- Email: [email protected]
Intensity of the n→π∗ symmetry-forbidden electronic transition in acetone by direct vibronic coupling mechanism
6 April 2001
Chemical Physics Letters 337 (2001) 331±334
www.elsevier.nl/locate/cplett
Intensity of the n ! p symmetry-forbidden electronic transition in acetone by direct vibronic coupling mechanism Alexandre B. Rocha, Carlos E. Bielschowsky * Departamento de Fõsico-Qõmica, Instituto de Quõmica, Universidade Federal do Rio de Janeiro, Cidade Universit aria, CT Bloco A. Rio de Janeiro, 21949-900 Rio de Janeiro, Brazil Received 6 November 2000; in ®nal form 13 February 2001
Abstract Absolute absorption intensities were calculated for the symmetry dipole forbidden n ! p transition in acetone. An analysis of the distribution per normal modes is performed and the results are compared with a recent calculation. Vibronic coupling mechanism is taken into account in a way that is dierent from the traditional Herzberg±Teller perturbation approach. In the present method the electronic transition moment is directly expanded in power series of the vibration normal coordinates. This approach was recently used for the equivalent n ! p transition in formaldehyde presenting an excellent agreement with the experimental results. Ó 2001 Elsevier Science B.V. All rights reserved.
1. Introduction The absorption spectrum of acetone in the nearultraviolet region has been investigated since a long time [1±8]. The ®rst singlet n ! p (1 A1 ! 1 A2 ) excited state is particularly important due to its photochemical interest. This kind of transition has another challenging feature, since it is symmetry-forbidden, only occurring by means of intensity-borrowing mechanism, where the intensity is borrowed from symmetry-allowed transitions due to vibronic coupling. Other classical examples of such processes are found in the nearultraviolet spectra of formaldehyde [9±14], benzene [15,16] and inner-shell spectrum of CH4 [17]. In the case of formaldehyde the kind of transition is the same as in acetone, i.e., n ! p (1 A1 ! 1 A2 ).
*
Corresponding author. Fax: +55-21-568-0725. E-mail address: [email protected] (C.E. Bielschowsky).
At 1956 Murrell and Pople [15] used the theory developed by Herzberg and Teller [18] on intensity borrowing through vibronic coupling and calculated the oscillator strength for benzene molecule by perturbation expansion. This method has been extensively used since then for dierent systems [12±14,19]. Liao et al. [8] have recently used a modern version of this approach to calculate the total intensity of the n ! p process in acetone. We have recently performed ab initio calculations for similar process in formaldehyde and CO2 [11] and CH4 [17] using a dierent scheme to describe the vibronic coupling, and obtained results in very good agreement with the experiments, not only on the total oscillator strength as well as on the contribution of each normal mode. This method consists, basically, of a direct expansion of the electronic transition moment along the normal coordinates of vibration of the ground state. The coupling is made by a superposition of con®gurations in a CI calculation.
