Larry Engelhardt

{Mo24Fe12} Macrocycles: Anion Templation with Large Polyoxometalate Guests

POM and circumstance: Nanometer-sized polyoxometalates (POMs) bring a new direction to anion-templated supramolecular chemistry. The Keggin (left) and Dawson-type (right) polyoxoanions direct the assembly of giant metallomacrocycles through an array of weak hydrogen-bonding interactions. The concerted action of multiple hydrogen bonds keeps the templating guests embedded within the hosts, even in the solution state.

Studies of Finite Molecular Chains: Synthesis, Structural, Magnetic and Inelastic Neutron Scattering Studies of Hexa- and Heptanuclear Chromium Horseshoes

We report the synthesis and structural characterisation of a family of finite molecular chains, specifically [{[R(2)NH(2)](3)[Cr(6)F(11)(O(2)CCMe(3))(10)]}(2)] (in which R=nPr 1, Et 2, nBu 3), [{Et(2)NH}(2){[Et(2)NH(2)](3)[Cr(7)F(12)(O(2)CCMe(3))(12)][HO(2)CCMe(3)](2)}(2)] (4), [{[Me(2)NH(2)](3)[Cr(6)F(11)(O(2)CCMe(3))(10)]2.5 H(2)O}(4)] (5) and [{[iPr(2)NH(2)](3)[Cr(7)F(12)(O(2)CCMe(3))(12)]}(2)] (6). The structures all contain horseshoes of chromium centres, with each Cr...Cr contact within the horseshoe bridged by a fluoride and two pivalates. The horseshoes are linked through hydrogen bonds to the secondary ammonium cations in the structure, leading to di- and tetra-horseshoe structures. Through magnetic measurements and inelastic neutron scattering studies we have determined the exchange coupling constants in 1 and 6. In 1 it is possible to distinguish two exchange interactions, J(A)=-1.1 meV and J(B)=-1.4 meV; J(A) is the exchange interactions at the tips of the horseshoe and J(B) is the exchange within the body of the horseshoe (1 meV=8.066 cm(-1)). For 6 only one interaction was needed to model the data: J=-1.18 meV. The single-ion anisotropy parameters for Cr(III) were also derived for the two compounds as: for 1, D(Cr)=-0.028 meV and |E(Cr)|=0.005 meV; for 6, D(Cr)=-0.031 meV. Magnetic-field-dependent inelastic neutron scattering experiments on 1 allowed the Zeeman splitting of the first two excited states and level crossings to be observed. For the tetramer of horseshoes (5), quantum Monte Carlo calculations were used to fit the magnetic susceptibility behaviour, giving two exchange interactions within the horseshoe (-1.32 and -1.65 meV) and a weak inter-horseshoe coupling of +0.12 meV. Multi-frequency variable-temperature EPR studies on 1, 2 and 6 have also been performed, allowing further characterisation of the spin Hamiltonian parameters of these chains.

Low-temperature magnetization and the excitation spectrum of antiferromagnetic Heisenberg spin rings

Accurate results are obtained for the low temperature magnetization versus magnetic field of Heisenberg spin rings consisting of an even number N of intrinsic spins s = 1/2, 1, 3/2, 2, 5/2, 3, 7/2 with nearest-neighbor antiferromagnetic (AF) exchange by employing a numerically exact quantum Monte Carlo method. A straightforward analysis of this data, in particular the values of the level-crossing fields, provides accurate results for the lowest energy eigenvalue E(N,S,s) for each value of the total spin quantum number S. In particular, the results are substantially more accurate than those provided by the rotational band approximation. For s 1 the dependence of E(N,S,s) on s can be described by a scaling relation, and this relation is shown to hold well for ring sizes up to N = 80 for all intrinsic spins in the range 3/2 <= s <= 7/2. Considering ring sizes in the interval 8 <= N <= 50, we find that the energy gap between the ground state and the first excited state approaches zero proportional to 1/N^a, where a = 0.76 for s = 3/2 and a = 0.84 for s = 5/2. Finally, we demonstrate the usefulness of our present results for E(N,S,s) by examining the Fe12 ring-type magnetic molecule, leading to a new, more accurate estimate of the exchange constant for this system than has been obtained heretofore.

