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The so-called "ultrafast" nuclear magnetic resonance (NMR) methods enable the collection of multidimensional spectra within a single scan. These experiments operate by replacing traditional t(1) time increments, with a series of combined radiofrequency-irradiation/magnetic-field-gradient manipulations that spatially encode the effects of the indirect-domain spin interactions. Barring the presence of sizable displacements, the spatial patterns thus imparted can be read out following a mixing period with the aid of oscillating acquisition gradients, leading to a train of t(2)-modulated echoes carrying in their positions and phases the indirect- and the direct-domain spin interactions. Both the initial spatial encoding as well as the subsequent spatial decoding procedures underlying ultrafast NMR were designed under the assumption that spins remain static within the sample during their execution. Most often this is not the case, and motion-related effects can be expected to affect the outcome of these experiments. The present paper focuses on analyzing the effects of diffusion in ultrafast two-dimensional (2D) NMR. Toward this end both analytical and numerical formalisms are derived, capable of dealing with the nonuniform spin manipulations, macroscopic sample sizes, and microscopic displacements involved in this kind of sequences. After experimentally validating the correctness of these formalisms these were used to analyze the effects of diffusion for a variety of cases, including ultrafast experiments on both rapidly and slowly diffusing molecules. A series of prototypical schemes were considered including discrete and continuous encoding modes, constant- and real-time manipulations, homo- and heteronuclear acquisitions, and single versus multiple quantum modalities. The effects of molecular diffusion were also compared against typical relaxation-driven losses as they happen in these various prototypical situations; from all these situations, general guidelines for choosing the optimal ultrafast 2D NMR scheme for a particular sample and condition could be deduced.

The thermodynamics and kinetics of a many-body system can be described in terms of a potential energy landscape in multidimensional configuration space. The partition function of such a landscape can be written in terms of a density of states, which can be computed using a variety of Monte Carlo techniques. In this paper, a new self-consistent Monte Carlo method for computing density of states is described that uses importance sampling and a multiplicative update factor to achieve rapid convergence. The technique is then applied to compute the equilibrium quench probability of the various inherent structures (minima) in the landscape. The quench probability depends on both the potential energy of the inherent structure and the volume of its corresponding basin in configuration space. Finally, the methodology is extended to the isothermal-isobaric ensemble in order to compute inherent structure quench probabilities in an enthalpy landscape.

Molecular ground-state energies and two-electron reduced density matrices (2-RDMs) have recently been computed without the many-electron wave function by constraining the 2-RDM to satisfy a complete set of three-positivity conditions for N representability [D. A. Mazziotti, Phys. Rev. A 74, 032501 (2006)]. Energies at both equilibrium and nonequilibrium geometries are obtained within 0.3% of the correlation energy. In this paper the authors extend this work to examine the accuracy of molecular properties, including multipole moments and components of the ground-state energy, relative to full configuration interaction (FCI). Comparisons are also made with 2-RDM methods with two-positivity conditions and two-positivity plus the generalized T1T2 conditions as well as several approximate wave function methods. Using the 2-RDM method with three-positivity conditions, the authors obtain dipole, quadrupole, and octupole moments for BeH2, BH, H2O, CO, and NH3 at equilibrium geometries that are within 0.04% of their FCI values. In addition, for the potential energy surface of N2, the 2-RDM method with three-positivity yields not only accurate total ground-state energies but also accurate expectation values of the kinetic energy operator, the electron-nuclei potential, and electron-electron repulsion.

The semiclassical method is characterized by finite forces and smooth, well-behaved trajectories, but also by multivalued representational functions that are ill behaved at caustics. In contrast, quantum trajectory methods--based on Bohmian mechanics (quantum hydrodynamics)--are characterized by divergent forces and erratic trajectories near nodes, but also well-behaved, single-valued representational functions. In this paper, we unify these two approaches into a single method that captures the best features of both, and in addition, satisfies the correspondence principle. Stationary eigenstates in one degree of freedom are the primary focus, but more general applications are also anticipated., (Copyright 2004 American Institute of Physics)