### Table of Contents

# 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 | …. |

### 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.

## 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 | …. | …. | …. | …. |

…. | …. | …. | …. | …. |

## Part III: Questions

- What is the effect of changing the exponents in a basis set?
- 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