The isotope effect induced by deuterium substituted species is observed in molecular properties, such as geometry, kinetics, and electronic state, of the molecules through nuclear-electron interaction. Theoretical considerations and experimental alignments have been studied by ab initio molecular orbital, density functional theory, and other empirical strategies. The Born-Oppenheimer approximation with nuclear vibrational wavefunction can treat isotope effect because nuclear mass effect account for the average distance of vibrational motion. In this study, we introduce Morse anharmonic oscillator model to calculate average internuclear distance of diatomic molecules having X-H bonding and X-D bonding. Morse parameters are determined by fitting to potential energy surface of molecular orbital and/or density functional calculations, and then the average distance are obtained as the expectation value of the analytical Morse vibrational wavefunction. Nuclear magnetic resonance shielding constants of the H/D isotopomer are calculated again on the average distance by using GIAO with B3LYP and CCSD calculation. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010
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