Tunneling Splitting Research Articles

A quantum many body model for the embedded electron spin decoherence in organic solids.

We present a generalized nuclear spin bath model for embedded electron spin decoherence in organic solids at low temperatures, which takes the crucial influence from hindered methyl group rotation tunneling into account. This new, quantum many body model, after resolved using the cluster correlation expansion method, predicts the decoherence profiles directly from the proton relative position and methyl group tunneling splitting inputs. Decoherence profiles from this model explain adequately the influence from both strongly and weakly hindered methyl groups to embedded electron spin decoherence: The former accelerates decoherence by increasing the nearest neighbor nuclear spin coupling, while the latter enhances coherence through a novel confinement like' mechanism, in which the very strong nuclear spin coupling from the tunneling splitting term suppresses those protons on the methyl rotors from participating in the bath dynamics. Both types of influences are successfully proven experimentally in representative organic polycrystalline matrices: methyl malonic acid for strongly hindered and acetamide for weakly hindered methyl groups, respectively.

Double Proton Transfer in the Dimer of Formic Acid: An Efficient Quantum Mechanical Scheme.

Double proton transfer plays an important role in biology and chemistry, such as with DNA base pairs, proteins and molecular clusters, and direct information about these processes can be obtained from tunneling splittings. Carboxylic acid dimers are prototypes for multiple proton transfer, of which the formic acid dimer is the simplest one. Here, we present efficient quantum dynamics calculations of ground-state and fundamental excitation tunneling splittings in the formic acid dimer and its deuterium isotopologues. These are achieved with a multidimensional scheme developed by us, in which the saddle-point normal coordinates are chosen, the basis functions are customized for the proton transfer process, and the preconditioned inexact spectral transform method is used to solve the resultant eigenvalue problem. Our computational results are in excellent agreement with the most recent experiments (Zhang et al., 2017; Li et al., 2019).

Full-dimensional (12D) variational vibrational states of CH4·F-: Interplay of anharmonicity and tunneling.

The complex of a methane molecule and a fluoride anion represents a 12-dimensional (12D), four-well vibrational problem with multiple large-amplitude motions, which has challenged the quantum dynamics community for years. The present work reports vibrational band origins and tunneling splittings obtained in a full-dimensional variational vibrational computation using the GENIUSH program and the Smolyak quadrature scheme. The converged 12D vibrational band origins and tunneling splittings confirm complementary aspects of the earlier full- and reduced-dimensionality studies: (1) the tunneling splittings are smaller than 0.02 cm-1; (2) a single-well treatment is not sufficient (except perhaps the zero-point vibration) due to a significant anharmonicity over the wells; and thus, (3) a full-dimensional treatment appears to be necessary. The present computations extend to a higher energy range than earlier work, show that the tunneling splittings increase upon vibrational excitation of the complex, and indicate non-negligible "heavy-atom" tunneling.

Low torsional barrier challenges in the microwave spectrum of 2,4-dimethylanisole.

Low barriers to internal rotations are especially challenging for both the experimental and theoretical determinations because they result in large tunneling splittings which are hard to assign and in potential functions that can be difficult to model. In the present work, the internal rotations of two methyl groups of 2,4-dimethylanisole were analyzed and modeled using a newly developed computer code, called ntop, adapted for fitting the high-resolution torsion-rotation spectra of molecules with two or more methyl rotors. The spectrum was measured using a pulsed molecular jet Fourier transform microwave spectrometer operating in the frequency range of 2.0-26.5 GHz, revealing internal rotation tunneling quintets with splittings of up to several gigahertz. The V3 potential barriers are 441.139(23) cm-1 and 47.649(30) cm-1 for the o- and p-methyl groups, respectively. Quantum chemical calculations predicted only one conformer with the methoxy group in the anti position related to the neighboring o-methyl group. While the results from geometry optimizations were reliable, ab initio calculations at the MP2 level did not reproduce the low torsional barriers, calling for further experiments on related systems and additional theoretical models.

Rotational Spectrum, Tunneling Motions, and Intramolecular Potential Barriers in Benzyl Mercaptan.

