Effective Hamiltonian Model Research Articles

Coupling of interfacial and spin-like coordinates in effective Hamiltonians for complete and critical wetting

In this paper the effects of including position-dependent stiffness coefficients in the coupled effective Hamiltonian models appropriate for both complete and critical wetting are considered. This analysis is motivated by a nonlinear functional renormalization group approach applied for the first time to two-field interface models, and cast in a simple matrix form. In particular we (i) determine the renormalization group flow of the capillary parameter and confirm that its renormalization at complete wetting is preserved at all orders and (ii) demonstrate that the stiffness instability mechanism is robust, and indeed strengthened, under the inclusion of coupling terms near critical wetting.

Stark levels analysis for Er 3+-doped oxide glasses: germanate and silicate

A model of effective crystal field Hamiltonian based on the principle of descending symmetry and using the symmetry group chain scheme is proposed to describe the average of local symmetries occupied by rare earth (RE) ions in glasses. Only three crystal field parameters, one for each rank, have to be fitted in this Hamiltonian. Based on the absorption and emission spectra measured in a conventional way at 13 K, the Stark levels in manifolds from 4I 15/2 to 2H 9/2 and their widths of Er 3+ in two oxide glasses: germanate and silicate, are investigated. In the process, the scalar crystal field strength, homogeneous and inhomogeneous effective widths of levels are analyzed, and the former models and results about optical properties of rare earth ions in glasses are discussed. The cubic crystal field term is found to give the major contribution to the crystal field strength around the rare earth ion when the weak axial distortion completely removes the degeneracy.

The Absorption Spectrum of HDO in the 16 300–16 670 and 18 000–18 350 cm−1 Spectral Regions

The absorption spectrum of HDO has been recorded by Intracavity Laser Absorption Spectroscopy in the 16 300–16 670 and 18 000–18 350 cm−1 spectral regions corresponding to the weak 2ν2 + 4ν3 and ν2 + 5ν3 bands, respectively. The ν2 + 5ν3 band centered at 18 208.434 cm−1 was found almost isolated and has been satisfactorily reproduced in the frame of the effective Hamiltonian model. On the other hand, the 2ν2 + 4ν3 band at 16 456.201 cm−1 is strongly perturbed as the (0 2 4) bright state is involved in a complex interaction scheme including the (1 0 4), (5 0 1), (1 5 2), and (1 11 0) states. The rovibrational assignment of these interacting states was greatly helped by the high-accuracy ab initio predictions performed by D. Schwenke and H. Partridge [J. Chem. Phys. 000–000 (2000)]. They could be partly modeled by an effective Hamiltonian which has allowed the assignment and reproduction of most of the observed transitions.

The 5VOH Overtone Transition of HDO

The absorption spectrum of HDO has been recorded by intracavity laser absorption spectroscopy in the 16 540–17 055 cm−1 spectral region corresponding to the 5ν3 band centered at 16 920 cm−1. The (0 0 5) vibrational state is found to be mostly isolated from the nearby rovibrational states. The corresponding rovibrational transitions were analyzed and fitted in the frame of the effective rotational Hamiltonian model in Pade–Borel approximants form. The spectroscopic parameters retrieved from the fitting reproduce 100 of the 109 determined energy levels with the root-mean-square deviation of 0.0072 cm−1, close to the experimental accuracy. From the integrated relative intensities of a- and b-type transitions, the angle between the transition moment and the OH bond is estimated to be 46.4°. This value is consistent with an increasing tilt of the transition dipole moment, away from the OH bond, when the OH stretching is excited. The evolution of the orientation of the transition dipole moment versus the vibrational excitation is then compared for the OH and OD overtone bands.

Two-dimensional filling in ordered and disordered systems

We consider filling or wedge-wetting transitions occurring in a (1 + 1)-dimensional wedge geometry with both thermal and random-bonddisorder using effective interfacial Hamiltonian models. Forordered systems the problem may be solved using transfer-matrixmethods for quite arbitrary choices of interfacial binding potentialand gives a complete classification of the possible criticalbehaviours. For random bonds the transition is studied forshort-ranged forces using the replica trick and the wedge-wettingcritical exponents are identified. Our results establish aremarkable relation between the mid-point height probabilitydistribution PF(l0) at filling transitions and the appropriatelydefined height distribution function Pπ(l;θπ) atplanar wetting transitions. We observe that provided the wettingspecific heat component αs = 0, then, in the scaling limit,PF(l0) = Pπ(l;θπ-α)where θπ is the contact angle and α is the tilt angleof the wedge. This relation completely determines the allowed values ofthe filling critical exponents in the fluctuation-dominatedregimes. Conjectures regarding interfacial fluctuation effects infinite-size two-dimensional systems are also made.

