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Theoretical study of the C3Cl radical and its cation
24 December 1999
Chemical Physics Letters 315 Ž1999. 224–232 www.elsevier.nlrlocatercplett
Theoretical study of the C 3 Cl radical and its cation Pilar Redondo, Jose´ R. Redondo, Carmen Barrientos, Antonio Largo
)
Departamento de Quımica Fısica, Facultad de Ciencias, UniÕersidad de Valladolid, 47005 Valladolid, Spain ´ ´ Received 22 June 1999; in final form 17 August 1999
Abstract A theoretical study of C 3 Cl and C 3 Clq isomers has been carried out. The global minimum for C 3 Cl is a cyclic C 2V species Ža three-membered ring with an exocyclic chlorine atom.. However, a quasi-linear CCCCl structure is predicted to lie only 3-5 kcal moly1 higher. This quasi-linear structure is floppy, since the linear arrangement lies only 2-3 kcal moly1 higher in energy. The cyclic and open-chain isomers have dipole moments of 1.986 and 3.363 D, respectively. In C 3 Clq the global minimum is a linear singlet species, the singlet cyclic isomer lying about 19 kcal moly1 higher. The ionization potentials of cyclic and open-chain C 3 Cl are estimated to be 9.17 and 8.21 eV, respectively, suggesting that these species should be easily ionized if present in the interstellar medium. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction The study of carbon clusters containing secondrow elements has received much attention in recent years. One of the main reasons for this interest is the detection in space of some of these compounds, such as CSi, C 2 Si, C 4 Si, CS, C 2 S, C 3 S and CP. So far no carbon-chlorine species has been detected in space. In fact, the only chlorine compound detected in the interstellar medium is HCl w1x, along with several metal chlorides observed in circumstellar shells w2x. However, although quite high, the abundance of HCl has been found to be lower than expected w1x, and photodissociation and reaction with Cq ions have been claimed to be the most important degradation mechanisms for HCl w3x. Both experimental w4–7x and theoretical w8,9x studies on the reaction of Cq
) Corresponding author. Fax: q34-983-423013; e-mail: [email protected]
ions with HCl concluded that this is a feasible process under interstellar conditions, and therefore a possible source of carbon-chlorine compounds, since the reaction product is CClq. Furthermore, there are other possible processes which could also lead to carbon-chlorine compounds. Blake et al. w10x in a general study of the chemistry of chlorine in dense interstellar clouds, suggested that the reaction of carbon atoms with H 2 Clq could also produce the CClq ion. An ab initio study w11x has predicted that, in fact, the major product should be HCClq, which could be a precursor of CCl through dissociative recombination. Another recent theoretical work w12x has shown that the HCCClq cation, a precursor of C 2 Cl, can be synthesized in the reaction of C 2 Hq with HCl. The reaction of Clq with acetylene was also considered in this work but, in that case, charge transfer is thermochemically and kinetically favored over production of HCCClq. Therefore it seems that CCl and C 2 Cl could be good candidates for interstellar detection. Since for
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 0 9 3 6 - 7
P. Redondo et al.r Chemical Physics Letters 315 (1999) 224–232
other second-row elements members of the C n X family have been detected in space up to n s 4, it is also possible that more complex carbon-chlorine compounds could be found in the interstellar medium. This work concerns the C 3 Cl species. In addition to their astrophysical significance, the C n X compounds are interesting on their own, since there is a crucial aspect concerning their molecular structure which is of general relevance. In the case of C 2 S and C 3 S, theoretical studies w13,14x have shown that the ground states are linear. On the other hand, binary silicon-carbon compounds prefer cyclic arrangements. Both experimental and theoretical studies of C 2 Si w15,16x agree in that the ground state is cyclic, whereas a theoretical study w17x on C 3 Si predicts a closed-shell four-membered ring with transannular C-C bonding as the ground state. Phosphorus-carbon binary compounds behave much like their sulfur analogues, since theoretical studies on both C 2 P w18x and C 3 P w19x predict linear ground states. However, the energy differences with the lowest-lying cyclic states is much smaller than in the case of the sulfur compounds. In the case of chlorine, previous studies on C 2 Cl w20,21x have shown that the ground state is linear. In fact, there are two different states, 2 P and 2 Sq, which are close in energy, the 2 P being the predicted ground state. For the related system containing hydrogen, C 3 H, a cyclic isomer corresponding to a 2 B 2 electronic state was found to be the ground state w22,23x, with the linear isomer Ž2 P . lying very close in energy Ž; 2 kcal moly1 .. Since there was no information about C 3 Cl which could help in its detection, the present work provides a theoretical study of C 3 Cl, as well as of the corresponding cation, C 3 Clq, in order to know its behavior upon ionization.
2. Computational methods The geometries of the different C 3 Cl and C 3 Clq isomers have been obtained at several levels of theory. Second-order Møller-Plesset ŽMP2. theory with the 6-31GŽd. and 6-311GŽd. basis sets w24,25x, including all electrons in the calculation, has been employed. The McLean and Chandler basis set w26x,
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supplemented with a set of d-functions, is used for chlorine in the calculations with the 6-311GŽd. basis set. We have also applied the density functional theory ŽDFT., selecting the B3LYP exchange-correlation functional w27x with the 6-311GŽd. basis set and the cc-pVTZ basis set of Dunning w28,29x. We must emphasize that in a previous study on similar . systems w30x ŽSiCq 3 , the B3LYP geometries and frequencies were found to be rather insensitive to the basis set, since both basis sets were shown to provide virtually the same results. In addition, for the lowest-lying isomers of C 3 Cl, we have obtained the optimized geometries employing other methods with the 6-31GŽd. basis set. In particular CASSCFŽ7,6. Žcomplete active space-SCF, where the active space is taken as seven electrons distributed in six orbitals., QCISD Žquadratic CI with singles and doubles. and CCSD Žcoupled-cluster. calculations were carried out. Harmonic vibrational frequencies have been computed on each optimized structure at its corresponding level of theory. These frequencies were employed to estimate the zero-point vibrational energy Ž ZPVE . correction. For this purpose, the MP2Žfull.r6-31GŽd. vibrational frequencies were conveniently scaled w31x. Electronic energies were computed at the fourthorder Møller-Plesset ŽMP4. level, QCISDŽT. level w32x Žquadratic CI with singles and doubles substitutions, followed by a perturbative treatment of triple substitutions. and CCSDŽT. Žcoupled-cluster single and double excitation model augmented with a noniterative triple excitation correction. w33x. Since we are dealing with open-shell systems, their wavefunction can be spin-contaminated, and this may affect the convergency of the MP series. Therefore we will also provide the projected MP4 values which should be more reliable in those cases. To assess the reliability of single-reference-based methods, configuration interaction calculations, CISDr6-31GŽd., were carried out for the different species. In all cases, the leading configuration clearly dominates the expansion, and the coefficient of the second configuration lies in the range 0.034-0.052, strongly suggesting that these species can be treated by single-reference-based methods. All calculations reported in this work were carried out with the GAUSSIAN-94 program package w34x.
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3. Results and discussion 3.1. C3 Cl isomers Three different C 3 Cl isomers have been characterized, corresponding to the structures depicted in Fig. 1. One should expect in principle a linear, or quasilinear, CCCCl arrangement as the most obvious candidate to the ground state, which corresponds to structure 1. Structure 2 is derived from a cyclic C 3 unit with chlorine attached to a carbon atom, whereas structure 3 can be viewed as a C 2 unit bonded to ClC through the chlorine atom. Other possibilities, such as four-membered rings, were searched for, but no stable structures were found. The lowest-lying electronic state for the linear species is 2 P, corresponding to the following electronic configuration
core4 7s 2 8s 2 9s 2 10s 2 2 p 4 11s 2 3p 4 4 p 1
quencies and infrared intensities are not given for the sake of space but are available upon request. It can be readily seen in Table 1 that isomer 1 is predicted to be linear at the MP2 and CASSCF levels, whereas at the QCISD, CCSD and B3LYP levels this species is clearly non-linear. Nevertheless we have also optimized this isomer at these three levels of theory in C`v symmetry and obtained an imaginary frequency, showing that the linear structure is not a true minimum at the QCISD, CCSD and B3LYP levels. The deviation from linearity is mainly reflected in the /C 2 C 3 Cl, whereas the /C 1C 2 C 3 at the QCISD, CCSD and B3LYP levels is still close to 1808. It is also worth noting that the C 2-C 3 bond distance is shorter for the linear arrangement, whereas the C 1-C 2 distance is shorter for the non-linear structure. This can be rationalize in terms of the valence-bond structures which can be depicted for this molecule:
Ž 1.
