Structures

About

Structure optimization in the context of Density Functional Theory (DFT) is a computational process used to find the most stable (lowest energy) configuration of a molecule or material. This process involves adjusting the positions of the atoms within the system to minimize the total energy, resulting in the most stable arrangement of atoms, which corresponds to the ground-state structure.

1. Basics of Density Functional Theory (DFT)

• DFT is a quantum mechanical method used to study the electronic structure of many-body systems, particularly atoms, molecules, and solids. Instead of solving the Schrödinger equation for the wavefunction, DFT focuses on the electron density as the central quantity.

• The total energy of a system in DFT is expressed as a functional of the electron density, which includes contributions from the kinetic energy of electrons, the potential energy due to nuclei, and electron-electron interactions.

2. Objective of Structure Optimization

The goal of structure optimization is to find the arrangement of atoms that corresponds to the minimum energy of the system. This minimum energy structure is the most stable form of the molecule or material under the given conditions (e.g., at zero temperature).

3. Steps in Structure Optimization

1. Initial Guess:

   • The process begins with an initial guess of the atomic positions. This guess could be based on experimental data, chemical intuition, or a previous calculation.

2. Calculation of Forces:

   • DFT calculations are performed to compute the forces acting on each atom. The force on an atom is related to the gradient of the total energy with respect to its position.

   • If the forces are non-zero, it indicates that the atoms are not in their most stable configuration.

3. Update of Atomic Positions:

   • The atomic positions are then updated based on the calculated forces. Various algorithms, such as steepest descent, conjugate gradient, or more sophisticated methods like Broyden–Fletcher–Goldfarb–Shanno (BFGS), can be used to move the atoms in the direction that reduces the forces (and thus the total energy).

4. Iteration:

   • The process of calculating forces and updating atomic positions is repeated iteratively. With each iteration, the system's total energy typically decreases as the atoms move closer to their optimal positions.

5. Convergence:

   • The optimization process continues until convergence criteria are met. These criteria usually include thresholds for the maximum force on any atom (which should approach zero) and changes in the total energy between iterations (which should become negligible).

   • At convergence, the structure is considered optimized, meaning the atoms are in a configuration where the forces on them are minimized, and the system is at its lowest possible energy.

4. Challenges and Considerations

• Local vs. Global Minima:

  • The optimization process may converge to a local minimum (a stable but not the lowest possible energy state). To find the global minimum (the true ground-state structure), multiple optimizations from different initial guesses might be required.

• Accuracy of the DFT Functional:

  • The choice of the exchange-correlation functional in DFT (such as LDA, GGA, or hybrid functionals) affects the accuracy of the optimization. Some functionals may better describe certain types of interactions (e.g., van der Waals forces), influencing the final optimized structure.

• Computational Cost:

  • Structure optimization can be computationally demanding, especially for large systems or complex potential energy surfaces. The number of iterations required for convergence and the computational cost of each DFT calculation contribute to the overall time required.

• Constraints:

  • In some cases, constraints may be applied during optimization (e.g., fixing certain bond lengths or angles) to explore specific configurations or to simulate certain physical conditions.

5. Applications of Structure Optimization in DFT

• Molecular Structure Determination: Finding the equilibrium geometries of molecules, including bond lengths, bond angles, and dihedral angles.

• Material Science: Optimizing the crystal structure of solids, surfaces, and interfaces to study their properties.

• Reaction Mechanisms: Determining transition states and intermediates by optimizing structures along reaction pathways.

• Nanotechnology: Optimizing the structures of nanoparticles, nanotubes, and other nanoscale materials to study their properties.

Summary:

Structure optimization in DFT is a critical step in computational chemistry and material science, allowing researchers to find the most stable configuration of a system by minimizing the total energy. Through iterative calculations of forces and energy, the atomic positions are adjusted until the system reaches its ground-state structure, providing insights into the geometry and properties of molecules and materials.

Method

To achieve the structures present in PFAS Studio V, the following steps are taken:

1. Removal of salt ions from InChI structures

2. Generation of structure with ETKDGv3

3. Optimization of the structure with MFF

4. Optimization of the structure with GFN2-xTB

5. Remaining property calculations on the GFN2-xTB structure.

Find

The structure can be found on the home page of PFAS Studio