Effective Hamiltonian Model Research Articles

High-sensitivity CW-cavity ringdown spectroscopy of 12CO 2 near 1.5 μm

The absorption spectrum of carbon dioxide in natural isotopic abundance has been recorded by CW-cavity ringdown spectroscopy with a setup based on fibered DFB lasers. By using a series of 31 DFB lasers, the CO 2 spectrum could be recorded in the 6132–6747 cm −1 region with a typical sensitivity of 5 × 10 −10 cm −1. More than 3300 line positions were measured and assigned to the 12C 16O 2 species while only 1159 (generally calculated) line positions are provided by the HITRAN database. Altogether, the band-by-band analysis has led to the determination of the rovibrational parameters of 53, 5, and 9 bands for the 12C 16O 2, 16O 12C 17O, and 16O 12C 18O isotopologues, respectively. For the three studied isotopologues, the majority of the observed line positions show an agreement close to the experimental uncertainty (3 × 10 −3 cm −1) with the predictions of their respective effective Hamiltonian models. Maximum deviations of the order of 0.03, 0.05, and 0.04 cm −1 were, however, evidenced for 12C 16O 2, 16O 12C 17O, and 16O 12C 18O, respectively. As some observed line positions show significant deviations from the predictions of the effective Hamiltonian model and as the observed data set has been recently enlarged by newly reported measurements, the observed line positions were gathered with all the data available in the literature in order to refine the set of effective Hamiltonian parameters of the 12C 16O 2 isotopic species. The refined set of 130 effective Hamiltonian parameters reproduces more than 29 000 observed line positions of 12C 16O 2 with an RMS = 0.002 cm −1. The comparison of our line positions values with those published earlier and with the line list provided by HITRAN is discussed.

Interfacial structure at a two-dimensional wedge filling transition: Exact results and a renormalization group study.

Interfacial structure and correlation functions near a two-dimensional wedge filling transition are studied using effective interfacial Hamiltonian models. An exact solution for short range binding potentials and results for Kratzer binding potentials show that sufficiently close to the filling transition a new length scale emerges and controls the decay of the interfacial profile relative to the substrate and the correlations between interfacial positions above different positions. This new length scale is much larger than the intrinsic interfacial correlation length, and it is related geometrically to the average value of the interfacial position above the wedge midpoint. The interfacial behavior is consistent with a breather mode fluctuation picture, which is shown to emerge from an exact decimation functional renormalization group scheme that keeps the geometry invariant.

"Spectrum-only" assignment of core-penetrating and core-nonpenetrating Rydberg states of calcium monofluoride

Rydberg states of calcium monofluoride in the n* = 17–20 region have been observed by ionization-detected optical–optical double-resonance spectroscopy via the D2Σ+ v = 1 intermediate state. All members of the six core-penetrating Rydberg series in the n* = 17–20 region and several components of the 17f and 17g core-nonpenetrating Rydberg states have been assigned. While the assignment of core-penetrating Rydberg states is straightforward without use of an effective Hamiltonian model, "spectrum-only" assignment of core-nonpenetrating states is complicated because strong l-uncoupling causes the core-nonpenetrating states to evolve rapidly from Hund's case (b) to Hund's case (d) coupling. We describe "spectrum-only" assignment procedures, developed in the spirit of Gerhard Herzberg, that can be used to assign optical–optical double-resonance spectra of core-penetrating and core-nonpenetrating Rydberg states using only information contained in the spectrum rather than predictions derived from an effective Hamiltonian model. The ambiguities that arise in the assignment of each class of states are discussed in detail.Key words: CaF, electric quadrupole moment, Rydberg states, laser spectroscopy.

