- Email: [email protected]
Ionic geometries of acetylene in the X 2Πu and B 2Σu+ ionic states
Volume 169, number I,2
CHEMICAL PHYSICS LETTERS
25 May 1990
IONIC GEOMETRIES OF ACETYLENE IN THE X*II, AND B ‘E; IONIC STATES Foo Tim CHAU Department ofApplied Biology and Chemical
Technology, Hong Kong Polytechnrc. Hung Horn, Hong Kong
Received 28 February 1990
Franck-Condon analyses are applied to the high-resolution photoelectron spectra of CzH2 and CLDI. From the first photoelectron bands, the CH and CC bond lengths are found to be respectively 1.076 and 1.250 8, for C2H: and I .080 and I .247 A for C,D: in the X zHUstate. Results obtained are compared with those by previous workers. As for the third photoelectron bands, simulated spectra of acetylenes agree well with observed ones. The CH and CC bond lengths thus deduced for the B %: state have values of respectively 1.271 and I.191 A for C,H$ and 1.276 and 1.178 k, for C2D:, The long CH bond length obtained for the acetylene ions is discussed.
1. Introduction Photoelectron (PE ) spectroscopy has been developed into a powerful tool in probing ionization processes of molecules [ 1,2 1. Due to great chemical interest, acetylene has been studied extensively by using the PE spectroscopic method [ 3-81. The PE spectrum of acetylene was first reported by Baker and Turner [ 3 1. Three PE bands were observed with the use of He1 (2 1.2 18 eV) light sources. These bands correspond to electronic transitions from the neutral ground state X ‘Z: to the X2&, A ‘&+ and B *Z: ionic states with ionization potentials at around 11.40, 16.36 and 18.38 eV respectively. Recently, with the adoption of the molecularbeam technique in their PE spectrometer, Reutt et al. [ 81 obtained high-resolution spectra of acetylene and acetylene-d* with vibronic structures not observed in previous studies. The first PE bands were found to consist mainly of a short progression in the v2, predominantly C-C stretching, mode accompanied by low-intensity features originating from the vq and v5 Renner-Teller active bending modes. Similar observation was reported by Dehmer and Dehmer [ 61. The vibrational-intensity distribution observed within the band indicates that the geometry of acetylene ion is linear in the ground ionic state
[81. The major peaks of the vibrational structure ob-
served in the third PE band of acetylene were first assigned by Baker and Turner [ 3 ] _ For this electronic state, the v1 frequency has a value less than that of vz in view of the C-H bonding and C-C antibonding character of the 20, electron removed. In the PE study by Reutt et al. [ 81, irregular profiles are exhibited in some peaks in the PE spectrum of acetylene. However, no excitations of non-totally symmetric modes were observed. This led them to propose that the acetylene ion is linear in the B*E+ state Qlantitative applications of the Franck-Condon (FC) principle on vibrational intensity distributions accompanying photoionization processes lead to structural determination of polyatomic molecules in the corresponding ionic states [ 9- 131. Several workers [4,12-141 adopted the approach to determine the ionic geometry of acetylene in the X’II, state. The ion was assumed to be linear. Since only the v, frequency was available from low-resolution spectra of acetylene [ 3,4], they had to assign different values for the v, frequency in their calculations. Rosenstock and co-workers [ 12,131 applied the generating-function method to reproduce vibrationalintensity distributions in the photoionization of acetylene and acetylene-d* near threshold. The vi mode was designated to have ionic frequency about 85% of that in the molecule. Thus, they deduced an increase in the C-C distance from 1.20 8, [ 15 ] in
0009-2614/90/$ 03.50 Q Elsevier Science Publishen B.V. (North-Holland )
43
Volume 169, number
1,2
CHEMICAL PHYSICS LETTERS
neutral acetylene to 1.250f0.005 8, in the ground ionic state with no significant change in the C-H distance, 1.06 8, [ 15 ] (table 1). Hollas and Sutherley [ 41 used their own PE spectral data and the parallelmode method [ lo] for vibrational-intensity calculations to determine the structural parameters of the acetylene ion. The results of calculations were found to be insensitive to the v1 frequency and close to those obtained by Rosenstock et al. [ 131 (table 1); Later, Heilbronner et al. [ 141 computed the ionic geometry of acetylene in the X2& state by adopting the method of Coon et al. [ lo] and utilizing the e matrix in the molecular state instead of L: in the X 211U state in FC analyses. The geometric changes thus derived are similar in magnitudes to those obtained by other workers [ 4,13 ] (table 1). The rotationally cold PE studies performed by Reutt et al. [ 81 on acetylene and acetylene-& allows accurate determination of ionic frequencies and vibrational intensities not available in previous PE studies [ 3,4]. In this work, FC treatment was car-
25 May I990
ried out on the first PE bands of acetylenes for deduction of ionic geometries of the species in the X 2KIU state. The results obtained are different from those by previous workers using similar methods. In addition, vibrational-intensity calculations were ap plied to the third PE bands of acetylenes to explain the vibrational fine structures observed and to determine geometries of the corresponding ions. The calculated structural parameters are compared with those derived from molecular-orbital calculations. The operation of vibronic interactions within the electronic state is also discussed in the light of the results obtained in this work.
