Phase changes in selected Lennard-Jones X13−nYn clusters

Abstract

Detailed studies of the thermodynamic properties of selected binary Lennard-Jones clusters of the type X 13Ϫn Y n ͑where nϭ1, 2, 3͒ are presented. The total energy, heat capacity, and first derivative of the heat capacity as a function of temperature are calculated by using the classical and path integral Monte Carlo methods combined with the parallel tempering technique. A modification in the phase change phenomena from the presence of impurity atoms and quantum effects is investigated.

The thermodynamic and ground state properties of the TIP4P water octamer

“…In a series of works [63][64][65][66][67][68][69][70] we have extended the reweighted random series approach [104][105][106][107][108][109][110] to the imaginary time path integral in manifolds that are mappable by stereographic projections. The random series expansion of the path consists of k m core terms and an additional 3k m tail terms,…”

“…͑1͒ is identical to the partial averaging method derived from the original random series representation of the Brownian bridge. [104][105][106][107][108][109][110] The centerpiece of the imaginary time path integral approach is the density matrix ͑q , qЈ , ␤͒. In manifolds the following equation is convenient for developing the proper importance sampling algorithms, [113][114][115] and to derive the expressions for the finite difference estimators of the energy and heat capacity,…”

“…Our methods based on stereographic projection coordinates have been tested on a number of simple systems solvable by basis set methods, and several molecular clusters. 64,67,69 We extend the reweighted random series method [104][105][106][107][108][109][110] and the finite difference estimators 108 for cubically convergent path integral simulations to manifolds. 68 DMC simulations are nearly as straightforward to implement in curved spaces mapped with stereographic projection coordinates as they are with Cartesian coordinates.…”

A stereographic projection path integral study of the coupling between the orientation and the bending degrees of freedom of water

“…͑55͒, which involves numerous accruing, factoring, and cancellations, is best left for symbolic processing software. 45 The final result is R = ͑I 11 + I 22 …”

Pressure dependent study of the solid-solid phase change in 38-atom Lennard-Jones cluster

“…͑5͒ is often applied in quantum simulations where derivatives of the potential are needed and continuous functions can be advantageous. 7,8 In simulations on Lennard-Jones systems, it is common to set ⑀Ј= ⑀, and we make that assignment in the current work.…”