Tkatchenko-Scheffler method with iterative Hirshfeld partitioning: Difference between revisions

Latest revision as of 15:01, 12 October 2023

The Tkatchenko-Scheffler method, which uses fixed neutral atoms as a reference to estimate the effective volumes of atoms-in-molecule (AIM) and to calibrate their polarizabilities and dispersion coefficients, fails to describe the structure and the energetics of ionic solids. As shown in references ^[1] and ^[2], this problem can be solved by replacing the conventional Hirshfeld partitioning used to compute properties of interacting atoms by the iterative scheme proposed by Bultinck^[3]. In this iterative Hirshfeld algorithm (HI), the neutral reference atoms are replaced with ions with fractional charges determined together with the AIM charge densities in a single iterative procedure. The algorithm is initialized with a promolecular density defined by non-interacting neutral atoms. The iterative procedure then runs in the following steps:

The Hirshfeld weight function for the step $i$ is computed as

w_A^{i}({\mathbf{r}}) = {n^{i}_A({\mathbf{r}})}/\left({\sum_B n^{i}_B({\mathbf{r}})}\right)

where the sum extends over all atoms in the system.

The number of electrons per atom is determined using

N_{A}^{i+1} = N_{A}^{i} + \int \left[ n_{A}^{i}(\mathbf{r}) - w_{A}^i(\mathbf{r})\,n(\mathbf{r}) \right]\,d^{3}\mathbf{r}.

New reference charge densities are computed using

n^{i+1}_A(\mathbf{r})  = n^{\text{lint}(N^i_A)}(\mathbf{r})\left [ \text{uint}(N^i_A)-N^i_A\right ] + n^{\text{uint}(N_A^i)}({\mathbf{r}})\left [ N^i_A - \text{lint}(N^i_A)\right ]

where $\text{lint}(x)$ expresses the integer part of $x$ and $\text{uint}(x)=\text{lint}(x)+1$ .

Steps (1) to (3) are iterated until the difference in the electronic populations between two subsequent steps ( $\Delta_{A}^{i} = \vert N_{A}^{i}-N_{A}^{i+1}\vert$ ) is less than a predefined threshold for all atoms. The converged iterative Hirshfeld weights ( $w_{A}^{i}$ ) are then used to define the AIM properties needed to evaluate the dispersion energy (see Tkatchenko-Scheffler method).

The Tkatchenko-Scheffler method with iterative Hirshfeld partitioning (TS-HI) is invoked by setting IVDW=21. The convergence criterion for iterative Hirshfeld partitioning (in e) can optionally be defined via the parameter HITOLER (the default value is 5e-5). Other optional parameters controlling the input for the calculation are as in the conventional Tkatchenko-Scheffler method. The default value of the adjustable parameter VDW_SR is 0.95 and corresponds to the PBE functional.

The TS-HI method is described in detail in reference ^[1] and its performance in optimization of various crystalline systems is examined in reference ^[2].

Mind:

This method requires the use of POTCAR files from the PAW dataset version 52 or later.
The input reference data for non-interacting atoms are available only for elements of the first six rows of the periodic table except of the lanthanides. If the system contains other elements, the user must provide the free-atomic parameters for all atoms in the system via VDW_ALPHA, VDW_C6, VDW_R0 (see Tkatchenko-Scheffler method defined in the INCAR file.
The charge-density dependence of gradients is neglected.
The DFT-TS/HI method is incompatible with the setting ADDGRID=.TRUE..
It is essential that a sufficiently dense FFT grid (controlled via NGXF, NGYF and NGZF) is used in the DFT-TS/HI - we strongly recommend to use PREC=Accurate} for this type of calculations (in any case, avoid using PREC=Low).
Defaults for the parameters controlling the damping function (VDW_S6, VDW_SR, VDW_D) are available only for the PBE functional. If a functional other than PBE is used, the value of VDW_SR must be specified in the INCAR file.
Ewald's summation in the calculation of $E_{disp}$ (controlled via LVDW_EWALD) implemented according to reference ^[4] is available as of VASP.5.3.4.
Hirshfeld charges for all configurations generated in a calculation are written out in the OUTCAR file. The corresponding table is introduced by the expression Hirshfeld charges:.