The rotational spectrum of benzyl mercaptan (parent and four isotopologues) has been assigned in a supersonic jet expansion using chirped-pulse Fourier transform microwave spectroscopy. The spectrum is characterized by torsional tunneling doublings, strongly perturbed by Coriolis interactions. The experimental rotational constants reveal that the sulfur atom is located above the ring plane in a gauche conformation. The torsion dihedral θ0 = φ (SCα-C1C2) is approximately 74°, according to a flexible molecular model calculation reproducing the energy separation (ΔE01 ∼ 2180.4 MHz) between the first two torsional substates. The global minimum configuration is 4-fold degenerate, corresponding to potential minima with θ0 ≈ ±74° and ±(180-74)°. The four equivalent minima are separated by potential barriers at θ = ±90°, 0°, or 180°. The tunneling splittings are caused by the potential barrier at θ = ± 90°, while the barriers at torsions of 0° or 180° are too large to generate detectable splittings. The tunnelling barrier has been determined as 248 cm-1, similar to the value obtained with high-level MP2 ab initio calculations (259 cm-1), but smaller than in benzyl alcohol (280 cm-1).

Observation of the Low‐Frequency Spectrum of the Water Dimer as a Sensitive Test of the Water Dimer Potential and Dipole Moment Surfaces

AbstractUsing the helium nanodroplet isolation setup at the ultrabright free‐electron laser source FELIX in Nijmegen (BoHeNDI@FELIX), the intermolecular modes of water dimer in the frequency region from 70 to 550 cm−1 were recorded. Observed bands were assigned to donor torsion, acceptor wag, acceptor twist, intermolecular stretch, donor torsion overtone, and in‐plane and out‐of‐plane librational modes. This experimental data set provides a sensitive test for state‐of‐the‐art water potentials and dipole moment surfaces. Theoretical calculations of the IR spectrum are presented using high‐level quantum and approximate quasiclassical molecular dynamics approaches. These calculations use the full‐dimensional ab initio WHHB potential and dipole moment surfaces. Based on the experimental data, a considerable increase of the acceptor switch and a bifurcation tunneling splitting in the librational mode is deduced, which is a consequence of the effective decrease in the tunneling barrier.

Observation of the Low-Frequency Spectrum of the Water Dimer as a Sensitive Test of the Water Dimer Potential and Dipole Moment Surfaces.

Using the helium nanodroplet isolation setup at the ultrabright free‐electron laser source FELIX in Nijmegen (BoHeNDI@FELIX), the intermolecular modes of water dimer in the frequency region from 70 to 550 cm−1 were recorded. Observed bands were assigned to donor torsion, acceptor wag, acceptor twist, intermolecular stretch, donor torsion overtone, and in‐plane and out‐of‐plane librational modes. This experimental data set provides a sensitive test for state‐of‐the‐art water potentials and dipole moment surfaces. Theoretical calculations of the IR spectrum are presented using high‐level quantum and approximate quasiclassical molecular dynamics approaches. These calculations use the full‐dimensional ab initio WHHB potential and dipole moment surfaces. Based on the experimental data, a considerable increase of the acceptor switch and a bifurcation tunneling splitting in the librational mode is deduced, which is a consequence of the effective decrease in the tunneling barrier.

Fourier-transform microwave spectroscopy on weakly bound complexes of CH2OO with Ar, CO, and N2

Pure rotational transitions of weakly bound complexes of the simplest Criegee intermediate CH2OO with Ar, CO, and N2 are observed by Fourier-transform microwave (FTMW) and FTMW-MW double-resonance spectroscopy. Many of the observed lines show doublet peaks associated with the tunneling splitting between the two equivalent configurations of the complexes. The intermolecular distances of the complexes are derived from the precise rotational constants determined in this study. The separations between two components of the doublet peaks observed for c-type transitions of CH2OO–Ar are satisfactorily demonstrated by a one-dimensional hindered rotor model for the internal rotation of the CH2OO monomer.

Multireference Ab Initio Studies of Magnetic Properties of Terbium-Based Single-Molecule Magnets.