High sensitivity cw-cavity ringdown and Fourier transform absorption spectroscopies of 13CO 2

The absorption spectrum of 13CO 2 has been recorded by cw-cavity ringdown spectroscopy with a new set up based on fibered DFB lasers. By using a series of 31 DFB lasers, the spectrum of carbon dioxide could be recorded in the 6130–6750 cm −1 region with a typical sensitivity of 5 × 10 −10 cm −1. The spectrum has also been recorded between 4400 and 8500 cm −1 with a Fourier transform spectrometer associated with a multi-pass cell (maximum path length of 105 m). The new observations obtained both by FTS and CRDS represent a significant extension of the available data. For instance, more than 4000 line positions were measured and assigned in the CRDS spectrum while only 232 line positions are listed in the HITRAN database. Altogether, the band by band analysis has led to the determination of the rovibrational parameters of 65, 7, and 24 bands for the 13C 16O 2, 16O 13C 17O, and 16O 13C 18O isotopomers, respectively. As some observed line positions show significant deviations from the predictions of the effective Hamiltonian model, the new observed line positions were gathered with the data available in the literature to refine the set of effective Hamiltonian parameters of the 13C 16O 2 isotopic species. The refined set of 96 effective Hamiltonian parameters reproduces more than 14 650 line positions of 13C 16O 2 with an RMS=0.002 cm −1. A detailed comparison with the line positions retrieved from Venus spectra and the line list provided by HITRAN is also presented and discussed.

Three-dimensional wedge filling in ordered and disordered systems

We investigate interfacial structural and fluctuation effects occurring at continuous fillingtransitions in 3D wedge geometries. We show that fluctuation-induced wedgecovariance relations that have been reported recently for 2D filling and wetting havemean-field or classical analogues that apply to higher-dimensional systems. Classicalwedge covariance emerges from analysis of filling in shallow wedges based on asimple interfacial Hamiltonian model and is supported by detailed numericalinvestigations of filling within a more microscopic Landau-like density functionaltheory. Evidence is presented that classical wedge covariance is also obeyed forfilling in more acute wedges in the asymptotic critical regime. For sufficientlyshort-ranged forces mean-field predictions for the filling critical exponents andcovariance are destroyed by pseudo-one-dimensional interfacial fluctuations. Weargue that in this filling fluctuation regime the critical exponents describing thedivergence of length scales are related to values of the interfacial wandering exponentζ(d) defined for planar interfaces in (bulk) two-dimensional(d = 2) andthree-dimensional (d = 3) systems. For the interfacial height , with θ the contactangle and α the wedgetilt angle, we find βw = ζ(2)/2(1−ζ(3)). For pure systems (thermal disorder) we recover the known resultβw = 1/4 predicted by interfacial Hamiltonian studies whilst for random-bond disorder we predictthe universal critical exponent even in the presence of dispersion forces. We revisit the transfer matrix theory ofthree-dimensional filling based on an effective interfacial Hamiltonian model and discussthe interplay between breather, tilt and torsional interfacial fluctuations. We show that thecoupling of the modes allows the problem to be mapped onto a quantum mechanicalproblem as conjectured by previous authors. The form of the interfacial height probabilitydistribution function predicted by the transfer matrix approach is shown to be consistentwith scaling and thermodynamic requirements for distances close to and far from the wedgebottom respectively.

Spin and Pseudo Spins in Theoretical Chemistry. A Unified View for Superposed and Entangled Quantum Systems

A unified picture for magnetism, superconductivity, quantum optics and other properties of molecule-based materials has been presented on the basis of effective model Hamiltonians, where necessary parameter values have been determined by the first principle calculations of cluster models and/or band models. These properties of the matetials are qualitatively discussed on the basis of the spin and pseudo-spin Hamiltonian models, where several quantum operators are expressed by spin variables under the two level approximation. As an example, ab initio broken-symmetry DFT calculations are performed for cyclic magnetic ring constructed of 34 hydrogen atoms in order to obtain effective exchange integrals in the spin Hamiltonian model. The natural orbital analysis of the DFT solution was performed to obtain symmetry-adapted molecular orbitals and their occupation numbers. Several chemical indices such as information entropy and unpaired electron density were calculated on the basis of the occupation numbers to elucidate the spin and pair correlations, and bonding characteristic (kinetic correlation) of this mesoscopic magnetic ring. Both classical and quantum effects for spin alignments and singlet spin-pair formations are discussed on the basis of the true spin Hamiltonian model in detail. Quantum effects are also discussed in the case of superconductivity, atom optics and quantum optics based on the pseudo spin Hamiltonian models. The coherent and squeezed states of spins, atoms and quantum field are discussed to obtain a unified picture for correlation, coherence and decoherence in future materials. Implications of theoretical results are examined in relation to recent experiments on molecule-based materials and molecular design of future molecular soft materials in the intersection area between molecular and biomolecular materials.

