Phase changes in selected Lennard-Jones X13−nYn clusters

de Almeida M, Marques JMC, Prudente FV. A thermodynamic view on the microsolvation of ions by rare gas: application to Li+ with argon

Parallel tempering Monte Carlo calculations on the Li⁺Ar_n microsolvation clusters have shown that the two peaks appearing in the heat capacity curve as a function of temperature correspond to the melting of the second and first solvation shells.

Atomistic modeling of thermodynamic equilibrium and polymorphism of iron

We develop two new modified embedded-atom method (MEAM) potentials for elemental iron, intended to reproduce the experimental phase stability with respect to both temperature and pressure. These simple interatomic potentials are fitted to a wide variety of material properties of bcc iron in close agreement with experiments. Numerous defect properties of bcc iron and bulk properties of the two close-packed structures calculated with these models are in reasonable agreement with the available first-principles calculations and experiments. Performance at finite temperatures of these models has also been examined using Monte Carlo simulations. We attempt to reproduce the experimental iron polymorphism at finite temperature by means of free energy computations, similar to the procedure previously pursued by Müller et al (2007 J. Phys.: Condens. Matter 19 326220), and re-examine the adequacy of the conclusion drawn in the study by addressing two critical aspects missing in their analysis: (i) the stability of the hcp structure relative to the bcc and fcc structures and (ii) the compatibility between the temperature and pressure dependences of the phase stability. Using two MEAM potentials, we are able to represent all of the observed structural phase transitions in iron. We discuss that the correct reproductions of the phase stability among three crystal structures of iron with respect to both temperature and pressure are incompatible with each other due to the lack of magnetic effects in this class of empirical interatomic potential models. The MEAM potentials developed in this study correctly predict, in the bcc structure, the self-interstitial in the (110) orientation to be the most stable configuration, and the screw dislocation to have a non-degenerate core structure, in contrast to many embedded-atom method potentials for bcc iron in the literature.

A rare event sampling method for diffusion Monte Carlo using smart darting

We identify a set of multidimensional potential energy surfaces sufficiently complex to cause both the classical parallel tempering and the guided or unguided diffusion Monte Carlo methods to converge too inefficiently for practical applications. The mathematical model is constructed as a linear combination of decoupled Double Wells [(DDW)(n)]. We show that the set (DDW)(n) provides a serious test for new methods aimed at addressing rare event sampling in stochastic simulations. Unlike the typical numerical tests used in these cases, the thermodynamics and the quantum dynamics for (DDW)(n) can be solved deterministically. We use the potential energy set (DDW)(n) to explore and identify methods that can enhance the diffusion Monte Carlo algorithm. We demonstrate that the smart darting method succeeds at reducing quasiergodicity for n ≫ 100 using just 1 × 10(6) moves in classical simulations (DDW)(n). Finally, we prove that smart darting, when incorporated into the regular or the guided diffusion Monte Carlo algorithm, drastically improves its convergence. The new method promises to significantly extend the range of systems computationally tractable by the diffusion Monte Carlo algorithm.

The ground state estimation by global optimization of an effective potential. Application to binary para-H(2)/ortho-D(2) molecular clusters

It is demonstrated how the problem of ground state estimation of an n-body system can be recast as the less demanding problem of finding the global minimum of an effective potential in the 3n-dimensional coordinate space. The latter emerges when the solution of the imaginary-time Schrödinger equation is approximated by a variational Gaussian wavepacket (VGW). The VGW becomes stationary in the infinite-imaginary-time limit. Such a stationary solution is not only exact for a harmonic potential, but it also provides a good approximation for a quantum state that is still localized in one of the basins of attraction, when, for example, the harmonic approximation may fail. The landscape of the effective potential is favorable for its global optimization, and is particularly suitable for optimization by GMIN, an open source program designed for global optimization using the basin-hopping algorithm. Consequently, the methodology is applied within GMIN to estimate the ground state structures of several binary para-H(2)/ortho-D(2) molecular clusters. The results are generally consistent with the previous observations for homogeneous para-H(2) and ortho-D(2) clusters, as well as for smaller binary clusters.

Quantum disordering versus melting in Lennard-Jones clusters

The ground states of Lennard-Jones clusters for sizes up to n=147 are estimated as a function of the de Boer quantum delocalization length Lambda , and the n-Lambda "phase diagram" is constructed. The increase in Lambda favors more disordered and diffuse structures over more symmetric and compact ones, eventually making the liquidlike motif most energetically favorable. The analogy between the quantum- and thermally-induced structural transitions is explored.