2. Methods of calculations Within a PE band, the intensities of individual vibrational components are proportional to the square of the overlap integrals (FC factors) in the assump tions of constant electronic transition moment and
Table I Geometries ‘I of acetylene and acetylene-h in various electronic states Species
Electronic state
CzH2 b’
x Ix+B
1.058
GH:
x 2rI”
1.06
Arc, (A)
A& (A)
rCH
(A)
rC.z
(A)
CCH (de&
Remark
1.208
180
1.250
180
FC analysis ‘)
180
FCanalysis ‘)
180
FC analysis ‘)
(0.005)
0.013
1.06
1.25
(0.01)
(0.01)
0.041 1.102
1.247
180
ab initio calculations ‘)
1.075 1.096 1.082
1.234 1.273 1.259
180 180 180
SCF calculations I1 MCSCF calculations 8) CISD calculations g)
0.012 0.018
0.044 0.042
1.070 1.076
1.252 1.250
180 180
set I h, set 11h,
0.034 0.039
1.100 1.080
I.242 1.247
180 180
setIh’ set II h,
Cz D:
x 2rI.
0.042 0.022
Cz H:
B%+”
0.213
-0.017
1.271
1.191
180
FC analysis h,
CLD:
B*Z+”
0.218
-0.030
1.276
1.178
180
FC analysis ‘)
a) Values within parentheses represent estimated errors of the corresponding quantities. b, Ref. [ 151. cJ Ref. [ 131. “‘Ref. [4]. ‘1 Ref. [ 141. ” Ref. [24]. g) Ref. [25]. h, Structural parameters obtained in this work with estimated errors of 2 0.002 and ? 0.005 A in the X *lIUand B *2: states respectively.
44
Volume169,number 1,2
CHEMICAL
PHYSICS LETTERS
constant photoionization cross section. The normal coordinates of the ionic state Q’ can be expressed in terms of those in the neutral ground state Q through the following expression [ 16] : Q’ = JQ+D”
(1)
with J being the Duschinsky rotation matrix [ 17 1, and D" a column vector with elements d: denoting the shifts between the two coordinate systems. In the harmonic-oscillator approximation, vibrational overlap integrals can be evaluated through the use of recurrence formulae [ 11,181 for a given set of D". In this work, an iterative procedure [ 111 was adopted in optimizing the geometric shifts D" to give the best agreement between the calculated and the observed vibrational intensities. To transform an optimized set of D" to the corresponding changes in internal symmetry-displacement coordinates AS between the two combining states, the following formulae can be used [ 161 AS= KD"
(3)
(4)
with L, being a transformation matrix. From these expressions, the Duschinsky matrix can be written as
1161 J=(c)-‘L,.
(5)
The symmetry coordinates S with 0: symmetry representation for linear acetylene molecules and ions are related to the internal coordinates [ 191 by S, =$(Arl +Ar,) , S,=AR
cos8
‘= ( sin 0
-sin0 cos e >
(7)
with f3being the rotation angle between normal coordinates of the two electronic states; if the rotation angle has a value of zero, J becomes a unit matrix. There is a one-to-one corresponding relationship for the two sets of normal coordinates (parallel-mode case).
3. Results and discussions
and S=&Q
ployed for the molecules while only symmetrized force constants F,(0,' )were considered for the ions. The QCMP 012 program from QCPE [ 221 was adapted for the vibrational analyses. The Duschinsky matrix J can be deduced from L, matrices from the two combining states as mentioned above. It can also be considered as a kind of transformation matrix. For the two-mode case, it has the form [ 23 ]
(2)
with S’ =s+As
25 May 1990
(6)
with ri and R denoting the CHi and the CC bond lengths, respectively. Once the $ matrices of acetylene in various electronic states are determined, the changes in bond lengths and, hence, the ionic geometries can be deduced_ $ matrices of acetylene molecules and ions were obtained by performing force-constant calculations on the observed vibrational frequencies [ 8,15,20] (table 2). In these calculations, harmonic-force constants [ 2 1 ] were em-
Normal-coordinate analyses were applied to acetylenes in the X ‘Zt, X 211Uand B ‘Z: states to obtain the L, matrices for geometry calculations. Harmonic-force constants 1211 were employed for the neutral ground state. As for the acetylene ions, iterative force-constant calculations were performed on C2H: and C2D$ to give the best agreement between computed and observed cr,’ vibrational frequencies [ 81. The symmetrized force constants F, (0,’ ), as given in table 2 for both the X ‘lTUand B *Z,’ states, reproduce observed frequencies within 0.7% and 1.52 respectively. The calculated v, frequency for C2H: in the ground ionic states is 3258 cm- I. In the ground ionic state, the computed force constants for the CC and CH symmetric-stretching modes reduce by about 15% from the corresponding quantities in the neutral molecular state, in parallel with the trend observed in vibrational frequencies (table 2) and calculated structural parameters for the X ‘Z: and the X *II” states. However, there is a dramatic reduction in the v, frequency in the B ‘CT t X ‘C: process, leading to a large difference in the CH-stretching force constant for the two electronic states involved. From the L, matrices obtained from vibrational analyses, J matrices were evaluated through eq. (5) 45
Volume 169, number I,2
CHEMICAL PHYSICS LETTERS
25 May 1990
Table 2 Molecular parameters ‘) of acetylenes and their ions in various electronic states x ‘2+ I CzHz Obs. freqs. (cm-‘) 3312.5 b’ l(o: ) 1973.5 b’ 2ta: 1 F,(ol)
x %”
B 2Z:
GD2
C2H2+
‘3’:
C2H:
C2Dd
2701=) 1762 c’
1829.0(2.5) d,
2572(16)d’ 1651(4) ‘I)
1815(20) d, 2500(20) d)
1475(20) d, 2275(20) d,
(mdynA-I)
F,(l, 1) F,(l>2) K(2,2)
6.3510” -0.1344ej 16.3410”
5.53 I) -0.12 f’ 13.52f’
3.00 r’ - 0.01 ‘) 15.10 f’
J(u~+)~’ J(l,l) J(1,2) J(2, 1) J(2,2) 0 (deg) B,
1.00 0.01 -0.01
1.00 0.03 -0.03
1.00 -0.6
1.00 - 1.5
0.28
0.37
0.96 -0.96 0.28
0.93 -0.93 0.37
- 74.0
-68.4
a’ Valueswith parentheses represent estimated errors of the corresponding quantities. b)Ref. [ 151. c, Ref. [20]. d)Ref. [S]. “Ref. [21].
