A New Interpretation of the Photoelectron Spectra of CrC2â - The

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A New Interpretation of the Photoelectron Spectra of CrC2Marc F.A. Hendrickx, Christophe Iftner, and Van Tan Tran J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp404815k • Publication Date (Web): 19 Jun 2013 Downloaded from http://pubs.acs.org on June 21, 2013

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The Journal of Physical Chemistry

A New Interpretation of the Photoelectron Spectra of CrC2Van Tan Trana, Christophe Iftnerb, and Marc F.A. Hendrickxa*

(a) Afdeling Kwantumchemie en Fysicochemie, Departement Chemie, Katholieke Universiteit Leuven, Celestijnenlaan 200F, B-3001 Heverlee-Leuven, Belgium (b) Laboratoire de Chimie et Physique Quantiques, IRSAMC, Université Paul Sabatier 118 route de Narbonne, 31062 Toulouse Cedex 09, France

Abstract In this work, the computational quantum chemical DFT, CASPT2, and RCCSD(T) methods have been utilized to investigate the geometric and electronic structures of cyclic and linear CrC2/0

clusters. The neutral ground state is firmly identified as the cyclic 5A1 state. For the anionic

cluster two as good as degenerate isomers were recognized, namely a cyclic 6A1 state and a linear 6Σ+ state. Therefore, assignments of the observed bands in the photoelectron spectra of CrC2- have been made based on both these isomers. With exception of the B band all other experimental observed bands could be ascribed to the cyclic isomer. The computed detachment energies show that the former band must be exclusively assigned to the ionization of the 6Σ+ of the linear structure, which can possibly also contribute to some higher energy bands. Additional support for the proposed assignments is provided by multidimensional Franck-Condon factor simulations for the 6A1→5A1 and 6A1→5B1 transitions that show a nearly perfect match with the observed vibrational progressions of the X and A bands in the 532 nm spectra. Keywords: chromium carbide, spectrum assignment, molecular structure, ab initio calculations, vibrational analysis. * Corresponding author

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Introduction The interaction between transition metals and carbon is of importance because it is relevant to the formation of modern materials such as metallo-carbohedrenes (met-cars) and metallofullerene.1-5 Small carbide clusters containing different kinds of transition metals that are believed to be the building blocks for new nanomaterials, have in the past been intensively investigated by means of a large amount of experimental and theoretical methods.6-23 More specifically, the stoichiometric CrC2- cluster with competing different low-lying isomers has been generated in the gas phase. For the purpose to unravel the geometric and electronic structure of the corresponding neutral cluster, the anion photoelectron spectra as recorded with photon energies of 355 and 532 nm by L.-S. Wang and coworkers are of great importance.14, 23 These well-resolved spectra contain useful and precise information about the electron detachment energies and vibrational properties, revealing the relative energetic positions of the involved neutral electronic states, their vibrational frequencies of the symmetric stretching modes and possible geometry changes which accompany the underlying ionization processes. Since, rather typically, these data are insufficient to experimentally identify the specific nature of the states, a computational quantum chemical study is unquestionably needed to interpret in full detail the experimental data and to render insights into the growth mechanisms of the new nanomaterials. Additionally, in the same experimental study the geometric and electronic structures of different isomers of CrC2-/0 were theoretically investigated with density functional theory (DFT) and couple-cluster (CCSD(T)) methods.23 Cyclic and linear isomers of CrC2-/0 clusters with a C2 moiety side-on or end-on bound to chromium, respectively, were identified as the most stable molecular entities. For the anionic cluster, the results showed that the 6A1 state of the cyclic isomer and the 6Σ+ state of linear structure possess nearly equal stability with an energy difference as small as 0.06 eV at the CCSD(T) level. The ground state of the neutral cluster was calculated to be the 5A1 of the cyclic isomer. On the other hand, by using the BPW91 functional, the X band of the anion photoelectron spectra was ascribed to the transition between 6A1 and 5

A1 states of the cyclic structure, while the C band was assigned to the 7A1 state of the same

isomer. The B band on the other hand, with its intensity depending on the experimental 2 ACS Paragon Plus Environment

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conditions, was proposed to originate from the 6Σ+→5Π transition of the linear structure. No attempt was undertaken to assign the A band and the higher energy bands in the anion photoelectron spectra. An effort in this direction was later made by carrying out TDDFT (timedependent density functional theory) calculations.21 Besides the C and E bands, all the observed bands were tentatively assigned to the cyclic isomer exclusively. The authors did not mention any results for the linear isomer, which was previously23 assumed to be responsible for the B band in the spectra. Due to the expected strong multireference wavefunction, as usual for unsaturated transition metal complexes, multireference methods such as CASSCF (complete active-space self-consistent field) and MRCI (multireference configuration interaction) were also applied to investigate the electronic structures of the CrC20/+ clusters.24-25 The MRCI calculations, with an active space of 14 electrons in 13 orbitals, reconfirmed the 5A1 of the cyclic isomer as the ground state of the neutral cluster. The 5Σ+ state of the linear isomer was evaluated to be much less stable by no less than 0.67 eV. Also the CCSD(T) calculations of the same work placed the 5 +

