A group theoretical algorithm to calculate the number of independent force constants of a molecule at any given order has been extended to treat linear molecules in a fashion analogous to nonlinear molecules. Using this algorithm to determine the independent force constants and a finite-difference formalism to obtain higher-order force constants from low-order analytic geometric derivatives of the electronic energy, the anharmonic force field of CO2 has been determined at the ab initio TZ2P SCF and QZ2P CCSD(T) levels. It is shown that accurate sextic force fields can be calculated from only analytic first derivatives if the wave function is tightly converged and the calculated forces are highly accurate. The calculated anharmonic force fields are compared to experimentally determined sextic force fields of CO2, and uncertainties and discrepancies in the experimental fields are discussed.
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