and therefore is subject to Renner-Teller splitting, giving two different states, 2AX and 2AY in C s symmetry. We have found that this structure is linear at certain levels of theory, whereas other theoretical methods predict that it is non-linear with 2AX electronic state. In Table 1 we show the geometrical parameters for isomer 1 obtained at several levels of theory, whereas the corresponding harmonic vibrational fre-
Fig. 1. Schematic representation of the different C 3 Cl isomers. The geometrical parameters for isomer 3 have been obtained at the MP2Žfull.r6-31GŽd. and B3LYPr6-311GŽd. Žin parentheses. lev˚ and angles in degrees. els. Distances are given in A
The first of this structures is dominant for non-linear arrangements, whereas the second one is the most contributing one for linear geometries. The energy differences between the linear and angular structures at several levels of theory are shown in Table 2. As can be seen only the MP2 level predicts that the linear arrangement is lower in energy, whereas at the MP4 level both structures are virtually iso-energetic. Employment of projected MP4 energies leads to a stability order in agreement with other correlated levels, such as QCISDŽT. or CCSDŽT.. The effect of the extension of the basis set has been analyzed at the B3LYP and QCISDŽT. levels. At the QCISDŽT. level the energy difference is slightly reduced Ž; 1 kcal moly1 . when passing from the 6-311GŽd. basis set to the cc-pVTZ one. Inclusion of diffuse and more polarization functions has also a small effect on B3LYP relative energies, since there is a difference of just 1.4 kcal moly1 between the relative energies with the 6-311GŽd. and 6-311 q GŽ3df. basis sets, whereas passing from a triple-zeta Žcc-pVTZ. to a quadruple-zeta Žcc-pVQZ. basis set reduces the energy difference in just 0.1 kcal moly1 . To summarize, higher-level correlation effects seem to favor the angular form, whereas
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Table 1 ˚ and angles in degrees Geometrical parameters for isomer 1 obtained at different levels of theory. Distances are in A
MP2Žfull.r6-31GŽd. MP2Žfull.r6-311GŽd. CASSCFŽ7,6.r6-31GŽd. QCISDr6-31GŽd. CCSDr6-31GŽd. B3LYPr6-311GŽd. B3LYPrcc-pVTZ
dŽC 1 –C 2 .
dŽC 2 –C 3 .
dŽC 3 –Cl.
/C 1C 2 C 3
/C 2 C 3 Cl
1.348 1.346 1.335 1.319 1.319 1.301 1.297
1.208 1.208 1.237 1.284 1.282 1.283 1.279
1.609 1.605 1.637 1.660 1.659 1.658 1.647
180.0 180.0 180.0 170.2 169.2 171.2 171.2
180.0 180.0 180.0 142.8 126.6 141.2 142.6
extension of the basis set tends to favor the linear arrangement. It is clear that the energy difference is very small for all methods, suggesting a floppy potential surface. Nevertheless it seems that the nonlinear arrangement is preferred, with the linear conformation lying about 2 kcal moly1 above in energy at the most reliable levels of theory. Furthermore, the ZPVE is estimated to be quite similar for both arrangements and therefore should not modify essentially the relative energy. For example, at the B3LYPr6-311GŽd. level both structures can be obtained, and the ZPVE is 6.84 kcal moly1 for the linear structure and 6.79 kcal moly1 for the non-linear one. Another important conclusion from Table 2 is that B3LYP, even with moderate basis sets, performs reasonably well leading to relative energies close to CCSDŽT. ones. Table 2 Energy differences Žin kcal moly1 . between the linear and nonlinear forms of isomer 1 at different levels of theory DE Žlinear– angular. MP2r6-311GŽd.rrB3LYPr6-311GŽd. MP4r6-311GŽd.rrB3LYPr6-311GŽd. PMPr6-311GŽd.rrB3LYPr6-311GŽd. B3LYPr6-311GŽd.rrB3LYPr6-311GŽd. B3LYPr6-311qGŽd.rrB3LYPr6-311GŽd. B3LYPr6-311qGŽ2d.rrB3LYPr6-311GŽd. B3LYPr6-311qGŽ3df.rrB3LYPr6-311GŽd. B3LYPrcc-pVTZrrB3LYPrcc-pVTZ B3LYPrcc-pVQZrrB3LYPrcc-pVTZ QCISDr6-31GŽd.rrQCISDr6-31GŽd. QCISDŽT.r6-311GŽd.rrQCISDr6-31GŽd. QCISDŽT.rcc-pVTZrrQCISDr6-31GŽd. CCSDŽT.rcc-pVTZrrB3YLPr6-311GŽd. CCSDŽT.rcc-pVTZrrCCSDr6-31GŽd.
y1.2 0.0 2.1 3.6 3.5 2.9 2.2 2.9 2.8 3.5 4.0 2.9 2.4 2.5
Concerning the vibrational frequencies we shall only comment the most salient features. In first place, the MP2 and B3LYP vibrational frequencies remain almost unaltered when the basis set changes. That is, MP2r6-31GŽd. and MP2r6-311GŽd. frequencies are nearly coincident, and also B3LYPr6311GŽd. and B3LYPrcc-pVTZ frequencies are virtually the same. This is also true for IR intensities. This behavior, together with the fact that the corresponding MP2 and B3LYP geometries Žsee Table 1. are almost unaffected when passing from one basis set to another, suggests that for systems of this kind MP2r6-31GŽd. and B3LYPr6-311GŽd. levels could be employed for obtaining geometries and vibrational frequencies. It is also interesting to note that there is good agreement between B3LYP and QCISD vibrational frequencies and IR intensities for the non-linear structure, whereas CCSD values are quite different. The most intense line is predicted at all levels of theory to be a C 2-C 3 stretching, which is predicted to be around 1930 cm -1 ŽB3LYP. or 2100 cm -1 ŽQCISD.. In order to provide more information about this species that could be useful for its possible experimental detection, we give other interesting properties. The predicted dipole moment with the 6-311GŽd. basis set is 3.363 D ŽB3LYP. and 3.276 D ŽMP2.. This is a relatively high value that should favor its observation. The rotational constants at the B3LYPr cc-pVTZ level are A s 165.292 GHz, B s 2.878 GHz and C s 2.829 GHz. On the other hand, the single rotational constant at the MP2Žfull.r6-311GŽd. level is B s 2.744 GHz. These values should be taken with caution given the rather floppy potential surface for this species.
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Isomer 2 has a 2 B 2 electronic state with the following electronic configuration
core4 6a21 7a21 8a21 3b 22 9a21 2b12 4b 22 3b12 10a21 5b12
Table 4 Energy differences Žin kcal moly1 . between the C 2v - and C s-symmetric forms of isomer 2 at different levels of theory
Ž 2.
The geometrical parameters at different levels are given in Table 3, whereas the corresponding vibrational frequencies and IR intensities are also available upon request. Both MP2 and B3LYP levels predict a C 2v -symmetric structure for this species. The geometries at both levels of theory are quite similar, and the cyclic C 3 unit is only slightly distorted, since the C 1-C 2 and C 2-C 3 bond distances are quite close and the angles take values near 608. On the other hand, at the CASSCF, QCISD and CCSD levels an imaginary frequency, associated to distortion of the C 3 unit, is obtained. Following this mode a C s structure with different C 1-C 2 and C 1-C 3 bond distances is found. In the C 2v -symmetric structure, the unpaired electron occupies a b 2 orbital which is C 1-C 2 and C 1-C 3 bonding. This molecular orbital is essentially localized on one of these bonds in the C s structure. We will also comment on the vibrational frequencies. MP2 and B3LYP vibrational frequencies and IR intensities are also in good agreement and remain almost unaltered upon extension of the basis set. Nevertheless, at the MP2 level the b 2 mode, corresponding to the bending of the C 3 cycle, has an non-physically large value, suggesting the possibility of symmetry breaking at this level of theory. However, our attempts to optimize this species at the MP2 level in C s symmetry always led to the C 2vsymmetric structure. At the B3LYP level the C 3 bending Ž812 cm -1 . is predicted to be the most intense line in the IR spectrum, although there are two other frequencies, around 1220 and 1650 cm -1 ,
D E ŽC 2v –C s . y2.88 y2.20 y2.24 y0.49 y0.53 y0.65 y0.70 y0.68 y0.82 0.01 y0.20 y0.19
MP2r6-311GŽd. MP4r6-311GŽd. PMP4r6-311GŽd. B3LYPr6-311GŽd. B3LYPr6-311qGŽd. B3LYPr6-311qGŽd. B3LYPr6-311qGŽ3df. B3LYPrcc-pVTZ B3LYPrcc-pVQZ QCISDŽT.r6-311GŽd. QCISDŽT.rcc-pVTZ CCSDŽT.rcc-pVTZ
which should also be rather intense. The predicted dipole moment for this species with the 6-311GŽd. basis set is lower than in the case of isomer 1, namely 1.632 D ŽMP2. or 1.986 D ŽB3LYP.. The energy difference between the C 2v and C s structures of 2 has been analyzed at several levels of theory, and the results are shown in Table 4. As general trends we may conclude that higher level correlation effects seem to slightly favor the C s structure, whereas extension of the basis set has again a minor effect but in any case favors the C 2v structure. The result is a very small energy difference, about 0.2 kcal moly1 at the most reliable level of theory, CCSDŽT.. Therefore it seems that the C 2v structure is preferred, but again a rather floppy surface is found. It is interesting to note the very good agreement between the B3LYP predictions and the CCSDŽT. result. Finally, we will briefly comment the main features of isomer 3, which is expected to be less stable
Table 3 ˚ and angles in degrees Geometrical parameters for isomer 2 obtained at different levels of theory. Distances are in A
MP2Žfull.r6-31GŽd. MP2Žfull.r6-311GŽd. B3LYPr6-311GŽd. B3LYPrcc-pVTZ CASSCFŽ7,6.r6-31GŽd. QCISDr6-31GŽd. CCSDr6-31GŽd.
dŽCl–C 1 .
dŽC 1 –C 2 .
dŽC 1 –C 3 .
dŽC 2 –C 3 .
