The Ehrenfest force in chemistry: a prospective model for mechanochemistry? Aldo de Jesús Mortera-Carbonell 1 , Evelio Franciscox 2 , Ángel Martín Pendás 2 and Jesús Hernández-Trujillo 1 1 National Autonomous University of Mexico, Mexico, 2 University of Oviedo, Spain The force concept in chemistry is important for the understanding of chemical processes. Particularly, mechanochemistry deals with the mechanical forces exerted on atoms or molecules that lead to chemical changes, an outstanding alternative to traditional methodologies. In order to model a force at the microscopic level, it is necessary to provide a solid definition of such force and the associated theoretical framework so that the correct physics for the system under study is obtained. This is the approach proposed in this work. The Ehrenfest force density is the electromagnetic force exerted on a volume element of the molecular electron density by the electrons and the nuclei of the whole system. The Feynman force, on the other hand, is defined as the electromagnetic force exerted on a nucleus by the rest of the particles. Both forces come from the corresponding quantum-mechanical theorems and are related to the energy of the system via the virial theorem 1 . The topology of the Ehrenfest force density and its integrated values over atomic regions defined by the Quantum Theory of Atoms in Molecules, provide valuable information regarding chemical phenomena 2-4 . Unfortunately, the presence of mathematical artifacts when the kinetic stress tensor is used to compute the Ehrenfest force vector field leads to doubtful results in regions far from the nuclei, complicating its applicability in chemistry 2 . The mechanics of formation of selected diatomic molecules in ground and excited electronic states is analyzed through the net Ehrenfest forces acting on the corresponding atoms, calculated using the Müller approximation to the pair density. Our results demonstrate that chemical bonding is the result of electron density accumulation between the nuclei as the atoms approach each other. Furthermore, there are no net repulsive forces exerted on the electron density at short range, being the system’s energy increase attributed to the Feynman internuclear force of repulsion. In addition, the topology of the Ehrenfest force density in real space for some benchmark systems is studied using the exact form of the pair density coming from highly-correlated multireference electronic structure methods. Overall, non-physical behavior or spurious points in the Ehrenfest force field are not obtained with this methodology, making it a promising tool for the study of molecular structure and its changes. We suggest that the Ehrenfest and Feynman forces could be integrated in a prospective model for the understanding of mechanochemistry at the molecular level. References 1. R. F. W. Bader, Atoms in Molecules: A Quantum Theory; Oxford University Press: Oxford, UK, 1990. 2. A. M. Pendás and J. Hernández-Trujillo, J. Chem. Phys. , 2012, 137 , 134101. 3. F. Cortés-Guzmán, G. Cuevas, A. M. Pendás and J. Hernández-Trujillo, Phys. Chem. Chem. Phys. , 2015, 17 , 19021. 4. J. Hernández-Trujillo, F. Cortés-Guzmán, D. Fang and R. F. W. Bader, Faraday Discuss. , 2007, 135 , 79.
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