References

[bucko:jctc:13-1] T. Bučko, S. Lebègue, J. Hafner, and J. G. Ángyán, J. Chem. Theory Comput. 9, 4293 (2013)

[bucko:jcp:14-2] T. Bučko, S. Lebègue, J. G. Ángyán, and J. Hafner, J. Chem. Phys. 141, 034114 (2014).

[bultinck:jcp:07-3] P. Bultinck, C. Van Alsenoy, P. W. Ayers, and R. Carbó Dorca, J. Chem. Phys. 126, 144111 (2007).

[kerber:jcc:08-4] T. Kerber and J. Sauer, J. Comput. Chem. 29, 2088 (2008).

[1]

[2]

[3]

[4]

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-The Tkatchenko-Scheffler (TS) dispersion correction method which uses fixed neutral atoms as a reference to estimate the effective volumes of atoms-in-molecule (AIM) and to calibrate their polarizabilities and dispersion coefficients (see {{TAG|Tkatchenko-Scheffler method}}) fails to describe the structure and the energetics of ionic solids. As shown in references <ref name="2013"/> and <ref name="2014"/>, this problem can be solved by replacing
+The {{TAG|Tkatchenko-Scheffler method}}, which uses fixed neutral atoms as a reference to estimate the effective volumes of atoms-in-molecule (AIM) and to calibrate their polarizabilities and dispersion coefficients, fails to describe the structure and the energetics of ionic solids. As shown in references {{cite|bucko:jctc:13}} and {{cite|bucko:jcp:14}}, this problem can be solved by replacing
-the conventional Hirshfeld partitioning used to compute properties of interacting atoms by the iterative scheme proposed by Bultinck<ref name="bultinck"/>. In this iterative Hirshfeld algorithm (HI), the neutral reference atoms are replaced with ions with fractional charges determined together with the AIM charge densities in a single iterative procedure. The algorithm is initialized with a promolecular density defined by non-interacting neutral atoms. The iterative procedure then runs in  the following steps:
+the conventional Hirshfeld partitioning used to compute properties of interacting atoms by the iterative scheme proposed by Bultinck{{cite|bultinck:jcp:07}}. In this iterative Hirshfeld algorithm (HI), the neutral reference atoms are replaced with ions with fractional charges determined together with the AIM charge densities in a single iterative procedure. The algorithm is initialized with a promolecular density defined by non-interacting neutral atoms. The iterative procedure then runs in the following steps:
 *The Hirshfeld weight function for the step <math>i</math> is computed as
-<math>w_A^{i}({\mathbf{r}}) = {n^{i}_A({\mathbf{r}})}/\left({\sum_B n^{i}_B({\mathbf{r}})}\right)</math>
+:<math>w_A^{i}({\mathbf{r}}) = {n^{i}_A({\mathbf{r}})}/\left({\sum_B n^{i}_B({\mathbf{r}})}\right)</math>
 where the sum extends over all atoms in the system.
+*The number of electrons per atom is determined using
-*The number of electrons per atomis determined using
+:<math> N_{A}^{i+1} = N_{A}^{i} + \int \left[ n_{A}^{i}(\mathbf{r}) - w_{A}^i(\mathbf{r})\,n(\mathbf{r}) \right]\,d^{3}\mathbf{r}.</math>
-<math> N_{A}^{i+1} = N_{A}^{i} + \int \left[ n_{A}^{i}(\mathbf{r}) - w_{A}^i(\mathbf{r})\,n(\mathbf{r}) \right]\,d^{3}\mathbf{r}.</math>
 *New reference charge densities are computed using
-<math>n^{i+1}_A(\mathbf{r})  = n^{\text{lint}(N^i_A)}(\mathbf{r})\left [ \text{uint}(N^i_A)-N^i_A\right ] + n^{\text{uint}(N_A^i)}({\mathbf{r}})\left [ N^i_A - \text{lint}(N^i_A)\right ]</math>
