SAIP2026

Calculation of the Ground State Energy of the Hydrogen Molecular Ion H2+ using a basis set derived from a shifted and scaled wavelet scaling function as basis set

7 Jul 2026, 15:20

20m

Lecture Hall DL2 (University of the Western Cape)

Oral Presentation Track G - Theoretical and Computational Physics Theoretical and Computational Physics

Speaker

Obiageli Ezenwachukwu (University of South Africa (UNISA))

Description

We use three dimensional basis functions based on a shifted and scaled Daubechies wavelet scaling function[1]
\begin{equation}
f_i(x)=\phi\left( x/h+x_{\rm max} /h -i\right)/\sqrt{h}\,.
\end{equation}
From the equation above, $h=x_{\rm max}/N$, $h$ is also the distance between the scaling functions, and $N$ is the number of intervals from the origin to $x_{\rm max}$. However, the modification of the basis functions was necessary to satisfy periodic boundary conditions in order to improve convergence.

This basis set is used to solve the three-dimensional Schr\"odinger equation in the box
$$[-x_{\rm max}:x_{\rm max}] \times [-x_{\rm max}:x_{\rm max}] \times [-x_{\rm max}:x_{\rm max}] \,.$$ We present the results of a calculation of the ground state energy of the hydrogen molecular ion $H_2^+$ as function of the
discretisation parameters. The matrix elements are evaluated with three dimensional repeated Gauss Legendre Integration.

Reasonable convergence is found. The energy values obtained are close to the literature values. In future, we will consider its possible application to calculating the properties of molecules using the density functional approach.

References

[1] Daubechies,I.(1988). Orthonormal bases of compactly supported wavelets.
Communications on Pure and Applied Mathematics, 41(7), 909-
996.

Presentation materials

19_Obiageli_Ezenwachukwu.pdf