Relativistic parameterization of the SCC-DFTB method

1
Relativistic parameterization of the SCC-DFTB
method

• Henryk Witek
• Institute of Molecular Science Department of
  Applied Chemistry
• National Chiao Tung University
• Hsinchu, Taiwan

2
Aims

• Provide the DFTB community with a general and
  easy-to-use tool for developing Slater-Koster
  files
• Develop a reliable set of SCC-DFTB parameters
  suitable for modeling chemical reactions

3
Requirements

• Important issues of the project
• general character
• relativistic framework
• well-defined procedure
• high automaticity
• error control test suite

4
Theoretical framework

• 4-component Dirac-Kohn-Sham equation
• Modification of relativistic Dirac-Slater code of
  J.P. Desclaux
• Comp. Phys. Comm. 1, 216 (1969)
• Comp. Phys. Comm. 9, 31 (1975)
• Density confinement
• Spinor confinement

5
Slater-Koster files

• One-center quantities
• orbital energies
• orbital hardness
• orbital spin-densities interaction parameters
• Two-center quantities
• Hamiltonian integrals
• overlap integrals
• repulsive potentials

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Input description

• Atomic information
• nuclear charge
• number of electrons
• shell occupations
• Method information
• exchange-correlation functional type
• confinement radius
• way to construct molecular XC potential
• density superposition
• potential superposition

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Output spinors of carbon
  atom electronic structure and final shell
energies     shell type      occupation
      final energy    
      1 S1/2           2.00  
          -11.29598       2 S1/2          
2.00              -0.44465       2 P1/2  
        1.00              -0.12665       2
P3/2           1.00              -0.12623  
radial overlap integrals for spinors     spinor
1        spinor 2            overlap integral  
                    1
S1/2          2 S1/2             -0.000000000022
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Output spinors of lead
  atom electronic structure and final shell
energies    shell type      occupation      
final energy        
  1 S1/2 2.00           -3256.80560      2
S1/2 2.00            -585.97772      2
P1/2 2.00            -564.09214      2
P3/2 4.00            -482.19388      3
S1/2 2.00            -141.89459
      5
D3/2 4.00              -0.79336      5
D5/2 6.00              -0.68107      6
S1/2 2.00              -0.33752      6
P1/2 2.00              -0.09002      6
P3/2 0.00               -0.04704
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Output spinors of lead
   radial overlap integrals for spinors   
spinor 1        spinor 2            overlap
integral               
      1 S1/2          2 S1/2        
     0.000000000068     1 S1/2          3 S1/2  
           0.000000000016     2 S1/2          3
S1/2              0.000000000186     2 P1/2    
     3 P1/2              0.000000000099     2
P3/2          3 P3/2              0.000000000094

     2 P3/2          6 P3/2            
 0.000000000048     3 P3/2          6 P3/2      
      -0.000000000358     4 P3/2          6 P3/2
            -0.000000001312     5 P3/2        
 6 P3/2              0.000000000096
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Output atomic density
  error for the fitted atomic density at grid
points    density           norm1            
 norm2             norm8           
             dn            
0.000010         0.000019         0.000104 
renormalization of fitted density       gt
density renormalized from 5.999981 to 6.000000
electrons
C
  error for the fitted atomic density at grid
points    density           norm1            
 norm2             norm8           
              dn          
 0.030532         0.049705         0.147628 
renormalization of fitted density       gt
density renormalized from 82.000529 to 82.000000
electrons
Pb
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radial density of lead
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Semi-relativistic orbitals

• Scalar relativistic valence orbitals are obtained
  by
• neglecting small component
• averaging spin-orbit components of every scalar
  orbital
• V.Heera, G. Seifert, P. Ziesche, J. Phys. B 17,
  519 (1984)

