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−Table of Contents
Basis Sets
In this exercise 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.
Part I: Different basis sets for H and H2
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 (Eh) |
|---|---|
| mybasis (from given input) | …. |
| basis try 1 | …. |
| basis try 2 | …. |
| …. | …. |
| pc-0 | …. |
| pc-1 | …. |
| pc-2 | …. |
3.Step
Repeat the procedure for H2. 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 H2
Based on the formula for the binding energy, you can now update your table.
∑Eproducts−∑Ereactants=E(H2)−2⋅E(H)
| Basis set | Energy H [Eh] | Energy H2 [Eh] | Distance H2 [Å] | Binding Energy H2 [Eh] |
|---|---|---|---|---|
| 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 H2 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