We present a rigorous characterization of the ground state structures of p-H2 clusters and their isotopologues using diffusion Monte Carlo combined with the inherent structures analysis. For the N = 19 cluster we explore the effect of “quantum melting” by quantifying the contributions of local minima to the ground state as a function of continuously varying particle mass. Doubling the cluster size leads to an enormous increase of its complexity: the ground state of (p-H2)38 is highly delocalized over a large number of minima representing all the funnels of the potential energy surface. The ground state of (o-D2)38 is also delocalized, but over a smaller subset of minima, which exclusively belong to the same disordered motif.

The diffusion Monte Carlo (DMC) method is applied to the water monomer, dimer, and hexamer using q-TIP4P/F, one of the most simple empirical water models with flexible monomers. The bias in the time step (Δτ) and population size (Nw) is investigated. For the binding energies, the bias in Δτ cancels nearly completely, whereas a noticeable bias in Nw remains. However, for the isotope shift (e.g, in the dimer binding energies between (H2O)2 and (D2O)2), the systematic errors in Nw do cancel. Consequently, very accurate results for the latter (within ∼0.01 kcal/mol) are obtained with moderate numerical effort (Nw ∼ 103). For the water hexamer and its (D2O)6 isotopomer, the DMC results as a function of Nw are examined for the cage and prism isomers. For a given isomer, the issue of the walker population leaking out of the corresponding basin of attraction is addressed by using appropriate geometric constraints. The population size bias for the hexamer is more severe, and to maintain accuracy similar to that of the dimer, Nw must be increased by ∼2 orders of magnitude. Fortunately, when the energy difference between the cage and prism is taken, the biases cancel, thereby reducing the systematic errors to within ∼0.01 kcal/mol when using a population of Nw = 4.8 × 105 walkers. Consequently, a very accurate result for the isotope shift is also obtained. Notably, both the quantum and isotope effects for the prism-cage energy difference are small.

We consider the harmonic inversion problem, and the associated spectral estimation problem, both of which are key numerical problems in NMR data analysis. Under certain conditions (in particular, in exact arithmetic) these problems have unique solutions. Therefore, these solutions must not depend on the inversion algorithm, as long as it is exact in principle. In this paper, we are not concerned with the algorithmic aspects of harmonic inversion, but rather with the sensitivity of the solutions of the problem to perturbations of the time-domain data. A sensitivity analysis was performed and the counterintuitive results call into question the common assumption made in “super-resolution” methods using non-uniform data sampling, namely, that the data should be sampled more often where the time signal has the largest signal-to-noise ratio. The numerical analysis herein demonstrates that the spectral parameters (such as the peak positions and amplitudes) resulting from the solution of the harmonic inversion problem are least susceptible to the perturbations in the values of data points at the edges of the time interval and most susceptible to the perturbations in the values at intermediate times.

It is demonstrated how the problem of ground state estimation of an n-body system can be recast as the less demanding problem of finding the global minimum of an effective potential in the 3n-dimensional coordinate space. The latter emerges when the solution of the imaginary-time Schrödinger equation is approximated by a variational Gaussian wavepacket (VGW). The VGW becomes stationary in the infinite-imaginary-time limit. Such a stationary solution is not only exact for a harmonic potential, but it also provides a good approximation for a quantum state that is still localized in one of the basins of attraction, when, for example, the harmonic approximation may fail. The landscape of the effective potential is favorable for its global optimization, and is particularly suitable for optimization by GMIN, an open source program designed for global optimization using the basin-hopping algorithm. Consequently, the methodology is applied within GMIN to estimate the ground state structures of several binary para-H2/ortho-D2 molecular clusters. The results are generally consistent with the previous observations for homogeneous para-H2 and ortho-D2 clusters, as well as for smaller binary clusters.

The ground states of Lennard-Jones clusters (LJn) for sizes up to n = 147 are estimated as a function of the de Boer quantum delocalization length, Λ, using the variational Gaussian wavepacket method. Consequently, the n−Λ phase diagram is constructed showing the ranges of stability of various structural motifs, including the Mackay and anti-Mackay icosahedra, several nonicosahedral but highly symmetric structures, and liquidlike (or disordered) structures. The increase in Λ favors more disordered and diffuse structures over more symmetric and compact ones, eventually making the liquidlike structures most energetically favorable.

The Gaussian wavepacket propagation method of Hellsing et al. [Chem. Phys. Lett. 122 (1985) 303] for the computation of equilibrium density matrices is revisited and modified. The variational principle applied to the ‘imaginary time’ Schrödinger equation provides the equations of motion for Gaussians in a resolution of , described by their width matrix, center and scale factor, all treated as dynamical variables. The method is computationally very inexpensive, has favorable scaling with the system size and, with the current implementation, is surprisingly accurate in a wide temperature range, even for cases involving quantum tunneling. Incorporation of symmetry constraints, such as reflection or particle statistics, is discussed as well.

The self-consistent phonons (SCP) method is a practical approach for computing structural and dynamical properties of a general quantum or classical many-body system while incorporating anharmonic effects. However, a convincing demonstration of the accuracy of SCP and its advantages over the standard harmonic approximation is still lacking. Here we apply SCP to classical Lennard-Jones (LJ) clusters and compare with numerically exact results. The close agreement between the two reveals that SCP accurately describes structural properties of the classical LJ clusters from zero-temperature (where the method is exact) up to the temperatures at which the chosen cluster conformation becomes unstable. Given the similarities between thermal and quantum fluctuations, both physically and within the SCP ansatz, the accuracy of classical SCP over a range of temperatures suggests that quantum SCP is also accurate over a range of quantum de Boer parameter Λ=ℏ/(σmε), which describes the degree of quantum character of the system.