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Large vs. small component
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Averaging spin-orbit split components of a spinor
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Output orbitals of carbon
  info about scalar atomic orbitals     num
   orbital     occupation       final energy    
  type           
       1       1s           2.00
-11.29598         core      2       2s  
      2.00   -0.44465         valence      3
      2p 2.00    -0.12637        
valence  error for the fitted curve at grid
points   orbital           norm1            
 norm2            norm8           
                2s      0.000231
       0.000721        0.005025      2p    
  0.000013       0.000025        0.000108 
renormalization after fit and neglecting small
component      gt orbital 2s renormalized from  
  0.999957   to     1.0d0      gt orbital 2p
renormalized from     0.999957   to     1.0d0
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Output orbitals for lead
  info about scalar atomic orbitals     num  
  orbital     occupation       final energy    
    type         
         1       1s           2.00  
        -3256.80560         core      2    
  2s           2.00            -585.97772    
    core      3       2p           6.00  
         -509.49330         core      4    
  3s           2.00            -141.89459    
    core      5       3p           6.00  
         -119.52024         core      6  
    3d          10.00             -94.16394  
      core      7       4s           2.00
            -32.79553         core      8  
    4p           6.00             -25.30912
        core      9       4d        
 10.00             -15.92391         core     
10       4f          14.00            
 -5.84011         core      11       5s    
      2.00              -5.53058      
 valence      12       5p           6.00    
         -3.33518        valence      13    
  5d        10.00            -0.72598  
     valence      14       6s          
2.00               -0.33752        valence   
  15       6p           2.00              
-0.06137        valence
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Output orbitals for lead
  fitting valence orbitals with gaussians 
error for the fitted curve at grid points 
 orbital           norm1              norm2      
      norm8                 
          5s        0.000048      
 0.000138        0.002025      5p      
 0.000047        0.000094        0.000988     
5d        0.000143        0.000245      
 0.000807      6s        0.000108      
 0.000257        0.003610      6p    
   0.000026        0.000045        0.000371 
renormalization after fit and neglecting small
component      gt orbital 5s renormalized from  
  0.999235   to     1.0d0      gt orbital 5p
renormalized from     0.990674   to     1.0d0   
  gt orbital 5d renormalized from     0.998799  
to     1.0d0      gt orbital 6s renormalized
from     0.999913   to     1.0d0      gt orbital
6p renormalized from     0.991615   to     1.0d0
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Relativistic vs. non-relativistic atomic
orbitals carbon atom
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Relativistic vs. non-relativistic atomic
orbitals carbon atom
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Relativistic vs. non-relativistic atomic
orbitals lead atom
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Relativistic vs. non-relativistic atomic
orbitals lead atom
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Confinement potential

• Additional term Vconf in Dirac-Kohn-Sham
  effective potential
• contraction of orbitals exponential tail
• relaxation of basis set
• additional variational parameter in the formalism

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Effect of the confinement potentialradial
density of Pb
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Repulsive potentials

• Effective two-center, distance-dependent
  potentials accounting for
• repulsion between atomic chemical cores
• double counting terms in electronic part
• Total DFTB energy is

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Constructing C-C repulsive potential
M. Sternberg, Ph.D. Thesis
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repulsive C-C potential
Malolepsza, Witek, and Morokuma, ChPL 412, 237
(2005)
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performance of new C-C potential
Malolepsza, Witek, and Morokuma, ChPL 412, 237
(2005)
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Resultant repulsive potentials
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Derivatives of repulsive potentials
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Analytical form of potentials
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Analytical form of potentials

• Atomization energies

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Analytical form of potentials

• Equilibrium structures

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First derivatives of repulsive potential
NO2 O3 NO2-
H2O2
H2O
H2O2
H3O NH3
O3
H2
O2
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First derivatives of repulsive potential
NO2-
HNO
NO2, HNO
NO
NH3
HNO
H2O2
H2O2
H3O
H2O
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Conclusions

• Convenient relativistic tool for automatic DFTB
  parameterization is suggested
• New form of potential parameterization is proposed

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Acknowledgements

• Christof Köhler
• Keiji Morokuma
• Marcus Elstner
• Thomas Frauenheim