/ClC 1C 2
1.667 1.661 1.680 1.672 1.675 1.677 1.674
1.370 1.376 1.370 1.367 1.422 1.397 1.398
1.370 1.376 1.370 1.367 1.332 1.353 1.354
1.393 1.395 1.376 1.369 1.392 1.400 1.390
150.6 149.5 150.2 150.0 146.5 147.8 147.5
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than the other two, since the chlorine atom is in a central position. The corresponding geometrical parameters are shown in Fig. 1, whereas the vibrational frequencies and IR intensities are not shown for the sake of space Žexperimental detection of this structure is rather unlikely., but are also available upon request. Both levels, MP2 and B3LYP, give similar geometries, the main discrepancy being the C 1-C 2 distance, which is shorter at the MP2 level and is very close to typical C-C triple-bond distances. Nevertheless, both geometries suggest that this isomer can be viewed as a C 2 unit weakly bonded to ClC, since the C 2-Cl distance is in both cases much longer than typical C-Cl bond distances. The difference between the C 1-C 2 distances computed at the MP2 and B3LYP levels is also reflected in the corresponding C 1-C 2 stretching frequencies, which are found at 2663 and 1870 cm -1 , respectively. However, both levels agree in that this frequency should have the highest intensity in the IR spectrum. The relative energies of the different C 3 Cl isomers at selected levels of theory are shown in Table 5. To assess the reliability of MP values, we provide the S 2 expectation values for the HFr6-311GŽd.
Table 5 Relative energies Žkcal moly1 . of the C 3 Cl isomers at different levels of theory MP2r6-311GŽd. a MP4r6-311GŽd. a PMP4r6-311GŽd. a G1 G2 G1ŽP. G2ŽP. B3LYPr6-311GŽd. b B3LYPr6-311qGŽd. b B3LYPr6-311qGŽ2d. b B3LYPr6-311qGŽ3df. b B3LYPrcc-pVTZ c B3LYPrcc-pVQZ c MP2r6-311GŽd. b MP4r6-311GŽd. b QCISDŽT.r6-311GŽd. b CCSDŽT.rcc-pVTZ b a
1
2
3
23.1 16.9 12.7 9.4 9.8 5.2 5.4 1.4 2.2 2.1 2.4 1.9 2.2 24.4 15.5 2.8 4.8
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
156.2 144.2 145.4 – – – – 135.9 – – – – – 172.5 161.4 131.4
Computed at the MP2Žfull.r6-31GŽd. geometry. Computed at the B3LYPr6-311GŽd. geometry. c Computed at the B3LYPrcc-pVTZ geometry. b
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wavefunction: 0.921 Ž1., 0.775 Ž2., and 1.022 Ž3.. The B3LYPr6-311GŽd. values are also given for comparison: 0.770 Ž1., 0.754 Ž2., and 0.916 Ž3.. The worst case is the higher-lying isomer 3, which has a rather high spin contamination at both levels of theory, whereas usually spin contamination is not a severe problem in most DFT calculations. In all cases, the cyclic isomer is shown to be the most stable one, whereas isomer 3 lies very high in energy as expected. The most interesting values are obviously the energy difference between 1 and 2. It is clear that the MPn relative energies do not change significantly with the geometry, since the MP2 and MP4 values at the MP2 and B3LYP geometries differ in just 1.4 kcal moly1 . Although the cyclic isomer lies always below isomer 1, it seems that inclusion of higher correlated levels reduces the energy gap Žcompare the MP2 and MP4 values.. This energy difference is also smaller when projected MP values are employed, since a reduction of about 4 kcal moly1 is obtained when passing from MP4 to PMP4. On the other hand, extension of the basis set slightly favors the cyclic structure, since the B3LYP relative energy increases from 1.4 to 2.4 kcal moly1 when passing from the 6-311GŽd. basis set to the 6-311 q GŽ3df.. The same effect is observed when Dunning’s ccpVTZ or cc-pVQZ basis sets are employed. At the B3LYP level a very small energy difference is found Ž2.2 kcal moly1 .. However, the most reliable levels of theory are perhaps QCISDŽT. and CCSDŽT. Žfor the latter we employed a larger basis set, namely cc-pVTZ., and both levels agree in that the cyclic isomer is lower in energy, with an energy difference around 3-5 kcal moly1 . We should mention that the ZPVE values are quite close for both isomers Ž6.79 kcal moly1 for 1 and 7.20 kcal moly1 for 2, at the B3LYPr6-311GŽd. level., and therefore inclusion of ZPVE should not change the main conclusion that a cyclic ground state is predicted for C 3 Cl. In addition, we have also applied the G1 and G2 methods w35x, obtaining an energy difference around 9-10 kcal moly1 . This relative energy is reduced to a value near 5 kcal moly1 when projected MPn values are employed to compute the different contributions to the G1 and G2 energies. The values obtained using projected MP energies are denoted G1ŽP. and G2ŽP. in Table 5. These values are in excellent agreement with the CCSDŽT. result, thus supporting the conclu-
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sion that the global minimum of C 3 Cl should be a cyclic structure. In the case of the C 3 H system w22,23x, we have already mentioned that a cyclic C 3 H isomer was found to be the ground state, and the linear isomer Ž2 P . lies very close in energy Ž; 2 kcal moly1 .. The linear isomer was also shown to be rather floppy, since it was found to be nearly iso-energetic with a bent structure. Therefore C 3 Cl seems to be more related to C 3 H than to other systems containing second-row atoms, such as C 3 Si, C 3 S or C 3 P. 3.2. C3 Cl q isomers Based on the results for C 3 Cl, only MP2r631GŽd. and B3LYPr6-311GŽd. methods will be employed for obtaining geometries and vibrational frequencies, whereas relative energies will be computed at the MP4, B3LYP and QCISDŽT. levels. We have found three different C 3 Clq isomers. Isomer 1 is a linear structure, although in the triplet surface is bent with a 3AX electronic state. Isomer 2 has a C 3 cyclic unit and has a 3 B 2 electronic state on the triplet surface. Finally, another cyclic structure with an exocyclic carbon atom, was found only on the singlet surface. The optimized geometries are shown in Fig. 2, whereas the corresponding vibrational frequencies and IR intensities are available upon request. We will briefly comment only the most salient features about these species. The electronic configuration for 1 Ž1 S . is derived from that of linear C 3 Cl, upon removal of the electron occupying the 4 p molecular orbital. The dominant valence-bond structures for the linear singlet species are the following
This explains why the C 2-C 3 bond distance is much shorter than the C 1-C 2 one. The 1 Ž1 S . species is found the be a true minimum at all levels of theory although a very small bending frequency is found at both MP2 Ž139 cm -1 . and B3LYP Ž113 cm -1 . levels. The most intense line in the IR spectrum is predicted to be a C-C stretching nearly 2200 cm -1 . The predicted dipole moment Žtaking the center of mass as
Fig. 2. MP2Žfull.r6-31GŽd. and B3LYPr6-311GŽd. Žin parentheses. optimized geometries for the different C 3 Clq isomers. Dis˚ and angles in degrees. tances are given in A
the origin. for this species is very low, namely about 0.323 D with the 6-311GŽd. basis set. The triplet state is obtained from the singlet upon 3p 4 p excitation. However the resulting structure is bent with a 3AX electronic state, since the linear triplet structure has an imaginary frequency. The main difference with the singlet linear state is the shorter C 1-C 2 distance, and also the much larger dipole moment, namely 2.483 D. The triplet state is also rather floppy, since it has a very low bending frequency at both MP2 and B3LYP levels. As for the singlet state the most intense line in the IR spectrum is predicted to be the C-C stretching near 1900 cm -1 . The singlet cyclic species, 2 Ž1A 1 ., has much shorter Cl-C 1 and C 2-C 3 bond distances than the neutral cyclic isomer, and its dipole moment is predicted to be nearly 1.255 D. This structure is shown to be a true minimum at the MP2 level, but it has an imaginary frequency at the B3LYP level. This is a bending frequency Žb 2 symmetry. whose associated mode corresponds to the loss of C 2v symmetry. We made optimizations of the geometry at the B3LYP
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P. Redondo et al.r Chemical Physics Letters 315 (1999) 224–232
