5882
J. Phys. Chem. 1993,97, 5882-5885
Alkali-Metal Dihalide Molecules. Electronic Spectrum Francisco B. C. Macbado,+ Guan-Zhi Ju,~and Ernest R. Davidson’ Department of Chemistry, Indiana University, Bloomington. Indiana 47405 Received: December 28, 1992; In Final Form: March 17, 1993
This paper reports the transition energies of the low-lying valence states of some alkali-metal dihalide (MX2) systems using the multireference single- and double-excitation configuration interaction method. The effect of the alkali metal on the vertical electronic transitions is studied and compared with the transitions calculated for the free X2- molecules. The results support the ultraviolet spectral assignment of the absorption bands near 300 nm for M+F2- and 340 nm for M+C12- to be the u u* transition.
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I. Introduction The transitions observed in the electronic spectra of alkalimetal dihalide (MX2) systems have been interpreted to be essentially localized on the X2- anion under the influence of the alkali metal. The ultraviolet absorption spectra of M+F2- and M+C12- (M = Li, Na, K,Cs) were obtained by Andrewsl near 300 and 340 nm, respectively. The transitions were assigned to be of the u-u*(2Zu+-2Zg+) type on the dihalide anion. This experimental work will be the basic reference for the present theoretical study. Recently, Ju and Davidson2 studied the electronic structure of the ground state of some alkali-metal dihalide molecules using the MGller-Plesset perturbation theory and configuration interaction methodologies. This work focused on the determination of the equilibrium structures for the ground states and on the relative reaction energy changes for the reaction M X2+ MX X. As far as we know, this is the first post-Hartree-Fock investigationon the electronicstructure of the alkali-metaldihalide molecules. At the Hartree-Fock level, Maessen and Cade3.4 carried out a detailed study of the electronic structure of some states of the MX2 molecules. The aim of this study concerns the electronic structure of some states of the MX2 systems. The electronic transition involving some low-lying valence states of LiF2, NaF2, LiC12, and NaCl2 have been studied using the multireference single- and double-excitation configuration interaction (MRSD-CI) method. For LiF2, the potential energy surfaces for the six valence states 2B2 (2), 2Al (2), 2BI(l), and 2A2 (1) were also calculated.
+
+
11. Methodology
The electronic structure of some valence states of alkali-metal dihalide molecules was investigated using the perturbation-theoryselected MRSD-CI wave function. In all calculations, the 6-3 11+G* split-valence polarization basis set was used. In the correlation treatment, only the 1s electrons on F, C1, and Na are left uncorrelated. Thus, 17, 23, 33, and 39 electrons are correlated for LiF2, NaF2, LiC12, and NaC12, respectively. For LiF2, the potential energy surfaces, E(Rl,R2), for the six valencestates2B2(2), 2A1(2), 2B1(l),and2A2(1) werecalculated using the MRSD-CI method for C, geometries. These six valence states correspond to the ground state and to the states which arise from excitation of an electron from the lower molecular orbitals, localized on the halide molecule anion, to the highest molecular orbital which is singly occupied in the ground-state configuration. The parameter R I corresponds to the halogen-halogen internu+ Permanent address: Instituto de Estudos Avansados, Centro Ttcnico Aeroespacial, Caixa Postal 6044, Sao Jost dos Campos, 12231 SP, Brazil. Permanent address: Institute of Theoretical Chemistry and Department of Chemistry, Shandong University, Jinan, People’s Republicof China 2501 00.
