9.13.1 Introduction

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.  301 Do H., Besley N. A.
J. Chem. Phys.
(2012), 137, pp. 134106. Link , 302 Do H., Besley N. A.
J. Phys. Chem. A
(2013), 117, pp. 5385. Link , 303 Do H., Besley N. A.
Phys. Chem. Chem. Phys.
(2013), 15, pp. 16214. Link , 755 Linton K. A., Wright T. G., Besley N. A.
Proc. Roy. Soc. London A
(2018), 376, pp. 20170152. Link .

Basin hopping (BH) is a more advanced technique for locating the global minimum on complex potential energy surfaces. ¹²⁷⁸ 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, ⁵⁵² 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 $T=\mathrm{\infty }$, 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.