0009-2614/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 1 ) 0 0 2 1 3 - 5
332
A.B. Rocha, C.E. Bielschowsky / Chemical Physics Letters 337 (2001) 331±334
In the present work, we calculate the optical oscillator for the n ! p process in acetone with this method and compare with the recent results of Liao et al. [8]. The present result for the total oscillator strength is in good agreement with that one reported by them and the experimental results [1,4]. In spite of it, the present values for some of the components, and in particular for the a2 normal modes, disagree with the results of Liao et al. [8]. 2. Theoretical considerations The theoretical procedure used in the present calculations was discussed in detail elsewhere [11]. Brie¯y, in the context of the Born±Oppenheimer approximation, the optical oscillator strength f00!kv for the excitation from the v 0 vibration level of the ground electronic state (k 0) to the vth vibration level of the kth electronic excited state is written, in atomic units, as 2 2 f00!kv 1 DEkv gk jhvkv jM Qjv00 ij ; 3 where M Q is the transition dipole moment whose x component is * + ! n X Mx Q wk ~ r; Q xi w0 ~ r; Q 2 i1
with equivalent expressions for y and z. In expression (1) gk is the degeneracy of the ®nal state, DEkv is the transition energy, r represent the n electron coordinates, Q are the coordinates of the nuclear normal modes of vibration, wk and vkv are, respectively, the electronic and vibrational wave functions of the (k; v) vibronic state. Summing expression (1) over all vibrational levels of the excited electronic state and considering the fact that the vibrational wave functions of the excited state form a complete set and approximating DEkv by DEk0 , one arrives at 2 f0!k 3 DEgk jhv00 jM 2 Qjv00 ij: 3 Harmonic approximation is used to obtain the vibrational wave function of the ground state
v00 Q1 ; Q2 ; . . . ; Qj
3N Y6
nL QL ;
4
L1
where nL QL is the wave function of the Lth individual normal mode of vibration. Inserting expression (4) into (3) we have X 2 f0!k hnL QL jML2 QL jnl QL i: DEgk 3 L 5 Finally we expand ML2 QL as a power series of individual normal modes: X 2 j ML2 QL jM 0j aj QL ; 6 j
2
where jM 0j is the transition moment for equilibrium position. This term vanishes for a dipole forbidden transition. The expansion coecients aj in expression (6), for each L normal mode, are determined by directly calculating ML2 QL for some QL values. The electronic wave functions for the dierent QL values are determined through the con®guration interaction method. Cross-terms are neglected. Integration of expression (5) with ML2 QL expanded in Taylor series and nL QL expressed as harmonic functions is made analytically. This is a particularly attractive feature of this method. 3. Results The geometry was optimized and the vibrational frequencies were calculated in a MP2/6311G level. For the calculation of the transition moments (oscillator strengths) the MRCI level of calculations with an 6-311 + G basis set was used. The MRCI calculations considered a virtual space constructed in the following way: First 91 con®gurations were built by considering single and double excitations from all the occupied orbitals, except for the core orbitals, to the unoccupied molecular orbital of b2 symmetry. Then, single excitations were performed from these con®gurations to an external space composed of 100 virtual orbitals, ending with 72 891 con®gurations. The virtual orbitals were built by the modi®ed virtual orbital (MVO) technique [21].
A.B. Rocha, C.E. Bielschowsky / Chemical Physics Letters 337 (2001) 331±334 Table 1 Expansion coecients aj for ML2 QL , Eq. (6), of the dierent vibrational modes Mode
a1
a2
a3
Q9 (a2 ) Q10 (a2 ) Q11 (a2 ) Q12 (a2 ) Q13 (b2 ) Q14 (b2 ) Q15 (b2 ) Q16 (b2 ) Q17 (b2 ) Q18 (b2 ) Q19 (b2 ) Q20 (b1 ) Q21 (b1 ) Q22 (b1 ) Q23 (b1 ) Q24 (b1 )
)0.000685 )0.00008 )0.00095 0.00003 0.00065 )0.00671 )7±0.00087 )0.00011 0.00061 0.00023 )0.00004 0.00002 0.00022 )0.00227 )0.00099 0.00007
0.00001 0.00118 0.03704 0.00024 0.00227 0.0002 0.03044 0.0031 0.0015 )0.00074 0.00105 )0.00015 0.00538 0.13829 0.02666 0.00232
