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exercises:common:geo_opt [2022/09/08 15:10] – 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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 The BFGS method is more efficient when the initial guess is not far from the minimum. The BFGS method is more efficient when the initial guess is not far from the minimum.
 </note> </note>
-<note> 
-**Potential energy surface**: the energy of a system, especially a collection of atoms, in terms of certain parameters, normally the positions of the atoms.  
  
 +
 +Mathematically, the minimum should fulfill two requirements: 
 +
 +1. The gradient should be zero, $\frac{dE}{dr} = 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 **Gradient**: the first derivative of the energy with respect to geometry, also termed the
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 **Hessian**: the second derivative of the energy with respect to geometry, $\frac{d^2E}{dr^2}$ **Hessian**: the second derivative of the energy with respect to geometry, $\frac{d^2E}{dr^2}$
 </note> </note>
- 
-Mathematically, the minimum should fulfill two requirements:  
- 
-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 $ 
  
 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.1662649806.txt.gz · Last modified: 2022/09/08 15:10 by jglan