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Franck-Condon factors for the ionization process SiF(X 2Π)→SiF+(X 1Σ+)
CHEMICAL PHYSICS LETTERS
Volume 150, number I,2
FRANCK-CONDON
FACTORS FOR THE IONIZATION
9 September 1988
PROCESS SiF(X 211+SiF+(X
Ix+)
S.P. KARNA and F. GREIN Department of Chemistry, University of New Brunswick, Fredericton. NB, Canada E3B 6E2
Received 26 May 1988
Franck-Condon factors ( FCFs) were calculated for SiF( X %)-SiF+ (X ‘Z+ ) and SiF( X ‘II) ASiF+ (a )II), using spectroscopic constants for SiF and SiF+ previously obtained by ab initio CI methods. The results are compared with experimental data for the electron-impact ionization of SiF. Besides the ground vibrational level, a number of transitions originating from higher vibrational levels of SiF are associated with sizable FCFs, explaining the “foot” observed in the ionization cross section.
1. Introduction
Recently, Hayes et al. [ 1 ] measured the absolute cross section for electron-impact ionization of the SiF radical. Their measured ionization threshold (IT) of 7.4kO.l eV for the process SiF+SiF+ is in good agreement with earlier experimental values of the ionization potential (IP) of SiF, 7.26 [ 21, 7.5 Z!Z 0.4 [ 31 and 7.45 eV [4]. Based upon this agreement, Hayes et al. concluded that the neutral radical SiF, which is formed by charge transfer neutralization of SiF+ in the a 3Fl state, is present only in its ground electronic state and predominantly in the ground vibrational level, A small “foot” in the spectrum of the ionization cross section, extending almost 1 eV below IT, indicates that a small fraction of SiF is vibrationally excited. Without knowledge of the molecular constants of SiF+, these authors were unable to explain the extent of vibrational excitation in the neutral molecule. Such information can be derived from a knowledge of the Franck-Condon factors (FCFs) between the vibrational levels of the participating electronic states of the ion and the neutral molecule. Calculation of the FCFs, however, requires accurate values of the equilibrium molecular constants. Whereas for the neutral molecule SiF extensive experimental data exist in the literature [ 5 1, no experimental information is available for the cation, SiF+. Fortunately, fairly accurate theoretical studies on the ground [ 6,7] and low-lying valence states [ 7 ] of
SiF+ have been reported. Kama and Grein [ 71 studied 24 low-lying molecular states of SiF+, dissociating to the lowest channels Si’(‘P) +F(‘P) and Si+ (‘P) + F( *P), as well as 18 low-lying states of SiF. For SiF, good agreement of the calculated spectroscopic constants with available experimental data was found. For SiF+, only the ground and the 1 3Fl excited state were found to be stable. The calculated excitation energy of 3.8 eV for a 31Tagrees with the estimate of 3.4-4.2 eV made by Hayes et al. The calculated adiabatic and vertical ionization potentials (AIP and VIP) are 6.87 and 7.05 eV, respectively, in good accord with experimental data. In view of the interest in the ionization process SiF+SiF+, we have calculated the FCFs between the X *II state of SiF and the two low-lying states X ‘Z+ and a ‘Il of SiF+, using the potential energy curves of ref. [ 7 1. The objective of this communication is to complement the studies made by Hayes et al. [ 11, and to provide information which could be of help in future studies of the ionization of SiF.
2. Calculations Additional points between the internuclear distances R = 2.8 and 4.0 a0 were calculated for X *lTof SiF and X ‘Z+ and a 311of SiF+. Basis sets and the theoretical methods have been described in ref. [ 7 1. The spectroscopic constants were obtained by least-
0 009-2614/88/$ 03.50 0 Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
171
Volume 150, number
I ,2
Table I Calculated spectroscopic constants X ‘I+ and 1 TI states of SiF+ a) Molecule
State
SiF
XQ
SiF+ SiF+
x ‘z+ I ‘l-l
r,
CHEMICAL
PHYSICS LETTERS
for the X % state of SiF and
(eV)
R, (A)
W (cm-‘)
B, (cm-‘)
Ob’ 6.90 11.68
1.611 1.542 1.553
841.1 1123.1 1032.8
0.5740 0.6267 0.6165
” The T, values listed for SiF+ also give the AIPs of SiF for the corresponding ionization. b, The calculated
E,,, of X *lJ is - 388.638436
hartree.
squares as well as spline fitting of the curves to polynomials of degree 7-9. The FCFs, defined as
4““.u’=
Is
vu,,,(R) YLl, (R) ~
*>
where lu,..and (r/,.are the vibrational wavefunctions of the lower and the upper electronic states, are obtained by numerical integration methods.
