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Theoretical electronic structure of the lowest-lying states of the LaI molecule
Journal of Molecular Spectroscopy 221 (2003) 1–6 www.elsevier.com/locate/jms
Theoretical electronic structure of the lowest-lying states of the LaI molecule F. Taher-Mansour,a A.R. Allouche,b and M. Aubert-Freconb,* b
a Universit e Libanaise, Facult e de G enie, route de l’a eroport, Beyrouth, Liban Laboratoire de Spectrom etrie Ionique et Mol eculaire UMR 5579, CNRS et Universit e Lyon I, Campus de La Doua, B^ at. Alfred Kastler, 43 Bd du 11 Novembre 1918 Bat 205, F69622 Villeurbanne Cedex, France
Received 25 October 2002; in revised form 6 March 2003
Abstract CAS-SCF/MRCI calculations have been performed for 11 molecular states in the representation 2Sþ1 KðþÞ (neglecting spin–orbit effects) for the molecule LaI. The corresponding 25 molecular states in the representation Xðþ=Þ (including spin–orbit effects) have been calculated using a semi-empirical spin–orbit pseudopotential built-up for lanthanum. Calculated potential energy curves and spectroscopic constants are reported, to the best of our knowledge they are the first ones from ab initio methods for this molecule. Ó 2003 Published by Elsevier Science (USA).
1. Introduction The present investigation is devoted to the prediction of the electronic spectrum of the LaI molecule. Among lanthanum monohalides the fluoride LaF is the species which has received the largest experimental interest [1– 10] while we knew of only one experimental study for both the monochloride LaCl [11] and the monoiodide LaI [12]. A recent ab initio theoretical investigation of the lowest-lying electronic states of LaF [13] was seen to produce predictions of a good quality when compared to highly accurate experimental data. Stimulated by both a lack of theoretical work on LaI and the existence of preliminary data obtained in our laboratory from high resolution laser-induced fluorescence LIF spectroscopy, we have performed an ab initio investigation of the low-lying states of this molecule, using an approach similar to that previously used to describe the isovalent species LaF. In this paper we present potential energy curves and spectroscopic constants calculated for 11 2Sþ1 KðþÞ (without spin–orbit effects) and 25 Xðþ=Þ (including spin–orbit effects) molecular states of LaI. The possible * Corresponding author. Fax: +33-4-72-43-15-07. E-mail address: [email protected] (M. Aubert-Frecon).
0022-2852/$ - see front matter Ó 2003 Published by Elsevier Science (USA). doi:10.1016/S0022-2852(03)00151-6
assignment previously proposed for the four low-lying states observed from high resolution LIF spectroscopy [12] are considered in the light of present results.
2. Computational approach Both species lanthanum and iodine are described in a pseudopotential scheme. Lanthanum is treated as a system with 46 inner electrons taken into account through a pseudopotential Wps (La) from [14]. The contracted Gaussian basis set used is derived from the literature one [14] augmented by f-type functions from [15]. For iodine, considered as a system with 46 inner electrons we used a pseudopotential [16] together with the corresponding Gaussian basis set. The LaI molecule in its lowest-lying states and in a range of internuclear distances around the equilibrium distance of its ground state is assumed to be mainly ionic. Therefore, spin– orbit (SO) effects are taken into account for Laþ while they are neglected for I which is assumed to be involved in the lowest-lying states of LaI mainly through its ground state. For lanthanum, SO effects are introduced via a semi-empirical spin–orbit pseudopotential ps WSO that we designed in our previous study of the electronic structure of the isovalent molecule LaF [13].
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Energy calculations for 11 states 2Sþ1 Kðþ=Þ of the molecule LaI have been performed using a CAS-SCF method. Correlation effects have been taken into account through MRCI calculations. Among the 18 electrons explicitly considered for LaI (46 core electrons for La as well as 46 core electrons for I were treated via pseudopotentials) 10 inner electrons were frozen in subsequent calculations so that eight valence electrons were explicitly treated. The active space contained 4r (La: 6s,5d0 , 7s,6d0 ), 2p (La: 5d1 ,6d1 ) and 2d (La: 5d2 ,6d2 ) orbitals. In the C2v symmetry this corresponds to 12 active molecular orbitals distributed into irreducible representations a1 ,b1 , b2 , and a2 in the following way: 6a1 ,2b1 , 2b2 , 2a2 , noted [6222]. The (doubly occupied) orbitals r(5pz ) and p(5p1 ) of the iodine species were considered as inactive in the CAS-SCF calculations. Multireference CI calculations (single and double excitations + Davidson correction) were performed to account for correlations effects for the eight valence electrons. The entire CAS-SCF configuration space was used as the reference in the MRCI calculations. For the a1 symmetry this results in 17 517 configuration state functions (CSF) for singlet states and 23 628 for triplet ones while for the b1 symmetry this corresponds to 12 858 and 20 058 CSF for singlet and triplet states, respectively. Energies including spin–orbit effects were obtained from the diagonalization of the matrix energy corresponding to the electrostatic Hamps iltonian + WSO . It was built-up on the basis of CAS-SCF wavefunctions while diagonal matrix elements came from CI + Davidson correction calculations. Calculations have been performed via the computational chemistry program MOLPRO [17] taking advantage of our graphical user interface GABEDIT [18].
