Table of Contents

GGA based surface science

GGA DFT calculations can be performed with CP2K relatively easily for many systems. While the CP2K reference manual lists all of the various options, the initial setup of a system is easy, and few details about the internals needs to be known. The input files provide here form a good template to start.

Crucial to start are a reasonable initial structure, and for condensed phase systems the size of the simulation cell. Once these are known, copy&paste might be enough to start the simulation.

Among the important parameters of the simulations are:

Assessing the influence of these parameters might be more challenging.

Dye anchoring to TiO$_2$

In this exercise you will compare two possible binding modes of acetic acid to anatase TiO$_2$. Acetic acid contains the carboxylic group. It is commonly used in Dye-Sensitized Solar Cells as an anchoring moiety to bind light harvesting dyes to semi-conducting substrates. We will therefore use acetic acid as a model of the more complex dye molecules, as done in this paper: 10.1021/jp4117563. To speedup calculations, only the smallest slab model is employed.

1. Task: Familiarize yourself with system and setup

job
#PBS -N mode1
#PBS -l select=2
#PBS -l walltime=0:20:0
#PBS -A y14
#PBS -j oe

cd $PBS_O_WORKDIR
module load cp2k

aprun -n 48 cp2k.popt -i mode1.inp -o mode1.out

2. Task: Binding induced density differences

We start with single point energy calculations on binding mode 1, to visualize the interaction between molecule and surface. The goal is to compute the binding induced density difference:

\[ \rho_\text{induced}= \rho_\text{slab-dye-complex} - \rho_\text{dye} - \rho_\text{slab} \]

First, we'll discuss in detail the structure and the choices made in the sample input file mode1.inp.

topics:

Second, we run the cp2k input and store the output for analysis and discussion. 

cp2k.popt -i mode1.inp -o mode1.out

In addition to the output mode1.out, other files are gerenated by CP2K named MODE1*

topics:

Third, we compute the changes in density induced by the binding. For this you will have to run three separate energy calculations:

  1. combined system bound in the first mode (file mode1.xyz)
  2. lone acetic acid molecule (just remove slab's coordinates from mode1.xyz), name the file mode1_dye.xyz
  3. lone TiO$_2$ slab (just remove the acid's coordinates from mode1.xyz), name the file mode1_slab.xyz

Create the .xyz files (check with vmd that they contain the right subsystems), and create mode1_dye.inp, mode1_slab.inp by changing both COORD_FILE_NAME and PROJECT accordingly.

After computing these input files, we analyze the results using a tool provided with cp2k cubecruncher.x that manipulates cube files (e.g. can compute difference). To build cubecruncher, make a copy of the code in your own directory and compile it: 

~$ module load cp2k
~$ cp -r $CP2K/../../tools/cubecruncher .
~$ cd cubecruncher
~$ module swap PrgEnv-cray PrgEnv-gnu
~$ make

Then run it as follows: 

~$ cubecruncher.x -i MODE1-ELECTRON_DENSITY-1_0.cube -subtract MODE1_dye-ELECTRON_DENSITY-1_0.cube -o tmp.cube
~$ cubecruncher.x -i tmp.cube -subtract MODE1_slab-ELECTRON_DENSITY-1_0.cube -center geo -o MODE1_delta.cube

You can visualize the resulting file MODE1_delta.cube with VMD.

What you get should look similar to this:

3. Task: relative stabilities

In order to compute the relative stability of mode1 and mode2, both configurations need to be geometry optimized.

To do so, turn off the generation of cubes (&E_DENSITY_CUBE OFF) in mode1.inp, change to RUN_TYPE GEO_OPT and adjust the project name. Create and run a similar input file for mode2.

input topics:

output topics:

Compare the final energies (ENERGY| Total FORCE_EVAL ( QS ) energy (a.u.):), and determine which mode is most stable. Does this agree with the values in table 1 of the manuscript cited ?

4. Task: ab initio molecular dynamics

This task is optional, and can be done near the end if time is available. Ab initio MD will be briefly discussed in a next exercise.

Perform a short ab initio molecular dynamics simulation of the system (~1000 steps, ~0.5ps) by changing to RUN_TYPE MD. After a couple of hours the job should be finished. Now analyze the OH distance in VMD. A possible outcome is :

What can you say about the hydrogen bond to the surface, relative acidity of the two oxygens ? Note that, in order to be statistically relevant, longer trajectories should be employed, and surface slab thickness will play an important role. Also compare to Fig. 7 of the paper referenced.