‘) The calculated force constants are estimated to have errors of ? 0.02 and f 0.05 mdyn A-’ in the X ‘II. and the B ‘z, respectively. B, The calculatedelements of the J matrices and the rotational anglesare estimated to have relative errors of 2 4%and 2 8%in the X *I& and the B ‘Z: states, respectively.
for different combining states. The J matrices obtained for the two ionic states (table 2) can be well represented by the corresponding rotation matrices as shown in eq. (7) with given values of 13.It can be seen that the J matrices for both C2H2+and C2D$ ions are close to unit matrices in the ground ionic state. This implies that the contributions of the two stretching normal coordinates in the X ‘xp’ and the X 21-lU states are similar to each other. However, this is not true for the B ‘E: state owing to a large change
in the CH vibrational frequency (table 2) and the CH bond length (table 1) in the electronic state with respect to the neutral ground state. Very large rotation angles of -74.0” and -68.4” (table 2) were obtained for C, HZ and CZD: , respectively. The FC-analysis procedure gives changes in the normal coordinates upon ionization. However, the signs of D” cannot be determined. The lx, orbital of acetylene possesses CC bonding character [ 1,5 ] and removal of an electron from the orbital should lead to an increase in the CC bond distance. In addition, both ionic frequencies of CH and CC totally symmetric modes have values lower in the X2& state than those in the X ‘Zp’ state. Hence, the two bond 46
lengths are assigned to be longer in the ground ionic state as other workers did [ 4,13,14]. The choice of signs for d; is based on these two criteria [ 11, Two different sets (I and II) of geometries were obtained for &HZ with different signs assigned for d& and &, (table 1). Structural parameters of C,D: as given in set I are rejected because the change in the CH bond length upon ionization is expected to be smaller than that in the CC bond in accord with the bonding properties of the 1% orbital [ 5 1. With regard to &HZ, the ionic geometry of set I is close to those determined by other workers [ 4,13,14] (table 1) . Since geometric shifts upon electronic transitions for both acetylene and acetylene-d, should have comparable magnitudes, structural parameters of set II are favored. Results of molecular-orbital calculations on the geometry of acetylene ion in the X ‘II, state [ 24,25 ] are also included in table 1 for comparison. Figs. 1 and 2 show the experimental [ 81 and calculated third PE band in the PE spectra of acetylenes. These simulated spectra were generated from structural parameters as listed in table 1. The vibrational components were assumed to have the
Volume 169, number 1,2
Lorentzian shape with a full-width at half-maximum of 40 meV. Assignments on the vibrational progressions are also shown based on results of FC analyses in this work. For &HZ, the (0, 1) peaks were assigned to have the same intensity in both the computed and observed spectra (fig. I), while for CzD2, the intensities of the ( 1, 1) peaks were adopted for normalization of the two kinds of spectra (fig. 2 ). The theoretical spectrum of CzH2 (fig. lb) agrees very well in both peak energies and intensities with the experimental vibrational structures with ionization potential less than 19.6 eV. However, the agreement is less satisfactory in peak intensities for high-energy components. As for C2DZ,the simulated spectrum well reproduces the major feature of the observed one (fig. 2). The calculated intensity for the (0, 1) peak is low compared to the experimental value (fig. 2a ) . However, an increase in the intensity of the corresponding transition by augmenting the geometric displacement d& will give FC factors of (u,, 1) and (v,, 2) progressions too high to be acceptable. The good agreement obtained for the calculated third PE bands of acetylenes with the experimental ones support the frequency assignment of Y’,< v; of acetylenes in the B 22,+ state proposed by Turner et al. [ 31. In investigating the third PE (3.v$
(2&l (W21 (O,V2)
h
18.6
19.0
IONIZATION
25 May 1990
CHEMICAL PHYSICS LETTERS
19.4
19.8
POTENTIAL
20.2 Cd’)
Fig. 1. The observed [8] (a) and calculated (b) third band in the PE spectrum of &HZ. The theoretical spectrum was generated from structural parameters as given in table 1. The Lorentzian peak shape with a full-width at half-maximum of 40 meV was assumed for individual vibrational components.
L
18.6
19.0
IONIZATION
19.4 19.8 20.2 POTENTIAL (eV)
Fig. 2. The observed [8] (a) and calculated (b) third band in the PE spectrum of C,D,. The theoretical spectrum was generated from structural parameters as given in table 1. The Lorentzian peak shape with a full-width at half-maximum of 40 meV was assumed for individual vibrational components.
