Basis Sets

In this exericse you will compare different basis sets and use them for computing the binding energy of an H2 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                                    ! Parametes 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 repulstion 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 scetion 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                         ! Specifes 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 H2.
H2 coordinates:

H 0 0 0     
H 0.75 0 0   

Binding energy:

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

You can now update your table:

- What is the effect of:

• increasing/decreasing the value of the exponents for the given basis?
• adding sets with p,d symmetry to the basis? You have the same effect in H and H2?

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