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A CASSCF-CI study of the ground and low-lying excited electronic states of C2H+2
Volume 2 12, number 6
CHEMICAL PHYSICS LETTERS
24 September 1993
A CASSCF-CI study of the ground and low-lying excited electronic states of C2H2+ Wolfgang P. Kt-aemer Max-Planck-Institute ofAstrophysics, W-8046 Garching, Germany
and Wolfram Koch lnstitut ftir Organische Chemie, Technische UniversitiilBerlin, W-1000 Berlin 12, Germany Received 30 June 1993; in final form 26 July 1993
Complete-active-space SCF and multi-reference configuration interaction calculations employing large Gaussian basis sets of the general contraction type have been carried out to determine the equilibrium structures and relative stabilities of the ground electronic state R ‘I& of the acetylene cation C,H; and its low-lying excited electronic states, the A ‘Zp’and B ‘C: states, as well as their HCC-H dissociation behavior. While the % and B states have linear equilibrium structures, the first excited A state has a trans-bent equilibrium geometry with a bond angle of approximately 112”. The C-H bond dissociation energy of the ion and parent neutral ground states were obtained in good agreement with experimental findings, whereas the first ionization potentials of C2H, and C,H derived from the differences between the energies of the ion and the parent neutral were found to be too small by about 0.2 eV. The present results were used to set a theoretical lower limit of 17.30eV for the appearance energy of the CzH+ radical ion by dissociative photoionization of C2HZand lo discuss possible reaction pathways for this process.
1. Introduction
Carbocations like the acetylene cation C2H: are important reaction intermediates in laboratory and interstellar space chemistry. But despite its importance, detailed microscopic knowledge of the ground and low-lying excited electronic states of &HZ is rather limited. Since emission spectra to the ground electronic state of the ion have not been observed, most information has come from photoionization [ 1] and photoelectron spectroscopy [ 2-41 of neutral acetylene in the gas phase as well as from matrix studies [ 51. In addition, a high-resolution difference frequency laser measurement of the v3 band of the x T& ground electronic state was performed and the spectra were analyzed in terms of effective spectroscopic constants [ 61. Apart from these experimental efforts, a few reliable theoretical ab initio studies have been carried out. Among these is a careful investi0009-2614/93/$
gation of the energetics of different electronic states of CaH: with acetylenic or vinylidenic geometries which was performed in order to find a qualitative explanation for the experimental difficulties to detect emission spectra of the x 5: --+.%‘IIU transition which is dipole allowed [7]. More recently, the rotation-vibration energy levels of the ~*fl, ground state of the ion were calculated using different levels of approximation to describe the nuclear dynamics
L&91. Appearance energies for &Hz
and some fragment ions of the parent neutral CZH2 have been measured in various experiments and controversial results were obtained for the C2H+ fragment ion produced in the dissociative ionization process [ lo141, C2Hz+hV-tC2H++H+e-.
(1)
From early photoionization experiments the appearance energy of CZH’ was deduced to be 17.22
06.00 D 1993 Elsevier Science Publishers B.V. All rights reserved.
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eV [lo] and 17.36+0.01 eV [ 11 1, whereas later photoionization efficiency measurements gave a much smaller value of about 16.8 eV [ 12,131. More recently, photoion-photoelectron coincidence (PIPECO) spectroscopy was applied to study the above dissociation process and an upper bound of 17.33 If:0.05 eV for the electron-ion appearance energy was determined [ 141. An attempt was made [ 151 to reconcile the existing contradictory experimental data. In the present contribution ab initio calculations are described characterizing some of the low-lying excited states of &Hz together with the 2 *rIU ground state. The reliability of the calculations was assessed by comparing the results of equivalent calculations for the ground states of the &HZ ion and the parent neutral &Hz with the corresponding experimental and other high-accuracy ab initio data. For the above dissociative photoionization process ( 1) a theoretical lower limit for the appearance energy of the C2H+ radical ion can be deduced from the results of the present calculations, and possible reaction mechanisms are discussed.
2. Computations General contracted Gaussian function basis sets of the atomic natural orbital (ANO) type [ 161 located at the atomic centers were employed in the present calculations to describe the molecular orbitals. Specifically, at the carbon centers the primitive sets composed of ( 14s9p4d3f) function were contracted to [ 5s4p2d 1f] functions and at the hydrogen centers the (8s4p3d) functions to [ 4s2pld]. More detailed information about selection and construction of the basis sets is given elsewhere [ 17,181. The resulting total basis set used throughout this study consists of 110 functions. Optimization of the molecular orbitals was achieved through full-valence complete-active-space (US) SCF calculations [ 191. In terms of Doohsymmetry labelling, the SCF ground electronic configuration of C2H$ can be characterized as g”n,:
1+~:2o,22af3o;lx:.