level following this mode Žin C S symmetry., and in all cases the C 3 cycle was broken and finally the linear singlet species 1 Ž1 S . was reached. On the other hand, the triplet species, 2 Ž3 B 2 ., is a true minimum at both MP2 and B3LYP levels with very similar vibrational frequencies in both cases. The geometrical parameters of the triplet cyclic species are closer to those of the neutral cyclic isomer. The dipole moment is quite high, 3.063 D, and there are two C-C stretching frequencies around 1300 and 1600 cm -1 , respectively, which are predicted to dominate the IR spectrum. The last C 3 Clq species is also cyclic, but with an exocyclic carbon atom and a C 2 Cl cyclic unit. In fact this structure can be viewed as the result of the interaction of a chlorine atom with a C-C bond of linear Cq 3 . Although one of the C-Cl bond distances is longer than typical C-Cl bond distances, it is clear that there is a certain interaction between both atoms. This species is a true minimum at both MP2 and B3LYP levels, even though it is expected to be rather unstable. The relative energies of the different C 3 Clq species are shown in Table 6. S 2 expectation values for triplet states at the HFr6-311GŽd. and B3LYP levels Žin parentheses. are as follows: 1 Ž3AX ., 2.561 Ž2.068.; 2 Ž3 B 2 ., 2.068 Ž2.007.. As can be seen the MPn results are virtually unaffected by the geometry, since they are quite similar when computed at the MP2 geometry or at the B3LYP one. All levels of theory agree in that the linear and cyclic isomers have singlet ground states, the lowest-lying triplet being the cyclic 3 B 2 species. The global minimum is Table 6 Relative energies Žkcal moly1 . of the C 3 Clq isomers at different levels of theory X
X
1 Ž1 S . 1 Ž3A . 2 Ž1A 1 . 2 Ž3 B 2 . 3 Ž1A . .a
MP2Žfull.r6-31GŽd MP2r6-311GŽd. a MP4r6-311GŽd. a PMP4r6-311GŽd. a B3LYPr6-311GŽd. b MP2r6-311GŽd. b MP4r6-311GŽd. b QCISDŽT.r6-311GŽd. b a b
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
54.8 55.8 58.6 49.3 38.0 55.7 57.7 41.2
17.8 17.9 23.6 23.6 23.1 16.9 22.4 19.2
32.2 33.8 40.0 38.8 32.8 33.4 39.4 32.3
Computed at the MP2Žfull.r6-31GŽd. geometry. Computed at the B3LYPr6-311GŽd. geometry.
94.2 93.4 87.3 87.3 82.5 93.0 86.3 77.7
231
the singlet linear structure, with the singlet cyclic 2 Ž1A 1 . species lying about 17-23 kcal moly1 , depending on the level of theory. It seems that inclusion of higher correlated effects tends to increase the energy difference, since it is greater at the MP4 level than at the MP2 one. As expected the less stable C 3 Clq species is isomer 3. Once we know the energetics of the C 3 Clq species, we may estimate the Žadiabatic. ionization potential of the C 3 Cl radical. In the case of cyclic C 3 Cl, we obtain a value of 9.17 eV at the QCISDŽT.r6-311GŽd. level. For the quasi-linear isomer Ž1., the IP is estimated to be much lower, 8.21 eV at the same level of theory. In both cases the IPs have been computed for the production of the corresponding cyclic or linear singlet C 3 Clq and both were found to be much lower than the IP of hydrogen Ž13.6 eV.. Therefore it is expected that if C 3 Cl is present in the interstellar medium it could be easily ionized. In fact, these values are much lower than the IPs of chlorine Ž13.00 eV. and carbon Ž11.27 eV..
4. Conclusions A theoretical study of the C 3 Cl isomers has been carried out. Predictions for their geometries and vibrational frequencies have been made at both MP2 and B3LYP levels. The main conclusion is that there are two isomers which are close in energy. All theoretical levels predict that the global minimum is a cyclic C 2V species Ža three-membered ring with an exocyclic chlorine atom.. However, a quasi-linear CCCCl structure is predicted to lie only about 3-5 kcal moly1 above the former at the most reliable levels of theory. This quasi-linear structure has been found to be rather floppy Žthe linear arrangement is found to be only about 2-3 kcal moly1 higher in energy.. Both isomers, cyclic and open-chain, have relatively high dipole moments, namely 1.986 and 3.363 D, respectively. We have also studied the C 3 Clq cation. In this case, the global minimum is predicted to be a linear singlet species, whereas the singlet cyclic isomer lies about 19 kcal moly1 higher in energy. The ionization potentials of cyclic and open-chain C 3 Cl are
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estimated to be 9.17 and 8.21 eV, respectively. These values suggest that these species should be easily ionized if present in interstellar medium. From our calculations on this kind of system, we have seen that the geometries and vibrational frequencies obtained at the MP2Žfull.r6-31GŽd. and B3LYPr6-311GŽd. levels are not severely altered upon extension of the basis set. In addition, the QCISDŽT. method seems a reasonable and less expensive alternative to CCSDŽT. for these systems, since both lead to very close relative energies. The B3LYP results, even with moderate basis sets, are also in rather good agreement with the CCSDŽT. values. Acknowledgements This research has been supported by the Ministerio de Educacion ´ y Cultura of Spain ŽDGICYT, Grant PB97-0399-C03-01. and by the Junta de Castilla y Leon ´ ŽGrant VA 21r97.. References w1x G.A. Blake, J. Keene, T.G. Phillips, Astrophys. J. 285 Ž1985. 501. w2x J. Cernicharo, M. Guelin, Astron. Astrophys. 183 Ž1987. L10. w3x E.F. Van Dishoeck, M.C. van Hemert, A. Dalgarno, J. Chem. Phys. 77 Ž1982. 3693. w4x V.G. Anicich, W.T. Huntress, J. Futrell, Chem. Phys. Lett. 40 Ž1976. 233. w5x V.G. Anicich, W.T. Huntress, Astrophys. J. Suppl. 62 Ž1986. 553. w6x C. Rebrion, J.B. Marquette, B.R. Rowe, D.C. Clary, Chem. Phys. Lett. 143 Ž1988. 130. w7x D.M. Sonnenfroh, J.M. Farrar, Astrophys. J. 335 Ž1988. 491. w8x C.E. Dateo, D.C. Clary, J. Chem. Phys. 90 Ž1989. 7216. w9x C. Barrientos, A. Largo, P. Redondo, F. Pauzat, Y. Ellinger, J. Phys. Chem. 97 Ž1993. 173. w10x G.A. Blake, V.G. Anicich, W.T. Huntress, Astrophys. J. 300 Ž1986. 415. w11x V.M. Rayon, C. Barrientos, A. Largo, J. Mol. Struct. ŽTHEOCHEM. 363 Ž1996. 319.
w12x V.M. Rayon, C. Barrientos, A. Largo, J. Mol. Struct. ŽTHEOCHEM. 432 Ž1998. 75. w13x D.J. Peeso, D.W. Fuing, T.T. Curtis, Chem. Phys. Lett. 166 Ž1990. 307. w14x Y. Xie, H.F. Schaefer, J. Chem. Phys. 96 Ž1992. 3714. w15x D.L. Michalopoulos, M.E. Geusic, P.R.R. Langridge-Smith, R.E. Smalley, J. Chem. Phys. 80 Ž1984. 3556. w16x R.S. Grev, H.F. Schaefer, J. Chem. Phys. 80 Ž1984. 3552. w17x I.L. Alberts, R.S. Grev, H.F. Schaefer, J. Chem. Phys. 93 Ž1990. 5046. w18x A. Largo, C. Barrientos, X. Lopez, J.M. Ugalde, J. Phys. Chem. 98 Ž1994. 3985. w19x E. del Rıo, ´ C. Barrientos, A. Largo, J. Phys. Chem. 100 Ž1996. 585. w20x A. Largo-Cabrerizo, C. Barrientos, Chem. Phys, Lett. 155 Ž1989. 550. w21x A. Largo, C. Barrientos, Chem. Phys. 138 Ž1989. 291. w22x J.F. Stanton, Chem. Phys. Lett. 237 Ž1995. 20. w23x R.I. Kaiser, C. Ochsenfeld, M. Head-Gordon, Y.T. Lee, A.G. Saito, Science 274 Ž1996. 1508. w24x M.M. Francl, W.J. Pietro, W.J. Hehre, J.S. Binkley, M.S. Gordon, D.J. DeFrees, J.A. Pople, J. Chem. Phys. 77 Ž1982. 3654. w25x R. Krishnan, J.S. Binkley, R. Seeger, J.A. Pople, J. Chem. Phys. 72 Ž1980. 650. w26x A.D. McLean, G.S. Chandler, J. Chem. Phys. 72 Ž1980. 5639. w27x P.J. Stephens, F.J. Devlin, C.F. Chablowski, M.J. Frisch, J. Phys. Chem. 98 Ž1994. 11623. w28x T.H. Dunning, J. Chem. Phys. 90 Ž1989. 1007. w29x D.E. Woon, T.H. Dunning, J. Chem. Phys. 98 Ž1993. 1358. w30x P. Redondo, A. Saguillo, A. Largo, J. Phys. Chem. 102 Ž1998. 3953. w31x D.J. DeFrees, A.D. McLean, J. Chem. Phys. 82 Ž1985. 333. w32x J.A. Pople, M. Head-Gordon, K. Raghavachari, J. Chem. Phys. 87 Ž1987. 5968. w33x K. Raghavachari, G.W. Trucks, J.A. Pople, M. Head-Gordon, Chem. Phys. Lett. 157 Ž1989. 479. w34x M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.J. Johnson, M.A. Robb, J.R. Cheeseman, T.A. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. AlLaham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. DeFrees, J. Baker, J.P. Stewart, M. HeadGordon, C. Gonzalez, J.A. Pople, GAUSSIAN 94, Gaussian, Pittsburgh, PA, 1995. w35x L.A. Curtiss, K. Raghavachari, G.W. Trucks, J.A. Pople, J. Chem. Phys. 94 Ž1991. 7221.
