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Theoretical study of the low-lying electronic states of the BaH+ molecular ion
Volume 204, number 3,4
CHEMICAL PHYSICS LETTERS
19 March 1993
Theoretical study of the low-lying electronic states of the BaH+ molecular ion A.R. Allouche a, F. Spiegelmann b and M. Aubert-F&on a ’ Laboratoire de Spectromktrie Ionique et Mokulaire ‘, Universitt!Lyon I, Bhtiment 20543 Boulevard du 11 h’ovembre 1918,69622 Vilieurbanne Cedex, France ’ Laboratoire de Physique Quantique (UA SOSCNRS), IR SAMC, UniversitkPaul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France
Received 26 October 1992
Results of a theoretical study of the electronic structure of all the molecular states of BaH ’ dissociating into the three lowest asymptotes Ba++H are reported. The method used is basically the same as that previously used with success to describe the and 9”) bound states are displayed. molecule BaH. Values of a set of spectroscopic constants for previously unknown1,3A/1’+’
1. Introduction
The electronic structure of BaH has recently been investigated [ 11, using a ten-electron relativistic pseudopotential for barium, performing configuration interaction calculations for three active electrons and introducing a core-polarization potential. Good agreement with recent experiments [ 2,3 ] has been obtained showing that this process provides accurate energy predictions. Using basically the same method, we present here the results of a theoretical investigation of the low-lying states of the corresponding (and a priori simplest) molecular ion BaH+ for which, to the best of our knowledge, no experimental information is available while theoretical results exist only for the ground state [4,5].
2. Summary of the method The theoretical method used to describe the lowlying states of BaH+ is essentially the same as the one we previously described and used for an investigation of the molecule BaH. Only the main features are reported here; all details may be found in ref. [ 11. The barium atom is treated through a ten-electron ’ URACNRSNo. 171.
non-empirical relativistic effective core potential [ 61. A CI calculation is performed for the two active eleG trons of BaH+; core polarization and core-valence correlation are taken into account through a core polarization potential [ 7 1. The Gaussian basis sets used are (7s7p4d2f/&6p4d2f) for barium and (9s4pld/ 7s4p Id) taken from work of O’Neil et al. [ 81 for hydrogen. The molecular orbitals are obtained from a Nesbet SCF calculation which considers the organization of the Ba+ + H bond with the following occupation numbers: one electron on Ba+ (6s) and one electron on H( 1s). Configuration interaction calculations are performed through the CIPSI algorithm involving three subspaces [ 9 1, S containing the most important determinants, M including the medium contributions and T including the remaining (small) contributions. The sizes of these subspaces are selected iteratively according to a criterion 9 related to the first-order correction of the wavefunction. For BaH+ all determinants corresponding to q>O.Ol have been included in the subspace S and all those corresponding to ~3 0.002 have been included in the subspace M. The dimensions of the CI subspace S so provided for BaH+ are 368 for the symmetries X, A and 192 for the l-I symmetry. The second-order perturbative contribution to the total energy obtained in that way is seen to be always smaller than 1.4~ low3 au (z 307 cm-‘) showing
0009-2614/93/$ 06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.
343
Volume 204, number 3,4
CHEMICAL PHYSICS LETTERS
Table I Spin-orbit splittings (in cm-t) for Ba+ and parameters of the radial part dnfnexp( -a/) States
5d’ (*D) 6P’ (rP)
19 March 1993
of the spin-orbit operators used
Radial part parameters
Spin-orbit splittings present calculations (before scaling; see text)
exp. *)
d
C
ff
1318 1789
801 1691
0.607739 0.945221
0.231422 0.309623
1.164779 0.900876
“Ref. [ll].
that present results should be close to those of a two valence electron full-C1 calculation. Spin-orbit effects have been taken into account through a non-empirical spin-orbit pseudopotential [ lo] for P and D states of barium. Values of the spinorbit splitting for the states 5d’ 2D and 6~’ ‘P of Ba+ obtained in that way are displayed in table 1. In order to reproduce the experimental values [ 111 from the spin-orbit operators considered, we have scaled their radial part written as c, exp( - cepr2)by a multiplicative factor dp reported in table 1. The use of such an ab initio spin-orbit pseudopotential seems to be adequate for BaH+, contrary to our previous calculations on BaH [ 11.
Fig. 1. Adiabatic energy curves for the states ‘,Z of BaH+ dissociating into the three lowest asymptotes Ba+ (‘L) + H (‘S); (-) ‘Z states, (’ . .) 5 states.