Vibrational spectra and intramolecular vibrational redistribution in highly excited deuterobromochlorofluoromethane CDBrClF: Experiment and theory

The rovibrational spectra of deuterobromochlorofluoromethane (CDBrClF) were measured at intermediate (0.1 cm−1) and high resolution (0.0024 cm−1 full bandwidth, half-maximum) by interferometric Fourier transform infrared spectroscopy in the range from the far infrared at 200 cm−1 to the near infrared (12 000 cm−1) covering all the fundamentals and CD stretching overtones up to polyad N=5. The spectra are completely analyzed in terms of their vibrational assignments to fundamentals, combinations and overtones. At high excitation the analysis reveals the dominant anharmonic coupling between four high frequency vibrational modes; the CD stretching (ν1), two CD bending (ν2,ν3), and the CF stretching mode (ν4). The analysis is carried out using effective model Hamiltonians including three and four vibrational degrees of freedom. We also present vibrational variational calculations on a grid in a four-dimensional normal coordinate subspace. The potential energy and the dipole moment function are calculated ab initio on this grid using self-consistent field second order Møller–Plesset perturbation theory (MP2). Experimental and theoretical results for band positions and integrated intensities as well as effective spectroscopic parameters are found to be in good agreement. The important anharmonic coupling between the CD chromophore and the CF stretching vibration can be described by an effective cubic Fermi resonance coupling constant ksff′≈(50±10) cm−1, which leads to intramolecular vibrational redistribution between the CD and CF chromophores on the femtosecond time scale. Time dependent intramolecular vibrational redistribution processes in CDBrClF are derived in various representations, including time dependent probability densities (“wave packets”) in coordinate space and finally time dependent entropy.

The vibrational spectrum of deuterated phosphaethyne: A quantum mechanical, classical, and semiclassical analysis

The vibrational spectrum of deuterated phosphaethyne (DCP) is analyzed in terms of quantum-mechanical variational calculations, classical mechanics (periodic orbits), and an effective Hamiltonian model. The quantum mechanical and classical calculations are performed with a new, spectroscopically accurate potential energy surface. The spectrum is governed by a 2 : 1 DC stretch : CP stretch anharmonic resonance, which already exists for the fundamentals. The bending degree of freedom is to a large extent decoupled. It is shown that several bifurcations in the classical phase space profoundly influence the quantum spectrum. For example, a new progression, which does not exist at very low excitation energies, comes into existence at intermediate energies. In contrast to HCP, the pure bending states gradually evolve along the isomerization path with increasing bending quantum number.

Visualizing intramolecular vibrational redistribution: expectation values of resonance operators

The expectation values of resonance operators can help to elucidate the mechanisms that underlie complicated, multidimensional vibrational dynamics, as represented by effective Hamiltonian models.

STUDY OF DIRECT CP ASYMMETRY IN B+→K0π+

The direct CP asymmetry (aCP) for the process B+→π+K0 is studied including the contributions arising from both the QCD and electroweak penguins and the long range inelastic final state interactions (IFSI). The usually neglected space-like penguins and the annihilation contributions are also taken into account in our analysis. The next-to-leading order low energy effective Hamiltonian and BSW model are used to evaluate the weak transition matrix elements. The effect of space-like and annihilation diagrams are studied using the Lepage and Brodsky model. We found that as a result of FSI, the CP asymmetry and the branching ratio are suppressed slightly in comparison to no FSI situation, but the obtained branching ratio with FSI agrees very well with the present experimental value. With our predicted value of aCP~1010, charged B mesons are required to resolve the CP asymmetry experimentally at 3σ level.

Wetting on non-planar and heterogeneous substrates

We report results of wetting on non-planar and heterogeneous surfaces calculated from an effective interfacial Hamiltonian model. The lack of translational invariance along the substrate induces a series of structural changes of the interface such as unbending and a number of non-thermodynamic singularities and can modify the location of the wetting transition. We show that the order of the wetting transition in the planar homogeneous system strongly affects the behaviour of the non-planar and heterogeneous surfaces.

Analysis and Deperturbation of the A2Π and B2Σ+ States of CaF

A laser excitation spectrum of the (0, 0) and (1, 1) bands of the CaF A2Π–X2Σ+ system was recorded. The present set of molecular constants for both A2Π and B2Σ+: states represents a vast improvement in precision over previously reported values because of the larger number of line position measurements and the use of a more reasonable effective Hamiltonian model which accounts explicitly for the A ∼ B interaction via off-diagonal matrix elements. The principal constants (in cm−1) are where uncertainties of 1ς are given in parentheses.