Fig. 1. Potential energy curves for the 1;3 Rðþ=Þ states. Full lines: 1 Rþ ; dashed line: 3 Rþ ; and dotted line: 3 R .
3. Results and discussion Calculations have been performed for 111 internu for 11 states in the clear distances in the range 2.5–3.6 A 2Sþ1 ðþÞ K (neglecting SO effects) and 25 representation states in the representation Xðþ=Þ (including SO effects). Potential energy curves (PECs) are drawn in Fig. 1 for the 1;3 Rðþ=Þ states and in Fig. 2 for the P, D, and U states, the zero of energy begin chosen at the bottom of the ground state X1 Rþ . As known from experiment the lowest-energy state is found to be the (1)1 Rþ state. Nevertheless, as for the LaF molecule, the (1)3 D-PEC is . In the seen to cross the (1)1 Rþ -PEC around R ¼ 3:47 A range of R considered here, the PECs for the states
Fig. 2. Potential energy curves for the 1;3 K states. Full lines: 3 D states; dashed lines: 3 P states; dotted line: 1 D state; dashed-dotted line: 1 P state; and points D: 3 U state.
Fig. 3. Potential energy curves for the states X ¼ 0=þ . Full lines: 0þ states and dashed lines: 0 states.
F. Taher-Mansour et al. / Journal of Molecular Spectroscopy 221 (2003) 1–6
(1)1 P and (1)1 D are found to be close to each other, the (1)1 D state being the lowest one, up to a crossing be. The tween the two states which takes place 3.16 A 1 þ energy curve of the (2) R state crosses the PECs of the , (1)3 U, (1)3 R , and (2)3 P states at 2.9, 3.34, and 3.5 A respectively. For states in the representation Xðþ=Þ , PECs are drawn in Fig. 3 for the symmetries X ¼ 0þ , 0 ; in Fig. 4 for the symmetry X ¼ 1 and in Fig. 5 for the symmetries
3
X ¼ 2; 3; 4, the zero of energy being chosen at the bottom of the ground state (1)0þ . All theses curves present no avoided crossing in the range of R considered here. We present in Table 1 the composition (in percentage) of the X state-wavefunctions in terms of the states SK, . For some states (18 among the calculated at R ¼ 3:0 A 25 investigated) the largest percentage exceeds 80% so that a main parent SK may be identified for the X state
Fig. 5. Potential energy curves for the states X ¼ 2; 3; 4. Full lines: X ¼ 2 states; dashed lines: X ¼ 3 states; and dotted line: X ¼ 4 state.
Fig. 4. Potential energy curves for the states X ¼ 1.
Table 1 Composition of X-state wavefunctions in terms of SK terms (in percentage) X [Main parent]
X1 R þ
(1)0þ [(1)1 Rþ ] (1)1[(1)3 D] (1)2[(1)3 D] (1)3[(1)3 D] (1)0 [(1)3 P] (2)0þ [(1)3 P] (2)1[(1)3 P] (2)2[(1)3 P] (3)2[(1)1 D] (3)1[(1)1 P] (4)1[(1)3 Rþ ] (2)0 [(1)3 Rþ ] (4)2[(1)3 U] (3)0þ (2)3[(1)3 U] (5)1 (4)0þ (1)4[(1)3 U] (3)0 [(2)3 P] (5)2[(2)3 P] (6)1 (5)0þ (7)1 (6)2 (3)3[(2)3 D]
99
(1)1 D
(2)1 Rþ
(1)3 D
(1)3 Rþ
(2)3 D
(1)1 P
4 1
1 11 86
4
9
1 95 95
87 3
2 1
2
(1)3 U
(2)3 P
(1)3 R
1 1 1
99 97 100
2
(1)3 P
96 98 87 87 12 10 2 5
2 1
2
96
3 5
97
48 1
50
18
34
34 28
60 22
100 18 36
1 1
1 59 79 97
2 3
100 81 29 55 36 19
34 44 5
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considered. For the seven remaining states the composition of their wavefunction spreads over several (2 or 3) states SK with a contribution larger than 18% so that the attribution of one main parent SK to those states is no longer possible. This situation is somewhat different from that previously observed for LaF [13] for which we identified a main parent for each X state. In order to calculate some spectroscopic constants: transition energy with respect to the energy minimum for the ground state Te , equilibrium internuclear distance Re , and harmonic frequency xe the calculated energy values were fitted to a polynomial in R, the significant degree of which being determined from the evaluation of the statistical error for the coefficients. It should be noted that for two states namely the (4)1[(1)3 Rþ ] and the (4)2[(1)3 U] we were able to determine with some accuracy only the position of the energy minimum by using a few points around this minimum due to the peculiar form of their respective PECs as
Fig. 6. Potential energy curves for the states (4)X ¼ 1 (full line) and (4)X ¼ 2 (dotted line) in a range near their bottom.
