We present a calculation of vibrational frequencies of formate on the AuPt(111) surface alloy including full anharmonicity and coupling of all six intramolecular degrees of freedom. This species is a key intermediate in methanol oxidation on this material. We use a modified version of the method of Manzhos and Carrington to compute the spectrum directly from a small number (<10,000) of DFT single-point energies, bypassing the construction of a potential energy surface. This is the first such calculation for a 4-atomic species at a surface. The spectrum is obtained using rectangular collocation and a small basis set of parameterized Hermite functions. The achievable accuracy of the order of several cm-1 corresponds to the typical experimental resolution. Using normal coordinates makes the equations simple and general and easily applicable to other systems. This calculation is doable on a PC. We predict that anharmonicity and coupling lower the fundamental frequencies by dozens of cm-1, which could affect species assignment.