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9.11 Optimising the Structure of Clusters

9.11.1 Introduction

(December 20, 2021)

The potential energy landscape of atomic and molecular clusters can be very complex with many minima which can have similar energies, and this complexity increases rapidly as the size of the clusters increases. Determining the global minimum of these clusters is challenging since it requires extensive searching over the potential energy surface. One approach to finding the low energy structures of these clusters is to perform many geometry optimizations starting at different initial coordinates. Q-Chem is able to perform such random searches for molecular clusters containing up to two different molecule types. In these searches the molecules are subjected to translations and rotations of their structure to generate a new starting structure. These searches are initiated by the JOBTYPE = RAND and it is necessary to specify the number of molecules of the different types and the number of atoms in the different types of molecules. For the optimization of atomic clusters, SEARCH_ATOMIC = TRUE and the number of atom swops performed in the structure generation (N_SWOP) can be specified. Some care has to be taken with the specification of the input structure in the $molecule section. All the atoms of the molecules of molecule type 1 must come before those of molecule type 2. Furthermore, the atoms of the same molecule should be together. For examples of these studies see Refs.  278 Do H., Besley N. A.
J. Chem. Phys.
(2012), 137, pp. 134106.
Link
, 279 Do H., Besley N. A.
J. Phys. Chem. A
(2013), 117, pp. 5385.
Link
, 280 Do H., Besley N. A.
Phys. Chem. Chem. Phys.
(2013), 15, pp. 16214.
Link
, 695 Linton K. A., Wright T. G., Besley N. A.
Proc. Roy. Soc. London A
(2018), 376, pp. 20170152.
Link
.

Example 9.39  A random search geometry optimization of the NO+.H2O cluster.

$molecule
   1 1
   N    0.5682008336    0.1585044954   -0.9009280260
   O   -0.3450383302   -0.5598328271   -0.4634299478
   O    1.7303273568    0.3403569345    0.4364171165
   H    2.5236300547   -0.2494576134    0.1485689942
   H    2.1020812302    1.2823911654    0.2570156558
$end

$rem
   JOBTYPE                     RAND
   METHOD                      B3LYP
   BASIS                       STO-3G
   SCF_CONVERGENCE             6
   MAX_SCF_CYCLES              100
   NSEARCH                     10
   N_MOL_TYPE                  2
   NMOL1                       1
   N_ATOM_TYPE_1               2
   NMOL2                       1
   N_ATOM_TYPE_2               3
   N_MOVES                     20
   MAXBOX                      10000
   MIN_SEPARATION              25
   MAX_DISPLACE                25
   SCF_NOCRASH                 TRUE
   TIGHTEN_CONVERG             TRUE
   GEOM_OPT_MAX_CYCLES         200
   GEOM_OPT_COORDS             0
   GEOM_OPT_TOL_DISPLACEMENT   1000
   GEOM_OPT_TOL_GRADIENT       300
   GEOM_OPT_TOL_ENERGY         100
$end

View output

Example 9.40  A random search geometry optimization of the He3Ne3 cluster.

$molecule
   0 1
   He   -1.3590894    3.0177788   -0.1662522
   He   -2.9853158    1.1444488    0.1036005
   He    0.5068109    1.3795209   -0.2168151
   Ne   -1.1002149   -0.5693061    0.0381894
   Ne    0.5981676    1.8697812    1.4685618
   Ne   -1.2376457    1.2597811   -0.0756066
$end

$rem
   JOBTYPE                     RAND
   METHOD                      B3LYP
   DFT_D                       EMPIRICAL_GRIMME
   BASIS                       STO-3G
   SCF_CONVERGENCE             6
   MAX_SCF_CYCLES              100

   NSEARCH                     10
   SEARCH_ATOMIC               TRUE
   N_SWOP                      4
   N_MOL_TYPE                  2
   NMOL1                       3
   N_ATOM_TYPE_1               1
   NMOL2                       3
   N_ATOM_TYPE_2               1
   N_MOVES                     20
   MAXBOX                      10000
   MIN_SEPARATION              25
   MAX_DISPLACE                25
   SCF_NOCRASH                 TRUE
   TIGHTEN_CONVERG             TRUE
   USE_INITIAL                 TRUE

   GEOM_OPT_MAX_CYCLES         200
   GEOM_OPT_COORDS             0
   GEOM_OPT_TOL_DISPLACEMENT   1000
   GEOM_OPT_TOL_GRADIENT       3000
   GEOM_OPT_TOL_ENERGY         1000
$end

View output

Basin hopping (BH) is a more advanced technique for locating the global minimum on complex potential energy surfaces. 1177 Wales D. J., Doye J. P. K.
J. Phys. Chem. A
(1997), 5111, pp. 101.
Link
The BH algorithm is essentially a combination of the Metropolis sampling technique and a gradient-based local search method. This has the effect of sampling the energy basins, where an energy basin is a certain part of the configuration space around a minimum on the PES that contains all the configurations that will relax into this minimum using downhill relaxations, instead of sampling the configuration space. To enhance the efficiency of the method, BH with occasional jumping is used, 506 Iwamatsu M., Okabe Y.
Chem. Phys. Lett.
(2004), 399, pp. 396.
Link
which incorporates a jumping move in addition to the standard Monte Carlo (MC) moves. Jumping is a MC move without local minimization at infinite temperature and, consequently, is always accepted. When the usual MC moves are rejected a number of times, the system is judged to be trapped at the local minimum. The temperature is raised to T=, and the MC jumping moves are executed several times to allow the system to escape from the local minimum. This provides an efficient way to escape from a local minimum and to explore the next basin of the valley when it is separated by high barriers. Depending on the size and complexity of the system being studied, a large number of MC_STEPS and/or MC_CYCLES to ensure the global minimum is found.

Example 9.41  A basin hopping search for the NO+(H2O) cluster.

$molecule
   1 1
   N     0.5682008336    0.1585044954   -0.9009280260
   O    -0.3450383302   -0.5598328271   -0.4634299478
   O     1.7303273568    0.3403569345    0.4364171165
   H     2.5236300547   -0.2494576134    0.1485689942
   H     2.1020812302    1.2823911654    0.2570156558
$end

$rem
  JOBTYPE          BH
  METHOD           B3LYP
  BASIS            STO-3G
  SCF_CONVERGENCE  6
  MAX_SCF_CYCLES   100

  MC_CYCLES             4
  MC_STEPS              5
  MC_TEMP               300
  MAX_DISPLACE          25
  MIN_SEPARATION        25
  MAXBOX                5000
  N_MOVES               20

  N_MOL_TYPE       2
  NMOL1            1
  N_ATOM_TYPE_1    2
  NMOL2            1
  N_ATOM_TYPE_2    3
  N_MOVES          20
  MAXBOX           10000
  MIN_SEPARATION   25
  MAX_DISPLACE     25
  SCF_NOCRASH      TRUE

  GEOM_OPT_MAX_CYCLES       200
  GEOM_OPT_COORDS           0
  GEOM_OPT_TOL_DISPLACEMENT 2000
  GEOM_OPT_TOL_GRADIENT     4000
  GEOM_OPT_TOL_ENERGY       400
$end

View output