3. Results and discussion Potential energy curves for the X *I-Istate of SiF and the X ‘C+ and 1 31Ylstates of SiF+ were calculated, and the corresponding spectroscopic constants are listed in table 1. The latter differ slightly from those reported in ref. [ 7 1. The adiabatic and vertical IPs are 6.91 and 7.09 eV, respectively, for Table 2 Franck-Condon v” SiF
cl 1 2 3 4 5 6 7 8 9
172
factor between the lowest vibrational
9 September
1988
SiF(X2n)+SiFf(X’C+),and 11.68and 11.77eV, respectively, for SiF (X 211) + SiF+ (a 311) . Hayes et al. estimated AE( SiF (X 211- SiF+ (a 311)) to be 10.7 to 11.5 eV, in good accord with the present theoretical calculations. The FCFs between SiF(‘lI) and SiF+(X ‘Z+) are listed in table 2. Included are the energy differences between various vibrational levels of SiF and SiF+. The O-O transition is calculated to occur at 6.93 eV, about 0.5 eV lower than the IT observed by Hayes et al. [ 11. Such a descrepancy is within the error limits for calculations’of this quality. The interest is focused on vibrational transitions of lower energy associated with high FCFs, in order to explain the foot in the observed spectrum. Using the notation (v”, v’ ), the ( 1, 0), (2, 0), (2, 1 ), and furthermore the (3, l), (4, l), (4, 2), (%2), (6,2), (7, 2), (8, 3 ) and (9, 4) transitions all have FCFs over 0.1. The lowest energy is 6.5 1 eV for (7,2), about 0.4 eV lower than (0,O). Although it appears unlikely that such high vibrational levels of SiF( X *II ) are populated, one should remember that in the experiment SiF was produced by higher pressure charge transfer (with Xe gas) neutralization of SiF+, which in turn was produced by discharge through SiF,. It is likely that a number of vibrational levels of SiF+ (a 311) were populated at the time of collision with Xe atoms, causing various levels of SiF( X ZIJ) to be populated. FCFs for the process SiF+ (a ‘II) 4 SiF( X ‘II) were calculated, demonstrating the validity of the previous statement. Again using the notation (Y” [ SiF( X *II) 1,
levels of SiF( X ‘IT) and SiF+ (X ‘C’ ) with energy difference
(in eV) in parentheses
v’ SiF+ 0
I
2
3
4
0.405(6.93) 0.334(6.83) 0.164(6.72) 0.063(6.63) 0.021(6.53) 0.007(6.43) 0.002(6.34) 0.013(6.24) 0.000(6.14) O.OOO(6.05)
0.359( 7.06) 0.000(6.96) 0.154(6.86) 0.214(6.76) 0.146(6.66) 0.073(6.57) 0.031(6.47) 0.071(6.37) 0.005 (6.28 ) 0.002(6.19)
0.165(7.20) 0.194(7.09) 0.108(6.99) 0.005(6.90) 0.112(6.80) 0.160(6.70) 0.122(6.60) 0.129(6.51) 0.035(6.41) 0.016(6.31)
0.054( 7.33) 0.255( 7.22) 0.019(7.12) 0.167(7.03) 0.039(6.93) 0.013(6.83) 0.095(6.73) 0.024(6.64) 0.104(6.54) 0.064(6.45)
0.013(7.45) 0.148(7.35) 0.190(7.25) 0.017(7.15) 0.091(7.05) 0.109(6.96) 0.009(6.86) 0.056(6.76) 0.090(6.67) 0.1 lO(6.58)
Volume 150, number I,2
CHEMICAL PHYSICS LETTERS
v’[SiF+(a311)]), the FCFs are 0.580 for (O,O), 0.327for(O, 1),0.370for(1,2) ,..., 0.310for(3,5), 0.319 for (4, 6), 0.315 for (5, 7), 0.309 for (6, 8), 0.307 for (7, 9), etc. In conclusion, a number of assumptions made by Hayes et al. have been confirmed. The a 311state of SiF+ is calculated to be 11.68 eV above the ground state of SiF, such that charge transfer neutralization of SiF+ by Xe (IP = 12.1 eV) produces the ground state of SiF. Assuming that at the time of charge transfer neutralization a number of vibrational levels of SiF+ were populated, calculated FCFs confirm that also a number of vibrational levels of SiF will be populated. Electron impact ionization of SiF, in turn, will show the (0, 0) excitation as well as excitations from higher vibrational levels of SiF, giving rise to the “foot” in the observed spectrum.