(2)
The full-valence CASSCF thus includes a full configuration interaction treatment of the nine valence 632
24 September1993
electrons in the active space of the 20,, 30,,20,, 1x, valence orbitals together with the next low-lying counterparts (3o,,, 4og, 4oU, 1s~~)whereas the 10~ and lo, orbitals were kept doubly occupied. Corresponding CASSCF calculations at lower symmetries (C,, or C,) were performed to investigate the HCC-H dissociation behavior and the general form of the cis/ tram bending potentials of the low-lying electronic states of the C2H: ion. Excitation energies, ionization potentials and dissociation energies, however, were determined in this study at the more accurate multireference configuration interaction (MR-CI) level of theory taking into account the main part of the dynamic correlation energy effects. In these MR-CI calculations it was not possible to use the complete CASSCF wavefunction as reference function and to include all single and double excitations from this reference, as this would lead to prohibitively large expansions. Thus the CI reference configuration list was restricted to include all occupations for which the coefficient of any one of its component spin couplings exceeded a threshold of 0.05 in the CASSCF wavefunction. With this selection scheme for the reference configurations unbalanced representations of different electronic systems were mostly avoided. CASSCF optimized orbitals were used as molecular orbital basis in the MR-CI calculations of the present study. The computations were done using an early version of the MOLCAS-1 program system [ 201.
3. Results Photoionization of acetylene with He I (21.218 eV) photons gives access to three different electronic states of the resulting &Hz+ ion: the ground electronic R 211Ustate for which photoelectron spectroscopy measurements are the main source for more detailed microscopic information, and the less well characterized excited x ‘Xi and B ‘C: states (using the term symbols of an assumed Dceh symmetry to represent the electronic states). The 2 *II” ground state of the ion is obtained when removing an electron from the least bonding orbital in acetylene, the doubly degenerate lx, orbital. For this state a linear equilibrium geometry was established by earlier experimental and theoretical stud-
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CHEMICALPHYSICSLETTERS
ies. Optimization of the bond distances at the MRCI level of theory gave Rcc= 1.25 18, and RCH= 1.079 A in perfect agreement with the most recent calculations at a comparable accuracy level Rcc= 1.259 8, and R,--= 1.082 A [ 81. Geometry parameters deduced previously from experimental data [ 2 1 ] have been Rcc = 1.255 A and RCH= 1.070 A, where the CH bond distance appears to be too short compared to the well established theoretical predictions. At the same MR-Cl level of theory applied in the present study, the three-dimensional potential energy surface for the stretching motions of the C2H$ ground state was recently calculated and was used together with a model Hamiltonian for the pure stretching vibrations to evaluate the corresponding rovibrational energy levels of the C2H$ ion [ 91. It was shown that in this case the high-frequency stretching motions can be evaluated separately from the low-frequency bendings in a very good approximation and the calculated stretching energies agree with the few available experimental frequencies within a couple of wavenumbers. C-H bond dissociation of the ground state leads to the formation of the C,H+ (8 3TI) radical ion. Optimization of the bond distances for this ion gave Rcc= 1.261 8, and RCH= I .077 A. As expected, these MR-CI optimized values are considerably shorter than previous theoretical predictions at the CASSCF level of theory of 1.300 and 1.094 8, [22] and 1.269 and 1.090 A [ 231, respectively. The dissociation energy was calculated here as De= 6.18 eV. After applying zero-vibration-energy corrections [ 241 the dissociation potential becomes Do=%87 eV, only 0.05 eV off the best value derived from experimental data, D, = 5.92 eV (see ref. [ 15 ] ). In order to minimize size-consistency problems the D, value was computed using the supermolecule approach. It is essential in these calculations to provide a balanced and space consistent description of the original ion and its dissociation products. For this purpose the CI reference configuration list was composed of all reference configurations needed for an accurate representation of the C2H: ion at its equilibrium geometry plus those reference configurations required to describe the dissociation products correctly. An optimized molecular orbital basis was generated in CASSCF calculations with an appropriately specified active space. The reliability of the theoret-
24 September 1993
