Application of the Gaussian Time-Dependent Hartree Method to the Study of the Ground State of Neon Clusters
The ground state properties of neon clusters are studied through the Gaussian Time-Dependent Hartree (G-TDH) method. The presence of significant quantum effects in these systems poses a significant challenge to its theoretical investigation, because it drastically reduces the number of atoms that can be simulated in a computer. The application of the G-TDH method alleviates this difficulty, and it allows to study the ground state properties as a function of cluster size without neglecting the quantum effects. The method is based on the construction of an approximate wavefunction for the whole system, consisting in a Hartree product of normalized single-particle wavepackets of Gaussian shape. These Gaussian functions are characterized by their widths, and their centroids in position and momentum spaces. Using the Dirac-Frenkel-McLachlan variational principle and the imaginary-time propagation technique, we obtain the equations of motion that describe how these parameters approach the values that better describe the ground state of the system, and they enable to synthesize the system wavefunction of the system and to compute the structural and energetic properties of the cluster in the ground state.
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