Girifalco Potential Research Articles

Effective intermolecular potential and critical point for C60 molecule

The approximate nonconformal (ANC) theory is applied to the C60 molecule. A new binary potential function is developed for C60, which has three parameters only and is obtained by averaging the site-site carbon interactions on the surface of two C60 molecules. It is shown that the C60 molecule follows, to a good approximation, the corresponding states principle with n-C8H18, n-C4F10 and n-C5F12. The critical point of C60 is estimated in two ways: first by applying the corresponding states principle under the framework of the ANC theory, and then by using previous computer simulations. The critical parameters obtained by applying the corresponding states principle, although very different from those reported in the literature, are consistent with the previous results of the ANC theory. It is shown that the Girifalco potential does not correspond to an average of the site-site carbon-carbon interaction.

Analytic equation of state and thermodynamic properties for solid FCC C60 over a wide range of pressures and temperatures

As an analytic approximation to the free volume theory (FVT), the analytic mean field potential (AMFP) approach is applied to the multi-exponential model solid. The analytic expressions for the equation of state (EOS) and thermodynamic quantities are derived. The formalism for the case of the double-exponential (DE) model is applied to the solid fcc C60. The four potential parameters are determined by fitting the experimental data of cohesive energy, lattice constant and compression curve of solid C60. The numerical results calculated show that the Girifalco potential is too hard and gives compression curve prominently deviated from experiments at high pressure, whereas the DE potential can well describe the thermo-physical properties of C60 system within wide pressure range. The calculated variation of lattice constant versus temperature relationship and compression curve for solid C60 by using the DE potential agree well with experimental data available. Especially the AMFP with DE potential predicted that the fcc C60 solid is stable up to 2440 K, the spinodal temperature, in good agreement with the result from molecular dynamic (MD) simulation. The AMFP is a useful approach to consider the anharmonic effects at high temperature for solid C60.

Comprehensive study of the thermodynamic properties of fullerene C60 along the liquid–vapour coexistence

We present a theoretical model for calculating the thermodynamic properties of liquid C60 by means of an improved equation of state (EOS), in which the particles interact via pairwise interaction composed of hard-core plus suitable linear combinations of three Yukawa functions. The proposed EOS provides simple analytical expressions for Helmholtz free energy and pressure, which are the basic ingredients to compute the liquid–vapour coexistence curve of C60 as well as all other thermodynamic properties for the bulk liquid and vapour phases. The comparisons with computer simulation results, based on Girifalco potential, suggest the importance of treating the attractive tail of the potential accurately. It is to be noted that the obtained results of the thermodynamic properties along the binodal curve of C60 exhibit interesting features; in particular, the vapour phase shows abnormal behaviour of its isothermal compressibility and configurational heat capacity. The estimated critical parameters Tc = 2008.8 K, ρc = 0.50 nm−3 and Pc = 54.8 bars are in good agreement with NVT-Monte Carlo simulation predictions. The critical parameters of C60 are compared with those of liquid metals, non-metals and some hydrocarbons.

Equation of state and thermodynamic functions for the fcc soft-core multiple-Yukawa solid and application to fullerenes with compressible molecular radius

The generalized free volume theory is applied to the soft-core multiple-Yukawa solid, and the hard-core multiple-Yukawa is included in as a special case. The expressions for equation of state and internal energy are derived. The formalism developed is applied to the ${\mathrm{C}}_{60}$, ${\mathrm{C}}_{76}$, and ${\mathrm{C}}_{84}$ solids. The effective diameter of ${\mathrm{C}}_{60}$ molecule is taken as the experimental value; the parameters of the double Yukawa (DY) potential for carbon-carbon atoms are determined through fitting the experimental data of cohesive energy, the lattice constant, and the compression curve of ${\mathrm{C}}_{60}$ solid at ambient temperature. The effective diameter of ${\mathrm{C}}_{76}$ and ${\mathrm{C}}_{84}$ molecules are determined through fitting the experimental lattice constants at ambient temperature. The numerical results of ${\mathrm{C}}_{60}$ solid from the soft-core DY potential are in good agreement with the experiments, including the lattice constant and compression curve. The lattice constant versus temperature relationship for ${\mathrm{C}}_{76}$ and ${\mathrm{C}}_{84}$ solids calculated from the DY potential is qualitatively in accordance with experimental data as same as the Girifalco potential. The compression curve of the ${\mathrm{C}}_{84}$ solid calculated from the DY potential deviates from and is softer than the experimental data available. The reason for deviation is discussed, and it is concluded that the influence of compressibility of fullerene molecules to thermophysical quantities is important at high-pressure conditions.

