Beyond the resonant dipole interaction model: resolution of a discrepancy between experimental and calculated structures of the carbon dioxide cyclic planar trimer.

A dimer and two trimers of carbon dioxide are known experimentally and have also been studied computationally. Whereas the calculated and experimental structures are in excellent agreement for the dimer and in fair agreement for the nonplanar trimer of C2 symmetry, the cyclic planar trimer shows a significant discrepancy in the angle beta which measures the deviation from D(3h) symmetry. All calculations yield for this angle values around 40 degrees in contrast to the experimental angle of (33.8+/-0.5) degrees . The latter was obtained from the experimental shift of the asymmetric vibrational stretch line of the trimer relative to the monomer using the resonant dipole-dipole interaction model. This model corresponds to the leading term in the molecular transition multipole expansion (TMPE) of the electrostatic coupling contribution to vibrational shifts. In this paper we go beyond the resonant dipole-dipole interaction model and include higher-order moments. To this end we use the first-order perturbation approach in combination with the (CO2)2 ab initio symmetry-adapted perturbation theory (SAPT)-s potential to calculate the vibrational shifts and scale the CO2 SAPT-s point charges to reproduce the experimental transition dipole moment of the gas-phase CO2 asymmetric stretch. The transition dipole-dipole term in the TMPE of the electrostatic coupling plays a predominant role in the vibrational shifts of the CO2 dimer and nonplanar trimer, however, to explain the vibrational shifts of the cyclic planar trimer the inclusion of the higher-order vibrationally induced moments is needed. As the angle beta in this trimer approaches the value of 40 degrees the dipole-dipole term in the electrostatic coupling disappears and the sum of the higher-order terms becomes important for the correct description of the vibrational shifts. Hence applying the resonant dipole-dipole interaction model to the experimentally observed vibrational shift for the cyclic planar trimer gives the wrong angle beta for this trimer. The higher-order terms in the TMPE of the electrostatic coupling which are not negligible for the vibrational shifts of the cyclic planar trimer include vibrationally induced dipole-octupole and quadrupole-quadrupole interactions.