344
3. Results Results have been obtained for all the molecular states dissociating into the three following asymptotesBa+(6s)2S+H(1~)2S, Ba+(5d)2D+H(ls)ZS and Ba+ (6~) *P+H( 1s) ‘S in the range of internuclear distances 2.5 4 RG 15 au. Two types of calculations have been performed, including or not spin-orbit coupling. 3.1. Spin-orbit effects neglected Twelve states labelled following the representation 2s+‘A(*), where A is the projection of the total or-
Fig. 2. Adiabatic energy curves for the states ‘~‘I3and ‘s3Aof BaH+ dissociating into Ba+(‘D) +H(2S) and Ba+(‘P) +H(%). (-) IfI states, ( ” .) ‘II states, (---) ‘,‘Astates (indistinguishable on the figure).
Volume 204, number 3,4
CHEMICAL
19 March 1993
PHYSICS LETTERS
bital angular momentum on the internuclear axis and the subscripts ( + ) denote the symmetry properties of the coordinate wavefunction, dissociate into the three asymptotes considered, i.e. three states ‘t3Z;+, two states 1,311and one state ‘,3A.Adiabatic energy curves are displayed in figs. 1 and 2 for the symmetries E and (II, A), respectively. Among the states investigated here, four are found to be repulsive, i.e. the three states 3C+ and the state ‘II dissociating to
Ba+ (5d) t H ( Is), the other eight ones being bound states. The solution of the radial equation for the nuclear motion through Hutson’s method [ 121 has provided at least 11, 6, 7, 3, 3, 4,2 and 2 vibrational energy levels for the XII;+, (2)‘C+, (3)‘Z+, ( I )313, ( 2)311, (2) ‘II, ( 1)3Aand ( 1) *A states, respectively. Corresponding values of vibrational energy G, and rotational constants B,, D, are presented in table 2. Spectroscopic constants have then been obtained
Table 2 Vibrational V
energies and rotational
constants
(in cm-’
) for the bound states ‘,j,l of BaH+
State (1)1x+
clG” B” 104D,
681
(2)%+
(3)‘C’
(lsn
(7-W
(2W
(1)‘A
(])‘A
250
247
222
225
173
139 1.655 2.64
137 1.631 2.65
376 1.426 3.55
368 1.403 3.55
3.578 0.98
2.041 1.33
1.590 0.65
2.128 2.20
1.969 1.62
2034 3.516 0.99
750 1.975 1.21
145 1.602 0.63
611 1.912 2.71
637 1.814 1.85
478
2 G, B” 104D,
3353 3.455
1236 1.913 1.12
1251 1.61 I 0.63
920 1.665 3.59
985 1.637 2.32
713 1.373 3.637
3 G, 8” 104D,
4644 3.393 0.98
1713 1.856 1.13
1761 1.614 0.63
4 G, B” IO’D,
5904 3.397 1.00
2172 1.786
2272 1.609
5 G, B” 104Dv
7128 3.260 1.01
2604 1.697 1.41
6 G, & 104D,
8318
7 G, B” 104D,
9412 3.124 1.05
8 Gv B, 104DU
10588 3.054 1.06
9 G” B, 104D,
11666 2.981 1.08
16 4 104D,
10 G, B, 104D,
0.98
3.193 1.03
1.21
1.807 2.18
I .609 2.72
879 1.114 4.876
0.62 2784 1.601 0.63 3284 3.589 0.63
12705 2.901 1.12
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Volume204, number 3,4
CHEMICALPHYSICSLETTERS
19March 1993
Table 3 Spectroscopicconstants (in cm-’ ) for the electronicstates I.51of BaH+ States
Constants R,(A)
(l)‘z+
(2)‘2+ (3)‘2’ (l)Q (2W (2W (t)3A (1)‘A
a) 2.156 b) 2.138 c) 2.164 2.847 3.242 2.737 2.862 2.948 3.086 3.108
r, (cm-‘)
0, (cm-‘)
o~d~(cm-’ )
Be(cm-‘)
ay,(cm-‘)
& (eV)
0
1370 I224
15
3.623
0.067
2.45 2.29
21237 33062 23675 39416 40061 24360 24382
503 494 463 465 363 291 287
6 -2 38 29 32 21 28
2.079 1.603 2.249 2.056 1.939 1.769 1.744
0.067 0.000 0.231 0.166 0.232 0.229 0.226
0.482 1.003 0.179 0.216 0.136 0.095 0.092
‘) Presentvalues. b, Ref. [ 6 1. ‘) Ref. [ 51.
