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# 9.13.1 Introduction

(July 14, 2022)

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 $molecule section. All the atoms of the molecules of molecule type 1 must come before those of molecule type 2. Furthermore, the atoms of the same molecule should be together. For examples of these studies see Refs. 291 Do H., Besley N. A. J. Chem. Phys. (2012), 137, pp. 134106. , 292 Do H., Besley N. A. J. Phys. Chem. A (2013), 117, pp. 5385. , 293 Do H., Besley N. A. Phys. Chem. Chem. Phys. (2013), 15, pp. 16214. , 733 Linton K. A., Wright T. G., Besley N. A. Proc. Roy. Soc. London A (2018), 376, pp. 20170152. . Example 9.45 A random search geometry optimization of the NO${}^{+}$.H${}_{2}$O 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_ENERGY         100
$end  Example 9.46 A random search geometry optimization of the He${}_{3}$Ne${}_{3}$ 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_ENERGY         1000
$end  Basin hopping (BH) is a more advanced technique for locating the global minimum on complex potential energy surfaces. 1245 Wales D. J., Doye J. P. K. J. Phys. Chem. A (1997), 5111, pp. 101. 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, 535 Iwamatsu M., Okabe Y. Chem. Phys. Lett. (2004), 399, pp. 396. 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 $T=\infty$, 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 9.47 A basin hopping search for the NO${}^{+}$(H${}_{2}$O) 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