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--- exercise:basis_sets [2014/03/25 13:02] – sclelia
+++ exercises:2014_ethz_mmm:basis_sets [2020/08/21 10:15] (current) – external edit 127.0.0.1
@@ Line 1: / Line 1: @@
 ====== 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:
+The cp2k basis set format is described in detail [[:basis_sets|here]].
-<code>
+===== Part I: Different basis sets for H and H2 =====
+==== 1.Step ====
+Run a calculation with the following input file. Comment lines are marked with !
+<code - 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
+
+0 0 1 1
+.35 1
+0 0 1 1
+.6 1
+     &END
+     POTENTIAL ALL                         ! Specifes that the potential is for all electron calculations.
+     &POTENTIAL                            ! Usual all electron potential for H
+    0    0
+.20000000    0
+     &END POTENTIAL
+    &END KIND
+  &END SUBSYS
+&END FORCE_EVAL
-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....
-    ...
 </code>
-\\
-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.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                          | .... |
+<note tip>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.. </note>
+Repeat the procedure for H2. \\
+H2 coordinates:
 <code>
-                 2 Sets
+H 0 0 0
- 0 0 1 1         Set 1: lmin=0 ; lmax=0 (→ s functions!) ; 1 exponent ; 1 contraction
+H 0.75 0 0
-.35 1          exponent1 of  set 1 ; contraction
-1 1 1 1         Set 2: lmin=1 ; lmax=1 (→ p functions!) ; 1 exponenet ; 1 contraction
-.6 1           exponent1 of set 2 ;  contraction
 </code>
+<note important> The H2 molecule does not have unpaired electrons. Remember to take out the LSD and MULTIPLICITY keywords. </note>
+===== Part II: Estimate the binding energy of H2 =====
+Binding energy: \\
+\[ \sum E_\text{products} -  \sum E_\text{rectants} = E(H_2) - 2 \cdot E(H) \]
+<note important> The binding energy value is significant only if the same basis is used for both reactants and products. </note>
+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
+  0  0  2  1
+.34480000          0.07929900
+.66049000          0.42422000
+  0  0  1  1
+.13669000          1.00000000
+H  pc-1
+  0  0  3  1
+.25200000          0.02282200
+.86870000          0.15564000
+.41821000          0.48898000
+  0  0  1  1
+.10610000          1.00000000
+  1  1  1  1
+.00000000          1.00000000
+H  pc-2
+  0  0  4  1
+.42300000          0.00240650
+.35000000          0.01848700
+.59930000          0.08974200
+.73513000          0.28111000
+  0  0  1  1
+.23167000          1.00000000
+  0  0  1  1
+.07414700          1.00000000
+  1  1  1  1
+.60000000          1.00000000
+  1  1  1  1
+.45000000          1.00000000
+  2  2  1  1
+.25000000          1.00000000
-===== Part I:  =====