Table 2 Spectroscopic constants for the lowest-lying molecular states of LaI States 1
þ
X R (1)3 D (1)3 P (1)1 D (1)1 P (1)3 Rþ (1)3 U (2)1 Rþ (1)3 R (2)3 P (2)3 D
2Sþ1
Te (cm1 )
) Re (A
xe (cm1 )
0 1408 3852 4597 4636 6448 7343 7696 8130 8518 9363
2.947 3.012 3.040 3.052 3.060 3.053 3.102 3.062 3.098 3.107 3.118
179.9 166.1 161.3 158.5 156.5 154.0 148.1 156.2 146.2 146.3 142.4
KðþÞ
Table 3 Spectroscopic constants for the lowest-lying molecular states Xðþ=Þ of LaI States
Te (cm1 )
) Re (A
xe (cm1 )
(1)0þ [(1)1 Rþ ] (2)0þ [(1)3 P] (3)0þ (4)0þ (5)0þ
0 3605 7200 8091 8988
2.949 3.036 3.089 3.094 3.099
179.8 162.3 146.7 140.7 146.9
(1)0 [(1)3 P] (2)0 [(1)3 Rþ ] (3)0 [(2)3 P]
3472 6607 8370
3.039 3.054 3.110
161.1 153.8 145.3
(1)1[(1)3 D] (2)1[(1)3 P] (3)1[(1)1 P] (4)1[(1)3 Rþ ] (5)1 (6)1 (7)1
937 3737 4684 6601 7772 8556 9362
3.014 3.041 3.055 3.053 3.105 3.107 3.111
165.7 160.4 163.2
(1)2[(1)3 D] (2)2[(1)3 P] (3)2[(1)1 D] (4)2[(1)3 U] (5)2[(2)3 P] (6)2
1353 4108 4672 6642 8473 9724
3.014 3.041 3.056 3.085 3.108 3.114
165.8 161.0 154.5
(1)3[(1)3 D] (2)3[(1)3 U] (1)3[(2)3 D]
1885 7297 9927
3.011 3.102 3.117
166.3 148.0 142.7
(1)4[(1)3 U]
8093
3.101
148.2
145.8 144.7 144.8
145.4 143.6
shown in Fig. 6. Results are displayed in Table 2 for the states 2Sþ1 KðþÞ and in Table 3 for the states Xðþ=Þ . The main parents SK for each state X for which they have been identified are also quoted in Table 3. In order to compare our predictions to the experimental data obtained from the analysis of high resolution fluorescence spectra of LaI [12], we calculated some vibrational transition energies DTv0 ;v00 ¼ Gv0 (excited state) ) Gv00 (X) for the four lowest excited states (1)3 D, (1)3 P, (1)1 D, and (1)1 P. Some results are summarised in Table 4. Calculations confirm that the ground state is the (1)1 Rþ state. The calculated value 179.9 cm1 for the xe of the ground state is quite near the experimental value 183.76 cm1 for DGvþ1=2 . The experimental Tv value observed at 1064.33 cm1 has been ascribed to a component i of the (1)3 D state, from experimental analysis. This is consistent with present calculations. The Tv value observed at 4839.21 cm1 has been attributed to a X ¼ 1 state. In that range of transition energies, there are two X ¼ 1 states: the (1)3 P1 and the (1)1 P1 . The better agreement with present predictions corresponds to the state (1)1 P1 as shown in Table 4. With an hypothesis of a 0–0 vibrational transition the discrepancy would be 200 cm1 while it would reach 1100 cm1 if we assume that the excited state is the (1)3 P1 . Furthermore the agreement is better between the experimental value of DGvþ1=2 and the calculated xe value for the singlet
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5
Table 4 Calculated vibrational transition energies DTv0 v00 and vibrational constants xe (in cm1 ), compared to experimental molecular constants Tv and DGvþ1=2 [12] Experimental Tv
Experimental DGvþ1=2
Excited state
Calculated xe
Excited state v0
Ground state v00
DTv0 v00
1064.33
174.39
(1)3 D1
165.7
(1)3 D2
165.8
0 1 0 0
0 0 0 1
930 1095 1346 1167
(1)3 P1
160.4
(1)1 P1
163.2
0 1 2 0 1
0 0 0 0 0
3726 3886 4046 4672 4834
(1)1 D2
154.5
0 1 2
0 0 0
4660 4813 4967
4839.21
164.24
5254.76
165.00
Table 5 Calculated spin–orbit splittings at the energy minima (in cm1 ) for the triplet states (1)3 P X X0 DE
0 0þ 133
DEtot
636
(1)3 D 0þ 1 132
1 2 371
