Lec21 (2) - h b ( x ( t )) = 1 if system is in B, 0 if its...

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10.675 LECTURE 21 RICK RAJTER 1. Today Rate Constants TPS Commitor Probability Distribution Transition Path Harvesting Chandler-Bennet Formalism for Rate Constants Examples Molden 2. TPS Many Pathways Find a saddle point, drop from each side Approach Postulate q Compute probability distribution If successful, compute D If not, go back to postulating a new q Pick any pathway that connects A to B in time τ . Pick another via a monte carlo pathway in space. Shooting - Take a point along the path and perturb the momentum. p i δp i + p io Date : Fall 2004. 1
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2 RICK RAJTER Run it forward and backward to A and B within time τ Shifting - Take a path and shift it by Δ x and run again. Stochastic MD to create phase space. Z AB = K + ABτ Z A How does one choose τ ? It’s determined by the method you use, and it’s usually ¿ 1ps. It generally needs to be greater than the relaxation time. 3. Chandler-Bennett Formalism x(t) is a point in phase space (r,p) along a trajectory x at time t h a ( x ( t )) = 1 if system is in A, 0 if it’s not in A
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Unformatted text preview: h b ( x ( t )) = 1 if system is in B, 0 if its not in B h a ( x (0)) h b ( x ( t )) k ( t ) = h a ( x ( t )) Related to the rate at which system goes to B trxn e K A r 1 xn = k A B + K B A Since system is almost always in A or always in B, h a + h b 1 trxn For barriers < K b T , k(t) reaches a plateau because e 1 K A B = h a ( x (0)) h b ( x ( t )) h a ( x (0)) K ( t ) = ( t ) P ( x ( )) = ( t ) P ( L ) Where L is the length, P(L) is the probability v ( t ) = h b ( x ( )) AB K b T P ( L ) = e G Recall from TST G K T ST = K b T e K b T h K b T K = k b T e G h If G G q then = h v ( t ) k b T so, can pick any q, and if you calculate v(t), can back out real reaction rate. Compute v(t) from harvesting TP trajectories go from A to B h b AB So, need to (in practice) get to a constant slope very quickly...
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Lec21 (2) - h b ( x ( t )) = 1 if system is in B, 0 if its...

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