Comparison of Taboo Search Methods for Atomic Cluster Global Optimization with a Basin-Hopping Algorithm.

The basin-hopping algorithm (BHA) allows for the efficient exploration of atomic cluster potential energy surfaces by random perturbations in configuration space, followed by energy minimizations. Here, the taboo search method is incorporated to prevent the search from revisiting recently visited regions of the search space. Two taboo search modes are implemented, one mode resets the search to random coordinates upon encountering the taboo region, while the other simply rejects any proposed move into the taboo region. These two modes are tested and compared on a variety of potential energy surfaces─several clusters where atomic interactions are described by the Lennard-Jones potential, and Au55 where a semi-empirical tight binding potential is used to describe atomic interactions. Some differences in performance between the two taboo search modes were noted for LJ38 and Au55, with the mode that rejects all hops into the taboo region performing better, offering a means to improve the efficiency of the BHA for multifunnel systems. However, both taboo search modes failed to significantly improve performance on multifunnel systems where more than two funnels were present in the system.

Improved walker population control for full configuration interaction quantum Monte Carlo.

Full configuration interaction quantum Monte Carlo (FCIQMC) is a stochastic approach for finding the ground state of a quantum many-body Hamiltonian. It is based on the dynamical evolution of a walker population in Hilbert space, which samples the ground state configuration vector over many iterations. Here, we present a modification of the original protocol for walker population control of Booth et al. [J. Chem. Phys. 131, 054106 (2009)] in order to achieve equilibration at a pre-defined average walker number and to avoid walker number overshoots. The dynamics of the walker population is described by a noisy damped harmonic oscillator and controlled by two parameters responsible for damping and forcing, respectively, for which reasonable values are suggested. We further introduce a population growth witness that can be used to detect annihilation plateaus related to overcoming the FCIQMC sign problem. Features of the new population control procedure such as precise walker number control and fast equilibration are demonstrated. The standard error of the shift estimator for the ground state energy as well as the population control bias is found to be unaffected by the population control procedure or its parameters. The improved control of the walker number, and thereby memory consumption, is a desirable feature required for automating FCIQMC calculations and requires minimal modifications to the existing code.

A Hundred-Year-Old Experiment Re-evaluated: Accurate Ab†Initio Monte†Carlo Simulations of the Melting of Radon.

State-of-the-art relativistic coupled-cluster theory is used to construct many-body potentials for the noble-gas element radon to determine its bulk properties including the solid-to-liquid phase transition from parallel tempering Monte Carlo simulations through either direct sampling of the bulk or from a finite cluster approach. The calculated melting temperature are 200(3) K and 200(6) K from bulk simulations and from extrapolation of finite cluster values, respectively. This is in excellent agreement with the often debated (but widely cited) and only available value of 202 K, dating back to measurements by Gray and Ramsay in 1909.

Accurate, Large-Scale Density Functional Melting of Hg: Relativistic Effects Decrease Melting Temperature by 160 K.

Using first-principles calculations and the "interface pinning" method in large-scale density functional molecular dynamics simulations of bulk melting, we prove that mercury is a liquid at room temperature due to relativistic effects. The relativistic model gives a melting temperature of 241 K, in excellent agreement with the experimental temperature of 234 K. The nonrelativistic melting temperature is remarkably high at 402 K.

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.

Melting of "non-magic" argon clusters and extrapolation to the bulk limit.

The melting of argon clusters ArN is investigated by applying a parallel-tempering Monte Carlo algorithm for all cluster sizes in the range from 55 to 309 atoms. Extrapolation to the bulk gives a melting temperature of 85.9 K in good agreement with the previous value of 88.9 K using only Mackay icosahedral clusters for the extrapolation [E. Pahl, F. Calvo, L. Koci, and P. Schwerdtfeger, "Accurate melting temperatures for neon and argon from ab initio Monte Carlo simulations," Angew. Chem., Int. Ed. 47, 8207 (2008)]. Our results for argon demonstrate that for the extrapolation to the bulk one does not have to restrict to magic number cluster sizes in order to obtain good estimates for the bulk melting temperature. However, the extrapolation to the bulk remains a problem, especially for the systematic selection of suitable cluster sizes.

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.

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.

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.

Up to fourth virial coefficients from simple and efficient internal-coordinate sampling: application to neon.

A simple and efficient internal-coordinate importance sampling protocol for the Monte Carlo computation of (up to fourth-order) virial coefficients ̅B(n) of atomic systems is proposed. The key feature is a multivariate sampling distribution that mimics the product structure of the dominating pairwise-additive parts of the ̅B(n). This scheme is shown to be competitive over routine numerical methods and, as a proof of principle, applied to neon: The second, third, and fourth virial coefficients of neon as well as equation-of-state data are computed from ab initio two- and three-body potentials; four-body contributions are found to be insignificant. Kirkwood-Wigner quantum corrections to first order are found to be crucial to the observed agreement with recent ab initio and experimental reference data sets but are likely inadequate at very low temperatures.

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.

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.