Σ state 0.96 eV above the cyclic 5A1. In this work, we will investigate in detail the geometric and electronic structures of the

cyclic and linear CrC2-/0 clusters by using either single-reference DFT and RCCSD(T), or multireference CASPT2 (complete active space second-order perturbation theory) methods. Very large basis sets calculations that correlate the outer-core electrons of chromium were performed in the present study with the aim to reach a sufficient recovery of the dynamic electron correlation. With the most accurate relative energies, we will propose assignments for all the observed bands in the anion photoelectron spectra. Additionally, multidimensional Franck-Condon factor simulations will be presented for the well resolved bands of the 532 nm photoelectron spectrum to ensure that our newly proposed assignment is correct.26-27 The necessary geometries, vibrational modes and frequencies for these simulations will be provided by the B3LYP hybrid DFT method, which has previously been proven to be satisfactorily capable for this purpose.



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Computational Approach Our calculations will explore in detail the two lowest energy isomers of the CrC2-/0 clusters which possess either a cyclic or linear conformation. As can be seen in Figure 1, the cyclic isomer is formed by a C2 moiety side-on bond to chromium, while the linear isomer has a C2 entity end-on bond to the metal centre. The actual symmetry of these two isomers is respectively C2v and C∞v. However, because only Abelian point groups are implemented in the employed MOLCAS and MOLPRO computer codes, the C2v point-group had to be utilized in the calculations. The nuclear skeleton of the cyclic structures is located in the YZ plane, while for the linear isomer the nuclei are placed along the Z axis.

In order to get an insight into the electronic structure of CrC2-/0 clusters, single point CASPT2 calculations were performed first for all the lowest states of each spin multiplicity and irreducible representation of the C2v point group based on the geometry of the anionic ground state as obtained with the B3LYP functional. For the cyclic CrC2-/0, the molecular orbitals were obtained from a CASSCF calculation with an active space of 10 or 11 electrons in 17 orbitals. This active space allows to accommodate the 3d, 3d’, and 4s orbitals of chromium and the 2p orbitals of carbon. For the linear CrC2-/0, the active space is obtained by distributing 14 or 15 electrons in 14 orbitals, which included the 3d and 4s orbitals of chromium and the 2s, 2p orbitals of carbon. ANO-RCC basis sets for both chromium and carbon with contraction schemes corresponding to [7s5p4d3f2g] and [5s4p3d2f] were used, respectively.28-29 In addition to the active space electrons, the 3s and 3p electrons of chromium were correlated in the perturbation step. The Douglas-Kroll Hamiltonian was used to include scalar-relativistic effects which are important in clusters containing transition metals.30-32 In order to remove intruder states, an imaginary shift of 0.1 was applied. The computationally efficient CASPT2 code of MOLCAS 7.6 package33 was used to perform the calculations.

Based on the CASSCF leading configurations for the low-lying states of CrC2-/0 clusters, DFT calculations were carried out. Structures of all the low-lying states are optimized within the C2v point groups by using the pure BP8634-35 and hybrid B3LYP34,

36-37

functionals. Def2-QZVP 4

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basis sets were employed for both chromium and carbon.38 Harmonic vibrational frequency calculations were performed to ensure that the stationary points found, represent minima on the potential energy surfaces of the corresponding states. The B3LYP geometric structures, harmonic vibrational modes and frequencies allow to calculate the multidimensional FranckCondon factors which can be compared to the relative intensities of peaks belonging to the vibrational progressions of the low-lying bands in the 532 nm experimental spectrum. All DFT calculations were executed with the TURBOMOLE 6.3 package39, while the multidimensional Franck-Condon factors were acquired with the FCLab II package40-41.

RCCSD(T) calculations were carried out by using the MOLPRO 2009 package.42 The augcc-pwCVnZ-DK43 and aug-cc-pVnZ-DK44 (n = T and 5) were utilized for chromium and carbon, respectively. The triple-ζ basis sets were used for geometry optimizations. For the purpose of improving the relative energies quintuple-ζ basis sets were employed for single point calculations on the triple-ζ optimized structures. ROHF calculations on the leading electronic configuration wavefunctions as identified by CASSCF, yielded the necessary orbitals for the subsequent RCCSD(T) calculations. In addition to the valence orbitals of chromium (3d, 4s) and carbon (2s, 2p), the outer-core orbitals of chromium (3s, 3p) were included in the correlation treatment. The Douglas-Kroll Hamiltonian up to the second-order was included to account for scalar-relativistic effects.



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Results and Discussion Most stable isomers of CrC2-/0 clusters. B3LYP, BP86, and RCCSD(T) structural parameters and relative energies for all low-lying states of the cyclic and linear CrC2-/0 clusters are collected in Table 1. B3LYP and BP86 harmonic vibrational frequencies of these states are also included in the same table. For the anionic cluster all three levels of computation concur that the lowest states are the 6A1 and the 6Σ+ states of the cyclic and the linear isomers, respectively. The pure BP86 and the hybrid B3LYP DFT methods identify the linear 6Σ+ state as about 0.10 eV more stable than the cyclic 6A1 structure, while the latter is computed to be 0.10 eV more stable at the RCCSD(T) level. Because these small energy differences most certainly fall within the expected error bars of the employed computational models, a definite conclusion cannot be drawn on the basis of these results but these two isomers should be considered as competitive ground states.

