Ab Initio Study of the Charge-Transfer Complex of Xenon and Dicarbon

Journal of Molecular Spectroscopy 216, 424–427 (2002) doi:10.1006/jmsp.2002.8674

Ab Initio Study of the Charge-Transfer Complex of Xenon and Dicarbon J¨urgen Breidung and Walter Thiel1 Max-Planck-Institut f¨ur Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 M¨ulheim an der Ruhr, Germany Received April 10, 2002

¨ RGER FOR HIS MANY CONTRIBUTIONS TO SCIENCE IN HONOR OF PROFESSOR HANS BU Correlated ab initio calculations with large basis sets are reported for C2 Xe. The complex has a linear structure and a considerable dipole moment due to charge transfer from xenon to dicarbon. The CXe interatomic potential is rather flat so that the predicted CXe distance remains uncertain even at the highest level employed (268 pm at BCCD(T)/VQZ + d-aug(C)). The calculations recover most of the observed red shift in the CC stretching wavenumber upon complexation and thus support the reported identification of C2 Xe in a xenon matrix. The properties of the C2 Xe complex are compared with those of the analogous C 2002 Elsevier Science (USA) charge-transfer complex F2 CCXe.  Key Words: ab initio calculations; equilibrium structure; fundamentals; xenon; charge-transfer complex. INTRODUCTION

A few years ago, a charge-transfer complex of difluorovinylidene F2 CC and xenon was prepared and detected in an argon matrix through experimental work in the groups of B¨urger and Sander (1). Despite the low binding energy, which was estimated to be at most 3 kcal/mol, the three observed infrared absorptions of this complex (1) are red-shifted by up to 52 cm−1 when compared with the corresponding fundamental bands in F2 CC (2). These shifts could be confirmed almost quantitatively by correlated ab initio calculations (1). A similar complex was found independently and almost simultaneously by Maier and Lautz (3) who identified a new infrared signal at 1767 cm−1 upon laser irradiation of acetylene in a xenon matrix. This signal was assigned to the CC stretching fundamental in the novel compound C2 Xe formed under these conditions. Compared to the analogous vibrational transition in the free dicarbon C2 molecule, this new band is red-shifted by 60 cm−1 . Only a small fraction of this shift could be reproduced computationally (3). Since such a discrepancy did not occur in our ab initio calculations on F2 CCXe (1) we decided to reinvestigate the vibrational spectrum of C2 Xe theoretically. In the present paper we report on our results. THEORETICAL METHODS

Quantum-chemical calculations were carried out at the correlated levels of second-order Møller–Plesset perturbation theory (MP2) (4) and Brueckner coupled cluster theory in 1 To whom correspondence should be addressed. E-mail: [email protected].

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which the molecular orbitals are defined such that all singleexcitation cluster amplitudes vanish (BCCD) (5, 6). The resulting Brueckner orbitals can be regarded as orbitals responding directly to nondynamical correlation (5). This coupled cluster approach was augmented by a perturbational estimate of the effects of connected triple excitations [BCCD(T)] (7). The calculations were performed with the GAUSSIAN98 (8) and MOLPRO2000 (9, 10) program packages. Several different basis sets were employed which are defined as follows: the smallest basis denoted as VTZ is the correlationconsistent polarized valence triple-zeta basis cc-pVTZ at the carbon atoms (11), whereas Xe is described by the ab initio energy-adjusted quasirelativistic pseudopotential ECP46MWB (replacing the 46 core electrons) (12) combined with the correlation-consistent valence triple-zeta basis SDB-cc-pVTZ that has recently been optimized (13) for the chosen pseudopotential. The second basis labeled VQZ is constructed in complete analogy to the VTZ basis, with the cc-pVTZ and SDB-cc-pVTZ sets substituted by the corresponding quadruple-zeta basis sets cc-pVQZ at C (11) and SDB-cc-pVQZ at Xe (13), respectively. The bonding between C2 and Xe in the target molecule C2 Xe is accompanied by a charge transfer from Xe to C2 (3). To account for this particular electronic structure, a single set of diffuse Gaussian functions of each angular momentum was added to VQZ at carbon to arrive at the third basis VQZ + aug(C); i.e., the cc-pVQZ basis at C was replaced by the corresponding augmented aug-cc-pVQZ set (14). The fourth basis with the acronym VQZ + aug(C, Xe) is derived from VQZ + aug(C) by the addition of low-exponent primitive Gaussian-type orbitals at Xe with the orbital exponents αs = 0.085659, αp = 0.054760, αd = 0.0894434, αf = 0.1323007, and αg = 0.221. Finally, the largest basis set used in this work is derived from