Theoretical studies of molecule-based magnetic conductors

Our theoretical efforts towards molecule-based magnetic conductors and superconductors on the basis of ab initio Hamiltonians and effective model Hamiltonians are summarized in relation to recently developed π–d systems, for which transition metal complexes have been used as spin sources. Organic π-electron donors or acceptors coupling with organic radicals (R) are also investigated as possible π–R interaction systems. In order to elucidate electronic and magnetic properties of these species, effective exchange integrals (Jab) for magnetic clusters are calculated by ab initio hybrid density functional (HDFT) methods. The ab initio Jab values are numerically reproduced by using model Hamitonians such as t–J, Kondo, Anderson and RKKY models. Theoretical possibilities of magnetic conductors and spin-mediated superconductors are elucidated on the basis of these models in the intermediate region for metal–insulator transitions. Interrelationships among magnetism, superconductivity and fluctuations in strongly correlated electron systems are discussed on the basis of the SO(5) and three-dimensional quantum electrodynamics (QED3) theories. External magnetic field effects such as Jaccarino–Peter effect are also examined for elucidation of magnetic field induced superconductivity. Implications of the calculated results are finally discussed in order to obtain a unified picture of many p–d, π–d and π–R molecule-based systems with strong electron correlations.

Non-Hermitian effective Hamiltonian and continuum shell model

The intrinsic dynamics of a system with open decay channels is described by an effective non-Hermitian Hamiltonian which at the same time allows one to find the external dynamics, - reaction cross sections. We discuss ways of incorporating this approach into the shell model context. Several examples of increasing complexity, from schematic models to realistic nuclear calculations (chain of oxygen isotopes), are presented. The approach is capable of describing a multitude of phenomena in a unified way combining physics of structure and reactions. Self-consistency of calculations and threshold energy dependence of the coupling to the continuum are crucial for the description of loosely bound states.

The overtone spectrum of C 2D 2 and C 2H 2 by ICLAS-VECSEL near 1 μm

The intracavity laser absorption spectra (ICLAS) of dideuteroacetylene, C 2D 2, and acetylene, C 2H 2, have been recorded between 1.03 and 0.99 μm with a vertical external cavity surface emitting laser (VECSEL) leading to the observation of seven and six bands, for C 2D 2 and C 2H 2 respectively, most of them newly reported. The strong ν 1+3 ν 3 band of C 2D 2 at 9794.07 cm −1 is found accompanied by the two Π–Π hot bands with v 4=1 and v 5=1 lower state and by the ν 2+3 ν 3+2 ν 4 band near 9935 cm −1 . This last band results from an intensity transfer from the ν 1+3 ν 3 band induced by the 1/244 anharmonic interaction. The ν 1+3 ν 3 band of 13 C 12 CD 2 , present in natural abundance in the sample, could also be detected at 9746.16 cm −1 in full agreement with local mode model predictions. The different bands of both C 2H 2 and C 2D 2 were found mostly unperturbed and the spectroscopic parameters retrieved from the rovibrational analyses agree satisfactorily with the predictions of the respective effective Hamiltonian models.

Weak overtone transitions of N 2O around 1.05 μm by ICLAS-VECSEL

The weak overtone transitions of nitrous oxide, N 2O, have been investigated around 1.05 μm by Fourier Transform spectroscopy and intracavity laser absorption spectroscopy (ICLAS) using different vertical external cavity surface emitting lasers (VECSELs). Nine bands were rotationally analyzed revealing the occurrence of some local rotational perturbations. The interaction mechanisms and the perturbers are univocally assigned on the basis of the effective Hamiltonian model. In two cases, interpolyad couplings were evidenced indicating that the polyad version of the effective Hamiltonian has to be extended to include Coriolis and interpolyad anharmonic interactions.