from usual fitting and their estimated values are displayed in table 3 for bound states. To the best of our knowledge, there exist no ex-
perimental results for BaH+ up to now and present determinations are the first theoretical ones for excited states. For the ground state X ‘Z+, previous theoretical investigations have been performed and their results are presented in table 3 for comparison. Fuentealba and Reyes [ 41 investigated alkaline-earth monohydride ions through a pseudoporential formalism including a core-polarization potential and valence correlation energy was taken into account through a local spin-density functional with corrections for self interaction. Kaupp et al. [ 51 performed lo-valence-electron pseudopotential calculations, valence and core-valence correlation being including through single-double configuration interaction with Davidson’s correction. The present value for the equilibrium bound distance, R,, lies between these two previous theoretical predictions. The quantitative agreement is good, our result being 0.8% higher than that from Fuentealba and Reyes and 0.4% lower than that from Kaupp et al. We have calculated the overlap of molecular CI wavefunctions with non-orthogonal valence-bond configurations built up from non-orthogonal atomic orbitals situated on Ba or H in order to check the nature of the states. Numerical results are shown at R=4 au in table 4. For all states investigated here, the weight of the configurations Ba’ + H is the largest showing that these configurations should play an 346
important role in the electronic structure of BaH+. At R=4 au, the largest overlap is obtained for the
configuration Ba+ (5d) +H( 1s) for the X ‘ZE+state while for the (2)‘C+ state it is obtained for the configuration Ba+ (6s) + H( Is). This may contribute to the small avoided crossing around 6 au between these two states. 3.2. Spin-orbit coupling included Twenty-three states labelled following the representation .Q(‘), where Q is the absolute value of the projection of the total electronic angular momentum on the internuclear axis, dissociate into the three asymptotes considered, i.e. five states Q=O+, five states .Q=O-, eight states 8=1, four states 52=2 and one state R=3. Potential energy curves are displayed in figs. 3-5. Among these states, seventeen are attractive and six are repulsive, i.e. three pairs of states (O+, 1) dissociating to Baf (6s 2S,,2), Ba+(5d2D,,,), Ba+( 5p*P,,,)+H( l~?Yi,,~), respectively. Solution of the radial equation for the nuclear motion has provided at least 11, 6, 6, 7, 3, 3, 3,3,2, 2,2,4, 3, 3, 3, 5 and 3 vibrational energy levels G, and rotational constants B,,, D, for (l)O*, (2)0+, (3)0’, (4)OC, (5)0+, (2)0-, (4)0-, (2)1, (3)1, (4)L (611, (711, (112, (2)2, (312, (4)2and ( 1)3 states, respectively. Spectroscopic constants have been estimated from these results and they are presented in table 4. For each state R we have also quoted in parentheses its “main” parent state /1. The
CHEMICAL PHYSICS LETTERS
19 March 1993 BoH’ (O=O”-
State.)
Fig. 3. Adiabatic energy curves for the states Q=O+ and Q=Oof BaH+ dissociating into the five lowest asymptotes Ba+(2L,)+H(ZS,,2). (-).Q=O’states, (...) Q=O- states.
R (0.“)
Fig. 4. Adiabatic energy curves for the states R= I of BaH+ dissociating into the five lowest asymptotesBa+ (*L,) + H(‘SI12) .
influence of spin-orbit coupling on spectroscopic constants (other than the positiqn of state TC) is measured by the difference 6 between the value of a given constant for a state .Q and the corresponding value for the “main” parent state A. Values of 6 are reported in table 5. It is seen that the influence of 347
Volume 204, number 3,4 _
CHEMICAL PHYSICS LETTERS
19 March 1993
B.W(lx3.2St&!.)
-0.2
spin-orbit coupling is small for the states O+ related to ‘I+ states. In fact, values for ( 1)O+ state are found to be identical to that obtained for the X ‘E+ state. This influence is somewhat larger for the states 0” ) related to II states. For the states 52~ 1,2 and 3 this influence is seen to be significantly larger, due to the fact that the corresponding wavefunctions are a mixing of ASZ components.
k
G i5-0.225 6 -0.25
-0.275
-0.3 -0.325
-0.35
4 -0.425
4 Table 5 Spectroxopic
6
B
12
14
R(0.“)
Fig. 5. Adiabatic energy curves for the states a=2 and D= 3 of BaH+ dissociating into Ba+(*D,)+H(‘S,,z) and Ba+(*P& +H(2S,,2). (-)9=2states, (.‘.)L2=3state.