+:<math>n^{i+1}_A(\mathbf{r})  = n^{\text{lint}(N^i_A)}(\mathbf{r})\left [ \text{uint}(N^i_A)-N^i_A\right ] + n^{\text{uint}(N_A^i)}({\mathbf{r}})\left [ N^i_A - \text{lint}(N^i_A)\right ]</math>
-where <math>\text{lint}(x)<?math> expresses the integer part of <math>x</math> and <math>\text{uint}(x)=\text{lint}(x)+1</math>.
-Steps (1) to (3) are iterated until the difference in the electronic populations between two subsequent steps (<math>\Delta_{A}^{i} = \vert N_{A}^{i}-N_{A}^{i+1}\vert</math>) is less than a predefined threshold for all atoms. The converged interative Hirshfeld weights (<math>w_{A}^{i}</math>) are then used to define the AIM properties needed to evaluate the dispersion energy (see {{TAG|Tkatchenko-Scheffler method}}).
+where <math>\text{lint}(x)</math> expresses the integer part of <math>x</math> and <math>\text{uint}(x)=\text{lint}(x)+1</math>.
-The DFT-TS calculation with iterative Hirshfeld partitioning (DFT-TS/HI) is invoked by setting {{TAG|IVDW}}=21. The convergence criterion for iterative Hirshfeld partitioning (in e) can optionally be defined via the parameter {{TAG|HITOLER}} (the default value is 5e-5). Other optional parameters controlling the input for the calculation are as in the conventional TS method (see {{TAG|Tkatchenko-Scheffler method}}). The default value of the adjustable parameter {{TAG|VDW_SR}} is 0.95 and corresponds to the PBE functional.
+Steps (1) to (3) are iterated until the difference in the electronic populations between two subsequent steps (<math>\Delta_{A}^{i} = \vert N_{A}^{i}-N_{A}^{i+1}\vert</math>) is less than a predefined threshold for all atoms. The converged iterative Hirshfeld weights (<math>w_{A}^{i}</math>) are then used to define the AIM properties needed to evaluate the dispersion energy (see {{TAG|Tkatchenko-Scheffler method}}).
-The PBE-TS/HI method is described in detail in reference <ref name="bucko2013"/> and its performance in optimization of various crystalline systems is examined in reference <ref name="bucko2014"/>.
+The Tkatchenko-Scheffler method with iterative Hirshfeld partitioning (TS-HI) is invoked by setting {{TAG|IVDW}}=21. The convergence criterion for iterative Hirshfeld partitioning (in e) can optionally be defined via the parameter {{TAG|HITOLER}} (the default value is 5e-5). Other optional parameters controlling the input for the calculation are as in the conventional {{TAG|Tkatchenko-Scheffler method}}. The default value of the adjustable parameter {{TAG|VDW_SR}} is 0.95 and corresponds to the PBE functional.
-== IMPORTANT NOTES ==
+The TS-HI method is described in detail in reference {{cite|bucko:jctc:13}} and its performance in optimization of various crystalline systems is examined in reference {{cite|bucko:jcp:14}}.
+{{NB|mind|
 *This method requires the use of {{TAG|POTCAR}} files from the PAW dataset version 52 or later.
-*The input reference data for non-interacting atoms are available only for elements of the first six rows of the periodic table except of the lanthanides. If the system contains other elements, the user must provide the free-atomic parameters for all atoms in the system via {{TAG|VDW_alpha}}, {{TAG|VDW_C6}}, {{TAG|VDW_R0}} (see {{TAG|Tkatchenko-Scheffler method}} defined in the {{TAG|INCAR}} file.