*
clear distance and R2 to the distance between the alkali-metal atom and the midpoint of the halogen-halogen axis. The molecular orbitals (MOs)used in the CI expansion for the LiF2 potential surfaces were the canonical Hartree-Fock orbitals for the first state in each symmetry. In the generation of the final wave functions, preliminary CI calculations were carried out for some R1 and R2 parameters with the purpose of selecting important configurations(coefficientsgreater than 0.05) to constitute the reference set to be used in the MRSD-CI calculations. Finally, configurations were selected by the secondorder Rayleigh-SchriMinger perturbation theory with energy contributions of all configurations outside the zeroth-order space within the first 15 000 space orbital products. The electronic transitions for LiF2, NaF2, LiC12, and NaC12 were calculated using MRSD-CI. The wave functions were constructed as described above. We concentrated this study on the C2” triangular structures. The calculations were only made for the vertical transitions at the equilibrium structure of the ground state of each molecule optimized from the UHF/631 1+G* calculations.2 Since we intended to calculate the transition moments, we used the same set of molecular orbitals for all states calculated, Le., the K orbitals5 calculated for the ground state of each molecule. The electronic transitions were also calculated for the four valence states of F2- and C12-, which arise from the same kind of excitation in the MX2 molecule, with the purpose of verifying the experimental assignment of the ultraviolet spectra. All calculations were performed using the MELD suite of electronic structure codes developpd in this laboratory.6
III. Results and Discussion A. Potential Surfaces. The potential surfaces calculated for LiF2 corresponding to the six valence states 2B2(2), 2A1(2), 2BI (l), and 2A2 (1) are presented in Figures 1-6. Although our main objective was concerned with the nature of the ground and excited states corresponding to the triangular ionic structure (M+X2-), the potential surfaces include some regions where different types of interactions are involved and the molecule presents another structure. We expect LiF2 to be a good example to represent the principal general features of the MX2 systems. Although we have used a different basis set, the Hartree-Fock results are similar to those obtained by Maessen and Cade.3.4 Hence, they are not reported. In the region where the molecule is well represented by the almost-equilateral triangle structure, as obtained by the Hartree-Fock method, the MRSD-CI calculations show a minimum for the ground state (2B2). The excited states, however, tend to present a minimum at the linear structure. At the equilibrium distance of the ground state, the orders of the electronic states are the same as that of the free F2molecular anion. As the lithium cation moves closer to locate between the two fluoride atoms, the orders of the states change.
0022-3654/93/2097-5882%04.00/0 0 1993 American Chemical Society
Alkali-Metal Dihalide Molecules. Electronic Spectrum
The Journal of Physical Chemistry, Vol. 97, No. 22, 1993 5883
41 2. N
lz
0.
-2
-4
3
4
5
6
I
'
t
8
R1 Figure 1. Potential energy surface, E ( R I , R ~ )for , LiF2 in the 12B2state. R I = F- -Fdistance and R2 = Li- -F2 distance. The energy contours start from -206.70 au (highest energy) with intervals of 0.01 au.
3
5
4
6
I
8
R1 Figure4. Potential energy surface, E ( R I , R ~ )for , LiF2 in the 2 2 A ~state. See footnotes in Figure 1 for the energy contours.
4
I
-41
. . 1 3
4
5
7
6
R1
Figure 2. Potential energy surface, E(Rl,R2), for LiF2 in the 22B2state. See footnotes in Figure 1 for the energy contours.
4
3
4
5
8
6
I
8
R1 Figure 5. Potential energy surface, E(Rl,R2), for LiF2 in the 12Blstate. See footnotes in Figure 1 for the energy contours.
1
2. N
d
0.
-2
-4
'
t
3
L
3
4
5
6
I
8
R1
Figure 3. Potential energy surface, E ( R I , R ~ )for , LiF2 in the 12Al state, See footnotes in Figure 1 for the energy contours.
For example, the dominant configuration in the ground state XZBz (22,+)at the bent structurecorresponds to the highest energy of the six states investigated at the linear geometry. In order to better understand these changes of order among the configurations, Figure 7 shows the potential curves for the two states in the symmetry 2B2. The Fz bond length ( R , ) is fixed at 6.0~~. Fromthefigures, wecanseethat thetwostates present anavoided crossing when the Li+ cation attains a distance around 2.0-1 Sao.
4
6
5
I
8
R1
Figure 6. Potential energy surface, E(R,,R2), for LiF2 in the 12A2state. See footnotes in Figure 1 for the energy contours.
