Tunneling Splitting Research Articles

Theoretical and Experimental Study of Weakly Bound CO2–(pH2)2 Trimers

The infrared spectrum of CO(2)-(pH(2))(2) trimers is predicted by performing exact basis-set calculations on a global potential energy surface defined as the sum of accurately known two-body pH(2)-CO(2) (J. Chem. Phys. 2010, 132, 214309) and pH(2)-pH(2) potentials (J. Chem. Phys. 2008, 129, 094304). These results are compared with new spectroscopic measurements for this species, for which 13 transitions are now assigned. A reduced-dimension treatment of the pH(2) rotation has been employed by applying the hindered-rotor averaging technique of Li, Roy, and Le Roy (J. Chem. Phys. 2010, 133, 104305). Three-body effects and the quality of the potential are discussed. A new technique for displaying the three-dimensional pH(2) density in the body-fixed frame is used, and shows that in the ground state the two pH(2) molecules are localized much more closely together than is the case for the two He atoms in the analogous CO(2)-(He)(2) species. A clear tunneling splitting is evident for the torsional motion of the two pH(2) molecules on a ring about the CO(2) molecular axis, in contrast to the case of CO(2)-(He)(2) where a more regular progression of vibrational levels reflects the much lower torsional barrier.

Application of nuclear permutation inversion group theory to the benzenium ion

Nuclear permutation-inversion (PI) group theory and the linear combination of localized wavefunctions (LCLW) method are applied to the proton “ring-walk” tunneling problem in C 6D 6H + and the benzenium ion ( C 6 H 7 + ) . For C 6D 6H + and C 6 H 7 + , the rigid and non-rigid MS groups are developed, and their corresponding correlation tables constructed. The reverse correlation relationship is combined with spin statistical restrictions to determine the number of allowed tunneling split levels for both ions. Through the use of the LCLW method and the WKB approximation, the qualitative pattern of the tunneling splitting is presented for C 6D 6H +. Application of the LCLW problem for the benzenium ion is presented, but the complete treatment to obtain the structure of the tunneling split levels is limited by the computational expense of obtaining the eigenvectors from the diagonalization of the 15 120 × 15 120 connectivity matrix.

The rotational spectra of the fluorobenzene⋯water and p-difluorobenzene⋯water dimers: Structure and internal dynamics

The rotational spectra of the weakly hydrogen-bonded complexes of fluorobenzene and p-difluorobenzene with water were measured in the frequency range from 3 to 15 GHz using pulsed molecular jet Fourier transform microwave spectrometers in Kiel and in Edmonton. Spectroscopic constants were derived from the spectra of several isotopologues of fluorobenzene⋯water, i.e. those containing H 2 16O, H 2 18O, HDO, and D 2O, and of p-difluorobenzene⋯water with H 2 16O, H 2 17O, H 2 18O, and D 2O. The structural parameters derived from the determined rotational constants correspond to planar (or nearly planar) structures of the complexes. The internal dynamics of the complexes are discussed with regard to the observed tunneling splittings of the rotational lines, which are a result of the hindered internal rotation of the water subunit.

Assigning Predissociation Infrared Spectra of Microsolvated Hydronium Cations H3O+⋅(H2)n (n=0, 1, 2, 3) by Ab Initio Molecular Dynamics

Messenger predissociation spectroscopy is an important experimental method to obtain vibrational spectra of molecular ions or complexes such as protonated water clusters H(+)⋅(H(2)O)(n) in the gas phase. However, the molecular properties and thus the linear infrared spectra may be modified upon microsolvation with typical messengers such as H(2) molecules or noble gas atoms. Employing ab initio molecular dynamics for the H(2)-microsolvated hydronium ion, we investigate these effects explicitly as a function of an increasing number of messengers up to filling the first microsolvation shell, that is, for H(3)O(+)⋅(H(2))(n) (n=0, 1, 2, 3). We find that microsolvation with H(2) lowers the inversion barrier of the hydronium core, which governs the inversion tunnel splitting due to umbrella motion, and thus accelerates the inversion dynamics. By comparison to experiment a comprehensive band assignment for the O-H stretching region is given, and thereby the observed blueshift of stretching bands with increasing n is explained. Furthermore, detailed analyses reveal intricate intra- and intermolecular anharmonic mode couplings induced by the messengers, which yield a rich vibrational dynamics in these, at first glance, simple systems. Finally, the virtues but also the shortcomings of the ab initio molecular dynamics approach to vibrational spectroscopy are discussed.

