In this study, the effects of anisotropy and quantum dot size on energy levels and nonlinear optical rectification of a D_{2}^{ + } molecular complex confined to a two-dimensional quantum dot are investigated. The energy eigenvalues and corresponding eigenfunctions of the resulting eigenvalue equation are obtained using the adiabatic approach and the two-dimensional diagonalization method. We conclude that the evolution of the energy spectrum depends predominantly on the anisotropy-induced change of geometric confinement size. In addition, it has been determined that the peak position of the nonlinear optical rectification shifts to lower or higher energies as the asymmetry of the system increases, depending on whether the QD is in the oblate or prolate case. This feature can be considered an advantage in tuning the nonlinear optical properties of systems based on two-dimensional semiconductor heterostructures.
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