constants for the bound electronic states B of BaH+. Differences 6 with corresponding
values for the “main”
parent state
A are also quoted
states
Constant T. (cm-‘)
R,(A)
(lP+((l)‘~+)
2.156
0, (cm-‘) 0
s=o
u)o+( v)‘c+) (3)O’((l)“W (4)0+((3)‘c+) (5)0+((2)‘n) (2)0-((1)“W (4)0-((wn) (2)l((lYW (3)l((lYA) (4)l((l)‘W (6)1((2)‘W (7)lw)w (1)2((lYW (2)2((l)3A+(l)‘A) (3)2((l)‘A+(l)‘A) (4)2((2)3w (1)3((1)‘A)
348
2.843 6= -0.004 2.766 SzO.029 3.237 6= -0.005 2.876 LO.014 2.725 6= -0.012 2.867 kO.005 2.779 6x0.042 3.006 6= -0.080 3.159 2.900 SzO.038 2.922 6= -0.026 2.83 1 LO.094 2.937 3.085 2.835 6= -0.027 3.064 6= -0.022
21213 6= -24 23594 S= -81 33006 6=-56 39033 k-383 23517 6=-158 38917 6= -499 23606 s= -69 24065 6= -295 24137 39145 k-271 40316 6~255 23688 6=13 24334 24678 39893 a=477 24665 a=305
1370 &O 503 6=0 443 k-20 490 6= -4 461 k-4 458 6=-5 455 L-10 402 6=-61 330 6=39 279 425 k-40 402 &39 342 6=-121 401 293 476 6= 11 299 6~8
0~.
(cm-’
1
15 6=0 7 6=1 27 6=-11 -2 LO 29 6=0 49 6= 11 37 6=8 45 6-7 59 6~32 29 37 S=8 31 k-1 32 6=-6 39 31 33 6=4 32 s=5
B. (cm-‘)
a. (cm-‘)
3.624 6=0.001 2.084 6=0.005 2.202 s= -0.047 I.602 6= -0.001 2.036 6= -0.020 2.268 f&o.019 2.050 6= - 0.006
0.067 &O 0.074 &0.007 0.184 s= -0.047
2.182 6= -0.067 1.864 6= 0.095 1.688 2.003 6= -0.053 1.974 6sO.035 2.102 a=-0.147 1.953 1.770 2.096 s=o.o40 1.795 6= 0.026
0.289 kO.058 0.374 6=0.145 0.216 0.205 6=0.039 0.202 6= - 0.030 0.267 kO.036 0.232 0.242 0.194 LO.028 0.25 7 LO.028
0.001 6=0.001 0.163 6= -0.003 0.299 kO.068 0.206 6= 0.040
Volume204,number 3.4
CHEMICALPHYSICS LETTERS
4. Conclusion The electronic structure of all the molecular states of BaH+ dissociating to the three lowest asymptotes Ba++H has been investigated through a ten-electron effective core potential and a core-polarization potential. Spin-orbit coupling has been taken into account through a non-empirical spin-orbit pseu-
dopotential. For the ground state, calculated values of spectroscopic constants are in good agreement with previous theoretical results, while present values for the excited states are, to the best of our knowledge, the first determination of their characteristics.
References [ 1] A.R. Allouche, G. Nicolas, J.C. Barthelat and F. Spiegelmann, J. Chem. Phys.96 (1992) 7646. [ZIG. Fabre, A. El Hachimi, R. Stringat, C. Effantin, A. Bernard, J. D’Incan and I. Vergks, J. Pbys. B 20 (I987) 1933. [3] A. Bernard, C. Effantin, J. D’lncan, G. Fabre, R. Stringat and R.F. Barrow, Mol. Phys. 67 (1989) 1.
19 March 1993
[ 41 P. Fuentealba and 0. Reyes, Mol. Pbys. 62 ( 1987) 129I. [5 ] M. Kaupp, P. von R. Schleyer, H. Stoll and H. Preuss, J. Chem. Phys. 94 (1991) 1360. [6] Ph. Durand and J.C. Barthelat, Theoret. Chim. Acta 38 (1975) 283; J.C. Barthelat and Ph. Durand, Gazz. C&m. ItaI.108 (1978) 225; Y. Bouteiller, C. Mijoule, N. Nizam, J.C. Barthelat,J.P. Daudey, M. Pelissier and B. Silvi, Mol. Phys. 65 (1988) 295. 17] W. Milller, J. Flesch and W. Meyer, J. Chem. Phys. 80 (1984) 3297; M. Foucrault, Ph. Millik and J.P. Daudey, J. Chem. Phys. 96 (1992) 1257. [ 8 ] S.V. O’Neil, P. Rosmus, D.W. Norcross and J.H. Werner, J. Chem. Phys. 85 (1986) 7232. [ 9 ] B. Huron, P. Rancurel and J.P. Malrieu, J. Chem. Phys. 58 (1973) 5475; S. Evangelisti, J.P. Daudey and J.P. Malrieu, Chem. Phys. 75 (1983) 91. [ IO] C. Teichteil, M. Pelissier and F. Spiegelmann, Chem. Phys. 81 (1983) 273. [ I1 ] C.E. Moore, Atomic energy levels, NBS (US GPO, Washington, I97 1). [ 121J.M. Hutson, J. Phys. B 14 (1981) 851.