The overtone spectrum of carbonyl sulfide in the region of the ν1+4 ν3 and 5 ν3 bands by ICLAS-VECSEL

The high-resolution overtone spectrum of OCS has been recorded in the region of the ν 1+4 ν 3 and 5 ν 3 bands by intracavity laser absorption spectroscopy based on an optically pumped vertical external cavity surface emitting laser (VECSEL). The extremely weak ν 1+4 ν 3 band at 8954.87 cm −1 was found to be isolated. The 5 ν 3 band at 10080.91 cm −1 is accompanied by two weaker bands at 9933.53 and 10114.02 cm −1 assigned to the 12 04–00 00 and 04 04–00 00 bands, respectively. In addition, the 01 15–01 10 hot band was detected together with the extremely weak band heads of the R branch of the 02 0,25–02 0,20 hot bands. Finally, the 5 ν 3 band of the 16O 12C 34S minor isotopomer, present in natural abundance in the sample, was also observed and rotationally analyzed. Effective state parameters could be retrieved by standard band-by-band rotational fitting of the line positions, leading to a typical rms of 0.006 cm −1 . The observed line positions were compared to the predictions of the global model described by Rhaibi et al. [J. Mol. Spectrosc. 191 (1998) 32–44]. In general, the agreement is excellent, close to the experimental uncertainty ( 0.01 cm −1 ) thus confirming the high predictive ability of this effective Hamiltonian model. Weak but significant deviations up to 0.1 cm −1 were, however, identified for two rotational levels of the highly excited 2,16 0,0 dark state, observed through a local interaction with the 00 05 state. In the case of the 16O 12C 34S isotopomer, the predicted line wavenumbers of the 5 ν 3 band were globally overestimated by about 0.04 cm −1 . The new data have been included in the corresponding global model, leading to almost unchanged values of the molecular parameters and a statistical agreement with the experiment.

Alternative representation of time-dependent Hamiltonians with application to laser-driven systems

A representation of time-dependent Hamiltonians that describe laser-driven systems is presented. Unlike the well-known time-independent dressed potentials that are functions of the characteristic parameter ${\ensuremath{\alpha}}_{0}=\sqrt{I}/{\ensuremath{\omega}}^{2},$ where $\ensuremath{\omega}$ and I are the laser frequency and intensity, this approach provides a time-averaged potential that depends explicitly on the field parameters; e.g., I, $\ensuremath{\omega},$ and shape of the laser pulse. The modified dressed potential is $\ensuremath{\Elzxh}$ independent and adds a classical time-independent potential barrier to the Kramers-Henneberger dressed potential. We show that this dynamical potential barrier is identical to the Kapitza effective classical potential energy obtained for the motion of a particle in a rapidly oscillating field. As an illustrative numerical example, a simple one-electron effective model Hamiltonian of xenon atom in strong laser field is studied. We show that the zero-order quasienergies obtained by our representation are reasonably accurate and the second order high-frequency perturbation calculations provide quite accurately the lifetime of the photoionized electron for a broad range of laser frequencies.

Interplay of quantum magnetic and potential scattering around Zn and Ni impurity ions in superconducting cuprates

To describe the scattering of superconducting quasiparticles from non-magnetic (Zn) or magnetic (Ni) impurities in optimally doped high T$_c$ cuprates, we propose an effective Anderson model Hamiltonian of a localized electron hybridizing with $d_{x^2-y^2}$-wave BCS type superconducting quasiparticles with an attractive scalar potential at the impurity site. Due to the strong local antiferromagnetic couplings between the original Cu ions and their nearest neighbors, the localized electron in the Ni-doped materials is assumed to be on the impurity sites, while in the Zn-doped materials the localized electron is distributed over the four nearest neighbor sites of the impurities with a dominant $d_{x^2-y^2}$ symmetric form of the wave function. With Ni impurities, two resonant states are formed above the Fermi level in the local density of states at the impurity site, while for Zn impurities a sharp resonant peak below the Fermi level dominates in the local density of states at the Zn site, accompanied by a small and broad resonant state above the Fermi level mainly induced by the potential scattering. In both cases, there are no Kondo screening effects. The local density of states and their spatial distribution at the dominant resonant energy around the substituted impurities are calculated for both cases, and they are in good agreement with the experimental results of scanning tunneling microscopy in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ with Zn or Ni impurities, respectively.

