Homonuclear Systems Research Articles

How to Tickle Spins with a Fourier Transform NMR Spectrometer

In the long bygone days of continuous-wave nuclear magnetic resonance (NMR) spectroscopy, a selected transition within a multiplet of a high-resolution spectrum could be irradiated by a highly selective continuous-wave (CW) radio-frequency (rf) field with a very weak amplitude ω(2)/(2π)≤J. This causes splittings of connected transitions, allowing one to map the connectivities of all transitions within the energy-level diagram of the spin system. Such "tickling" experiments stimulated the invention of two-dimensional spectroscopy, but seem to have been forgotten for nearly 50 years. We show that tickling can readily be achieved in homonuclear systems with Fourier transform spectrometers by applying short pulses in the intervals between the sampling points. Extensions to heteronuclear systems are even more straightforward since they can be carried out using very weak CW rf fields.

Homonuclear decoupling for liquid-state NMR

We present a solution to the problem of decoupling of a homonuclear two-spin system having weak isotropic scalar coupling. We describe non-selective pulse sequences that create an effective field perpendicular to the coupling interaction over a broad range of chemical shifts, with a magnitude proportional to the chemical shifts. Effective decoupling is achieved when the difference in chemical shifts imprinted on the perpendicular field is sufficiently larger than the coupling between the spins. The proposed methods scale down the chemical shifts. The pulse sequences may be useful in various applications in nuclear magnetic resonance spectroscopy.

Validation of binuclear descriptor for mixed transition metal oxide supported electrocatalytic water oxidation

The energy profiles of the di-hydroxo – di-oxo – peroxo pathway are discussed for a set of 3d transition metal oxides comprising V(III–V), Cr(III–V), Mn(II–IV, Mn(III–V), Fe(II–IV), Co(II–IV) and Ni(II–IV) using density functional theory (DFT). Two classes of oxides were identified. The first class, comprising V(III–V), Cr(III–V) and Fe(II–IV), displays exothermicity for the oxidation of di-hydroxo to di-oxo versus the tyrosine/tyrosyl-radical (TyrOH/TyrO) couple and endothermicity for the subsequent OO bond formation ([−/+] class), while the second class, comprising Mn(III–V), Co(II–IV) and Ni(II–IV), shows endothermicity with respect to the oxidation step and exothermicity for the OO bond formation ([+/−] class). The energetics of the endothermicity (exothermicity) for the oxidation step is reflected in the exothermicity (endothermicity) of the subsequent OO bond formation step. Mn(II–IV) is not part of any of the two classes. Instead it shows zero exothermicity with respect to TyrOH/TyrO for the oxidation step and a small endothermicity for the OO bond formation step. Despite the promising energy profile Mn(II–IV) is argued to be inactive due to a large activation barrier. A set of improved hetero-nuclear candidate catalysts is predicted by mixing [−/+] with [+/−] transition metal oxides. A simple and efficient method to estimate the energy profile of mixed transition metal oxides from the homo-nuclear systems is demonstrated. The validity of this procedure is checked and agreement with the explicitly calculated values is found. All considered heteronuclear candidate catalysts display enhanced performance compared to the pure homonuclear systems.

Acquisition strategy to obtain quantitative diffusion NMR data

Pulsed Gradient Spin Echo (PGSE) diffusion NMR experiments constitute a powerful tool for analyzing complex mixtures because they can in principle separate the NMR spectra of each mixture component. However, because these experiments intrinsically rely on spin echoes, they are traditionally regarded as non-quantitative, due to the signal attenuation caused by longitudinal (T1) and transverse (T2) nuclear magnetic relaxation during the rather long delays of the pulse sequence. Alternatively to the quantitative Direct Exponential Curve Resolution Algorithm (qDECRA) approach proposed by Antalek (J. Am. Chem. Soc. 128 (2006) 8402–8403), this work presents an acquisition strategy that renormalizes this relaxation attenuation using estimates of the T1 and T2 relaxation times for all the nuclei in the mixture, as obtained directly with the pulse sequence used to record the PGSE experiment. More specifically, it is shown that only three distinct PGSE experiments need to be recorded, each with a specific set of acquisition parameters. For small- and medium-sized molecules, only T1 is required for obtaining accurate quantification. For larger molecular weight species, which typically exhibit short T2 values, estimates of T2 must also be included but only a rough estimation is required. This appears fortunate because these data are especially hard to obtain with good accuracy when analyzing homonuclear scalar-coupled systems. Overall, the proposed methodology is shown to yield a quantification accuracy of ±5%, both in the absence and in the presence of spectral overlap, giving rise – at least, in our hands – to results that superseded those achieved by qDECRA, while requiring substantially less experimental time.