Analytic equation of state for solid fccC60based on generalized free-volume theory

Based on generalized free-volume theory (GFVT), analytic expressions for the equation of state and internal energy are derived in this paper. The harmonic expansion of the GFVT gives analytic expressions for the Debye characteristic temperature and Gr\uneisen coefficient. The developed formalism is used to study the thermophysical properties of solid fcc ${\mathrm{C}}_{60}$. For the intermolecular forces, a generalized Girifalco potential based on the Lennard-Jones $(n\text{\ensuremath{-}}6)$ potential is utilized. In the numerical calculations, two sets of parameters are considered. One set is taken from the original Girifalco potential, and the other is determined from the experimental data for solid fcc ${\mathrm{C}}_{60}$ (called the modified Girifalco potential). The numerical results demonstrate first that the GFVT results are in good agreement with the Monte Carlo and molecular dynamics simulations at both low and high temperatures. The results deduced from the unsymmetrized self-consistent field approach by Zubov et al. and from our harmonic expansion are both in accordance with the GFVT at low temperature, but fail at high temperatures. Second, the modified Girifalco potential is much softer than the original Girifalco potential, and gives an improved description for the properties of real-life ${\mathrm{C}}_{60}$. Third, the GFVT can satisfactorily describe the anharmonic effect.

Analytic equation of state for FCC C60 solid based on analytic mean-field potential approach

The analytic mean-field approach (AMFP) was applied to the FCC C60 solid. For the intermolecular forces the Girifalco potential has been utilized. The analytic expressions for the Helmholtz free energy, internal energy and equation of state have been derived. The numerical results of thermodynamic quantities are compared with the molecular dynamic (MD) simulations and the unsymmetrized self-consistent field approach (CUSF) in the literature. It is shown that our AMFP results are in good agreement with the MD data both at low and high temperatures. The results of CUSF are in accordance with the AMFP at low temperature, but at high temperature the difference becomes prominent. Especially the AMFP predicted that the FCC C60 solid is stable upto 2202 K, the spinodal temperature, in good agreement with 2320 K from the MD simulation. However, the CUST just gives 1916 K, a temperature evidently lower than the MD data. The AMFP qualifies as a useful approach that can reasonably consider the anharmonic effects at high temperature.

A model equation of state of liquidC60 and thermodynamic properties along the liquid–vapour coexistence curve

We present a model equation of state forC60 based on a variational series mean spherical approximation for a double Yukawa fluid. This allowsus to investigate the liquid–vapour coexistence curve and calculate the thermodynamic properties ofliquid C60. The comparisons with computer simulation results, based on the Girifalco potential, suggest theimportance of treating the attractive tail of the potential accurately. The estimated critical parameters,Tc = 1943 K,ρc = 0.477 nm−3 and Pc = 34.2 bar, are in good agreement with Gibbs ensemble Monte Carlo simulation predictions. Theresults are discussed, making reference to previous studies.

Geometry Optimization and Conformational Analysis of (C60)N Clusters Using a Dynamic Lattice‐Searching Method

A newly developed unbiased global optimization method, named dynamic lattice searching (DLS), is used to locate putative global minima for all (C6O)N clusters with Girifalco potential up to N=150. A simple greedy strategy is adopted for the basic frame, so DLS has a very high convergence speed and may converge at various configurations. As most structures are packed by basic tetrahedra, some sequences are defined by both configurations and the size of the basic tetrahedra. A sequence-based conformational analysis is carried out with the defined sequences by counting the hit number over 10,000 independent DLS runs for all the cases up to N = 5. It was found that the hit rate of a sequence is related to the size of the basic tetrahedra. U.e of this method proved that the Leary tetrahedral sequence is dominant in a certain range of cluster sizes, although the sequence has no potential energy advantage. The calculation results are also consistent with those of annealing experiments at high temperature, both in magic numbers and height of the peaks in the mass spectrum.