For the neutral cluster, all the calculations undoubtedly show a much more stable cyclic isomer when compared to any linear electronic state. RCCSD(T), as our highest level of computation, places its 5A1 ground state at 0.89 eV below the lowest linear state, which is identified as the high spin 7Σ+. Both DFT methods employed, agree on this aspect by predicting a more stable cyclic structure of 0.68 eV to as much as 0.91 eV, at the B3LYP and the BP86 levels respectively. All computational methods further agree that the cyclic ground state is firmly separated from the excited states. Indeed, RCCSD(T) places the equilibrium structure of the 5B1, as the lowest cyclic excited state, at 0.37 eV above the 5A1 ground state. For the linear structure the situation is much less obvious. The 5Π state is calculated by RCCSD(T) to be only 0.07 eV higher than the 7Σ+. It should however be mentioned that the former state is not stable because, due its spatial degeneracy, it is subject to a Renner-Teller distortion. The B3LYP and BP86 imaginary frequencies of 235i and 310i cm-1 for the 5B1 component, respectively, confirm this prediction. When following the corresponding vibrational normal mode, both DFT methods arrived at the 5A1 ground state of the cyclic CrC2. On the other hand, our DFT frequency calculations for the second component, the 5B2, does not show any imaginary frequency and therefore the CrCC bond angle remains 180° after geometry optimization. 6 ACS Paragon Plus Environment

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Concerning the relative sequence of the low-lying states of the linear isomer there is a discrepancy between the DFT methods at the one hand and RCCSD(T) on the other. RCCSD(T) positions the 5Π well above the 7Σ+, with an energy gap between them amounting to 0.07 eV. At the DFT level this is no longer the case. Both employed functionals identify the 5Π as the lowest state. Because the couple cluster results may be subject to uncertainties due to multireference effects, CASSCF and CASPT2 calculations were performed as well. These results will be discussed in a subsequent paragraph in relation to the interpretation of the anion photoelectron spectra. As an additional advantage the CASSCF active space orbitals have been proven in the past26-27, 4546

to be particularly well suited for obtaining a detailed insight into the electronic structure of

the various spectroscopic relevant states. This information is of importance for the assignment of the experimental spectra.

Electronic structures of CrC2-/0. CASSCF molecular orbitals of the active space and the corresponding electron occupation numbers of the principle configuration of the cyclic 6A1 anionic state are depicted in Figure 2. All five singly occupied orbitals of this sextet state possess a main contribution from chromium, i.e. the 10a1 (3dx2-y2), 11a1 (4s,4p), 4b1 (3dxz), 5b2 (3dyz), and 1a2 (3dxy) orbitals. The remaining 12a1 (4s+3dz2) valence chromium orbital is unoccupied. For the C2 moiety of the cluster, the 8a1 (σ), 9a1 (π), and 3b1 (π) orbitals are doubly occupied and of bonding nature between the two carbon atoms. This opposed to the 6b2 (π*), 2a2 (π*), and 7b2 (σ*) orbitals which are unoccupied and antibonding with respect to the C-C bond. These observations allow us to characterize the ground state of the anionic cluster as a typical transition metal complex consisting of a bonding between a chromium cation in an oxidation state of +1 and a C22- ligand. In the context of the metal-ligand bond, the above mentioned predominantly chromium orbitals are to a certain extent antibonding (4b1 and 12a1), nonbonding (10a1, 11a1, and 1a2), or bonding (5b2). In the latter molecular orbital, electron density is transferred from the metal dyz into the πy* empty orbital of the C22- ligand. Therefore, the cyclic CrC2 cluster illustrates the Dewar–Chatt– Duncanson model as it is frequently encountered in organometallic chemistry. The 5A1 ground 7 ACS Paragon Plus Environment


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state of the neutral cluster can be seen as formed by the removal of an electron from the singly occupied 11a1 (4s,4p) orbital of 6A1. Therefore, the oxidation state of chromium will increase to +2.

The CASSCF molecular orbitals of the principle configuration of the second candidate ground state for the anionic cluster, i.e. the linear 6Σ+ state, are depicted in Figure 3. Similar to the 6A1 of the cyclic isomer, five valence metal orbitals of chromium, namely the 11a1 (3dx2-y2), 12a1 (4s,4p), 4b1 (3dxz), 4b2 (3dyz), and 1a2 (3dxy) orbitals, are singly occupied. The remaining valence orbital 13a1 (4s+3dz2) of chromium is unoccupied. The three doubly occupied orbitals in Figure 3 are the 10a1 (σ), 3b1 (π), and 3b2 (π) C-C bonding orbitals, while the three unoccupied orbitals are the three antibonding C-C orbitals: 14a1 (σ*), 5b1 (π*), and 5b2 (π*). Therefore, the electronic structures of the anionic linear cluster and the anionic cyclic isomer agree to the same oxidation state scheme of Cr+1C2-2. For the neutral linear cluster, the 7Σ+ electronic ground state is obtained by an ionization from the doubly occupied 10a1 ligand orbital of the 6Σ+. Schematically this state corresponds to the following notation: Cr+1C2-1. The 5Π state on the other hand, is formed by detachment of an electron from the singly occupied 4b2 (3dyz) orbital of 6Σ+, and as a result, answers to a different formal charge distribution of Cr+2C2-2. Assignment of the photoelectron spectra of CrC2-. Figure 4 contains the photoelectron spectrum of CrC2-/0 up to 3.1 eV as recorded with photon energies of 355 nm.14, 23 The lower binding energy end of the spectrum exhibits two well-resolved bands. The lowest energy X band displays a sharp maximum at 1.68 eV, which is interpreted as its VDE. The less intense A band possesses more structure and a VDE of 2.08 eV. Additionally, six higher energy bands, labeled B, C, D, and E with vertical detachments energies of 2.36 eV, 2.47 eV, 2.68 eV and 2.89 eV were measured. Besides these bands, two additional bands appear in the experimental spectrum at 3.16 eV (F band) and 3.41 eV (G band), which due to their high energies are difficult to calculate and therefore will not be considered in this study. Furthermore, due to its relative intensity dependence on the source condition, the B band was assumed to originate from a different isomer than the other bands. By using BPW91 ionization 8 ACS Paragon Plus Environment