349
CHEMICAL PHYSICS LETTERS
19 March 1993
Theoretical study of the low-lying electronic states of the BaH+ molecular ion A.R. Allouche a, F. Spiegelmann b and M. Aubert-F&on a ’ Laboratoire de Spectromktrie Ionique et Mokulaire ‘, Universitt!Lyon I, Bhtiment 20543 Boulevard du 11 h’ovembre 1918,69622 Vilieurbanne Cedex, France ’ Laboratoire de Physique Quantique (UA SOSCNRS), IR SAMC, UniversitkPaul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France
Received 26 October 1992
Results of a theoretical study of the electronic structure of all the molecular states of BaH ’ dissociating into the three lowest asymptotes Ba++H are reported. The method used is basically the same as that previously used with success to describe the and 9”) bound states are displayed. molecule BaH. Values of a set of spectroscopic constants for previously unknown1,3A/1’+’
1. Introduction
The electronic structure of BaH has recently been investigated [ 11, using a ten-electron relativistic pseudopotential for barium, performing configuration interaction calculations for three active electrons and introducing a core-polarization potential. Good agreement with recent experiments [ 2,3 ] has been obtained showing that this process provides accurate energy predictions. Using basically the same method, we present here the results of a theoretical investigation of the low-lying states of the corresponding (and a priori simplest) molecular ion BaH+ for which, to the best of our knowledge, no experimental information is available while theoretical results exist only for the ground state [4,5].
2. Summary of the method The theoretical method used to describe the lowlying states of BaH+ is essentially the same as the one we previously described and used for an investigation of the molecule BaH. Only the main features are reported here; all details may be found in ref. [ 11. The barium atom is treated through a ten-electron ’ URACNRSNo. 171.
non-empirical relativistic effective core potential [ 61. A CI calculation is performed for the two active eleG trons of BaH+; core polarization and core-valence correlation are taken into account through a core polarization potential [ 7 1. The Gaussian basis sets used are (7s7p4d2f/&6p4d2f) for barium and (9s4pld/ 7s4p Id) taken from work of O’Neil et al. [ 81 for hydrogen. The molecular orbitals are obtained from a Nesbet SCF calculation which considers the organization of the Ba+ + H bond with the following occupation numbers: one electron on Ba+ (6s) and one electron on H( 1s). Configuration interaction calculations are performed through the CIPSI algorithm involving three subspaces [ 9 1, S containing the most important determinants, M including the medium contributions and T including the remaining (small) contributions. The sizes of these subspaces are selected iteratively according to a criterion 9 related to the first-order correction of the wavefunction. For BaH+ all determinants corresponding to q>O.Ol have been included in the subspace S and all those corresponding to ~3 0.002 have been included in the subspace M. The dimensions of the CI subspace S so provided for BaH+ are 368 for the symmetries X, A and 192 for the l-I symmetry. The second-order perturbative contribution to the total energy obtained in that way is seen to be always smaller than 1.4~ low3 au (z 307 cm-‘) showing
0009-2614/93/$ 06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.
343
Volume 204, number 3,4
CHEMICAL PHYSICS LETTERS
Table I Spin-orbit splittings (in cm-t) for Ba+ and parameters of the radial part dnfnexp( -a/) States
5d’ (*D) 6P’ (rP)
19 March 1993
of the spin-orbit operators used
Radial part parameters
Spin-orbit splittings present calculations (before scaling; see text)
exp. *)
d
C
ff
1318 1789
801 1691
0.607739 0.945221
0.231422 0.309623
1.164779 0.900876
“Ref. [ll].
that present results should be close to those of a two valence electron full-C1 calculation. Spin-orbit effects have been taken into account through a non-empirical spin-orbit pseudopotential [ lo] for P and D states of barium. Values of the spinorbit splitting for the states 5d’ 2D and 6~’ ‘P of Ba+ obtained in that way are displayed in table 1. In order to reproduce the experimental values [ 111 from the spin-orbit operators considered, we have scaled their radial part written as c, exp( - cepr2)by a multiplicative factor dp reported in table 1. The use of such an ab initio spin-orbit pseudopotential seems to be adequate for BaH+, contrary to our previous calculations on BaH [ 11.
Fig. 1. Adiabatic energy curves for the states ‘,Z of BaH+ dissociating into the three lowest asymptotes Ba+ (‘L) + H (‘S); (-) ‘Z states, (’ . .) 5 states.