We investigate how different chemical environments influence magnetic properties of terbium(III) (Tb)-based single-molecule magnets (SMMs), using first-principles relativistic multireference methods. Recent experiments showed that Tb-based SMMs can have exceptionally large magnetic anisotropy and that they can be used for experimental realization of quantum information applications, with a judicious choice of chemical environment. Here, we perform complete active space self-consistent field calculations including relativistic spin-orbit interaction for representative Tb-based SMMs such as TbPc2 and TbPcNc in three charge states. We calculate the low-energy electronic structure from which we compute the Tb crystal-field (CF) parameters and construct an effective pseudospin Hamiltonian. Our calculations show that the ligand type and fine points of molecular geometry do not affect the gap between the ground-state and first-excited doublets, whereas the latter varies weakly with oxidation number. On the other hand, higher-energy levels have a strong dependence on all these characteristics. For neutral TbPc2 and TbPcNc molecules, the Tb magnetic moment and ligand spin are parallel to each other and the coupling strength between them does not depend much on the ligand type and details of the atomic structure. However, ligand distortion and molecular symmetry play a crucial role in transverse CF parameters which lead to tunnel splitting. The tunnel splitting induces quantum tunneling of magnetization by itself or by combining with other processes. Our results provide insights into the mechanisms of magnetization relaxation in the representative Tb-based SMMs.

Weakly bound molecular dimers: Intramolecular vibrational fundamentals, overtones, and tunneling splittings from full-dimensional quantum calculations using compact contracted bases of intramolecular and low-energy rigid-monomer intermolecular eigenstates.

We present a method for the efficient calculation of intramolecular vibrational frequencies, and their tunneling splittings, in weakly bound molecular dimers, together with the intermolecular vibrational states within each intramolecular vibrational manifold. The approach involves the partitioning of the dimer's vibrational Hamiltonian into two reduced-dimension Hamiltonians, a rigid-monomer one for the intermolecular vibrations and the other for all intramolecular vibrational degrees of freedom, and a remainder. The eigenstates of the two reduced-dimension Hamiltonians are used to build up a product contracted basis for the diagonalization of the full vibrational Hamiltonian. The key idea is that because of weak coupling between inter- and intra-molecular vibrational modes, the full-dimensional eigenstates in the low-energy portions of the manifolds associated with the intramolecular vibrational excitations can be computed accurately in a compact basis that includes a relatively small number of rigid-monomer intermolecular eigenstates, spanning a range of energies much below those of the intramolecular vibrational states of interest. In the application to the six-dimensional (6D) problem of (HF)2, we show that this approach produces results in excellent agreement with those in the literature, with a fraction of the basis states required by other methods. In fact, accurate energies of the intramolecular vibrational fundamentals and overtones are obtained using 6D bases that include 4D rigid-monomer intermolecular vibrational eigenstates extending to only 500-1000 cm-1, far below the HF-stretch fundamental of about 4000 cm-1. The method thus holds particular promise with respect to calculations on complexes with greater numbers of vibrational degrees of freedom.

Topological quantum oscillation of magnetization in the Josephson φ0 junction

Abstract We show that the ground state tunnel splitting of the magnetization can be topologically quenched in a nanomagnetic Josephson φ 0 junction. Due to the relative strength of the spin-orbit interaction the tunnel splitting is found to oscillate with the bias current applied to the junction as well as the magnetic field along the hard axis. Spin-coherent-state path integrals are used to obtain an analytic expression for the tunnel splitting controlled by topological interference of two tunnel paths of opposite windings and the condition in which the tunnel splitting is frozen. This feature is expected to be observable in existing experimental technique.

Theoretical studies of infrared spectra for the N2-N2O complex: The tunneling effects of fundamental and combination bands.

This study is a continuation of our previously published research for the N2-N2O complex [Journal of Chemical Physics 143 (2015) 154304], and focuses on predicting the quantum tunneling effects of infrared fundamental and combination bands. A new four-dimensional intermolecular potential energy surface (PES) was constructed for the vibrational excited state upon the N2O ν1 excitation at the same calculated level with the previous PES of ground state. Compared with the ground state, two equivalent T-shaped global minima are found to be slightly different in both structural parameters and binding energies. Based on the PESs of ground and vibrational excited states, the vibrational shift of infrared spectrum for the fundamental band in the N2O ν1 region is determined to be a blue shift of 1.29 cm-1 for 14N2-N2O, which is in qualitative agreement with the experimentally observed value of 2.233 cm-1 [Journal of Chemical Physics 140 (2014) 044332]. Furthermore, for the fundamental and disrotation bands, the calculated tunneling splitting is almost the same for the ground and vibrational excited states, so the tunneling effects cannot be observed for these bands using the infrared spectroscopic technique. Nevertheless for the infrared combination bands, our calculated results suggest that the tunneling effects for the torsion and twice disrotation bands are significantly larger, and the predicted infrared spectra display obvious differences for the different sub-states. If the sensitivity of infrared spectrometer is high enough, it is interesting to investigate the quantum tunneling effects experimentally.

