Elke Pahl

Accurate Melting Temperatures for Neon and Argon from Ab Initio Monte Carlo Simulations

Although studied experimentally for centuries, the melting of solids is still a fascinating phenomenon whose underlying mechanisms are not yet well understood. Predicting melting points is a nontrivial task: The standard computational method relies on analyzing the free energies of the solid and liquid phases obtained independently by thermodynamic or Gibbs–Duhem integration; this approach suffers from the difficulty of calibration. Alternatively, in coexistence methods the interface between the two phases must be described explicitly; this interface is often hard to stabilize. An alternative idea, which we pursue herein, is to obtain information about the melting transition by studying finite clusters and extrapolating the results to infinitely large systems. Here we present for the first time calculated melting temperatures reaching experimental accuracy obtained from Monte Carlo simulations of NeN and ArN clusters consisting of a “magic number” N of atoms (N = 13, 55, 147, 309, 561, 923) and of bulk samples. This was achieved by the use of accurate interaction potentials obtained from precise ab initio data having the same computational efficiency as the widely used empirical Lennard-Jones (LJ) potential, and without any experimental input whatsoever. Argon and neon adopt the face-centered cubic (fcc) periodic packing in the solid state, but their clusters with N< 1000 are most stable as complete Mackay icosahedra. The number of atoms in the first six shells of the

Evidence for Low‐Temperature Melting of Mercury owing to Relativity

An old problem solved: Monte Carlo simulations using the diatomic-in-molecule method derived from accurate ground- and excited-state relativistic calculations for Hg2 show that the melting temperature for bulk mercury is lowered by 105 K, which is due to relativistic effects.

Extension of quantized Hamilton dynamics to higher orders

The quantized Hamilton dynamics (QHD) method, which was introduced and developed in J. Chem. Phys. 113, 6557 (2000) to the second order, is extended to the third and fourth orders. The QHD formalism represents an extension of classical mechanics and allows for the derivation of a hierarchy of equations of motion which converge with the quantum-mechanical limit. Here, the second, third, and fourth order QHD approximations are applied to two model problems: the decay of a particle in a metastable cubic potential and the intermode energy exchange observed in the Henon–Heiles system. The QHD results exhibit good convergence with the quantum data with increasing order yet preserve the computational efficiency of classical calculations. The second order QHD approximation already does an excellent job in maintaining the zero-point energy in the Henon–Heiles system and describing moderate tunneling events in the metastable potential. Extensions to higher orders substantially improve the QHD results for deep tunne...

A highly accurate potential energy curve for the mercury dimer.

The potential energy curve of the electronic ground state of the mercury dimer based on CCSD(T) calculations at the complete basis set (CBS) limit, including corrections for the full triples DeltaT and explicit spin-orbit (SO) interactions at the CCSD(T) level of theory, is presented. In the far long-range part, the potential energy curve is complemented by symmetry-adapted perturbation theory calculations. Potential curves of an analytically simple, extended Lennard-Jones form are obtained from very accurate fits to the CBS/CCSD(T)+SO and CBS/CCSD(T)+SO+DeltaT data. The Hg(2) potential curves yield dissociation energies of D(e)=424/392 cm(-1) and equilibrium distances of r(e)=3.650/3.679 A at the CBS/CCSD(T)+SO and CBS/CCSD(T)+SO+DeltaT levels of theory, respectively. By including perturbative quadruple corrections in our coupled-cluster calculations and corrections from correlating the 4f-core, we arrive at a final dissociation energy of D(e)=405 cm(-1), in excellent agreement with the experimentally estimated value of 407 cm(-1) by Greif and Hensel. In addition, the rotational and vibrational spectroscopic constants as well as the second virial coefficient B(T) in dependence of the temperature T are calculated and validated against available experimental and theoretical data.

Diatomics-in-Molecules Modeling of Many-Body Effects on the Structure and Thermodynamics of Mercury Clusters.

The stable structures and melting behavior of Hgn clusters, 2 ≤ n < 60, have been theoretically investigated using an updated diatomics-in-molecules (DIM) model initially proposed by Kitamura [Chem. Phys. Lett.2006, 425, 2056]. Global optimization and sampling at finite temperature are achieved on the basis of hierarchical and nested Markov chain Monte Carlo methods, respectively. The DIM model predicts highly symmetric icosahedral global minima that are generally similar to the standard van der Waals atomic clusters, without any indication of distorted or low-coordinated geometries, but also at variance with the global minima found with the pairwise Hg2 potential. The combined influences of surface and many-body effects due to s-p mixing are considerable on the melting point: although the model predicts a bulk melting temperature in fair agreement with experimental results, it is found to decrease with increasing cluster size.