Required Files

(right) click on the filename to download to your local machine.

mode1.inp
&GLOBAL
  ! the project name is made part of most output files... useful to keep order 
  PROJECT MODE1
  ! various runtypes (energy, geo_opt, etc.) available.
  RUN_TYPE ENERGY             
&END GLOBAL

&FORCE_EVAL
  ! the electronic structure part of CP2K is named Quickstep
  METHOD Quickstep
  &DFT
    ! basis sets and pseudopotential files can be found in cp2k/data
    BASIS_SET_FILE_NAME BASIS_MOLOPT
    POTENTIAL_FILE_NAME GTH_POTENTIALS            

    ! Charge and multiplicity
    CHARGE 0
    MULTIPLICITY 1

    &MGRID
       ! PW cutoff ... depends on the element (basis) too small cutoffs lead to the eggbox effect.
       ! certain calculations (e.g. geometry optimization, vibrational frequencies,
       ! NPT and cell optimizations, need higher cutoffs)
       CUTOFF [Ry] 400 
    &END

    &QS
       ! use the GPW method (i.e. pseudopotential based calculations with the Gaussian and Plane Waves scheme).
       METHOD GPW 
       ! default threshold for numerics ~ roughly numerical accuracy of the total energy per electron,
       ! sets reasonable values for all other thresholds.
       EPS_DEFAULT 1.0E-10 
       ! used for MD, the method used to generate the initial guess.
       EXTRAPOLATION ASPC 
    &END

    &POISSON
       PERIODIC XYZ ! the default, gas phase systems should have 'NONE' and a wavelet solver
    &END

    &PRINT
       ! at the end of the SCF procedure generate cube files of the density
       &E_DENSITY_CUBE ON
       &END E_DENSITY_CUBE
    &END

    ! use the OT METHOD for robust and efficient SCF, suitable for all non-metallic systems.
    &SCF                              
      SCF_GUESS ATOMIC ! can be used to RESTART an interrupted calculation
      MAX_SCF 30
      EPS_SCF 1.0E-6 ! accuracy of the SCF procedure typically 1.0E-6 - 1.0E-7
      &OT
        ! an accurate preconditioner suitable also for larger systems
        PRECONDITIONER FULL_SINGLE_INVERSE
        ! the most robust choice (DIIS might sometimes be faster, but not as stable).
        MINIMIZER CG
      &END OT
      &OUTER_SCF ! repeat the inner SCF cycle 10 times
        MAX_SCF 10
        EPS_SCF 1.0E-6 ! must match the above
      &END
    &END SCF

    ! specify the exchange and correlation treatment
    &XC
      ! use a PBE functional 
      &XC_FUNCTIONAL 
         &PBE
         &END
      &END XC_FUNCTIONAL
      ! adding Grimme's D3 correction (by default without C9 terms) 
      &VDW_POTENTIAL
         POTENTIAL_TYPE PAIR_POTENTIAL 
         &PAIR_POTENTIAL
            PARAMETER_FILE_NAME dftd3.dat
            TYPE DFTD3
            REFERENCE_FUNCTIONAL PBE
            R_CUTOFF [angstrom] 16
         &END
      &END VDW_POTENTIAL
    &END XC
  &END DFT
 
  ! description of the system
  &SUBSYS
    &CELL 
      ! unit cells that are orthorhombic are more efficient with CP2K
      ABC [angstrom] 10.2270 11.3460 20.000
    &END CELL

    ! atom coordinates can be in the &COORD section,
    ! or provided as an external file.
    &TOPOLOGY
      COORD_FILE_NAME mode1.xyz
      COORD_FILE_FORMAT XYZ
    &END

