Quantum anharmonic densities of states using the Wang–Landau method

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.

Phase space theory of evaporation in neon clusters: the role of quantum effects

Unimolecular evaporation of neon clusters containing between 14 and 148 atoms is theoretically investigated in the framework of phase space theory. Quantum effects are incorporated in the vibrational densities of states, which include both zero-point and anharmonic contributions, and in the possible tunneling through the centrifugal barrier. The evaporation rates, kinetic energy released, and product angular momentum are calculated as a function of excess energy or temperature in the parent cluster and compared to the classical results. Quantum fluctuations are found to generally increase both the kinetic energy released and the angular momentum of the product, but the effects on the rate constants depend nontrivially on the excess energy. These results are interpreted as due to the very few vibrational states available in the product cluster when described quantum mechanically. Because delocalization also leads to much narrower thermal energy distributions, the variations of evaporation observables as a function of canonical temperature appear much less marked than in the microcanonical ensemble. While quantum effects tend to smooth the caloric curve in the product cluster, the melting phase change clearly keeps a signature on these observables. The microcanonical temperature extracted from fitting the kinetic energy released distribution using an improved Arrhenius form further suggests a backbending in the quantum Ne(13) cluster that is absent in the classical system. Finally, in contrast to delocalization effects, quantum tunneling through the centrifugal barrier does not play any appreciable role on the evaporation kinetics of these rather heavy clusters.

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.