bands of acetylenes, Reutt et al. [ 8 ] pointed out that despite irregular profiles observed for individual peaks, the vibrational structures follow a reasonably harmonic progression. This explains why the harmonic-oscillator approximation adopted in the present work describes the experimental spectra well. However, detailed analyses of the third PE bands require a consideration of vibronic interactions between the B2C: state with other electronic states
[261. As mentioned previously, the magnitudes of geometric distortions Ari depend on the choice of signs for d:. For the B ‘C,+ state of acetylene, d,& and d& were assigned to have positive and negative values respectively based on the frequency changes upon ionization as well as the bonding properties of the 20, orbital from which an electron is removed. Molecular-orbital calculations [ 1,5] indicate that the 20, orbital possesses CH bonding and CC antibonding character. The CH and CC bond lengths thus obtained for CIH: and C,D,’ in the B ‘Z: state have values of respectively 1.271 and 1.191 8, and 1.276 and I. 178 A with estimated errors of ? 0.002 and &0.005 A. Though the vibrational structures of the third PE bands of acetylene and acetylene-d2 are markedly different from each other (figs. la and 2a),
Volume 169, number 1,2
CHEMICAL PHYSICS LETTERS
the calculated CH and CC bond lengths are close to one another. This further supports the results obtained in this work. The large increase in the CH bond length from 1.058 to about 1.27 8, accompanying the B ‘C,++A ‘Ci transition is consistent with the drastic diminution in the corresponding force constant F,( I, 1) from 6.3510 to 3.00 mdyn A-’ (table 2). In a recent work on the second PE band of methane [ 271, a long CH bond length was obtained and found to be 1.279 4 0.004 A in the A ‘A, state, compared to 1.27 1 8, obtained for C&Hz+in the B 2Z,’ state. Long CH bond lengths are also observed in other molecules. For instance, the CH+ ion has bond lengths of 1.2325 and 1.2344 A in the B ‘A and A ‘II states, respectively [ 28 1.
4. Conclusion Franck-Condon analyses were applied to the first and third PE bands of C2H,+ and C2D2+obtained by Reutt et al. [ 8 1, The ionic geometries thus obtained for acetylenes in the ground ionic state have values close to those in the neutral ground state. From results of calculations, structural parameters determined by previous workers [4,13,14] are found to be inconsistent in the light of isotopic data available. With regard to the third PE bands, simulated spectra of CzHz and CZD2agree well with observed ones. The ionic geometries thus deduced for the two acetylenes in the B ‘C: state are of comparable magnitudes. A very long CH bond length of 1.27 8, was obtained. However, detailed analyses of the third PE bands require a consideration of vibronic interactions between the B *Z,+ state and other electronic states
1281.
Acknowledgement
This work was supported by the Earmarked Grant of UPGC of Hong Kong. I would like to acknowledge helpful discussions with Dr. Leif Karlsson of the Physics Department of Uppsala University, Sweden. 48
25 May 1990
References [ 1] D.W. Turner, C. Baker, A.D. Baker and C.R. Brundle, Molecular photoelectron spectroscopy ( Wiley-Interscience, New York, 1970). [2] P.K. Ghosh, Introduction to photoelectron spectroscopy (Wiley-Interscience, New York, 1983). [ 3 ] C. Baker and D.W. Turner, Proc. Roy. Sot. A 308 ( 1968 )
[4] h. Hollas and T.A. Sutherley, Mol. Phys. 2 1 ( 1971) 183. [5] K. Kimura, S. Katsumata, Y. Achiba, T. Yamazaki and S. Iwata, Handbook of He1 photoelectron spectra of fundamental organic molecules (Japan Sci. Sot. Press, Tokyo, 1981) . [6] P.M. Dehmer and J.L. Dehmer, J. Electron Spectry. 28 (1982) 145. [7]D.M.P. Holland, J.B. West, A.C. Parr, D.L. Ederer, R. Stockbauer, R.D. Buff and J.L. Dehmer, J. Chem. Phys. 78 (1983) 124. [S] J.E. Reutt, L.S. Wang, J.E. Pollard, D.J. Trevor, Y.T. Lee and D.A. Shirley, J. Chem. Phys. 84 ( 1986) 3022. [9] G.L. Goodman and J. Berkowitz, in: Molecular ions (Plenum Press, New York, 1983). [IO] J.B. Coon, R.E. deWames and CM. Loyd, J. Mol. Spectry. 8 (1962) 285. [ 111 F.T. Chau, J. Electron Spectry. 48 ( 1989) 389. [ 121T.E. Sharp and H.M. Rosenstock, J. Chem. Phys. 4 1 ( 1964) 3453. [ 131 R. Botter, V.H. Dibeler, J.A. Walker and H.M. Rosenstock, J. Chem. Phys. 44 (1966) 1271. [ 141 E. Heilbronner, K.A. Muszkat and J. Schaublin, Helv. Chim. Acta 54 (1971) 58. 151G. Herzberg, Electronic spectra and electronic structure of polyatomic molecules (VanNostrandReinhold,NewYork, 1966). 161 W.L. Smith and P.A. Warsop, Trans. Faraday Sot. 64 (1968) 1165. 171 F. Duschinsky, Acta Physicochim. URSS 7 (1937) 551. 181H. Kupkaand P.H. Cribb, J. Chem. Phys. 85 (1986) 1303. 191S.J. Cyvin, Molecular vibration and mean square amplitudes (Elsevier, Amsterdam, 1968). [20] T. Shimanouchi, Tables of molecular vibrational frequencies, Vol. 1, NSRDSNBS 39 (US GPO, Washington, 1972). [21] G. Strey and I.M. Mills, J. Mol. Spectry. 59 (1976) 103. [22 ] D.F. McIntosh, M.R. Peterson and T.J. O’leary, QCMP 0 I2 program, QCPE, Indiana University. [23] R.N. DixonandCR. Webster, Mol. Phys. 41 (1980) 441. [24] W.A. Lathan, W.J. Hehre, L.A. Curtiss and J.A. Pople, J. Am. Chem. Sot. 93 ( 1971) 6377. [25] T.J. Lee, J.E. Rice and H.F. Schaefer III, J. Chem. Phys. 86 (1987) 3051. [ 261 H. Koppei, W. Domcke and L.S. Cederbaum, Advan. Chem. Phys. 57 (1984) 59. [27] M. Carlsson-Gothe, B. Wannberg, L. Karlsson, S. Svensson, P. Baltzer, F.T. Chau and M.Y. Adam, submitted for publication. [ZS] K.P. Huber and G. Henberg, Constants of diatomic molecules (Van Nostrand Reinhold, New York, 1979).