Acknowledgement
9 September 1988
the authors’ attention, and U. Meier for helpful suggestions on the computation of FCFs. The Natural Science and Engineering Research Council of Canada provided operating funds, and the University of New Brunswick alloted sufficient computer time.
References [ I] T.R. Hayes, R.C. Wetzel, F.A. Baiocchi and R.S. Freund, J. Chem. Phys. 88 (1988) 823. J.W.C. John& and R.F. Barrow, Proc. Phys. Sot. (London) A71 (1958)476. ‘IT.C. Ehlert and J.L. Margrave, J. Chem. Phys. 41 ( 1964) 1066. 0. Appelblad, R.F. Barrow and R.D. Verma, J. Phys. B 1 (1968) 274. K.P. Huber and G. Herzberg, Molecular spectra and molecular structure, Vol. 4. Constants of diatomic molecules (Van Nostrand Reinhold, New York, 1979). [6] J.M. Robbe, J. Mol. Spectry. 112 (1985) 223. [ 71 S.P. Kama and F. Grein, J. Mol. Spectry. 122 (1987) 28.
Thanks to Dr. P.J. Bruna for bringing ref. [ 1] to
173
Volume 150, number I,2
FRANCK-CONDON
FACTORS FOR THE IONIZATION
9 September 1988
PROCESS SiF(X 211+SiF+(X
Ix+)
S.P. KARNA and F. GREIN Department of Chemistry, University of New Brunswick, Fredericton. NB, Canada E3B 6E2
Received 26 May 1988
Franck-Condon factors ( FCFs) were calculated for SiF( X %)-SiF+ (X ‘Z+ ) and SiF( X ‘II) ASiF+ (a )II), using spectroscopic constants for SiF and SiF+ previously obtained by ab initio CI methods. The results are compared with experimental data for the electron-impact ionization of SiF. Besides the ground vibrational level, a number of transitions originating from higher vibrational levels of SiF are associated with sizable FCFs, explaining the “foot” observed in the ionization cross section.