ical prediction of the ion dissociation energy was assessed by performing corresponding calculations also for neutral acetylene for which most recently numerous experimental and theoretical efforts were undertaken to determine accurately the HCC-H bond energy (see ref. [ 2.51 and references therein). After optimization of the acetylene bond distances (Rcc= 1.206 k ( 1.203 A) and RcH= 1.060 A (1.060 8,) in perfect agreement with the experimental numbers given in parentheses), and using the previously determined equilibrium geometry for the C2H radical [ 26 1, the corresponding dissociation energies were obtained as 0,x5.95 eV and Do=5.6Cl eV. The Do value compares well with that obtained in a recent systematic theoretical investigation of the C-H bond dissociation problem in acetylene, 5.64 f0.04 eV [ 271, and it is also in rather good agreement with all the recent experimental determinations which are in the range from 5.68 to 5.70 eV (cf. ref. [25] ). Ionization potentials were determined here simply as the difference between the energy of the parent neutral molecule and the energy of the ion. This indirect determination suffers from the fact that the two independent calculations of the electronic systems differing by one electron are necessarily slightly unbalanced, leading in general to ionization energies which are too small. Adiabatic and vertical ionization potentials of the parent acetylene were calculated here with CzH2 and CIH: at their separately optimized equilibrium geometries (IP,) or using the &Hz geometry throughout (IP,,,). Due to the differences in the equilibrium bond distances of the ion and the parent neutral, the vertical ionization energy is more appropriate for a direct comparison with experimental data. Present MR-CI calculations gave IP,=ll.ll eV and IP,,,=11.21 eV. As was expected, both values are too small compared to the recent most accurate experimental determination of the first ionization potential of acetylene, IP = 11,403 & 0.005 cV [ 31. Corresponding ionization potential calculations were also carried out for the ethenyl radical C2H (8 *C’), the dissociation product after C-H bond breaking in acetylene. The present MR-CI results are IP,= 11.36 eV, 11.45 eV. From a careful evaluation of the IPvert= results of a PIPECO spectroscopy study of the dissociative photoionization reaction of C2H2 (see eq. ( 1) ) and a C-H bond energy determination of &Hz 633
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[28J, the most reliable experimentally based value for the first ionization energy of C&I was derived in an indirect way as 11.6 1 ? 0.07 eV [ 14 1. In both cases the present theoretical determinations (vertical ionization energies IP,,,) are systematically about 0.2 eV smaller than the experimental results. Photoelectron spectra corresponding to the second ionization potential of acetylene show strongly excited low-frequency bending progressions which indicate a nonlinear equilibrium geometry for this state. Temperature-dependent studies further revealed dominant hot band contributions from the transbending mode, v4 [ 31. A CZh geometry was therefore assigned on the basis of Franck-Condon considerations and the appropriate term symbol is A 2A, for this state. Present calculations confirmed the transbent equilibrium geometry with a bond angle of a(trans)= 112” and the bond distances Rcc= 1.263 A and R,,= 1.180 A. The adiabatic excitation energy was determined here as T,=4.8 I eV leading to a second ionization potential of the parent acetylene of 16.29 eV which is fortuitously in perfect agreement with the experimental value 16.297 IO.005 eV [ 3,151. For the linear geometry of this state (‘IZ: ) the vertical ionization energy of IP,,= 16.9 eV was determined. Earlier theoretical studies using different methods have arrived at similar results, namely 17.3 eV from CEPA (coupled electron pair approximation) [ 71 and 16.98 eV from many-body Green function calculations [ 291. Diabatically HCC-H bond dissociation for this linear configuration results in the release of a proton and the formation of C2H (3 221;‘),about 2 eV above the dissociation limit of the C2H: ground state. The third band in the photoelectron spectrum of C2H2 represents the B “CT ionic state formed by the removal of a 20, electron from the acetylene ground state. Present CASSCF calculations show that this state has a linear equilibrium geometry. Bond distance optimizations at the MR-Cl level of theory yield Rcc= 1.193 A and R,--= 1.191 A. The vertical excitation energy was obtained here as 7.2 eV, which corresponds to a vertical ionization energy of 18.7 eV. Previous theoretical results are 19.2 eV [ 71 and 18.89 eV [ 291. These theoretical numbers are much larger than the experimental value of 18.39 1k 0.005 eV for the third ionization potential of acetylene [3,151. 634
24
September 1993
The present calculated results of the energetics of these low-lying electronic states of the C2H: ion and of the parent neutral C2H2 are summarized in the energy level diagram shown in fig. 1. Additional calculations were carried out to investigate the existance of other excited states of C2H: in the low-energy region. At vertical excitation energies of about 5.5 CV and 6.3 CV two states were found, which, using D,, symmetry labelling, are characterized as 4Fls and *Q, respectively, cocresponding to a In,+lx, excitation from the C2H: ground state. The quartet state is most probably identical with the 4A2 state mentioned in ref. [7]. The A” components of the two IIp states were found in calculations on the CASSCF level to be cisbent with bond angles of about 130”. On the HCCH dissociation potential the A” components have strong non-adiabatic couplings with the A” components of two other doublet and quartet II states . ..(3a’)2(4a’)2(5a’)2(6a’)(7a’)la”) -...(3a’)2(4a’)2(5a’)(6a’)2(7a’)(la”).
(3)
E/eV
20.0 CIH;IB*I;I
IP,,,,=11.21 cv Ill.LOeVI
AEIC&l’1:1730eV 11733ew
0'
I
Do = 5.60 eV (5.68Nl /
I I
C,H,(X’I,I
Fig. 1. Energyleveldiagramfor low-lyingelectronicstatesof &Hz and C2H2+and their dissociation products. Present calculated energiesare showntogether with the corresponding experimental numbers given in parentheses.