Computer simulation study of the ground-state structures of singly ionized clusters ofC60molecules

Using a model potential which combines the spherically averaged Girifalco potential and a point polarizable dipole electrostatic model, we computed the ground-state structures of singly ionized clusters of ${\mathrm{C}}_{60}$ molecules and compared the results with predictions derived for neutral ${\mathrm{C}}_{60}$ clusters using Girifalco's potential. The structures of the simulated ionized fullerene clusters were similar to those of the corresponding neutral clusters, in keeping with the conclusions inferred recently by Branz et al. [Phys. Rev. B $66,$ 094107 (2002)] from time-of-flight mass spectrometry experiments.

Analytical implementation and critical tests of fluid thermodynamic perturbation theory

We appreciably broaden the scope of existing thermodynamic perturbation theory for pure fluids in several ways. Analytical approximation strategies are combined to express the thermodynamic properties of fluids in analytical and/or algebraic form and applied to a generalized class of pair potentials. The results are illustrated by comparing previously reported simulation measurements with our predictions obtained using a new class of generalized Lennard-Jones potential functions with independently adjustable repulsive and attractive length scales. Results are also obtained for various purely repulsive fluids, including inverse-power potentials with exponents ranging from 12 to 72 and a Lennard-Jones repulsive reference fluid. Applications to argon (Lennard-Jones) and C60 (Girifalco potential) are used to probe the limits of applicability of first-order perturbation theory to systems with very short range attractive potentials. Furthermore, we discuss the role of these new results in a number of additional applications.

Theoretical Study of Thermodynamic Properties of a Family of Fullerites from C36 to C96 in the Equilibrium with Their Vapors

On the basis of the correlative method of the unsymmetrized self-consistent field that yields the account of the strong anharmonicity of the lattice vibrations, it has been calculated the temperature dependence of saturated vapor pressure of higher and smaller fullerites, from C36 up to C96, and their thermodynamic properties along their sublimation curves. We have used the intermolecular potential of Girifalco with parameters recently calculated for these fullerenes. The calculations were accomplished up to the temperature of loss of stability (spinodal point) Ts. We compare our results with available experimental data and with quantities calculated earlier for the magnitudes of the most widespread of the fullerites, the C60. The behavior of some characteristics is considered in their dependence on the number of atoms in the molecule. The saturated vapor pressures up to the spinodal points of the two-phase systems crystal−gas is approximated by the formula log Psat = A − (B/T) − CT, where the last term i...

Adsorption and diffusion on nanoclusters of C 60 molecules

The adsorption and the energy barriers for diffusion on clusters of C 60 molecules are studied by means of quenched molecular dynamics simulations. The interaction among the C 60 molecules is modeled by means of the Girifalco potential. Three different clusters structures are considered: a truncated octahedron of 38 molecules, an icosahedron of 55 molecules and a truncated decahedron of 75 molecules.

On the Limit of the Thermodynamic Stability of Superheated Crystals and Mechanisms of Its Loss

Using the correlative method of unsymmetrized self-consistent field for strongly anharmonic crystals, the thermodynamic stability and the mechanism its loss is studied for crystals with various types of the chemical bond. The following interaction potentials are utilized: the Lennard-Jones pairwise potential together with Axilrod - Teller three-body one for simple van der Waals crystals (solid Ar), effective interionic pairwise potential proposed by Schiff for a metal (Na) and the Girifalco potential for fullerites (C60). In the first and third cases, the FCC lattice becomes unstable because the isothermal bulk modulus BT becomes zero. For fullerites, the shearing coefficient C44 goes to zero as well. Solid Na losses its stability when other shearing coefficient CT11 - CT12 becomes zero.