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energies the B band could indeed be attributed to the CrCC linear isomer, whereas the X and the C bands were ascribed as transitions between the 6A1 anionic cyclic ground state and the neutral cyclic 5A1 ground state and 7A1 excited state.23 An opposing assignment appeared two years later in the literature.21 With the exception of the C and E bands, this TDDFT theoretical study proposed assignments for the bands as exclusively originating from ionization transitions between cyclic structures. It is the purpose of the present contribution to examine closely the existing contradiction. In this respect the RCCSD(T) and CASPT2 vertical detachment energies of Table 2, as calculated at the equilibrium geometries of the cyclic and linear ground states, will prove to be valuable.

As has been argued in the above discussion, the 6A1 state of the cyclic and the 6Σ+ state of linear isomers have more or less the same stability at the B3LYP, BP86, and RCCSD(T) level. Therefore, our assignment for the photoelectron spectra of CrC2- will be based on both these isomers. The lowest band (X band) in the spectra is ascribed to the 6A1→5A1 ionization of the cyclic isomer. The CASPT2 and RCCSD(T) VDEs for this ionization are 1.69 eV and 1.80 eV, respectively, and reproduce quite well the experimental value of 1.68 eV. The A band starting at 2.08 eV is assigned to the 6A1→5B1 transition. The CASPT2 method predicts a VDE of 1.77 eV that is somewhat smaller than the experiment for this ionization, while RCCSD(T) provides a better match of 2.14 eV. This assignment is different from the previous TDDFT B3LYP calculations, which attributed the transition to the 7A1 with a detachment energy of 2.12 eV to the A band, and the transition to the 5B1 with a detachment energy of 2.19 eV to the B band at 2.30 eV.21

The interpretation of the B, C, and D bands in the range of 2.30 eV to 2.68 eV in the experimental spectrum is far more difficult than that of the X and A bands, because the electron binding energies of these three bands are very close. Fortunately, due to the fact that the intensity of the B band depends on the experimental conditions, this band was proposed to originate from the linear CrCC isomer. According to the previous pure BPW91 functional DFT calculations, the 6Σ+→5Π transition was ascribed to the B band starting at 2.30 eV with vertical detachment energy of 2.39 eV.23 In the same work, the vertical detachment energy of the



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transition to the 7Σ+ is calculated to be 2.72 eV, which is 0.33 eV higher than the transition to the 5

Π. The same result is obtained with our BP86 and B3LYP calculations for which the 7Σ+ is

evaluated to be 0.33 eV and 0.17 eV higher than the 5Π. In contrast to DFT, our CASPT2 and RCCSD(T) results in Table 2 show that the 7Σ+ is calculated to be 0.44 eV and 0.21 eV more stable than the 5Π. For this reason, we propose that the B band is the result of the 6Σ+→7Σ+ ionization. The corresponding CASPT2 and RCCSD(T) VDEs are 2.29 eV and 2.62 eV, respectively, which are situated around the experimental value of 2.36 eV. The C band at 2.47 eV in the experimental spectrum is suggested to originate from the 6A1→7A1 transition. Again, compared to this experimental value and the RCCSD(T) ionization energy of 2.69 eV, CASPT2 predicts a much smaller VDE of 2.01 eV. This is the result of two errors that both cause the CASPT2 VDE to be too small. Firstly, as can be seen in Table 2, CASPT2 ionization energies are always calculated smaller than the experimental and RCCSD(T) values due to the insufficient recovery of the dynamical electron correlation energy, which is larger for the ionic ground state when compared to the neutral states (smaller number of electrons). Secondly, for the same reason and because of the Fermi hole, high-spin states are predicted to be more stable than lower spin states by CASPT2. Continuing with the assignment of the spectrum, the D band at 2.68 eV can be the result of either a 6A1→5B2 ionization of the cyclic isomer or the 6Σ+→5Π (5B2) transition of the linear isomer. The VDEs calculated for these two ionizations are 2.39 and 2.73 eV at the CASPT2 and 2.48 and 2.83 eV at the RCCSD(T) level. For the E band our computational results show that it can be attributed to the 6A1→5A2 transition of the cyclic isomer or the 6Σ+→5Σ+ transition of the linear isomer. The VDEs calculated for these two ionizations are 2.74 eV and 2.97 eV at the CASPT2 level and 2.98 eV and 3.04 eV at the RCCSD(T) level, which are in good agreement with the experimental value of 2.89 eV. A graphical overview of the above assignments is given in Figure 4 in which the arrows indicate the RCCSD(T) VDEs. Compared to the previous theoretical studies21,

23

the presently proposed assignments are new except for the X band, which is

unanimously assigned to the 5A1 ground state of the cyclic isomer.