Matter-wave solitons in heteronuclear atomic Bose-Einstein condensates with synchronously controllable interactions and potentials

We investigate exact matter-wave soliton pairs of two-component heteronuclear atomic Bose-Einstein condensates with tunable interactions and harmonic potentials by using a combination of the homogeneous balance principle and the $F$-expansion technique. Our results show that exact matter-wave soliton pairs are asymmetric where their existence requires some restrictive conditions corresponding to experimentally controllable interactions and harmonic potential parameters. In contrast to homonuclear systems, the potentials for two components in heteronuclear systems are different, which is due to the mass of two components being unequal. Considering two explicit situations of the interaction parameters, we further explore the collision dynamics of the soliton pairs with opposite velocities by synchronously controlling the interaction and potential parameters. The collision dynamics occur during and after the simultaneous evaporative cooling of two condensates. The results show that collisions are elastic and that the solitons after the collision can keep their identities. In addition, we find that the amplitudes of the soliton pairs periodically grow with time during the cooling process and, for the same initial conditions, the collision time of the soliton pair without gain is delayed compared with that with gain. We also discuss how to observe these new phenomena in future experiments.

Calculation of exchange energies using algebraic perturbation theory

An algebraic perturbation theory is presented for efficient calculations of localized states and hence of exchange energies, which are the differences between low-lying states of the valence electron of a molecule, formed by the collision of an ion ${Y}^{+}$ with an atom $X$. For the case of a homonuclear molecule these are the gerade and ungerade states and the exchange energy is an exponentially decreasing function of the internuclear distance. For such homonuclear systems the theory is used in conjunction with the Herring-Holstein technique to give accurate exchange energies for a range of intermolecular separations $R$. Since the perturbation parameter is essentially $1/R$, this method is suitable for large $R$. In particular, exchange energies are calculated for ${{X}_{2}}^{+}$ systems, where $X$ is H, Li, Na, K, Rb, or Cs.

Localization of inner-shell photoelectron emission and ICD in Ne2

With photon energies 10 eV above the K-edge the 1s photoionization of neon dimers was measured by using COLd Target Recoil Ion Momentum Spectroscopy. All decay channels resulting in the breakup Ne+ + Ne+ and Ne2+ + Ne+were identified. The latter was used to investigate the localization or delocalization of vacancies in the homonuclear diatomic system.

High-Resolution Solid-State NMR Investigation of the Phase Transition in Decamethylferrocene−Acenaphthenequinone Charge-Transfer Complex

A charge-transfer complex composed of decamethylferrocene (D) and acenaphthenequinone (A) was prepared. The material was a 1:1 neutral complex with a mixed-stack structure and exhibited a phase transition at -16 degrees C. High-resolution (13)C and (1)H NMR spectroscopy revealed that an inclination of A with respect to D occurs below the phase-transition temperature. The (1)H spin-diffusion rates of the complex undergoing high-speed magic-angle spinning (MAS) were measured to determine the shortest (1)H-(1)H distance r between D and A. To analyze the experimental results, we derived the analytical expression of the spin-diffusion rate W(z) for a homonuclear multispin system undergoing MAS. It was found that W(z) for the complex is proportional only to 1/r(6) under high-speed MAS conditions. On the basis of this relationship and the crystal structure at 20 degrees C, it was determined that the shortest (1)H-(1)H distance r at -27.7 degrees C (below the phase transition temperature) is 0.4 A shorter than that at 20 degrees C. Given this information, a plausible model of the low-temperature structure is discussed.

Simulations of ICl−(CO2)nPhotodissociation: Effects of Structure, Excited State Charge Flow, and Solvent Dynamics

Experiments on the photodissociation of ICl(-) within size-selected CO(2) clusters [Nadal, M. E.; Kleiber, P. D.; Lineberger, W. C. J. Chem. Phys. 1996, 105, 504.] differ from analogous experiments on homonuclear systems in two major ways: an early onset of caged, ICl(-)-based products with cluster size peaking at n = 5 and a rapid decline of caging after n = 5 in favor of dissociated, Cl(-)-based fragments. Using an effective Hamiltonian model for the solute electronic structure and nonadiabatic MD trajectories, we have simulated the photodissociation of these clusters and found good agreement between experimental and simulated product distributions. The strong preference of the solvent for chlorine in the initial cluster structure, along with favorable kinematics, leads to the efficient caging at small n. At all cluster sizes, the Cl(-)-based fragments are formed by an adiabatic process and are accompanied by spin-orbit excited iodine. Caging of ICl(-) also occurs on the excited state potential surface, and electronic relaxation is not observed during the 100 ps trajectories. For n > 5, the initially caged products appear to be metastable, decaying to solvent-separated Cl(-)...I pairs that subsequently dissociate, leading to the falloff in the caging fraction in the larger clusters.