344
3. Results Results have been obtained for all the molecular states dissociating into the three following asymptotesBa+(6s)2S+H(1~)2S, Ba+(5d)2D+H(ls)ZS and Ba+ (6~) *P+H( 1s) ‘S in the range of internuclear distances 2.5 4 RG 15 au. Two types of calculations have been performed, including or not spin-orbit coupling. 3.1. Spin-orbit effects neglected Twelve states labelled following the representation 2s+‘A(*), where A is the projection of the total or-
Fig. 2. Adiabatic energy curves for the states ‘~‘I3and ‘s3Aof BaH+ dissociating into Ba+(‘D) +H(2S) and Ba+(‘P) +H(%). (-) IfI states, ( ” .) ‘II states, (---) ‘,‘Astates (indistinguishable on the figure).
Volume 204, number 3,4
CHEMICAL
19 March 1993
PHYSICS LETTERS
bital angular momentum on the internuclear axis and the subscripts ( + ) denote the symmetry properties of the coordinate wavefunction, dissociate into the three asymptotes considered, i.e. three states ‘t3Z;+, two states 1,311and one state ‘,3A.Adiabatic energy curves are displayed in figs. 1 and 2 for the symmetries E and (II, A), respectively. Among the states investigated here, four are found to be repulsive, i.e. the three states 3C+ and the state ‘II dissociating to
Ba+ (5d) t H ( Is), the other eight ones being bound states. The solution of the radial equation for the nuclear motion through Hutson’s method [ 121 has provided at least 11, 6, 7, 3, 3, 4,2 and 2 vibrational energy levels for the XII;+, (2)‘C+, (3)‘Z+, ( I )313, ( 2)311, (2) ‘II, ( 1)3Aand ( 1) *A states, respectively. Corresponding values of vibrational energy G, and rotational constants B,, D, are presented in table 2. Spectroscopic constants have then been obtained
Table 2 Vibrational V
energies and rotational
constants
(in cm-’
) for the bound states ‘,j,l of BaH+
State (1)1x+
clG” B” 104D,
681
(2)%+
(3)‘C’
(lsn
(7-W
(2W
(1)‘A
(])‘A
250
247
222
225
173
139 1.655 2.64
137 1.631 2.65
376 1.426 3.55
368 1.403 3.55
3.578 0.98
2.041 1.33
1.590 0.65
2.128 2.20
1.969 1.62
2034 3.516 0.99
750 1.975 1.21
145 1.602 0.63
611 1.912 2.71
637 1.814 1.85
478
2 G, B” 104D,
3353 3.455
1236 1.913 1.12
1251 1.61 I 0.63
920 1.665 3.59
985 1.637 2.32
713 1.373 3.637
3 G, 8” 104D,
4644 3.393 0.98
1713 1.856 1.13
1761 1.614 0.63
4 G, B” IO’D,
5904 3.397 1.00
2172 1.786
2272 1.609
5 G, B” 104Dv
7128 3.260 1.01
2604 1.697 1.41
6 G, & 104D,
8318
7 G, B” 104D,
9412 3.124 1.05
8 Gv B, 104DU
10588 3.054 1.06
9 G” B, 104D,
11666 2.981 1.08
16 4 104D,
10 G, B, 104D,
0.98
3.193 1.03
1.21
1.807 2.18
I .609 2.72
879 1.114 4.876
0.62 2784 1.601 0.63 3284 3.589 0.63
12705 2.901 1.12
345
Volume204, number 3,4
CHEMICALPHYSICSLETTERS
19March 1993
Table 3 Spectroscopicconstants (in cm-’ ) for the electronicstates I.51of BaH+ States
Constants R,(A)
(l)‘z+
(2)‘2+ (3)‘2’ (l)Q (2W (2W (t)3A (1)‘A
a) 2.156 b) 2.138 c) 2.164 2.847 3.242 2.737 2.862 2.948 3.086 3.108
r, (cm-‘)
0, (cm-‘)
o~d~(cm-’ )
Be(cm-‘)
ay,(cm-‘)
& (eV)
0
1370 I224
15
3.623
0.067
2.45 2.29
21237 33062 23675 39416 40061 24360 24382
503 494 463 465 363 291 287
6 -2 38 29 32 21 28
2.079 1.603 2.249 2.056 1.939 1.769 1.744
0.067 0.000 0.231 0.166 0.232 0.229 0.226
0.482 1.003 0.179 0.216 0.136 0.095 0.092
‘) Presentvalues. b, Ref. [ 6 1. ‘) Ref. [ 51.
