Orbitally decomposed total energy

OpenMX Ver. 3.8 provides a useful tool which decomposes the total energy into each contribution associated with each basis function, where the decomposition is performed based on projection onto basis functions [52]. To calculate the orbitally decomposed total energy, you only have to include the following keyword :

    Energy.Decomposition      on        # on|off, default=off

Let us illustrate the energy decomposition by performing a total energy calculation of a methane molecule. The calculation as an example can be performed as follows:

     % mpirun -np 5 openmx Methane_ED.dat > met_ed.std &
  

where the input file 'Methane_ED.dat' can be found in the directory 'work'. After finishing the calculation, you may obtain 'met_ed.out'. The part of the file is shown below:

***********************************************************
***********************************************************
            Decomposed energies in Hartree unit
***********************************************************
***********************************************************

  Total energy (Hartree) = -8.211785052271326

  Decomposed energies (Hartree) with respect to atom

                Utot              Ukin       Una        Unl         UH1       Uxc        Ucore+UH0   ....
     1    C     -6.243003591519    4.35570   -3.60738   -0.46891    0.04429   -2.07053   -4.49616    ....
     2    H     -0.492195364934    0.55505   -0.65038    0.07550    0.00194   -0.32311   -0.15119    ....
     3    H     -0.492195365803    0.55505   -0.65038    0.07550    0.00194   -0.32311   -0.15119    ....
     4    H     -0.492195365620    0.55505   -0.65038    0.07550    0.00194   -0.32311   -0.15119    ....
     5    H     -0.492195364395    0.55505   -0.65038    0.07550    0.00194   -0.32311   -0.15119     ....


  Decomposed energies (Hartree) with respect to atomic orbital

    1    C          Utot       Ukin       Una        Unl         UH1       Uxc        Ucore+UH0  ....
            multiple
  s           0    -0.99031    0.42241   -0.86057    0.25892    0.02993   -0.49514   -0.34586    ....
  s           1    -0.35138    0.07196   -0.05748    0.01543   -0.00793   -0.02750   -0.34586    ....
  px          0    -0.66726    1.12787   -0.81140   -0.20353    0.02767   -0.46201   -0.34586    ....
  py          0    -0.66726    1.12792   -0.81145   -0.20353    0.02767   -0.46201   -0.34586    ....
  pz          0    -0.66726    1.12787   -0.81140   -0.20353    0.02767   -0.46201   -0.34586    ....
  px          1    -0.35264    0.13909   -0.06429   -0.04675   -0.00847   -0.02636   -0.34586    ....
  py          1    -0.35265    0.13898   -0.06425   -0.04671   -0.00847   -0.02634   -0.34586    ....
  d3z^2-r^2   0    -0.36902    0.01512   -0.01556    0.00188   -0.00684   -0.01776   -0.34586    ....
  dx^2-y^2    0    -0.36670    0.00504   -0.00519    0.00063   -0.00756   -0.01376   -0.34586    ....
  dxy         0    -0.37018    0.02017   -0.02076    0.00251   -0.00648   -0.01977   -0.34586    ....
  dxz         0    -0.36554    0.00000   -0.00000   -0.00000   -0.00793   -0.01175   -0.34586    ....
  dyz         0    -0.37018    0.02017   -0.02076    0.00251   -0.00648   -0.01977   -0.34586    ....


    2    H          Utot       Ukin       Una        Unl         UH1       Uxc        Ucore+UH0  ....
            multiple
  s           0    -0.33391    0.47169   -0.57150    0.06541    0.02977   -0.30769   -0.02160    ....
  s           1    -0.02386    0.08350   -0.07922    0.01042   -0.00146   -0.01550   -0.02160    ....
  d3z^2-r^2   0    -0.02690   -0.00007    0.00009   -0.00007   -0.00527    0.00002   -0.02160    ....
  dx^2-y^2    0    -0.02686    0.00003    0.00002   -0.00005   -0.00528    0.00001   -0.02160    ....
  dxy         0    -0.02695   -0.00016    0.00023   -0.00019   -0.00527    0.00004   -0.02160    ....
  dxz         0    -0.02686    0.00005   -0.00001   -0.00002   -0.00528    0.00000   -0.02160    ....
  dyz         0    -0.02686    0.00001    0.00001   -0.00001   -0.00528    0.00001   -0.02160    ....

    3    H          Utot       Ukin       Una        Unl         UH1       Uxc        Ucore+UH0  ....
            multiple
  s           0    -0.33391    0.47169   -0.57150    0.06541    0.02977   -0.30769   -0.02160    ....
  s           1    -0.02386    0.08350   -0.07922    0.01042   -0.00146   -0.01550   -0.02160    ....
  d3z^2-r^2   0    -0.02688   -0.00003    0.00009   -0.00009   -0.00527    0.00002   -0.02160    ....
  dx^2-y^2    0    -0.02688   -0.00000    0.00002   -0.00003   -0.00528    0.00000   -0.02160    ....
  ...
  ..
  .

It is found that the total energy is exactly decomposed to atomic and orbital contributions. The energy decomposition method will be useful to analyze how local distortion such as impurities and vacancies affects the energy stability/instability for the neighbors. It is also anticipated that the orbital decomposition of the total energy allows us to analyze physical mechanism for a wide variety of phenomena.