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exercises:2014_ethz_mmm:basis_sets

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# 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 the following:

Nsets
n1 lmin lmax Nexp Ncontr
exp1 contr1 contr2 contr3 ...
exp2 contr4 contr5 contr6 ...
Nexp....
n2 lmin lmax Nexp Ncontr
exp1 contr1 contr2 contr3 ...
exp2 contr4 contr5 contr6 ...
Nexp....
...

Nsets = number of sets.
n1,n2… = main quantum number (but it gets ignored by the program!)
lmin = min l (angular quantum number) of the set ( s = 0 ; p = 1 ; d = 2 …)
lmax = max l (angular quantum number) of the set ( s = 0 ; p = 1 ; d = 2 …)
Nexp = number of exponents of the set
Ncontr = number of contaction coefficients per angular quantum number

As an example:

      2                 2 Sets
1 0 0 1 1         Set 1: lmin=0 ; lmax=0 (→ s functions!) ; 1 exponent ; 1 contraction
0.35 1          exponent1 of  set 1 ; contraction
1 1 1 1 1         Set 2: lmin=1 ; lmax=1 (→ p functions!) ; 1 exponenet ; 1 contraction
0.6 1           exponent1 of set 2 ;  contraction

## 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                                    ! 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 eletcron 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 ….
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..

Repeat the procedure for H2.
H2 coordinates:

H 0 0 0
H 0.8 0 0   
The H2 molecule does not have unpaired electrons. Remember to take out the LSD and MULTIPLICITY keywords.

## Part II: Estimate the binding energy of H2

Binding energy:

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

The binding energy value is significant only if the same basis is used for both reactants and products.

You can now update your table:

Basis set Energy H (Eh) Energy H2 (Eh) 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:

• 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?

## Part IV: Additional 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