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Franck-Condon simulations. In order to further substantiate the above made assignments, Franck-Condon simulations for the first two bands of the spectrum as measured with 532 nm photons, were carried out. The resulting experimental resolution of the X and A bands, as shown in Figure 5c, revealed that they both are composed of vibrational progressions. The X band is made up of five distinct peaks corresponding to a harmonic vibrational frequency of 510 (20) cm-1. The A band contains four peaks with an energy interspacing of 520 (20) cm-1. Figure 5a and 5b display graphical representations of the calculated Franck-Condon factors for the 6A1→5A1 and

6

A1→5B1

ionizations, respectively. They were derived by using the B3LYP optimized geometries and vibrational frequencies of Table 1, and of course the wave functions of the corresponding normal modes. By comparing the relative intensities of the peaks within the two progressions, it can be concluded that there is a nearly perfect match between theory and experiment for both bands. Also, the vibrational frequencies of 480 cm-1 (X band) and 517cm-1 (A band) of the Cr-(C2) symmetric stretching mode are in good agreement with their experimental values of 510 cm-1 and 520 cm-1, respectively. The occurrence of these progressions can be exclusively ascribed to the substantial decreases of the Cr-C bond distances from 2.084 Å for 6A1 to 1.988 Å for 5A1, and to 1.987 Å for 5B1. Indeed, for these ionizations, the C-C bond remains almost unchanged, i.e. 1.270 Å for 6A1, 1.273 Å for 5A1, and 1.288 Å for 5B1. Overall, it is possible to conclude undoubtedly that the X band of the photoelectron spectra of CrC2- originates from the 6A→5A1 ionization, whereas the A band is the result of the 6A1→5B1 transition.



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Conclusion The geometric and electronic structures of the cyclic and linear CrC2-/0 clusters were investigated by using the BP86 and B3LYP density functional theory methods, and the single reference RCCSD(T) and multireference CASPT2 wave function methods. All computational levels indicate that, for the anionic cluster, the 6A1 of the cyclic isomer and the 6Σ+ of the linear isomer possess a nearly equal stability. For the neutral cluster, the 5A1 of cyclic isomer is predicted to be the ground state. An oxidation state scheme of (Cr+1C2-2) is proposed for both isomeric ground states of the anionic clusters. The oxidation state of chromium in the 5A1 neutral cyclic ground state increases to +2 due to the fact that this state is formed from the 6A1 state by a one-electron detachment out of a 4s,4p hybrid orbital on chromium. Further on, all observed bands of the anion photoelectron spectra could be assigned by using both the cyclic and linear isomeric ground states as the initial states. With exception of the B band all bands studied of the 355 nm spectrum could be ascribed to ionizations from the cyclic 6A1. The B band, for which the relative intensity depends on the experimental conditions, is assigned to the transition between the linear the 6Σ+ and 7Σ+ states. The D and E bands might be due to the 6 +

Σ →5Π and 6Σ+→5Σ+ ionizations. A B3LYP Franck-Condon simulation of the 532 nm spectrum

successfully reproduced the experimental vibrational progressions of the X and A band, confirming these bands as the 6A1→5A1 and 6A1→5B1 transitions. With respect to the existing literature and the exception of the X band, the presently reported findings constitute an entirely new assignment for the other bands of the experimental spectra, which are based on the most elaborate quantum chemical calculations that are preformed on the title complexes up to date.


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References 1. Guo, B. C.; Kerns, K. P.; Castleman, A. W. Ti8C12+-Metallo-Carbohedrenes: a New Class of Molecular Clusters. Science 1992, 255 (5050), 1411-1413. 2. Guo, B. C.; Wei, S.; Purnell, J.; Buzza, S.; Castleman, A. W. Metallo-Carbohedrenes M8C12+ (M = V, Zr, Hf, and Ti): a Class of Stable Molecular Cluster Ions. Science 1992, 256 (5056), 515-516. 3.

Shinohara, H. Endohedral Metallofullerenes. Rep. Prog. Phys. 2000, 63 (6), 843-892.

