md2011-06-note_Part_5

md2011-06-note_Part_5 - In contrast to Ehrenfest MD, now...

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I In contrast to Ehrenfest MD, now the minimum of h H e i must be reached in each time step, for instance by diagonalizing the Hamiltonian. I It is possible to consider also a certain excited state Ψ k , k > 0 within the Born-Oppenheimer method, but without any interferences with other states (because of the zero coupling operator C kl ). I Early adaptations of Born-Oppenheimer MD were semi-empirical [J. Am. Chem. Soc. 95, 8160–8164 (1973)] , [Chem. Phys. Lett. 32, 11 (1975)] , but an ab initio approach emerged soon [J. Chem. Phys. 68, 4406–4410 (1976)] . Notes
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O± ²³´ Eµµ¶·¶´±·¸ ¹µ AIMD M´²³¹º» I The Ehrenfest method requires a short time step due to electron dynamics, whereas Born-Oppenheimer method can use a time step based on much slower motion of the nuclei. I On the other hand, in the case of BOMD, one needs to solve the electronic structure problem self-consistently after each time step. I In the Ehrenfest method, this is not required due to the propagating electronic wave function. I
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md2011-06-note_Part_5 - In contrast to Ehrenfest MD, now...

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