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--- howto:cdft [2018/11/02 12:44] – [Selected examples] nholmber
+++ howto:cdft [2018/11/02 12:45] – [Available constraints] nholmber
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 {{ howto:cdft-becke-atomicsize.png?400}}{{ howto:cdft-becke.png?400 }}\\
-**Figure 2.** Comparison of the Voronoi (lines) and Becke partitioning (contours) schemes. At left, the Becke partitioning is performed without atomic size information. At right, the size of the red atom is 30 % larger than the black atoms, and the contours of the red atom extend farther than without atomic size adjustments.
+**Figure 3.** Comparison of the Voronoi (lines) and Becke partitioning (contours) schemes. At left, the Becke partitioning is performed without atomic size information. At right, the size of the red atom is 30 % larger than the black atoms, and the contours of the red atom extend farther than without atomic size adjustments.
-The Voronoi and, by extension, the Becke partitioning methods treat each element equally. This leads to unphysical partial charges in most systems. For example, the Becke scheme predicts a positive charge on oxygen and a negative charge on hydrogen in water (see examples for input files). This problem can be remedied by accounting for atomic radii during the partitioning. This behavior is activated by the keyword [[inp>FORCE_EVAL/DFT/QS/CDFT/BECKE_CONSTRAINT#ADJUST_SIZE|ADJUST_SIZE]] and the atomic radii are defined with the keyword [[inp>FORCE_EVAL/DFT/QS/CDFT/BECKE_CONSTRAINT#ATOMIC_RADII|ATOMIC_RADII]]. The atomic radii should be set to values that reflect the system under simulation, e.g. using additive covalent radii for covalent molecules or Shannon's ionic radii for ionic compounds. An example on how atomic size adjustments affect the Becke cell functions has been visualized above in Figure 2 at right, where the size of the red atom is set to a value 30 % larger than the black atoms causing the red atom's contours to extend farther than without atomic size adjustments.
+The Voronoi and, by extension, the Becke partitioning methods treat each element equally. This leads to unphysical partial charges in most systems. For example, the Becke scheme predicts a positive charge on oxygen and a negative charge on hydrogen in water (see examples for input files). This problem can be remedied by accounting for atomic radii during the partitioning. This behavior is activated by the keyword [[inp>FORCE_EVAL/DFT/QS/CDFT/BECKE_CONSTRAINT#ADJUST_SIZE|ADJUST_SIZE]] and the atomic radii are defined with the keyword [[inp>FORCE_EVAL/DFT/QS/CDFT/BECKE_CONSTRAINT#ATOMIC_RADII|ATOMIC_RADII]]. The atomic radii should be set to values that reflect the system under simulation, e.g. using additive covalent radii for covalent molecules or Shannon's ionic radii for ionic compounds. An example on how atomic size adjustments affect the Becke cell functions has been visualized above in Figure 3 at right, where the size of the red atom is set to a value 30 % larger than the black atoms causing the red atom's contours to extend farther than without atomic size adjustments.
 The algorithmic implementation of the Becke density partitioning method has been detailed [[doi>10.1021/acs.jctc.6b01085|here]]. In brief, this involves iterating over each atom pair permutation $\{\mathbf{R}_i, \mathbf{R}_j\}, j\neq i$ at every real space grid point $\mathbf{r}$. This leads to a poor scaling with respect to the system size (cell size and planewave cutoff) and the number of atoms within the system, and is particularly troublesome for  solvated system simulations. The computational cost of the Becke method can be considerably decreased by noting that only the grid points within a cutoff distance $R_{cutoff}$ ([[inp>FORCE_EVAL/DFT/QS/CDFT/BECKE_CONSTRAINT#CUTOFF_TYPE|CUTOFF_TYPE]]) of atoms involved in constraints actually need to be considered. The other grid points can be efficiently screened with constraint atom centered spherical Gaussian functions, activated by the keyword [[inp>FORCE_EVAL/DFT/QS/CDFT/BECKE_CONSTRAINT#CAVITY_CONFINE|CAVITY_CONFINE]] and controlled by other keywords of the form CAVITY_*. The exact details of this confinement scheme and why it can be used are explained in the implementation paper.