Tkatchenko-Scheffler method with iterative Hirshfeld partitioning
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 [math]\displaystyle{ i }[/math] is computed as
- [math]\displaystyle{ 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
- [math]\displaystyle{ 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]\displaystyle{ 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]\displaystyle{ \text{lint}(x) }[/math] expresses the integer part of [math]\displaystyle{ x }[/math] and [math]\displaystyle{ \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]\displaystyle{ \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]\displaystyle{ w_{A}^{i} }[/math]) are then used to define the AIM properties needed to evaluate the dispersion energy (see Tkatchenko-Scheffler method).
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].
Usage
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.
Mind:
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Related tags and articles
HITOLER, VDW_SR, VDW_ALPHA, VDW_C6, VDW_R0, VDW_S6, VDW_D, LVDW_EWALD, IVDW, Tkatchenko-Scheffler method, Self-consistent screening in Tkatchenko-Scheffler method, Many-body dispersion energy, Many-body dispersion energy with fractionally ionic model for polarizability
References
- ↑ a b T. Bučko, S. Lebègue, J. Hafner, and J. G. Ángyán, J. Chem. Theory Comput. 9, 4293 (2013)
- ↑ a b T. Bučko, S. Lebègue, J. G. Ángyán, and J. Hafner, J. Chem. Phys. 141, 034114 (2014).
- ↑ P. Bultinck, C. Van Alsenoy, P. W. Ayers, and R. Carbó Dorca, J. Chem. Phys. 126, 144111 (2007).
- ↑ T. Kerber, M. Sierka, and J. Sauer, J. Comput. Chem. 29, 2088 (2008).