than for the triplet state. The Tv value observed at 5254.76 cm1 has been assumed to correspond to the state (1)1 D2 from the experimental analysis. In that energy range the X ¼ 2 states are those corresponding to the (1)3 P and (1)1 D states. The calculated transition energies for the (1)3 P2 are too low when compared to the experimental value, while it may be considered as compatible with the assumption of the (1)1 D2 state. The discrepancy would be of 600 cm1 in the hypothesis of a 0–0 transition and of 400 cm1 in the hypothesis of a 1–0 vibrational transition. When comparing the calculated electronic structure for LaF and LaI, it should be noted that the eight lowest states are the same. The ground state is (1)1 Rþ and crosses the (1)3 D state in the right part of the energy from the curve, at a distance of 0.4 and of 0.5 A equilibrium position for LaF and LaI, respectively. The transition energies for the eight lowest states decrease largely from LaF to LaI. The largest transition energies which correspond to the (2)1 Rþ state are 11 900 cm1 for LaF and 7700 cm1 for LaI. Nevertheless the energy difference between the (1)1 D and (1)3 D states remains quite similar for the two molecules (calculated values: 3190 cm1 for LaI and 3400 cm1 for LaF) so that there is an inversion in the lowest second and third excited states when going from LaF ((1)1 D, (1)3 P) to LaI ((1)3 P, (1)1 D). This is analog to the situation pre-
1 2 416 948
(1)3 U 2 3 532
2 3 655
3 4 796
1451
viously observed for scandium monofluoride and monoiodide [19]. Spin–orbit splittings: DE ¼ EðX0 Þ EðXÞ as well as the largest one DEtot (from the highest to the lowest component) evaluated at the well position for the triplet states for which we were able to identify the spin–orbit components, i.e., the states (1)3 P0;0þ;1;2 , (1)3 D1;2;3 , and (1)3 U2;3;4 , are summarised in Table 5. For these states the multiplet components are found to be unequally spaced as was observed for the LaF molecule both from experiment [8,9] and from calculations [13]. Large spin– orbit splittings are obtained for both states (1)3 D and (1)3 U, in agreement with the large experimental atomic values for Laþ [(1)3 DJ ] and Laþ [(1)3 FJ ], respectively. Calculated values are similar for the two molecules LaF and LaI. This could be expected due to the fact that in present calculations these two molecules are assumed to be describable by Laþ + X (1 S0 ) and that only spin– orbit effects for Laþ have been taken into account.
4. Conclusion An ab initio investigation of the lowest-lying molecular states of LaI has been performed via CAS-SCF and MRCI (SD + Davidson correction) calculations. Spin–orbit effects have been introduced through a
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semi-empirical spin–orbit pseudopotential designed for lanthanum. Potential energy curves and spectroscopic constants have been obtained for 11 2Sþ1 KðþÞ and 25 Xðþ=Þ states. We knew no previous ab initio study of the electronic structure for this molecule. In the light of present calculations the possible assignment proposed for the four low-lying states observed from LIF spectroscopy [12] have been confirmed.
Acknowledgments Many thanks are due to Professors Christiane Effantin, Jean dÕIncan, and Alain Bernard for many valuable discussions and for their critical reading of the manuscript.
References [1] R.F. Barrow, M.W. Bastin, D.L.G. Moore, C.J. Pott, Nature 215 (1967) 1072–1073. [2] H. Schall, C. Linton, R.W. Field, J. Mol. Spectrosc. 100 (1983) 437–448. [3] B. Simard, A.M. James, J. Chem. Phys. 97 (1992) 4669–4678. [4] L.A. Kaledin, J.E. McCord, M.C. Heaven, J. Opt. Soc. Am. B 11 (1994) 219–224. [5] L.A. Kaledin, A.L. Kaledin, M.C. Heaven, J. Mol. Spectrosc. 182 (1997) 50–56.