Decoherence measurements in crystals of molecular magnets

Decoherence processes in crystals of molecular magnets are prototypical for interacting electronic spin systems. We analyze the Landau-Zener dynamics of the archetypical TbPc$_2$ complex diluted in a diamagnetic monocrystal. The dependence of the tunneling probability on the field sweep rate is evaluated in the framework of the recently proposed master equation in which the decoherence processes are described through a phenomenological Lindblad operator. Thus, we showcase low temperature magnetic measurements that complement resonant techniques in determining small tunnel splittings and dephasing times.

Spectra of the D2O dimer in the O-D fundamental stretch region: Vibrational dependence of tunneling splittings and lifetimes.

The fundamental O-D stretch region (2600-2800 cm-1) of the fully deuterated water dimer (D2O)2 is studied using a pulsed supersonic slit jet source and a tunable optical parametric oscillator source. Relatively high spectral resolution (0.002 cm-1) enables all six dimer tunneling components to be observed, in most cases, for the acceptor asymmetric O-D stretch, the donor free O-D stretch, and the donor bound O-D stretch vibrations. The dominant acceptor switching tunneling splittings are observed to decrease moderately in the excited O-D stretch states, to roughly 75% of their ground state values, whereas the smaller donor-acceptor interchange splittings show more dramatic and irregular decreases. Excited state predissociation lifetimes, as determined from the observed line broadening, show large variations (0.2 ≤ τ ≤ 5 ns) depending on the vibrational state, K-value, and tunneling symmetry. Another very weak band is tentatively assigned to a combination mode involving an intramolecular O-D stretch plus an intermolecular twist overtone. Asymmetric O-D stretch bands of the mixed isotopologue dimers D2O-DOH and D2O-HOD are also observed and analyzed.

A periodic Numerov approach applied to the torsional tunneling splitting in hydrogen peroxide, aliphatic alcohols and phenol

Abstract The adapted Numerov approach was extended to periodic problems and applied to the torsional tunneling splitting of six increasingly complex target systems carrying a hydroxy-group. The deviations from experiment remained on the order of 1 cm−1, except for phenol in which the exceptionally small ground-state tunneling-splitting of 0.0017 cm−1 was found in very good agreement with the experimental value of 0.0019 cm−1. Overall, the accuracy of the periodic Numerov approach for the treatment of torsional tunneling is on the same order as alternative approaches, but at a substantially reduced computational demand due to the restriction of the problem to the respective degree of freedom.

Fracturing evolution analysis of Beishan granite under true triaxial compression based on acoustic emission and strain energy

The study of rock fracturing is a fundamental research topic in rock mechanics and engineering. In this paper, based on complete stress–strain curves obtained under TTC and the corresponding AE and strain energy results, the mechanical properties and fracturing process of Beishan granite are studied. A representative test result (σ2 = 75 MPa, σ3 = 20 MPa) is selected to analyse and illustrate the three-dimensional fracturing process of the Beishan granite. The results show that the variations in the characteristics of the brittle fracture behaviour, AE and strain energy of Beishan granite change with σ2 or σ3 following certain relationships, and the mechanisms driving these various relationships are very different. The AE and strain energy characteristics of Beishan granite are also quite different among the five fracturing evolution stages. The variations in the increments of AE count, AE event and total elastic strain energy per unit time (ΔSc/Δt, ΔSe/Δt and ΔUe/Δt) are studied at different times and under different stresses during rock failure. The rock fracturing evolution can be illustrated through the variation in these parameters, providing deep insight. This research provides a perspective for studying deep underground fracture-forming processes, such as earthquakes, tunnel sudden failure, spalling, splitting and rockburst.

The role of the quadrupolar interaction in the tunneling dynamics of lanthanide molecular magnets

Quantum tunneling dominates the low temperature magnetization dynamics in molecular magnets and presents features that are strongly system dependent. The current discussion is focused on the terbium(III) bis(phtalocyanine) ([TbPc2]−1) complex that should serve as a prototypical case for lanthanide molecular magnets. We analyze numerically the effect of non-axial interactions on the magnitude of the intrinsic tunnel splitting and show that usual suspects like the transverse ligand field and Zeeman interaction fail to explain the experimentally observed dynamics. We then propose through the nuclear quadrupolar interaction a viable mechanism that mixes, otherwise almost degenerate hyperfine states.