Chemical Physics Letters 315 Ž1999. 224–232 www.elsevier.nlrlocatercplett
Theoretical study of the C 3 Cl radical and its cation Pilar Redondo, Jose´ R. Redondo, Carmen Barrientos, Antonio Largo
)
Departamento de Quımica Fısica, Facultad de Ciencias, UniÕersidad de Valladolid, 47005 Valladolid, Spain ´ ´ Received 22 June 1999; in final form 17 August 1999
Abstract A theoretical study of C 3 Cl and C 3 Clq isomers has been carried out. The global minimum for C 3 Cl is a cyclic C 2V species Ža three-membered ring with an exocyclic chlorine atom.. However, a quasi-linear CCCCl structure is predicted to lie only 3-5 kcal moly1 higher. This quasi-linear structure is floppy, since the linear arrangement lies only 2-3 kcal moly1 higher in energy. The cyclic and open-chain isomers have dipole moments of 1.986 and 3.363 D, respectively. In C 3 Clq the global minimum is a linear singlet species, the singlet cyclic isomer lying about 19 kcal moly1 higher. The ionization potentials of cyclic and open-chain C 3 Cl are estimated to be 9.17 and 8.21 eV, respectively, suggesting that these species should be easily ionized if present in the interstellar medium. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction The study of carbon clusters containing secondrow elements has received much attention in recent years. One of the main reasons for this interest is the detection in space of some of these compounds, such as CSi, C 2 Si, C 4 Si, CS, C 2 S, C 3 S and CP. So far no carbon-chlorine species has been detected in space. In fact, the only chlorine compound detected in the interstellar medium is HCl w1x, along with several metal chlorides observed in circumstellar shells w2x. However, although quite high, the abundance of HCl has been found to be lower than expected w1x, and photodissociation and reaction with Cq ions have been claimed to be the most important degradation mechanisms for HCl w3x. Both experimental w4–7x and theoretical w8,9x studies on the reaction of Cq
) Corresponding author. Fax: q34-983-423013; e-mail: [email protected]
ions with HCl concluded that this is a feasible process under interstellar conditions, and therefore a possible source of carbon-chlorine compounds, since the reaction product is CClq. Furthermore, there are other possible processes which could also lead to carbon-chlorine compounds. Blake et al. w10x in a general study of the chemistry of chlorine in dense interstellar clouds, suggested that the reaction of carbon atoms with H 2 Clq could also produce the CClq ion. An ab initio study w11x has predicted that, in fact, the major product should be HCClq, which could be a precursor of CCl through dissociative recombination. Another recent theoretical work w12x has shown that the HCCClq cation, a precursor of C 2 Cl, can be synthesized in the reaction of C 2 Hq with HCl. The reaction of Clq with acetylene was also considered in this work but, in that case, charge transfer is thermochemically and kinetically favored over production of HCCClq. Therefore it seems that CCl and C 2 Cl could be good candidates for interstellar detection. Since for
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 0 9 3 6 - 7
P. Redondo et al.r Chemical Physics Letters 315 (1999) 224–232
other second-row elements members of the C n X family have been detected in space up to n s 4, it is also possible that more complex carbon-chlorine compounds could be found in the interstellar medium. This work concerns the C 3 Cl species. In addition to their astrophysical significance, the C n X compounds are interesting on their own, since there is a crucial aspect concerning their molecular structure which is of general relevance. In the case of C 2 S and C 3 S, theoretical studies w13,14x have shown that the ground states are linear. On the other hand, binary silicon-carbon compounds prefer cyclic arrangements. Both experimental and theoretical studies of C 2 Si w15,16x agree in that the ground state is cyclic, whereas a theoretical study w17x on C 3 Si predicts a closed-shell four-membered ring with transannular C-C bonding as the ground state. Phosphorus-carbon binary compounds behave much like their sulfur analogues, since theoretical studies on both C 2 P w18x and C 3 P w19x predict linear ground states. However, the energy differences with the lowest-lying cyclic states is much smaller than in the case of the sulfur compounds. In the case of chlorine, previous studies on C 2 Cl w20,21x have shown that the ground state is linear. In fact, there are two different states, 2 P and 2 Sq, which are close in energy, the 2 P being the predicted ground state. For the related system containing hydrogen, C 3 H, a cyclic isomer corresponding to a 2 B 2 electronic state was found to be the ground state w22,23x, with the linear isomer Ž2 P . lying very close in energy Ž; 2 kcal moly1 .. Since there was no information about C 3 Cl which could help in its detection, the present work provides a theoretical study of C 3 Cl, as well as of the corresponding cation, C 3 Clq, in order to know its behavior upon ionization.
2. Computational methods The geometries of the different C 3 Cl and C 3 Clq isomers have been obtained at several levels of theory. Second-order Møller-Plesset ŽMP2. theory with the 6-31GŽd. and 6-311GŽd. basis sets w24,25x, including all electrons in the calculation, has been employed. The McLean and Chandler basis set w26x,
225
supplemented with a set of d-functions, is used for chlorine in the calculations with the 6-311GŽd. basis set. We have also applied the density functional theory ŽDFT., selecting the B3LYP exchange-correlation functional w27x with the 6-311GŽd. basis set and the cc-pVTZ basis set of Dunning w28,29x. We must emphasize that in a previous study on similar . systems w30x ŽSiCq 3 , the B3LYP geometries and frequencies were found to be rather insensitive to the basis set, since both basis sets were shown to provide virtually the same results. In addition, for the lowest-lying isomers of C 3 Cl, we have obtained the optimized geometries employing other methods with the 6-31GŽd. basis set. In particular CASSCFŽ7,6. Žcomplete active space-SCF, where the active space is taken as seven electrons distributed in six orbitals., QCISD Žquadratic CI with singles and doubles. and CCSD Žcoupled-cluster. calculations were carried out. Harmonic vibrational frequencies have been computed on each optimized structure at its corresponding level of theory. These frequencies were employed to estimate the zero-point vibrational energy Ž ZPVE . correction. For this purpose, the MP2Žfull.r6-31GŽd. vibrational frequencies were conveniently scaled w31x. Electronic energies were computed at the fourthorder Møller-Plesset ŽMP4. level, QCISDŽT. level w32x Žquadratic CI with singles and doubles substitutions, followed by a perturbative treatment of triple substitutions. and CCSDŽT. Žcoupled-cluster single and double excitation model augmented with a noniterative triple excitation correction. w33x. Since we are dealing with open-shell systems, their wavefunction can be spin-contaminated, and this may affect the convergency of the MP series. Therefore we will also provide the projected MP4 values which should be more reliable in those cases. To assess the reliability of single-reference-based methods, configuration interaction calculations, CISDr6-31GŽd., were carried out for the different species. In all cases, the leading configuration clearly dominates the expansion, and the coefficient of the second configuration lies in the range 0.034-0.052, strongly suggesting that these species can be treated by single-reference-based methods. All calculations reported in this work were carried out with the GAUSSIAN-94 program package w34x.
