Potential energy optimization

Schlegel H B 1995 Geometry optimization on potential energy surfaces Modern Electronic Structure Theory vo 2, ed D R Yarkony (Singapore World Scientific) pp 459-500... 

Keywords, protein folding, tertiary structure, potential energy surface, global optimization, empirical potential, residue potential, surface potential, parameter estimation, density estimation, cluster analysis, quadratic programming... 

Fig. 1. Optimization of the Onsager-Machlup action for the two dimensional harmonic oscillator. The potential energy is U(x,y) = 25i/ ), the mass is 1...

To carry out ageometry optimization (minimi/atioiT), IlyperCh em starts with a set of Cartesian coordinates for a molecule and tries to find anew set of coordinates with a minimum potential energy. Yon should appreciate that the potential energy surface is very complex, even for a molecule containing only a few dihedral an gles. 

Th c Newton-Raph son block dingotial method is a second order optim izer. It calculates both the first and second derivatives of potential energy with respect to Cartesian coordinates. I hese derivatives provide information ahont both the slope and curvature of lh e poten tial en ergy surface, Un like a full Newton -Raph son method, the block diagonal algorilh m calculates the second derivative matrix for one atom at a lime, avoiding the second derivatives with respect to two atoms. 

One cannot simply optimi/e the position of each atom in sequence and say the job is done. Any change in an atomic position brings about a small change in the forces on all the other atoms. Optimization has to be repeated until the lowest rnoleeular potential energy is found that satisfies all the forees on all the atoms. The final location of an atom will, in general, be at a position that is some small distance from the position it would have if it were not influenced by the other atoms in the molecule. 

Variational transition state theory (VTST) is formulated around a variational theorem, which allows the optimization of a hypersurface (points on the potential energy surface) that is the elfective point of no return for reactions. This hypersurface is not necessarily through the saddle point. Assuming that molecules react without a reverse reaction once they have passed this surface... 

To calculate the properties of a molecule, you need to generate a well-defined structure. A calculation often requires a structure that represents a minimum on a potential energy surface. HyperChem contains several geometry optimizers to do this. You can then calculate single point properties of a molecule or use the optimized structure as a starting point for subsequent calculations, such as molecular dynamics simulations. 

Transition state search algorithms rather climb up the potential energy surface, unlike geometry optimization routines where an energy minimum is searched for. The characterization of even a simple reaction potential surface may result in location of more than one transition structure, and is likely to require many more individual calculations than are necessary to obtain equilibrium geometries for either reactant or product. 

Once HyperChem calculates potential energy, it can obtain all of the forces on the nuclei at negligible additional expense. This allows for rapid optimization of equilibrium and transition-state geometries and the possibility of computing force constants, vibrational modes, and molecular dynamics trajectories. 

HyperChem can calculate geometry optimizations (minimizations) with either molecular or quantum mechanical methods. Geometry optimizations find the coordinates of a molecular structure that represent a potential energy minimum. 

For a potential energy V and Cartesian coordinates rj, the optimized coordinates satisfy this equation ... 

Characterize a potential energy minimum. Ageometry optimization results in anew structure at a minimum. You can examine atomic coordinates and energy of this structure. 

Overcome potential energy barriers and force a molecule into a lower energy conformation than the one you might obtain using geometry optimization alone. 

---