Spectroscopy and dynamics of the isolated sp2 CH chromophore in trideuteroacetaldehyde CD3CHO as derived from extrapolated SDCI ab initio calculations

Ab initio CI potential energy (PES) and dipole moment (DMS) surfaces have been calculated with singles and doubles excitation configuration interaction (SDCI) for the 2-dimensional isolated sp2 CH chromophore subspace of trideuteroacetaldehyde (CD3CHO). Different extrapolation schemes to full-CI have been applied after the extrapolation to full-SDCI. Vibrational band centres and absolute intensities are determined variationally on six extrapolated surfaces. The band centres are analysed within the effective Hamiltonian model for isolated CH chromophores and the effective spectroscopic parameters are compared for the different extrapolation schemes. Time dependent population evolution for vibrational quantum motion with a pure CH stretching state being initially populated is calculated for some of the extrapolated surfaces within the effective Hamiltonian model.

Unexpected simplicity in the S1–S dispersed fluorescence spectra of C213H2

We have recorded dispersed fluorescence (DF) spectra (18 cm−1 resolution) from the JKaKc=110 rotational level of six vibrational levels in the S1 (Ã 1Au) state of C213H2. Improvements in our methods of recording and calibrating DF spectra, that have enhanced the quality of our data sets, are briefly discussed. More than 50 fractionated bright state patterns associated with approximately conserved polyad quantum numbers have been extracted from our DF data sets using a spectroscopic pattern recognition technique, extended cross correlation. These polyads extend to internal energies as high as 20 000 cm−1 above the zero-point vibrational level. The polyad fractionation patterns observed at high energy are surprisingly simple relative to the corresponding patterns of C212H2. Comparison between the DF spectra of C213H2 and C212H2 reveals slower intramolecular vibration redistribution in C213H2, particularly with nonzero quanta of CC stretch excitation. More than 15 patterns were extracted above the energy at which acetylene↔vinylidene isomerization is predicted to be energetically feasible (∼15 200 cm−1) and the dynamical information encoded in these patterns is addressed. In particular, we have analyzed a subset of the C213H2 polyads, the pure bending polyads, those with zero quanta of excitation in each of the stretch modes, (Ns=v1+v2+v3=0). The observed pure bending levels are reproduced to a root-mean-square error of <1.5 cm−1 by two different effective Hamiltonian models: an 11 parameter normal-mode and a 13 parameter local-mode model.

Renormalization of an effective model hamiltonian by a counterterm

An ill-defined integral equation for modeling the mass-spectrum of mesons is regulated with an additional but unphysical parameter. This parameter dependance is removed by renormalization. Illustrative graphical examples are given.

Intracavity laser absorption spectroscopy of N 2O with a vertical external cavity surface emitting laser

The Intracavity Laser Absorption Spectrum (ICLAS) of nitrous oxide, 12 N 2 16 O , has been recorded between 9560 and 9980 cm −1 with a Vertical External Cavity Surface Emitting Laser (VECSEL). Thirteen bands were observed, 11 of which are new. The rovibrational analysis has revealed the occurrence of a number of local perturbations due to anharmonic or Coriolis couplings, which could be analysed on the basis of the polyad model of effective Hamiltonian.

High-resolution analysis of the ν 2 +2ν 3 band of HDO

The Fourier transform spectrum of the ν2 + 2ν3 band of the HDO molecule was recorded with a resolution of 0.02 cm-1. The spectrum was rotational analysed and the spectroscopic parameters of the (0,1,2) state were estimated in terms of Watson's effective rotational Hamiltonian model and also the model in the Pade-Borel approximation form. They reproduce the upper energy levels with an accuracy close to the experimental uncertainty of 0.001 cm-1.