+*The input reference data for non-interacting atoms are available only for elements of the first six rows of the periodic table except of the lanthanides. If the system contains other elements, the user must provide the free-atomic parameters for all atoms in the system via {{TAG|VDW_ALPHA}}, {{TAG|VDW_C6}}, {{TAG|VDW_R0}} (see {{TAG|Tkatchenko-Scheffler method}} defined in the {{TAG|INCAR}} file.
 *The charge-density dependence of gradients is neglected.
-*The DFT-TS/HI method is incompatible with the setting {{TAG|ADDGRID}}=''.TRUE.''.
+*The DFT-TS/HI method is incompatible with the setting {{TAG|ADDGRID}}{{=}}''.TRUE.''.
-*It is essential that a sufficiently dense FFT grid (controlled via {{TAG|NGFX(Y,Z)}}) is used in the DFT-TS/HI - we strongly recommend to use {{TAG|PREC}}=''Accurate''} for this type of calculations (in any case, avoid using {{TAG|PREC}}''=Low'').
+*It is essential that a sufficiently dense FFT grid (controlled via {{TAG|NGXF}}, {{TAG|NGYF}} and {{TAG|NGZF}}) is used in the DFT-TS/HI - we strongly recommend to use {{TAG|PREC}}{{=}}''Accurate''} for this type of calculations (in any case, avoid using {{TAG|PREC}}{{=}}''Low'').
 *Defaults for the parameters controlling the damping function ({{TAG|VDW_S6}}, {{TAG|VDW_SR}}, {{TAG|VDW_D}}) are available only for the PBE functional. If a functional other than PBE is used, the value of {{TAG|VDW_SR}} must be specified in the {{TAG|INCAR}} file.
-*Ewald's summation in $E_{disp}$ calculation (controlled via {\tt LVDW\_EWALD})
+*Ewald's summation in the calculation of <math>E_{disp}</math> (controlled via {{TAG|LVDW_EWALD}}) implemented according to reference {{cite|kerber:jcc:08}} is available as of VASP.5.3.4.
-implemented according to Ref.~\cite{Kerber:08}
+*Hirshfeld charges for all configurations generated in a calculation are written out in the {{TAG|OUTCAR}} file. The corresponding table is introduced by the expression ''Hirshfeld charges:''.}}
-is available as of VASP.5.3.4
-\item
+== Related tags and articles ==
-conventional and iterative Hirshfeld charges for all configurations
+{{TAG|HITOLER}},
-generated in a calculation are written in OUTCAR. The corresponding
+{{TAG|VDW_SR}},
-tables are introduced
+{{TAG|VDW_ALPHA}},
-by expressions "Hirshfeld charges:" and "Hirshfeld-I charges:".
+{{TAG|VDW_C6}},
+{{TAG|VDW_R0}},
+{{TAG|VDW_S6}},
+{{TAG|VDW_D}},
+{{TAG|LVDW_EWALD}},
+{{TAG|IVDW}},
+{{TAG|Tkatchenko-Scheffler method}},
+{{TAG|Self-consistent screening in Tkatchenko-Scheffler method}},
+{{TAG|Many-body dispersion energy}},
+{{TAG|Many-body dispersion energy with fractionally ionic model for polarizability}}
 == References ==
-<references>
+<references/>
-<ref name="2013"/>
-<ref name="bucko2013">[http://pubs.acs.org/doi/full/10.1021/ct400694h?src=recsys T. Bucko, S. Lebègue, J. Hafner, and J. G. Ángyán, J. Chem. Theory. Comput. 9, 4293 (2013)]</ref>
-<ref name="bucko2014">[http://aip.scitation.org/doi/full/10.1063/1.4890003 T. Bucko, S. Lebègue, J. G. Ángyán, and J. Hafner, J. Chem. Phys. 141, 034114 (2014).]</ref>
-<ref name="bultinck">http://dugi-doc.udg.edu/bitstream/handle/10256/3198/527.pdf?sequence=1 P. Bultinck, C. Van Alsenoy, P. W. Ayers, and R. Carbó Dorca, J. Chem. Phys. 126, 144111 (2007). ]</ref>
-</references>
 ----
-[[The_VASP_Manual|Contents]]
+[[Category:Exchange-correlation functionals]][[Category:van der Waals functionals]][[Category:Theory]]
-[[Category:INCAR]]