Based on the idea of molecular orbital (MO) propagation, we propose a novel effective method for predicting initial guesses for the self-consistent-field calculations in direct ab initio molecular dynamics (AIMD) simulations. This method, called LIMO, adopts the Lagrange interpolation (LI) polynomial technique and predicts initial MO coefficients at the next AIMD step by using several previous results. Taking into account the crossing and/or mixing of MOs leads to orbital invariant formulas for the LIMO method. We also propose a simple method for determining the optimal degree of the LI polynomial, which corresponds to the number of previous steps. Numerical tests confirm that this proposed method is both effective and feasible.
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