As seen in experiments with poly(3-hexylthiophene), substitution of hydrogen with deuterium on the main chain alone decreases crystallinity. To understand this effect, a general formalism for analysis of the dipole moments and polarizabilities incorporating quantum nuclei, is developed. The formalism, based on quantum dynamics of the proton/deuteron and on the perturbative analysis of the dipole interaction energy, accounts for the anharmonicity of a potential energy surface and for the anisotropy of molecular dipole moments. The formalism is implemented within the Discrete Variable Representation and the Density Functional Theory describing, respectively, the quantum proton/deuteron on the thiophene ring and the electronic structure of the 27-atom model polymer chain, embedded into a larger crystalline environment. The isotope effect is mainly attributed to the differences in the zero-point energy of the CH/CD bonds and to the isotope-dependence of the dipole-dipole inter-chain interactions.dipole interactions, isotope effect on crystallinity, nuclear quantum effects, perturbation theory, quantum dynamics
| INTRODUCTIONIt is increasingly recognized that nuclear quantum effects (NQEs) associated with light nuclei, such as protons, may influence structure, dynamics and properties of large molecular systems and materials. The NQE studies are mainly focused on the zero-point vibrational energy (ZPE), delocalization of the nuclear wavefunction and quantum tunneling [1][2][3][4] . Liquid water is the prime example of a system in which NQEs are particularly important because of the central role of the hydrogen bonding on its properties [5][6][7] . The difference in stability of the hydrogen bonding and its deuterium-substituted equivalent is due to the interplay of two competing quantum effects: the ZPE of vibrations and quantum tunneling. Some other systems, which may be influenced by the quantum behavior of the nuclei, are two-dimensional materials [3,8] and conducting polymers [9,10] .Recent experiments have shown that selective deuteration of conducting polymers may change their optoelectronic properties [9] . For example, in an organic photovoltaic heterojunction, consisting of poly(3-hexylthiophene) (P3HT) and phenyl-C61-butyric acid methyl ester (PCBM), selective deuteration of the hexyl side-chain of P3HT affects the open circuit voltage, V oc , through fluctuation of the energy levels of the electron donor (P3HT) and acceptor (PCBM). Because of the difference in fluctuations of H and D in their respective ground vibrational states due to the nuclear wavefunction delocalization, the rates of the charge transfer across a heterojunction and of the recombination are different for the protonated and deuterated versions of P3HT. This shifts the balance of charges across the P3HT:PCBM junction and leads to lowering of V oc by 0.24 eV upon the side-chain deuteration of P3HT [10] . A few other recent notable examples of experimentally observed H/D isotope effects are polymerization of benzene [11] , stability of organi...