Ab initio determination of a rather accurate force constant for a given wave function

Abstract

In this research, an attempt has been made to modify present methods of force constant calculation to have a rather simple and accurate procedure in order to check the accuracy of a given ab initio wave function. After a brief survey of literature, it is found that at neighborhood of equilibrium the bottom of potential surface, which is potential curve in two-dimensional space, is not exactly quadratic, in spite of its appearance, which looks like parabola. Nth degree polynomial must be fitted to different points of potential curve, which are obtained by an ab initio total energy calculation. The obtained polynomial is the best potential for a given ab initio wave function, and can predict a rather accurate force constant and bond length belonging to the corresponding wave function. It is also found that a particular n-degree polynomial cannot be generalized and used for any molecule. Additionally, in order to reduce the percentage of error in evaluation of force constant, it has been demonstrated that the selection of basis set is important. The force constant for diatomic molecules such as H2, LiH and BH obtained by FSGO wave functions are 6.189mdyne/Å (7.22%), 1.063mdyne/Å (3.61%) and 3.189mdyne/Å (4.77%), respectively. While the corresponding values calculated by using total energies obtained by SCF wave function for basis set RHF/6-311G∗∗ are 6.283mdyne/Å (8.71%), 1.061mdyne/Å (3.04%) and 3.359mdyne/Å (10.35%), respectively. These values are also compared with those of gaussian 98 program (Pople's package), which are 12.55mdyne/Å (117.13%), 1.361mdyne/Å (32.70%) and 3.971mdyne/Å (30.45%), respectively. The method is used for determination of krr and kθθ of H2O, when the FSGO method is used: they are 7.98mdyne/Å (−5.56%) and 1.30mdyne/Å (70.13%), respectively, and when gaussian 98 package is used: they are 9.76mdyne/Å (15.52%) and 2.79mdyne/Å (267.0%), respectively. Our method is also compared with the force method (Pulay). It is demonstrated that the proposed method gives less error for non-exact wave functions than those of force method. Then it can be applied for both exact and non-exact wave functions.