MEAM Potential for Si-Ge: Difference between revisions

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==Potential for Pure Elements==
==Potential for Pure Elements==


===Original MEAM Potential for Au===
===MEAM Potential for Si===


As an example, we first describe the original 'Au' potential whose parameters are given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992).
We use the 'Si4' potential whose parameters are originally given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).


The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Au' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.
The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.


<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
elt lat z ielement atwt alpha b0 b1 b2 b3
'Au' 'fcc' 12. 79 196.967 6.34090112 5.449 2.20 6 2.20
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5


⚫
<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Au}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
4.07 3.93 1.04 1.0 1.58956328 1.50776392 2.60609758 1. 3


⚫
<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' / <math>\sqrt{2}</math>.

⚫
<math>\rho_0^{\rm Au}</math> = '''rozero''' will be important only for cross-potential.

⚫
'''ibar''' is a setting used in the equation of state (EOS). It selects the
G(gamma) function in Eq (4) and (5) on the paper by BJ LEE: Phys. Rev. B 64, 184102 (2001)

While the functional form is quite different, the modulus is almost not affected by
the choice of ibar.

===New 2nn MEAM Potential for Au===

We now explain the newer 2nn MEAM potential whose parameters are given by Lee, Shim and Baskes, Phys. Rev. B 68, 144112 (2003), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential are specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines which correspond to 'AuBt' are given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'AuBt' 'fcc' 12. 79 196.967 6.59815965 5.77 2.20 6.0 2.20



<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Au}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
alat esub asub t0 t1 t2 t3 rozero ibar
4.073 3.93 1.00 1.0 1.7 1.64 2.0 1. 3
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.48 0


Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' / <math>\sqrt{2}</math>.
Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.


⚫
<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.
We can see that from 'Au' to 'AuBt', the following parameters are changed. The new parameters correspond to values given in Table I of Lee, Shim and Baskes, PRB (2003).


⚫
'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.
<math>\alpha</math> <math>\beta_i^{(0)}</math> <math>A_i</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math>
'Au' 6.34090112 5.449 1.04 1.58956328 1.50776392 2.60609758
'AuBt' 6.59815965 5.77 1.00 1.7 1.64 2.0


⚫
The modification made in Ryu and Cai JPCM (2010) is specified in the '''AuSi2nn.meam''' file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.
Note that in Table I of Lee et al. (2003), <math>t^{(1)} = 2.90</math>, while in the '''meamf''' file, t1 = 1.7. This is because of the '''augt1''' parameter. In '''meam_setup_done.F''', there is a line

t1_meam(:) = t1_meam(:) + augt1 * 3.d0/5.d0 * t3_meam(:)

This means that if '''augt1''' = 1.0, then the ''true'' value of t1 is 1.7 + 0.6 * 2.0 = 2.9.

'''augt1''' is specified in the '''AuSi2nn.meam''' file, as described below.

⚫
The '''AuSi2nn.meam''' file contains several lines that are relevant for the pure Au potential. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.


erose_form = 3
erose_form = 3
rc = 4.5
rc = 4.5
attrac(1,1) = -0.182 (<math>\gamma</math>)
attrac(2,2) = -0.36 (<math>\gamma</math>)
repuls(1,1) = 4.0 (<math>\lambda</math>)
repuls(2,2) = 16.0 (<math>\lambda</math>)
Cmin(1,1,1) = 0.8 (<math>C_{\rm min}</math>)
Cmin(2,2,2) = 1.85 (<math>C_{\rm min}</math>)
augt1 = 1


Note that we label the atomic species of Au as 1. The variable <math>d = 0.05</math> is hard coded in '''meam_setup_done.F''' (when repuls < 5.0).
Note that we label the atomic species of Si as 2.


===MEAM Potential for Si===
===MEAM Potential for Ge===


We use the 'Si4' potential whose parameters are originally given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).
We use the 'Si4' potential whose parameters are originally given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).
Line 113: Line 77:
Note that we label the atomic species of Si as 2.
Note that we label the atomic species of Si as 2.


==Cross Potential between Au and Si==
==Cross Potential between Ge and Si==


The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).
The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

Revision as of 00:02, 2 March 2017

MEAM Potential for Au-Si

Xiaohan Zhang and Wei Cai

Created Mar, 2017, Last modified Mar, 2017

This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference: "A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60.

Potential for Pure Elements

MEAM Potential for Si

We use the 'Si4' potential whose parameters are originally given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential is specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below. 