1. Introduction
Recently, Hayes et al. [ 1 ] measured the absolute cross section for electron-impact ionization of the SiF radical. Their measured ionization threshold (IT) of 7.4kO.l eV for the process SiF+SiF+ is in good agreement with earlier experimental values of the ionization potential (IP) of SiF, 7.26 [ 21, 7.5 Z!Z 0.4 [ 31 and 7.45 eV [4]. Based upon this agreement, Hayes et al. concluded that the neutral radical SiF, which is formed by charge transfer neutralization of SiF+ in the a 3Fl state, is present only in its ground electronic state and predominantly in the ground vibrational level, A small “foot” in the spectrum of the ionization cross section, extending almost 1 eV below IT, indicates that a small fraction of SiF is vibrationally excited. Without knowledge of the molecular constants of SiF+, these authors were unable to explain the extent of vibrational excitation in the neutral molecule. Such information can be derived from a knowledge of the Franck-Condon factors (FCFs) between the vibrational levels of the participating electronic states of the ion and the neutral molecule. Calculation of the FCFs, however, requires accurate values of the equilibrium molecular constants. Whereas for the neutral molecule SiF extensive experimental data exist in the literature [ 5 1, no experimental information is available for the cation, SiF+. Fortunately, fairly accurate theoretical studies on the ground [ 6,7] and low-lying valence states [ 7 ] of
SiF+ have been reported. Kama and Grein [ 71 studied 24 low-lying molecular states of SiF+, dissociating to the lowest channels Si’(‘P) +F(‘P) and Si+ (‘P) + F( *P), as well as 18 low-lying states of SiF. For SiF, good agreement of the calculated spectroscopic constants with available experimental data was found. For SiF+, only the ground and the 1 3Fl excited state were found to be stable. The calculated excitation energy of 3.8 eV for a 31Tagrees with the estimate of 3.4-4.2 eV made by Hayes et al. The calculated adiabatic and vertical ionization potentials (AIP and VIP) are 6.87 and 7.05 eV, respectively, in good accord with experimental data. In view of the interest in the ionization process SiF+SiF+, we have calculated the FCFs between the X *II state of SiF and the two low-lying states X ‘Z+ and a ‘Il of SiF+, using the potential energy curves of ref. [ 7 1. The objective of this communication is to complement the studies made by Hayes et al. [ 11, and to provide information which could be of help in future studies of the ionization of SiF.
2. Calculations Additional points between the internuclear distances R = 2.8 and 4.0 a0 were calculated for X *lTof SiF and X ‘Z+ and a 311of SiF+. Basis sets and the theoretical methods have been described in ref. [ 7 1. The spectroscopic constants were obtained by least-
0 009-2614/88/$ 03.50 0 Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
171
Volume 150, number
I ,2
Table I Calculated spectroscopic constants X ‘I+ and 1 TI states of SiF+ a) Molecule
State
SiF
XQ
SiF+ SiF+
x ‘z+ I ‘l-l
r,
CHEMICAL
PHYSICS LETTERS
for the X % state of SiF and
(eV)
R, (A)
W (cm-‘)
B, (cm-‘)
Ob’ 6.90 11.68
1.611 1.542 1.553
841.1 1123.1 1032.8
0.5740 0.6267 0.6165
” The T, values listed for SiF+ also give the AIPs of SiF for the corresponding ionization. b, The calculated
E,,, of X *lJ is - 388.638436
hartree.
squares as well as spline fitting of the curves to polynomials of degree 7-9. The FCFs, defined as
4““.u’=
Is
vu,,,(R) YLl, (R) ~
*>
where lu,..and (r/,.are the vibrational wavefunctions of the lower and the upper electronic states, are obtained by numerical integration methods.
3. Results and discussion Potential energy curves for the X *I-Istate of SiF and the X ‘C+ and 1 31Ylstates of SiF+ were calculated, and the corresponding spectroscopic constants are listed in table 1. The latter differ slightly from those reported in ref. [ 7 1. The adiabatic and vertical IPs are 6.91 and 7.09 eV, respectively, for Table 2 Franck-Condon v” SiF
cl 1 2 3 4 5 6 7 8 9
172
factor between the lowest vibrational
9 September
1988