High resolution spectroscopy of CH 3OD involving the ground and first excited torsional states in the vibrational ground state

In this work, the reduced eighth order Hamiltonian parameters of CH 3OD have been determined using the high resolution Fourier transform far-infrared (FIR) assigned transitions in the ground and first excited torsional states. The data set consisted of 2348 FIR transitions with the rotational angular momentum J<21 and K<7. In order to achieve stability of the fit 275 microwave (MW) and millimetre-wave (MMW) transitions have also been included in the data set. This has been fitted with a recently developed eighth order effective Hamiltonian model to derive the molecular parameters. The results indicate that the model developed for the parent methanol species is valid for the methanol-OD species as well. The fit converged with an overall deviation of 0.0008 cm −1, which is of the same order of magnitude as the uncertainty of the Fourier transformed peaks. The results will allow the energy levels of the molecule to be calculated with much more improved precision which will be useful for the discovery of new FIR laser emission and the discovery of this molecular species in interstellar space.

Spectroscopic investigation of the generation of “isomerization” states: Eigenvector analysis of the bend-CP stretch polyad

The highly excited vibrational levels of HCP exhibit a regular energy level and intensity pattern characteristic of 2:1 bend-CP stretch polyads. Stimulated by the experimental observation of vibrational levels with rotational constants (B-values) 5%–10% larger than other observed levels, Schinke and co-workers noticed that these large-B levels were characterized by atypical nodal structures indicative of large amplitude motion along the minimum energy HCP↔CPH isomerization path [J. Chem. Phys. 107, 9818 (1997)]. In this paper, we show that the transition from “normal-mode-type” to “isomerization” vibrational states arises naturally out of a traditional spectroscopic (algebraic) effective Hamiltonian polyad model. A global least squares fit, based on this polyad Heff model, shows that all of the observed “isomerization” states belong to polyads and that the eigenvectors of this Heff model have the qualitatively distinct nodal structure first noticed by Schinke and co-workers. The “isomerization” states are not indicative of a breakdown of the polyad model; rather they are a natural consequence of this traditional spectroscopic model.

Pure bending dynamics in the acetylene X̃ 1Σg+ state up to 15 000 cm−1 of internal energy

We investigate the large-amplitude bending dynamics of acetylene, in its ground electronic state, using an effective Hamiltonian model that reproduces all relevant experimental data, up to 15 000 cm−1 in internal energy, with 1.4 cm−1 accuracy (1σ). The experimental data which make this analysis possible are derived from the dispersed fluorescence (DF) data set that we recently reported [J. P. O’Brien et al., J. Chem. Phys. 108, 7100 (1998)] for the acetylene à 1Au→X̃ 1Σg+ system, which includes DF spectra recorded from five different vibrational levels of the à 1Au state. A numerical pattern recognition technique has permitted the assignment of polyad quantum numbers to observed transitions in these spectra, with up to 15 000 cm−1 in internal energy. Here we analyze a special subset of the identified polyads, those which involve excitation exclusively in the trans and cis bending modes: the pure bending polyads. The bending dynamics that is encoded in these polyads is analyzed using both frequency and time-domain formalisms. Among the conclusions of this analysis is that, in many ways, the observed bending dynamics is somewhat simpler at 15 000 than it is at 10 000 cm−1; this rather surprising result is explained in terms of qualitative changes in the structures of the pure bending polyads as a function of increasing internal energy.

Spectroscopy and dynamics of 5f states of Es 3+ in LaF 3

Using time- and wavelength-resolved laser-induced fluorescence methods, the 5f state spectroscopy and photodynamics of 253Es 3+ in LaF 3 have been investigated. Based on an effective operator Hamiltonian model and approximating the metal ion site symmetry as C 2 v , a set of crystal field parameters has been obtained that fit the 56 assigned levels associated with the seven states of Es 3+ that were observed. The 5F 5 emitting state of Es 3+ exhibited a decay rate that approached the expected purely radiative decay of the state. This suggests that the shorter lifetime previously found for this state of Es 3+ in LaCl 3 arose from radiation damage induced by α decay of 253Es.

Inelastic final-state interactions in B → VV →π K processes

We study the final-state interactions in $B \to \pi K$ decays through $B \to VV \to \pi K$ processes where the inelastic rescattering occurs via single pion exchange. The next-to-leading order low energy effective Hamiltonian and BSW model are used to evaluate the weak transition matrix elements and the final-state interactions. We found that the final-state interaction effects in $B \to \rho K^* \to \pi K$ processes are significant. The Fleischer-Mannel relation about the CKM angle $\gamma$ may be significantly modified.

