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--- exercises:common:neb [2022/09/08 15:23] – jglan
+++ exercises:common:neb [2022/09/08 21:16] – jglan
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 ====== Nudged elastic band======
-This exercise is adopted from [[exercises:2019_uzh_acpc2:ex03 | here ]], which is initially created by Kristjan Eimre and Jinggang Lan
+Regtest see: [[https://github.com/cp2k/cp2k/tree/master/tests/NEB|cp2k/tests/NEB/]]
+Manual see: [[https://manual.cp2k.org/cp2k-2022_1-branch/CP2K_INPUT/MOTION/BAND.html | %MOTION%BAND]]
+Reference:
+[[https://aip.scitation.org/doi/10.1063/1.1323224 | J. Chem. Phys. 113, 9978 (2000)]] for IT-NEB;
+[[https://aip.scitation.org/doi/10.1063/1.1329672 | J. Chem. Phys. 113, 9901 (2000)]] for CI-NEB
 ===== Introduction =====
+Consider a potential energy surface (PES) as below, the goal is to find the saddle point, transition structure between reactant and prodcut. The commonly-used algorithms include [[https://manual.cp2k.org/cp2k-2022_1-branch/CP2K_INPUT/MOTION/BAND.html|NEB]],[[https://manual.cp2k.org/cp2k-2022_1-branch/CP2K_INPUT/MOTION/GEO_OPT/TRANSITION_STATE.html|DIMER]] etc
+{{:exercises:common:pes.jpg?400|}}
+<note>Maxima or Saddle Points (maximum in one direction but minimum in other directions) have one or more negative (imaginary) frequencies.
+</note>
+Mathematically, the saddle point should fulfill the requirements:
+. The gradient should be zero, $\frac{dE}{dr} = 0 $
+. The sign of Hessian should be negative,  $\frac{d^2E}{dr^2} < 0 $
+. Only ONE negative (imaginary) frequency
 ===== Exercies =====