    ! MOLOPT basis sets are fairly costly,
    ! but in the 'DZVP-MOLOPT-SR-GTH' available for all elements
    ! their contracted nature makes them suitable
    ! for condensed and gas phase systems alike.
    &KIND H                              
      BASIS_SET DZVP-MOLOPT-SR-GTH         
      POTENTIAL GTH-PBE-q1             
    &END KIND
    &KIND C
      BASIS_SET DZVP-MOLOPT-SR-GTH
      POTENTIAL GTH-PBE-q4
    &END KIND
    &KIND O
      BASIS_SET DZVP-MOLOPT-SR-GTH
      POTENTIAL GTH-PBE-q6
    &END KIND
    &KIND Ti
      BASIS_SET DZVP-MOLOPT-SR-GTH
      POTENTIAL GTH-PBE-q12
    &END KIND
  &END SUBSYS
&END FORCE_EVAL

! how to propagate the system, selection via RUN_TYPE in the &GLOBAL section
&MOTION
 &GEO_OPT
   OPTIMIZER BFGS ! Good choice for 'small' systems (use LBFGS for large systems)
   MAX_ITER  100
   MAX_DR    [bohr] 0.003 ! adjust target as needed
   &BFGS
   &END
 &END
 &MD
   ENSEMBLE NVT  ! sampling the canonical ensemble, accurate properties might need NVE
   TEMPERATURE [K] 300
   TIMESTEP [fs] 0.5
   STEPS 1000
   # GLE thermostat as generated at http://epfl-cosmo.github.io/gle4md 
   # GLE provides an effective NVT sampling.
   &THERMOSTAT
     REGION MASSIVE
     TYPE GLE
     &GLE
       NDIM 5
       A_SCALE [ps^-1] 1.00
       A_LIST    1.859575861256e+2   2.726385349840e-1   1.152610045461e+1  -3.641457826260e+1   2.317337581602e+2
       A_LIST   -2.780952471206e-1   8.595159180871e-5   7.218904801765e-1  -1.984453934386e-1   4.240925758342e-1
       A_LIST   -1.482580813121e+1  -7.218904801765e-1   1.359090212128e+0   5.149889628035e+0  -9.994926845099e+0
       A_LIST   -1.037218912688e+1   1.984453934386e-1  -5.149889628035e+0   2.666191089117e+1   1.150771549531e+1
       A_LIST    2.180134636042e+2  -4.240925758342e-1   9.994926845099e+0  -1.150771549531e+1   3.095839456559e+2
     &END GLE
   &END THERMOSTAT
 &END
&END
mode1.xyz
116

