QM/MM with Auxiliary DFT

International audience; This chapter describes the theoretical background of the quantum mechanical/molecular mechanical (QM/MM) implementation in deMon2k within the framework of auxiliary density functional theory (ADFT). It aims to give the reader an overview of the current state of the art of this QM/MM implementation and perspectives for its future development. To this end, we first derive the ADFT working equations for the QM and QM/MM energy and gradient expressions. Based on the joint QM/MM gradient expression, we present algorithms for QM/MM structure optimizations, transition-state searches and molecular dynamics simulations. The use of auxiliary density perturbation theory (ADPT) in the framework of QM/MM is discussed using illustrative implementations including analytic second-order ADFT energy derivatives, nuclear magnetic resonance chemical shift calculations and excited state calculations using time-dependent ADFT. The chapter closes with the description of a transformation program used to generate deMon2k QM/MM inputs.