====== Hartree-Fock exchange for the dihydrogen cation ======

The goal of this exercise is to calculate the dissociate enery profile of the [[wp>Dihydrogen_cation|dihydrogen cation]] $H_2^+$.
The curve should be record for three different fractions of Hartree-Fock exchange:
  * 0% HF exchange, 100% PBE exchange
  * 50% HF exchange, 50% PBE exchange
  * 100% HF exchange, 0% PBE exchange

===== Questions =====
  * Report the dissociation curve for the $H^+_2$ ion, for the three fractions of Hartree-Fock exchange employed.

===== Required Files =====

==== Input File ====
<code - H2ion.inp>
&GLOBAL
  PROJECT H2ion
  RUN_TYPE ENERGY
&END GLOBAL

&FORCE_EVAL
  METHOD Quickstep
  &DFT
    ! data-files for basis-set and pseudo-potentials
    BASIS_SET_FILE_NAME HFX_BASIS  
    POTENTIAL_FILE_NAME POTENTIAL
    
    &MGRID              ! resolution of finest grid, higher values give more accurate results
      CUTOFF 400
    &END MGRID

    &POISSON            ! Non periodic calculation needs Poisson solver
      PERIODIC NONE
      PSOLVER  WAVELET
    &END POISSON
    
    &SCF                 ! need to achieve SCF-convergence at large H-H distances
      &OT
        PRECONDITIONER FULL_ALL
      &END OT
    &END SCF
    
    CHARGE 1             ! H2 cation is positively charged...
    MULTIPLICITY 2       ! ...and therefore in a doublet spin state...
    LSD                  ! ...so that we have to run an unrestricted Kohn-Sham calculation
    
    &XC                  ! Exchange and Correlation settings
      &XC_FUNCTIONAL
        &PBE
          SCALE_X 0.5   ! amount of PBE eXchange (vary consistently with the HF/FRACTION)
          SCALE_C 1.0    ! amount of PBE Correlation. DO NOT VARY!!!!!!
        &END
      &END XC_FUNCTIONAL
      &HF
        FRACTION 0.5    ! amount of HF eXchange (vary consistently with PBE/SCALE_X)
        &SCREENING
          EPS_SCHWARZ 1.0E-10
        &END
      &END HF
    &END XC
  &END DFT

  &SUBSYS
    &TOPOLOGY
      &CENTER_COORDINATES  ! keep atoms away from box borders, would confuse Poisson solver
      &END
    &END
    &CELL
      ABC 15.0 15.0 15.0
      PERIODIC NONE  ! Non periodic calculation. 
    &END CELL
    &COORD
       H    0.0   0.0   0.0
       H    0.42  0.0   0.0  ! vary H-H distance to record dissociation profile
    &END COORD
    &KIND H
      BASIS_SET DZVP-GTH
      POTENTIAL GTH-PBE-q1
    &END KIND
  &END SUBSYS
&END FORCE_EVAL
</code>

==== Basis Set ====
<code - HFX_BASIS>
H DZVP-GTH
  3
  1  0  0  3  1
        8.3744350009  -0.0283380461 
        1.8058681460  -0.1333810052 
        0.4852528328  -0.3995676063 
  1  0  0  1  1
        0.1658236932   1.0000000000
  2  1  1  1  1
        0.7270000000   1.0000000000
#
C DZVP-GTH
  3
  2  0  1  3  1  1
        4.3362376436   0.1490797872  -0.0878123619
        1.2881838513  -0.0292640031  -0.2775560300
        0.4037767149  -0.6882040510  -0.4712295093
  2  0  1  1  1  1
        0.1187877657   1.0000000000   1.0000000000
  3  2  2  1  1
        0.5500000000   1.0000000000
</code>

==== Pseudo Potential ====
<code - POTENTIAL>
H GTH-PBE-q1
    1
     0.20000000    2    -4.17890044     0.72446331
    0
#
C GTH-PBE-q4
    2    2
     0.33847124    2    -8.80367398     1.33921085
    2
     0.30257575    1     9.62248665
     0.29150694    0
</code>