VOLUME 88, NUMBER 25 PHYSICAL REVIEW LETTERS 24 JUNE 2002 Potential-Energy Landscapes of Simple Liquids Pooja Shah and Charusita Chakravarty* Department of Chemistry, Indian Institute of Technology– Delhi, Hauz Khas, New Delhi: 110016, India (Received 7 December 2001; published 5 June 2002) Changes in the potential-energy surface as a function of the range and curvature of the pair potential are studied using isothermal-isobaric ensemble Monte Carlo simulations of Morse liquids. The configu- rational energies of stationary points are found to be linear functions of the fraction of imaginary modes, with slopes that are proportional to the range of the potential. The relative energies of saddles, minima, and instantaneous configurations show qualitatively different behavior for short, long, and intermediate range potentials, which imply corresponding variations in liquid state relaxation dynamics. DOI: 10.1103/PhysRevLett.88.255501 PACS numbers: 61.20.Lc The potential-energy surface, U, of an interacting col- lection of atoms is a scalar function of the 3N -dimensional position vector, r , and contains, in principle, all the infor- mation necessary to understand the collective properties. The inherent structure approach concentrates on the prop- erties of local minima of Ur  and has provided a very use- ful descriptive tool for understanding melting and the glass transition [1–9]. Recent work has focused on the proper- ties of stationary points or inherent saddles of the potential energy surface (PES), which correspond to absolute min- ima of the pseudopotential surface, W r   1 2 j=Uj 2 , in or- der to understand the glass transition [10 – 15]. Model glass formers, such as the binary Lennard-Jones mixture, the bi- nary soft-sphere mixture, and the modified Lennard-Jones (MLJ) liquid, have been shown to undergo a transition from saddle-dominated to minima-dominated dynamical regimes at the mode-coupling transition temperature, T MC . Saddles are stationary points of order 1 or more and mark the border between adjoining basins of two minima. For T . T MC , the system is localized largely in border re- gions and basin hopping is facile. Below T MC , the sys- tem occupies interiors of the basins of local minima, and basin hopping becomes an activated process. A computa- tional problem arises in the mapping of absolute minima of the pseudopotential, W r , to the stationary points of the true potential Ur  because any minimization algo- rithm will also tend to sample low-lying minima of W r  which correspond to inflection points of Ur , rather than true saddles [16]. Careful numerical investigation of this issue, however, shows that the number of inflection direc- tions is always very small and does not significantly affect the statistical estimates of saddle properties [14,15,17,18]. Therefore these low-lying minima of W r  may be desig- nated as quasisaddles (abbreviated to saddles in this work) and may be regarded as constituting a dynamically signifi- cant set of points on the PES which show a qualitative change in properties near the mode-coupling transition temperature [10,16]. Since a glass may be viewed as a very high-viscosity liquid, it is expected that many of the statistical features of the stationary points of the PES of glass formers will be shared by simple liquids, as shown recently in the case of the Lennard-Jones (LJ) liquid [19]. The present study explores the physical significance of the inherent saddles by studying the correlation between their statistical prop- erties and generic features of the interatomic potential for simple liquids. In particular, we study liquids bound by Morse pair potentials V a r   ee 2a12r r e  2 1 2 2e (1) sharing a common well depth, e, and equilibrium pair dis- tance, r e , but with different values of the range parameter, a, which is inversely correlated with the range and soft- ness of the potential. We show that changes in the saddle properties with a reflect the changing topography of the PES and provide insights into how the system dynamics is likely to change as the pair potential changes in curvature and range. These results should be fairly general, since the Morse potentials can be used to fit bulk and diatomic data for a wide range of systems, e.g., metallic systems have a  3, rare gases have a  6, while a very short-range system such as C 60 has a  13.7 [20]. Since this work focuses on the liquid state, rather than the glassy regime, it is not necessary to include a many-body potential term to inhibit crystallization. Isothermal-isobaric ensemble Monte Carlo simulations of Morse liquids with 4 #a# 12 are performed at temperatures, T , between 0.675 and 1.5 and pressure P  0.933 [21–23]. A rhombic dodecahedral simulation cell with 125 particles was used. Spherical potential cut- off distances of 2.5r e and long-range corrections were employed. The 100 instantaneous configurations were sampled from runs of length 5 3 10 6 . Starting with an instantaneous configuration, local minimizations on the Ur  and W r  surfaces were used to generate the cor- responding inherent minimum and saddle, respectively, keeping volume constant during the minimization. A lim- ited memory quasi-Newton method for multidimensional optimization, referred to as the LBFGS algorithm, was used for the local minimizations [24]. Finite potential cutoffs imply that minimization with maximum precision will be difficult and a high proportion of low-lying minima of W r  may be sampled [25]. Based on the recent work on this issue [14–19], a convergence criteria of 10 29 for 255501-1 0031-9007 02 88(25) 255501(4)$20.00 © 2002 The American Physical Society 255501-1