4. Bethune, D. S.; Johnson, R. D.; Salem, J. R.; Devries, M. S.; Yannoni, C. S. Atoms in Carbon Cages: the Structure and Properties of Endohedral Fullerenes. Nature 1993, 366 (6451), 123-128. 5. Li, S.; Wu, H. B.; Wang, L. S. Probing the Electronic Structure of Metallocarbohedrenes: M8C12 (M=Ti, V, Cr, Zr, Nb). J. Am. Chem. Soc. 1997, 119 (32), 7417-7422. 6. Arbuznikov, A. V.; Hendrickx, M. Quantum Chemical Study of the Geometric and Electronic Structure of the CoC2 Molecule. Chem. Phys. Lett. 2000, 320 (5-6), 575-581. 7. Arbuznikov, A. V.; Hendrickx, M.; Vanquickenborne, L. G. Quantum Chemical Study of the Geometric and Electronic Structure of the FeC2 Molecule. Chem. Phys. Lett. 1999, 310 (5-6), 515-522. 8. Bates, S. A.; Rhodes, J. A.; Rittby, C. M. L.; Graham, W. R. M. Fourier Transform Infrared Observation of the ν1(σ) Mode of Linear CoC3 Trapped in Solid Ar. J. Chem. Phys. 2007, 127 (6), 064506. 9. Bates, S. A.; Rittby, C. M. L.; Graham, W. R. M. Fourier Transform Infrared Isotopic Study of Linear CrC3: Identification of the ν1(σ) Mode. J. Chem. Phys. 2006, 125 (7), 074506. 10. Clemmer, D. E.; Jarrold, M. F. Metal-Containing Carbon Clusters: Structures, Isomerization, and Formation of NbCn+ Clusters. J. Am. Chem. Soc. 1995, 117 (34), 8841-8850. 11. Dai, D. G.; Roszak, S.; Balasubramanian, K. Electronic Structures of Niobium Carbides: NbCn (n = 3-8). J. Phys. Chem. A 2000, 104 (43), 9760-9769. 12. Hendrickx, M. F. A.; Clima, S. Adiabatic Electron Affinities of ScC2 and ScC3 Evaluated by a Multiconfigurational Approach. Chem. Phys. Lett. 2004, 388 (4-6), 284-289. 13. Hendrickx, M. F. A.; Clima, S. An Ab Initio Study of the Equilibrium Structure and Bonding of FeC2 and FeC3 Clusters and Their Anions. Chem. Phys. Lett. 2004, 388 (4-6), 290-296. 14. Li, X.; Wang, L. S. Electronic Structure and Chemical Bonding Between the First Row Transition Metals and C2: A Photoelectron Spectroscopy Study of MC2- (M = Sc, V, Cr, Mn, Fe, and Co). J. Chem. Phys. 1999, 111 (18), 8389-8395. 15. Majumdar, D.; Roszak, S.; Balasubramanian, K. Electronic Structure and Spectroscopic Properties of Electronic States of VC2, VC2-, and VC2+. J. Chem. Phys. 2003, 118 (1), 130-141. 16. Redondo, P.; Barrientos, C.; Largo, A. Small Carbon Clusters Doped with Vanadium Metal: A Density Functional Study of VCn (n = 1-8). J. Chem. Theory Comput. 2006, 2 (3), 885-893. 17. Roszak, S.; Majumdar, D.; Balasubramanian, K. Electronic Structure and Spectroscopic Properties of Electronic States of ScC3 and ScC3-. J. Chem. Phys. 2002, 116 (23), 10238-10246. 18. Sumathi, R.; Hendrickx, N. Quantum Chemical Calculations on the Structure and Electronic Properties of TiC2. Chem. Phys. Lett. 1998, 287 (5-6), 496-502.