Using Group Theory to Obtain Eigenvalues of Nonsymmetric Systems by Symmetry Averaging

If the Hamiltonian in the time independent Schrödinger equation, HΨ = EΨ, is invariant under a group of symmetry transformations, the theory of group representations can help obtain the eigenvalues and eigenvectors of H. A finite group that is not a symmetry group of H is nevertheless a symmetry group of an operator Hsym projected from H by the process of symmetry averaging. In this case H = Hsym + HR where HR is the nonsymmetric remainder. Depending on the nature of the remainder, the solutions for the full operator may be obtained by perturbation theory. It is shown here that when H is represented as a matrix [H] over a basis symmetry adapted to the group, the reduced matrix elements of [Hsym] are simple averages of certain elements of [H], providing a substantial enhancement in computational efficiency. A series of examples are given for the smallest molecular graphs. The first is a two vertex graph corresponding to a heteronuclear diatomic molecule. The symmetrized component then corresponds to a homonuclear system. A three vertex system is symmetry averaged in the first case to Cs and in the second case to the nonabelian C3v. These examples illustrate key aspects of the symmetry-averaging process.

Stimulating the production of deeply bound RbCs molecules with laser pulses: the role of spin–orbit coupling in forming ultracold molecules

We investigate the possibility of forming deeply bound ultracold RbCs molecules by a two-color photoassociation experiment. We compare the results with those for Rb2 in order to understand the characteristic differences between heteronuclear and homonuclear molecules. The major differences arise from the different long-range potential for excited states. Ultracold 85Rb and 133Cs atoms colliding on the X 1Σ+ potential curve are initially photoassociated to form excited RbCs molecules in the region below the Rb(5S)+Cs(6P1/2) asymptote. We explore the nature of the Ω=0+ levels in this region, which have mixed A 1Σ+ and b 3Π character. We then study the quantum dynamics of RbCs by a time-dependent wavepacket (TDWP) approach. A wavepacket is formed by exciting a few vibronic levels and is allowed to propagate on the coupled electronic potential energy curves. We calculate the time dependence of the overlap between the wavepacket and ground-state vibrational levels. For a detuning of 7.5 cm−1 from the atomic line, the wavepacket for RbCs reaches the short-range region in about 13 ps, which is significantly faster than for the homonuclear Rb2 system; this is mostly because of the absence of an R−3 long-range tail in the excited-state potential curves for heteronuclear systems. We give a simple semiclassical formula that relates the time taken to the long-range potential parameters. For RbCs, in contrast to Rb2, the excited-state wavepacket shows a substantial peak in singlet density near the inner turning point, and this produces a significant probability of de-excitation to form ground-state molecules bound by up to 1500 cm−1. The short-range peak depends strongly on non-adiabatic coupling and is reduced if the strength of the spin–orbit coupling is increased. Our analysis of the role of spin–orbit coupling concerns the character of the mixed states in general and is important for both photoassociation and stimulated Raman de-excitation.

The magnetic two-centre problem: Stability and critical bonding

Stability properties of the homonuclear diatomic one-electron system are investigated by finite-elements methods. Assuming the Born–Oppenheimer approximation and parallel magnetic fields, the computed critical charges for stability and metastability reveal a surprisingly simple dependence on the magnetic field strength B.

NMR implementation of adiabatic SAT algorithm using strongly modulated pulses

NMR implementation of adiabatic algorithms face severe problems in homonuclear spin systems since the qubit selective pulses are long and during this period, evolution under the Hamiltonian and decoherence cause errors. The decoherence destroys the answer as it causes the final state to evolve to mixed state and in homonuclear systems, evolution under the internal Hamiltonian causes phase errors preventing the initial state to converge to the solution state. The resolution of these issues is necessary before one can proceed to implement an adiabatic algorithm in a large system where homonuclear coupled spins will become a necessity. In the present work, we demonstrate that by using "strongly modulated pulses" (SMPs) for the creation of interpolating Hamiltonian, one can circumvent both the problems and successfully implement the adiabatic SAT algorithm in a homonuclear three qubit system. This work also demonstrates that the SMPs tremendously reduce the time taken for the implementation of the algorithm, can overcome problems associated with decoherence, and will be the modality in future implementation of quantum information processing by NMR.

The magnetic two-centre problem: Nuclear fusion catalyzed by ultrastrong fields?

