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k center dot p formula for use with linearized augmented plane waves

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We provide k center dot p formalism within the full-potential linearized augmented plane-wave (LAPW) method. Unlike the pure plane waves, the LAPW functions do not behave trivially in moving from k to k+q and their incompleteness as a basis set should be taken into account. Derivatives of the sphere matching coefficients play the key role, for which we find a simple formula. Concrete formula for the k center dot p matrix elements is derived and numerically tested. Generalized second-order perturbation theory allowing for a degenerate case is presented and the literally exact electronic band gradients and curvatures are accessible.

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