Binding Energy of the Benzene Dimer
- Questions
- Required files

Binding Energy of the Benzene Dimer

The goal of this exercise is to compute the interaction energy for a π-stacked benzene dimer, with three different methods:

PBE with no dispersion interaction
PBE with parametrized dispersion interaction (PBE-DFTD3)
MP2 (Møller-Plesset perturbation theory)

The formula to compute the interaction energy is: \[E_\text{interaction}= E_\text{dimer}- 2 E_\text{benzene}\]

The equilibrium distance between the $\pi$-stacked benzene rings has to be obtained through geometry optimization for every level of theory separately. Since the cost of MP2 calculations are very hight, we provide you with the readily optimized geometry for this method. For the other two methods (PBE, PBE-DFTD3) this provided geometry has to be re-optimized.

You will also require energy calculations of the single benzene molecule. You can extract the coordinates of a single benzene ring with VMD or a text editor. Again, the geometry has to be optimized separately for each method. The correct geometry for MP2-benzene can be found at the end of the exercise and, due to time issues, should not be re-optimized.

Questions

Report interaction energy and equilibrium distance for each method

Required files

DFT-D3 Parameters

Download here

This file is compressed with gzip. To unpack it run:

$ gunzip dftd3.dat.gz

Input File

benzene_dimer.inp

&GLOBAL
  PROJECT      benzene_dimer
  RUN_TYPE     ENERGY
&END GLOBAL

&FORCE_EVAL
  METHOD         Quickstep
  &DFT

!specification of external basis and potential files
    BASIS_SET_FILE_NAME    ./BASIS
    POTENTIAL_FILE_NAME    ./POTENTIALS

!section to ensure stable and correct simulations
    &MGRID
      CUTOFF    400
    &END MGRID
    &QS
      METHOD GPW
      EPS_DEFAULT  1.0E-8
      EPS_PGF_ORB  1.0E-8
    &END QS
    &SCF
      SCF_GUESS ATOMIC
      EPS_SCF 1.0E-6
      MAX_SCF 40
      &OT
        MINIMIZER       CG
        PRECONDITIONER  FULL_SINGLE_INVERSE
      &END
      &OUTER_SCF
        EPS_SCF 1.0E-6
        MAX_SCF 10
      &END
    &END SCF
    
    &POISSON            ! Non periodic calculation needs Poisson solver
      PERIODIC NONE
      PSOLVER  WAVELET
    &END POISSON

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!This is the section for PBE calculations
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!&XC
!     &XC_FUNCTIONAL PBE                         ! PBE functional
!     &END
!&END XC
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!This is the section for PBE-DFTD3 calculations
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!&XC
!     &XC_FUNCTIONAL PBE                         ! PBE functional + ... 
!     &END
!      &VDW_POTENTIAL                            ! ... dispersion interactions
!         POTENTIAL_TYPE PAIR_POTENTIAL           
!         &PAIR_POTENTIAL
!            TYPE DFTD3                          ! computed with the DFTD3 method 
!            REFERENCE_FUNCTIONAL PBE
!            ! that requires the following parameters (in external file, specified here)
!            PARAMETER_FILE_NAME ./dftd3.dat     
!            R_CUTOFF 15                         ! cutoff raddius for the dispersion interactions
!         &END PAIR_POTENTIAL
!      &END 
!&END XC
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!This is the section for MP2 calculations
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!    &XC
!      &XC_FUNCTIONAL NONE                       
!      &END XC_FUNCTIONAL
!       &HF                                      ! MP2 runs on top of a parent 100%HF calculation
!         FRACTION    1.0                        ! 100% hf
!         &SCREENING                             ! Screening of the electronic repulstion up to the given threshold. Section is needed
!           EPS_SCHWARZ          1.0E-9
!         &END SCREENING
!         &MEMORY
!           MAX_MEMORY  1800                     ! uses some memory to store data and not recompute each step
!         &END
!       &END HF
!       &WF_CORRELATION                          ! this section actually sets up MP2 on top of the parent calculation
!         METHOD  RI_MP2_GPW
!         &RI_MP2                                ! parameters infulencing the calculation
!           BLOCK_SIZE       1                   ! Larger BLOCK_SIZE reduces communication but requires more memory
!         &END
!         &WFC_GPW
!         &END
!         MEMORY    1800
!         NUMBER_PROC  1
!       &END
!    &END XC
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!


  &END DFT
  
  &SUBSYS
    &CELL
      ABC [angstrom]  15 15 15
      PERIODIC NONE           ! Non periodic calculation.
    &END CELL
    
    &COORD
! specification of an external file with coordinates 
@INCLUDE 'benzene_dimer.coord'                    
    &END
    
    &TOPOLOGY
      &CENTER_COORDINATES       ! keep atoms away from box borders, would confuse Poisson solver
      &END
    &END TOPOLOGY
 
!specification of external basis sets and potentials. The name of the files is given above.   
    &KIND H
      BASIS_SET         cc-TZ
      RI_AUX_BASIS_SET  RI_TZ  ! auxiliary basis set, only used by MP2 
      POTENTIAL         GTH-HF-q1      
    &END KIND
    &KIND C
      BASIS_SET         cc-TZ
      RI_AUX_BASIS_SET  RI_TZ  ! auxiliary basis set, only used by MP2 
      POTENTIAL         GTH-HF-q4
    &END KIND
  &END SUBSYS
&END FORCE_EVAL