At this distance, the order of the states is changed. The ground state which is associated with the 2Zu+of the Fz- state changes to be a 211rstate and vice versa for the second state. By placing the alkali-metal atom between the two halogen atoms, these strong modifications in the configurations are reflected in the potential surfaceswhere somelocal minima appear between the RZdistances equal to 1.5-0.0a0. B. Electronic Transitions. The main aim of this investigation concerns the electronic transitions involving some low-lying
Machado et al.
TABLE Ik MRSD-CIResults for LiCll and NaC12 Molecules
energy'
nm
type
TMb
AE,d nm
fc
LiC12 -926.8604 -926.8145 -926.7831 -926.7758 -926.7639 -926.7296
992 590 539 471 348
-
u* r*-u* r-u* r+u* u+u* T*
0.0584 1.0 X 104 0.0284 4.2 X le5 1.0946 0.0771 2.0821 0.3774
338
NaC12 X2B2(2Ztu) 12Ad2no) 22B;&Ii) 12B1(211J 12A1(211J 22A1(2Ztg) 0
-108 1.3326 -1081.2835 -1081.2625 -1081.2473 -1081.2291 -1081.2026
925 ?T*+u* 649 **-a* 534 T + U* 440 T + U* 350 u+ U*
0.0488 7 . 0 X lo4 0.0460 9.9 X 0.8349 0.0481 2.2823 0.4514
345
Energies are given in hartrees. TM is the transition moments in au.
f is the oscillator strength. Experimental results.'
TABLE IIk MRSDCI Results for F2- and Cl2- Molecules -206.78'
'
'
'
'
1
0
'
'
'
3
2
'
'
4
'
state
5
2Ztu
R,(a,) Figure 7. Potential energy for LiF2 in the 12B2 and 22B2 states. The 0 : 12B2state; (A) 22B2state. distance R I(F- -F) is fixed equal to 6 . 0 ~ ~ (+)
TABLE I: MRSDCI Results for LiF2 and NaF2 Molecules state
energy"
X'B2('2+,) l'A2('II,) 2'B?('II,) l'Bl('IIu) l'Al('II,) 2'A,('Z+,)
-206.7865 -206.7102 -206.6917 -206.6582 -206.6572 -206.6197
X'B?('Z+,) 1'A2(TIg) Z'B?('II,) l'Bl('lI,) l'Al(?II,) 2'A,('Z+,)
-361.2566 -361.1859 -361.1750 -361.1351 -361.1279 -361.0976
nm
596 481 355 352 273
type LiF'
-
T*+u* r* u* T-
f'
AE,*nm
U*
0.5383 0.0250 1.6644 0.3081
300 h 3
r * + u* r* u*
0.0309 4.5 X 0.0341 6.3 X
T+U* T+U* U-U*
0.3231 0.0090 1.7240 0.3151
310
Energies are given in hartrees. TM is the transition moments in au.
'fis the oscillator strength. Experimental results.' valence states of M+F2- and M+C12- (M = Li, Na) molecules. The experimental observation of Andrewsl about the influence of the alkali metal cation on the u- u* transitions is also studied. The MXz molecules were assumed to have an isosceles triangle structure. All the results refer to thevertical transition calculated at the theoretical equilibrium structure of the ground state for each molecule. The calculated electronic transition results of M+Fz- and M+C12-arepresented in Tables I and 11,respectively. The results of the free X2- molecules are presented in Table 111. In Tables I and 11, the states corresponding to the analogues X2- are given in parentheses. These MRSD-CI results support the experimental attributions of the electronic spectra obtained by Andrews.] The essential conclusions obtained by the Hartree-Fock level4 are alsoconsistent with this CI investigation. At the CI level, the transition energy of the u a* type can be directly compared with the experimental one. First, notice the results of the alkali-metal difluoride molecule (Table I) and those calculated for the free Fz- molecule (Table 111). The strong transition obtained experimentally and assigned
-
211s
'nu
221tE
-199.2607 -199.1922 -199.1437 -199.1123
f'
666 390 307
r*-u*
0.0360
5.9X
1.8188
0.3273
0.0519
1.1 X lo4
2.4969
0.5154
A+U*
u-u*
Cl2-
2Ztu 'ng
211u
-919.3843 -919.3250 -919,2906 -919.2603
770 486 368
?Y*+u* T--CU* U-U*
Energies are given in hartrees. TM is the transition moments in au. C f i s the oscillator strength.
