Molecular Structures from Density Functional Calculations with Simulated Annealing

The geometrical structure of any aggregate of atoms is one of its basic properties and, in principle, straightforward to predict. One chooses a structure, determines the total energy E of the system of electrons and ions, and repeats the calculation for all possible geometries. The ground state structure is that with the lowest energy. A quantum mechanical calculation of the exact wave function Ψ would lead to the total energy, but this is practicable only in very small molecules. Furthermore, the number of local minima in the energy surface increases dramatically with increasing molecular size. While traditional ab initio methods have had many impressive successes, these difficulties have meant that they have focused on systems with relatively few local minima, or have used experiment or experience to limit the range of geometries studied. On the other hand, calculations for much larger molecules and extended systems are often forced to use simplifying assumptions about the interatomic forces that limit their predictive capability. The approach described here avoids both of these extremes: Total energies of predictive value are calculated without using semi‐empirical force laws, and the problem of multiple minima in the energy surface is addressed. The density functional formalism, with a local density approximation for the exchange‐correlation energy, allows one to calculate the total energy for a given geometry in an efficient, if approximate, manner. Calculations for heavier elements are not significantly more difficult than for those in the first row and provide an ideal way to study bonding trends. When coupled with finite‐temperature molecular dynamics, this formalism can avoid many of the energetically unfavorable minima in the energy surface. We show here that the method leads to surprising and exciting results.