4.5. Example: Li+, Na+, and Cs+ in (C6H6)6

Tip

The sample input and output files can be found in testfiles/rigidmol/2-mben.

4.5.1. Global Optimization

The systems here are benzene-solvated cations: \(\mathrm{Li}^{+}\), \(\mathrm{Na}^{+}\) and \(\mathrm{Cs}^{+}\) in \(\left(\mathrm{C}_6\mathrm{H}_6\right)_{6}\). The parameter files are misc/charmm36/li.xyz, misc/charmm36/na.xyz, misc/charmm36/cs.xyz, and misc/charmm36/c6h6.xyz.

Let’s first consider \(\mathrm{Li}^{+}\).

Step 1: Prepare an input file named li-ben6.inp with the following content:

li-ben.inp
1li-ben.cluster # cluster file name
220             # population size
320             # maximal generations
43              # scout limit
510.00000000    # amplitude
6li-ben         # save optimized configuration
730             # number of LMs to be saved

Step 2: Copy misc/charmm36/li.xyz and misc/charmm36/c6h6.xyz to the current path. Then prepare the cluster file named li-ben.cluster with the following content:

li-ben.cluster
12
2c6h6.xyz   6
3li.xyz     1
4* 10.0000

Step 3: Run the global optimization:

$ rigidmol li-ben.inp > li-ben.out

After a few seconds, You will find the global minimum in li-ben-OPT.xyz and local minima in li-ben-LM.

For \(\mathrm{Na}^{+}\) and \(\mathrm{Cs}^{+}\), the global optimization procedure is similar. Below, the global minima are visualized (li-ben/0.xyz, na-ben/0.xyz, and cs-ben/0.xyz).

alternate text alternate text alternate text

4.5.2. Many-Body Energy Decomposition Analysis

You can also do a many-body energy decomposition analysis (MB-EDA) for these clusters. Its detail can be seen in Theoretical Background and For Molecular Clusters: Many-Body Energy Decomposition Analysis. Here, we just show how to perform MB-EDA for li-ben-OPT.xyz.

You can follow the same procedure given in Example: (H2O)6, giving an input file:

li-ben-mbedas.inp
  1basis
  2    def2-svp
  3end
  4
  5scf
  6    charge    +1 # Total charge.
  7    spin2p1    1
  8    type       U
  9end
 10
 11grimmedisp
 12    type bj
 13end
 14
 15eda
 16    type      mb_tso
 17    mb_level  4
 18    frag  0 1 1-12
 19    frag  0 1 13-24
 20    frag  0 1 25-36
 21    frag  0 1 37-48
 22    frag  0 1 49-60
 23    frag  0 1 61-72
 24    frag +1 1 73
 25end
 26
 27mol
 28    C     -1.75006483     -2.50086495     -1.46649878
 29    C     -2.81068652     -1.66329526     -1.11472696
 30    C     -2.62823535     -0.67551816     -0.14457631
 31    C     -1.38516251     -0.52531075      0.47380254
 32    C     -0.32454082     -1.36288045      0.12203072
 33    C     -0.50699198     -2.35065754     -0.84811994
 34    H     -1.89204211     -3.26951948     -2.22143701
 35    H     -3.77800267     -1.78018143     -1.59592790
 36    H     -3.45357435     -0.02375051      0.12916029
 37    H     -1.24318522      0.24334377      1.22874077
 38    H      0.64277533     -1.24599428      0.60323166
 39    H      0.31834702     -3.00242519     -1.12185654
 40    C      3.51095455      1.53702219     -0.03149057
 41    C      3.47459063      2.77605637     -0.67465209
 42    C      2.43502071      3.67007163     -0.40967021
 43    C      1.43181471      3.32505273      0.49847320
 44    C      1.46817863      2.08601855      1.14163471
 45    C      2.50774855      1.19200328      0.87665283
 46    H      4.31991249      0.84132993     -0.23769046
 47    H      4.25525071      3.04453813     -1.38133777
 48    H      2.40672359      4.63424502     -0.91015619
 49    H      0.62285677      4.02074499      0.70467308
 50    H      0.68751856      1.81753679      1.84832039
 51    H      2.53604567      0.22782990      1.37713881
 52    C      3.35416479     -1.90024170     -1.71678785
 53    C      3.01689469     -2.79729695     -2.73252676
 54    C      2.66461236     -4.11089136     -2.41542864
 55    C      2.64960014     -4.52743052     -1.08259161
 56    C      2.98687024     -3.63037527     -0.06685271
 57    C      3.33915257     -2.31678086     -0.38395083
 58    H      3.62829891     -0.87804723     -1.96354282
 59    H      3.02857667     -2.47316066     -3.76969427
 60    H      2.40216048     -4.80894860     -3.20584141
 61    H      2.37546602     -5.54962499     -0.83583665
 62    H      2.97518826     -3.95451156      0.97031480
 63    H      3.60160445     -1.61872362      0.40646194
 64    C      0.43458154      0.03908166     -3.51702644
 65    C      0.56674764      1.10282928     -2.62195220
 66    C     -0.54649842      1.87721022     -2.28848303
 67    C     -1.79191058      1.58784355     -2.85008809
 68    C     -1.92407668      0.52409593     -3.74516233
 69    C     -0.81083062     -0.25028501     -4.07863150
 70    H      1.30087174     -0.56351524     -3.77652080
 71    H      1.53588414      1.32800440     -2.18493062
 72    H     -0.44365132      2.70498169     -1.59196732
 73    H     -2.65820078      2.19044045     -2.59059373
 74    H     -2.89321318      0.29892081     -4.18218391
 75    H     -0.91367771     -1.07805648     -4.77514721
 76    C     -2.48564491      3.61935571      0.59972959
 77    C     -3.72351363      3.35244886      0.01097963
 78    C     -4.64114686      2.52357083      0.65989779
 79    C     -4.32091137      1.96159965      1.89756592
 80    C     -3.08304265      2.22850650      2.48631588
 81    C     -2.16540942      3.05738454      1.83739772
 82    H     -1.77157395      4.26436040      0.09476356
 83    H     -3.97270980      3.78975531     -0.95213074
 84    H     -5.60441333      2.31587319      0.20175299
 85    H     -5.03498233      1.31659497      2.40253195
 86    H     -2.83384648      1.79120005      3.44942625
 87    H     -1.20214295      3.26508217      2.29554252
 88    C      1.23249791     -0.30306981      3.95943104
 89    C      1.60956722     -1.57772484      3.53134455
 90    C      0.63823565     -2.55761031      3.31565089
 91    C     -0.71016524     -2.26284075      3.52804372
 92    C     -1.08723456     -0.98818572      3.95613021
 93    C     -0.11590298     -0.00830025      4.17182387
 94    H      1.98835509      0.45944372      4.12727651
 95    H      2.65884598     -1.80710431      3.36606782
 96    H      0.93165792     -3.54950261      2.98252885
 97    H     -1.46602242     -3.02535428      3.36019825
 98    H     -2.13651332     -0.75880625      4.12140694
 99    H     -0.40932526      0.98359205      4.50494591
100   Li     -1.01852524     -0.30118202     -1.75537589
101end
102
103task
104   eda b3lyp
105end

The explaination of this input file can be found in Example: (H2O)6. The only important point is:

  1. Line 6: The total charge is +1.

  2. Line 24: The charge of lithium cation is +1.

Do the calculation:

$ qbics li-mben-mseda.inp -n 24 > li-mben-mseda.out

Now open li-mben-mseda.out:

li-mben-mbedas.out
 1Table 5. Summary (kcal/mol).
 2---------------------------------------------------------------------------------------------------------------------------------
 3    Interactions         delE_el         delE_xc         delE_pl         delE_ct       delE_bsse       delE_disp        delE_tot
 4---------------------------------------------------------------------------------------------------------------------------------
 5   SUM of 2-body -4.83698400E+01  4.61490292E+01 -4.83508895E+01 -3.37925281E+01  9.22607552E+00 -4.34771067E+01 -1.18615259E+02
 6   SUM of 3-body -2.23649606E-08  2.58074315E-01  1.33815835E+01  5.88305181E+00  1.80200373E+00  8.76525397E+00  3.00899673E+01
 7   SUM of 4-body  4.13056277E-08  1.59841995E-01 -5.50102044E-01  8.45709613E-01 -2.03912279E+00 -2.67547883E+00 -4.25915201E+00
 8          Remain -1.31621640E-08  1.51216649E-02  7.61257854E-02 -2.89732759E-01  4.59645632E-01  3.26936075E-03  2.64429671E-01
 9---------------------------------------------------------------------------------------------------------------------------------
10             SUM -4.83698400E+01  4.65820672E+01 -3.54432822E+01 -2.73534994E+01  9.44860210E+00 -3.73840622E+01 -9.25200144E+01
11---------------------------------------------------------------------------------------------------------------------------------

From this table, we can see that the 2-, 3-, and 4-body contribution to the total interaction energy is -118.61, +30.09, and -4.26 kcal/mol, respectively. Since 3-body energy is positive, this term is destablizing the cluster, being anti-cooperative. This is completely different from water clusters in Example: (H2O)6. The anti-cooperativity is mostly contributed from polarization, charge transfer, and dispersion interactions.