[6] J. Verges, C. Effantin, J. dÕIncan, A. Bernard, E.A. Shenyasvskaya, J. Mol. Spectrosc. 198 (1999) 196–198. [7] A. Bernard, C. Effantin, J. dÕIncan, J. Verges, J. Mol. Spectrosc. 202 (2000) 163–165. [8] A. Bernard, C. Effantin, J. dÕIncan, J. Verges, J. Mol. Spectrosc. 204 (2000) 55–59. [9] A. Bernard, C. Effantin, E.A. Shenyasvskaya, J. dÕIncan, J. Mol. Spectrosc. 207 (2001) 211–215. [10] C. Effantin, J. dÕIncan, A. Bernard, J. Mol. Spectrosc. 216 (2002) 166–167. [11] J. Xin, L. Klynning, Phys. Scripta 49 (1994) 209–213. [12] C. Effantin, J. dÕIncan, A. Bernard, E.A. Shenyasvskaya, A. Topouzkhanian, G. Wannous, J. Mol. Spectrosc. 192 (1998) 394– 398. [13] K. Fahs, A.R. Allouche, M. Korek, M. Aubert-Frecon, J. Chem. Phys. 117 (2002) 3715–3720. [14] W.J. Stevens, M. Krauss, H. Basch, P.G. Jasien, Can. J. Chem. 70 (1992) 612–630. [15] X. Cao, M. Dolg, J. Chem. Phys. 115 (2001) 7348–7355. [16] Stuttgart pseudopotential (ECP46MDF) taken from MOLPRO. [17] MOLPRO is a package of ab initio programs written by H.-J. Werner and P.J. Knowles, with contributions from R.D. Amos, A. Bernhardsson, A. Berning, P. Celani, D.L. Cooper, M.J.O. Deegan, A.J. Dobbyn,F. Eckert, C. Hampel, G. Hetzer, T. Korona, R. Lindh, A.W. Lloyd, S.J. McNicholas, F.R. Manby, W. Meyer, M.E. Mura, A. Nicklass, P. Palmieri, R. Pitzer, G. Rauhut, M. Sch€ utz, H. Stoll, A.J. Stone, R. Tarroni, T. Thorsteinsson. [18] GABEDIT a graphical user interface for the use of MOLPRO available at our website: http://lasim.univ-lyon1.fr/allouche/gabedit. [19] C. Effantin, E.A. Shenyasvskaya, J. dÕIncan, A. Bernard, A. Topouzkhanian, G. Wannous, J. Mol. Spectrosc. 185 (1997) 245– 249.
Theoretical electronic structure of the lowest-lying states of the LaI molecule F. Taher-Mansour,a A.R. Allouche,b and M. Aubert-Freconb,* b
a Universit e Libanaise, Facult e de G enie, route de l’a eroport, Beyrouth, Liban Laboratoire de Spectrom etrie Ionique et Mol eculaire UMR 5579, CNRS et Universit e Lyon I, Campus de La Doua, B^ at. Alfred Kastler, 43 Bd du 11 Novembre 1918 Bat 205, F69622 Villeurbanne Cedex, France
Received 25 October 2002; in revised form 6 March 2003
Abstract CAS-SCF/MRCI calculations have been performed for 11 molecular states in the representation 2Sþ1 KðþÞ (neglecting spin–orbit effects) for the molecule LaI. The corresponding 25 molecular states in the representation Xðþ=Þ (including spin–orbit effects) have been calculated using a semi-empirical spin–orbit pseudopotential built-up for lanthanum. Calculated potential energy curves and spectroscopic constants are reported, to the best of our knowledge they are the first ones from ab initio methods for this molecule. Ó 2003 Published by Elsevier Science (USA).
1. Introduction The present investigation is devoted to the prediction of the electronic spectrum of the LaI molecule. Among lanthanum monohalides the fluoride LaF is the species which has received the largest experimental interest [1– 10] while we knew of only one experimental study for both the monochloride LaCl [11] and the monoiodide LaI [12]. A recent ab initio theoretical investigation of the lowest-lying electronic states of LaF [13] was seen to produce predictions of a good quality when compared to highly accurate experimental data. Stimulated by both a lack of theoretical work on LaI and the existence of preliminary data obtained in our laboratory from high resolution laser-induced fluorescence LIF spectroscopy, we have performed an ab initio investigation of the low-lying states of this molecule, using an approach similar to that previously used to describe the isovalent species LaF. In this paper we present potential energy curves and spectroscopic constants calculated for 11 2Sþ1 KðþÞ (without spin–orbit effects) and 25 Xðþ=Þ (including spin–orbit effects) molecular states of LaI. The possible * Corresponding author. Fax: +33-4-72-43-15-07. E-mail address: [email protected] (M. Aubert-Frecon).
0022-2852/$ - see front matter Ó 2003 Published by Elsevier Science (USA). doi:10.1016/S0022-2852(03)00151-6
assignment previously proposed for the four low-lying states observed from high resolution LIF spectroscopy [12] are considered in the light of present results.
2. Computational approach Both species lanthanum and iodine are described in a pseudopotential scheme. Lanthanum is treated as a system with 46 inner electrons taken into account through a pseudopotential Wps (La) from [14]. The contracted Gaussian basis set used is derived from the literature one [14] augmented by f-type functions from [15]. For iodine, considered as a system with 46 inner electrons we used a pseudopotential [16] together with the corresponding Gaussian basis set. The LaI molecule in its lowest-lying states and in a range of internuclear distances around the equilibrium distance of its ground state is assumed to be mainly ionic. Therefore, spin– orbit (SO) effects are taken into account for Laþ while they are neglected for I which is assumed to be involved in the lowest-lying states of LaI mainly through its ground state. For lanthanum, SO effects are introduced via a semi-empirical spin–orbit pseudopotential ps WSO that we designed in our previous study of the electronic structure of the isovalent molecule LaF [13].
