Instantaneous normal mode (INM) analysis of a set of bulk Morse systems is performed to monitor t... more Instantaneous normal mode (INM) analysis of a set of bulk Morse systems is performed to monitor the changes in the curvature distribution that occur as a result of changing the range and curvature of the Morse potential. The liquids are bound by Morse pair potentials, and share a ...
Canonical ensemble Monte Carlo simulations of 55-atom Morse clusters are used to study the effect... more Canonical ensemble Monte Carlo simulations of 55-atom Morse clusters are used to study the effect of the range of the pair interaction on the cluster melting transition. Several different structural indicators are employed to monitor the solid–liquid transition and to locate the melting ...
Quasi-saddles or inherent saddles of the potential energy surface, U , of a liquid are defined as... more Quasi-saddles or inherent saddles of the potential energy surface, U , of a liquid are defined as configurations which correspond to absolute minima of the pseudo-potential surface, W = |∇U | 2 , as identified by a multi-dimensional minimisation procedure. The sensitivity of statistical properties of inherent saddles to the convergence criteria of the minimisation procedure is investigated using, as a test system, a simple liquid bound by a quadratically shifted Lennard-Jones pair potential with continuous zeroth, first and second derivatives at the cutoff distance. The variation in statistical properties of saddles is studied over a range of error tolerances spanning five orders of magnitude. The largest value of the tolerance corresponds to that used for the unshifted LJ liquids in a previous work (J. Chem. Phys. 115, 8784 ). Based on our results, it is clear that there are no qualitative changes in statistical properties of saddles over this range of error tolerances and even the quantitative changes are small. The lowest magnitude eigenvalue, |ω 2 0 |, of the Hessian is, however, found to be very sensitive to the tolerance; as the tolerance is decreased, |ω 2 0 | is found to show an overall decrease. This indicates that if convergence criteria are not strict, absolute or low-lying minima of W (r) will be diagnosed as having no inflexion directions. The results also show that it is not possible to set up an unambiguous numerical criterion to further classify the quasi-saddles into true saddles which contain no zero curvature, non-translational normal modes and inflexion points which have one or more zero-curvature normal mode directions.
Isothermal-isobaric ensemble Monte Carlo simulations are used to study the melting of Morse solid... more Isothermal-isobaric ensemble Monte Carlo simulations are used to study the melting of Morse solids. At a given pressure, the temperature at which the solid ceases to be metastable and also the fractional changes in density and potential energy increase with decreasing range of ...
Pair-additive Morse potentials are used to illustrate the effect of varying range and curvature o... more Pair-additive Morse potentials are used to illustrate the effect of varying range and curvature of the pair interaction on the potential energy landscape and the melting transition. The potential energy landscape is analysed in terms of the configurational energies and normal mode properties of instantaneous, saddle and quenched configurations sampled from isothermal-isobaric ensemble simulations. Distinctive statistical features of the three categories of configurations in the liquid and solid phases, as well as changes in landscape properties on melting, are discussed. Comparisons are made with quantum and classical Lennard-Jones systems.
Changes in the potential-energy surface as a function of the range and curvature of the pair pote... more 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 configurational 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.
Quasi-saddles or inherent saddles of the potential energy surface, $U$, of a liquid are defined a... more Quasi-saddles or inherent saddles of the potential energy surface, $U$, of a liquid are defined as configurations which correspond to absolute minima of the pseudo-potential surface, $W =\wf$, as identified by a multi-dimensional minimisation procedure. The sensitivity of statistical properties of inherent saddles to the convergence criteria of the minimisation procedure is investigated using, as a test system, a simple liquid bound by a quadratically shifted Lennard-Jones pair potential with continuous zeroth, first and second derivatives at the cut-off distance. The variation in statistical properties of saddles is studied over a range of error tolerances spanning five orders of magnitude. The largest value of the tolerance corresponds to that used for the unshifted LJ liquids in a previous work (J. Chem. Phys. {\bf 115}, 8784 (2001)). Based on our results, it is clear that there are no qualitative changes in statistical properties of saddles over this range of error tolerances and even the quantitative changes are small. The lowest magnitude eigenvalue, $| \omega_0^2|$, of the Hessian is, however, found to be very sensitive to the tolerance; as the tolerance is decreased, $| \omega_0^2|$ is found to show an overall decrease. This indicates that if convergence criteria are not strict, absolute or low-lying minima of $W(\br)$ will be diagnosed as having no inflexion directions. The results also show that it is not possible to set up an unambiguous numerical criterion to further classify the quasi-saddles into true saddles which contain no zero curvature, non-translational normal modes and inflexion points which have one or more zero-curvature normal mode directions.
The relationship between the behaviour at melting and the range and softness of interatomic poten... more The relationship between the behaviour at melting and the range and softness of interatomic potentials is explored using Monte Carlo simulations of bulk Morse and Lennard-Jones systems. The range parameter of the Morse interaction is tuned to mimic the variation ...
The configurational energies, order parameters and normal mode spectra associated with inherent s... more The configurational energies, order parameters and normal mode spectra associated with inherent structure, inherent saddle, and instantaneous configurations of the bulk Lennard-Jones system are compared. Instantaneous structures are generated by sampling configurations from ...