Monte Carlo Simulation of the Phase Diagram of C60 Using Two Interaction Potentials. Enthalpies of Sublimation

A first-principles interaction potential proposed by Pacheco and Ramalho (PRP) and the effective potential of Girifalco (GP) have been used to model the whole phase diagram of C60 by Gibbs ensemble and Gibbs−Duhem integration Monte Carlo methods. The triple-point properties were determined by a direct method recently proposed by us (Comput. Phys. Commun. 2001, 141, 403). It is based on the behavior of the Gibbs ensemble vapor−liquid simulations at the low-temperature limit, and it does not involve free-energy calculations. A stable liquid phase for temperatures between 1570 ± 20 K and 2006 ± 27 K is predicted with the PRP model and for temperatures between 1529 ± 36 K and 1951 ± 28 K with the GP model. According to these results, the liquid phase for C60 extends over ∼450 K, a temperature range considerably wider than the ones reported by other authors on the basis of free-energy calculations and density functional approaches. Nonetheless, the present results are in good agreement with the theoretical pre...

Microscopic theories of model macromolecular fluids and fullerenes: The role of thermodynamic consistency

We investigate the accuracy of two well-known integral equation theories (IETs) of the fluid state, namely, the modified hypernetted chain (MHNC) approximation and the hybridized mean spherical approximation (HMSA), as applied to systems characterized by short-range interactions. The theoretical approaches are implemented by enforcing their thermodynamic consistency according to two different strategies: in one case the equality of the isothermal compressibility, as calculated via the virial and fluctuation routes from structure to thermodynamics, is imposed [“local” consistency (LC)]; in the other case the equality of the pressure as calculated either via the two previous routes, or via the virial and the energy routes, is imposed [“global” consistency (GC)]. We show that for the class of potentials at issue the GC is in general considerably more accurate than the LC. We document this result by investigating the performances of the MHNC and the HMSA, as applied to the calculation of the thermodynamic and structural properties of the hard-core Yukawa (HCY) potential, the Derjaguin–Landau–Vervey–Overbeek (DLVO) potential and the Girifalco potential for fullerenes. The obtained results are then compared with Monte Carlo simulation data, that we also produce for the same model systems. As far as the HCY potential is concerned, the investigation covers a range of the Yukawa inverse decay length, z, spanning from z=1.8 when the interaction mimics the Lennard-Jones 12-6 potential, to z=7 when the potential mimics the “effective” short range interaction between globular proteins in a highly charge-screened aqueous solution. IETs are then applied to the DLVO potential with charge and Hamaker constant values which fit the dynamical interaction factor of lysozyme in a solution of high ionic strength, and to the Girifalco potential with parameters appropriate to model C60 and C70. It emerges from the present study that the GC is able to provide Helmholtz free energies and chemical potentials which compare quite favorably with the simulation data. As a consequence, we are able to show that the GC estimates of the phase coexistence densities for the HCY and Girifalco potential agree almost quantitatively with the Monte Carlo ones, by thus definitely improving upon previous results obtained within the LC. We also comment on the relevance of confident phase diagram determinations from IETs, in connection with the prediction of protein crystallization. Possible extensions of the present thermodynamic consistency strategies to more sophisticated theories and realistic models of protein solutions and fullerenes are finally suggested.

Application of valence force field theory, tight binding approximation and Girifalco potential in the study of thermodynamic and elastic properties of C 60 in detail

In this paper we calculated the second order elastic constants (SOECs) of C 60 using tight binding approximation (TBA) and valence force field theory (VFFT). To the SOECs obtained from Girifalco potential we added the contribution of Coloumb forces obtained through Martins prescription and the corrected values so obtained compare favorably with those of TBA and VFFT and also with literature values. We also derived the pressure derivatives of SOECs obtained through TBA and VFFT. In addition we calculated bond stretching force constant ∝ and bond bending force constants β and also their pressure derivatives. The ratio ∝/β compares favorably with several compounds for which these calculations have been made. The longitudinal ω L and transverse ω T frequencies have been calculated by two different methods. The calculated band positions are in satisfactory agreement with each other. Even though C 60 is not isotropic, sample calculations of γ g L and γ g T have been made so as to have an insight into these quantities. A second method due to Bhatia and Singh has also been applied to calculate these quantities. But this method gives a high γ g T value while it gives a good γ g L value. Reasons for this high value of γ g T have been discussed. The longitudinal ω L and transverse ω T frequencies of C 60 have been calculated through the use of calculated elastic constants. We also used the Nath–Smith–De Launey equation to calculate the band position. The calculated and observed band absorption position agree well. The calculated ω T value has been used to compute K T the bulk modulus with a modified Szigete's equation taking into consideration the existence of a small amount of Coloumb forces and the calculated value is found to be in good agreement with Duclose value. The effective charge on C 60 has been obtained through Martin's equation and the elastic constant C 44 has been evaluated through Martin's prescription. The effective charge found to be 0.21 e is in satisfactory agreement with that of Lu et al. [24] who found the effective charge to be 0.27 e. The pressure derivative of γ g th, the thermal Grüneisen constant has been evaluated and also through the second derivative of η and δ, the Bhatia Singh's parameters and the value is found to be −0.01 Kbar −1 and this value of γ′ g has been used to evaluate the second Grüneisen constant Q and the Anderson Grüneisen constant δ T AG. A new equation has been derived through the use of the derivative of SOECs C 11 ′ and η′ to evaluate γ g th which is found to be in good agreement with the measured value. The pressure derivative of bulk modulus ( K T) has been calculated. The estimated heat capacity is in fair agreement with experiment and the calculated value of K T using the computed value of ω T is found to be in reasonable agreement with that modified by Szigeti equation.