0.0 0.0 )0.01572 0.0 0.0 )0.00015 )0.02234 )0.00131 0.0 0.00131 )0.00054 0.00022 0.00328 )0.10475 )0.01266 0.0
The vertical excitation energy obtained in the calculations for the symmetry dipole forbidden n ! p transition with this methodology was 4.43 eV. The frequencies used to compute the oscillator strengths by means of Eq. (5) above were scaled by 0.9496 [20]. We have used the GAMESS package [22]. In what concerns the expansion of ML2 QL , only positive values for QL are considered in the ®tting
333
process. This is possible because ML2 QL is an even function and, as consequence, we can perform the integration of Eq. (5) for positive values of QL and multiply the result by a factor of 2. The coecients used in the ®tting process, for the distinct vibrational modes, are shown in Table 1. Table 2 shows the present calculated values to the optical oscillator strength, f, for the n ! p in acetone compared with the recent theoretical results of Liao et al. [8] and the experimental results [1,4]. Table 2 shows that the present total f values are in excellent agreement with those of Liao et al. [8], and both results agree reasonably with the experiments. This could suggest that the results of both calculations are equivalent. This is really not true since the distribution per modes is dierent, as can be shown in Table 2. In particular, the calculations of Liao et al. predicted that 94% of the total oscillator strength are due to b1 inducing modes. The remaining 6% are due to b2 inducing modes. The contribution of a2 modes is completely unimportant following their analysis. The present calculations show another picture, the b1 mode being as well dominant, with 66.29% of the total oscillator strength. In our calculations the b2 represents 6.8% of the total f, which agree very well with Liao et al.'s result. The great dierence is related to the
Table 2 Comparison of the present calculated optical oscillator strengths for n ! p transition in acetone with theoretical [8] and experimental [1,4] results Mode
f (present)
Q9 (a2 ) Q10 (a2 ) Q11 (a2 ) Q12 (a2 ) Q13 (b2 ) Q14 (b2 ) Q15 (b2 ) Q16 (b2 ) Q17 (b2 ) Q18 (b2 ) Q19 (b2 ) Q20 (b1 ) Q21 (b1 ) Q22 (b1 ) Q23 (b1 ) Q24 (b1 )
7:60 10 1:05 10 1:41 10 3:06 10 2:01 10 5:27 10 1:33 10 8:74 10 3:94 10 3:74 10 1:46 10 1:07 10 1:53 10 5:67 10 1:43 10 1:49 10
5
% (present)
Total
3:40 10
4
6 5 7 6 6 6 6 6 7 6 5 9 5 4 5
22.36 0.31 4.15 0.09 0.59 1.55 0.39 2.57 1.16 0.11 0.43 3.15 0.00045 16.67 42.10 4.37 100
f [8]
f [1]
3:05 10 1:71 10 2:75 10 7:81 10 1:10 10 2:73 10 2:00 10 6:32 10 6:39 10 5:99 10 1:77 10 1:58 10 9:55 10 8:78 10 1:82 10 5:26 10
7
3:62 10
4
f [4]
8 9 8 7 6 7 7 7 7 5 5 7 5 4 5
4 10
4
4:16 10
4
334
A.B. Rocha, C.E. Bielschowsky / Chemical Physics Letters 337 (2001) 331±334
a2 modes. From the calculation of Liao et al., they are completely unimportant. The present results indicate that they contribute with about 26.91% of the total oscillator strength. Both theoretical results show that the CO out of plane wagging is the most eective mode to borrow intensity. The disagreement of the present approach with that based on the perturbation expansion for the distribution of the inducing modes has also appeared in the case of formaldehyde [11]. In this case there is an experimental result [9] which was able to separate the contribution per mode, showing that in general the results based on the Herzberg±Teller-like ®rst-order perturbation expansion tend to be overestimated for certain modes while underestimated for others, and the present direct approach shows a much better agreement with the experimental distribution of the total intensity. These statements can be veri®ed in Table 1 of [11]. In the acetone case there is much less experimental and theoretical work than formaldehyde. Particularly remarkable is the fact that the experimental values for the oscillator strength are very old. There is no experimental work, to our knowledge, that has determined the contribution per modes to the total oscillator strength. Needless to say that the new experimental results would be very welcomed. Acknowledgements The authors would like to acknowledge CNPq and Capes for the ®nancial support.