Instantaneous normal mode (INM) analysis of a set of bulk Morse systems is performed to monitor t... more Instantaneous normal mode (INM) analysis of a set of bulk Morse systems is performed to monitor the changes in the curvature distribution that occur as a result of changing the range and curvature of the Morse potential. The liquids are bound by Morse pair potentials, and share a ...
Canonical ensemble Monte Carlo simulations of 55-atom Morse clusters are used to study the effect... more Canonical ensemble Monte Carlo simulations of 55-atom Morse clusters are used to study the effect of the range of the pair interaction on the cluster melting transition. Several different structural indicators are employed to monitor the solid–liquid transition and to locate the melting ...
Quasi-saddles or inherent saddles of the potential energy surface, U , of a liquid are defined as... more Quasi-saddles or inherent saddles of the potential energy surface, U , of a liquid are defined as configurations which correspond to absolute minima of the pseudo-potential surface, W = |∇U | 2 , as identified by a multi-dimensional minimisation procedure. The sensitivity of statistical properties of inherent saddles to the convergence criteria of the minimisation procedure is investigated using, as a test system, a simple liquid bound by a quadratically shifted Lennard-Jones pair potential with continuous zeroth, first and second derivatives at the cutoff distance. The variation in statistical properties of saddles is studied over a range of error tolerances spanning five orders of magnitude. The largest value of the tolerance corresponds to that used for the unshifted LJ liquids in a previous work (J. Chem. Phys. 115, 8784 ). Based on our results, it is clear that there are no qualitative changes in statistical properties of saddles over this range of error tolerances and even the quantitative changes are small. The lowest magnitude eigenvalue, |ω 2 0 |, of the Hessian is, however, found to be very sensitive to the tolerance; as the tolerance is decreased, |ω 2 0 | is found to show an overall decrease. This indicates that if convergence criteria are not strict, absolute or low-lying minima of W (r) will be diagnosed as having no inflexion directions. The results also show that it is not possible to set up an unambiguous numerical criterion to further classify the quasi-saddles into true saddles which contain no zero curvature, non-translational normal modes and inflexion points which have one or more zero-curvature normal mode directions.
Isothermal-isobaric ensemble Monte Carlo simulations are used to study the melting of Morse solid... more Isothermal-isobaric ensemble Monte Carlo simulations are used to study the melting of Morse solids. At a given pressure, the temperature at which the solid ceases to be metastable and also the fractional changes in density and potential energy increase with decreasing range of ...
Pair-additive Morse potentials are used to illustrate the effect of varying range and curvature o... more Pair-additive Morse potentials are used to illustrate the effect of varying range and curvature of the pair interaction on the potential energy landscape and the melting transition. The potential energy landscape is analysed in terms of the configurational energies and normal mode properties of instantaneous, saddle and quenched configurations sampled from isothermal-isobaric ensemble simulations. Distinctive statistical features of the three categories of configurations in the liquid and solid phases, as well as changes in landscape properties on melting, are discussed. Comparisons are made with quantum and classical Lennard-Jones systems.
Changes in the potential-energy surface as a function of the range and curvature of the pair pote... more 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 configurational 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.
Quasi-saddles or inherent saddles of the potential energy surface, $U$, of a liquid are defined a... more Quasi-saddles or inherent saddles of the potential energy surface, $U$, of a liquid are defined as configurations which correspond to absolute minima of the pseudo-potential surface, $W =\wf$, as identified by a multi-dimensional minimisation procedure. The sensitivity of statistical properties of inherent saddles to the convergence criteria of the minimisation procedure is investigated using, as a test system, a simple liquid bound by a quadratically shifted Lennard-Jones pair potential with continuous zeroth, first and second derivatives at the cut-off distance. The variation in statistical properties of saddles is studied over a range of error tolerances spanning five orders of magnitude. The largest value of the tolerance corresponds to that used for the unshifted LJ liquids in a previous work (J. Chem. Phys. {\bf 115}, 8784 (2001)). Based on our results, it is clear that there are no qualitative changes in statistical properties of saddles over this range of error tolerances and even the quantitative changes are small. The lowest magnitude eigenvalue, $| \omega_0^2|$, of the Hessian is, however, found to be very sensitive to the tolerance; as the tolerance is decreased, $| \omega_0^2|$ is found to show an overall decrease. This indicates that if convergence criteria are not strict, absolute or low-lying minima of $W(\br)$ will be diagnosed as having no inflexion directions. The results also show that it is not possible to set up an unambiguous numerical criterion to further classify the quasi-saddles into true saddles which contain no zero curvature, non-translational normal modes and inflexion points which have one or more zero-curvature normal mode directions.
The relationship between the behaviour at melting and the range and softness of interatomic poten... more The relationship between the behaviour at melting and the range and softness of interatomic potentials is explored using Monte Carlo simulations of bulk Morse and Lennard-Jones systems. The range parameter of the Morse interaction is tuned to mimic the variation ...
The configurational energies, order parameters and normal mode spectra associated with inherent s... more The configurational energies, order parameters and normal mode spectra associated with inherent structure, inherent saddle, and instantaneous configurations of the bulk Lennard-Jones system are compared. Instantaneous structures are generated by sampling configurations from ...
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