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VQZ + aug(C) by replacing the aug-cc-pVQZ basis at C by the doubly augmented basis d-aug-cc-pVQZ (15). This basis served mainly as a check on convergence and is denoted here as VQZ + d-aug(C). Spherical harmonics were used throughout. The carbon 1slike core molecular orbitals were always constrained to be doubly occupied (frozen core approximation). Following Maier and Lautz (3) a linear structure for C2 Xe was assumed and optimized. For the purpose of comparison, the bond length of C2 was also optimized. Analytic energy gradients as implemented in the GAUSSIAN98 program (8) were used at the MP2 level of theory, and numerical gradients were employed at the BCCD(T) level with MOLPRO2000 (9). The largest internal gradient components at the stationary points were always less than 1 × 10−5 au. At the computed equilibrium geometries, harmonic force fields were evaluated either analytically in Cartesian coordinates (MP2) employing the GAUSSIAN98 program (8), or numerically in internal coordinates from BCCD(T) energies (step sizes 0.005 Bohr for bond distances and 1◦ for bond angles). The normal modes and the harmonic vibrational frequencies were obtained in the usual manner (16, 17). All mass-dependent data in this study refer to the principal isotopomer 12 C2 132 Xe. At the BCCD(T) level electric dipole moments were determined as numerical derivatives of the potential energy with respect to a finite field component (0.0005 au) using the MOLPRO2000 program (9). To determine the binding energy of C2 Xe, the energy differences E between this species and its fragments C2 and Xe were evaluated at the MP2 and BCCD(T) levels of theory. To adjust E for the lack of completeness of the chosen orbital basis, the counterpoise correction (18) for basis set superposition errors was applied. The counterpoise-corrected binding energy E CP is given by E CP = E C2 Xe − E C2 (R) − E Xe (R), where E C2 (R) and E Xe (R) are the calculated total energies of the C2 and Xe fragments using the full atomic orbital basis of the complete system (C2 Xe) but excluding the nuclear charge of the absent fragment. RESULTS AND DISCUSSION

Table 1 contains the computed equilibrium bond lengths and electric dipole moments in C2 Xe, assuming a linear geometry. Maier and Lautz (3) have pointed out why such a linear structure is plausible: the bonding between C2 and Xe is mainly due to a charge transfer with the Xe atom donating electron density to the lowest unoccupied molecular orbital (LUMO) in C2 , and this acceptor orbital (3σg ) is oriented along the internuclear axis. Dicarbon has a large electron affinity of 3.27 eV (19), which enables C2 to accept electron density from Xe (3). This situation is similar to that in F2 CC which also has a large electron affinity (2.26 eV (20)) and can therefore act as an electron acceptor towards Xe (1). Furthermore, the assumption of a linear structure in C2 Xe is consistent with highly correlated ab initio calcula-

TABLE 1 Computed Equilibrium Bond Lengths re (pm) and Electric Dipole Moments µe (D) in C2 Xe Method MP2

BCCD(T)

Basis VTZb VQZ VQZ + aug(C) VQZ + aug(C, Xe) VQZ + d-aug(C) VTZ VQZ VQZ + aug(C) VQZ + aug(C, Xe) VQZ + d-aug(C)c

re (CC)

re (CXe)

µe a

126.5 126.1 126.2 126.2 126.2 125.5 125.1 125.3 125.3 125.4

305.9 305.0 302.6 304.1 302.5 283.8 280.7 269.0 273.4 268.0

0.20 0.14 0.17 0.12 0.17 1.60 1.69 2.20 1.97 2.25

a

The dipole vector is directed from the C2 fragment to the Xe atom. NPA charges from MP2/VTZ at the given geometry: Xe + 0.083 e, C(central) − 0.116 e, C(terminal) + 0.033 e. c NPA charges from MP2/VTZ at the given geometry: Xe + 0.182 e, C(central) − 0.222 e, C(terminal) + 0.040 e. b

tions for the van der Waals complex between C2 and Ar (21): the global energy minimum is found for the linear C2 -Ar geometry while a saddle point is predicted for the T-shaped structure. Correspondingly, our current BCCD(T) calculations yield a Tshaped structure for C2 Xe (point group symmetry C2v ) which is a saddle point about 1 kcal/mol higher in energy than the linear structure, with a very large CXe distance of about 420 pm (cf. Table 1). Therefore, we shall restrict our attention to the linear geometry of C2 Xe in the present study. Turning to the data in Table 1, it is seen that for a given basis set BCCD(T) predicts somewhat shorter CC (0.8–1.0 pm) and considerably shorter CXe (22.1–34.5 pm) bonds than MP2. At both theoretical levels convergence in re (CC) appears to be achieved with the VQZ + aug(C) basis; the use of larger basis sets changes re (CC) by at most 0.1 pm. Focusing on the three largest basis sets presently employed (VQZ plus diffuse atomic orbitals), MP2 predicts a CXe bond distance of about 303 pm whereas the more reliable BCCD(T) treatment yields a value close to 270 pm (see Table 1). This large spread reflects the extreme flatness of the CXe interatomic potentials in C2 Xe and implies a large uncertainty of the computed distances. In any case, the re (CXe) values are significantly smaller than the sum of the van der Waals radii of C and Xe which amounts to 386 pm (22). On the other hand, the experimental CXe bond distances in the [C6 F5 Xe]+ cation and in the (C6 F5 )2 Xe molecule from Xray diffraction are much shorter, viz. 208 pm and 235–239 pm, respectively (23, 24). For a given basis set, the BCCD(T) values of the electric dipole moment in C2 Xe are 8–16 times larger than the corresponding MP2 values (see Table 1). Apparently, the charge transfer from Xe to C2 is much more pronounced at the BCCD(T) than at the MP2 level. Natural population analysis (NPA) indicates that this is partly due to the differences in the optimized bond lengths: the MP2/VTZ NPA charges increase significantly with