Anharmonically-coupled local mode to normal mode Hamiltonian transformations: beyond the x, K -relations

Attention is focused on the quantitative relationships between the parameters of the normal mode and the local mode effective Hamiltonian models of anharmonic stretching vibrations. R. G. Della Valle (1988, Molec. Phys., 63, 611) has demonstrated the general relationship between the harmonically coupled anharmonic (Morse) oscillators (HCAO) model and the normal mode model of X-H (or X-D or other weakly coupled) stretching vibrations of polyatomic molecules. Here we consider more fully the relationship between the normal mode and the anharmonically coupled local mode models for X-H stretching vibrations. The local mode Hamiltonian is expressed in terms of boson shift operators and these operators are then transformed into the corresponding normal mode model operators. Such relationships have already been derived for the special cases of H2X (Baggott, J. E., 1988, Molec. Phys., 65, 739), XH3 (C3v) and XH4 (Td) (Law, M. M., and Duncan, J. L., 1994, Molec. Phys., 83, 757) and here they are derived systematically for arbitrary local mode stretching systems. Explicit relationships are derived for molecules of the symmetry types of allene, ethylene and benzene respectively. These relationships between the unconstrained normal mode and anharmonically coupled local mode models allow for more reliable schemes for the relaxation of the HCAO x, K -relations than those suggested hitherto. In an application to the ethylene-d4 overtone spectrum a much improved fit to experimental data is obtained using a compact anharmonically coupled local mode model and the consequences for the corresponding normal mode model demonstrated. The generality of our results is emphasized by the application to systems involving non-equivalent bonds, illustrated with reference to HCN/DCN. Approximations in these local to normal mode transformations (such as the assumption of a unitary transformation) are discussed. The models presented here may be supplemented with appropriate matrix elements to take account of Fermi resonances in the same straightforward manner as the HCAO model.

Microwave spectrum of the furan–CO van der Waals complex

The microwave spectrum of the furan–CO van der Waals complex has been measured between 6–19 GHz with a pulsed nozzle Fourier transform microwave spectrometer. Due to a large amplitude motion of the CO subunit between two equivalent minima, the observed rotational transitions were split into two components. Their center frequencies were compatible with an asymmetric rotor with CO located above the plane of furan. The rotational spectrum has been analyzed using an effective model Hamiltonian that accounts for an internal rotation between furan and CO hindered by a low barrier.

Ultrafast reaction dynamics in cluster ions: Simulation of the transient photoelectron spectrum of I2−Arn photodissociation

Combining an effective Hamiltonian model of electronic structure with nonadiabatic molecular dynamics simulations, we calculate the recently measured transient photoelectron spectrum of I2− dissociated inside a cluster of argon atoms. We find good agreement between calculated and experimental spectra. The transient spectral shifts reflect the dynamics of both the I2− and argon degrees of freedom, revealing pathways and time scales for dissociation, recombination, and vibrational relaxation.

Hubbard and Heisenberg Models for Four-Site Four-Electron Systems. Group-Theoretical Interrelationships and Applications to Multinuclear Transition-Metal Clusters

Abstract Hubbard models for four-site four-electron {4,4} systems are analytically solved to elucidate group-theoretical interrelationships between effective model Hamiltonians for radical clusters, metal clusters, Cu4O4, and so on. The group operations used for this purpose are permutation group (SN), spatial symmetry (PN), spin rotation (S), and time-reversal (T). The magnetic (color) group (T × S) is utilized for determination of the magnetic symmetry of spin structures obtained on the basis of the classical Heisenberg model; namely a vector representation of radical spins. The magnetic double group theory (T × S × PN) is used for characterization of general Hartree–Fock solutions (GHF) involving axial, helical, and torsional spin density waves for {4,4} systems. The spin-optimized SCF solutions are constructed from the spin projection of the GHF solutions (T × S × PN) by the use of the permutation symmetry (SN). The SN group is also used for the quantum Heisenberg model for {4,4} systems. In order to show the interrelationships between these model Hamiltonians, the electronic states of {4,4} systems with the D4h, Td, and D3h symmetries are constructed by the use of the magnetically ordered general spin orbitals which have been determined by the GHF calculations. The spin-optimized SCF solutions for {4,4} systems examined here are equivalent to the full CI wavefunctions satisfying both spatial and spin symmetries. The relative contributions of the spin polarization (SP) and doubly excited configurations in the GHF, projected GHF and SO-SCF wavefunctions are clarified to elucidate possible mechanisms of spin alignments and antiferromagnetic spin correlations. Implications of these computational results are discussed in relation to quantum and classical representations of spin alignments in molecular magnetic materials such as iron–sulfur clusters. Molecular magnets having helical and torsional spin structures are designed and discussed in relation to the most general spin alignment in the species.