MP2 optimized Coordinates

benzene_dimer-MP2.xyz

      24
 
  H         8.5709951714        6.1617188657        9.1769626364
  C         8.0387778483        5.9757981379        8.2528397815
  C         6.6427474511        5.9561428224        8.2430496957
  H         6.0937543445        6.1249650636        9.1610309894
  C         5.9546039990        5.7314555716        7.0475649921
  H         4.8717398728        5.7196290593        7.0404902271
  C         6.6635660065        5.5279574532        5.8611612413
  H         6.1300650069        5.3536860275        4.9350551393
  C         8.0615723757        5.5446390494        5.8709776417
  H         8.6121087088        5.3836499080        4.9523278088
  C         8.7479484762        5.7683467907        7.0666774749
  H         9.8306982448        5.7893185194        7.0736980974
  H         6.4284687494        8.8405192314        5.8228620343
  H         8.9057373702        8.8752743844        5.8387264727
  C         6.9607954533        9.0255100555        6.7471184900
  C         8.3568440363        9.0439429763        6.7567676586
  C         6.2520232187        9.2329626290        7.9335080936
  C         9.0454365692        9.2673522387        7.9522880615
  H         5.1692478273        9.2131682112        7.9263504668
  H        10.1283042427        9.2780238064        7.9594286415
  C         6.9387312641        9.4553058890        9.1292884396
  C         8.3367433685        9.4704785560        9.1388664843
  H         6.3883177411        9.6163935534       10.0479844468
  H         8.8703567259        9.6435467092       10.0651664724

benzene_single-MP2.xyz

      12

  H         6.1262627761        7.1212715024        5.4828227563
  H         8.5732243361        7.5001625689        5.2622083944
  C         6.7242262925        7.2913230904        6.3696466162
  C         8.1119736218        7.5056915052        6.2411303862
  C         6.1180158107        7.2967148061        7.6292415320
  C         8.8755347118        7.7265259429        7.3870351849
  H         5.0517765554        7.1342555694        7.7226358929
  H         9.9417304949        7.8913874915        7.3106848370
  C         6.9022569902        7.5193295225        8.7662224005
  C         8.2690952105        7.7333521589        8.6460673286
  H         6.4422124064        7.5272841315        9.7460678529
  H         8.8675237526        7.9040662104        9.5317665736

Basis Set

BASIS

 #
H  cc-TZ
  6
  1  0  0  3  1
       10.8827241585  -0.0167058885
        3.0968750876  -0.0627538300
        0.9874518162  -0.1917521975
  1  0  0  1  1
        0.3450687533   1.0000000000
  1  0  0  1  1
        0.1492693554   1.0000000000
  2  1  1  1  1
        1.4070000000   1.0000000000
  2  1  1  1  1
        0.3880000000   1.0000000000
  3  2  2  1  1
        1.0570000000   1.0000000000
#
C  cc-TZ
  6
  2  0  1  3  1  1
        5.3685662937   0.0974901974  -0.0510969367
        1.9830691554   0.1041996677  -0.1693035193
        0.6978346167  -0.3645093878  -0.3579933930
  2  0  1  1  1  1
        0.2430968816   1.0000000000   1.0000000000
  2  0  1  1  1  1
        0.0812865018   1.0000000000   1.0000000000
  3  2  2  1  1
        1.0970000000   1.0000000000
  3  2  2  1  1
        0.3180000000   1.0000000000
  4  3  3  1  1
        0.7610000000   1.0000000000
#
#
 H   RI_TZ
  10
  1  0  0  1  1
        8.5115919487        1.0000000000
  1  0  0  1  1
        1.8744684087        1.0000000000
  1  0  0  1  1
        0.5632515602        1.0000000000
  1  0  0  1  1
        0.3698299759        1.0000000000
  1  1  1  1  1
        2.3711712242        1.0000000000
  1  1  1  1  1
        1.1794161391        1.0000000000
  1  1  1  1  1
        0.6050431621        1.0000000000
  1  2  2  1  1
        1.8092525711        1.0000000000
  1  2  2  1  1
        1.1433220615        1.0000000000
  1  3  3  1  1
        1.8065804513        1.0000000000
#
 C   RI_TZ
  20
  1  0  0  1  1
       22.2608165950        1.0000000000
  1  0  0  1  1
        7.1315246807        1.0000000000
  1  0  0  1  1
        3.5380450775        1.0000000000
  1  0  0  1  1
        1.2333453175        1.0000000000
  1  0  0  1  1
        0.2821517353        1.0000000000
  1  0  0  1  1
        0.3468258230        1.0000000000
  1  1  1  1  1
        7.2975063903        1.0000000000
  1  1  1  1  1
        3.7896065213        1.0000000000
  1  1  1  1  1
        1.0633834831        1.0000000000
  1  1  1  1  1
        0.2356430320        1.0000000000
  1  1  1  1  1
        0.5078423493        1.0000000000
  1  2  2  1  1
        9.9000557486        1.0000000000
  1  2  2  1  1
        2.3408375066        1.0000000000
  1  2  2  1  1
        1.5195338451        1.0000000000
  1  2  2  1  1
        0.5788522388        1.0000000000
  1  2  2  1  1
        0.3721345858        1.0000000000
  1  3  3  1  1
        1.9332589728        1.0000000000
  1  3  3  1  1
        1.1560553410        1.0000000000
  1  3  3  1  1
        0.4987261239        1.0000000000
  1  4  4  1  1
        1.2175667359        1.0000000000
#

Pseudo-Potentials

POTENTIALS

#
H GTH-HF-q1
    1    0    0    0
    0.196680577426       2   -4.122010670148    0.685113494453
       0
#    
C GTH-HF-q4
    2    2    0    0
    0.315416975333       2   -8.867306339232    1.255277018021
       1
    0.301022709314       1    9.800185699152

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