Quantum transitions in Lennard-Jones clusters

The ground states of Lennard-Jones (LJ) clusters are estimated by finding the Gaussian wave packets that minimize the energy functional. A "phase diagram" for LJ_{n} as a function of size (n=31,...,45) and de Boer quantum delocalization length (Lambdain[0;0.3]) is constructed, showing the stability ranges for the two competing structural motifs, the Mackay and anti-Mackay icosahedra. An increase of Lambda has an effect similar to heating and as such may induce structural transformations.

Rigid quantum Monte Carlo simulations of condensed molecular matter: Water clusters in the n=2→8 range

The numerical advantage of quantum Monte Carlo simulations of rigid bodies relative to the flexible simulations is investigated for some simple systems. The results show that if high frequency modes in molecular condensed matter are predominantly in the ground state, the convergence of path integral simulations becomes nonuniform. Rigid body quantum parallel tempering simulations are necessary to accurately capture thermodynamic phenomena in the temperature range where the dynamics are influenced by intermolecular degrees of freedom; the stereographic projection path integral adapted for quantum simulations of asymmetric tops is a significantly more efficient strategy compared with Cartesian coordinate simulations for molecular condensed matter under these conditions. The reweighted random series approach for stereographic path integral Monte Carlo is refined and implemented for the quantum simulation of water clusters treated as an assembly of rigid asymmetric tops.

Combining smart darting with parallel tempering using Eckart space: application to Lennard-Jones clusters

The smart-darting algorithm is a Monte Carlo based simulation method used to overcome quasiergodicity problems associated with disconnected regions of configurations space separated by high energy barriers. As originally implemented, the smart-darting method works well for clusters at low temperatures with the angular momentum restricted to zero and where there are no transitions to permutational isomers. If the rotational motion of the clusters is unrestricted or if permutational isomerization becomes important, the acceptance probability of darting moves in the original implementation of the method becomes vanishingly small. In this work the smart-darting algorithm is combined with the parallel tempering method in a manner where both rotational motion and permutational isomerization events are important. To enable the combination of parallel tempering with smart darting so that the smart-darting moves have a reasonable acceptance probability, the original algorithm is modified by using a restricted space for the smart-darting moves. The restricted space uses a body-fixed coordinate system first introduced by Eckart, and moves in this Eckart space are coupled with local moves in the full 3N-dimensional space. The modified smart-darting method is applied to the calculation of the heat capacity of a seven-atom Lennard-Jones cluster. The smart-darting moves yield significant improvement in the statistical fluctuations of the calculated heat capacity in the region of temperatures where the system isomerizes. When the modified smart-darting algorithm is combined with parallel tempering, the statistical fluctuations of the heat capacity of a seven-atom Lennard-Jones cluster using the combined method are smaller than parallel tempering when used alone.

Multiple structural transformations in Lennard-Jones clusters: Generic versus size-specific behavior

The size-temperature "phase diagram" for Lennard-Jones clusters LJn with sizes up to n=147 is constructed based on the analysis of the heat capacities and orientational bond order parameter distributions computed by the exchange Monte Carlo method. Two distinct types of "phase transitions" accompanied by peaks in the heat capacities are proven to be generic. Clusters with Mackay atom packing in the overlayer undergo a lower-temperature melting (or Mackay-anti-Mackay) transition that occurs within the overlayer. All clusters undergo a higher-temperature transition, which for the three-layer clusters is proven to be the 55-atom-core-melting transition. For the two-layer clusters, the core/overlayer subdivision is ambiguous, so the higher-temperature transition is better characterized as the breaking of the local icosahedral coordination symmetry. A pronounced size-specific behavior can typically be observed at low temperatures and often occurs in clusters with highly symmetric global minima. An example of such behavior is LJ135, which undergoes a low-temperature solid-solid transition, besides the two generic transitions, i.e., the overlayer reconstruction and the core melting.

