Effect of Topological Defect on the Energy and Thermodynamics of Linear Molecules with Pseudoharmonic Potential in a Global Monopole Spacetime

In this work, we investigate the vibrational properties and thermodynamic behaviour of a linear molecule subjected to a pseudoharmonic potential in the background spacetime of a global monopole. By formulating the Schr & ouml;dinger equation using the Laplace-Beltrami operator and solving the resulting radial equation with the Asymptotic Iteration Method (AIM), closed-form expressions for the energy eigenvalues are obtained. The presence of the global monopole, characterised by the parameter alpha, modifies the effective centrifugal term and rescales the vibrational spectrum, leading to shifts in both the energy spacing and the ground-state energy. Using the derived spectrum, the vibrational partition function is constructed, from which key thermodynamic quantities - including the internal energy, specific heat capacity, Helmholtz free energy, and entropy -are analytically evaluated. Our results show that the topological defect significantly influences the thermal properties of the molecule, with stronger monopole effects enhancing the population of excited vibrational states and increasing the vibrational entropy. In the limit alpha -> 1 , the standard flat-space results are recovered. These findings highlight the role of spacetime topology in molecular spectroscopy and extend the study of molecular systems in curved backgrounds to the thermodynamic regime.