It has long been puzzling regarding the atomistic origin of the pressure-induced Raman optical phonon stiffening that generally follows a polynomial expression with coefficients needing physical indication. Here, we show that an extension of the bond-order-length-strength correlation mechanism and a local bond average approach to the pressure domain have led to an analytical solution to connect the pressure-induced Raman optical phonon stiffening directly to the bonding identities of the specimen and the response of the bonding identities to the applied stimulus. It is found that the pressure-induced blue-shift of Raman optical phonons arises from the bond compression and energy storage exerted by the compressive stress. Agreement between predictions and experimental measurements lead to the clarification of the detailed form for the polynomial coefficients, which provide an atomistic understanding of the physical mechanism of the external pressure induced energy gain, thermally induced bond expansion, as well as means of determining the mode atomic cohesive energy in a specimen.