quemb.molbe.eri_sparse_DF.approx_S_abs¶
- quemb.molbe.eri_sparse_DF.approx_S_abs(mol, nroots=500)¶
Compute the approximated absolute overlap matrix.
The calculation is only exact for uncontracted, cartesian basis functions. Since the absolute value is not a linear function, the value after contraction and/or transformation to spherical-harmonics is approximated via the RHS of the triangle inequality:
\[\int |\phi_i(\mathbf{r})| \, |\phi_j(\mathbf{r})| \, d\mathbf{r} \leq \sum_{\alpha,\beta} |c_{\alpha i}| \, |c_{\beta j}| \int |\chi_\alpha(\mathbf{r})| \, |\chi_\beta(\mathbf{r})| \, d\mathbf{r}\]