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A generalization of the local density approximation (LDA) method for systems with strong Coulomb correlations is described which gives a correct description of the Mott insulators. The LDA+U method takes into account orbital dependence of the Coulomb and exchange interactions which is absent in the LDA. The scheme can be regarded as a `first-principles' method because there are no adjustable parameters. When applied to the transition metal and rare-earth metal compounds, the LDA+U method gives a qualitative improvement compared with the LDA not only for excited-state properties such as energy gaps but also for ground-state properties such as magnetic moments and interatomic exchange parameters. The orbital-dependent rotationally invariant LDA+U potential gives a correct orbital polarization and a corresponding Jahn - Teller distortion as well as polaron formation.

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A recently developed dynamical mean-field theory in the iterated perturbation theory approximation was used as a basis for construction of the "first principles" calculation scheme for investigating electronic structure of strongly correlated electron systems. This scheme is based on Local Density Approximation (LDA) in the framework of the Linearized Muffin-Tin-Orbitals (LMTO) method. The classical example of the doped Mott-insulator La1−xSrxTiO3 was studied by the new method and the results showed qualitative improvement in agreement with experimental photoemission spectra.