2
F. Taher-Mansour et al. / Journal of Molecular Spectroscopy 221 (2003) 1–6
Energy calculations for 11 states 2Sþ1 Kðþ=Þ of the molecule LaI have been performed using a CAS-SCF method. Correlation effects have been taken into account through MRCI calculations. Among the 18 electrons explicitly considered for LaI (46 core electrons for La as well as 46 core electrons for I were treated via pseudopotentials) 10 inner electrons were frozen in subsequent calculations so that eight valence electrons were explicitly treated. The active space contained 4r (La: 6s,5d0 , 7s,6d0 ), 2p (La: 5d1 ,6d1 ) and 2d (La: 5d2 ,6d2 ) orbitals. In the C2v symmetry this corresponds to 12 active molecular orbitals distributed into irreducible representations a1 ,b1 , b2 , and a2 in the following way: 6a1 ,2b1 , 2b2 , 2a2 , noted [6222]. The (doubly occupied) orbitals r(5pz ) and p(5p1 ) of the iodine species were considered as inactive in the CAS-SCF calculations. Multireference CI calculations (single and double excitations + Davidson correction) were performed to account for correlations effects for the eight valence electrons. The entire CAS-SCF configuration space was used as the reference in the MRCI calculations. For the a1 symmetry this results in 17 517 configuration state functions (CSF) for singlet states and 23 628 for triplet ones while for the b1 symmetry this corresponds to 12 858 and 20 058 CSF for singlet and triplet states, respectively. Energies including spin–orbit effects were obtained from the diagonalization of the matrix energy corresponding to the electrostatic Hamps iltonian + WSO . It was built-up on the basis of CAS-SCF wavefunctions while diagonal matrix elements came from CI + Davidson correction calculations. Calculations have been performed via the computational chemistry program MOLPRO [17] taking advantage of our graphical user interface GABEDIT [18].
Fig. 1. Potential energy curves for the 1;3 Rðþ=Þ states. Full lines: 1 Rþ ; dashed line: 3 Rþ ; and dotted line: 3 R .
3. Results and discussion Calculations have been performed for 111 internu for 11 states in the clear distances in the range 2.5–3.6 A 2Sþ1 ðþÞ K (neglecting SO effects) and 25 representation states in the representation Xðþ=Þ (including SO effects). Potential energy curves (PECs) are drawn in Fig. 1 for the 1;3 Rðþ=Þ states and in Fig. 2 for the P, D, and U states, the zero of energy begin chosen at the bottom of the ground state X1 Rþ . As known from experiment the lowest-energy state is found to be the (1)1 Rþ state. Nevertheless, as for the LaF molecule, the (1)3 D-PEC is . In the seen to cross the (1)1 Rþ -PEC around R ¼ 3:47 A range of R considered here, the PECs for the states
Fig. 2. Potential energy curves for the 1;3 K states. Full lines: 3 D states; dashed lines: 3 P states; dotted line: 1 D state; dashed-dotted line: 1 P state; and points D: 3 U state.
Fig. 3. Potential energy curves for the states X ¼ 0=þ . Full lines: 0þ states and dashed lines: 0 states.
F. Taher-Mansour et al. / Journal of Molecular Spectroscopy 221 (2003) 1–6
(1)1 P and (1)1 D are found to be close to each other, the (1)1 D state being the lowest one, up to a crossing be. The tween the two states which takes place 3.16 A 1 þ energy curve of the (2) R state crosses the PECs of the , (1)3 U, (1)3 R , and (2)3 P states at 2.9, 3.34, and 3.5 A respectively. For states in the representation Xðþ=Þ , PECs are drawn in Fig. 3 for the symmetries X ¼ 0þ , 0 ; in Fig. 4 for the symmetry X ¼ 1 and in Fig. 5 for the symmetries
3
X ¼ 2; 3; 4, the zero of energy being chosen at the bottom of the ground state (1)0þ . All theses curves present no avoided crossing in the range of R considered here. We present in Table 1 the composition (in percentage) of the X state-wavefunctions in terms of the states SK, . For some states (18 among the calculated at R ¼ 3:0 A 25 investigated) the largest percentage exceeds 80% so that a main parent SK may be identified for the X state
Fig. 5. Potential energy curves for the states X ¼ 2; 3; 4. Full lines: X ¼ 2 states; dashed lines: X ¼ 3 states; and dotted line: X ¼ 4 state.
Fig. 4. Potential energy curves for the states X ¼ 1.
