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exercises:common:geo_opt [2022/09/08 15:07] – jglanexercises:common:geo_opt [2024/02/22 12:00] (current) – [Exercies] fnunes
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 ===== Introduction ===== ===== Introduction =====
  
-Geometry optimization is a process of changing the system's geometry (the nuclear coordinates and potentially the lattice vectors) to minimize the total energy of the systems.+**Geometry optimization** is a process of changing the system's geometry (the nuclear coordinates and potentially the lattice vectors) to minimize the total energy of the systems.  
 + 
 +**Potential energy surface** describes the energy of a system, especially a collection of atoms, in terms of certain parameters, normally the positions of the atoms. 
  
  
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 </note> </note>
  
-Gradient: the first derivative of the energy with 
-respect to geometry, also termed the 
-Force, $f = -\frac{dE}{dr}$. 
-Hessian:  the second derivative of the energy with respect to geometry, $\frac{d^2E}{dr^2}$ 
  
 Mathematically, the minimum should fulfill two requirements:  Mathematically, the minimum should fulfill two requirements: 
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 1. The gradient should be zero, $\frac{dE}{dr} = 0 $ 1. The gradient should be zero, $\frac{dE}{dr} = 0 $
  
-2. The sign of Hessian (second derivative) should be all positive,  $\frac{d^2E}{dr^2} > 0 $+2. The sign of Hessian should be all positive,  $\frac{d^2E}{dr^2} > 0 $ 
 + 
 +<note> 
 + 
 +**Gradient**: the first derivative of the energy with respect to geometry, also termed the 
 +Force, $f = -\frac{dE}{dr}$. 
 + 
 +**Hessian**: the second derivative of the energy with respect to geometry, $\frac{d^2E}{dr^2}$ 
 +</note>
  
 To ensure these requirements, one should perform [[exercises:common:vib| Vibrational Analysis]] to examine the eigenvalues of the Hessian. If there are some negative values, it means this point is not the minimum. To ensure these requirements, one should perform [[exercises:common:vib| Vibrational Analysis]] to examine the eigenvalues of the Hessian. If there are some negative values, it means this point is not the minimum.
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-===== Exercies =====+===== Exercises =====
  
 In this exercise, you will perform geometry optimization using DFT. See [[https://manual.cp2k.org/cp2k-2022_1-branch/CP2K_INPUT/MOTION/GEO_OPT.html|GEO_OPT]] In this exercise, you will perform geometry optimization using DFT. See [[https://manual.cp2k.org/cp2k-2022_1-branch/CP2K_INPUT/MOTION/GEO_OPT.html|GEO_OPT]]
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 </code> </code>
  
 +<code - H2O.xyz> 
 +3
 +Water
 +O 5 5.00000 5.11779
 +H 5 5.75545 4.52884
 +H 5 4.24455 4.52884
 +</code>
  
 You can also directly open an XYZ file in VMD to visualize it: You can also directly open an XYZ file in VMD to visualize it:
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 ===== Applications ===== ===== Applications =====
  
 +Geometry optimization has been widely used in surface science and computational catalysis. Based on electronic structure theory or force fields, the structures are optimized under 0 K to calculate the potential energy. To obtain the Gibbs free energy, one can use
 +$G = E_{DFT} + ZPE - TS$, where the latter two terms can be estimated by the [[exercises:common:vib| Vibrational Analysis]] . 
  
- +{{ :science:doi_10_1021_acscatal_5b00396_pub.png?direct&800 | Design of Lewis Pair-Functionalized Metal 
 +Organic Frameworks for CO_2 Hydrogenation}} 
 +Jingyun Ye & J. Karl Johnson; 2015; Design of Lewis Pair-Functionalized Metal 
 +Organic Frameworks for CO<sub>2</sub> Hydrogenation 
 +[[ doi>10.1021/acscatal.5b00396 | ACS Catal. 5: 2921−2928 ]]
  
exercises/common/geo_opt.1662649647.txt.gz · Last modified: 2022/09/08 15:07 by jglan