Stereographic projection path-integral simulations of (HF)n clusters

We perform several quantum canonical ensemble simulations of (HF)(n) clusters. The HF stretches are rigid, and the stereographic projection path-integral method is employed for the simulation in the resulting curved configuration space. We make use of the reweighted random series techniques to accelerate the convergence of the path-integral simulation with respect to the number of path coefficients. We develop and test estimators for the total energy and heat capacity based on a finite difference approach for non-Euclidean spaces. The quantum effects at temperatures below 400 K are substantial for all sizes. We observe interesting thermodynamic behaviors in the quantum simulations of the octamer and the heptamer.

Structural transformations and melting in neon clusters: quantum versus classical mechanics

The extraordinary complexity of Lennard-Jones (LJ) clusters, which exhibit numerous structures and "phases" when their size or temperature is varied, presents a great challenge for accurate numerical simulations, even without accounting for quantum effects. To study the latter, we utilize the variational Gaussian wave packet method in conjunction with the exchange Monte Carlo sampling technique. We show that the quantum nature of neon clusters has a substantial effect on their size-temperature "phase diagrams," particularly the critical parameters of certain structural transformations. We also give a numerical confirmation that none of the nonicosahedral structures observed for some classical LJ clusters are favorable in the quantum case.

The properties of ion-water clusters. II. Solvation structures of Na+, Cl−, and H+ clusters as a function of temperature

Ion-water-cluster properties are investigated both through the multistate empirical valence bond potential and a polarizable model. Equilibrium properties of the ion-water clusters H+(H2O)100, Na+(H2O)100, Na+(H2O)20, and Cl-(H2O)17 in the temperature region 100-450 K are explored using a hybrid parallel basin-hopping and tempering algorithm. The effect of the solid-liquid phase transition in both caloric curves and structural distribution functions is investigated. It is found that sodium and chloride ions largely reside on the surface of water clusters below the cluster melting temperature but are solvated into the interior of the cluster above the melting temperature, while the solvated proton was found to have significant propensity to reside on or near the surface in both the liquid- and solid-state clusters.

Structural Transitions and Melting in LJ74-78 Lennard-Jones Clusters from Adaptive Exchange Monte Carlo Simulations

Phase changes in Lennard-Jones (LJ) clusters containing between 74 and 78 atoms are investigated by means of exchange Monte Carlo simulations in the canonical ensemble. The replica temperatures are self-adapted to facilitate the convergence. Although the 74- and 78-atom clusters have icosahedral global minima, the clusters with 75-77 atoms have decahedral ground-state structures and they undergo a structural transition to icosahedral minima before melting. The structural transitions are characterized by quenching and by looking at the Q4 and Q6 orientational bond order parameters. The transition temperatures are estimated to be 0.114, 0.065, and 0.074 reduced units for LJ75, LJ76, and LJ77, respectively. These values, their ordering and the associated latent heats are compared with other estimates based on the harmonic superposition approach.

Parallel tempering simulations of the 13-center Lennard-Jones dipole-dipole cluster (muD=0-->0.5 a.u.)

We investigate the thermodynamic behavior of the thirteen center uniform Lennard-Jones dipole-dipole cluster [(LJDD)(13)] for a wide range of dipole moment strengths. We find a relatively wide range of potential parameters where solid-solid coexistence manifests itself. Using structural characterization methods we determine the shape of the few isomers that contribute to the solid-solid coexistence region. The thermal distributions of the size of the net dipole moment are broad even at the coldest temperatures of the simulation where the (LJDD)(13) cluster is solid.

A reweighted random series method for stereographic projection path integrals

A set of general reweighted random series methods for metric affine spaces is developed. The extension of the theorems to metric affine spaces demands the introduction of a configuration-independent reference metric tensor; this geometric object is used to treat the path expansion coefficients beyond the core path, in both the partial averaging and the reweighted random series approach. Numerical tests are conducted by simulating a particle in a ring. The reweighted random series results show better convergence properties and better statistical quality at a fraction of the cost compared with the related partial averaging simulation.