Ti       -0.0179479198       -0.0078042700       -0.0922850421
O         0.4497915479        0.0007412647        1.9321232563
Ti       -1.4316444492       -0.0089893346        2.8221490912
O        -1.7887110897        0.0007867236        0.7998892697
O        -3.2081345298        0.0411605531        3.6695321087
O        -1.8010755493       -1.8874663742        2.8216777686
Ti       -3.7269830403       -1.9006613639        3.6517557753
O         0.3830863054       -1.8910765741       -0.0700021876
Ti        3.7557586944       -1.8917451634        2.9143676586
O         3.3146470921       -0.0011081937        2.8729289358
O        -4.6680663094       -1.8855446073        2.0338712494
O        -5.4086768695       -1.8843459443        4.3991860126
Ti       -0.0282285127       -3.7757033787       -0.0787156736
O         0.4462623263       -3.7813137083        1.9359917441
Ti       -1.3999537875       -3.7707056149        2.8874421519
O        -1.7903153040       -3.7850263943        0.8021001791
O        -3.2390175951       -3.7978185279        3.6716494047
O        -1.7864035184       -5.6734792481        2.8627360747
Ti       -3.7357623244       -5.6788609282        3.4482649850
O         0.3837694100       -5.6723382681       -0.0690470865
Ti        3.7205660980       -5.6668034549        2.9114784222
O         3.3236114384       -3.7787921003        2.8721776992
O        -4.6689995455       -5.6807480198        1.9358553242
O        -5.3525041570       -5.6742752842        4.3359372112
Ti       -0.0314402214        3.7828933451       -0.0777664638
O         0.4518754735        3.7839662632        1.9399715530
Ti       -1.3792280628        3.7857276911        2.9025413153
O        -1.7909627210        3.7866794195        0.8027290293
O        -3.2026665631        3.7827561658        3.7306777258
O        -1.7857471998        1.9013100770        2.8154049594
Ti       -3.7307612355        1.9120465523        3.4387577457
O         0.3836352141        1.8909325251       -0.0691199251
Ti        3.7223424203        1.8887162901        2.9133081650
O         3.3250830331        3.7807500488        2.8687333178
O        -4.6728325926        1.9008997868        1.9326739591
O        -5.3457700344        1.8899459254        4.3344454640
Ti       -1.4852085406       -0.0011927086       -3.7100466053
O        -1.0850586016       -0.0008795951       -1.6147031707
Ti       -2.8526945884       -0.0039467894       -0.7412906371
O        -3.3269327110       -0.0004491456       -2.7420242486
O        -4.7289708978       -0.0017641392       -0.0618098107
O        -3.2591453480       -1.8898583454       -0.7264179834
Ti       -5.1372070666       -1.8918692243       -0.0012386637
O        -1.0878410276       -1.8908975100       -3.6681494905
Ti        2.2953566326       -1.8945802968       -0.7324918911
O         1.8572641703       -0.0016921856       -0.7344045642
O         4.0371444331       -1.8910414726       -1.5881377025
O         3.3210868792       -1.8907741455        0.8191885244
Ti       -1.4878179598       -3.7811586802       -3.7059227721
O        -1.0853532342       -3.7809408508       -1.6116052274
Ti       -2.8450252555       -3.7788195849       -0.7274776599
O        -3.3267379004       -3.7812381637       -2.7423527944
O        -4.7300872942       -3.7790968457       -0.0598090260
O        -3.2604741093       -5.6718710426       -0.7338292499
Ti       -5.1447866872       -5.6729502955       -0.0741564861
O        -1.0884608345       -5.6727912820       -3.6676316873
Ti        2.2684209803       -5.6717142765       -0.7217304029
O         1.8574125893       -3.7804564443       -0.7330818756
