In the last decades, the investigation of electronic properties has become one of the most studied field in quantum chemistry. In this context, many different computational approaches have been developed to describe the properties of complex systems, characterized by a target molecule/chromophore embedded in an external environment. The computational strategies to include environmental effects are indeed valuable tools used to bridge the gap between theory and experiment.<br/>In this contribution, we face this problem by discussing the recent developments in the framework of multilevel quantum-embedding approaches, defined in the framework of both Hartree-Fock (HF) and Density Functional Theory (DFT). The methods are defined in the molecular orbital (MO) basis of the target system (the active fragment) only. This feature automatically allows for a saving in the computational cost, because the inactive MOs are not involved in the self consistent field (SCF) procedure. Such a feature is also exploited in the extension of the methods to the calculation of molecular properties. Here, we showcase the accuracy of the methods for selected test cases.

Describing complex systems with multilevel methods

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