Ab initio MRD-CI study of the electronic spectrum of linear C5H+

Journal of Molecular Structure (Theochem) 623 (2003) 335–340 www.elsevier.com/locate/theochem

Ab initio MRD-CI study of the electronic spectrum of linear C5Hþ Jan Haubrich, Max Mu¨hlha¨user*, Sigrid D. Peyerimhoff Institut fur Physikalische und Theoretische Chemie, Universita¨t Bonn, Wegelerstrasse 12, 53115 Bonn, FRG, Germany Received 21 May 2002; accepted 18 November 2002

Abstract Ab initio multi-reference configuration interaction (MRD-CI) calculations are performed to predict the vertical electronic spectrum of linear C5Hþ, a species of astrophysical interest. Two transitions at 5.48 eV (11Sþ ˆ X1Sþ) and 5.73 eV (21Sþ ˆ X1Sþ) are computed with relatively large oscillator-strength. In addition the first dipole-allowed electronic transition is calculated at 2.52 eV (11P ˆ X1Sþ). q 2003 Elsevier Science B.V. All rights reserved. Keywords: C5Hþ; Multi-reference configuration interaction; Vertical electronic spectrum; Astrophysical cationic hydrocarbon cluster

1. Introduction During the last years small carbon clusters Cn (n # 20) have attracted much theoretical and experimental interest [1,2]. Various neutral clusters were detected in interstellar media like stars, comets and molecular clouds [1,2]. Besides neutral carbon clusters also cationic carbon clusters and hydrocarbon clusters are of interest for astrophysical and chemical reasons and are expected to play an important role in the understanding of combustion processes and chemical vapor deposition. Furthermore it is believed that hydrocarbon clusters with a large carbon to hydrogen ratio like C5Hþ play an important role as possible carriers of the diffuse interstellar bands (DIBs) and in interstellar ion chemistry as an astrochemical precursor of C5 [3]. C5Hþ can be formed by low-pressure electron impact on benzene vapour [4] or in reaction of Cþ 3 * Corresponding author. Fax: þ 49-228-739-064. E-mail address: [email protected] (M. Mu¨hlha¨user).

with HCCH [5] and has been studied with several methods including Fourier transform mass spectrometry (FTMS) and selected ion-flow techniques (SIFT) [6,7], focusing also on reactions with CO, D2 or O2 [8,9]. Further insight into the electronic structure of its excited states could come from electron absorption spectroscopy. Since theoretical studies are an almost ideal tool to predict approximate wavelengths and transition properties, it is the aim, of this study to provide a guideline for such experimental work on the electronic spectrum of C5Hþ. Similar theoretical computations have recently been successful for a number of carbon clusters [10 –14] and with the present study this work is extended to C5Hþ.

2. Computational techniques The equilibrium geometry of linear C5Hþ was adopted from Ref. [3]. It was obtained using the coupled electron pair approximation (CEPA) and a basis set of 111 contracted Gaussians. Numbering the

0166-1280/03/$ - see front matter q 2003 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 6 - 1 2 8 0 ( 0 2 ) 0 0 7 5 7 - 1

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molecule in line from C(1) to H, the bond ˚ , C(2)C(3) ¼ distances are C(1)C(2) ¼ 1.335 A ˚ , C(3)C(4) ¼ 1.335 A ˚ , C(4)C(5) ¼ 1.227 A ˚, 1.254 A ˚. C(5)H ¼ 1.075 A The computations of the electronically excited states were performed with the multi-reference single and double excitation configuration interaction method MRD-CI implemented in the DIESEL program [15]. The automatic selection of reference configurations was carried out with a summation threshold of 0.82, which means that the sum of the squared coefficients of all reference configurations selected for each state (root) is above 0.82. The set of reference configurations per irreducible representation (IRREP) was in the range between 34 and 42. An analysis of the molecular orbitals (MO) involved in this selected reference configurations justified the prior choice of treating the 20 valence electrons active, while keeping the remaining electrons in doubly occupied orbitals (frozen). From the set of reference configurations (mains) all single and double excitations in the form of configuration state functions (CSFs) are generated and all configurations with an energy contribution DE(T) above a given threshold T are selected, i.e. the contribution of a configuration larger than this value relative to the energy of the reference set is included in the final wavefunction. A selection threshold of T ¼ 1026 hartree is used. The effect of those configurations which contribute less than T ¼ 1026 hartree is accounted for in the energy computation (E(MRD-CI)) by a perturbative extrapolation [16,17]. The contribution of higher excitations is estimated by applying a generalised Langhoff – Davidson correction formula E(MRDCI þ Q) ¼ E(MRD-CI) 2 (1 2 c 20) [E(ref) 2 E(MRD-CI)]/c20, where c20 is the sum of squared coefficients of the reference species in the total CI wavefunction and E(ref) is the energy of the reference configurations. The MRD-CI calculations are performed in the abelian subgroup C2v : In order to keep the computation at a manageable size, only up to a maximum of eight singlet states per irreducible representation (IRREP) are computed and the number of selected CSFs directly included in the energy calculations are as large as 4.8 million selected from a total space of 8.6 million generated configurations.