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TABLE 2 Computed Harmonic Vibrational Wavenumbers ωi (cm−1 ) in C2 Xe Method MP2 a

BCCD(T)

Basis

ω1 (CC str)

ω2 (CXe str)

ω3 (bend)

VTZ VQZ VQZ + aug(C) VQZ + aug(C, Xe) VQZ + d-aug(C) VTZ VQZ VQZ + aug(C) VQZ + aug(C, Xe) VQZ + d-aug(C)

1834 (300) 1835 (344) 1826 (398) 1829 (379) 1826 (403) 1824 1829 1817 1820 1815

111 (0.01) 118 (0.11) 124 (0.04) 121 (0.10) 125 (0.04) 52 59 76 67 77

192 (109) 198 (123) 214 (147) 202 (124) 213 (146) 121 143 151 131 78

a Infrared band intensities (km/mol) in parentheses (double harmonic approximation).

decreasing CXe distance (see footnotes in Table 1). However, even at optimized BCCD(T) geometries with their shorter CXe distances, the dipole moments from MP2 remain smaller than those from BCCD(T), implying that BCCD(T) favors intrinsically more charge transfer in this system. Table 2 shows theoretical results for the harmonic vibrational wavenumbers of C2 Xe. The MP2 and BCCD(T) data for the CC stretching wavenumber ω1 are quite similar, i.e., for a given basis the BCCD(T) values are smaller than their MP2 counterparts only by 6–11 cm−1 . Considerably larger differences occur for the CXe stretching (ω2 ) and the bending (ω3 ) wavenumbers where the BCCD(T) values are typically smaller by 48–59 and 55–71 cm−1 , respectively. The BCCD(T)/VQZ + d-aug(C) result for ω3 is much smaller (78 cm−1 ) than the other BCCD(T) values for ω3 (121–151 cm−1 ). We have checked this problem and found that the BCCD(T)/VQZ-based results for ω3 are numerically rather sensitive to the choice of the step size used in the finite-difference calculation of the bending force constants (see Theoretical Methods) whereas the BCCD(T)/VTZ value for ω3 and all other values in Table 2 are numerically stable. Therefore, the present BCCD(T)/VQZ-based values of ω3 should be viewed with some caution. Theoretical infrared band intensities are also reported in Table 2 (in parentheses). The CC stretching vibration in C2 Xe causes a strong change in the molecular electric dipole moment which results in a large absorption intensity of the associated fundamental band. This is easily understood when realizing that both carbon atoms carry electric charges of opposite sign in C2 Xe. Thus, it is not surprising that this band could be detected in the infrared spectrum (3). The bending fundamental is predicted to be reasonably intense, whereas the CXe stretching band should be extremely weak. Table 3 contains the computed equilibrium bond lengths and harmonic vibrational wavenumbers in the free dicarbon molecule (X 1 g+ ) as well as the differences (shifts) between the respective calculated CC harmonic stretching wavenumbers in