References [1] H. Ley, B. Arends, Z. Phys. Chem. B 12 (1931) 132. [2] W.A. Noyes Jr., A.B.F. Dunacan, W.M. Manning, J. Chem. Phys. 2 (1934) 717. [3] H.L. MucMurry, J. Chem. Phys. 9 (1941) 231. [4] E.E. Worden Jr., Spectrochim. Acta 22 (1966) 21. [5] M. Baba, I. Hanazaki, Chem. Phys. Lett. 103 (1983) 93. [6] M. Baba, I. Hanazaki, U. Nagashima, J. Chem. Phys. 82 (1985) 3938. [7] G. Herzberg, Electronic Spectra and Electronic Structure of Polyatomic Molecules, Krieger, NJ, 1991. [8] D.W. Liao, A.M. Mebel, M. Hayashi, Y.J. Shiu, Y.T. Chen, S.H. Lin, J. Chem. Phys. 111 (1999) 205 (references therein). [9] S.J. Strickler, R.J. Barnhart, J. Phys. Chem. 86 (1982) 448. [10] J.A. Pople, J.W. Sidman, J. Chem. Phys. 27 (1957) 1270. [11] A.B. Rocha, C.E. Bielschowsky, Chem. Phys. 253 (2000) 51. [12] M. Roche, H.H. Jae, J. Chem. Phys. 60 (1974) 1193. [13] W.C. Johnson, J. Chem. Phys. 63 (1975) 2144. [14] F. Pauzat, B. Levy, P.H. Millie, Mol. Phys. 39 (1980) 375. [15] J.N. Murrell, J.A. Pople, Proc. Phys. Soc. London A 69 (1956) 245. [16] L. Ziegler, A.C. Albrecht, J. Chem. Phys. 60 (1974) 3558. [17] A.B. Rocha, C.E. Bielschowsky, J. Mol. Struct. (THEOCHEM) 539 (2001) 145. [18] G. Herzberg, E. Teller, Z. Phys. Chem. B 21 (1933) 410. [19] A.M. Mebel, M. Hayashi, S.H. Lin, Chem. Phys. Lett. 274 (1997) 281. [20] A.P. Scott, L. Radom, J. Phys. Chem. 100 (1996) 16502. [21] C.W. Bauschlicher Jr., J. Chem. Phys. 72 (1980) 880. [22] M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen, S.J. Su, T.L. Windus, M. Dupuis, J.A. Montgomery, J. Comp. Chem. 14 (1993) 1347.
Chemical Physics Letters 337 (2001) 331±334
www.elsevier.nl/locate/cplett
Intensity of the n ! p symmetry-forbidden electronic transition in acetone by direct vibronic coupling mechanism Alexandre B. Rocha, Carlos E. Bielschowsky * Departamento de Fõsico-Qõmica, Instituto de Quõmica, Universidade Federal do Rio de Janeiro, Cidade Universit aria, CT Bloco A. Rio de Janeiro, 21949-900 Rio de Janeiro, Brazil Received 6 November 2000; in ®nal form 13 February 2001
Abstract Absolute absorption intensities were calculated for the symmetry dipole forbidden n ! p transition in acetone. An analysis of the distribution per normal modes is performed and the results are compared with a recent calculation. Vibronic coupling mechanism is taken into account in a way that is dierent from the traditional Herzberg±Teller perturbation approach. In the present method the electronic transition moment is directly expanded in power series of the vibration normal coordinates. This approach was recently used for the equivalent n ! p transition in formaldehyde presenting an excellent agreement with the experimental results. Ó 2001 Elsevier Science B.V. All rights reserved.
1. Introduction The absorption spectrum of acetone in the nearultraviolet region has been investigated since a long time [1±8]. The ®rst singlet n ! p (1 A1 ! 1 A2 ) excited state is particularly important due to its photochemical interest. This kind of transition has another challenging feature, since it is symmetry-forbidden, only occurring by means of intensity-borrowing mechanism, where the intensity is borrowed from symmetry-allowed transitions due to vibronic coupling. Other classical examples of such processes are found in the nearultraviolet spectra of formaldehyde [9±14], benzene [15,16] and inner-shell spectrum of CH4 [17]. In the case of formaldehyde the kind of transition is the same as in acetone, i.e., n ! p (1 A1 ! 1 A2 ).
*
Corresponding author. Fax: +55-21-568-0725. E-mail address: [email protected] (C.E. Bielschowsky).