The carbon AO basis set employed in this calculation is taken from Huzinaga – Dunning [18] and consists of 9s5p Gaussians in a 5s3p contraction and an additional d polarization function with an exponent of a ¼ 0.75. Previous work on C5 and C6 [13] showed that enlarging this basis by Rydberg functions or by employing more functions in the polarization and correlation description will change the results for transition energies generally by less than 0.2 eV. This basis is flexible with respect to polarization and electron correlation and is considered to be fairly balanced for all states treated. For hydrogen a correlation consistent AO basis set of double zeta quality (cc-pVDZ) is used for the calculations [19].

3. Results and discussion 3.1. Vertical excitation energies The electronic configuration for the X1Sþ ground state of C5Hþ is …4s2 5s2 1p4 6s2 2p4 (Fig. 1). Possible low-energy singlet states relative to this configuration are listed in Table 1. Since

Fig. 1. Schematic diagram of the MO energy spectrum (valence electrons only) of the ground state configuration of linear C5Hþ. The values were obtained at the SCF-level. Occupied MOs are marked with arrows.

J. Haubrich et al. / Journal of Molecular Structure (Theochem) 623 (2003) 335–340 Table 1 Low-lying singlet electronic states of the linear C5Hþ as expected from qualitative MO-theory. The lowest X1Sþ state configuration is …4s2, 5s2, 1p4, 6s2, 2p4/3p0, 4p0, 7s0 (valence electrons only) Excitation

Configuration

States

– 2p ! 3p 6s ! 3p 1p ! 3p 5s ! 3p 2p ! 4p 6s ! 4p 6s2 ! 3p2 6s 2p ! 3p2 1p 6s ! 3p2 2p2 ! 3p2

2p4 2p3 3p1 6s1 2p4 3p1 1p3 6s2 2p4 3p1 5s1 1p4 6s2 2p4 3p1 2p3 3p0 4p1 6s1 2p4 3p0 4p1 6s0 2p4 3p2 6s1 2p3 3p2 6s1 1p3 2p4 3p2 6s2 2p2 3p2

1 þ

S S , S , D 1 P 1 þ 1 2 1 S , S , D 1 P 1 þ 1 2 1 S , S , D 1 P 1 þ 1 2 1 S , S , D 1 P(3), 1F 1 P(3), 1F 1 þ S (3), 1S2, 1D(2), 1G

1 þ 1 2 1

Table 2 Calculated transition energies DE (eV) and oscillator strengths f from the X1Sþ state of C5Hþ to its low-lying electronic states. The electronic configuration of the X1Sþ state is …4s2, 5s2, 1p4, 6s2, 2p4/3p0, 4p0, 7s0 (valence electrons only). The oscillator strengths are given for one of the degenerate component of the upper state only State

Excitation

DE

f

X1Sþ 1 P 1 D 1 2 S 1 P 1 D 1 F 1 2 S 1 þ S

Groundstate 6s ! 3p 2p ! 3 2p ! 3p 6s, 2p ! 3p2 (6s ! 3p) 1p ! 3p 6s, 2p ! 3p2 (6s ! 3p) 1p ! 3p 2p ! 3p 2p2 ! 3p2 2p2 ! 3p2 2p ! 3p 6s, 2p ! 3p2 (6s ! 3p) 6s ! 4p 2p ! 4p 2p ! 4p 2p2 ! 3p2 2p2 ! 3p2 2p ! 4p 6s, 1p ! 3p2 (6s ! 3p) 2p2 ! 3p2 (2p ! 3p) 2p2 ! 3p2 6s, 1p ! 3p2 6s, 1p ! 3p2