A computer simulation study of the static structure and dynamic properties of liquid C60 using Girifalco's potential

Using Girifalco's potential to describe the interaction between two C60 molecules, we performed computer simulations to analyze the static structure and dynamic properties of liquid C60, and calculated its diffusion constant and shear viscosity. Our dynamical calculations predict that this yet-unobserved liquid does not support collective phenomena.

Solidlike-to-Liquidlike Transition in Small Clusters ofC60Molecules or Transition-Metal Atoms

Using Girifalco's potential, we performed molecular dynamics (MD) simulations of $({\mathrm{C}}_{60}{)}_{7}$ that show, for the first time, that a small fullerene cluster with no nonsurface molecules can achieve a liquidlike state. This contrasts with earlier work on $({\mathrm{C}}_{60}{)}_{13}$, but parallels Sawada and Sugano's findings concerning small clusters of transition-metal atoms (TMAs). Repetition of Sawada and Sugano's MD simulations using longer runs showed that, as in the case of $({\mathrm{C}}_{60}{)}_{7}$, for seven-atom TMA clusters the solidlike-to-liquidlike transition is gradual and its completion is marked by a peak in the specific heat curve.

Monte Carlo simulation study of the high-temperature phase diagram of model C60 molecules

The constant-NVT Monte Carlo simulation is performed for model C60 molecules interacting via the Girifalco potential and a full free-energy analysis is made to predict the high-temperature phase diagram. The repulsive part of the C60 potential is very steep and the attractive part is relatively short-ranged. For such a system accurate computations of the virial pressure are difficult in simulations and it is argued that the discrepancies among the previous results for the phase diagram of C60 can partly be attributed to the uncertainties of the virial pressure involved in simulations. To avoid this difficulty we take the energy route to calculate equation of state (EOS), in which the absolute (Helmholtz) free energy is obtained by performing isochoric integration of the excess internal energy. A difficulty of the energy route in the high-temperature limit is resolved by the aid of an analytic method. The exact second and third virial coefficients are also used in the analysis of the fluid EOS. The pressure route is taken to calculate the EOS of the solid phase, in which the virial pressure is numerically more stable than in the fluid phase. The resulting high-temperature phase diagram of C60 is quite systematic and free from uncertainties, and the liquid–vapor critical point is found at Tc=1980 K and ρc=0.44 nm−3, whereas the triple point at Tt=1880 and ρt=0.74 nm−3, confirming the existence of a stable liquid phase over the range of ∼100 K.

Simple Model for the Equation of State and Orientational Order-Disorder Transition of C60Solid under Pressure

A simple model is proposed for the equation of state of C 60 solid under pressure up to ∼12 GPa and used to analyze selected experimental data. The model consists of a semiempirical modification of the Girifalco potential and is constructed such that it complies with basic experimental results such as the volume change associated with the orientational order-disorder transition observed at 260 K under normal pressure. We primarily concentrate on the experimental data of Ludwig et al. , which seem the most plausible at low pressure and are the most systematic at high pressure. It is shown that the model can actually be constructed to yield quite well the experimental result in the whole range of pressure.