At 1956 Murrell and Pople [15] used the theory developed by Herzberg and Teller [18] on intensity borrowing through vibronic coupling and calculated the oscillator strength for benzene molecule by perturbation expansion. This method has been extensively used since then for dierent systems [12±14,19]. Liao et al. [8] have recently used a modern version of this approach to calculate the total intensity of the n ! p process in acetone. We have recently performed ab initio calculations for similar process in formaldehyde and CO2 [11] and CH4 [17] using a dierent scheme to describe the vibronic coupling, and obtained results in very good agreement with the experiments, not only on the total oscillator strength as well as on the contribution of each normal mode. This method consists, basically, of a direct expansion of the electronic transition moment along the normal coordinates of vibration of the ground state. The coupling is made by a superposition of con®gurations in a CI calculation.
0009-2614/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 1 ) 0 0 2 1 3 - 5
332
A.B. Rocha, C.E. Bielschowsky / Chemical Physics Letters 337 (2001) 331±334
In the present work, we calculate the optical oscillator for the n ! p process in acetone with this method and compare with the recent results of Liao et al. [8]. The present result for the total oscillator strength is in good agreement with that one reported by them and the experimental results [1,4]. In spite of it, the present values for some of the components, and in particular for the a2 normal modes, disagree with the results of Liao et al. [8]. 2. Theoretical considerations The theoretical procedure used in the present calculations was discussed in detail elsewhere [11]. Brie¯y, in the context of the Born±Oppenheimer approximation, the optical oscillator strength f00!kv for the excitation from the v 0 vibration level of the ground electronic state (k 0) to the vth vibration level of the kth electronic excited state is written, in atomic units, as 2 2 f00!kv 1 DEkv gk jhvkv jM Qjv00 ij ; 3 where M Q is the transition dipole moment whose x component is * + ! n X Mx Q wk ~ r; Q xi w0 ~ r; Q 2 i1
with equivalent expressions for y and z. In expression (1) gk is the degeneracy of the ®nal state, DEkv is the transition energy, r represent the n electron coordinates, Q are the coordinates of the nuclear normal modes of vibration, wk and vkv are, respectively, the electronic and vibrational wave functions of the (k; v) vibronic state. Summing expression (1) over all vibrational levels of the excited electronic state and considering the fact that the vibrational wave functions of the excited state form a complete set and approximating DEkv by DEk0 , one arrives at 2 f0!k 3 DEgk jhv00 jM 2 Qjv00 ij: 3 Harmonic approximation is used to obtain the vibrational wave function of the ground state
v00 Q1 ; Q2 ; . . . ; Qj
3N Y6
nL QL ;
4
L1
where nL QL is the wave function of the Lth individual normal mode of vibration. Inserting expression (4) into (3) we have X 2 f0!k hnL QL jML2 QL jnl QL i: DEgk 3 L 5 Finally we expand ML2 QL as a power series of individual normal modes: X 2 j ML2 QL jM 0j aj QL ; 6 j
2
where jM 0j is the transition moment for equilibrium position. This term vanishes for a dipole forbidden transition. The expansion coecients aj in expression (6), for each L normal mode, are determined by directly calculating ML2 QL for some QL values. The electronic wave functions for the dierent QL values are determined through the con®guration interaction method. Cross-terms are neglected. Integration of expression (5) with ML2 QL expanded in Taylor series and nL QL expressed as harmonic functions is made analytically. This is a particularly attractive feature of this method. 3. Results The geometry was optimized and the vibrational frequencies were calculated in a MP2/6311G level. For the calculation of the transition moments (oscillator strengths) the MRCI level of calculations with an 6-311 + G basis set was used. The MRCI calculations considered a virtual space constructed in the following way: First 91 con®gurations were built by considering single and double excitations from all the occupied orbitals, except for the core orbitals, to the unoccupied molecular orbital of b2 symmetry. Then, single excitations were performed from these con®gurations to an external space composed of 100 virtual orbitals, ending with 72 891 con®gurations. The virtual orbitals were built by the modi®ed virtual orbital (MVO) technique [21].