How Trifluoroacetone Interacts with Water

The rotational spectra of five isotopologues of the molecular adduct 1,1,1-trifluoroacetone-water have been assigned using pulsed-jet Fourier-transform microwave spectroscopy. All rotational transitions appear as doublets, due to the internal rotation of the methyl group. Analysis of the tunneling splittings allows one to determine accurately the height of the 3-fold barrier to internal rotation of the methyl group and its orientation, leading to V(3) = 3.29 kJ·mol(-1) and ∠(a,i) = 67.5°, respectively. The water molecule is linked to the keton molecule on the side of the methyl group through a O-H···O hydrogen bond and a C-H···O intermolecular contact, lying in the effective plane of symmetry of the complex.

Renormalization of the tunnel splitting in a rotating nanomagnet

We study spin tunneling in a magnetic nanoparticle with biaxial anisotropy that is free to rotate about its anisotropy axis. Exact instanton of the coupled equations of motion is found that connects degenerate classical energy minima. We show that mechanical freedom of the particle renormalizes magnetic anisotropy and increases the tunnel splitting.

Ro-torsional energy correlation between the high barrier and free-internal-rotor limits: The case of the skew chain molecule HSOH

Skew-chain molecules, such as HSOH, exhibit exotic behavior due to coupling of torsion and rotation. In particular, the torsional tunneling splittings vary cyclically in magnitude with axial rotational quantum number, K, with a period depending on the ratio of the moments of inertia for their end moieties. Although successfully modeled using a variety of approaches (algebraic, reduced-dimensional, and full-dimensional) a conceptual understanding of this cyclic variation for HSOH has not been presented. We do this here, using the reduced-dimension Generalized Semi-Rigid Bender (GSRB) approach to establish the correlation between states at the free-rotor (zero-barrier) limit and those at the more physical high-barrier limit. In this context we present the symmetries and appropriate quantum numbers for the states in these two limiting cases. We show that the cyclic variation of the magnitude of the torsional splittings originates in the energy level-structure in the zero-barrier limit combined with the correlation to the high-barrier limit. This allows us to give a simple recipe for calculating the period of this cyclic variation in any such skew-chain molecule, based only on the moments of inertia of the two end moieties.

Ring-polymer instanton method for calculating tunneling splittings

The semiclassical instanton expression for the tunneling splitting between two symmetric wells is rederived, starting from the ring-polymer representation of the quantum partition function. This leads to simpler mathematics by replacing functional determinants with matrix determinants. By exploiting the simple Hückel-like structure of the matrices, we derive an expression for the instanton tunneling splitting in terms of a minimum on the potential surface of a linear polymer. The latter is a section cut out of a ring polymer, consisting of an infinite number of beads, which describes a periodic orbit on the inverted potential surface. The approach is straightforward to generalize to multiple dimensions, and we demonstrate that it is computationally practical by carrying out instanton calculations of tunneling splittings in HO(2) and malonaldehyde in full dimensionality.

