# How to achieve Löwdin transformation?

I use Gaussian 09 to obtain the Hamiltonian and overlap matrices, $$H_0$$ and $$S_0,$$ where the B3LYP functional and the 6-31G basis set are adopted. Then how to transform the system to an orthogonal basis using Löwdin transformation?

\begin{align} H_1 &= S_0^{-\frac{1}{2}}H_0S_0^{-\frac{1}{2}} \\ H &= U^\dagger H_1U \end{align}

• Are you wondering how to perform Löwdin population analysis in Gaussian? Oct 7, 2019 at 14:20
• No, I just want to make an orthogonal transformation of the Hamiltonian matrix. Oct 8, 2019 at 8:12
• chemistry.stackexchange.com/questions/22124/… Oct 24, 2019 at 14:26