0.0 2.52 2.90 2.98 5.19 5.20 5.21 5.27 5.48

– 0.007 – – 0.001 – – – 0.5

5.73

0.3

5.79 6.39 6.52 6.54

0.002 0.02 0.0002 –

6.60

–

6.79 6.82 6.88 7.06 7.58

0.002 0.02 – – –

1 þ

the energy levels of the 2p, 6s, 1p and 5s MOs are close, all single excitations from these fully occupied MOs into the 3p LUMO are expected to be low-lying. Furthermore, single excitations from 6s and 2p into the 4p MO may lead to additional low-energy states. In addition double excitations into the 3p LUMO have to be considered. Table 2 summarises the computed vertical excitation energies obtained for the low-lying excitations together with the corresponding oscillator-strengths f. The first dipole-allowed transition 1P ˆ X1Sþ obtained at 2.52 eV corresponds to 6s ! 3p excitation. The 2prarr;3p excitation leads to close-lying 1 D and 1S2 states (2.90 and 2.98 eV, respectively) and to the strong transition 1Sþ ˆ X1Sþ computed at 5.48 eV. The latter transition is obtained with relatively large oscillator-strength characteristic for a p –pp type excitation. This 1Sþ state wave-function shows some contribution of the 2p2 ! 3p2 doubleexcitation, which is the reason for a certain reduction in the p –pp intensity calculation. The other linear combination leads to the second dominating 1 þ S ˆ X1Sþ transition, which is found at 5.73 eV; again the large oscillator-strength can be attributed to the contribution of the 2p ! 3p excitation. The double-excitation 2p2 ! 3p2 also leads to the 1S2 state computed at 6.60 eV, the 1Sþ state calculated at 6.82 eV and one component of the nearby 1D. The double-excitation 2p2 ! 3p2 is the minor contribution to the 2p ! 4p excitation leading to the 1S2 states obtained at 6.54 and at 6.60 eV. This 2p ! 4p

337

S

1

P P 1 þ S 1 2 S 1

1 2

S

1

P S 1 D 1 F 1 P

1 þ

excitation gives also rise to the dipole-allowed 1Sþ state at 6.52 eV. The double excitation 6s 2p ! 3p2 results in two 1 P states at 5.19 and 5.79 eV and a 1F state computed at 5.21 eV. All three states show contributions from the 6s ! 3p single excitation explaining the magnitude of the oscillator-strengths computed for these transitions. The states 1S2 (5.27 eV) and 1D (5.20 eV) result from 1p ! 3p excitation. The 1P state computed at 6.39 eV corresponds to the 6s ! 4p excitation and is obtained with a sizeable f-value of 0.02. The excitation 6s 1p ! 3p2 leads to two high-lying 1P states and another 1F state. At this point a comparison of the C5Hþ spectrum with the spectrum of its isoelectronic counterpart C5 is appropriate [13]. Addition of the hydrogen affects in the main the s-type orbitals. The p-MOs are very little changed, so that the 1pu, 1pg and 2pu of C5

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correspond to the 1p, 2p and 3p of C5Hþ. There is some variation since the C5Hþ structure is more alternant while the bonds in C5 are almost equal. The almost isoenergetic 5su and 6sg in C5 mix with the hydrogen orbital in C5Hþ and as a result the energy difference between these two becomes much larger and 5s (corresponding to 6sg) is stabilised considerably relative to 6s (originating from 5su). This effect has been discussed in a comparison of C6, C6H and HC6Hþ [14]. Furthermore the gerade and ungerade symmetry is lifted in C5Hþ, which allows greater mixing of states. The first Pg and Pu transitions in C5 are calculated [13] at 2.8 and 2.9 eV, corresponding to 5su ! 2pu and 6sg ! 2pu transitions. The corresponding 6s ! 3p transition in C5Hþ is computed at 2.5 eV because of the less stable 6s relative to its 5su origin. The 1pg ! 2pu excitations in C5 [13] show a low-lying Du and S2 u state (around 2.5 eV) compared to the close-lying 1 D and 1S2 states in C5Hþ (around 2.9 eV) originating from 2p ! 3p transitions and a large separation to the Sþ u species (around 6.0 eV) which is responsible for high absorption intensity in this energy region; this splitting is also present in C5Hþ, i.e. the 1Sþ state (2p ! 3p) of C5Hþ is calculated around 5.5 eV and mixes with the 2p2 ! 3p2 state which has its origin in C5 in 2 2 the Sþ g state (1pg ! 1pu) to which transitions from the ground-state are dipole-forbidden. Consistent explanations of the other transitions in C5Hþ relative to C5 are also possible. The 1p ! 3p excitation in C5Hþ results in the 1D and 1S2 states found at around 5.2 eV. This excitation corresponds to a 1pu ! 2pu promotion in C5 and the S2 g and Dg states are found at comparable transitionenergies of about 5.0 eV. The double excitation 5su 1pg ! 2p2u in C5 leads to two Pu states computed at 5.73 and 6.5 eV and a Fu state obtained at 6.05 eV. The corresponding excitation of C5Hþ is 6s 2p ! 3p2, for which two 1P states are obtained around 5.19 and 5.79 eV and also a 1 F state at 5.21 eV. Concluding we find similar states for both isoelectronic molecules at comparable energies. As expectable from the changes in the MO-levels the energy shift of states resulting from pure p- to pp-type excitations is generally smaller than those of states

