Analysis of exponent values in Gaussian‐type functions for development of protonic and deuteronic basis functions

We analyzed the exponent (α) values in Gaussian‐type functions (GTF) for protons and deuterons in BH 3 , CH 4 , NH 3 , H 2 O, HF, and their deuterated molecules for the development of nuclear basis functions, which are used for molecular orbital (MO) calculations that directly include nuclear quantum effects. The optimized α (α opt ) value in the single s‐ type ([1 s ]) GTF for protons is changed due to the difference in flexibility of the electronic basis sets. The difference between the energy obtained by using the α opt value for each molecule and that obtained by using the average α (α ave ) value for these exponents with the 6‐31G( d,p ) electronic basis function is only 2 × 10 −5 a.u. The α ave values of protonic and deuteronic [1 s ] GTFs by the present calculation are 24.1825 and 35.6214, respectively. We found that the α ave values enable the evaluation of the total energy and the geometrical changes in hydrogen bonding, such as O…HO, O…HN, and O…HC, while the α opt value became small by forming a hydrogen bond. The result using only the [1 s ] GTF for the protonic and deuteronic basis functions is sufficient to explain the differences of energy and geometry induced by the H/D isotope effect, although the total energy of ∼5 × 10 −4 a.u. was improved by using the s‐, p‐, and d‐ type ([1 s 1 p 1 d ]) GTFs for protons and deuterons. We clearly demonstrate that the protonic and deuteronic basis functions based on the α ave value enable us to apply the method to other sample molecules (glycine, malonaldehyde, and formic acid dimer). The protonic and deuteronic basis functions we developed treat the quantum effects of protons and deuterons effectively and extend the application range of the MO calculation to include nuclear quantum effects. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006