A.B. Rocha, C.E. Bielschowsky / Chemical Physics Letters 337 (2001) 331±334 Table 1 Expansion coecients aj for ML2 QL , Eq. (6), of the dierent vibrational modes Mode
a1
a2
a3
Q9 (a2 ) Q10 (a2 ) Q11 (a2 ) Q12 (a2 ) Q13 (b2 ) Q14 (b2 ) Q15 (b2 ) Q16 (b2 ) Q17 (b2 ) Q18 (b2 ) Q19 (b2 ) Q20 (b1 ) Q21 (b1 ) Q22 (b1 ) Q23 (b1 ) Q24 (b1 )
)0.000685 )0.00008 )0.00095 0.00003 0.00065 )0.00671 )7±0.00087 )0.00011 0.00061 0.00023 )0.00004 0.00002 0.00022 )0.00227 )0.00099 0.00007
0.00001 0.00118 0.03704 0.00024 0.00227 0.0002 0.03044 0.0031 0.0015 )0.00074 0.00105 )0.00015 0.00538 0.13829 0.02666 0.00232
0.0 0.0 )0.01572 0.0 0.0 )0.00015 )0.02234 )0.00131 0.0 0.00131 )0.00054 0.00022 0.00328 )0.10475 )0.01266 0.0
The vertical excitation energy obtained in the calculations for the symmetry dipole forbidden n ! p transition with this methodology was 4.43 eV. The frequencies used to compute the oscillator strengths by means of Eq. (5) above were scaled by 0.9496 [20]. We have used the GAMESS package [22]. In what concerns the expansion of ML2 QL , only positive values for QL are considered in the ®tting
333
process. This is possible because ML2 QL is an even function and, as consequence, we can perform the integration of Eq. (5) for positive values of QL and multiply the result by a factor of 2. The coecients used in the ®tting process, for the distinct vibrational modes, are shown in Table 1. Table 2 shows the present calculated values to the optical oscillator strength, f, for the n ! p in acetone compared with the recent theoretical results of Liao et al. [8] and the experimental results [1,4]. Table 2 shows that the present total f values are in excellent agreement with those of Liao et al. [8], and both results agree reasonably with the experiments. This could suggest that the results of both calculations are equivalent. This is really not true since the distribution per modes is dierent, as can be shown in Table 2. In particular, the calculations of Liao et al. predicted that 94% of the total oscillator strength are due to b1 inducing modes. The remaining 6% are due to b2 inducing modes. The contribution of a2 modes is completely unimportant following their analysis. The present calculations show another picture, the b1 mode being as well dominant, with 66.29% of the total oscillator strength. In our calculations the b2 represents 6.8% of the total f, which agree very well with Liao et al.'s result. The great dierence is related to the
Table 2 Comparison of the present calculated optical oscillator strengths for n ! p transition in acetone with theoretical [8] and experimental [1,4] results Mode
f (present)
Q9 (a2 ) Q10 (a2 ) Q11 (a2 ) Q12 (a2 ) Q13 (b2 ) Q14 (b2 ) Q15 (b2 ) Q16 (b2 ) Q17 (b2 ) Q18 (b2 ) Q19 (b2 ) Q20 (b1 ) Q21 (b1 ) Q22 (b1 ) Q23 (b1 ) Q24 (b1 )
7:60 10 1:05 10 1:41 10 3:06 10 2:01 10 5:27 10 1:33 10 8:74 10 3:94 10 3:74 10 1:46 10 1:07 10 1:53 10 5:67 10 1:43 10 1:49 10
5
% (present)
Total
3:40 10
4
6 5 7 6 6 6 6 6 7 6 5 9 5 4 5
22.36 0.31 4.15 0.09 0.59 1.55 0.39 2.57 1.16 0.11 0.43 3.15 0.00045 16.67 42.10 4.37 100
f [8]
f [1]
3:05 10 1:71 10 2:75 10 7:81 10 1:10 10 2:73 10 2:00 10 6:32 10 6:39 10 5:99 10 1:77 10 1:58 10 9:55 10 8:78 10 1:82 10 5:26 10
