The discrete variational method and embedded-cluster model within the framework of the two-component density functional theory and firstprinciple method are used to calculate the positron states of monovacancy in aluminum. The effect of the crystal field in which the cluster is embedded, magnitude of the cluster and frozen-core density approximation on the distribution of positron density and the positron annihilation characteristics are analyzed. The influence of the fully self-consistent scheme and the conventional scheme on the calculation of positron states in solids is discussed.