The inherent dynamics of a molecular liquid: Geodesic pathways through the potential energy landscape of a liquid of linear molecules

Abstract

Because the geodesic pathways that a liquid follows through its potential energy landscape govern its slow, diffusive motion, we suggest that these pathways are logical candidates for the title of a liquid's “inherent dynamics.” Like their namesake “inherent structures,” these objects are simply features of the system's potential energy surface and thus provide views of the system's structural evolution unobstructed by thermal kinetic energy. This paper shows how these geodesic pathways can be computed for a liquid of linear molecules, allowing us to see precisely how such molecular liquids mix rotational and translational degrees of freedom into their dynamics. The ratio of translational to rotational components of the geodesic path lengths, for example, is significantly larger than would be expected on equipartition grounds, with a value that scales with the molecular aspect ratio. These and other features of the geodesics are consistent with a picture in which molecular reorientation adiabatically follows translation—molecules largely thread their way through narrow channels available in the potential energy landscape.

Potential energy landscape and inherent dynamics of a hard-sphere fluid

“…That is, for each thermodynamic state, the lengths along the contour of the geodesic g must themselves scale with the direct initial-(i)-to-final-(f ) distance in configuration space R [64,67]. [r j (f ) − r j (i)] 2 (4.1)…”

“…As we described in a number of studies of atomic and molecular liquids [64,66,67], the first task is invariably to select from the equilibrium ensemble a number of pairs of liquid configurations R(i) and R(f ) that can serve as initial (i) and final (f ) liquid configurations for geodesics. Each pair has to be separated by a direct distance R = |R(f ) − R(i)| large enough to apply Eq.…”

“…For continuous potential, paths consistent with this requirement arise automatically if we continually take small steps in the direction of the final configuration, provided we make liberal use of the gradient of the potential to guide us back towards the boundary of the energy-allowed region whenever we find ourselves taking on too high a potential energy [64,67]. However, hard-core potentials would seem to call for a rather different strategy.…”

“…With these forces in hand, one could certainly try to apply precisely the same geodesic-path-finding algorithm that we have been using for soft potentials [64,67]. What one discovers, though, is that systems whose potential energy landscape is prescribed by Eqs.…”

“…The alternative that we employ here is the landscapegeodesic approach [63][64][65], a strategy that has proven useful in a number of liquid-state applications [64,66,67]. The question posed now is not what the optimum configurations in the landscape are, but what the optimum pathways are that travel from configuration to configuration within our equilibrium ensemble-an idea that is equally well defined for hard and soft potentials [68].…”