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In order to increase the accuracy of the linearized augmented plane wavemethod (LAPW) we present a new approach where the plane wave basis function isaugmented by two different atomic radial components constructed at twodifferent linearization energies corresponding to two different electron bands(or energy windows). We demonstrate that this case can be reduced to thestandard treatment within the LAPW paradigm where the usual basis set isenriched by the basis functions of the tight binding type, which go to zerowith zero derivative at the sphere boundary. We show that the task is closelyrelated with the problem of extended core states which is currently solved byapplying the LAPW method with local orbitals (LAPW+LO). In comparison withLAPW+LO, the number of supplemented basis functions in our approach is doubled,which opens up a new channel for the extension of the LAPW and LAPW+LO basissets. The appearance of new supplemented basis functions absent in the LAPW+LOtreatment is closely related with the existence of the $\dot{u}_l-$component inthe canonical LAPW method. We discuss properties of additional tight bindingbasis functions and apply the extended basis set for computation of electronenergy bands of lanthanum (face and body centered structures) and hexagonalclose packed lattice of cadmium. We demonstrate that the new treatment giveslower total energies in comparison with both canonical LAPW and LAPW+LO, withthe energy difference more pronounced for intermediate and poor LAPW basissets.

Extension of the basis set of linearized augmented plane wave method (LAPW) by using supplemented tight binding basis functions