Electric Field: Maker \textit{and} Breaker of Molecular co-operativity: the paradigm of (CH$_{3}$OH)---(H$_{2}$O)$_{n}$ [$n=$1-4] hetero-clusters*

Hydrogen-bonded hetero-clusters of methanol and water: (CH$_{3}$OH)---(H$_{2}$O)$_{n}$ [$n=$1-4], when subjected to an externally applied dipolar electrostatic field, exhibit remarkable stability up to their characteristic maximal threshold field strengths. Moderate fields below the threshold endow a given cluster with enhanced stability against dissociation, whereas beyond the threshold its HOMO-LUMO gap abruptly closes down, resulting into structural breakdown. The electric field thus plays a dual role of a maker \textit{and} breaker of molecular co-operativity in a hydrogen-bonding scenario. \textit{Ab initio} investigations on these clusters employing M06-2X hybrid functional with a 6-311$++$G(2d, 2p) basis set reveal the structural evolution of the conformers with increasing electric field strengths: structural deformations, enhancement in their dipole moments with concomitant decrease in their HOMO-LUMO gaps interspersed with abrupt changes in these attributes when the clusters ``open out.'' Energetics quantify the stability of the clusters in field, while the IR vibrational spectra bring out shifts in the normal modes with marked emergence of exotic low-frequency O-H stretches as precursors of breakdown at the threshold field strengths.