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19. Tono, K.; Terasaki, A.; Ohta, T.; Kondow, T. Electronic and Geometric Structures of Co2Cn- and V2Cn : Initial Growth Mechanisms of Late and Early 3d Transition-Metal Carbide Clusters. J. Chem. Phys. 2002, 117 (15), 7010-7016. 20. Wang, L. S.; Li, X. Vibrationally Resolved Photoelectron Spectroscopy of the First Row Transition Metal and C3 Clusters: MC3- (M = Sc, V, Cr, Mn, Fe, Co, and Ni). J. Chem. Phys. 2000, 112 (8), 3602-3608. 21. Yuan, Y. B.; Deng, K. M.; Liu, Y. Z.; Tang, C. M. Assignment of Photoelectron Spectra of MC2 (M= V, Cr, Fe, and Co). Chin. Phys. Lett. 2006, 23 (7), 1761-1764. 22. Zhai, H. J.; Liu, S. R.; Li, X.; Wang, L. S. Photoelectron Spectroscopy of Mono-Niobium Carbide Clusters NbCn- (n = 2-7): Evidence for a Cyclic to Linear Structural Transition. J. Chem. Phys. 2001, 115 (11), 5170-5178. 23. Zhai, H. J.; Wang, L. S.; Jena, P.; Gutsev, G. L.; Bauschlicher, C. W. Competition Between Linear and Cyclic Structures in Monochromium Carbide Clusters CrCn- and CrCn (n = 2-8): A Photoelectron Spectroscopy and Density Functional Study. J. Chem. Phys. 2004, 120 (19), 8996-9008. 24. Rayόn, V. M.; Redondo, P.; Barrientos, C.; Largo, A. Structure and Bonding in First-Row Transition-Metal Dicarbides: Are They Related to the Stability of Met-cars? Chem. Eur. J. 2006, 12 (26), 6963-6975. 25. Rayόn, V. M.; Redondo, P.; Barrientos, C.; Largo, A. Structure and Bonding in First-Row Transition Metal Dicarbide Cations MC2+. J. Phys. Chem. A 2007, 111 (28), 6345-6353. 26. Tran, V. T.; Hendrickx, M. F. A. Description of the Geometric and Electronic Structures Responsible for the Photoelectron Spectrum of FeO4-. J. Chem. Phys. 2011, 135 (9), 094505. 27. Tran, V. T.; Hendrickx, M. F. A. Assignment of the Photoelectron Spectra of FeS3-/0 by Density Functional Theory, CASPT2, and RCCSD(T) Calculations. J. Phys. Chem. A 2011, 115 (47), 13956–13964. 28. Roos, B. O.; Lindh, R.; Malmqvist, P.-Å.; Veryazov, V.; Widmark, P. O. New Relativistic ANO Basis Sets for Transition Metal Atoms. J. Phys. Chem. A 2005, 109 (29), 6575-6579. 29. Roos, B. O.; Lindh, R.; Malmqvist, P.-Å.; Veryazov, V.; Widmark, P. O. Main Group Atoms and Dimers Studied with a New Relativistic ANO Basis Set. J. Phys. Chem. A 2004, 108 (15), 2851-2858. 30. Ishikawa, Y.; Vilkas, M. J. Relativistic Quantum Mechanics of Many-Electron Systems. J. Mol. Struct.-Theochem 2001, 573, 139-169. 31. Reiher, M.; Wolf, A. Exact Decoupling of the Dirac Hamiltonian. II. The Generalized Douglas-KrollHess Transformation up to Arbitrary Order. J. Chem. Phys. 2004, 121 (22), 10945-10956. 32. Reiher, M.; Wolf, A. Exact Decoupling of the Dirac Hamiltonian. I. General Theory. J. Chem. Phys. 2004, 121 (5), 2037-2047. 33. Karlström, G.; Lindh, R.; Malmqvist, P.-Å.; Roos, B. O.; Ryde, U.; Veryazov, V.; Widmark, P. O.; Cossi, M.; Schimmelpfennig, B.; Neogrady, P.; Seijo, L. MOLCAS: a Program Package for Computational Chemistry. Comp. Mater. Sci. 2003, 28 (2), 222-239. 34. Becke, A. D. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys. Rev. A 1988, 38 (6), 3098-3100. 35. Perdew, J. P. Density-Functional Approximation for the Correlation Energy of the Inhomogeneous Electron Gas. Phys. Rev. B 1986, 33 (12), 8822-8824.


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36. Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98 (7), 5648-5652. 37. Lee, C. T.; Yang, W. T.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37 (2), 785-789. 38. Weigend, F.; Ahlrichs, R. Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy. Phys. Chem. Chem. Phys. 2005, 7 (18), 3297-3305. 39. TURBOMOLE V6.3 2011, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989-2007, TURBOMOLE GmbH, since 2007; available from http://www.turbomole.com. 40. All Franck–Condon simulations have been carried out using FC-LabII Version 2009.a, a computational package developed by Schriever, C.; Cockett, M.C.R. and Pugliesi I. The latest information on program updates, a basic introduction to Franck–Condon simulations and a free download of the software can be found at http://www.fclab2.net/. 41. Pugliesi, I.; Müller-Dethlefs, K. The Use of Multidimensional Franck-Condon Simulations to Assess Model Chemistries: A Case Study on Phenol. J. Phys. Chem. A 2006, 110 (14), 4657-4667. 42. Werner, H.-J.; Knowles, P. J.; Manby, F. R.; Schütz, M.; et al. MOLPRO, version 2009.1, a package of ab initio programs, see http://www.molpro.net. 43. Balabanov, N. B.; Peterson, K. A. Systematically Convergent Basis Sets for Transition Metals. I. AllElectron Correlation Consistent Basis Sets for the 3d Elements Sc-Zn. J. Chem. Phys. 2005, 123 (6), 064107. 44. Kendall, R. A.; Dunning, T. H.; Harrison, R. J. Electron Affinities of the First-Row Atoms Revisited Systematic Basis Sets and Wave Functions. J. Chem. Phys. 1992, 96 (9), 6796-6806. 45. Hendrickx, M. F. A.; Tran, V. T. On the Electronic and Geometric Structures of FeO2-/0 and the Assignment of the Anion Photoelectron Spectrum. J. Chem. Theory Comput. 2012, 8 (9), 3089-3096. 46. Tran, V. T.; Hendrickx, M. F. A. A CASPT2 Description of the Electronic Structures of FeO3-/0 in Relevance to the Anion Photoelectron Spectrum. J. Chem. Theory Comput. 2011, 7 (2), 310-319.



