The ground state estimation by global optimization of an effective potential. Application to binary...

It is demonstrated how the problem of ground state estimation of an n-body system can be recast as the less demanding problem of finding the global minimum of an effective potential in the 3n-dimensional coordinate space. The latter emerges when the solution of the imaginary-time Schrödinger equation is approximated by a variational Gaussian wavepacket (VGW). The VGW becomes stationary in the infinite-imaginary-time limit. Such a stationary solution is not only exact for a harmonic potential, but it also provides a good approximation for a quantum state that is still localized in one of the basins of attraction, when, for example, the harmonic approximation may fail. The landscape of the effective potential is favorable for its global optimization, and is particularly suitable for optimization by GMIN, an open source program designed for global optimization using the basin-hopping algorithm. Consequently, the methodology is applied within GMIN to estimate the ground state structures of several binary para-H(2)/ortho-D(2) molecular clusters. The results are generally consistent with the previous observations for homogeneous para-H(2) and ortho-D(2) clusters, as well as for smaller binary clusters.