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Do you know what a potential energy surface (PES) is? What is its secret?
Potential Energy Surface (PES) is well-known and important in computational chemistry. It describes the relationship between the potential energy of a molecular system (such as a collection of atoms) and its geometric structure. The secret of this surface is that it can reveal the potential pathways of molecular reactions and help scientists understand and predict the kinetic and thermodynamic behavior of chemical reactions.
Understanding PES will help us find stable molecular structures and transition states during reaction studies.
Definition of Potential Energy Surface
The potential energy surface is an energy function determined by the atomic interaction forces within a molecule. It describes the potential energy of a molecular system under different geometric structures. Each point represents a specific geometric structure and its corresponding energy. On this surface, local minima usually correspond to stable structures of the molecule, while saddle points or transition states are key points during the reaction process.
The process of geometry optimization
Geometry optimization is the process of finding the geometry that minimizes the energy on the PES. This process is not only applicable to single molecules, but also to ions, condensed matter, and reaction transition states. The goal of geometry optimization is to obtain close to zero forces and reach a stationary point on the PES.
When performing the geometry optimization of the water molecule, we aimed to obtain the hydrogen-oxygen bond lengths and hydrogen-oxygen-hydrogen angles in order to minimize the forces.
Searching for transition states
In many chemical reactions, the transition state is key to the reaction kinetics, which corresponds to the saddle point on the PES. Finding the transition state can be achieved by different methods, including local methods and semi-global methods. These methods can help chemists understand the energy changes in the reaction process and further explore the reaction mechanism.
Optimization methods in practice
In the practice of geometric optimization, the choice of algorithm is crucial. For most practical systems, computing the Hessian matrix is too expensive, so it is usually estimated based on the calculated gradient parameters. Additionally, choosing the right coordinate system (e.g., internal versus Cartesian) can significantly impact the success and efficiency of the optimization.
Many modern computational chemistry software packages include routines for automatically generating reasonable coordinate systems for optimizing calculations.
Comparison of vertical and horizontal optimization
Geometry optimization is different from molecular dynamics simulations. The latter simulates the movement of molecules in time and is affected by temperature and chemical forces. However, the main purpose of geometry optimization is to minimize the forces acting on atoms, so often the same minimum energy structure is obtained on different optimization paths, but there is no physically meaningful trajectory.
Future Research Directions
With the continuous development of computational chemistry technology, the study of potential energy surfaces will become a continuous hot topic. Whether it is to derive new materials from existing molecular structures or to deeply understand the details of molecular reactions, PES can provide indispensable information support. How exactly does the so-called chemical reaction mechanism unfold on this surface?