-
0.0315 5.0 X 10.' 0.0292 5.4 X
NaF2 646 559 375 354 286
TMb
(I
U*
T - C U*
u
TM"
type
AE, nm F2-
'Ztg
AE,
energy'
to be of the u u* type is calculated to be at 273 and 286 nm dependingon whether the alkali metal is Li+ or Na+,respectively. The experimental values are 300 3 and 310 nm. For the free F2-, it is at 307 nm. Although the calculated results differ by about 24 nm from the experimentalvalues, the differencebetween the LiFz and NaFz transitions is approximately the same. For M+C12-, although the difference between the experimental and theoretical results is smaller, the differencebetween the transitions with different metals is larger. These numerical uncertainties could be attributed to the basis set quality, but it is important to note that the characteristics in the u u* transition for M+Xz- as a function of M+ and Xaare the same as those observed experimentally. The wavelength increases from Li+ to Na+. Also, the alkali-metal effect on the Clz- transition is found to be small. Observe from the tables that thevalues of the oscillator strength are larger for the transitions involving the C11- molecules. This could explain the experimental uncertainly in the M+F2- spectra. Also, the absorption observed at 750 nm for C12- in the KCl lattice7 (cf. under calculated result of 770 nm for the free C12-) will be more difficult to observe for Fz-. In spite of the red absorption being very weak, this result predicts that it should be around 667 nm for F2-.
*
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IV. Conclusions The potential surfaces calculated for LiF2 are expected to be a good representation of the MX2 systems. They show that the orders of the states change when going from the nearly-equilateral triangle structure to the linear one. These changes in the configurations of the states a a m t for the avoided crossing in the states of the same symmetry and explain the local minima in the potential surfacesfor placing the alkali-metal atom between the two halogen atoms.
Alkali-Metal Dihalide Molecules. Electronic Spectrum The electronictransition calculations support the experimental attributions of the electronic spectra obtained by Andrews.' Also, the essential conclusions obtained at the HartreeFock level4are consistent with these present CI results. However, we were able to compare the u- u* transition with the experimental one. The electronicspectra of the M+X2-systems, at the nearly-equilateral triangle structure, are similar to the free X2- molecules perturbed by the alkali-metal cation. The oscillator strengths are larger for the transitions in the C12-systems than in the F2- systems, which could explain the uncertainties in the M+F2-exbrimentalspectra. The results also support the experimental assignment' of the 750nm band of Cl2- in a KCl lattice to be a A* u* transition.
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Acknowledgment. This work was supported, in part, by a grant from the National Science Foundation. F. B. C. Machado is
The Journal of Physical Chemistry, Vol. 97, No. 22, 1993 5885 grateful to Conselho Nacional de Desenvolvimento C i e n t h o e Tecnol6gico (CNPq) of Brazil for financial support and to Instituto de Estudos Avangados (IEAv-CTA) of Brazil for the opportunity to carry out research at Indian University.
References and Notes (1) Andrews, L. J. Am. Chem. SOC.1976, 98, 2147. (2) Ju, G. Z.; Davidson, E. R. J. Phys. Chem. 1992, 96, 3683. (3) Maessen, B.; Cade, P. E. J . Chem. Phys. 1984, 80, 2618. (4) Maessen, B.; Cade, P. E. J . Chem. Phys. 1984, 80, 5120. (5) Feller, D.; Davidson, E. R. J . Chem. Phys. 1981, 74, 3977. (6) The MELD series of electronic structure code was developcd by McMurchie, L. E.; Elbert, S. T.; Langhoff, S. R.; Davidson, E. R. and was extensively modified by Feller, D. and Rawlings, D. C. (7) Delbeq,C. J.;Smaller,B.;Yuster,P.H.Phys. Rev. 1958,111,1235.