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CHEMICALPHYSICSLETTERS
These ‘l-l and 4Tl states correspond to a 30,-+3o, excitation from the ground state. They were found here to be unstable against C-H bond breaking. The two possible spin components of the ‘II state dissociate to the ‘fl or 31Tstates of the CzHf ion. At bent geometries and an enlarged C-H bond length, the A’ component of the ‘TI state has also a strong interaction with the A state . ..(3a’)2(4a’)2(5a’)(6a’)2(1a”)2 *...(3a’)2(4a’)2(5a’)(6a’)(7a’)(la”)2
(4)
and is actually the adiabatic continuation of the HCC-H dissociation potential of this state. In contrast to the diabatic result described above, dissociation along this adiabatic potential thus leads to C-H bond breaking and the formation of C2Hf (2 311) as dissociation product. This dissociation limit lies only about 1.35 eV above the potential minimum of the trans-bent A 2A, state. Assuming the Franck-Condon approximation to be appropriate to describe the formation of the excited ion state in photoionization experiments, it follows that the ion is produced in excited vibrational levels, mostly CH stretching levels close to the dissociation limit with a high tendency to dissociate on a short time scale. This gives an additional explanation for the fact that emission spectra from the A state to the R ‘l-l,, ground state have not been observed so far, although this transition is formally dipole allowed. The vertical first ionization potentials IP,,, were obtained here at the approximation level of the present calculations about 0.2 eV too small compared to the most reliable experimental results and the C-H dissociation energies only slightly (about 0.05 eV) smaller than the Do values derived from experimental data. With these corrections for the first ionization energies of C2H2 and C2H and for the dissociation energies of C2H2 and C2 Hi , a theoretical lower limit for the appearance energy of CzH+ radical formation in the dissociative photoionization of acetylene (see eq. (1)) can thus be established at AE( C,H+) = 17.33 and 17.30 eV, respectively. These values for the theoretical lower limit turn out to be identical with the estimated upper bound of AE( C2H+ ) = 17.33 & 0.05 eV obtained from recent PIPECO spectra measurements of &Hz+ and GH+
24 September 1993
Formation of C,H* ions in the photodissociative process (1) at the much lower appearance energy of 16.8 eV (see refs. [ 12,131) appears to be rather questionable in view of the results of the present calculations. The energy difference of about 0.5 eV to the present theoretical lower limit for the appearance energy of the C2H+ radical ion is too large to be explained in terms of kinetic effects. Therefore it seems to be more likely that the low-energy feature in the photodissociation spectra of &Hz corresponds to the [ 14,301. ion pair dissociation limit H-+CzH+ Several attempts have been made to provide a qualitative picture of the reaction pathway for reaction ( 1) [ 15 1. The present calculations show that in one case photoionization from the C2Hz ground state first leads to the formation of the first excited A state of C2H: which then dissociates via the nonadiabatic coupling (4) to form the C,H+ (R ‘l-I) dissociation product. From the present calculations it also follows that an alternative pathway exists at slightly higher energies. In this case the predissdciated excited *I& state of the ion is formed by 1n,+ 1ng excitation from the initial ground state and through the non-adiabatic coupling (3) this state tinally also dissociates to produce the CzH+ radical ion. The relative efficiency of the two reaction pathways depends critically on the strenghts of the nonadiabatic couplings ( 3 ) and (4). We are grateful to the referee for bringing to our attention three more studies on the C2H: cation [ 31-331. Among these, ref. [31], apart from providing an excellent compilation of all the relevant previous theoretical and experimental work on C2Hz and in addition to the information already published in ref. [ 61, presents a detailed account of the infrared measurement of the V) antisymmetric C-H stretching band of C2H$ as well as of its isotopic species 13C2H: and DC2H+. Predictions of rotational frequencies are made in ref. [ 321. Finally in ref. [ 3 3 1, results of density functional calculations of the C-H dissociation in acetylene and other systems are communicated. At the more accurate level of the nonlocal spin density approach the calculated dissociation energy of &Hz (Do= 5.76 eV), its first ionization energy (IP= I 1.28 eV), and the appearance energy of CzHf (AE= 17.38 eV) are in good
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CHEMICAL
PHYSICS LETTERS
agreement with the results of the present molecular orbital based MR-CI calculations.
Acknowledgement The calculations were carried out on the IBM 3090300E computers at the Gesellschaft fiir Wissenschaftliche Datenverarbeitung (GWD-Gijttingen) and the IBM Scientific Center (Heidelberg), whose services arc gratefully acknowledged.
References [ 1 ] Y. Ono, E.A. Osuch and C.Y. Ng, J. Chem. Phys. 76 ( 1982 ) 3905. [Z]P.M. Dehmer, J. Electron Spectry. Relat. Phenom. 28 (1982) 145. [3] 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. [4] ST. Pratt, P.M. Dehmer and J.L. Dehmer, J. Chem. Phys. 95 (1991) 6238. [S] D. Forney, M.E. Jacox and W.E. Thompson, J. Mol. Spectry. 153 (1992) 680. [6] M.W. Crofton, M.F. Jagod, B.D. Rehfuss and T. Oka, J. Chem. Phys. 86 (1987) 3755. [7] P. Rosmus, P. Botschwina and J.P. Maier, Chem. Phys. Letters, 84 (1981) 71. [8] T.J. Lee, J.E. Rice and H.F. Schaefer III, J. Chem. Phys. 86 (1987) 3051. [9] W.P. Kraemer, V. spirko and B.O. Roos, J. Mol. Spectry. 141 (1990) 43. [lo] R. Botter, V.M. Dibeler, J.A. Walker and H.M. Rosenstock, J. Chem. Phys. 44 (1966) 1271. [ 111 V.H. Dibeler, J.A. Walker and K.E. McCulloh, J. Chem. Phys. 59 (1973) 2264.