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Table 1. Structural parameters, harmonic vibrational frequencies, and adiabatic detachment energies of the low-lying states of CrC2-/0 as calculated at the B3LYP, BP86 and RCCSD(T) levels. (a) RCCSD(T) geometries are optimized with the triple-ζ basis sets, whereas the corresponding adiabatic detachment energies are calculated with the quintuple-ζ basis sets. B3LYP Clusters

BP86 -1

RCCSD(T) -1

States

Cr-C, C-C (Å)

ADE (eV)

Frequencies (cm )

Cr-C, C-C (Å)

ADE (eV)

Frequencies (cm )

4

2.051, 1.268

0.54

235, 473, 1795

2.010, 1.287

0.70

172, 465, 1692

4

2.056, 1.278

0.68

258, 477, 1747

2.008, 1.297

0.87

273, 484, 1642

6

2.084, 1.270

0.00

294, 456, 1781

2.041, 1.286

0.00

5

1.988, 1.273

1.72

364, 480, 1764

1.953, 1.291

5

B1

1.987, 1.288

2.01

348, 517, 1684

CrC2

6 +

1.923, 1.259

-0.08

Linear CrC2

7 +

Cyclic

CrC2

A1 B1 A1

Cyclic CrC2

Linear

A1

Σ Σ

(a)

Cr-C, C-C (Å)

ADE (eV)

335, 470, 1695

2.056, 1.284

0.00

1.78

353, 500, 1669

1.953, 1.292

1.68

1.62 (X)

1.952, 1.307

2.14

381, 536, 1595

1.969, 1.303

2.05

2.01 (A)

153, 488, 1877

1.902, 1.273

-0.10

164, 480, 1790

1.911, 1.276

0.10

1.988, 1.229

2.40

138, 442, 1976

1.947, 1.244

2.69

138, 452, 1889

1.971, 1.245

2.57

5

5

1.894, 1.286

2.23

235i, 151, 452, 1790

1.847, 1.297

2.36

310i, 153, 494, 1717

1.823, 1.298

2.64

5

5

1.894, 1.286

2.23

150, 451, 1790

1.847, 1.297

2.36

153, 494, 1715

1.823, 1.298

2.64

Π ( B1) Π ( B2)

Exp. ADE (eV)

2.30 (B)

2.68 (D)


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Table 2. Vertical detachment energies (VDEs) of CrC2- as calculated at the CASPT2 and RCCSD(T) levels. (a) In the active space, in addition to the 3d,4s orbitals of chromium, and 2p orbitals of carbon, the double-shell effect on chromium is included by adding the 3d’ orbitals for the cyclic isomer, whereas the 2s orbitals of carbon are included for the linear isomer. VDE (eV) Cluster

States

Leading Configuration

CASPT2

(a)

RCCSD(T)

Exp. (eV)

CrC2

6

2 2 1 1 0 2 1 1 1 8a1 9a1 10a1 11a1 12a1 3b1 4b1 5b2 1a2 (92%)

0.00

0.00

Cyclic CrC2

5

2 2 1 0 0 2 1 1 1 8a1 9a1 10a1 11a1 12a1 3b1 4b1 5b2 1a2

(89%)

1.69

1.80

1.68 (X)

5

2 2 1 0 1 2 0 1 1 8a1 9a1 10a1 11a1 12a1 3b1 4b1 5b2 1a2 (82%)

1.77

2.14

2.08 (A)

5

2 2 1 0 1 2 1 0 1 8a1 9a1 10a1 11a1 12a1 3b1 4b1 5b2 1a2 (91%)

2.39

2.48

2.47 (C)

7

1 2 1 1 0 2 1 1 1 8a1 9a1 10a1 11a1 12a1 3b1 4b1 5b2 1a2 (91%)

2.01

2.69

2.68 (D)

5

2 2 1 0 1 2 1 1 0 8a1 9a1 10a1 11a1 12a1 3b1 4b1 5b2 1a2

2.89 (E)

Cyclic

A1 A1 B1 B2 A1 A2

Linear

- 6 + CrC2 Σ

Linear CrC2

2.98

+ 1

4

2

2

(91%)

0.00

0.00

+ 1

+ 1

4

2

2

2.29

2.62

2.36 (B)

+ 2

+ 1

4

1

2

2.73

2.83

2.68 (D)

+ 2

+ 0

4

2

2

2.97

3.04

2.89 (E)

(10σ ) (11σ ) 3π 4π 1δ (82%)

7 +

Σ

5

2.74

+ 2

(10σ ) (11σ ) 3π 4π 1δ (82%) 5

Π ( B2) (10σ ) (11σ ) 3π 4π 1δ (63%)

5 +

Σ

(10σ ) (11σ ) 3π 4π 1δ (90%)



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Figure 1. Coordinate systems used for the C2v structure of cyclic Cr-C2-/0 and the C∞v structure of linear CrCC-/0.


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Figure 2. Pseudo-natural CASSCF molecular orbital plots for the 6A1 state of the cyclic CrC2ordered by symmetry properties in columns and their natural occupation numbers in parentheses. Chromium nucleus positioned at the left hand side of the cluster.



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Figure 3. Pseudo-natural CASSCF molecular orbital plots for the 6Σ+ state of the linear CrCCcluster order by symmetry properties in columns and their natural occupation numbers in parentheses. Chromium nucleus positioned at the left hand side of the cluster.


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Figure 4. Experimental photoelectron spectrum of CrC2- in the range from 1.0 eV to 3.1 eV as measured with 355 nm photon energy23 and the proposed assignments. Arrows represent RCCSD(T) adiabatic detachment energies for the different ionizations.



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Figure 5. Frank-Condon factor simulations for the 6A1→5A1 (a), 6A1→5B1 (b) ionizations and the photoelectron spectrum of CrC2- as recorded with 532 nm photons (c).23 Insets depict the vibrational normal modes that are responsible for the progression.


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