A heuristic model of damped quantum rotation effects in nuclear magnetic resonance spectra

The damped quantum rotation (DQR) theory describes temperature effects in NMR spectra of hindered molecular rotators composed of identical atoms arranged in regular N-gons. In the standard approach, the relevant coherent dynamics are described quantum mechanically and the stochastic, thermally activated motions classically. The DQR theory is consistent. In place of random jumps over one, two, etc., maxima of the hindering potential, here one has damping processes of certain long-lived coherences between spin-space correlated eigenstates of the rotator. The damping-rate constants outnumber the classical jump-rate constants. The jump picture is recovered when the former cluster appropriately around only as many values as the number of the latter. The DQR theory was confirmed experimentally for hindered methyl groups in solids and even in liquids above 170 K. In this paper it is shown that for three-, four-, and sixfold rotators, the Liouville space equations of NMR line shapes, derived previously with the use of the quantum mechanical reduced density matrix approach, can be be given a heuristic justification. It is based on an equation of motion for the effective spin density matrix, where the relevant spin hamiltonian contains randomly fluctuating terms. The occurrence of the latter can be rationalized in terms of fluctuations of the tunneling splittings between the torsional sublevels of the rotator, including momentary liftings of the Kramers degeneracies. The question whether such degeneracy liftings are physical or virtual is discussed. The random terms in the effective hamiltonian can be Monte Carlo modeled as piecewise constant in time, which affords the stochastic equation of motion to be solved numerically in the Hilbert spin space. For sixfold rotators, this way of calculating the spectra can be useful in the instances where the Liouville space formalism of the original DQR theory is numerically unstable.

Structural and magnetic studies of original tetranuclear CoII–LnIII complexes (LnIII = Gd, Tb, Y)

The syntheses, structural determinations and magnetic studies of tetranuclear Co(II)-Ln(III) complexes (Ln = Y, Gd, Tb) involving orthovanillin as main ligand are described. The structural studies demonstrate that centrosymmetric tetranuclear Co(2)-Ln(2) complex molecules with a defect-dicubane central core are obtained, with hexacoordinate Co ions in deformed octahedral environments and nine-coordinate lanthanide ions. The Co ions are linked by two hydroxo bridges and each Co ion is also involved in a double phenoxo-hydroxo bridge with the two Ln ions, so that each hydroxo group is triply linked to the two Co and one Gd ions. The four metal ions are coplanar. A ferromagnetic Co-Ln interaction operates in the Co(2)-Ln(2) complexes (Ln = Gd, Tb), along with a D zero-field splitting term for the cobalt ion and a weak ferromagnetic Co-Co interaction. The SMM behaviour of the Co(2)-Gd(2) complex is confirmed by observation of hysteresis loops, as a consequence of the slowing down of relaxation for this tetranuclear complex. The Co(2)-Tb(2) complex does not behave as a SMM, what could result from a subtractive combination of the Tb and Co anisotropies and an increased transverse anisotropy, leading to large tunnel splittings and quantum tunneling of magnetization.

Thermal Conductivity of Glasses Induced by Nuclear Quadrupole Interaction at Ultra Low Temperatures

It is investigated how nuclear degrees of freedom of tunneling system (TS) inherent in amorphous solids influence its acoustic properties. It was shown in our previous papers that below 10 mK nuclear quadrupole interaction breaks down the coherent tunneling. This phenomenon results in appearance of the quasi-gap in the distribution function for the tunneling amplitude splitting. The quasi-gap is responsible for the plateau in the temperature dependence of the real part of a dielectric permittivity or speed of sound. In this paper we are interested in ultrasonic absorption and thermal conductivity which are intimately connected. We demonstrate that there exists a temperature interval in a millikelvin region where the sound absorption behavior changes drastically from the behavior predicted by the standard tunneling model (STM). In particular, the sound absorption increases approximately by an order of magnitude. Since in the millikelvin region the heat transport is due to acoustic phonons, the thermal conductivity also should demonstrate a strong increase as compared to standard tunneling model. The application of a strong magnetic field is known to restore the coherent tunneling and the standard distribution for the tunneling splitting amplitude. Thus, one can expect that in a strong magnetic field the thermal conductivity should drop in the temperature interval where the coherent tunneling was initially destroyed.