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[ 121 Y. Ono and C.Y. Ng, J. Chem. Phys. 74 (1981) 6985. [ 131 T. Hayaishi, S. Iwata, M. Sasanuma, E. Ishiguro, Y. Morioka, Y. Iida and M. Nakamura, I. Phys. B 1.5 (1982) 79. [ 141 K. Norwood and C.Y. Ng, J. Chem. Phys. 91 (1989) 2898. [ 151 C.E. van der Mej, J. van Eck and A. Niehaus, Chem. Phys. 119(1988) 135. [ 161 I. Almliifand P.R. Taylor, J. Chem. Phys. 86 (1987) 4070. [ 171 R. Lindh, B.O. Roosand W.P. Kraemer, Chem. Phys. Letters 139 (1987) 407. [ 181 P.O. Widmark, P.-k. Malmqvist and B.O. Ross, Theoret. Chim. Acta 77 (1990) 291. [ 191 B.O. Roos. P.R. Taylor and P.E.M. Siegbahn, Chem. Phys. 48 (1980) 157. [20] B.O. Roos, G. Karlstriim, P.-A. Malmqvist, A.J. Sadlej and P.-O. Widmark, in: MOTECC-90, Modem techniques in computational chemistry, ed. E. Clementy (ESCOM, Leiden, 1990). [21] J.M. Hollasand T.A. Sutherlay, Mol. Phys. 21 (1971) 183. [22] K. Hashimoto, S. Iwata and Y. Osamura, Chem. Phys. Letters 174 (1990) 649. [ 231 W. Koch and G. Frenking, J. Chem. Phys. 93 (1990) 802 1. [24] L.A. Curtiss and J.A. Pople, J. Chem. Phys. 91 ( 1989) 2420. [25] B.A. Balko, J. ZhangandY.T. Lee,J.Chem. Phys.94 (1991) 7958. [26] W.P. Kraemer, B.O. Roos, P.R. Bunker and P. Jensen, J. Mol. Spectry. 120 (1986) 236. [ 271 C.W. Bauschlicher Jr., S.R. Langhoff and P.R. Taylor, Chem. Phys. Letters 171 ( 1990) 42. [28] A.M. WodtkeandY.T. Lee, J. Phys. Chem. 89 (1985) 4744. [29] L.S. Cederbaum, G. Hohlneicher and W. von Niessen, Mol. Phys. 26 (1973) 1405. [ 301 H. Shiromaru, Y. Achiba, K. Kimura and Y.T. Lee, J. Phys. Chem. 91 (1987) 17. [ 311 M.F. Jagod, M. Riisslein, CM. Gabrys, B.D. Rehfuss, F. Scappini, M.W. Crofton and T. Oka, J. Chem. Phys. 97 (1992)7111. [ 32 ] M. RCisslein, M.F. Jagod, CM. Gabrys and T. Oka, Ap. J. 382 (1991) L51. [33 1J. Andzelm, C. Sosa and R.A. Eades, J. Phys. Chem. 97 (1993) 4664.
CHEMICAL PHYSICS LETTERS
24 September 1993
A CASSCF-CI study of the ground and low-lying excited electronic states of C2H2+ Wolfgang P. Kt-aemer Max-Planck-Institute ofAstrophysics, W-8046 Garching, Germany
and Wolfram Koch lnstitut ftir Organische Chemie, Technische UniversitiilBerlin, W-1000 Berlin 12, Germany Received 30 June 1993; in final form 26 July 1993
Complete-active-space SCF and multi-reference configuration interaction calculations employing large Gaussian basis sets of the general contraction type have been carried out to determine the equilibrium structures and relative stabilities of the ground electronic state R ‘I& of the acetylene cation C,H; and its low-lying excited electronic states, the A ‘Zp’and B ‘C: states, as well as their HCC-H dissociation behavior. While the % and B states have linear equilibrium structures, the first excited A state has a trans-bent equilibrium geometry with a bond angle of approximately 112”. The C-H bond dissociation energy of the ion and parent neutral ground states were obtained in good agreement with experimental findings, whereas the first ionization potentials of C2H, and C,H derived from the differences between the energies of the ion and the parent neutral were found to be too small by about 0.2 eV. The present results were used to set a theoretical lower limit of 17.30eV for the appearance energy of the CzH+ radical ion by dissociative photoionization of C2HZand lo discuss possible reaction pathways for this process.
1. Introduction
Carbocations like the acetylene cation C2H: are important reaction intermediates in laboratory and interstellar space chemistry. But despite its importance, detailed microscopic knowledge of the ground and low-lying excited electronic states of &HZ is rather limited. Since emission spectra to the ground electronic state of the ion have not been observed, most information has come from photoionization [ 1] and photoelectron spectroscopy [ 2-41 of neutral acetylene in the gas phase as well as from matrix studies [ 51. In addition, a high-resolution difference frequency laser measurement of the v3 band of the x T& ground electronic state was performed and the spectra were analyzed in terms of effective spectroscopic constants [ 61. Apart from these experimental efforts, a few reliable theoretical ab initio studies have been carried out. Among these is a careful investi0009-2614/93/$
gation of the energetics of different electronic states of CaH: with acetylenic or vinylidenic geometries which was performed in order to find a qualitative explanation for the experimental difficulties to detect emission spectra of the x 5: --+.%‘IIU transition which is dipole allowed [7]. More recently, the rotation-vibration energy levels of the ~*fl, ground state of the ion were calculated using different levels of approximation to describe the nuclear dynamics
L&91. Appearance energies for &Hz
and some fragment ions of the parent neutral CZH2 have been measured in various experiments and controversial results were obtained for the C2H+ fragment ion produced in the dissociative ionization process [ lo141, C2Hz+hV-tC2H++H+e-.