from usual fitting and their estimated values are displayed in table 3 for bound states. To the best of our knowledge, there exist no ex-
perimental results for BaH+ up to now and present determinations are the first theoretical ones for excited states. For the ground state X ‘Z+, previous theoretical investigations have been performed and their results are presented in table 3 for comparison. Fuentealba and Reyes [ 41 investigated alkaline-earth monohydride ions through a pseudoporential formalism including a core-polarization potential and valence correlation energy was taken into account through a local spin-density functional with corrections for self interaction. Kaupp et al. [ 51 performed lo-valence-electron pseudopotential calculations, valence and core-valence correlation being including through single-double configuration interaction with Davidson’s correction. The present value for the equilibrium bound distance, R,, lies between these two previous theoretical predictions. The quantitative agreement is good, our result being 0.8% higher than that from Fuentealba and Reyes and 0.4% lower than that from Kaupp et al. We have calculated the overlap of molecular CI wavefunctions with non-orthogonal valence-bond configurations built up from non-orthogonal atomic orbitals situated on Ba or H in order to check the nature of the states. Numerical results are shown at R=4 au in table 4. For all states investigated here, the weight of the configurations Ba’ + H is the largest showing that these configurations should play an 346
important role in the electronic structure of BaH+. At R=4 au, the largest overlap is obtained for the
configuration Ba+ (5d) +H( 1s) for the X ‘ZE+state while for the (2)‘C+ state it is obtained for the configuration Ba+ (6s) + H( Is). This may contribute to the small avoided crossing around 6 au between these two states. 3.2. Spin-orbit coupling included Twenty-three states labelled following the representation .Q(‘), where Q is the absolute value of the projection of the total electronic angular momentum on the internuclear axis, dissociate into the three asymptotes considered, i.e. five states Q=O+, five states .Q=O-, eight states 8=1, four states 52=2 and one state R=3. Potential energy curves are displayed in figs. 3-5. Among these states, seventeen are attractive and six are repulsive, i.e. three pairs of states (O+, 1) dissociating to Baf (6s 2S,,2), Ba+(5d2D,,,), Ba+( 5p*P,,,)+H( l~?Yi,,~), respectively. Solution of the radial equation for the nuclear motion has provided at least 11, 6, 6, 7, 3, 3, 3,3,2, 2,2,4, 3, 3, 3, 5 and 3 vibrational energy levels G, and rotational constants B,,, D, for (l)O*, (2)0+, (3)0’, (4)OC, (5)0+, (2)0-, (4)0-, (2)1, (3)1, (4)L (611, (711, (112, (2)2, (312, (4)2and ( 1)3 states, respectively. Spectroscopic constants have been estimated from these results and they are presented in table 4. For each state R we have also quoted in parentheses its “main” parent state /1. The
CHEMICAL PHYSICS LETTERS
19 March 1993 BoH’ (O=O”-
State.)
Fig. 3. Adiabatic energy curves for the states Q=O+ and Q=Oof BaH+ dissociating into the five lowest asymptotes Ba+(2L,)+H(ZS,,2). (-).Q=O’states, (...) Q=O- states.
R (0.“)
Fig. 4. Adiabatic energy curves for the states R= I of BaH+ dissociating into the five lowest asymptotesBa+ (*L,) + H(‘SI12) .
influence of spin-orbit coupling on spectroscopic constants (other than the positiqn of state TC) is measured by the difference 6 between the value of a given constant for a state .Q and the corresponding value for the “main” parent state A. Values of 6 are reported in table 5. It is seen that the influence of 347
Volume 204, number 3,4 _
CHEMICAL PHYSICS LETTERS
19 March 1993
B.W(lx3.2St&!.)
-0.2
spin-orbit coupling is small for the states O+ related to ‘I+ states. In fact, values for ( 1)O+ state are found to be identical to that obtained for the X ‘E+ state. This influence is somewhat larger for the states 0” ) related to II states. For the states 52~ 1,2 and 3 this influence is seen to be significantly larger, due to the fact that the corresponding wavefunctions are a mixing of ASZ components.
k
G i5-0.225 6 -0.25
-0.275
-0.3 -0.325
-0.35
4 -0.425
4 Table 5 Spectroxopic
6
B
12
14
R(0.“)
Fig. 5. Adiabatic energy curves for the states a=2 and D= 3 of BaH+ dissociating into Ba+(*D,)+H(‘S,,z) and Ba+(*P& +H(2S,,2). (-)9=2states, (.‘.)L2=3state.