                                                    
elt  lat   z    ielement   atwt      alpha    b0       b1     b2    b3   
'Si4' 'dia' 4.     14     28.086     4.87     4.4     5.5    5.5   5.5   



 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_i^0}
   Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A_i}
   Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t_i^{(0)}}
   Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t_i^{(1)}}
        Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t_i^{(2)}}
         Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t_i^{(3)}}
     Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_0^{\rm Si}}

 alat  esub  asub t0     t1          t2           t3     rozero  ibar
 5.431 4.63  1.  1.0    3.13        4.47          -1.8      1.48    0

Note that the nearest neighbor distance Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_i^0 } = alat Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \times \sqrt{3}/4} for the diamond cubic structure.

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_0^{\rm Si}} = rozero will be important only for cross-potential.

ibar is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the AuSi2nn.meam file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis. 

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \gamma}
)
repuls(2,2) = 16.0  (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lambda}
)
Cmin(2,2,2) = 1.85  (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C_{\rm min}}
)

Note that we label the atomic species of Si as 2.

MEAM Potential for Ge

We use the 'Si4' potential whose parameters are originally given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential is specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below. 

                                      Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha_i}
      Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta_i^{(0)}}
    Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta_i^{(1)}}
  Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta_i^{(2)}}
  Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta_i^{(3)}}

elt  lat   z    ielement   atwt      alpha    b0       b1     b2    b3   
'Si4' 'dia' 4.     14     28.086     4.87     4.4     5.5    5.5   5.5   



Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (R_i^0)}
 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_i^0}
   Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A_i}
   Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t_i^{(0)}}
   Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t_i^{(1)}}
        Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t_i^{(2)}}
         Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t_i^{(3)}}
     Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_0^{\rm Si}}

 alat  esub  asub t0     t1          t2           t3     rozero  ibar
 5.431 4.63  1.  1.0    3.13        4.47          -1.8      1.48    0

Note that the nearest neighbor distance Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_i^0 } = alat Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \times \sqrt{3}/4} for the diamond cubic structure.

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_0^{\rm Si}} = rozero will be important only for cross-potential.

ibar is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the AuSi2nn.meam file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis. 

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \gamma}
)
repuls(2,2) = 16.0  (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lambda}
)
Cmin(2,2,2) = 1.85  (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C_{\rm min}}
)

Note that we label the atomic species of Si as 2.

Cross Potential between Ge and Si

The parameters for the cross potential are specified in AuSi2nn.meam file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010). 

re(1,2) = 2.700    (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r_e}
)
delta(1,2) = 0.125   (related to Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_c}
, see below)
lattce(1,2) = b1
alpha(1,2) = 5.819     (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha}
)
attrac(1,2) = 0.0      
repuls(1,2) = 0.26     (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \gamma}
)
Cmin(1,1,2) = 1.9     (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C_{\min}(1,1,2)}
)
Cmin(1,2,1) = 0.95     (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C_{\min}(1,2,1)}
)
Cmin(1,2,2) = 1.85     (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C_{\min}(1,2,2)}
)
Cmin(2,2,1) = 1.0     (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C_{\min}(2,2,1)}
)

Table 3 of Ryu and Cai (2010) gives Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_c ({\rm AuSi}) = 4.155} . This value is related to delta(1,2) through

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_c ({\rm AuSi}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Si}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155} .

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_0^{\rm Si} / \rho_0^{\rm Au}} = 1.48 because of the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_0^{\rm Si}} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_0^{\rm Au}} values specified above.

Cmax = 2.8 is the default value.

Benchmark in MD++

Compile the code using the following command. 

make meam-lammps build=R SYS=gpp

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Au (FCC). You can download the si-au.tcl from the link. 

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are 

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC). 

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are 

 a0 = 5.43100051581 Angstrom 
 Ecoh = -4.63000000205 eV


Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1). 

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are 

 a0 = 5.4 Angstrom 
 Ecoh = -4.155000000083061 eV

Impurity energy

Use the following command to compute the impurity of a Au atom in Si DC lattice. 

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size 

cell size, Eimp(eV)
3x3x3      3.914
4x4x4      3.968
5x5x5      3.987
10x10x10   4.005
20x20x20   4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2, is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_2 = 3.968} (eV) for a Au atom in Si DC crystal. So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.


Use the following command to compute the impurity of a Si atom in Au fcc lattice. 

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2      0.639
3x3x3      0.660
4x4x4      0.665
5x5x5      0.667
10x10x10   0.669
20x20x20   0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2, is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_1 = 0.636} (eV) for a Si atom in Au FCC crystal. So it seems that for a Si in Au FCC crystal, the predicted results here using the 2x2x2 cell corresponds to the value in JPCM (2010).

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