Simple models and powerful tools for seeking a comprehensive understanding of the magnetic properties of molecular magnets

The Heisenberg model provides a simple but powerful theoretical platform for modelling magnetic molecules. In this article, we demonstrate that--despite its simplicity--an isotropic Heisenberg model successfully provides a comprehensive description of the magnetic properties of the {Fe₈}-cubane and the {Cr₁₂Cu₂} magnetic molecules. However, in order to achieve this success, it is necessary to employ a variety of sophisticated experimental and theoretical techniques. These include the use of pulsed-field measurements to observe a high-field (41 T) ground-state level crossing in the {Fe₈}-cubane system, and tunnel-diode oscillator measurements, which we use to observe excited-state level crossings in the {Cr₁₂Cu₂} ring. For these two systems, the theoretical modelling was carried out using matrix diagonalization and quantum Monte Carlo calculations, respectively.

Quantum Monte Carlo Simulations and High-Field Magnetization Studies of Antiferromagnetic Interactions in a Giant Hetero-Spin Ring

Chromium lanthanide heterometallic wheel complexes {Cr8 Ln8 } (Ln=Gd, Dy and Y) with alternating metal centres are presented. Quantum Monte Carlo simulations reveal antiferromagnetic exchange-coupling constants with an average of 2.1 K within the {Cr8 Gd8 } wheel, which leads to a large ground spin state (ST =16) that is confirmed by magnetization studies up to 20 Tesla. The {Cr8 Dy8 } wheel is a single-molecule magnet.

Level crossings and zero-field splitting in the {Cr8}-cubane spin cluster studied using inelastic neutron scattering and magnetization

Inelastic neutron scattering (INS) in variable magnetic field and high-field magnetization measurements in the millikelvin temperature range were performed to gain insight into the low-energy magnetic excitation spectrum and the field-induced level crossings in the molecular spin cluster {Cr(8)}-cubane. These complementary techniques provide consistent estimates of the lowest level-crossing field. The overall features of the experimental data are explained using an isotropic Heisenberg model, based on three distinct exchange interactions linking the eight Cr(III) paramagnetic centers (spins s = 3/2), that is supplemented with a relatively large molecular magnetic anisotropy term for the lowest S = 1 multiplet. It is noted that the existence of the anisotropy is clearly evident from the magnetic field dependence of the excitations in the INS measurements, while the magnetization measurements are not sensitive to its effects.

Magnetic resonance: Using computer simulations and visualizations to connect quantum theory with classical concepts

We discuss how computers can be used to solve the ordinary differential equations that provide a quantum mechanical description of magnetic resonance. By varying the parameters in these equations and visually exploring how these parameters affect the results, students can quickly gain insights into the nature of magnetic resonance that go beyond the standard presentation found in quantum mechanics textbooks. The results were generated using an IPython notebook, which we provide as an online supplement with interactive plots and animations.

Modern cosmology: Interactive computer simulations that use recent observational surveys

We present a collection of new, open-source computational tools for numerically modeling recent large-scale observational data sets using modern cosmology theory. Specifically, these tools will allow both students and researchers to constrain the parameter values in competitive cosmological models, thereby discovering both the accelerated expansion of the universe and its composition (e.g., dark matter and dark energy). These programs have several features to help the non-cosmologist build an understanding of cosmological models and their relation to observational data: a built-in collection of several real observational data sets; sliders to vary the values of the parameters that define different cosmological models; real-time plotting of simulated data; and

Quantum Monte Carlo simulations of a giant {Ni 21 Gd 20 } cage with a S = 91 spin ground state

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Extending the {(Mo)MO5}12M30 capsule keplerate sequence: a {Cr30} cluster of S=3/2 metal centers with a {Na(H2O)12} encapsulate

calculations of the goodness of fit for each choice of parameters (theory) and observational data (experiment). The current list of built-in observations includes several recent supernovae Type Ia surveys, baryon acoustic oscillations, the cosmic microwave background radiation, gamma-ray bursts, and measurements of the Hubble parameter. In this article, we discuss specific results for testing cosmological models using these observational data. These programs can be found at this http URL