corresponding to transitions with s-type MO participation. 3.2. Geometry of excited states From the outcome of several cluster studies we performed recently [10,11,13] and in accordance with our computed low vibrational frequencies of 123 and 297 cm21 for cis- and trans-bending modes, respectively, we expect the potential energy surface (PES) of the ground and low-lying excited states to be flat for cis- and trans-bending, so that a progression in the bending modes is quite likely. Therefore we studied symmetric cis- and transbendings at an angle of 208 following the displacement-patterns of the lowest vibrational frequencies (Fig. 2). The bond lengths are kept fixed at the equilibrium distances. For 208 cis-bending the X1A0 ground state (X1Sþ in C1v symmetry) is found only 0.08 eV higher in energy than the linear structure, thus confirming as expected a flat PES. The first 1P state splits upon bending into 1A0 and 1A00 components. Transitions from the bent ground state to both components are computed with similar f-values as in the linear arrangement of nuclei. Furthermore upon bending the first 1D state also splits into 1A0 and 1A00 and transitions from the bent X1A0 ground state become dipole-allowed ( f ¼ 0.001). In addition transitions from the ground state to the first A00 , corresponding to

Fig. 2. Geometries of studied cis- and trans-bent C5Hþ at an angle of 208 following the displacement-patterns of the lowest vibrational frequencies.

J. Haubrich et al. / Journal of Molecular Structure (Theochem) 623 (2003) 335–340

an 1S2 in C1v symmetry, show oscillator strength ( f ¼ 0.001). For trans-bending the first 1P and 1D states split into 1A0 and 1A00 components. Transitions from the bent X1A0 to the four states corresponding to the 1P and 1D states and the 1A00 resulting from the 1S2 state become dipole-allowed. The calculated f-values at 208 are between 0.002 and 0.006. The PES of all states examined possess their minima at the linear geometry, but bending is (as expected from our recent studies on the carbon clusters C4, C5 and C11 [10,11,13] and the present vibrational analysis at the DFT-B3LYP/6-31Gp level [20]) a low energy process. The fact that the energies of the ground state for cis- and trans-bending is erroneously of the same size (0.03 – 0.08 eV) despite the higher vibrational frequency (297 cm21) of trans-bending when compared to cis-bending (123 cm21) can serve as an error margin for the present calculations. The small derivations (DE for cis-bending erroneously higher by 0.05 eV than for trans-bending) show that the calculated values obtained from different methodological and technical treatment (different CI spaces in Cs and C1v ) are consistent.

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transitions will be distributed over a number of narrowly spaced vibrational levels. We hope the present predictions will serve as a guideline for further experimental characterisation of C5Hþ.

Acknowledgements Michael Hanrath, this laboratory, is thanked for improvements in the DIESEL program package. The present study is part of a GreekGerman collaborative linkage grant ‘DAAD Program Griechenland IKYDIA 2001’. The financial support from DAAD is gratefully acknowledged. Basis sets were obtained from the Extensible Computational Chemistry Environment Basis Set Database, Version 11/29/01, as developed and distributed by the Molecular Science Computing Facility, Environmental and Molecular Sciences Laboratory which is part of the Pacific Northwest Laboratory, P.O. Box 999, Richland, Washington 99352, USA, and funded by the US Department of Energy.

References 4. Summary and conclusion We performed multi-reference configuration interaction MRD-CI calculations for ground and excited states of linear C5Hþ to predict approximate transition energies and oscillator strengths for the electronic spectrum up to 7.5 eV. Two transitions at 5.48 eV (11Sþ ˆ X1Sþ) and 5.73 eV (21Sþ ˆ X1Sþ) are computed with large fvalues as expected for p –pp type excitations. In addition the first dipole allowed transition (11P ˆ X1Sþ) is computed at 2.52 eV with a somewhat smaller oscillator strength. A comparison with the spectrum of C5 is made and changes are consistent with orbital stabilisation due to the hydrogen. cis- and trans-Bending potential energy curves of the ground state and selected low-lying excited states are expected to be very flat, so that the electronic

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