J. Phys. Chem. B 1997, 101, 9137
9137
COMMENTS Comment on “Monte Carlo Study of Small Benzene Clusters. 1. Structure and Internal Motions” J. A. Niesse and Howard R. Mayne* Department of Chemistry, UniVersity of New Hampshire, Durham, New Hampshire 03824 ReceiVed: June 3, 1997 Dulles and Bartell1 recently proposed a new potential energy function for benzene clusters. The chief aim of this paper is to study the structure and dynamics of such clusters. In their paper, the authors give the geometry and potential energy of a proposed global minimum of the benzene dimer. We have recently developed a global minimization technique based on the idea of genetic algorithms, the space fixed modified genetic algorithm (SFMGA).2 We have applied this method to the benzene dimer problem using the Dulles-Bartell potential. We report here a lower dimer potential energy (-10.630 kJ mol-1) than that reported by Dulles and Bartell (-10.582 kJ mol-1). The geometry of the dimer is given in Figure 1. The coordinates of the atomic sites are given in Table 1. (There is a typographical error in the Appendix of ref 1. The C-C intersite distance should be 1.401 Å.) The runs were carried out as follows. There were 10 individuals in the population. Six genetic operators were used with equal weighting: inversion; arithmetic and geometric averaging; one-, two- and N-point crossovers. An elitist strategy was adopted, with the best two parents carrying over intact into the next generation. Several independent runs were carried out. Roughly 80% succeeded in finding the GM we propose here. The average number of generations needed to find the GM in these runs was 180. The ability of the SFMGA to find unsuspected global minima has been pointed out for silicon clusters.3 The SFMGA is a powerful minimization tool that explores the potential surface in a highly nonlocal manner. The advantage of this is that the technique is undeterred by high-energy saddle points between local minima, which may cause difficulties for searches based on molecular dynamics or Monte Carlo approaches.
S1089-5647(97)01801-4 CCC: $14.00
Figure 1. Benzene dimer geometry for potential energy global minimum proposed here. Two different views are shown.
TABLE 1: Cartesian Coordinates for Each Atomic Site in Calculated Global Minimum of (C6H6)2 Potential Energy atom
x [Å]
y [Å]
z [Å]
C1 C2 C3 C4 C5 C6 H7 H8 H9 H10 H11 H12 C13 C14 C15 C16 C17 C18 H19 H20 H21 H22 H23 H24
1.401 000 0.700 500 -0.700 500 -1.401 000 -0.700 500 0.700 500 2.432 000 1.216 000 -1.216 000 -2.432 000 -1.216 000 1.216 000 -0.206 939 0.986 856 1.770 428 1.360 205 0.166 409 -0.617 162 -0.783 572 1.288 741 2.648 945 1.936 837 -0.135 475 -1.495 680
0.000 000 1.213 302 1.213 302 0.000 000 -1.213 302 -1.213 302 0.000 000 2.106 174 2.106 174 0.000 000 -2.106 174 -2.106 174 -0.119 304 0.570 408 1.023 041 0.785 962 0.096 249 -0.356 384 -0.452 398 0.744 875 1.530 602 1.119 056 -0.078 218 -0.863 945
0.000 000 0.000 000 0.000 000 0.000 000 0.000 000 0.000 000 0.000 000 0.000 000 0.000 000 0.000 000 0.000 000 0.000 000 5.988 163 6.237 062 5.167 511 3.849 061 3.600 162 4.669 713 6.775 249 7.207 314 5.350 677 3.061 975 2.629 910 4.486 547
References and Notes (1) Dulles, F. J.; Bartell, L. S. J. Phys. Chem. 1995, 99, 17100. (2) Niesse, J. A.; Mayne, H. R. J. Chem. Phys. 1996, 105, 4700. (3) Niesse, J. A.; Mayne, H. R. Chem. Phys. Lett. 1996, 261, 576.
© 1997 American Chemical Society