Computing vibration-rotation-tunnelling levels of HOD dimer.

Using an accurate 6D water dimer potential energy surface, we compute vibration-rotation-tunnelling levels of HOD dimer, by assuming that the two monomers are rigid. HOD dimer has two isomers, a D-bonded isomer and an H-bonded isomer, and the wavefunctions of both isomers have amplitude in four wells. HOD dimer is important because, unlike the case of H2O dimer or D2O dimer, it is possible to measure the largest tunnelling splitting. Results for HOD dimer, therefore facilitate the testing of H2O dimer potentials. In J. Chem. Phys., 1995, 102, 1114, experimental results were interpreted in terms of 1D models. Experimental splittings of both isomers, obtained by fitting an energy level equation to spectra, are in good agreement with those we compute.

Single molecule magnet behaviors of Zn4Ln2 (Ln = DyIII, TbIII) complexes with multidentate organic ligands formed by absorption of CO2 in air through in situ reactions.

In this work, we report the syntheses, crystal structures and magnetic properties of three novel Zn-Ln mixed metal complexes, namely [Zn4Dy2(L1)2(L2)2(N3)2]Cl2·2H2O (1), [Zn4Tb2(L1)2(L2)2(Cl)2][ZnN3Cl3]·2H2O (2), and [Zn4Gd2(L1)2(L2)2(Cl)2][ZnN3Cl3]·2H2O (3), in which L12- and L23- were formed from the ligand L [L = N1,N3-bis(3-methoxysalicylidene)diethylenetriamine] through in situ reactions. Interestingly, carbon dioxide in air was absorbed in the process of forming carbamate ligand L23-; this can be ascribed to the insertion of CO2 into M-N amide bonds. Moreover, 1 and 2 represent the first series of 3d-4f SMMs containing carbamate ligands by fixation of CO2 in air. Single-crystal X-ray diffraction analyses reveal that the crystal structures of 1 and 2 are anion-dependent, i.e., the apical positions of the two ZnII ions in 1 and 2 are occupied by an N atom of N3- and by Cl-, respectively. However, the topologies of 2 and 3 are similar. Two ZnII ions and one LnIII (Ln = Dy (1), Tb (2) and Gd (3)) form nearly linear trinuclear [Zn2Ln] units which are double-bridged by two L23- ligands. Magnetic studies reveal that two complexes show single molecule magnet behavior under a direct current (dc) field, with effective energy barriers (Ueff) of 30.66(5) K for 1 and 8.87(3) K for 2. Ab initio calculations reveal that the DyIII ions in 1 and the TbIII ions in 2 are axial in nature; however, a difference in the tunnel splitting of 1 and 2 leads to variation in the magnetization blockades of the two complexes. Theoretical calculations also indicate that the directions of the main magnetic axes severely deviate from the coordination atoms of the first spheres of DyIII and TbIII in 1 and 2; thus further results in poor SMM behavior of the two complexes.

The complete conformational panorama of formanilide-water complexes: the role of water as a conformational switch.

The microsolvated complexes of formanilide, generated in a supersonic expansion, have been observed by Fourier transform microwave spectroscopy. Three 1 : 1 and one 1 : 2 formanilide-water adducts have been observed and their structures characterized by the measurement of isotopologue rotational spectra. In one of the monohydrated complexes and in the dihydrated complex, formanilide adopts a cis-configuration. In these species water closes sequential cycles with the cis amino and carbonyl groups through a network of N-HO and O-HO hydrogen bonds. Furthermore, in these complexes cis-formanilide has almost the same non planar configuration observed in the monomer. In the two monohydrated complexes detected with trans-formanilide, a planar skeleton is detected with water interacting solely with either the amino (N-H··O bond) or the carbonyl group (O-HO[double bond, length as m-dash]C bond). The observed tunnelling splittings show a rich intermolecular dynamics in those complexes. The results seem to indicate that complexation with water switches the configuration of formanilide from trans, which is more stable for the bare monomer, to cis, which is more stable for the hydrated complexes.