r
CHEMICAL PHYSICS LETTERS
25 May 1990
IONIC GEOMETRIES OF ACETYLENE IN THE X*II, AND B ‘E; IONIC STATES Foo Tim CHAU Department ofApplied Biology and Chemical
Technology, Hong Kong Polytechnrc. Hung Horn, Hong Kong
Received 28 February 1990
Franck-Condon analyses are applied to the high-resolution photoelectron spectra of CzH2 and CLDI. From the first photoelectron bands, the CH and CC bond lengths are found to be respectively 1.076 and 1.250 8, for C2H: and I .080 and I .247 A for C,D: in the X zHUstate. Results obtained are compared with those by previous workers. As for the third photoelectron bands, simulated spectra of acetylenes agree well with observed ones. The CH and CC bond lengths thus deduced for the B %: state have values of respectively 1.271 and I.191 A for C,H$ and 1.276 and 1.178 k, for C2D:, The long CH bond length obtained for the acetylene ions is discussed.
1. Introduction Photoelectron (PE ) spectroscopy has been developed into a powerful tool in probing ionization processes of molecules [ 1,2 1. Due to great chemical interest, acetylene has been studied extensively by using the PE spectroscopic method [ 3-81. The PE spectrum of acetylene was first reported by Baker and Turner [ 3 1. Three PE bands were observed with the use of He1 (2 1.2 18 eV) light sources. These bands correspond to electronic transitions from the neutral ground state X ‘Z: to the X2&, A ‘&+ and B *Z: ionic states with ionization potentials at around 11.40, 16.36 and 18.38 eV respectively. Recently, with the adoption of the molecularbeam technique in their PE spectrometer, Reutt et al. [ 81 obtained high-resolution spectra of acetylene and acetylene-d* with vibronic structures not observed in previous studies. The first PE bands were found to consist mainly of a short progression in the v2, predominantly C-C stretching, mode accompanied by low-intensity features originating from the vq and v5 Renner-Teller active bending modes. Similar observation was reported by Dehmer and Dehmer [ 61. The vibrational-intensity distribution observed within the band indicates that the geometry of acetylene ion is linear in the ground ionic state
[81. The major peaks of the vibrational structure ob-
served in the third PE band of acetylene were first assigned by Baker and Turner [ 3 ] _ For this electronic state, the v1 frequency has a value less than that of vz in view of the C-H bonding and C-C antibonding character of the 20, electron removed. In the PE study by Reutt et al. [ 81, irregular profiles are exhibited in some peaks in the PE spectrum of acetylene. However, no excitations of non-totally symmetric modes were observed. This led them to propose that the acetylene ion is linear in the B*E+ state Qlantitative applications of the Franck-Condon (FC) principle on vibrational intensity distributions accompanying photoionization processes lead to structural determination of polyatomic molecules in the corresponding ionic states [ 9- 131. Several workers [4,12-141 adopted the approach to determine the ionic geometry of acetylene in the X’II, state. The ion was assumed to be linear. Since only the v, frequency was available from low-resolution spectra of acetylene [ 3,4], they had to assign different values for the v, frequency in their calculations. Rosenstock and co-workers [ 12,131 applied the generating-function method to reproduce vibrationalintensity distributions in the photoionization of acetylene and acetylene-d* near threshold. The vi mode was designated to have ionic frequency about 85% of that in the molecule. Thus, they deduced an increase in the C-C distance from 1.20 8, [ 15 ] in
0009-2614/90/$ 03.50 Q Elsevier Science Publishen B.V. (North-Holland )
43
Volume 169, number
1,2
CHEMICAL PHYSICS LETTERS
neutral acetylene to 1.250f0.005 8, in the ground ionic state with no significant change in the C-H distance, 1.06 8, [ 15 ] (table 1). Hollas and Sutherley [ 41 used their own PE spectral data and the parallelmode method [ lo] for vibrational-intensity calculations to determine the structural parameters of the acetylene ion. The results of calculations were found to be insensitive to the v1 frequency and close to those obtained by Rosenstock et al. [ 131 (table 1); Later, Heilbronner et al. [ 141 computed the ionic geometry of acetylene in the X2& state by adopting the method of Coon et al. [ lo] and utilizing the e matrix in the molecular state instead of L: in the X 211U state in FC analyses. The geometric changes thus derived are similar in magnitudes to those obtained by other workers [ 4,13 ] (table 1). The rotationally cold PE studies performed by Reutt et al. [ 81 on acetylene and acetylene-& allows accurate determination of ionic frequencies and vibrational intensities not available in previous PE studies [ 3,4]. In this work, FC treatment was car-
25 May I990
ried out on the first PE bands of acetylenes for deduction of ionic geometries of the species in the X 2KIU state. The results obtained are different from those by previous workers using similar methods. In addition, vibrational-intensity calculations were ap plied to the third PE bands of acetylenes to explain the vibrational fine structures observed and to determine geometries of the corresponding ions. The calculated structural parameters are compared with those derived from molecular-orbital calculations. The operation of vibronic interactions within the electronic state is also discussed in the light of the results obtained in this work.
2. Methods of calculations Within a PE band, the intensities of individual vibrational components are proportional to the square of the overlap integrals (FC factors) in the assump tions of constant electronic transition moment and
Table I Geometries ‘I of acetylene and acetylene-h in various electronic states Species
Electronic state
CzH2 b’
x Ix+B
1.058
GH:
x 2rI”
1.06
Arc, (A)
A& (A)
rCH
(A)
rC.z
(A)
CCH (de&
Remark
1.208
180
1.250
180
FC analysis ‘)
180
FCanalysis ‘)
180
FC analysis ‘)
(0.005)
0.013
1.06
1.25
(0.01)
(0.01)
0.041 1.102
1.247
180
ab initio calculations ‘)
1.075 1.096 1.082
1.234 1.273 1.259
180 180 180
SCF calculations I1 MCSCF calculations 8) CISD calculations g)
0.012 0.018
0.044 0.042
1.070 1.076
1.252 1.250
180 180
set I h, set 11h,
0.034 0.039
1.100 1.080
I.242 1.247
180 180
setIh’ set II h,
Cz D:
x 2rI.