Millimeter-wave spectroscopy of H2CCD: Tunneling splitting and ortho-para mixing interaction

The H(2)C=CD isotopic species of vinyl radical produced in a supersonic jet expansion by ultraviolet laser photolysis was studied by millimeter-wave spectroscopy. Due to the tunneling motion of the α deuteron, the ground state is split into two components, 0(+) and 0(-). Tunneling-rotation transitions connecting the lower (0(+)) and upper (0(-)) components of the tunneling doublet were observed in the frequency region of 184-334 GHz, including three R- and two Q-branch transitions. Three and two pure rotational transitions in the K(a)=0 and 1 stacks, respectively, were also observed for each of the 0(+) and 0(-) states in the frequency region of 52-159 GHz. Least-squares analysis of the observed frequencies for the tunneling-rotation and pure rotational transitions with well resolved hyperfine structures yielded a set of precise molecular constants, among which the tunneling splitting in the ground state was determined to be ΔE(0)=1187.234(17) MHz, which is 1/14 that for H(2)C=CH. The potential barrier height derived from the observed tunneling splitting by an analysis of the tunneling dynamics using a one-dimensional model is 1545 cm(-1), consistent with the value 1568 cm(-1) obtained for the normal vinyl. The observed spectrum was found to be perturbed by a hyperfine interaction connecting ortho and para levels. The constant for the interaction, which we call the ortho-para mixing Fermi contact interaction, has been determined to be δa(F) ((β))=68.06(53) MHz. This is believed to be the first definite detection of such an interaction. By this interaction the ortho and para states of H(2)C=CD are mixed up to about 0.1%. The constant is more than 1000 times larger than spin-rotation interaction constants that cause ortho-para mixing in closed shell molecules and suggests extremely rapid conversion between the ortho and para nuclear spin isomers of H(2)C=CD.

High resolution electronic spectroscopy of 9-fluorenemethanol in the gas phase: New insights into the properties of Π-hydrogen bonds

Rotationally resolved S(1)←S(0) fluorescence excitation spectra of 9-fluorenemethanol (9FM) and deuterated 9-fluorenemethanol (9FMD) have been observed and assigned. Two conformers were detected; sym-9FM and unsym-9FM. The sym conformer has the -OH group symmetrically placed above the fluorene short axis, with its hydrogen atom pointing towards the top of an aromatic ring, whereas the unsym conformer has the -OH group tilted away from this axis, with its hydrogen atom pointing towards the side of an aromatic ring. Only the sym conformer shows a tunneling splitting associated with the torsional motion of the -OH group; the unsym conformer is "rigid." Additionally, a third subband was observed in the spectrum of sym-9FMD, evidencing secondary minima on the potential energy surfaces of the ground and excited electronic states. Studies of these surfaces along the -OH torsional coordinate provide new insights into the properties of π-hydrogen bonds.

Communication: Prediction of the rate constant of bimolecular hydrogen exchange in the water dimer using an ab initio potential energy surface

We report the properties of two novel transition states of the bimolecular hydrogen exchange reaction in the water dimer, based on an ab initio water dimer potential [A. Shank et al., J. Chem. Phys. 130, 144314 (2009)]. The realism of the two transition states is assessed by comparing structures, energies, and harmonic frequencies obtained from the potential energy surface and new high-level ab initio calculations. The rate constant for the exchange is obtained using conventional transition state theory with a tunneling correction. We employ a one-dimensional approach for the tunneling calculations using a relaxed potential from the full-dimensional potential in the imaginary-frequency normal mode of the saddle point, Q(im). The accuracy of this one-dimensional approach has been shown for the ground-state tunneling splittings for H and D-transfer in malonaldehyde and for the D+H(2) reaction [Y. Wang and J. M. Bowman, J. Chem. Phys. 129, 121103 (2008)]. This approach is applied to calculate the rate constant for the H(2)O+H(2)O exchange and also for H(2)O+D(2)O→2HOD. The local zero-point energy is also obtained using diffusion Monte Carlo calculations in the space of real-frequency-saddle-point normal modes, as a function of Q(im).

