Benchmark calculations of the ² D Rydberg spectrum of lithium

The recently implemented algorithm for calculating the leading relativistic corrections for D states of an atom with an arbitrary number of electrons is used to perform calculations of the lowest eleven (Formula presented.) Rydberg states of lithium. The corrections are obtained as expectation values of the corresponding relativistic operators with the non-relativistic wave functions expanded in terms of all-electron explicitly correlated Gaussian (ECG) functions. The wave functions are generated using the standard variational method and the finite-nuclear-mass (FNM) approach. The non-linear parameters of the ECGs are variationally optimised using a algorithm that employs the analytical energy gradient determined with respect to these parameters. Infinite-nuclear-mass calculations are also performed. The calculated FNM state energies for (Formula presented.) Li and (Formula presented.) Li are used to calculate isotopic shifts of the inter-state transition energies. The calculated interstate transitions are in good agreement with the high-quality experimental results.