Phase changes in Lennard-Jones mixed clusters with composition ArnXe6−n (n=0,1,2)

We have carried out parallel tempering Monte Carlo calculations on the binary six-atom mixed Lennard-Jones clusters, Ar(n)Xe(6-n) (n=0,1,2). We have looked at the classical configurational heat capacity C(V)(T) as a probe of phase behavior. All three clusters show a feature in the heat capacity in the region of 15-20 K. The Ar(2)Xe(4) cluster exhibits a further peak in the heat capacity near 7 K. We have also investigated dynamical properties of the Ar(2)Xe(4) cluster as a function of temperature using molecular dynamics. We report the interbasin isomerization rate and the bond fluctuation parameter obtained from these calculations. At 7 K, the isomerization rate is on the order of 0.01 ns(-1); at 20 K, the isomerization rate is greater than 10 ns(-1). Furthermore, at 7 K, the bond fluctuation parameter is less than 3%; at 20 K, it is in the range of 10-15% (depending on the sampling time used). Using this information, together with Monte Carlo quenching data, we assign the 15-20 K feature in the heat capacity to a solid-liquid phase change and the 7-K peak to a solid-solid phase change. We believe this is the smallest Lennard-Jones cluster system yet shown to exhibit solid-solid phase change behavior.

Partial averaging and the centroid virial estimator for stereographic projection path-integral simulations in curved spaces

We develop and test three different partial averaging theories for the stereographic projection path integral in curved spaces. Additionally, we adapt and test the centroid virial estimator for the kinetic energy in curved spaces. We tested both a confining as well as a nonconfining potential for the particle in a ring. All three partial averaging theories are demonstrated to converge linearly in the asymptotic region with k(-2)max, the number of Fourier coefficients. We use an error estimator to determine the optimal parameters for an extrapolation to infinite kmax. We verify that the centroid virial estimator (derived from the primitive DeWitt path-integral formula) converges to the kinetic energy for both confining and nonconfining potentials.

Thermodynamics and equilibrium structure of Ne38 cluster: Quantum mechanics versus classical

The equilibrium properties of classical Lennard-Jones (LJ38) versus quantum Ne38 Lennard-Jones clusters are investigated. The quantum simulations use both the path-integral Monte Carlo (PIMC) and the recently developed variational-Gaussian wave packet Monte Carlo (VGW-MC) methods. The PIMC and the classical MC simulations are implemented in the parallel tempering framework. The classical heat capacity Cv(T) curve agrees well with that of Neirotti et al. [J. Chem. Phys. 112, 10340 (2000)], although a much larger confining sphere is used in the present work. The classical Cv(T) shows a peak at about 6 K, interpreted as a solid-liquid transition, and a shoulder at approximately 4 K, attributed to a solid-solid transition involving structures from the global octahedral (Oh) minimum and the main icosahedral (C5v) minimum. The VGW method is used to locate and characterize the low energy states of Ne38, which are then further refined by PIMC calculations. Unlike the classical case, the ground state of Ne38 is a liquidlike structure. Among the several liquidlike states with energies below the two symmetric states (Oh and C5v), the lowest two exhibit strong delocalization over basins associated with at least two classical local minima. Because the symmetric structures do not play an essential role in the thermodynamics of Ne38, the quantum heat capacity is a featureless curve indicative of the absence of any structural transformations. Good agreement between the two methods, VGW and PIMC, is obtained. The present results are also consistent with the predictions by Calvo et al. [J. Chem. Phys. 114, 7312 (2001)] based on the quantum superposition method within the harmonic approximation. However, because of its approximate nature, the latter method leads to an incorrect assignment of the Ne38 ground state as well as to a significant underestimation of the heat capacity.

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

Phase change phenomena in clusters are often modeled by augmenting physical interaction potentials with an external constraining potential to handle evaporation processes in finite temperature simulations. These external constraining potentials exert a pressure on the cluster. The influence of this constraining pressure on phase change phenomena in 38-atom Lennard-Jones clusters is investigated, and it is demonstrated that modest changes in the parameters of the constraining potential can lead to an order of magnitude change in the constraining pressure. At sufficiently high pressures the solid to solidlike phase change region in the 38-atom Lennard-Jones cluster is completely eliminated.

Taming the rugged landscape: Production, reordering, and stabilization of selected cluster inherent structures in the X13−nYn system

We present studies of the potential energy landscape of selected binary Lennard-Jones 13 atom clusters. The effect of adding selected impurity atoms to a homogeneous cluster is explored. We analyze the energy landscapes of the studied systems using disconnectivity graphs. The required inherent structures and transition states for the construction of disconnectivity graphs are found by combination of conjugate gradient and eigenvector-following methods. We show that it is possible to controllably induce new structures as well as reorder and stabilize existing structures that are characteristic of higher-lying minima. Moreover, it is shown that the selected structures can have experimentally relevant lifetimes.