# Open SourceMolecular Dynamics

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exercises:2015_ethz_mmm:basis_sets

# 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.

## Part I: Different basis sets for H and H$_2$

### 1.Step

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


### 2.Step

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 :

Basis set Energy H ($E_h$)
mybasis (from given input) ….
basis try 1 ….
basis try 2 ….
…. ….
pc-0 ….
pc-1 ….
pc-2 ….

Is always good to keep record of self-created basis sets, to track the effect of a change in value and number of exponents, contractions….etc..

### 3.Step

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.

The H$_2$ molecule does not have unpaired electrons. Remember to take out the LSD and MULTIPLICITY keywords.

## Part II: Estimate the binding energy of H$_2$

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

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

Basis set Energy H [$E_h$] Energy H$_2$ [$E_h$] Distance H$_2$ [$Å$] Binding Energy H$_2$ [$E_h$]
mybasis (from given input) …. …. …. ….
basis try 1 …. …. …. ….
basis try 2 …. …. …. ….
…. …. …. …. ….
pc-0 …. …. …. ….
pc-1 …. …. …. ….
pc-2 …. …. …. ….
…. …. …. …. ….

The binding energy is only significant if all terms were calculated with the same basis-set.

## Part III: Questions

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?

## Appendix: Literature Basis Sets

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