0.042 0.022
Cz H:
B%+”
0.213
-0.017
1.271
1.191
180
FC analysis h,
CLD:
B*Z+”
0.218
-0.030
1.276
1.178
180
FC analysis ‘)
a) Values within parentheses represent estimated errors of the corresponding quantities. b, Ref. [ 151. cJ Ref. [ 131. “‘Ref. [4]. ‘1 Ref. [ 141. ” Ref. [24]. g) Ref. [25]. h, Structural parameters obtained in this work with estimated errors of 2 0.002 and ? 0.005 A in the X *lIUand B *2: states respectively.
44
Volume169,number 1,2
CHEMICAL
PHYSICS LETTERS
constant photoionization cross section. The normal coordinates of the ionic state Q’ can be expressed in terms of those in the neutral ground state Q through the following expression [ 16] : Q’ = JQ+D”
(1)
with J being the Duschinsky rotation matrix [ 17 1, and D" a column vector with elements d: denoting the shifts between the two coordinate systems. In the harmonic-oscillator approximation, vibrational overlap integrals can be evaluated through the use of recurrence formulae [ 11,181 for a given set of D". In this work, an iterative procedure [ 111 was adopted in optimizing the geometric shifts D" to give the best agreement between the calculated and the observed vibrational intensities. To transform an optimized set of D" to the corresponding changes in internal symmetry-displacement coordinates AS between the two combining states, the following formulae can be used [ 161 AS= KD"
(3)
(4)
with L, being a transformation matrix. From these expressions, the Duschinsky matrix can be written as
1161 J=(c)-‘L,.
(5)
The symmetry coordinates S with 0: symmetry representation for linear acetylene molecules and ions are related to the internal coordinates [ 191 by S, =$(Arl +Ar,) , S,=AR
cos8
‘= ( sin 0
-sin0 cos e >
(7)
with f3being the rotation angle between normal coordinates of the two electronic states; if the rotation angle has a value of zero, J becomes a unit matrix. There is a one-to-one corresponding relationship for the two sets of normal coordinates (parallel-mode case).
3. Results and discussions
and S=&Q
ployed for the molecules while only symmetrized force constants F,(0,' )were considered for the ions. The QCMP 012 program from QCPE [ 221 was adapted for the vibrational analyses. The Duschinsky matrix J can be deduced from L, matrices from the two combining states as mentioned above. It can also be considered as a kind of transformation matrix. For the two-mode case, it has the form [ 23 ]
(2)
with S’ =s+As
25 May 1990
(6)
with ri and R denoting the CHi and the CC bond lengths, respectively. Once the $ matrices of acetylene in various electronic states are determined, the changes in bond lengths and, hence, the ionic geometries can be deduced_ $ matrices of acetylene molecules and ions were obtained by performing force-constant calculations on the observed vibrational frequencies [ 8,15,20] (table 2). In these calculations, harmonic-force constants [ 2 1 ] were em-
Normal-coordinate analyses were applied to acetylenes in the X ‘Zt, X 211Uand B ‘Z: states to obtain the L, matrices for geometry calculations. Harmonic-force constants 1211 were employed for the neutral ground state. As for the acetylene ions, iterative force-constant calculations were performed on C2H: and C2D$ to give the best agreement between computed and observed cr,’ vibrational frequencies [ 81. The symmetrized force constants F, (0,’ ), as given in table 2 for both the X ‘lTUand B *Z,’ states, reproduce observed frequencies within 0.7% and 1.52 respectively. The calculated v, frequency for C2H: in the ground ionic states is 3258 cm- I. In the ground ionic state, the computed force constants for the CC and CH symmetric-stretching modes reduce by about 15% from the corresponding quantities in the neutral molecular state, in parallel with the trend observed in vibrational frequencies (table 2) and calculated structural parameters for the X ‘Z: and the X *II” states. However, there is a dramatic reduction in the v, frequency in the B ‘CT t X ‘C: process, leading to a large difference in the CH-stretching force constant for the two electronic states involved. From the L, matrices obtained from vibrational analyses, J matrices were evaluated through eq. (5) 45
Volume 169, number I,2
CHEMICAL PHYSICS LETTERS
25 May 1990
Table 2 Molecular parameters ‘) of acetylenes and their ions in various electronic states x ‘2+ I CzHz Obs. freqs. (cm-‘) 3312.5 b’ l(o: ) 1973.5 b’ 2ta: 1 F,(ol)
x %”
B 2Z:
GD2
C2H2+
‘3’:
C2H:
C2Dd
2701=) 1762 c’
1829.0(2.5) d,
2572(16)d’ 1651(4) ‘I)
1815(20) d, 2500(20) d)
1475(20) d, 2275(20) d,
(mdynA-I)
F,(l, 1) F,(l>2) K(2,2)
6.3510” -0.1344ej 16.3410”
5.53 I) -0.12 f’ 13.52f’
3.00 r’ - 0.01 ‘) 15.10 f’
J(u~+)~’ J(l,l) J(1,2) J(2, 1) J(2,2) 0 (deg) B,
1.00 0.01 -0.01
1.00 0.03 -0.03
1.00 -0.6
1.00 - 1.5
0.28
0.37
0.96 -0.96 0.28
0.93 -0.93 0.37
- 74.0
-68.4
a’ Valueswith parentheses represent estimated errors of the corresponding quantities. b)Ref. [ 151. c, Ref. [20]. d)Ref. [S]. “Ref. [21].
