).
State R e (~,) co e (cm 1) T~ ( c m - 1) Do (eV) /~o (D)
X 1 ]~+ 2.08 1433 0 2.60 2.42
3A 2.13 1352 2805 2.24 3.63
a 317 2.12 1341 5147 1.92 2.32
117 2.13 1309 6226 1.80 3.95
1,5 2.16 1299 6510 1.77 0.25
3d# 2.19 1240 10612 2.00 4.89
~Z + 2.20 1203 11794 1.20 - 0.49
317 (II) 2.19 1228 11 956 1.83 4.24
a E - 2.18 1247 12035 1.86 5.40
A 1~+ (17) 2.20 1230 13 025 2.17 2.17
3A (II) 2.24 1166 14 020 1.61 1.63
B 1 17 (II) 2.16 1293 15 729 1.77 3.24
31-I (III) 2.09 1377 15 880 1.81 3.14
3E (II) 2.17 1251 16 107 1.35 4.17
1F 2.18 1260 16838 1.88 6.51
lqb 2.18 1259 17 333 1.79 4.46
1A (II) 2.18 1234 17 427 1.60 5.49
1A (III) 2.20 1226 20 109 - 2.21
C 117 (III) 2.19 1342 20 170 - 6.15
b 3A (III) 2.10 1364 23 256 - 4.48
It is evident from table 13 that the 1II state is not the ground state of LaH. Hence, D a s and Balasubramanian (DB) argued that the A state of Bernard and Bacis should be reassigned to the X 1Z+ ground state of LaH. D a s and Balasubramanian suggested reassignment of the Bernard-Bacis assignment in accordance with table 13. These suggested assignments are also consistent with LaF (Barrow et al. 1967, Schall et al.
1987). The ground state of LaF is n o w well k n o w n to be a X 1Z+ state. For LaF excited A 1Z+, B 1II, C q-I, D 132+ and E 1 2 + states have been observed and assigned through the analysis of A *-- X, B ~ X, C ~ X, D ~ X, and E ~ X systems. The Voo values for these transitions are 11 662, 16 184, 20 960, 22 485 and 22 574 cm 71, respectively. The well- characterized spectra of LaF supported the assignment in table 12.
The A 132 + ~ X 1E + system predicted at 13 000 cm - 1 has not yet been observed. The corresponding transition for LaF has been observed at 11 662 c m - 1. The B ~--~X system, with a theoretically predicted Te value of 15 7 3 0 c m - 1 , is consistent with the Voo band head of the experimentally observed B,--~A system (15 619 cm-1). It is also consistent with the rotational analysis of Bernard and Bacis which suggested that A2 = + 1 for this transition. For LaF, this system appears with Voo = 16 184 c m - 1 .
The C--*A system of Bernard and Bacis with a Voo = 1 8 5 9 5 c m -1 was found to be most consistent with the C I I I ~ X 1E+ system by DB, with a theoretical T e = 20 170 c m - 1 . Likewise, the triplet-triplet transition observed with Voo = 16 000 c m - 1 was assigned to b3A~--~aaI-I by D B with a theoretical V o o = 1 8 1 0 0 c m -1. The differences between theoretical and experimental values were found to be within the error bars of calculations for excited states.
66 K. BALASUBRAMANIAN TABLE 14
Contribution of various leading configurations to the SOCI wavefunctions at the equilibrium geometries of the electronic states of LaH. Reproduced from Das and Balasubramanian (1990).
State Electronic configurations (percentage)
i•+ 102262 (86), 102 152 (6), 102 In 2 (4) 3A; 1A 10220 15 (97); 1022~ 15 (87), lo 2 1~ 2 (10) 3I~; 11-[ 10220 112 (95); 10220 in (74), lo 2 15 1~ (20)
3(I); 11~ 10215 17t (95;90)
3y+ lo 2 20 30 (52), 102 20 40 (24), 162 20 5o (12)
3y- 102 152 (60), 102 1"~ 2~ (4), 102 2'~ 3~ (4), 102 1"~ 2 (3), 102 15 25 (3) 3H(II); iH(II) lo 2 15 1~ (86; 56), 1o 2 20 in (3; 16)
1Z+(II) lo 2 20 30 (23), lo 2 152 (32), lo 2 20 40 (11), lo 2 20 50 (10)
3A(II) 1o220 15 (42), 10230 15 (17), 10240 18 (14), 10250 18 (10), lo26o 15 (7) 3]~-(II) lo 2 152 (30), lo 2 1"~ 2~ (12), lo 2 17t 3~ (12), lo 2 1~ 2 (5), lo 2 2~t 3~z (5) 31](11I); 1H(III) lo 2 2o in (55), 10220 2~z (22); lo 2 15 in (39), lo22o 172 (17), lo 2 15 2~ (16)
iF lo 2162 (95)
1A(II) 10220 15 (40), lo 21~ 2 (11), 10230 l~ (8), lo 21~2~ (8), 10240 16 (7) 1A(III) lo 21-~ 2 (36), lo 220 1~) (22), lo 21~ 2~ (13), lo 21~ 3~ (9)
aA(III) lo 21-~ 2n (41), lo 21~ 3~ (17), lo 2 1~ 4~ (12), lo 22"tt 5~ (9)
The dipole m o m e n t s in table 13 are large a n d positive suggesting L a + H - polarities.
Some of the excited states have very large dipole m o m e n t s showing significant La + H - charge separations.
Table 14 shows the weights of the leading configurations for the electronic states of L a H . Even the g r o u n d state of L a H is a mixture of 10220 2, 102~) 2 a n d l•2"lr, 2 configurations. T h e excited electronic states are considerably m o r e complex as evidenced from table 14.
We n o w c o m p a r e the properties of ScH, YH, and L a H . In c o m p a r i n g the R e values of the three molecules in their l y + g r o u n d states, we note that there is a sharp rise in
o
c o m p a r i n g the b o n d lengths of ScH with YH. However, the b o n d lengths of Y H (1.95 A)
o
and L a H (2.08 A) are quite similar. This is primarily because of the sharp rise in the 5py orbital participation in Y H c o m p a r e d to ScH. A l t h o u g h the 6p p o p u l a t i o n decreases for L a H , the 6s p o p u l a t i o n rises slightly. The La(5d) p o p u l a t i o n is e n h a n c e d in the 1Z + state.
Figure 16 c o m p a r e d the Des of ScH, Y H and LaH. We note that the M - H b o n d strength is significantly e n h a n c e d in going from ScH to YH, but the D r decreases in going f r o m Y H a n d L a H .
A n o t h e r q u a n t i t y of interest is the #e/Re ratio. This quantity c o m p a r e s the extent of charge transfer in the three species. As seen from fig. 17, the ize/R ~ values are similar for ScH and YH, b u t dramatically increases for L a H . This suggests significant ionic character of the L a - H bond.
T h e lo valence orbital of L a H is c o m p o s e d of La(6s) + H(ls) while the 2o orbital is c o m p o s e d of La(Sd), La(6pz ) and H(ls). Of course, the ~t a n d ~ orbitals are n o n - b o n d i n g . T h e M u I l i k e n - p o p u l a t i o n analysis of the i £ + g r o u n d state of L a H revealed that the La p o p u l a t i o n is 6s 1's2 6pO.22 5dO.97.