O         4.0285990372       -5.6721054737       -1.6077890803
O         3.3201243312       -5.6722897918        0.8087243331
Ti       -1.4884820434        3.7822906244       -3.7073217712
O        -1.0847762013        3.7818636329       -1.6113017246
Ti       -2.8439453199        3.7841411650       -0.7265400935
O        -3.3267270296        3.7819066970       -2.7433025606
O        -4.7312054524        3.7823723470       -0.0697069103
O        -3.2595288817        1.8897668415       -0.7334187674
Ti       -5.1446141745        1.8933189943       -0.0754881482
O        -1.0885182339        1.8906776867       -3.6679434552
Ti        2.2687722606        1.8941648243       -0.7213872473
O         1.8555780589        3.7824519637       -0.7335160805
O         4.0283551896        1.8906904137       -1.6083035670
O         3.3194888527        1.8901215845        0.8082989311
Ti        1.3702533850       -0.0107406935        3.4478828397
O        -2.6375196242       -0.0002691731       -5.1384544425
Ti       -4.2555253076       -0.0004346746       -4.2635860836
O        -0.2706997157       -0.0070914550        4.3327078320
O         4.0252034756       -0.0000815787       -3.6655962284
O        -4.7789243271       -1.8904283625       -4.5262265362
Ti        3.6276350884       -1.8913012322       -3.6941431294
O         1.8693336769       -1.8883429262        3.7243207414
Ti        0.8648978359       -1.8921733057       -4.2643698117
O         0.3356892769       -0.0005951329       -4.5283168344
O         2.4831990038       -1.8910320844       -5.1341360953
O         1.7891597814       -1.8911498456       -2.7417208102
Ti        1.3675607179       -3.7714249561        3.4584460387
O        -2.6361368408       -3.7817733748       -5.1377491017
Ti       -4.2537976019       -3.7816703567       -4.2621660812
O        -0.2527486810       -3.7773208994        4.3296691681
O         4.0251551834       -3.7817133665       -3.6656274881
O        -4.7792586102       -5.6728660382       -4.5273909859
Ti        3.6247553952       -5.6729206250       -3.7048960624
O         1.9006169442       -5.6721819263        3.7282320026
Ti        0.8602204280       -5.6728510136       -4.2616392365
O         0.3358111887       -3.7815283986       -4.5276229355
O         2.4785034911       -5.6729185089       -5.1373985723
O         1.7869078663       -5.6728807589       -2.7423620036
Ti        1.3817457800        3.7823928879        3.4589497419
O        -2.6363646230        3.7820140473       -5.1385122329
Ti       -4.2543090361        3.7822671573       -4.2626609244
O        -0.2374835922        3.7781640807        4.3379058406
O         4.0248222240        3.7818879520       -3.6667895479
O        -4.7794862202        1.8903770813       -4.5277962247
Ti        3.6243254290        1.8913422637       -3.7051707738
O         1.8974839341        1.8882474143        3.7289879155
Ti        0.8600377417        1.8920214690       -4.2620560393
O         0.3346421543        3.7821159876       -4.5275899679
O         2.4782941685        1.8909856222       -5.1376874872
O         1.7866749487        1.8910410218       -2.7427494459
H        -3.2770955004       -2.4268873548        8.1687296457
C        -3.1978647566       -1.3575831172        7.9359146369 
H        -4.2239524320       -0.9733256879        7.8414028480
H        -2.6752907472       -0.8249390527        8.7355765151
C        -2.5132448898       -1.1924834089        6.6141051521 
O        -2.8755597850       -1.8460118394        5.6163779603
O        -1.5275649623       -0.3212592281        6.6009413157
H        -1.0670534373       -0.2549619720        5.6840567874
mode2.xyz
116