Sensitivity of the thermal and acoustic virial coefficients of argon to the argon interaction potential

Second, third, and fourth thermal and acoustic virial coefficients between 100 and 1000 K are computed for different argon interaction models derived from combinations of accurate two- and three-body potentials. Differences between the various interaction models tested mirror the presumed order in the accuracy of these models, but are not well captured at the level of the lowest-order contributions in the virial expansion: While the second- and third-order virial coefficients are found to be rather insensitive to small variations in the two- and three-body potentials, more pronounced differences in higher-order coefficients are currently of limited use in assessing the accuracy of the interaction potential due to difficulties in the unambiguous experimental determination of these higher-order coefficients. In contrast, pressure-volume and speed-of-sound data--both of which are experimentally known to highest accuracies--are found to be insensitive to small variations in the interaction model. All but the least accurate models reproduce experimental pressure-volume and speed-of-sound data near-quantitatively in regions where the (fourth-order) virial expansions apply. All quantities considered are found to be completely unaffected by a non-vanishing quadruple-dipole four-body potential.

Adiabatic and nonadiabatic effects of nuclear dynamics in spectra of decaying states: Auger spectrum of HF

An all ab initio calculation of the Auger spectrum of HF is presented which includes the effects introduced by nuclear dynamics. The involved potential curves of the core‐ionized decaying state and the dicationic final states are computed by CASSCF. On these curves, the wave‐packet dynamics is performed in an exact manner. Special attention is paid to the transition to the 1Π(2σ−1,1π−1) final state where an avoided crossing between this state and a satellite state is found within the region of decay. By vibronic coupling, the satellite gains intensity which influences the shape of the spectrum. The experimental spectrum is very well reproduced.

Towards J/mol Accuracy for the Cohesive Energy of Solid Argon

The cohesive energies of argon in its cubic and hexagonal closed packed structures are computed with an unprecedented accuracy of about 5 J mol(-1) (corresponding to 0.05 % of the total cohesive energy). The same relative accuracy with respect to experimental data is also found for the face-centered cubic lattice constant deviating by ca. 0.003 Å. This level of accuracy was enabled by using high-level theoretical, wave-function-based methods within a many-body decomposition of the interaction energy. Static contributions of two-, three-, and four-body fragments of the crystal are all individually converged to sub-J mol(-1) accuracy and complemented by harmonic and anharmonic vibrational corrections. Computational chemistry is thus achieving or even surpassing experimental accuracy for the solid-state rare gases.

Communication: Ab initio Joule-Thomson inversion data for argon.

The Joule-Thomson coefficient μ(H)(P, T) is computed from the virial equation of state up to seventh-order for argon obtained from accurate ab initio data. Higher-order corrections become increasingly more important to fit the low-temperature and low-pressure regime and to avoid the early onset of divergence in the Joule-Thomson inversion curve. Good agreement with experiment is obtained for temperatures T > 250 K. The results also illustrate the limitations of the virial equation in regions close to the critical temperature.

Frozen local hole approximation

The frozen local hole approximation (FLHA) is an adiabatic approximation which is aimed to simplify the correlation calculations of valence and conduction bands of solids and polymers or, more generally, of the ionization potentials and electron affinities of any large system. Within this approximation correlated local hole states (CLHSs) are explicitly generated by correlating local Hartree-Fock (HF) hole states, i.e., (N-1)-particle determinants in which the electron has been removed from a local occupied orbital. The hole orbital and its occupancy are kept frozen during these correlation calculations, implying a rather stringent configuration selection. Effective Hamilton matrix elements are then evaluated with the above CLHSs; diagonalization finally yields the desired correlation corrections for the cationic hole states. We compare and analyze the results of the FLHA with the results of a full multireference configuration interaction with single and double excitations calculation for two prototype model systems, (H2)n ladders and H-(Be)n-H chains. Excellent numerical agreement between the two approaches is found. Comparing the FLHA with a full correlation treatment in the framework of quasidegenerate variational perturbation theory reveals that the leading contributions in the two approaches are identical. In the same way it could be shown that a much less demanding self-consistent field (SCF) calculation around a frozen local hole fully recovers, up to first order, all the leading single excitation contributions. Thus, both the FLHA and the above SCF approximation are well justified and provide a very promising and efficient alternative to fully correlated wave-function-based treatments of the valence and conduction bands in extended systems.