Electron-electron and electron-nucleus correlation effects on exponent (α) values of Gaussian-type functions (GTFs) for quantum protons and deuterons in BH3, CH4, NH3, H2O, and HF molecular systems and their deuterated counterparts were analyzed using the second-order Møller-Plesset (MP2) level of theory of the multicomponent molecular orbital (MCMO-MP2) method. This method can simultaneously determine both nuclear and electronic wave functions. Results showed that the average α value (αave) of the optimized α in single s-type ([1s]) GTF for a proton and a deuteron is similar to that determined using the Hartree-Fock level of the MCMO (MCMO-HF) method. In contrast, due to the electron-nucleus correlation effect, the s- and p-type ([1s1p]) GTFs are delocalized compared with those determined using the MCMO-HF method. For the H-bonded complexes, differences in the interaction energy induced by the H/D isotope effect were clearly evident because the DY bond distance for D complex is longer than the HY for H complex. Also, the basis set superposition error for the interaction energy in every H complex was similar to that in every D complex. The results here clearly demonstrate that the protonic and deuteronic basis functions based on αave values for correlation effects can be applied to the detailed analysis of the quantum effects of protons and the H/D isotope effect in widespread fields that involve H bonds and weak interactions, such as the function of biological molecules, chemical reaction processes, and the design of new materials.

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