Double-well Shape Research Articles

Vibronic Structure of the Permanganate Absorption Spectrum from Time-Dependent Density Functional Calculations

The UV absorption spectrum of the permanganate anion is a prototype transition-metal complex spectrum. Despite this being a simple d0 Td system, for which a beautiful spectrum with detailed vibrational structure has been available since 1967, the assignment of the second and third bands is still very controversial. The issue can be resolved only by an elucidation of the intricate vibronic structure of the spectrum. We investigate the vibronic coupling by means of linear-response time-dependent density functional calculations. By means of a diabatizing scheme that employs the transition densities obtained in the TDDFT calculations in many geometries around Re, we construct a Taylor series expansion in the normal coordinates of a diabatic potential energy matrix, coupling 24 excited states. The simulated vibronic structure is in good agreement with the experimental absorption spectrum after the adjustment of some of the calculated vertical excitation energies. The peculiar blurred vibronic structure of the second band, which is a very distinctive feature of the experimental spectrum, is fully reproduced in the calculations. It is caused by the double-well shape of the adiabatic energy surface along the Jahn-Teller active e mode of the allowed 1E state arising from the second 1T2 state, which exhibits a Jahn-Teller splitting into 1B2 and 1E states. We trace the double-well shape to an avoided crossing between two diabatic states with different orbital-excitation character. The crossing can be explained at the molecular orbital level from the Jahn-Teller splitting of the set of 7t2{3d(xy), 3d(xz), 3d(yz)} orbitals (the LUMO + 1), to which the excitations characterizing the diabatic states take place. In contrast to its character in the two well regions, at Re the 2(1)T2 state is not predominantly an excitation to the LUMO + 1, but has more HOMO - 1 --> LUMO (2e = {3d(x2-y2), 3d(z2)}) character. The changing character of the 2(1)T2 - 1E state along the e mode implies that the assignment of the experimental bands to single orbital transitions is too simplistic intrinsically. This spectrum, and notably the blurring of the vibronic structure in the second band, can be understood only from the extensive configurational mixing and vibronic coupling between the excited states. This solves the long-standing assignment problem of these bands.

Origin of soft mode in SbSe xS 1– xI crystals

The behaviour of the potential energy V( z) of the B 1u (A 1) symmetry soft-mode vibrations of atoms in the direction of the z( c ) axis of SbSe x S 1– x I crystals ( x=0, 0.15, 0.45, 1) upon the normal coordinate (relative displacements of atoms) was investigated in the region of the phase transition temperatures. For this B 1u (A 1) symmetry soft mode, the potential energy barrier height Δ V, the potential energy V( z), its harmonic and anharmonic terms were studied as functions of the mixture composition x and temperature T. The dependence of the soft mode frequency ω S upon the composition x and temperature has been established assuming the double-well shape of the potential energy (per atom) V( z).

Investigation of the Soft Mode of SbSBrxI1−x Crystals

The behaviour of the potential energy V(z) of the B 1u (A 1 ) symmetry soft mode vibrations of atoms in the direction of the z(c) axis of SbSBrxI 1−x crystals (x = 0, 0.2, 0.75, 1) upon the normal coordinate (relative displacements of atoms) was investigated in the region of the phase transition temperatures. For this B 1u (A 1 ) symmetry soft mode, the potential energy barrier height ΔV, the potential energy V(z), its harmonic and anharmonic terms were studied as functions of the mixture composition x and temperature T. The dependence of the soft mode frequency ωS upon the composition x and temperature has been established assuming the double-well shape of the potential energy (per atom) V(z). By employing A 1u (A 2 ) symmetry coordinates, the force constants C of interaction between molecular chains have been obtained. The type of the phase transition has been established by calculating the Rhodes–Wohlfarth factor R. To calculate this factor, the ratio /ΔV depending upon the mixture composition was employed. It has been found that for mixed crystals with x < 0.8, the phase transition is intermediate between order–disorder and displacive types, and for crystals with x > 0.8, the phase transition is of displacive type.

Cusp Singularities in the Magnetization Curve of Frustrated Kondo Necklace Model

Magnetization processes of frustrated Kondo necklace model are studied by means of a density matrix renormalization group (DMRG) method and an elementary band theory based on a bond-operator formalism. The DMRG calculations clearly show the cusp singularity in a low-magnetization region ($0<m<1/2$) besides that in a high-magnetization region ($1/2<m<1$) which is expected from previous studies on the magnetization curve of the Majumdar-Ghosh model. An appearance mechanism of the low-magnetization cusp is interpreted in terms of a double-well shape of a low-energy band arising from frustrations between nearest- and next-nearest-neighbor interactions. We also discuss critical behaviors of magnetization near the cusp and obtain a phase diagram showing whether the cusp appears in the magnetization curve or not.

Adhesive switching of membranes: experiment and theory.