ChemInform Abstract: Bidimensional Tunneling Dynamics of Malonaldehyde and Hydrogenoxalate Anion. A Comparative Study

One‐dimensional and bidimensional tunneling splittings have been calculated in malonaldehyde (MA) and hydrogenoxalate anion (HX) systems. Two different monodimensional paths have been considered: the intrinsic reaction path (IRP) and the linear reaction path (LRP). A bidimensional model that includes the coupling between the proton transfer motion and the vibration of the heavy atoms is then used. We find that with the bidimensional model the splittings are 2 orders of magnitude greater than the monodimensional ones, and close to the previous experimental and theoretical values for the MA when zero point energy is introduced. At all levels of calculation we obtain that the splitting is greater in the MA than in the HX. This fact is attributed to the different size of the rings through which the proton transfer occurs.

ChemInform Abstract: Structure of 3-Chlorotropolone.

C7H5C102, Mr = 156.6, monoclinic, P21/c, a = 8.476 (2), b = 12.241 (2), c = 8.170 (2) A, /3 -- 126.47 °, V= 681.7 A 3, z = 4, Dx = 1.525 g cm -3, A(Cu Ka) = 1.54184 A, /z = 44.63 cm-~, F(000) = 320, T = 293 K, R -- 0.046 for 833 reflections with I > 3tr(I). The hydroxylic proton forms a bifurcated hydrogen bond with carbonyl O atoms, one branch intramolecular and the other intermolecular. The latter intermolecular branches form a hydrogen- bonded dimer, which is roughly planar. Introduction. The structures of tropolone and some tropolone derivatives have been studied. It has been shown that 5,isopropyltropolone (Berg, Karlasson, (P~.tti & Wiehager, 1976) as well as tropolone manouchi & Sasada, 1973) forms a bifurcated hydrogen bond with the carbonyl O atoms, one branch being intramolecular and other intermolecu- lar. On the other hand, 4-isopropyltropone does not form a dimer, but O...O hydrogen bonds of 2.8 A link the molecules in a chain (Derry & Hamor, 1972). Very recently, we have measured the electronic spectra of the isolated 3-chlorotropolone (Tsuji, Sekiya, Nishimura, Mori & Takeshita, 1991) and 3-bromotropolone (Sekiya, Sasaki, Nishimura, Mori & Takeshita, 1990). The observation of tunnel splitting provides conclusive evidence for the de- localization of the proton. We have found that the hydroxylic proton is delocalized in 3-chlorotro- polone, whereas the proton is localized in 3- bromotropolone. It has been suggested that the localization of the hydroxylic proton strongly depends on the planarity of the molecule. In order to examine the effect of the substitution of a C1 atom on the molecular and crystal structure, an X-ray

A generalized reactive force field for nonlinear hydrogen bonds: Hydrogen dynamics and transfer in malonaldehyde

Using molecular dynamics (MD) simulations, the spectroscopy and dynamics of malonaldehyde is investigated. To this end, the recently proposed molecular mechanics with proton transfer (MMPT) potential is generalized to nonlinear hydrogen bonds. The calculated properties for malonaldehyde in both gas and condensed phases, including equilibrium geometries, infrared spectra, tunneling splittings, and hydrogen transfer rates, compare well with previous experimental and computational works. In particular, by using a harmonic bath averaged (HBA) Hamiltonian, which is based on a reaction path Hamiltonian, it is possible to estimate the tunneling splitting in an efficient manner. It is found that a zero point corrected barrier of 6.7 kcal/mol and effective masses of 1.234 (i.e., 23.4% larger than the mass of a physical H-atom) and 1.117 (for the physical D-atom) are consistent with the measured splittings of 21.6 and 2.9 cm(-1), respectively. The HBA Hamiltonian also yields a pair of hydrogen transfer fundamentals at 1573 and 1267 cm(-1), similar to results obtained with a reaction surface Hamiltonian on a MP2/6-31G(**) potential energy surface. This amounts to a substantial redshift of more than 1000 cm(-1) which can be rationalized by comparison with weakly (HCO(+): rare gas) and strongly (H(2)O-H(+)-OH(2)) proton-bound systems. Hydrogen transfer rates in vacuum and water were determined from the validated MMPT potential and it is found that the solvent enhances the rate by a factor of 5 at 300 K. The rates of 2.4/ns and 10/ns are commensurate with previous density functional tight binding ab initio MD studies.

