md2011-06-note_Part_3

Md2011-06-note_Part_ - I Note that this equation holds separately for each decoupled electronic state k I The nuclei move according to classical

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Unformatted text preview: I Note that this equation holds separately for each decoupled electronic state k . I The nuclei move according to classical machanics in an effective potential U BO k , which is given by the Born-Oppenheimer potential energy surface E k . I E k is obtained by solving simultaneously the time-independent electronic Schrödinger equation for the k th state at the given nuclear configuration { R l ( t ) } . I Because we now directly obtain the forces from the Born-Oppenheimer total energy E k , this approach is often called Born-Oppenheimer molecular dynamics . I Because the time-independent Schrödinger equation was utilized for the electronic system, this approach doesn’t maintain the quantum mechanical time evolution of the system. Notes I Another approach, which does maintain the QM time evolution, involves directly separating the total wave function Φ ( { r i } , { R I } ; t ) so that the classical limit can be imposed for the nuclei only....
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This note was uploaded on 02/14/2012 for the course CSE 6590 taught by Professor Kotakoski during the Winter '12 term at York University.

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Md2011-06-note_Part_ - I Note that this equation holds separately for each decoupled electronic state k I The nuclei move according to classical

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