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3. Results and discussion 3.1. C3 Cl isomers Three different C 3 Cl isomers have been characterized, corresponding to the structures depicted in Fig. 1. One should expect in principle a linear, or quasilinear, CCCCl arrangement as the most obvious candidate to the ground state, which corresponds to structure 1. Structure 2 is derived from a cyclic C 3 unit with chlorine attached to a carbon atom, whereas structure 3 can be viewed as a C 2 unit bonded to ClC through the chlorine atom. Other possibilities, such as four-membered rings, were searched for, but no stable structures were found. The lowest-lying electronic state for the linear species is 2 P, corresponding to the following electronic configuration
core4 7s 2 8s 2 9s 2 10s 2 2 p 4 11s 2 3p 4 4 p 1
quencies and infrared intensities are not given for the sake of space but are available upon request. It can be readily seen in Table 1 that isomer 1 is predicted to be linear at the MP2 and CASSCF levels, whereas at the QCISD, CCSD and B3LYP levels this species is clearly non-linear. Nevertheless we have also optimized this isomer at these three levels of theory in C`v symmetry and obtained an imaginary frequency, showing that the linear structure is not a true minimum at the QCISD, CCSD and B3LYP levels. The deviation from linearity is mainly reflected in the /C 2 C 3 Cl, whereas the /C 1C 2 C 3 at the QCISD, CCSD and B3LYP levels is still close to 1808. It is also worth noting that the C 2-C 3 bond distance is shorter for the linear arrangement, whereas the C 1-C 2 distance is shorter for the non-linear structure. This can be rationalize in terms of the valence-bond structures which can be depicted for this molecule:
Ž 1.
and therefore is subject to Renner-Teller splitting, giving two different states, 2AX and 2AY in C s symmetry. We have found that this structure is linear at certain levels of theory, whereas other theoretical methods predict that it is non-linear with 2AX electronic state. In Table 1 we show the geometrical parameters for isomer 1 obtained at several levels of theory, whereas the corresponding harmonic vibrational fre-
Fig. 1. Schematic representation of the different C 3 Cl isomers. The geometrical parameters for isomer 3 have been obtained at the MP2Žfull.r6-31GŽd. and B3LYPr6-311GŽd. Žin parentheses. lev˚ and angles in degrees. els. Distances are given in A
The first of this structures is dominant for non-linear arrangements, whereas the second one is the most contributing one for linear geometries. The energy differences between the linear and angular structures at several levels of theory are shown in Table 2. As can be seen only the MP2 level predicts that the linear arrangement is lower in energy, whereas at the MP4 level both structures are virtually iso-energetic. Employment of projected MP4 energies leads to a stability order in agreement with other correlated levels, such as QCISDŽT. or CCSDŽT.. The effect of the extension of the basis set has been analyzed at the B3LYP and QCISDŽT. levels. At the QCISDŽT. level the energy difference is slightly reduced Ž; 1 kcal moly1 . when passing from the 6-311GŽd. basis set to the cc-pVTZ one. Inclusion of diffuse and more polarization functions has also a small effect on B3LYP relative energies, since there is a difference of just 1.4 kcal moly1 between the relative energies with the 6-311GŽd. and 6-311 q GŽ3df. basis sets, whereas passing from a triple-zeta Žcc-pVTZ. to a quadruple-zeta Žcc-pVQZ. basis set reduces the energy difference in just 0.1 kcal moly1 . To summarize, higher-level correlation effects seem to favor the angular form, whereas
P. Redondo et al.r Chemical Physics Letters 315 (1999) 224–232
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Table 1 ˚ and angles in degrees Geometrical parameters for isomer 1 obtained at different levels of theory. Distances are in A
MP2Žfull.r6-31GŽd. MP2Žfull.r6-311GŽd. CASSCFŽ7,6.r6-31GŽd. QCISDr6-31GŽd. CCSDr6-31GŽd. B3LYPr6-311GŽd. B3LYPrcc-pVTZ
dŽC 1 –C 2 .
dŽC 2 –C 3 .
dŽC 3 –Cl.
/C 1C 2 C 3
/C 2 C 3 Cl
1.348 1.346 1.335 1.319 1.319 1.301 1.297
1.208 1.208 1.237 1.284 1.282 1.283 1.279
1.609 1.605 1.637 1.660 1.659 1.658 1.647
180.0 180.0 180.0 170.2 169.2 171.2 171.2
180.0 180.0 180.0 142.8 126.6 141.2 142.6
extension of the basis set tends to favor the linear arrangement. It is clear that the energy difference is very small for all methods, suggesting a floppy potential surface. Nevertheless it seems that the nonlinear arrangement is preferred, with the linear conformation lying about 2 kcal moly1 above in energy at the most reliable levels of theory. Furthermore, the ZPVE is estimated to be quite similar for both arrangements and therefore should not modify essentially the relative energy. For example, at the B3LYPr6-311GŽd. level both structures can be obtained, and the ZPVE is 6.84 kcal moly1 for the linear structure and 6.79 kcal moly1 for the non-linear one. Another important conclusion from Table 2 is that B3LYP, even with moderate basis sets, performs reasonably well leading to relative energies close to CCSDŽT. ones. Table 2 Energy differences Žin kcal moly1 . between the linear and nonlinear forms of isomer 1 at different levels of theory DE Žlinear– angular. MP2r6-311GŽd.rrB3LYPr6-311GŽd. MP4r6-311GŽd.rrB3LYPr6-311GŽd. PMPr6-311GŽd.rrB3LYPr6-311GŽd. B3LYPr6-311GŽd.rrB3LYPr6-311GŽd. B3LYPr6-311qGŽd.rrB3LYPr6-311GŽd. B3LYPr6-311qGŽ2d.rrB3LYPr6-311GŽd. B3LYPr6-311qGŽ3df.rrB3LYPr6-311GŽd. B3LYPrcc-pVTZrrB3LYPrcc-pVTZ B3LYPrcc-pVQZrrB3LYPrcc-pVTZ QCISDr6-31GŽd.rrQCISDr6-31GŽd. QCISDŽT.r6-311GŽd.rrQCISDr6-31GŽd. QCISDŽT.rcc-pVTZrrQCISDr6-31GŽd. CCSDŽT.rcc-pVTZrrB3YLPr6-311GŽd. CCSDŽT.rcc-pVTZrrCCSDr6-31GŽd.
y1.2 0.0 2.1 3.6 3.5 2.9 2.2 2.9 2.8 3.5 4.0 2.9 2.4 2.5
Concerning the vibrational frequencies we shall only comment the most salient features. In first place, the MP2 and B3LYP vibrational frequencies remain almost unaltered when the basis set changes. That is, MP2r6-31GŽd. and MP2r6-311GŽd. frequencies are nearly coincident, and also B3LYPr6311GŽd. and B3LYPrcc-pVTZ frequencies are virtually the same. This is also true for IR intensities. This behavior, together with the fact that the corresponding MP2 and B3LYP geometries Žsee Table 1. are almost unaffected when passing from one basis set to another, suggests that for systems of this kind MP2r6-31GŽd. and B3LYPr6-311GŽd. levels could be employed for obtaining geometries and vibrational frequencies. It is also interesting to note that there is good agreement between B3LYP and QCISD vibrational frequencies and IR intensities for the non-linear structure, whereas CCSD values are quite different. The most intense line is predicted at all levels of theory to be a C 2-C 3 stretching, which is predicted to be around 1930 cm -1 ŽB3LYP. or 2100 cm -1 ŽQCISD.. In order to provide more information about this species that could be useful for its possible experimental detection, we give other interesting properties. The predicted dipole moment with the 6-311GŽd. basis set is 3.363 D ŽB3LYP. and 3.276 D ŽMP2.. This is a relatively high value that should favor its observation. The rotational constants at the B3LYPr cc-pVTZ level are A s 165.292 GHz, B s 2.878 GHz and C s 2.829 GHz. On the other hand, the single rotational constant at the MP2Žfull.r6-311GŽd. level is B s 2.744 GHz. These values should be taken with caution given the rather floppy potential surface for this species.
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Isomer 2 has a 2 B 2 electronic state with the following electronic configuration
core4 6a21 7a21 8a21 3b 22 9a21 2b12 4b 22 3b12 10a21 5b12
Table 4 Energy differences Žin kcal moly1 . between the C 2v - and C s-symmetric forms of isomer 2 at different levels of theory
Ž 2.