7
3:62 10
4
f [4]
8 9 8 7 6 7 7 7 7 5 5 7 5 4 5
4 10
4
4:16 10
4
334
A.B. Rocha, C.E. Bielschowsky / Chemical Physics Letters 337 (2001) 331±334
a2 modes. From the calculation of Liao et al., they are completely unimportant. The present results indicate that they contribute with about 26.91% of the total oscillator strength. Both theoretical results show that the CO out of plane wagging is the most eective mode to borrow intensity. The disagreement of the present approach with that based on the perturbation expansion for the distribution of the inducing modes has also appeared in the case of formaldehyde [11]. In this case there is an experimental result [9] which was able to separate the contribution per mode, showing that in general the results based on the Herzberg±Teller-like ®rst-order perturbation expansion tend to be overestimated for certain modes while underestimated for others, and the present direct approach shows a much better agreement with the experimental distribution of the total intensity. These statements can be veri®ed in Table 1 of [11]. In the acetone case there is much less experimental and theoretical work than formaldehyde. Particularly remarkable is the fact that the experimental values for the oscillator strength are very old. There is no experimental work, to our knowledge, that has determined the contribution per modes to the total oscillator strength. Needless to say that the new experimental results would be very welcomed. Acknowledgements The authors would like to acknowledge CNPq and Capes for the ®nancial support.
References [1] H. Ley, B. Arends, Z. Phys. Chem. B 12 (1931) 132. [2] W.A. Noyes Jr., A.B.F. Dunacan, W.M. Manning, J. Chem. Phys. 2 (1934) 717. [3] H.L. MucMurry, J. Chem. Phys. 9 (1941) 231. [4] E.E. Worden Jr., Spectrochim. Acta 22 (1966) 21. [5] M. Baba, I. Hanazaki, Chem. Phys. Lett. 103 (1983) 93. [6] M. Baba, I. Hanazaki, U. Nagashima, J. Chem. Phys. 82 (1985) 3938. [7] G. Herzberg, Electronic Spectra and Electronic Structure of Polyatomic Molecules, Krieger, NJ, 1991. [8] D.W. Liao, A.M. Mebel, M. Hayashi, Y.J. Shiu, Y.T. Chen, S.H. Lin, J. Chem. Phys. 111 (1999) 205 (references therein). [9] S.J. Strickler, R.J. Barnhart, J. Phys. Chem. 86 (1982) 448. [10] J.A. Pople, J.W. Sidman, J. Chem. Phys. 27 (1957) 1270. [11] A.B. Rocha, C.E. Bielschowsky, Chem. Phys. 253 (2000) 51. [12] M. Roche, H.H. Jae, J. Chem. Phys. 60 (1974) 1193. [13] W.C. Johnson, J. Chem. Phys. 63 (1975) 2144. [14] F. Pauzat, B. Levy, P.H. Millie, Mol. Phys. 39 (1980) 375. [15] J.N. Murrell, J.A. Pople, Proc. Phys. Soc. London A 69 (1956) 245. [16] L. Ziegler, A.C. Albrecht, J. Chem. Phys. 60 (1974) 3558. [17] A.B. Rocha, C.E. Bielschowsky, J. Mol. Struct. (THEOCHEM) 539 (2001) 145. [18] G. Herzberg, E. Teller, Z. Phys. Chem. B 21 (1933) 410. [19] A.M. Mebel, M. Hayashi, S.H. Lin, Chem. Phys. Lett. 274 (1997) 281. [20] A.P. Scott, L. Radom, J. Phys. Chem. 100 (1996) 16502. [21] C.W. Bauschlicher Jr., J. Chem. Phys. 72 (1980) 880. [22] M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen, S.J. Su, T.L. Windus, M. Dupuis, J.A. Montgomery, J. Comp. Chem. 14 (1993) 1347.