(1)
From early photoionization experiments the appearance energy of CZH’ was deduced to be 17.22
06.00 D 1993 Elsevier Science Publishers B.V. All rights reserved.
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eV [lo] and 17.36+0.01 eV [ 11 1, whereas later photoionization efficiency measurements gave a much smaller value of about 16.8 eV [ 12,131. More recently, photoion-photoelectron coincidence (PIPECO) spectroscopy was applied to study the above dissociation process and an upper bound of 17.33 If:0.05 eV for the electron-ion appearance energy was determined [ 141. An attempt was made [ 151 to reconcile the existing contradictory experimental data. In the present contribution ab initio calculations are described characterizing some of the low-lying excited states of &Hz together with the 2 *rIU ground state. The reliability of the calculations was assessed by comparing the results of equivalent calculations for the ground states of the &HZ ion and the parent neutral &Hz with the corresponding experimental and other high-accuracy ab initio data. For the above dissociative photoionization process ( 1) a theoretical lower limit for the appearance energy of the C2H+ radical ion can be deduced from the results of the present calculations, and possible reaction mechanisms are discussed.
2. Computations General contracted Gaussian function basis sets of the atomic natural orbital (ANO) type [ 161 located at the atomic centers were employed in the present calculations to describe the molecular orbitals. Specifically, at the carbon centers the primitive sets composed of ( 14s9p4d3f) function were contracted to [ 5s4p2d 1f] functions and at the hydrogen centers the (8s4p3d) functions to [ 4s2pld]. More detailed information about selection and construction of the basis sets is given elsewhere [ 17,181. The resulting total basis set used throughout this study consists of 110 functions. Optimization of the molecular orbitals was achieved through full-valence complete-active-space (US) SCF calculations [ 191. In terms of Doohsymmetry labelling, the SCF ground electronic configuration of C2H$ can be characterized as g”n,:
1+~:2o,22af3o;lx:.
(2)
The full-valence CASSCF thus includes a full configuration interaction treatment of the nine valence 632
24 September1993
electrons in the active space of the 20,, 30,,20,, 1x, valence orbitals together with the next low-lying counterparts (3o,,, 4og, 4oU, 1s~~)whereas the 10~ and lo, orbitals were kept doubly occupied. Corresponding CASSCF calculations at lower symmetries (C,, or C,) were performed to investigate the HCC-H dissociation behavior and the general form of the cis/ tram bending potentials of the low-lying electronic states of the C2H: ion. Excitation energies, ionization potentials and dissociation energies, however, were determined in this study at the more accurate multireference configuration interaction (MR-CI) level of theory taking into account the main part of the dynamic correlation energy effects. In these MR-CI calculations it was not possible to use the complete CASSCF wavefunction as reference function and to include all single and double excitations from this reference, as this would lead to prohibitively large expansions. Thus the CI reference configuration list was restricted to include all occupations for which the coefficient of any one of its component spin couplings exceeded a threshold of 0.05 in the CASSCF wavefunction. With this selection scheme for the reference configurations unbalanced representations of different electronic systems were mostly avoided. CASSCF optimized orbitals were used as molecular orbital basis in the MR-CI calculations of the present study. The computations were done using an early version of the MOLCAS-1 program system [ 201.
3. Results Photoionization of acetylene with He I (21.218 eV) photons gives access to three different electronic states of the resulting &Hz+ ion: the ground electronic R 211Ustate for which photoelectron spectroscopy measurements are the main source for more detailed microscopic information, and the less well characterized excited x ‘Xi and B ‘C: states (using the term symbols of an assumed Dceh symmetry to represent the electronic states). The 2 *II” ground state of the ion is obtained when removing an electron from the least bonding orbital in acetylene, the doubly degenerate lx, orbital. For this state a linear equilibrium geometry was established by earlier experimental and theoretical stud-
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ies. Optimization of the bond distances at the MRCI level of theory gave Rcc= 1.25 18, and RCH= 1.079 A in perfect agreement with the most recent calculations at a comparable accuracy level Rcc= 1.259 8, and R,--= 1.082 A [ 81. Geometry parameters deduced previously from experimental data [ 2 1 ] have been Rcc = 1.255 A and RCH= 1.070 A, where the CH bond distance appears to be too short compared to the well established theoretical predictions. At the same MR-Cl level of theory applied in the present study, the three-dimensional potential energy surface for the stretching motions of the C2H$ ground state was recently calculated and was used together with a model Hamiltonian for the pure stretching vibrations to evaluate the corresponding rovibrational energy levels of the C2H$ ion [ 91. It was shown that in this case the high-frequency stretching motions can be evaluated separately from the low-frequency bendings in a very good approximation and the calculated stretching energies agree with the few available experimental frequencies within a couple of wavenumbers. C-H bond dissociation of the ground state leads to the formation of the C,H+ (8 3TI) radical ion. Optimization of the bond distances for this ion gave Rcc= 1.261 8, and RCH= I .077 A. As expected, these MR-CI optimized values are considerably shorter than previous theoretical predictions at the CASSCF level of theory of 1.300 and 1.094 8, [22] and 1.269 and 1.090 A [ 231, respectively. The dissociation energy was calculated here as De= 6.18 eV. After applying zero-vibration-energy corrections [ 241 the dissociation potential becomes Do=%87 eV, only 0.05 eV off the best value derived from experimental data, D, = 5.92 eV (see ref. [ 15 ] ). In order to minimize size-consistency problems the D, value was computed using the supermolecule approach. It is essential in these calculations to provide a balanced and space consistent description of the original ion and its dissociation products. For this purpose the CI reference configuration list was composed of all reference configurations needed for an accurate representation of the C2H: ion at its equilibrium geometry plus those reference configurations required to describe the dissociation products correctly. An optimized molecular orbital basis was generated in CASSCF calculations with an appropriately specified active space. The reliability of the theoret-