Ti        0.0150786099       -0.0030604155       -0.2374201259
O         0.4515580466       -0.0646282100        1.8001155831
Ti       -1.5073356783       -0.0021026124        2.5525864818
O        -1.7759961007       -0.0002275800        0.6680111337
O        -3.3291162152       -0.0023490698        3.0696212715
O        -1.7197127142       -1.8809866556        2.8642842575
Ti       -3.6978004404       -1.8661667177        3.6084326925
O         0.3785074831       -1.8945596770       -0.1980298452
Ti        3.7996574045       -1.9219539316        2.8301270999
O         3.3305054330       -0.0058364403        2.7942261562
O        -4.6900333011       -1.9659285303        1.9448925419
O        -5.3925681292       -1.8976344334        4.3248895668
Ti       -0.0283064667       -3.7737024590       -0.1507446117
O         0.4475870469       -3.7803762159        1.8621586431
Ti       -1.3713031978       -3.7725215345        2.8511642577
O        -1.7912822225       -3.7729870345        0.7436262925
O        -3.1963784791       -3.7804631987        3.6648868231
O        -1.7705984874       -5.6752809020        2.8039139185
Ti       -3.7092032911       -5.6725438342        3.3897938268
O         0.3841910583       -5.6739517448       -0.1381224421
Ti        3.7513121067       -5.6747221635        2.8551954028
O         3.3367138059       -3.7840186471        2.8127851513
O        -4.6560725160       -5.6733549533        1.8776383238
O        -5.3204369054       -5.6669271369        4.2778026483
Ti       -0.0266777619        3.7696389407       -0.1491534163
O         0.4524897086        3.7857220830        1.8631418152
Ti       -1.3730627656        3.7742135603        2.8371003388
O        -1.7905256319        3.7786525562        0.7422177730
O        -3.1948630000        3.7795989881        3.6670918260
O        -1.7343662633        1.8899845272        2.8090040137
Ti       -3.6974632076        1.8668219133        3.5884163764
O         0.3822543310        1.8874843004       -0.1432095900
Ti        3.7864567490        1.9054527096        2.8508016360
O         3.3675002865        3.7799021368        2.8626057027
O        -4.6840457398        1.9746044749        1.9466850498
O        -5.3729095331        1.8414022655        4.3320391075
Ti       -1.5079668291       -0.0008456767       -3.7989215478
O        -1.0951317039        0.0022938033       -1.7345576883
Ti       -2.8929121223       -0.0000735048       -0.8782772455
O        -3.3736661811        0.0005357865       -2.8128806833
O        -4.7193863680        0.0001570116       -0.0748056115
O        -3.2632860440       -1.8860154449       -0.7956216654
Ti       -5.1307996411       -1.8978086035       -0.0398179095
O        -1.1320787396       -1.8909803808       -3.7440163178
Ti        2.3133857413       -1.9061341614       -0.8099170994
O         1.8786839357        0.0011314062       -0.8069543100
O         4.0385009963       -1.8895616393       -1.6570045786
O         3.3115055560       -1.8920970172        0.7501369741
Ti       -1.5256127358       -3.7819843403       -3.7701763163
O        -1.0940683369       -3.7869847697       -1.6789541127
Ti       -2.8425313294       -3.7819322313       -0.7839726892
O        -3.3422315516       -3.7760564219       -2.8030699366
O        -4.7315665522       -3.7831312336       -0.1321164185
O        -3.2580399316       -5.6728032840       -0.7985618810
Ti       -5.1462151180       -5.6726106968       -0.1400092932
O        -1.1340144859       -5.6732616791       -3.7388880843
Ti        2.2670101177       -5.6749205566       -0.7762329495
O         1.8631140907       -3.7853073574       -0.7974118985
O         4.0263575475       -5.6730177766       -1.6715945206
O         3.3250517248       -5.6784227751        0.7515944134
Ti       -1.5248867442        3.7818848512       -3.7712820230
O        -1.0907299886        3.7812336768       -1.6778258037
Ti       -2.8428177895        3.7841675976       -0.7861032158
O        -3.3397902383        3.7762483047       -2.8026235400
O        -4.7304156316        3.7842200412       -0.1318958639
O        -3.2645051173        1.8869138058       -0.7933488063
Ti       -5.1241443302        1.8993249071       -0.0252297449
O        -1.1314283131        1.8906347021       -3.7440419862
Ti        2.3185671036        1.9017475834       -0.7833845676
O         1.8597419566        3.7800089897       -0.7974665372
O         4.0344536794        1.8895028649       -1.6315658326
O         3.3098310076        1.8936248995        0.7823280807
Ti        1.4537853090       -0.0347286638        3.2604875735
O        -2.6845024000        0.0000746592       -5.2147510734
Ti       -4.2967571219        0.0018586454       -4.3442818967
O        -0.2511143909        0.1328085915        4.2720687411
O         3.9819696258        0.0012627538       -3.7355131655
O        -4.8038476957       -1.8889916108       -4.5923792314
Ti        3.5953547314       -1.8907810205       -3.7642624098
O         1.8553660493       -1.8815919187        3.6062633048
Ti        0.8351449362       -1.8959349617       -4.3196742869
O         0.3119042183       -0.0001283684       -4.5915870901
O         2.4377532123       -1.8915585194       -5.2027330310
O         1.7783437087       -1.8888222418       -2.8082665928
Ti        1.3904951140       -3.7857957693        3.3690175525
O        -2.6814201117       -3.7831847959       -5.2025558657
Ti       -4.2854691947       -3.7801054852       -4.3136778334
O        -0.2074321278       -3.7970194791        4.2709539045
O         3.9820256895       -3.7800854351       -3.7356644708
O        -4.7961377238       -5.6736624399       -4.5471769110
Ti        3.5917963887       -5.6730897244       -3.7666434973
O         1.9069112439       -5.6781980199        3.6136248160
Ti        0.8312484616       -5.6732029738       -4.3044789530
O         0.3186267326       -3.7822693739       -4.5479829736
O         2.4335197920       -5.6733247069       -5.1986406627
O         1.7786689446       -5.6734212363       -2.7982114552
Ti        1.3984968329        3.7644681343        3.3685503422
O        -2.6815455972        3.7828337111       -5.2024703087
Ti       -4.2855071694        3.7788568387       -4.3128750844
O        -0.2044150611        3.7319133608        4.2704391005
O         3.9827213914        3.7789077586       -3.7330838039
O        -4.8039829955        1.8898269577       -4.5907748518
Ti        3.5899147654        1.8912350407       -3.7590482617
O         1.8739898095        1.8720733323        3.5992207033
Ti        0.8344557677        1.8954291350       -4.3129140724
O         0.3192643376        3.7819866970       -4.5466934222
O         2.4382493211        1.8919495801       -5.1986096411
O         1.7788752457        1.8885973165       -2.8025129463
H        -1.3211320733       -0.5901398003        7.3622691450
C        -2.2774669737       -0.0487846563        7.3616031246
H        -2.9713818519       -0.6195053843        7.9928436643
H        -2.1415146457        0.9598101494        7.7628564958
C        -2.8081585120       -0.0061954447        5.9550273922
O        -3.0662415287       -1.1345711119        5.4074245732
O        -2.9500441444        1.1398319329        5.4010622063
H        -0.3897742635        1.0153182782        4.6757696096