SiF(X2n)+SiFf(X’C+),and 11.68and 11.77eV, respectively, for SiF (X 211) + SiF+ (a 311) . Hayes et al. estimated AE( SiF (X 211- SiF+ (a 311)) to be 10.7 to 11.5 eV, in good accord with the present theoretical calculations. The FCFs between SiF(‘lI) and SiF+(X ‘Z+) are listed in table 2. Included are the energy differences between various vibrational levels of SiF and SiF+. The O-O transition is calculated to occur at 6.93 eV, about 0.5 eV lower than the IT observed by Hayes et al. [ 11. Such a descrepancy is within the error limits for calculations’of this quality. The interest is focused on vibrational transitions of lower energy associated with high FCFs, in order to explain the foot in the observed spectrum. Using the notation (v”, v’ ), the ( 1, 0), (2, 0), (2, 1 ), and furthermore the (3, l), (4, l), (4, 2), (%2), (6,2), (7, 2), (8, 3 ) and (9, 4) transitions all have FCFs over 0.1. The lowest energy is 6.5 1 eV for (7,2), about 0.4 eV lower than (0,O). Although it appears unlikely that such high vibrational levels of SiF( X *II ) are populated, one should remember that in the experiment SiF was produced by higher pressure charge transfer (with Xe gas) neutralization of SiF+, which in turn was produced by discharge through SiF,. It is likely that a number of vibrational levels of SiF+ (a 311) were populated at the time of collision with Xe atoms, causing various levels of SiF( X ZIJ) to be populated. FCFs for the process SiF+ (a ‘II) 4 SiF( X ‘II) were calculated, demonstrating the validity of the previous statement. Again using the notation (Y” [ SiF( X *II) 1,
levels of SiF( X ‘IT) and SiF+ (X ‘C’ ) with energy difference
(in eV) in parentheses
v’ SiF+ 0
I
2
3
4
0.405(6.93) 0.334(6.83) 0.164(6.72) 0.063(6.63) 0.021(6.53) 0.007(6.43) 0.002(6.34) 0.013(6.24) 0.000(6.14) O.OOO(6.05)
0.359( 7.06) 0.000(6.96) 0.154(6.86) 0.214(6.76) 0.146(6.66) 0.073(6.57) 0.031(6.47) 0.071(6.37) 0.005 (6.28 ) 0.002(6.19)
0.165(7.20) 0.194(7.09) 0.108(6.99) 0.005(6.90) 0.112(6.80) 0.160(6.70) 0.122(6.60) 0.129(6.51) 0.035(6.41) 0.016(6.31)
0.054( 7.33) 0.255( 7.22) 0.019(7.12) 0.167(7.03) 0.039(6.93) 0.013(6.83) 0.095(6.73) 0.024(6.64) 0.104(6.54) 0.064(6.45)
0.013(7.45) 0.148(7.35) 0.190(7.25) 0.017(7.15) 0.091(7.05) 0.109(6.96) 0.009(6.86) 0.056(6.76) 0.090(6.67) 0.1 lO(6.58)
Volume 150, number I,2
CHEMICAL PHYSICS LETTERS
v’[SiF+(a311)]), the FCFs are 0.580 for (O,O), 0.327for(O, 1),0.370for(1,2) ,..., 0.310for(3,5), 0.319 for (4, 6), 0.315 for (5, 7), 0.309 for (6, 8), 0.307 for (7, 9), etc. In conclusion, a number of assumptions made by Hayes et al. have been confirmed. The a 311state of SiF+ is calculated to be 11.68 eV above the ground state of SiF, such that charge transfer neutralization of SiF+ by Xe (IP = 12.1 eV) produces the ground state of SiF. Assuming that at the time of charge transfer neutralization a number of vibrational levels of SiF+ were populated, calculated FCFs confirm that also a number of vibrational levels of SiF will be populated. Electron impact ionization of SiF, in turn, will show the (0, 0) excitation as well as excitations from higher vibrational levels of SiF, giving rise to the “foot” in the observed spectrum.
Acknowledgement
9 September 1988
the authors’ attention, and U. Meier for helpful suggestions on the computation of FCFs. The Natural Science and Engineering Research Council of Canada provided operating funds, and the University of New Brunswick alloted sufficient computer time.
References [ I] T.R. Hayes, R.C. Wetzel, F.A. Baiocchi and R.S. Freund, J. Chem. Phys. 88 (1988) 823. J.W.C. John& and R.F. Barrow, Proc. Phys. Sot. (London) A71 (1958)476. ‘IT.C. Ehlert and J.L. Margrave, J. Chem. Phys. 41 ( 1964) 1066. 0. Appelblad, R.F. Barrow and R.D. Verma, J. Phys. B 1 (1968) 274. K.P. Huber and G. Herzberg, Molecular spectra and molecular structure, Vol. 4. Constants of diatomic molecules (Van Nostrand Reinhold, New York, 1979). [6] J.M. Robbe, J. Mol. Spectry. 112 (1985) 223. [ 71 S.P. Kama and F. Grein, J. Mol. Spectry. 122 (1987) 28.
Thanks to Dr. P.J. Bruna for bringing ref. [ 1] to
173