Basis Sets

In this exercise you will compare different basis sets and use them for computing the binding energy of an H$_2$ molecule.

The cp2k basis set format is described in detail here.

Run a calculation with the following input file. Comment lines are marked with !

mybasis.inp

 
&GLOBAL
  PROJECT H-mybasis
  RUN_TYPE ENERGY
&END GLOBAL

&FORCE_EVAL
  METHOD Quickstep                         ! Electronic structure method (DFT,...)
  
  &DFT
  LSD                                      ! Requests a spin-polarized calculation for non paired electrons
  MULTIPLICITY 2                           ! Multiplicity = 2S+1 (S= total spin momentum)
    &POISSON                               ! Solver requested for non periodic calculations  
      PERIODIC NONE                        
      PSOLVER  WAVELET                     ! Type of solver
    &END POISSON
    &QS                                    ! Parameters needed to set up the Quickstep framework
      METHOD GAPW                          ! Method: gaussian and augmented plane waves 
    &END QS
    &XC                                    ! Parameters needed to compute the electronic exchange potential 
      &XC_FUNCTIONAL NONE                  ! No xc_functional
      &END XC_FUNCTIONAL
      &HF                                  ! Hartree Fock exchange. In this case is 100% (no fraction specified).                    
        &SCREENING                         ! Screening of the electronic repulsion up to the given threshold. This section is needed
          EPS_SCHWARZ 1.0E-10              ! Threshold specification
        &END SCREENING
      &END HF 
    &END XC
  &END DFT
  
  &SUBSYS
    &TOPOLOGY                              ! Section used to center the molecule in the simulation box. Useful for big molecules 
      &CENTER_COORDINATES                  
      &END
    &END
    &CELL
      ABC 10.0 10.0 10.0
      PERIODIC NONE                        ! Non periodic calculations. That's why the POISSON section is needed 
    &END CELL
    &COORD
     H   0.0 0.0 0.0                           
    &END COORD
    &KIND H
     &BASIS                                ! Basis set for H
     2
     1 0 0 1 1
     0.35 1
     1 0 0 1 1
     0.6 1
     &END
     POTENTIAL ALL                         ! Species that the potential is for all electron calculations.
     &POTENTIAL                            ! Usual all electron potential for H 
     1    0    0
     0.20000000    0
     &END POTENTIAL
    &END KIND
  &END SUBSYS
&END FORCE_EVAL

Try to change the basis set, and report the obtained energy values for H. After a couple of tries on your own, try to use some of the literature basis sets (given at the end of this exercise). At the end, you should get a table like this :

Repeat the procedure for H$_2$. For this you will have to add a second H atom to the coordinate section and run a geometry optimization to determine the equilibrium distance. Howto run a geometry optimization was covered in a previous exercise. Note that the equilibrium distance will depend on your basis set.

Based on the formula for the binding energy, you can now update your table.

\[ \sum E_\text{products} - \sum E_\text{reactants} = E(H_2) - 2 \cdot E(H) \]

1. What is the effect of changing the exponents in a basis set?
2. What is the effect of adding p- and d-function to the basis set? Do H and H$_2$ respond differently?

H  pc-0
  2
  1  0  0  2  1
          4.34480000          0.07929900
          0.66049000          0.42422000
  1  0  0  1  1
          0.13669000          1.00000000

H  pc-1
  3
  1  0  0  3  1
         12.25200000          0.02282200
          1.86870000          0.15564000
          0.41821000          0.48898000
  1  0  0  1  1
          0.10610000          1.00000000
  1  1  1  1  1
          1.00000000          1.00000000

H  pc-2
  6
  1  0  0  4  1
         75.42300000          0.00240650
         11.35000000          0.01848700
          2.59930000          0.08974200
          0.73513000          0.28111000
  1  0  0  1  1
          0.23167000          1.00000000
  1  0  0  1  1
          0.07414700          1.00000000
  1  1  1  1  1
          1.60000000          1.00000000
  1  1  1  1  1
          0.45000000          1.00000000
  1  2  2  1  1
          1.25000000          1.00000000