24 September 1993
ical prediction of the ion dissociation energy was assessed by performing corresponding calculations also for neutral acetylene for which most recently numerous experimental and theoretical efforts were undertaken to determine accurately the HCC-H bond energy (see ref. [ 2.51 and references therein). After optimization of the acetylene bond distances (Rcc= 1.206 k ( 1.203 A) and RcH= 1.060 A (1.060 8,) in perfect agreement with the experimental numbers given in parentheses), and using the previously determined equilibrium geometry for the C2H radical [ 26 1, the corresponding dissociation energies were obtained as 0,x5.95 eV and Do=5.6Cl eV. The Do value compares well with that obtained in a recent systematic theoretical investigation of the C-H bond dissociation problem in acetylene, 5.64 f0.04 eV [ 271, and it is also in rather good agreement with all the recent experimental determinations which are in the range from 5.68 to 5.70 eV (cf. ref. [25] ). Ionization potentials were determined here simply as the difference between the energy of the parent neutral molecule and the energy of the ion. This indirect determination suffers from the fact that the two independent calculations of the electronic systems differing by one electron are necessarily slightly unbalanced, leading in general to ionization energies which are too small. Adiabatic and vertical ionization potentials of the parent acetylene were calculated here with CzH2 and CIH: at their separately optimized equilibrium geometries (IP,) or using the &Hz geometry throughout (IP,,,). Due to the differences in the equilibrium bond distances of the ion and the parent neutral, the vertical ionization energy is more appropriate for a direct comparison with experimental data. Present MR-CI calculations gave IP,=ll.ll eV and IP,,,=11.21 eV. As was expected, both values are too small compared to the recent most accurate experimental determination of the first ionization potential of acetylene, IP = 11,403 & 0.005 cV [ 31. Corresponding ionization potential calculations were also carried out for the ethenyl radical C2H (8 *C’), the dissociation product after C-H bond breaking in acetylene. The present MR-CI results are IP,= 11.36 eV, 11.45 eV. From a careful evaluation of the IPvert= results of a PIPECO spectroscopy study of the dissociative photoionization reaction of C2H2 (see eq. ( 1) ) and a C-H bond energy determination of &Hz 633
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[28J, the most reliable experimentally based value for the first ionization energy of C&I was derived in an indirect way as 11.6 1 ? 0.07 eV [ 14 1. In both cases the present theoretical determinations (vertical ionization energies IP,,,) are systematically about 0.2 eV smaller than the experimental results. Photoelectron spectra corresponding to the second ionization potential of acetylene show strongly excited low-frequency bending progressions which indicate a nonlinear equilibrium geometry for this state. Temperature-dependent studies further revealed dominant hot band contributions from the transbending mode, v4 [ 31. A CZh geometry was therefore assigned on the basis of Franck-Condon considerations and the appropriate term symbol is A 2A, for this state. Present calculations confirmed the transbent equilibrium geometry with a bond angle of a(trans)= 112” and the bond distances Rcc= 1.263 A and R,,= 1.180 A. The adiabatic excitation energy was determined here as T,=4.8 I eV leading to a second ionization potential of the parent acetylene of 16.29 eV which is fortuitously in perfect agreement with the experimental value 16.297 IO.005 eV [ 3,151. For the linear geometry of this state (‘IZ: ) the vertical ionization energy of IP,,= 16.9 eV was determined. Earlier theoretical studies using different methods have arrived at similar results, namely 17.3 eV from CEPA (coupled electron pair approximation) [ 71 and 16.98 eV from many-body Green function calculations [ 291. Diabatically HCC-H bond dissociation for this linear configuration results in the release of a proton and the formation of C2H (3 221;‘),about 2 eV above the dissociation limit of the C2H: ground state. The third band in the photoelectron spectrum of C2H2 represents the B “CT ionic state formed by the removal of a 20, electron from the acetylene ground state. Present CASSCF calculations show that this state has a linear equilibrium geometry. Bond distance optimizations at the MR-Cl level of theory yield Rcc= 1.193 A and R,--= 1.191 A. The vertical excitation energy was obtained here as 7.2 eV, which corresponds to a vertical ionization energy of 18.7 eV. Previous theoretical results are 19.2 eV [ 71 and 18.89 eV [ 291. These theoretical numbers are much larger than the experimental value of 18.39 1k 0.005 eV for the third ionization potential of acetylene [3,151. 634
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The present calculated results of the energetics of these low-lying electronic states of the C2H: ion and of the parent neutral C2H2 are summarized in the energy level diagram shown in fig. 1. Additional calculations were carried out to investigate the existance of other excited states of C2H: in the low-energy region. At vertical excitation energies of about 5.5 CV and 6.3 CV two states were found, which, using D,, symmetry labelling, are characterized as 4Fls and *Q, respectively, cocresponding to a In,+lx, excitation from the C2H: ground state. The quartet state is most probably identical with the 4A2 state mentioned in ref. [7]. The A” components of the two IIp states were found in calculations on the CASSCF level to be cisbent with bond angles of about 130”. On the HCCH dissociation potential the A” components have strong non-adiabatic couplings with the A” components of two other doublet and quartet II states . ..(3a’)2(4a’)2(5a’)2(6a’)(7a’)la”) -...(3a’)2(4a’)2(5a’)(6a’)2(7a’)(la”).