constants for the bound electronic states B of BaH+. Differences 6 with corresponding
values for the “main”
parent state
A are also quoted
states
Constant T. (cm-‘)
R,(A)
(lP+((l)‘~+)
2.156
0, (cm-‘) 0
s=o
u)o+( v)‘c+) (3)O’((l)“W (4)0+((3)‘c+) (5)0+((2)‘n) (2)0-((1)“W (4)0-((wn) (2)l((lYW (3)l((lYA) (4)l((l)‘W (6)1((2)‘W (7)lw)w (1)2((lYW (2)2((l)3A+(l)‘A) (3)2((l)‘A+(l)‘A) (4)2((2)3w (1)3((1)‘A)
348
2.843 6= -0.004 2.766 SzO.029 3.237 6= -0.005 2.876 LO.014 2.725 6= -0.012 2.867 kO.005 2.779 6x0.042 3.006 6= -0.080 3.159 2.900 SzO.038 2.922 6= -0.026 2.83 1 LO.094 2.937 3.085 2.835 6= -0.027 3.064 6= -0.022
21213 6= -24 23594 S= -81 33006 6=-56 39033 k-383 23517 6=-158 38917 6= -499 23606 s= -69 24065 6= -295 24137 39145 k-271 40316 6~255 23688 6=13 24334 24678 39893 a=477 24665 a=305
1370 &O 503 6=0 443 k-20 490 6= -4 461 k-4 458 6=-5 455 L-10 402 6=-61 330 6=39 279 425 k-40 402 &39 342 6=-121 401 293 476 6= 11 299 6~8
0~.
(cm-’
1
15 6=0 7 6=1 27 6=-11 -2 LO 29 6=0 49 6= 11 37 6=8 45 6-7 59 6~32 29 37 S=8 31 k-1 32 6=-6 39 31 33 6=4 32 s=5
B. (cm-‘)
a. (cm-‘)
3.624 6=0.001 2.084 6=0.005 2.202 s= -0.047 I.602 6= -0.001 2.036 6= -0.020 2.268 f&o.019 2.050 6= - 0.006
0.067 &O 0.074 &0.007 0.184 s= -0.047
2.182 6= -0.067 1.864 6= 0.095 1.688 2.003 6= -0.053 1.974 6sO.035 2.102 a=-0.147 1.953 1.770 2.096 s=o.o40 1.795 6= 0.026
0.289 kO.058 0.374 6=0.145 0.216 0.205 6=0.039 0.202 6= - 0.030 0.267 kO.036 0.232 0.242 0.194 LO.028 0.25 7 LO.028
0.001 6=0.001 0.163 6= -0.003 0.299 kO.068 0.206 6= 0.040
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4. Conclusion The electronic structure of all the molecular states of BaH+ dissociating to the three lowest asymptotes Ba++H has been investigated through a ten-electron effective core potential and a core-polarization potential. Spin-orbit coupling has been taken into account through a non-empirical spin-orbit pseu-
dopotential. For the ground state, calculated values of spectroscopic constants are in good agreement with previous theoretical results, while present values for the excited states are, to the best of our knowledge, the first determination of their characteristics.
References [ 1] A.R. Allouche, G. Nicolas, J.C. Barthelat and F. Spiegelmann, J. Chem. Phys.96 (1992) 7646. [ZIG. Fabre, A. El Hachimi, R. Stringat, C. Effantin, A. Bernard, J. D’Incan and I. Vergks, J. Pbys. B 20 (I987) 1933. [3] A. Bernard, C. Effantin, J. D’lncan, G. Fabre, R. Stringat and R.F. Barrow, Mol. Phys. 67 (1989) 1.
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[ 41 P. Fuentealba and 0. Reyes, Mol. Pbys. 62 ( 1987) 129I. [5 ] M. Kaupp, P. von R. Schleyer, H. Stoll and H. Preuss, J. Chem. Phys. 94 (1991) 1360. [6] Ph. Durand and J.C. Barthelat, Theoret. Chim. Acta 38 (1975) 283; J.C. Barthelat and Ph. Durand, Gazz. C&m. ItaI.108 (1978) 225; Y. Bouteiller, C. Mijoule, N. Nizam, J.C. Barthelat,J.P. Daudey, M. Pelissier and B. Silvi, Mol. Phys. 65 (1988) 295. 17] W. Milller, J. Flesch and W. Meyer, J. Chem. Phys. 80 (1984) 3297; M. Foucrault, Ph. Millik and J.P. Daudey, J. Chem. Phys. 96 (1992) 1257. [ 8 ] S.V. O’Neil, P. Rosmus, D.W. Norcross and J.H. Werner, J. Chem. Phys. 85 (1986) 7232. [ 9 ] B. Huron, P. Rancurel and J.P. Malrieu, J. Chem. Phys. 58 (1973) 5475; S. Evangelisti, J.P. Daudey and J.P. Malrieu, Chem. Phys. 75 (1983) 91. [ IO] C. Teichteil, M. Pelissier and F. Spiegelmann, Chem. Phys. 81 (1983) 273. [ I1 ] C.E. Moore, Atomic energy levels, NBS (US GPO, Washington, I97 1). [ 121J.M. Hutson, J. Phys. B 14 (1981) 851.
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