We report on a study of a model bioadhesion system: giant vesicles in contact with a supported lipid bilayer. Embedded in both membranes are very low concentrations of homophilic recognition molecules (contact site A receptors) competing with higher concentrations of repeller molecules: polyethylene glycol (PEG) lipids. These repellers mimic the inhibiting effect of the cell glycocalyx on adhesion. The effective adhesive interaction between the two membranes is probed by interferometric analysis of thermal fluctuations. We find two competing states of adhesion: initial weak adhesion is followed by slower aggregation of the adhesion molecules into small, tightly bound clusters that coexist with the regions of weak adhesion. We interpret our results in terms of a double-well intermembrane potential, and we present a theoretical analysis of the intermembrane interaction in the presence of mobile repeller molecules at a fixed chemical potential that shows that the interaction potential indeed should have just such a double-well shape. At a fixed repeller concentration we recover a conventional purely repulsive potential. We discuss the implications of our findings in terms of a general amplification mechanism of the action of sparse adhesion molecules by a nonspecific double-well potential. We also discuss the important role of the Helfrich undulation force for the proposed scenario.

Atom oscillations in the scanning tunneling microscope

The atom tunneling across the potential barrier separating the surface and the tip of the scanning tunneling microscope is investigated by semiclassical methods, and by integrating numerically the time-dependent Schr\"odinger equation. It is shown that the barrier crossing is explained by the resonance phenomenon of quantum coherence oscillations, rather than by exponential decay. The occurrence of these resonances at the variation of the bias voltage is studied for the first two isomeric states of a Xe atom in a surface-tip potential of double-well shape. The resonant bias voltages for these two states practically coincide, and at the first common resonance the effect of the environmental temperature is discussed. The results provide a useful frame for understanding the mechanism of atom transfer in scanning tunneling microscopy.

Double well model V( r) = ar2 + br4 + cr6 with a < 0 and perturbation method with triangular propagators

We propose a new version of the Rayleigh-Schrödinger perturbation prescription suitable for tridiagonal zero-order Hamiltonians. It picks up an unusual model space and its unperturbed propagators remain easily invertible lower triangular matrices as a consequence. Its efficiency is illustrated on sextic potentials with double-well shape.

On CuCrP2S6: Copper Disorder, Stacking Distortions, and Magnetic Ordering

The pseudo-one-particle potential for Cu1 in CuCrP2S6 was calculated from the room temperature (RT) structural model and shown to have a double-well shape straddling the center of the CuS6 octahedron. It is argued that this finding supports the thermal hopping interpretation of the RT copper disorder in this compound. The RT monoclinic unit cell parameters were also remeasured and found to be consistent with the presence of out-of-plane packing deformations. Last, the antiferromagnetic structure of the CrIII moments below TN ≈ 30 K was determined using neutron powder diffraction.

Bond alternation and electronic structure of poly(perinaphthalene)

It is shown on the Hartree-Fock level of theory that Peierls distortions of two different bond alternation patterns are possible for poly(perinaphthalene). In the structurally related oligomeric systems, the stabilization of a given type of bond length distortion results from the boundary conditions as imposed by different end groups. For the polymer the π-π electron interaction is found to give preference to the bond alternation observed in oligorylenes. Nevertheless, the adiabatic potential energy surface has a double-well shape, with two almost degenerate minima separated by a low potential barrier.

Exact kink solutions in a new non-linear hyperbolic double-well potential

The authors propose a model of a kink bearing Hamiltonian with a new non-linear potential V( phi , mu ) whose double-well shape can be varied continuously as a function of the parameter mu and which has the phi 4 potential as a particular case. Exact classical kink solutions that depend on mu are obtained. The rest masses and rest energies of the kinks are also determined.

Effective potential of latticeφ4theory

The structure of the effective potential for lattice ${\ensuremath{\varphi}}^{4}$ theory is discussed. It is shown that the effective potential $V(\stackrel{^}{\ensuremath{\varphi}})$ is undefined in an infinite lattice system for certain values of $\stackrel{^}{\ensuremath{\varphi}}$ if spontaneous symmetry breaking occurs. It is also shown that $\frac{{d}^{2}V}{d{\stackrel{^}{\ensuremath{\varphi}}}^{2}}\ensuremath{\ge}0$ for all $\ensuremath{\varphi}$, thus precluding the familiar double-well shape suggested by the classical potential. These results do not depend on the spacetime dimensionality of the lattice or upon the particulars of any loop expansion. A graphical approximation procedure for the effective potential is formulated and compares very favorably with Monte Carlo results. Comparisons with strong-coupling-expansion predictions are also made.

Lattice dynamical calculations of the mean square amplitudes of crystalline biphenyl

The molecular mean-square-amplitude matrix of crystalline biphenyl, C12H10, is calculated with an intermolecular potential of the atom-atom type. The effect of the presence of the low-lying torsional mode, which interacts with translational modes, is discussed. The Born S-matrix method is used, and proves to be an excellent approximation, which takes about ⅕ of the computer time of the exact calculation. The resulting amplitudes are in fair agreement with experiment, and show that the extremely high amplitude of libration about the long molecular axis may be satisfactorily explained without assuming a double-well shape for the torsional potential.