The geometrical parameters at different levels are given in Table 3, whereas the corresponding vibrational frequencies and IR intensities are also available upon request. Both MP2 and B3LYP levels predict a C 2v -symmetric structure for this species. The geometries at both levels of theory are quite similar, and the cyclic C 3 unit is only slightly distorted, since the C 1-C 2 and C 2-C 3 bond distances are quite close and the angles take values near 608. On the other hand, at the CASSCF, QCISD and CCSD levels an imaginary frequency, associated to distortion of the C 3 unit, is obtained. Following this mode a C s structure with different C 1-C 2 and C 1-C 3 bond distances is found. In the C 2v -symmetric structure, the unpaired electron occupies a b 2 orbital which is C 1-C 2 and C 1-C 3 bonding. This molecular orbital is essentially localized on one of these bonds in the C s structure. We will also comment on the vibrational frequencies. MP2 and B3LYP vibrational frequencies and IR intensities are also in good agreement and remain almost unaltered upon extension of the basis set. Nevertheless, at the MP2 level the b 2 mode, corresponding to the bending of the C 3 cycle, has an non-physically large value, suggesting the possibility of symmetry breaking at this level of theory. However, our attempts to optimize this species at the MP2 level in C s symmetry always led to the C 2vsymmetric structure. At the B3LYP level the C 3 bending Ž812 cm -1 . is predicted to be the most intense line in the IR spectrum, although there are two other frequencies, around 1220 and 1650 cm -1 ,
D E ŽC 2v –C s . y2.88 y2.20 y2.24 y0.49 y0.53 y0.65 y0.70 y0.68 y0.82 0.01 y0.20 y0.19
MP2r6-311GŽd. MP4r6-311GŽd. PMP4r6-311GŽd. B3LYPr6-311GŽd. B3LYPr6-311qGŽd. B3LYPr6-311qGŽd. B3LYPr6-311qGŽ3df. B3LYPrcc-pVTZ B3LYPrcc-pVQZ QCISDŽT.r6-311GŽd. QCISDŽT.rcc-pVTZ CCSDŽT.rcc-pVTZ
which should also be rather intense. The predicted dipole moment for this species with the 6-311GŽd. basis set is lower than in the case of isomer 1, namely 1.632 D ŽMP2. or 1.986 D ŽB3LYP.. The energy difference between the C 2v and C s structures of 2 has been analyzed at several levels of theory, and the results are shown in Table 4. As general trends we may conclude that higher level correlation effects seem to slightly favor the C s structure, whereas extension of the basis set has again a minor effect but in any case favors the C 2v structure. The result is a very small energy difference, about 0.2 kcal moly1 at the most reliable level of theory, CCSDŽT.. Therefore it seems that the C 2v structure is preferred, but again a rather floppy surface is found. It is interesting to note the very good agreement between the B3LYP predictions and the CCSDŽT. result. Finally, we will briefly comment the main features of isomer 3, which is expected to be less stable
Table 3 ˚ and angles in degrees Geometrical parameters for isomer 2 obtained at different levels of theory. Distances are in A
MP2Žfull.r6-31GŽd. MP2Žfull.r6-311GŽd. B3LYPr6-311GŽd. B3LYPrcc-pVTZ CASSCFŽ7,6.r6-31GŽd. QCISDr6-31GŽd. CCSDr6-31GŽd.
dŽCl–C 1 .
dŽC 1 –C 2 .
dŽC 1 –C 3 .
dŽC 2 –C 3 .
/ClC 1C 2
1.667 1.661 1.680 1.672 1.675 1.677 1.674
1.370 1.376 1.370 1.367 1.422 1.397 1.398
1.370 1.376 1.370 1.367 1.332 1.353 1.354
1.393 1.395 1.376 1.369 1.392 1.400 1.390
150.6 149.5 150.2 150.0 146.5 147.8 147.5
P. Redondo et al.r Chemical Physics Letters 315 (1999) 224–232
than the other two, since the chlorine atom is in a central position. The corresponding geometrical parameters are shown in Fig. 1, whereas the vibrational frequencies and IR intensities are not shown for the sake of space Žexperimental detection of this structure is rather unlikely., but are also available upon request. Both levels, MP2 and B3LYP, give similar geometries, the main discrepancy being the C 1-C 2 distance, which is shorter at the MP2 level and is very close to typical C-C triple-bond distances. Nevertheless, both geometries suggest that this isomer can be viewed as a C 2 unit weakly bonded to ClC, since the C 2-Cl distance is in both cases much longer than typical C-Cl bond distances. The difference between the C 1-C 2 distances computed at the MP2 and B3LYP levels is also reflected in the corresponding C 1-C 2 stretching frequencies, which are found at 2663 and 1870 cm -1 , respectively. However, both levels agree in that this frequency should have the highest intensity in the IR spectrum. The relative energies of the different C 3 Cl isomers at selected levels of theory are shown in Table 5. To assess the reliability of MP values, we provide the S 2 expectation values for the HFr6-311GŽd.
Table 5 Relative energies Žkcal moly1 . of the C 3 Cl isomers at different levels of theory MP2r6-311GŽd. a MP4r6-311GŽd. a PMP4r6-311GŽd. a G1 G2 G1ŽP. G2ŽP. B3LYPr6-311GŽd. b B3LYPr6-311qGŽd. b B3LYPr6-311qGŽ2d. b B3LYPr6-311qGŽ3df. b B3LYPrcc-pVTZ c B3LYPrcc-pVQZ c MP2r6-311GŽd. b MP4r6-311GŽd. b QCISDŽT.r6-311GŽd. b CCSDŽT.rcc-pVTZ b a
1
2
3
23.1 16.9 12.7 9.4 9.8 5.2 5.4 1.4 2.2 2.1 2.4 1.9 2.2 24.4 15.5 2.8 4.8
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
156.2 144.2 145.4 – – – – 135.9 – – – – – 172.5 161.4 131.4
Computed at the MP2Žfull.r6-31GŽd. geometry. Computed at the B3LYPr6-311GŽd. geometry. c Computed at the B3LYPrcc-pVTZ geometry. b
229
wavefunction: 0.921 Ž1., 0.775 Ž2., and 1.022 Ž3.. The B3LYPr6-311GŽd. values are also given for comparison: 0.770 Ž1., 0.754 Ž2., and 0.916 Ž3.. The worst case is the higher-lying isomer 3, which has a rather high spin contamination at both levels of theory, whereas usually spin contamination is not a severe problem in most DFT calculations. In all cases, the cyclic isomer is shown to be the most stable one, whereas isomer 3 lies very high in energy as expected. The most interesting values are obviously the energy difference between 1 and 2. It is clear that the MPn relative energies do not change significantly with the geometry, since the MP2 and MP4 values at the MP2 and B3LYP geometries differ in just 1.4 kcal moly1 . Although the cyclic isomer lies always below isomer 1, it seems that inclusion of higher correlated levels reduces the energy gap Žcompare the MP2 and MP4 values.. This energy difference is also smaller when projected MP values are employed, since a reduction of about 4 kcal moly1 is obtained when passing from MP4 to PMP4. On the other hand, extension of the basis set slightly favors the cyclic structure, since the B3LYP relative energy increases from 1.4 to 2.4 kcal moly1 when passing from the 6-311GŽd. basis set to the 6-311 q GŽ3df.. The same effect is observed when Dunning’s ccpVTZ or cc-pVQZ basis sets are employed. At the B3LYP level a very small energy difference is found Ž2.2 kcal moly1 .. However, the most reliable levels of theory are perhaps QCISDŽT. and CCSDŽT. Žfor the latter we employed a larger basis set, namely cc-pVTZ., and both levels agree in that the cyclic isomer is lower in energy, with an energy difference around 3-5 kcal moly1 . We should mention that the ZPVE values are quite close for both isomers Ž6.79 kcal moly1 for 1 and 7.20 kcal moly1 for 2, at the B3LYPr6-311GŽd. level., and therefore inclusion of ZPVE should not change the main conclusion that a cyclic ground state is predicted for C 3 Cl. In addition, we have also applied the G1 and G2 methods w35x, obtaining an energy difference around 9-10 kcal moly1 . This relative energy is reduced to a value near 5 kcal moly1 when projected MPn values are employed to compute the different contributions to the G1 and G2 energies. The values obtained using projected MP energies are denoted G1ŽP. and G2ŽP. in Table 5. These values are in excellent agreement with the CCSDŽT. result, thus supporting the conclu-
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sion that the global minimum of C 3 Cl should be a cyclic structure. In the case of the C 3 H system w22,23x, we have already mentioned that a cyclic C 3 H isomer was found to be the ground state, and the linear isomer Ž2 P . lies very close in energy Ž; 2 kcal moly1 .. The linear isomer was also shown to be rather floppy, since it was found to be nearly iso-energetic with a bent structure. Therefore C 3 Cl seems to be more related to C 3 H than to other systems containing second-row atoms, such as C 3 Si, C 3 S or C 3 P. 3.2. C3 Cl q isomers Based on the results for C 3 Cl, only MP2r631GŽd. and B3LYPr6-311GŽd. methods will be employed for obtaining geometries and vibrational frequencies, whereas relative energies will be computed at the MP4, B3LYP and QCISDŽT. levels. We have found three different C 3 Clq isomers. Isomer 1 is a linear structure, although in the triplet surface is bent with a 3AX electronic state. Isomer 2 has a C 3 cyclic unit and has a 3 B 2 electronic state on the triplet surface. Finally, another cyclic structure with an exocyclic carbon atom, was found only on the singlet surface. The optimized geometries are shown in Fig. 2, whereas the corresponding vibrational frequencies and IR intensities are available upon request. We will briefly comment only the most salient features about these species. The electronic configuration for 1 Ž1 S . is derived from that of linear C 3 Cl, upon removal of the electron occupying the 4 p molecular orbital. The dominant valence-bond structures for the linear singlet species are the following