Table 1 Composition of X-state wavefunctions in terms of SK terms (in percentage) X [Main parent]
X1 R þ
(1)0þ [(1)1 Rþ ] (1)1[(1)3 D] (1)2[(1)3 D] (1)3[(1)3 D] (1)0 [(1)3 P] (2)0þ [(1)3 P] (2)1[(1)3 P] (2)2[(1)3 P] (3)2[(1)1 D] (3)1[(1)1 P] (4)1[(1)3 Rþ ] (2)0 [(1)3 Rþ ] (4)2[(1)3 U] (3)0þ (2)3[(1)3 U] (5)1 (4)0þ (1)4[(1)3 U] (3)0 [(2)3 P] (5)2[(2)3 P] (6)1 (5)0þ (7)1 (6)2 (3)3[(2)3 D]
99
(1)1 D
(2)1 Rþ
(1)3 D
(1)3 Rþ
(2)3 D
(1)1 P
4 1
1 11 86
4
9
1 95 95
87 3
2 1
2
(1)3 U
(2)3 P
(1)3 R
1 1 1
99 97 100
2
(1)3 P
96 98 87 87 12 10 2 5
2 1
2
96
3 5
97
48 1
50
18
34
34 28
60 22
100 18 36
1 1
1 59 79 97
2 3
100 81 29 55 36 19
34 44 5
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F. Taher-Mansour et al. / Journal of Molecular Spectroscopy 221 (2003) 1–6
considered. For the seven remaining states the composition of their wavefunction spreads over several (2 or 3) states SK with a contribution larger than 18% so that the attribution of one main parent SK to those states is no longer possible. This situation is somewhat different from that previously observed for LaF [13] for which we identified a main parent for each X state. In order to calculate some spectroscopic constants: transition energy with respect to the energy minimum for the ground state Te , equilibrium internuclear distance Re , and harmonic frequency xe the calculated energy values were fitted to a polynomial in R, the significant degree of which being determined from the evaluation of the statistical error for the coefficients. It should be noted that for two states namely the (4)1[(1)3 Rþ ] and the (4)2[(1)3 U] we were able to determine with some accuracy only the position of the energy minimum by using a few points around this minimum due to the peculiar form of their respective PECs as
Fig. 6. Potential energy curves for the states (4)X ¼ 1 (full line) and (4)X ¼ 2 (dotted line) in a range near their bottom.
Table 2 Spectroscopic constants for the lowest-lying molecular states of LaI States 1
þ
X R (1)3 D (1)3 P (1)1 D (1)1 P (1)3 Rþ (1)3 U (2)1 Rþ (1)3 R (2)3 P (2)3 D
2Sþ1
Te (cm1 )
) Re (A
xe (cm1 )
0 1408 3852 4597 4636 6448 7343 7696 8130 8518 9363
2.947 3.012 3.040 3.052 3.060 3.053 3.102 3.062 3.098 3.107 3.118
179.9 166.1 161.3 158.5 156.5 154.0 148.1 156.2 146.2 146.3 142.4
KðþÞ
Table 3 Spectroscopic constants for the lowest-lying molecular states Xðþ=Þ of LaI States
Te (cm1 )
) Re (A
xe (cm1 )
(1)0þ [(1)1 Rþ ] (2)0þ [(1)3 P] (3)0þ (4)0þ (5)0þ
0 3605 7200 8091 8988
2.949 3.036 3.089 3.094 3.099
179.8 162.3 146.7 140.7 146.9
(1)0 [(1)3 P] (2)0 [(1)3 Rþ ] (3)0 [(2)3 P]
3472 6607 8370
3.039 3.054 3.110
161.1 153.8 145.3
(1)1[(1)3 D] (2)1[(1)3 P] (3)1[(1)1 P] (4)1[(1)3 Rþ ] (5)1 (6)1 (7)1
937 3737 4684 6601 7772 8556 9362
3.014 3.041 3.055 3.053 3.105 3.107 3.111
165.7 160.4 163.2
(1)2[(1)3 D] (2)2[(1)3 P] (3)2[(1)1 D] (4)2[(1)3 U] (5)2[(2)3 P] (6)2
1353 4108 4672 6642 8473 9724
3.014 3.041 3.056 3.085 3.108 3.114
165.8 161.0 154.5
(1)3[(1)3 D] (2)3[(1)3 U] (1)3[(2)3 D]
1885 7297 9927
3.011 3.102 3.117
166.3 148.0 142.7
(1)4[(1)3 U]
8093
3.101
148.2
145.8 144.7 144.8
145.4 143.6
shown in Fig. 6. Results are displayed in Table 2 for the states 2Sþ1 KðþÞ and in Table 3 for the states Xðþ=Þ . The main parents SK for each state X for which they have been identified are also quoted in Table 3. In order to compare our predictions to the experimental data obtained from the analysis of high resolution fluorescence spectra of LaI [12], we calculated some vibrational transition energies DTv0 ;v00 ¼ Gv0 (excited state) ) Gv00 (X) for the four lowest excited states (1)3 D, (1)3 P, (1)1 D, and (1)1 P. Some results are summarised in Table 4. Calculations confirm that the ground state is the (1)1 Rþ state. The calculated value 179.9 cm1 for the xe of the ground state is quite near the experimental value 183.76 cm1 for DGvþ1=2 . The experimental Tv value observed at 1064.33 cm1 has been ascribed to a component i of the (1)3 D state, from experimental analysis. This is consistent with present calculations. The Tv value observed at 4839.21 cm1 has been attributed to a X ¼ 1 state. In that range of transition energies, there are two X ¼ 1 states: the (1)3 P1 and the (1)1 P1 . The better agreement with present predictions corresponds to the state (1)1 P1 as shown in Table 4. With an hypothesis of a 0–0 vibrational transition the discrepancy would be 200 cm1 while it would reach 1100 cm1 if we assume that the excited state is the (1)3 P1 . Furthermore the agreement is better between the experimental value of DGvþ1=2 and the calculated xe value for the singlet
