QC/MM

pDynamo is a powerful computational chemistry package that offers a range of capabilities for quantum chemistry and molecular simulations. One of its notable features is the seamless incorporation of QC/MM (Quantum Chemistry / Molecular Mechanics) potentials. QCMM potentials in pDynamo allow for the combination of quantum mechanical and classical mechanical treatments within the same simulation. This integration enables the study of complex systems where both accurate electronic structure calculations and efficient classical force field models are required. This approach divides the system into two regions: a quantum region, where the electronic structure is explicitly treated using methods such as density functional theory (DFT) or wavefunction-based methods, and a classical region, where a force field is employed to describe the interactions (Figure 1). The general Hamiltonian of the system is constructed by considering the sum of three terms.

The first term accounts for the interactions within the quantum region. It describes the behavior of the quantum mechanical entities, such as electrons and their interactions with each other and with the atomic nuclei in the quantum region. This term is typically derived from quantum mechanical principles and equations. In this case, the specific form of the quantum mechanical Hamiltonian depends on the chosen level of theory and the electronic structure method being employed. 

The second term represents the interactions within the classical region. It captures the classical mechanical interactions between atoms, such as bond stretching, angle bending, and non-bonded interactions like van der Waals and electrostatic forces. Classical force field models are used to describe these interactions, and empirical parameters are employed to approximate their behavior.

The third term is the bridge that connects the quantum and classical regions, forming the hybrid system. This term incorporates the interactions between the two regions. It includes contributions such as the interaction of the electrons in the quantum region with the partial charges of the atoms in the classical region. This term allows for the polarization effect, where the force field charges exert an influence on the quantum region. Additionally, it encompasses other interactions of a purely classical nature, such as the Coulombic interactions between the nuclei of the quantum region and the partial charges of the classical region, as well as the Lennard Jones type interactions between the atoms of the quantum region and the atoms of the classical region.

Finally, it is worth mentioning that the only classical parameters that need to be assigned to atoms in the quantum region are those for calculating Lennard-Jones type interactions. These parameters are used exclusively in the hybrid part of the Hamiltonian and play a crucial practical role, especially in simulations involving changes in the system’s coordinates. The Lennard-Jones interactions prevent the quantum and classical regions from collapsing into each other.

By combining these terms, the overall Hamiltonian in the QC/MM framework effectively captures the behavior of both the quantum and classical regions, enabling a comprehensive description of the hybrid system.