Employing the finite-element method (FEM), accurate potential energy curves for the ground state of the homonuclear system consisting of two (static) protons and one electron within a parallel homogeneous magnetic field are computed. The shrinking of the internuclear equilibrium separation with growing magnetic field strength is investigated under quantitative and qualitative aspects. In particular, we study the problem whether this leads to significantly enhanced nuclear fusion rates in the processes d (t, n) α and p (p, e+ ν) d.

The pseudopure state in homonuclear dipolar coupling spin systems

Preparation of the pseudopure states in homonuclear systems of dipolar coupling spins is closely examined. An extremely important role of the non-diagonal part of zeroth-order coherence in the construction of the pseudopure state has been shown. Simulations of the preparation process of pseudopure states with the real molecular structures (a rectangular (1-chloro-4-nitrobenzene molecule), a chain (hydroxyapatite molecule), a ring (benzene molecule) and a double ring (cyclopentane molecule)) open the way to experimental NMR testing of the obtained results. The proposed method could be considered as a fruitful technology for quantum computation.

Solid-state NMR three-qubit homonuclear system for quantum-information processing: Control and characterization

A three-qubit 13C solid-state nuclear magnetic resonance (NMR) system for quantum information processing, based on the malonic acid molecule, is used to demonstrate high-fidelity universal quantum control via strongly-modulating radio-frequency pulses. This control is achieved in the strong-coupling regime, in which the timescales of selective qubit addressing and of two-qubit interactions are comparable.

Quantifying Aromaticity at the Molecular and Supramolecular Limits: Comparing Homonuclear, Heteronuclear, and H-Bonded Systems.

The aromatic/antiaromatic characteristics of B-N and P-N analogues of benzene and cyclobutadiene have been studied using quantum chemical methods. We use established parameters such as nucleus-independent chemical shifts, charge density at the ring critical point, and stabilization energies to quantify the nature of interactions in these molecular systems. B3N3H6 and N3P3F6 resemble benzene in being aromatic, albeit to a lesser extent, while B2N2H4 and N2P2F4 are found to be aromatic, opposite to that for cyclobutadiene. A σ-π separation analysis has been performed to critically examine the contributions from the π electrons compared to that from the σ backbone. The structural aspects in the weak interaction limits such as the H-bonded cyclic trimers of HX (X = F, Cl, and Br) have also been investigated. Even in such weak interaction limits, these cyclic systems are found to be substantially stable. These H-bonded systems exhibit nonlocal polarizations across the full-perimeter of the ring that lead to aromaticity. We propose the term "H-bonded aromaticity" for such closed-loop weakly delocalized systems. This new formalism of aromaticity has the potential to explain structures and properties in supramolecular systems.

Theoretical Group 14 Chemistry. 4. Cyclotriplumbanes: Relativistic and Substituents Effects.

We report a study on the first newly synthesized homonuclear lead ring system, the cyclotriplumbane Pb3R6. Its geometrical features can be best reproduced using perturbation theory (MP2) together with the Stuttgart-Dresden basis set and ECP for lead. The experimentally observed tilting of the groups R in the cyclotriplumbanes is attributed to the bonding situation: the lead-lead contacts, formed from weak interactions of plumbylene lone pairs with empty p orbitals of neighboring lead atoms, try to maximize overlap. Surprisingly and in contrast to the inert pair effect, hybridization of the former plumbylene lone pair orbitals in the cyclotriplumbane Pb3R6 is observed, depending on the substituent. Hybrid orbitals with a 6s orbital contribution of only about 40% are found. Hydrogen atoms and methyl groups promote this effect, while for phenyl substitution the expected 6s lone pair orbital is identified as the bond-forming orbital.

Energy bounds for isoelectronic molecular sets and the implicated order

By representing molecules as vectors whose components are their nuclear charges, a theorem that allows to order Born-Oppenheimer energies of sets of isoprotonic-isoelectronic molecules is stated. Upper and lower bounds for these sets are derived, along with other general energy inequalities involving homonuclear systems and molecules with common molecular fragments. These inequalities imply that the sets of molecules under consideration are endowed with the structure of a partially ordered set (POSET). Some properties related to this structure are discussed.

Ultracold Collisions Involving Heteronuclear Alkali Metal Dimers

We carry out the first quantum dynamics calculations on ultracold atom-diatom collisions in isotopic mixtures. The systems studied are spin-polarized 7Li + 6Li7Li, 7Li + 6Li2, 6Li + 6Li7Li, and 6Li + 7Li2. Reactive scattering can occur for the first two systems even when the molecules are in their ground rovibrational states, but is slower than vibrational relaxation in homonuclear systems. Implications for sympathetic cooling of heteronuclear molecules are discussed.