Simulated annealing with floating Gaussians: Hellmann-Feynman forces without corrections

An all-electron density-functional-based molecular-dynamical algorithm for static and dynamic studies of atomic clusters is formulated and discussed. A time-dependent fictitious Lagrangian that depends on both the classical nuclear positions as well as the quantum-mechanical electronic variational parameters is introduced. By integrating the resulting equations of motion, the static ground state of a many-electron and -nuclei system may be found. A floating Gaussian formulation is introduced, and we demonstrate that, by allowing the nonlinear Gaussian parameters and positions to vary so as to minimize the total energy, the Pulay corrections to the Hellmann-Feynman force vanish. Further advantages of this method over conventional diagonalization schemes are that it allows for a compact self-optimizing basis set and that the algorithm is not susceptible to numerical instabilities when nearly, or exact, linear dependencies are encountered. By expanding the electronic wave functions in terms of floating s-type Gaussian orbitals, the method is illustrated with applications to the ${\mathrm{Li}}_2$ molecule and the Ne atom. Results are in excellent agreement with other theoretical results and experiments.