C2 Xe and C2 . For a given basis, BCCD(T) yields CC equilibrium distances and CC harmonic stretching wavenumbers that are smaller than those from MP2 (by 1.0–1.1 pm and 30–35 cm−1 , respectively). Compared with experiment (25), the equilibrium internuclear distance in C2 is overestimated by 0.35 pm at the BCCD(T)/VQZ + aug(C) level which is mainly due to the neglect of innershell correlation contributions to re (CC) (26). At the same level, the harmonic stretching wavenumber ωe in C2 is—of course somewhat fortuitously—in virtually perfect agreement with the experimental value (see Table 3). The CC bond in C2 is calculated to be 0.5–0.8 pm shorter than the CC bond in the complex C2 Xe (see Tables 2 and 3). This is in line with the prediction that in C2 Xe the CC harmonic stretching wavenumber is red-shifted by 46–59 cm−1 (MP2) and 21–40 cm−1 [BCCD(T)], respectively (see Table 3). Experimentally, the CC stretching fundamental in C2 Xe is observed at 1767.0 cm−1 in a xenon matrix (3). Maier and Lautz (3) compare this value with the harmonic wavenumber of C2 in the gas phase (1854.6 cm−1 (27)) to conclude that the CC stretching fundamental in C2 Xe is red-shifted by as much as 87.6 cm−1 . It seems more appropriate to compare the measured fundamental wavenumber in C2 Xe with the fundamental (anharmonic) instead of the harmonic wavenumber in C2 , i.e., with 1827.5 cm−1 (25), which leads to a red shift of 60.5 rather than 87.6 cm−1 (3). Our best present calculation [BCCD(T)/VQZ + d-aug(C)] is capable of recovering nearly two-thirds (40 cm−1 ) of the corrected shift, while the MP2 calculations with the two largest basis sets (VQZ + aug(C) and VQZ + d-aug(C)) reproduce this shift almost quantitatively (59 cm−1 ). Of course, such perfect agreement at the MP2 level is fortuitous to some extent, especially when considering that the experimental data for C2 Xe were obtained in a xenon matrix and not in the gas phase. Maier and Lautz (3) also carried out MP2 calculations with the smaller LANL2DZ basis set, but they could only recover a rather small fraction of the observed red shift (about 28% of 60.5 cm−1 , i.e., 16.8 cm−1 ).

TABLE 3 Computed Equilibrium Bond Lengths re (pm) and Harmonic Vibrational Wavenumbers ωe (cm−1 ) in C2 (X 1 Σ+ g ), and the Associated Shifts (cm−1 ) of ω1 in C2 Xe with Respect to ωe in C2 Method MP2

BCCD(T)

Exp. a b

Ref. (25). See text.

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Basis

re (CC)

ωe (CC str)

Shift

VTZ VQZ VQZ + aug(C) VQZ + d-aug(C) VTZ VQZ VQZ + aug(C) VQZ + d-aug(C)

126.0 125.6 125.6 125.6 125.0 124.5 124.6 124.6 124.25a

1880 1887 1885 1885 1845 1856 1854 1855 1854.7a

−46 −52 −59 −59 −21 −27 −37 −40 −60.5b

CHARGE-TRANSFER COMPLEX OF XENON AND DICARBON

TABLE 4 Computed Binding Energies (kcal/mol) in C2 Xe Method MP2

BCCD(T)

a

Basis VTZ VQZ VQZ + aug(C) VQZ + aug(C, Xe) VQZ + d-aug(C) VTZ VQZ VQZ + aug(C) VQZ + aug(C, Xe) VQZ + d-aug(C)

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REFERENCES

E

ECPa

−2.8 −3.2 −3.9 −3.5 −4.2 −1.0 −1.2 −2.1 −1.6 −2.4

−2.3 −2.9 −3.2 −3.2 −3.3 0.0 −0.8 −1.2 −1.2 −1.2

Including counterpoise correction, see text.

Obviously, such smaller basis sets are insufficient for this purpose. In the dicarbon anion C− 2 the fundamental wavenumber (1757.8 cm−1 (25)) is red-shifted by 69.7 cm−1 compared to neutral C2 , i.e., by a similar amount as in C2 Xe (see above). This is qualitatively consistent with a strong charge transfer from Xe to C2 in C2 Xe (3). The harmonic wavenumbers ωe −1 in C− 2 and C2 differ by 73.7 cm , close to the observed shift −1 of 69.7 cm . Obviously, the contributions from anharmonicity largely cancel in this case. By analogy, we expect that the difference between the computed harmonic wavenumbers ω1 in C2 Xe and ωe in C2 (see Table 3) is close to the difference of the associated fundamental (anharmonic) wavenumbers observed experimentally. Finally, Table 4 presents the computed binding energies in C2 Xe at various theoretical levels. Taking counterpoise corrections into account, the binding energy is predicted to be about 3 kcal/mol at the MP2 level and about 1 kcal/mol at the more reliable BCCD(T) level. Hence, the complex is only very weakly bound and will dissociate easily at higher temperatures.

CONCLUSIONS

The charge-transfer complexes F2 CCXe (1) and C2 Xe (3) are similar in many respects. Their electronic structure is characterized by a donation of electron density from Xe to the LUMO of the acceptor leading to planar (1) and linear (3) structures, respectively. The resulting binding energies are very small (1–3 kcal/mol at different theoretical levels), and the CXe interatomic potential is quite flat (implying a large uncertainty in the predicted CXe distances). In spite of the rather weak interactions, there are considerable red shifts in the CC stretching frequencies, i.e., experimentally in the order of 52 cm−1 (1) and 60 cm−1 (3). These shifts are well reproduced by correlated ab initio calculations provided that sufficiently large basis sets are employed. These ab initio results thus support the identification of F2 CCXe (1) and C2 Xe (3).

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