‘) The calculated force constants are estimated to have errors of ? 0.02 and f 0.05 mdyn A-’ in the X ‘II. and the B ‘z, respectively. B, The calculatedelements of the J matrices and the rotational anglesare estimated to have relative errors of 2 4%and 2 8%in the X *I& and the B ‘Z: states, respectively.
for different combining states. The J matrices obtained for the two ionic states (table 2) can be well represented by the corresponding rotation matrices as shown in eq. (7) with given values of 13.It can be seen that the J matrices for both C2H2+and C2D$ ions are close to unit matrices in the ground ionic state. This implies that the contributions of the two stretching normal coordinates in the X ‘xp’ and the X 21-lU states are similar to each other. However, this is not true for the B ‘E: state owing to a large change
in the CH vibrational frequency (table 2) and the CH bond length (table 1) in the electronic state with respect to the neutral ground state. Very large rotation angles of -74.0” and -68.4” (table 2) were obtained for C, HZ and CZD: , respectively. The FC-analysis procedure gives changes in the normal coordinates upon ionization. However, the signs of D” cannot be determined. The lx, orbital of acetylene possesses CC bonding character [ 1,5 ] and removal of an electron from the orbital should lead to an increase in the CC bond distance. In addition, both ionic frequencies of CH and CC totally symmetric modes have values lower in the X2& state than those in the X ‘Zp’ state. Hence, the two bond 46
lengths are assigned to be longer in the ground ionic state as other workers did [ 4,13,14]. The choice of signs for d; is based on these two criteria [ 11, Two different sets (I and II) of geometries were obtained for &HZ with different signs assigned for d& and &, (table 1). Structural parameters of C,D: as given in set I are rejected because the change in the CH bond length upon ionization is expected to be smaller than that in the CC bond in accord with the bonding properties of the 1% orbital [ 5 1. With regard to &HZ, the ionic geometry of set I is close to those determined by other workers [ 4,13,14] (table 1) . Since geometric shifts upon electronic transitions for both acetylene and acetylene-d, should have comparable magnitudes, structural parameters of set II are favored. Results of molecular-orbital calculations on the geometry of acetylene ion in the X ‘II, state [ 24,25 ] are also included in table 1 for comparison. Figs. 1 and 2 show the experimental [ 81 and calculated third PE band in the PE spectra of acetylenes. These simulated spectra were generated from structural parameters as listed in table 1. The vibrational components were assumed to have the
Volume 169, number 1,2
Lorentzian shape with a full-width at half-maximum of 40 meV. Assignments on the vibrational progressions are also shown based on results of FC analyses in this work. For &HZ, the (0, 1) peaks were assigned to have the same intensity in both the computed and observed spectra (fig. I), while for CzD2, the intensities of the ( 1, 1) peaks were adopted for normalization of the two kinds of spectra (fig. 2 ). The theoretical spectrum of CzH2 (fig. lb) agrees very well in both peak energies and intensities with the experimental vibrational structures with ionization potential less than 19.6 eV. However, the agreement is less satisfactory in peak intensities for high-energy components. As for C2DZ,the simulated spectrum well reproduces the major feature of the observed one (fig. 2). The calculated intensity for the (0, 1) peak is low compared to the experimental value (fig. 2a ) . However, an increase in the intensity of the corresponding transition by augmenting the geometric displacement d& will give FC factors of (u,, 1) and (v,, 2) progressions too high to be acceptable. The good agreement obtained for the calculated third PE bands of acetylenes with the experimental ones support the frequency assignment of Y’,< v; of acetylenes in the B 22,+ state proposed by Turner et al. [ 31. In investigating the third PE (3.v$
(2&l (W21 (O,V2)
h
18.6
19.0
IONIZATION
25 May 1990
CHEMICAL PHYSICS LETTERS
19.4
19.8
POTENTIAL
20.2 Cd’)
Fig. 1. The observed [8] (a) and calculated (b) third band in the PE spectrum of &HZ. The theoretical spectrum was generated from structural parameters as given in table 1. The Lorentzian peak shape with a full-width at half-maximum of 40 meV was assumed for individual vibrational components.
L
18.6
19.0
IONIZATION
19.4 19.8 20.2 POTENTIAL (eV)
Fig. 2. The observed [8] (a) and calculated (b) third band in the PE spectrum of C,D,. The theoretical spectrum was generated from structural parameters as given in table 1. The Lorentzian peak shape with a full-width at half-maximum of 40 meV was assumed for individual vibrational components.
