Fermi resonance between the N-H stretching (ν₁ and ν₃) and the overtone of N-H bending (2ν₄) in ammonia has hindered the interpretation and assignments of experimental spectra of small ammonia clusters. In this work, we carried out anharmonic vibrational calculations using MP2/aug-cc-pVDZ to examine the vibrational spectra of (NH₃)n=1-5 with a focus on the size evolution. The enhancement of hydrogen bond strength due to cooperative effects will cause ν₁ and ν₄ to red-shift and blue-shift, respectively, when the size of the cluster increases. Our calculations show that the energy order of fundamental of ν₁ and overtone of ν₄ is reversed between n = 3 and n = 4. Therefore, while the resultant mixed levels do not show remarkable shifts in their peak positions, the main identity of these mixed levels changes and this causes significant re-distribution of their intensities. Furthermore, our ab initio anharmonic calculation scheme can directly evaluate the coupling strength between different N-H stretching and overtone of N-H bending without any experimental parameters, thus leading us to a simpler picture to understand the Fermi resonance in (NH₃)_n.

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