Confining molecules within nano-cavities like fullerenes quantizes their translational motion while preserving well-defined rovibrational states. The resulting structures, termed endofullerenes—with H2O@C60 being a prominent example—can be assembled into larger architectures such as carbon nanotubes, producing endofullerene "peapods." Within these assemblies, polar molecules couple through dipole-dipole interactions. The interplay between interaction strength and the spacing of monomer rovibrational levels can drive the system from a disordered to an ordered phase, a transition known as a quantum phase transition (QPT). Such a transition has recently been predicted for one-dimensional water [1,2]. We will discuss several computational tools for investigating these confined molecular chains. The first is the density matrix renormalization group (DMRG), and we will outline its capabilities for treating confined rotors [3,4]. For systems beyond one dimension, Path Integral Monte Carlo (PIMC) methods become more suitable, and we will present results obtained using discretized Gibbs sampling PIMC [6,7]. Finally, we will examine the conditions under which water chains can exhibit ferroelectric behavior.

[1] T. Serwatka, R. Melko, A. Burkov, and P.-N. Roy, A quantum phase transition in the one-dimensional water chain, Phys. Rev. Lett. 130, 026201 (2023).
[2] T. Serwatka, and P.-N. Roy, Quantum Criticality and Universal Behavior in Molecular Dipolar Lattices of Endofullerenes, J. Phys. Chem. Lett. 14, 24, 5586 (2023).
[3] T. Serwatka, P.-N. Roy, "Ground state of asymmetric tops with DMRG: water in one dimension", J. Chem. Phys. 156, 044116 (2022).
[4] T. Serwatka, and P.-N. Roy, Ferroelectric water chains in carbon nanotubes: creation and manipulation of ordered quantum phases, J. Chem. Phys. 15, 234301 (2022).
[5] T. Serwatka, and P.-N. Roy, Quantum criticality in chains of planar rotors with dipolar interactions, J. Chem. Phys. 160, 104302 (2024).
[6] M. S. Moeed, T. Serwatka, and P.-N. Roy, Pair Approximating the Action for Molecular Rotations in Path Integral Monte Carlo. J. Chem. Phys. 162, 024113 (2025).
[7] W. Zhang, M. S. Moeed, A. Bright, T. Serwatka, E. De Oliveira, and P.-N. Roy, Path integral Monte Carlo in a discrete variable representation with Gibbs sampling: dipolar planar rotor chain. J. Chem. Phys. 162, 014106 (2025).