Nanothermodynamics of large iron clusters by means of a flat histogram Monte Carlo method.

The thermodynamics of iron clusters of various sizes, from 76 to 2452 atoms, typical of the catalyst particles used for carbon nanotubes growth, has been explored by a flat histogram Monte Carlo (MC) algorithm (called the σ-mapping), developed by Soudan et al. [J. Chem. Phys. 135, 144109 (2011), Paper I]. This method provides the classical density of states, gp(Ep) in the configurational space, in terms of the potential energy of the system, with good and well controlled convergence properties, particularly in the melting phase transition zone which is of interest in this work. To describe the system, an iron potential has been implemented, called "corrected EAM" (cEAM), which approximates the MEAM potential of Lee et al. [Phys. Rev. B 64, 184102 (2001)] with an accuracy better than 3 meV/at, and a five times larger computational speed. The main simplification concerns the angular dependence of the potential, with a small impact on accuracy, while the screening coefficients S(ij) are exactly computed with a fast algorithm. With this potential, ergodic explorations of the clusters can be performed efficiently in a reasonable computing time, at least in the upper half of the solid zone and above. Problems of ergodicity exist in the lower half of the solid zone but routes to overcome them are discussed. The solid-liquid (melting) phase transition temperature T(m) is plotted in terms of the cluster atom number N(at). The standard N(at)(-1/3) linear dependence (Pawlow law) is observed for N(at) >300, allowing an extrapolation up to the bulk metal at 1940 ±50 K. For N(at) <150, a strong divergence is observed compared to the Pawlow law. The melting transition, which begins at the surface, is stated by a Lindemann-Berry index and an atomic density analysis. Several new features are obtained for the thermodynamics of cEAM clusters, compared to the Rydberg pair potential clusters studied in Paper I.

A new Monte Carlo method for getting the density of states of atomic cluster systems.

A novel Monte Carlo flat histogram algorithm is proposed to get the classical density of states in terms of the potential energy, g(E(p)), for systems with continuous variables such as atomic clusters. It aims at avoiding the long iterative process of the Wang-Landau method and controlling carefully the convergence, but keeping the ability to overcome energy barriers. Our algorithm is based on a preliminary mapping in a series of points (called a σ-mapping), obtained by a two-parameter local probing of g(E(p)), and it converges in only two subsequent reweighting iterations on large intervals. The method is illustrated on the model system of a 432 atom cluster bound by a Rydberg type potential. Convergence properties are first examined in detail, particularly in the phase transition zone. We get g(E(p)) varying by a factor 10(3700) over the energy range [0.01 < E(p) < 6000 eV], covered by only eight overlapping intervals. Canonical quantities are derived, such as the internal energy U(T) and the heat capacity C(V)(T). This reveals the solid to liquid phase transition, lying in our conditions at the triple point. This phase transition is further studied by computing a Lindemann-Berry index, the atomic cluster density n(r), and the pressure, demonstrating the progressive surface melting at this triple point. Some limited results are also given for 1224 and 4044 atom clusters.

Temperature effects on the rovibrational spectra of pyrene-based PAHs.

Absorption infrared spectra have been computed for a variety of polycyclic aromatic hydrocarbon molecules of the pyrene family, taking into account anharmonicity and temperature effects, rovibrational quantization, and couplings. The energy levels are described by a second-order perturbative expansion of the rovibrational Hamiltonian in the vibrational and rotational quantum numbers, as relevant for a symmetric-top molecule, with ingredients obtained from quantum chemistry calculations. Multicanonical Monte Carlo simulations are carried out to compute bidimensional IR intensity histograms as a function of total energy and vibrational frequency, which then provide the absorption spectrum at arbitrary temperatures via a Laplace transformation. The main spectral features analyzed for neutral, anionic, and cationic pyrene indicate a strong dependence on temperature, in agreement with existing laboratory experiments, and a significant contribution of rotational degrees of freedom to the overall broadenings. The spectral shifts and broadenings reveal some sensitivity of anharmonicities to the charge and protonation states and, in the case of protonated pyrene and pyrenyl cation, on possible isomers and between aromatic and aliphatic C-H bands. Implications of the present work to the general issue of interstellar emission features are discussed.

Finite-temperature IR spectroscopy of polyatomic molecules: a theoretical assessment of scaling factors.

With a recently developed simulation method (Basire, M.; et al. J. Phys. Chem. A 2009, 113, 6947), the infrared vibrational spectra of several polyatomic molecules are calculated over a broad range of temperature, taking into account quantum, anharmonic, and couplings effects. Anharmonic force fields, generated from static first-principle calculations, are sampled in the microcanonical ensemble to provide energy-resolved absorption intensities and their finite temperature analogues after Laplace transformation. Effective anharmonic frequencies are characterized as a continuous function of temperature for vinyl fluoride, the N-acetyl-Phe-NH(2) peptide, and protonated naphthalene. These frequencies generally deviate increasingly from the harmonic value with increasing temperature, although the overestimation due to the harmonic approximation is particularly salient for high-frequency modes. Anharmonicities may also be sufficient to alter structural assignment of experimental spectra with respect to empirically scaled harmonic bands. These results emphasize some possible limitations and inaccuracies inherent to using such static scaling factors for correcting harmonic IR spectra.

Temperature and anharmonic effects on the infrared absorption spectrum from a quantum statistical approach: application to naphthalene.

A method is developed to calculate the finite-temperature infrared absorption spectrum of polyatomic molecules with energy levels described by a second-order Dunham expansion. The anharmonic couplings are fully incorporated in the calculation of the quantum density of states, achieved using a Wang-Landau Monte Carlo procedure, as well as in the determination of transition energies. Additional multicanonical simulations provide the microcanonical absorption intensity as a function of both the absorption wavelength and the internal energy of the molecule. The finite-temperature spectrum is finally obtained by Laplace transformation of this microcanonical histogram. The present scheme is applied to the infrared spectrum of naphthalene, for which we quantify the shifting, broadening, and third-order effects as a continuous function of temperature. The influence of anharmonicity and couplings is manifested on the nontrivial variations of these features with increasing temperature.

Quantum densities of states of fluxional polyatomic systems from a superposition approximation.

The superposition method is used to calculate quantum densities of states of polyatomic systems with multiple isomeric structures. For each isomer, anharmonicities are included rigorously using a Dunham expansion of the vibrational energy levels and short exchange Monte Carlo simulations are used to compute the individual quantum densities of states. The method is applied to the computation of thermodynamical properties of the Ar(13) and Ne(13) clusters. The canonical heat capacities are found in very satisfactory agreement with the predictions of quantum or semiclassical sampling methods.

Quantum anharmonic densities of states using the Wang-Landau method.

The Wang-Landau sampling method is adapted to the calculation of quantum densities of states for fully coupled anharmonic systems. The accuracy of the method is illustrated against exact counting for two molecules with separable oscillators, namely, the Zundel complex H(5)O(2) (+) and the Na(11) cluster. Application to the fully coupled naphthalene molecule (C(10)H(8)) reveals significant deviations in the finite temperature thermodynamical properties that are not captured by simple perturbation theory. There are no limitations in the size of the molecules that can be treated with this method.