====== 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 [[:basis_sets|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 !
&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 [[geometry_optimization|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 =====
- 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