F. Taher-Mansour et al. / Journal of Molecular Spectroscopy 221 (2003) 1–6
5
Table 4 Calculated vibrational transition energies DTv0 v00 and vibrational constants xe (in cm1 ), compared to experimental molecular constants Tv and DGvþ1=2 [12] Experimental Tv
Experimental DGvþ1=2
Excited state
Calculated xe
Excited state v0
Ground state v00
DTv0 v00
1064.33
174.39
(1)3 D1
165.7
(1)3 D2
165.8
0 1 0 0
0 0 0 1
930 1095 1346 1167
(1)3 P1
160.4
(1)1 P1
163.2
0 1 2 0 1
0 0 0 0 0
3726 3886 4046 4672 4834
(1)1 D2
154.5
0 1 2
0 0 0
4660 4813 4967
4839.21
164.24
5254.76
165.00
Table 5 Calculated spin–orbit splittings at the energy minima (in cm1 ) for the triplet states (1)3 P X X0 DE
0 0þ 133
DEtot
636
(1)3 D 0þ 1 132
1 2 371
than for the triplet state. The Tv value observed at 5254.76 cm1 has been assumed to correspond to the state (1)1 D2 from the experimental analysis. In that energy range the X ¼ 2 states are those corresponding to the (1)3 P and (1)1 D states. The calculated transition energies for the (1)3 P2 are too low when compared to the experimental value, while it may be considered as compatible with the assumption of the (1)1 D2 state. The discrepancy would be of 600 cm1 in the hypothesis of a 0–0 transition and of 400 cm1 in the hypothesis of a 1–0 vibrational transition. When comparing the calculated electronic structure for LaF and LaI, it should be noted that the eight lowest states are the same. The ground state is (1)1 Rþ and crosses the (1)3 D state in the right part of the energy from the curve, at a distance of 0.4 and of 0.5 A equilibrium position for LaF and LaI, respectively. The transition energies for the eight lowest states decrease largely from LaF to LaI. The largest transition energies which correspond to the (2)1 Rþ state are 11 900 cm1 for LaF and 7700 cm1 for LaI. Nevertheless the energy difference between the (1)1 D and (1)3 D states remains quite similar for the two molecules (calculated values: 3190 cm1 for LaI and 3400 cm1 for LaF) so that there is an inversion in the lowest second and third excited states when going from LaF ((1)1 D, (1)3 P) to LaI ((1)3 P, (1)1 D). This is analog to the situation pre-
1 2 416 948
(1)3 U 2 3 532
2 3 655
3 4 796
1451
viously observed for scandium monofluoride and monoiodide [19]. Spin–orbit splittings: DE ¼ EðX0 Þ EðXÞ as well as the largest one DEtot (from the highest to the lowest component) evaluated at the well position for the triplet states for which we were able to identify the spin–orbit components, i.e., the states (1)3 P0;0þ;1;2 , (1)3 D1;2;3 , and (1)3 U2;3;4 , are summarised in Table 5. For these states the multiplet components are found to be unequally spaced as was observed for the LaF molecule both from experiment [8,9] and from calculations [13]. Large spin– orbit splittings are obtained for both states (1)3 D and (1)3 U, in agreement with the large experimental atomic values for Laþ [(1)3 DJ ] and Laþ [(1)3 FJ ], respectively. Calculated values are similar for the two molecules LaF and LaI. This could be expected due to the fact that in present calculations these two molecules are assumed to be describable by Laþ + X (1 S0 ) and that only spin– orbit effects for Laþ have been taken into account.
4. Conclusion An ab initio investigation of the lowest-lying molecular states of LaI has been performed via CAS-SCF and MRCI (SD + Davidson correction) calculations. Spin–orbit effects have been introduced through a
6
F. Taher-Mansour et al. / Journal of Molecular Spectroscopy 221 (2003) 1–6
semi-empirical spin–orbit pseudopotential designed for lanthanum. Potential energy curves and spectroscopic constants have been obtained for 11 2Sþ1 KðþÞ and 25 Xðþ=Þ states. We knew no previous ab initio study of the electronic structure for this molecule. In the light of present calculations the possible assignment proposed for the four low-lying states observed from LIF spectroscopy [12] have been confirmed.
Acknowledgments Many thanks are due to Professors Christiane Effantin, Jean dÕIncan, and Alain Bernard for many valuable discussions and for their critical reading of the manuscript.
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