Relativistic basis sets of double-zeta, triplezeta, and quadruple-zeta quality have been optimized for the lanthanide elements La-Lu. The basis sets include SCF exponents for the occupied spinors and for the 6p shell, exponents of correlating functions for the valence shells (4f, 5d and 6s) and the outer core shells (4d, 5s and 5p), and diffuse functions, including functions for dipole polarization of the 4f shell. A finite nuclear size was used in all optimizations. The basis sets are illustrated by calculations on YbF. Prescriptions are given for constructing contracted basis sets. The basis sets are available as an internet archive and from the Dirac program web site, http://dirac.chem.sdu.dk.The increasing use of all-electron four-component methodology for relativistic effects in molecular structure calculations brings with it a need for high-quality basis sets. Several other authors have generated basis sets at the SCF level for part or all of the periodic table, either with the Dirac Hamiltonian or with the Douglas-Kroll-Hess Hamiltonian [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. While some of these basis sets include correlating functions, a number of them lack the functions needed for valence and outer core correlation and polarization of the SCF sets. In a series of papers [20][21][22][23][24][25][26][27], Dyall has focused on providing consistent basis sets of doublezeta (dz), triple-zeta (tz), and quadruple-zeta (qz) quality for the heavy elements, including correlating functions for the valence and outer core orbitals in the style of the correlation consistent basis sets [28][29][30][31]. So far these basis sets have covered the 4s, 5s, 6s, and 7s blocks; the 4p, 5p, and 6p blocks; the 4d and 5d transition series; and the actinides. This paper continues the series by presenting basis sets for the lanthanides. Work is in progress on the 3d and 6d transition series and the 7p block.The lanthanides have similar challenges to the actinides, but also have some unique features, as far as basis sets are concerned. As for the actinides, the 5d orbital is occupied for several members of the series (La, Ce, Gd, and Lu), and is low-lying for many of the early members of the series. It is in fact doubly occupied in some excited states early in the series. It must therefore be included in the basis set Electronic supplementary material The online version of this article (doi:10.1007/s00214-009-0725-7) contains supplementary material, which is available to authorized users.