This explains why the C 2-C 3 bond distance is much shorter than the C 1-C 2 one. The 1 Ž1 S . species is found the be a true minimum at all levels of theory although a very small bending frequency is found at both MP2 Ž139 cm -1 . and B3LYP Ž113 cm -1 . levels. The most intense line in the IR spectrum is predicted to be a C-C stretching nearly 2200 cm -1 . The predicted dipole moment Žtaking the center of mass as
Fig. 2. MP2Žfull.r6-31GŽd. and B3LYPr6-311GŽd. Žin parentheses. optimized geometries for the different C 3 Clq isomers. Dis˚ and angles in degrees. tances are given in A
the origin. for this species is very low, namely about 0.323 D with the 6-311GŽd. basis set. The triplet state is obtained from the singlet upon 3p 4 p excitation. However the resulting structure is bent with a 3AX electronic state, since the linear triplet structure has an imaginary frequency. The main difference with the singlet linear state is the shorter C 1-C 2 distance, and also the much larger dipole moment, namely 2.483 D. The triplet state is also rather floppy, since it has a very low bending frequency at both MP2 and B3LYP levels. As for the singlet state the most intense line in the IR spectrum is predicted to be the C-C stretching near 1900 cm -1 . The singlet cyclic species, 2 Ž1A 1 ., has much shorter Cl-C 1 and C 2-C 3 bond distances than the neutral cyclic isomer, and its dipole moment is predicted to be nearly 1.255 D. This structure is shown to be a true minimum at the MP2 level, but it has an imaginary frequency at the B3LYP level. This is a bending frequency Žb 2 symmetry. whose associated mode corresponds to the loss of C 2v symmetry. We made optimizations of the geometry at the B3LYP
™
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level following this mode Žin C S symmetry., and in all cases the C 3 cycle was broken and finally the linear singlet species 1 Ž1 S . was reached. On the other hand, the triplet species, 2 Ž3 B 2 ., is a true minimum at both MP2 and B3LYP levels with very similar vibrational frequencies in both cases. The geometrical parameters of the triplet cyclic species are closer to those of the neutral cyclic isomer. The dipole moment is quite high, 3.063 D, and there are two C-C stretching frequencies around 1300 and 1600 cm -1 , respectively, which are predicted to dominate the IR spectrum. The last C 3 Clq species is also cyclic, but with an exocyclic carbon atom and a C 2 Cl cyclic unit. In fact this structure can be viewed as the result of the interaction of a chlorine atom with a C-C bond of linear Cq 3 . Although one of the C-Cl bond distances is longer than typical C-Cl bond distances, it is clear that there is a certain interaction between both atoms. This species is a true minimum at both MP2 and B3LYP levels, even though it is expected to be rather unstable. The relative energies of the different C 3 Clq species are shown in Table 6. S 2 expectation values for triplet states at the HFr6-311GŽd. and B3LYP levels Žin parentheses. are as follows: 1 Ž3AX ., 2.561 Ž2.068.; 2 Ž3 B 2 ., 2.068 Ž2.007.. As can be seen the MPn results are virtually unaffected by the geometry, since they are quite similar when computed at the MP2 geometry or at the B3LYP one. All levels of theory agree in that the linear and cyclic isomers have singlet ground states, the lowest-lying triplet being the cyclic 3 B 2 species. The global minimum is Table 6 Relative energies Žkcal moly1 . of the C 3 Clq isomers at different levels of theory X
X
1 Ž1 S . 1 Ž3A . 2 Ž1A 1 . 2 Ž3 B 2 . 3 Ž1A . .a
MP2Žfull.r6-31GŽd MP2r6-311GŽd. a MP4r6-311GŽd. a PMP4r6-311GŽd. a B3LYPr6-311GŽd. b MP2r6-311GŽd. b MP4r6-311GŽd. b QCISDŽT.r6-311GŽd. b a b
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
54.8 55.8 58.6 49.3 38.0 55.7 57.7 41.2
17.8 17.9 23.6 23.6 23.1 16.9 22.4 19.2
32.2 33.8 40.0 38.8 32.8 33.4 39.4 32.3
Computed at the MP2Žfull.r6-31GŽd. geometry. Computed at the B3LYPr6-311GŽd. geometry.
94.2 93.4 87.3 87.3 82.5 93.0 86.3 77.7
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the singlet linear structure, with the singlet cyclic 2 Ž1A 1 . species lying about 17-23 kcal moly1 , depending on the level of theory. It seems that inclusion of higher correlated effects tends to increase the energy difference, since it is greater at the MP4 level than at the MP2 one. As expected the less stable C 3 Clq species is isomer 3. Once we know the energetics of the C 3 Clq species, we may estimate the Žadiabatic. ionization potential of the C 3 Cl radical. In the case of cyclic C 3 Cl, we obtain a value of 9.17 eV at the QCISDŽT.r6-311GŽd. level. For the quasi-linear isomer Ž1., the IP is estimated to be much lower, 8.21 eV at the same level of theory. In both cases the IPs have been computed for the production of the corresponding cyclic or linear singlet C 3 Clq and both were found to be much lower than the IP of hydrogen Ž13.6 eV.. Therefore it is expected that if C 3 Cl is present in the interstellar medium it could be easily ionized. In fact, these values are much lower than the IPs of chlorine Ž13.00 eV. and carbon Ž11.27 eV..
4. Conclusions A theoretical study of the C 3 Cl isomers has been carried out. Predictions for their geometries and vibrational frequencies have been made at both MP2 and B3LYP levels. The main conclusion is that there are two isomers which are close in energy. All theoretical levels predict that the global minimum is a cyclic C 2V species Ža three-membered ring with an exocyclic chlorine atom.. However, a quasi-linear CCCCl structure is predicted to lie only about 3-5 kcal moly1 above the former at the most reliable levels of theory. This quasi-linear structure has been found to be rather floppy Žthe linear arrangement is found to be only about 2-3 kcal moly1 higher in energy.. Both isomers, cyclic and open-chain, have relatively high dipole moments, namely 1.986 and 3.363 D, respectively. We have also studied the C 3 Clq cation. In this case, the global minimum is predicted to be a linear singlet species, whereas the singlet cyclic isomer lies about 19 kcal moly1 higher in energy. The ionization potentials of cyclic and open-chain C 3 Cl are
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estimated to be 9.17 and 8.21 eV, respectively. These values suggest that these species should be easily ionized if present in interstellar medium. From our calculations on this kind of system, we have seen that the geometries and vibrational frequencies obtained at the MP2Žfull.r6-31GŽd. and B3LYPr6-311GŽd. levels are not severely altered upon extension of the basis set. In addition, the QCISDŽT. method seems a reasonable and less expensive alternative to CCSDŽT. for these systems, since both lead to very close relative energies. The B3LYP results, even with moderate basis sets, are also in rather good agreement with the CCSDŽT. values. Acknowledgements This research has been supported by the Ministerio de Educacion ´ y Cultura of Spain ŽDGICYT, Grant PB97-0399-C03-01. and by the Junta de Castilla y Leon ´ ŽGrant VA 21r97.. References w1x G.A. Blake, J. Keene, T.G. Phillips, Astrophys. J. 285 Ž1985. 501. w2x J. Cernicharo, M. Guelin, Astron. Astrophys. 183 Ž1987. L10. w3x E.F. Van Dishoeck, M.C. van Hemert, A. Dalgarno, J. Chem. Phys. 77 Ž1982. 3693. w4x V.G. Anicich, W.T. Huntress, J. Futrell, Chem. Phys. Lett. 40 Ž1976. 233. w5x V.G. Anicich, W.T. Huntress, Astrophys. J. Suppl. 62 Ž1986. 553. w6x C. Rebrion, J.B. Marquette, B.R. Rowe, D.C. Clary, Chem. Phys. Lett. 143 Ž1988. 130. w7x D.M. Sonnenfroh, J.M. Farrar, Astrophys. J. 335 Ž1988. 491. w8x C.E. Dateo, D.C. Clary, J. Chem. Phys. 90 Ž1989. 7216. w9x C. Barrientos, A. Largo, P. Redondo, F. Pauzat, Y. Ellinger, J. Phys. Chem. 97 Ž1993. 173. w10x G.A. Blake, V.G. Anicich, W.T. Huntress, Astrophys. J. 300 Ž1986. 415. w11x V.M. Rayon, C. Barrientos, A. Largo, J. Mol. Struct. ŽTHEOCHEM. 363 Ž1996. 319.
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