bands of acetylenes, Reutt et al. [ 8 ] pointed out that despite irregular profiles observed for individual peaks, the vibrational structures follow a reasonably harmonic progression. This explains why the harmonic-oscillator approximation adopted in the present work describes the experimental spectra well. However, detailed analyses of the third PE bands require a consideration of vibronic interactions between the B2C: state with other electronic states
[261. As mentioned previously, the magnitudes of geometric distortions Ari depend on the choice of signs for d:. For the B ‘C,+ state of acetylene, d,& and d& were assigned to have positive and negative values respectively based on the frequency changes upon ionization as well as the bonding properties of the 20, orbital from which an electron is removed. Molecular-orbital calculations [ 1,5] indicate that the 20, orbital possesses CH bonding and CC antibonding character. The CH and CC bond lengths thus obtained for CIH: and C,D,’ in the B ‘Z: state have values of respectively 1.271 and 1.191 8, and 1.276 and I. 178 A with estimated errors of ? 0.002 and &0.005 A. Though the vibrational structures of the third PE bands of acetylene and acetylene-d2 are markedly different from each other (figs. la and 2a),
Volume 169, number 1,2
CHEMICAL PHYSICS LETTERS
the calculated CH and CC bond lengths are close to one another. This further supports the results obtained in this work. The large increase in the CH bond length from 1.058 to about 1.27 8, accompanying the B ‘C,++A ‘Ci transition is consistent with the drastic diminution in the corresponding force constant F,( I, 1) from 6.3510 to 3.00 mdyn A-’ (table 2). In a recent work on the second PE band of methane [ 271, a long CH bond length was obtained and found to be 1.279 4 0.004 A in the A ‘A, state, compared to 1.27 1 8, obtained for C&Hz+in the B 2Z,’ state. Long CH bond lengths are also observed in other molecules. For instance, the CH+ ion has bond lengths of 1.2325 and 1.2344 A in the B ‘A and A ‘II states, respectively [ 28 1.
4. Conclusion Franck-Condon analyses were applied to the first and third PE bands of C2H,+ and C2D2+obtained by Reutt et al. [ 8 1, The ionic geometries thus obtained for acetylenes in the ground ionic state have values close to those in the neutral ground state. From results of calculations, structural parameters determined by previous workers [4,13,14] are found to be inconsistent in the light of isotopic data available. With regard to the third PE bands, simulated spectra of CzHz and CZD2agree well with observed ones. The ionic geometries thus deduced for the two acetylenes in the B ‘C: state are of comparable magnitudes. A very long CH bond length of 1.27 8, was obtained. However, detailed analyses of the third PE bands require a consideration of vibronic interactions between the B *Z,+ state and other electronic states
1281.
Acknowledgement
This work was supported by the Earmarked Grant of UPGC of Hong Kong. I would like to acknowledge helpful discussions with Dr. Leif Karlsson of the Physics Department of Uppsala University, Sweden. 48
25 May 1990
References [ 1] D.W. Turner, C. Baker, A.D. Baker and C.R. Brundle, Molecular photoelectron spectroscopy ( Wiley-Interscience, New York, 1970). [2] P.K. Ghosh, Introduction to photoelectron spectroscopy (Wiley-Interscience, New York, 1983). [ 3 ] C. Baker and D.W. Turner, Proc. Roy. Sot. A 308 ( 1968 )
[4] h. Hollas and T.A. Sutherley, Mol. Phys. 2 1 ( 1971) 183. [5] K. Kimura, S. Katsumata, Y. Achiba, T. Yamazaki and S. Iwata, Handbook of He1 photoelectron spectra of fundamental organic molecules (Japan Sci. Sot. Press, Tokyo, 1981) . [6] P.M. Dehmer and J.L. Dehmer, J. Electron Spectry. 28 (1982) 145. [7]D.M.P. Holland, J.B. West, A.C. Parr, D.L. Ederer, R. Stockbauer, R.D. Buff and J.L. Dehmer, J. Chem. Phys. 78 (1983) 124. [S] J.E. Reutt, L.S. Wang, J.E. Pollard, D.J. Trevor, Y.T. Lee and D.A. Shirley, J. Chem. Phys. 84 ( 1986) 3022. [9] G.L. Goodman and J. Berkowitz, in: Molecular ions (Plenum Press, New York, 1983). [IO] J.B. Coon, R.E. deWames and CM. Loyd, J. Mol. Spectry. 8 (1962) 285. [ 111 F.T. Chau, J. Electron Spectry. 48 ( 1989) 389. [ 121T.E. Sharp and H.M. Rosenstock, J. Chem. Phys. 4 1 ( 1964) 3453. [ 131 R. Botter, V.H. Dibeler, J.A. Walker and H.M. Rosenstock, J. Chem. Phys. 44 (1966) 1271. [ 141 E. Heilbronner, K.A. Muszkat and J. Schaublin, Helv. Chim. Acta 54 (1971) 58. 151G. Herzberg, Electronic spectra and electronic structure of polyatomic molecules (VanNostrandReinhold,NewYork, 1966). 161 W.L. Smith and P.A. Warsop, Trans. Faraday Sot. 64 (1968) 1165. 171 F. Duschinsky, Acta Physicochim. URSS 7 (1937) 551. 181H. Kupkaand P.H. Cribb, J. Chem. Phys. 85 (1986) 1303. 191S.J. Cyvin, Molecular vibration and mean square amplitudes (Elsevier, Amsterdam, 1968). [20] T. Shimanouchi, Tables of molecular vibrational frequencies, Vol. 1, NSRDSNBS 39 (US GPO, Washington, 1972). [21] G. Strey and I.M. Mills, J. Mol. Spectry. 59 (1976) 103. [22 ] D.F. McIntosh, M.R. Peterson and T.J. O’leary, QCMP 0 I2 program, QCPE, Indiana University. [23] R.N. DixonandCR. Webster, Mol. Phys. 41 (1980) 441. [24] W.A. Lathan, W.J. Hehre, L.A. Curtiss and J.A. Pople, J. Am. Chem. Sot. 93 ( 1971) 6377. [25] T.J. Lee, J.E. Rice and H.F. Schaefer III, J. Chem. Phys. 86 (1987) 3051. [ 261 H. Koppei, W. Domcke and L.S. Cederbaum, Advan. Chem. Phys. 57 (1984) 59. [27] M. Carlsson-Gothe, B. Wannberg, L. Karlsson, S. Svensson, P. Baltzer, F.T. Chau and M.Y. Adam, submitted for publication. [ZS] K.P. Huber and G. Henberg, Constants of diatomic molecules (Van Nostrand Reinhold, New York, 1979).
r