Knowledge Bank

We present an accurate 12-D basis set calculation of the lowest 100 energy levels of the C$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$H$\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$ molecule. A Smolyak non-product quadrature grid, a pruned product basis set, and the Lanczos algorithm are used. This scheme allows one to reduce the size of the basis set by almost 7 orders of magnitude (from $9\times 1012$ to $1.3\times 106$) and the size of the quadrature grid by almost 6 orders of magnitude (from 5.6$\times 1013$ to $1.52\times 108$). Basis pruning and the nonproduct quadrature grid therefore enable us to solve a problem, numerically exactly, that would be impossible without these tools.