High-resolution rotational spectroscopy of NNOH +, DCS +, [formula omitted], Ar ⋯ DCO +, and [formula omitted

The rotational spectra of the protonated molecules NNOH + and DCS +, and the ion complexes Ar ⋯ D 3 + , Ar ⋯ DCO +, and Ar ⋯ HNN + have been detected by Fourier transform microwave spectroscopy at high spectral resolution, in which the supersonic molecular beam expands along the axis of the Farby–Perot cavity. These new measurements either better resolve or reveal additional line structure not observed in the previous lower resolution studies. Precise nitrogen or deuterium quadrupole coupling constants have been determined for the first time for both ions and Ar ⋯ DCO +; a tunneling splitting of 72 ± 5 kHz has been measured for the 1 0 , 1 → 0 0 , 0 transition of Ar ⋯ D 3 + .

The Rotational Structure of the Origin Band of the Pulsed-Field-Ionization, Zero-Kinetic-Energy Photoelectron Spectra of Propene-h6 and Propene-d6

The pulsed-field-ionization zero-kinetic-energy photoelectron spectra of the origin band of the + 2A′′ ← 1A′ transition of propene (C3H6) and perdeuterated propene (C3D6) have been recorded at high resolution, allowing for the partial resolution of the rotational structure. The analysis of the spectra in the realm of the orbital ionization model for rigid-rotor asymmetric-top molecules enabled the determination of the adiabatic ionization energy of propene and the rotational constants of C3H6+ and C3D6+. The tunneling splittings resulting from the hindered rotation of the methyl group could not be resolved, and the analysis was therefore carried out in the Cs molecular symmetry group. Angular momentum contributions of pπ, dπ, and dδ character were included in the single-center expansion describing the molecular orbital out of which ionization occurs, leading to the selection rules |ΔN| = |N+ − N′′| ≤ 2 and ΔKa = Ka+ − Ka′′ = ±1, ±2 and to photoelectron partial waves with angular momentum quantum number up to l = 3. The observation of a strong spectral feature associated with ΔKa = 0 indicates the importance of vibronic interactions.

Group-theoretical investigation of the tunneling splitting patterns of enolic acetylacetone

Extensive experimental and theoretical studies for enolic acetylacetone have been presented in the literature, but studies of the tunneling splitting patterns are still lacking. In this work we adopt the C s symmetry equilibrium structure and apply a group-theoretical formalism to study the tunneling splitting pattern of the ground vibrational level of enolic acetylacetone. Enolic acetylacetone has three large-amplitude motions, one intramolecular hydrogen transfer and two methyl torsions. Therefore, the C s structure of enolic acetylacetone has 18 (3 × 3 × 2) equivalent equilibrium molecular frameworks, nine (3 × 3) of them are from the two methyl torsions, and two are from the intramolecular hydrogen transfer. Tunneling motions among the 18 equivalent molecular frameworks split the ground vibrational level into eight sublevels: A 1, A 4, E 1, E 2, E 3, E 4, G(1) and G(2). In enolic acetylacetone the intramolecular hydrogen transfer induces a rearrangement of the CC, CO single and double bonds, and then triggers two additional 60° internal rotations, one in each of the two methyl groups attached to the hydrogen-bonded malonaldehyde ring. This interaction further complicates the tunneling splitting patterns and increases the difficulty of spectral analysis. In this work the influence of the intramolecular hydrogen transfer on the energy order of the eight sublevels is determined by a group-theoretical formalism.