N-body:Many-body QM:QM vibrational frequencies: Application to small hydrogen-bonded clusters

We present an efficient method for reproducing CCSD(T) (i.e., the coupled-cluster method with single, double and perturbative connected triple excitations) optimized geometries and harmonic vibrational frequencies for molecular clusters with the N-body:Many-body QM:QM technique. In this work, all 1-body through N-body interactions are obtained from CCSD(T) computations, and the higher-order interactions are captured at the MP2 level. The linear expressions from the many-body expansion facilitate a straightforward evaluation of geometrical derivative properties (e.g., gradients and Hessians). For (H₂O)_n clusters (n = 3–7), optimized structures obtained with the 2-body:Many-body CCSD(T):MP2 method are virtually identical to CCSD(T) optimized geometries. Harmonic vibrational frequencies calculated with this 2-body:Many-body approach differ from CCSD(T) frequencies by at most a few cm⁻¹. These deviations can be systematically reduced by including more terms from the many-body expansion at the CCSD(T) level. Maximum deviations between CCSD(T) and 3-body:Many-body CCSD(T):MP2 frequencies are typically only a few tenths of a cm⁻¹ for the H₂O clusters examined in this work. These results are obtained at a fraction of the wall time of the supermolecular CCSD(T) computation, and the approach is well-suited for parallelization on relatively modest computational hardware.