(3)
E/eV
20.0 CIH;IB*I;I
IP,,,,=11.21 cv Ill.LOeVI
AEIC&l’1:1730eV 11733ew
0'
I
Do = 5.60 eV (5.68Nl /
I I
C,H,(X’I,I
Fig. 1. Energyleveldiagramfor low-lyingelectronicstatesof &Hz and C2H2+and their dissociation products. Present calculated energiesare showntogether with the corresponding experimental numbers given in parentheses.
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These ‘l-l and 4Tl states correspond to a 30,-+3o, excitation from the ground state. They were found here to be unstable against C-H bond breaking. The two possible spin components of the ‘II state dissociate to the ‘fl or 31Tstates of the CzHf ion. At bent geometries and an enlarged C-H bond length, the A’ component of the ‘TI state has also a strong interaction with the A state . ..(3a’)2(4a’)2(5a’)(6a’)2(1a”)2 *...(3a’)2(4a’)2(5a’)(6a’)(7a’)(la”)2
(4)
and is actually the adiabatic continuation of the HCC-H dissociation potential of this state. In contrast to the diabatic result described above, dissociation along this adiabatic potential thus leads to C-H bond breaking and the formation of C2Hf (2 311) as dissociation product. This dissociation limit lies only about 1.35 eV above the potential minimum of the trans-bent A 2A, state. Assuming the Franck-Condon approximation to be appropriate to describe the formation of the excited ion state in photoionization experiments, it follows that the ion is produced in excited vibrational levels, mostly CH stretching levels close to the dissociation limit with a high tendency to dissociate on a short time scale. This gives an additional explanation for the fact that emission spectra from the A state to the R ‘l-l,, ground state have not been observed so far, although this transition is formally dipole allowed. The vertical first ionization potentials IP,,, were obtained here at the approximation level of the present calculations about 0.2 eV too small compared to the most reliable experimental results and the C-H dissociation energies only slightly (about 0.05 eV) smaller than the Do values derived from experimental data. With these corrections for the first ionization energies of C2H2 and C2H and for the dissociation energies of C2H2 and C2 Hi , a theoretical lower limit for the appearance energy of CzH+ radical formation in the dissociative photoionization of acetylene (see eq. (1)) can thus be established at AE( C,H+) = 17.33 and 17.30 eV, respectively. These values for the theoretical lower limit turn out to be identical with the estimated upper bound of AE( C2H+ ) = 17.33 & 0.05 eV obtained from recent PIPECO spectra measurements of &Hz+ and GH+
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Formation of C,H* ions in the photodissociative process (1) at the much lower appearance energy of 16.8 eV (see refs. [ 12,131) appears to be rather questionable in view of the results of the present calculations. The energy difference of about 0.5 eV to the present theoretical lower limit for the appearance energy of the C2H+ radical ion is too large to be explained in terms of kinetic effects. Therefore it seems to be more likely that the low-energy feature in the photodissociation spectra of &Hz corresponds to the [ 14,301. ion pair dissociation limit H-+CzH+ Several attempts have been made to provide a qualitative picture of the reaction pathway for reaction ( 1) [ 15 1. The present calculations show that in one case photoionization from the C2Hz ground state first leads to the formation of the first excited A state of C2H: which then dissociates via the nonadiabatic coupling (4) to form the C,H+ (R ‘l-I) dissociation product. From the present calculations it also follows that an alternative pathway exists at slightly higher energies. In this case the predissdciated excited *I& state of the ion is formed by 1n,+ 1ng excitation from the initial ground state and through the non-adiabatic coupling (3) this state tinally also dissociates to produce the CzH+ radical ion. The relative efficiency of the two reaction pathways depends critically on the strenghts of the nonadiabatic couplings ( 3 ) and (4). We are grateful to the referee for bringing to our attention three more studies on the C2H: cation [ 31-331. Among these, ref. [31], apart from providing an excellent compilation of all the relevant previous theoretical and experimental work on C2Hz and in addition to the information already published in ref. [ 61, presents a detailed account of the infrared measurement of the V) antisymmetric C-H stretching band of C2H$ as well as of its isotopic species 13C2H: and DC2H+. Predictions of rotational frequencies are made in ref. [ 321. Finally in ref. [ 3 3 1, results of density functional calculations of the C-H dissociation in acetylene and other systems are communicated. At the more accurate level of the nonlocal spin density approach the calculated dissociation energy of &Hz (Do= 5.76 eV), its first ionization energy (IP= I 1.28 eV), and the appearance energy of CzHf (AE= 17.38 eV) are in good
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agreement with the results of the present molecular orbital based MR-CI calculations.
Acknowledgement The calculations were carried out on the IBM 3090300E computers at the Gesellschaft fiir Wissenschaftliche Datenverarbeitung (GWD-Gijttingen) and the IBM Scientific Center (Heidelberg), whose services arc gratefully acknowledged.
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