Potential-energy curve for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>a</mml:mi><mml:msup><mml:mspace width="0.16em"/><mml:mn>3</mml:mn></mml:msup><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi>u</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math> state of a lithium dimer with Slater-type orbitals
Michał Lesiuk, Monika Musiał, Robert Moszyński
Abstract
We report state-of-the-art ab initio calculations of the potential energy curve for the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$ state of the lithium dimer, conducted to achieve spectroscopic accuracy ($<1\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$) without any prior adjustment to fit the corresponding experimental data. The nonrelativistic clamped-nuclei component of the interaction energy is calculated with a composite method involving a six-electron coupled cluster and full configuration interaction theories combined with basis sets of Slater-type orbitals ranging in quality from double to sextuple zeta. We additionally include both the leading-order relativistic and adiabatic corrections, and find both of these effects to be non-negligible within the present accuracy standards. The potential energy curve developed by us allowed us to calculate molecular parameters (${D}_{e}, {D}_{0}, {\ensuremath{\omega}}_{e}$, etc.) for this system, as well as the corresponding vibrational energy levels, with an error of only about $0.2--0.4 {\mathrm{cm}}^{\ensuremath{-}1}$. We also report an ab initio value for the scattering length of two $^{2}S$ lithium atoms.