The infrared-ultraviolet dispersed fluorescence spectrum of acetylene: New classes of bright states

Single rotational levels of ungerade vibrational levels, 2ν3′+ν6′ and 3ν3′+ν6′ (both with bu symmetry), in the à 1Au electronically excited state of acetylene were excited by an IR-UV double resonance scheme via the ν3″ fundamental level in the X̃ 1Σg+ state, and the rotationally resolved dispersed fluorescence (DF) spectra were recorded at 3.2–4.5 cm−1 resolution. The term values of the new ungerade levels were determined within an accuracy of 0.56 cm−1(1σ) through careful calibration achieved by frequency standard atomic Fe and Hg lines. A total of 111 new ungerade vibrational levels with Σu+, Σu−, and Δu symmetry below 10 000 cm−1 was identified in the high-resolution IR-UV-DF spectra, which provide access to new classes of X̃ 1Σg+ bright states: (i) (0,v2″,0,v4″1,1−1)Σu+, (0,v2″,0,v4″1,11)Δu, and (0,v2″,0,v4″3,1−1)Δu, which are the Franck–Condon (FC) bright levels from the nν3′+ν6′ (n=2,3) levels in the à 1Au state; (ii) (0,v2″,0,v4″−1,11)Σu− levels which appear through the a-axis Corioris interaction between nν3′+ν6′ and nν3′+ν4′ (n=2,3) in the à 1Au state; and (iii) (0,v2″,1,v4″0,0)Σu+ and (0,v2″,1,v4″2,0)Δu levels which gain transition intensity from the Duschinsky effect associated with the bent-linear ÖX̃ transition. All observed ungerade term values and previously determined gerade and ungerade term values below 10 000 cm−1 were fitted by two effective model Hamiltonians, i.e., a pure-bend effective Hamiltonian and a stretch–bend effective Hamiltonian. The stretch–bend effective Hamiltonian is expressed in terms of 31 Dunham expansion parameters and 11 anharmonic resonance parameters associated with (i) five stretch–bend anharmonic resonances; (ii) one stretch–stretch and two bend–bend Darling–Dennison resonances; and (iii) one vibrational l resonance. The parameters in this Hamiltonian were determined from a least-squares fit of 287 vibrational term values (111 new ungerade levels, 128 levels from absorption, 1 level from stimulated Raman, 13 levels from stimulated emission pumping (SEP), and 34 levels from UV-DF spectroscopy) below 10 000 cm−1 with a standard deviation of σ=1.21 cm−1. The FC patterns for the v4″=odd ungerade levels, (0,v2″,0,v4″,1), in the IR-UV-DF spectra were derived, and the nodes along the v4″ trans-bend mode were found at v4″=11 via the 2ν3′+ν6′ upper state, and at v4″=9 and 15 via the 3ν3′+ν6′ upper state, which is consistent with the ν3′ dependence of the FC patterns observed in previous UV-DF studies.

Ionization-detected optical–optical double resonance spectroscopic studies of moderate energy Rydberg states of calcium monofluoride

This paper describes a systematic investigation of quasi-bound Rydberg states of calcium monofluoride (CaF) existing between the molecule's υ+ = 0 and 1 ionization thresholds. Experiments utilized ionization-detected optical–optical double resonance spectroscopy to assign states as belonging to one of the six core-penetrating ([Formula: see text] [Formula: see text] 2) or to a core-nonpenetrating ([Formula: see text] [Formula: see text] 3) Rydberg series. Most states observed had effective principal quantum number, ν, between 12 and 18 and one quantum of vibrational excitation in the CaF+ ion-core, although lower ν, υ [Formula: see text] = 2 states were also identified. Core-nonpenetrating states were observed both directly and through avoided crossings with core-penetrating states. Five of the seven [Formula: see text] components in the f-complexes derived from Ca+, 13f and n = 14f, have been identified. We present a detailed analysis of the CaF electronic structure for 12.5 [Formula: see text] ν [Formula: see text] 14.6, υ = 1 using an effective Hamiltonian model to describe CaF+ ion-core-induced [Formula: see text]-mixing between [Formula: see text] [Formula: see text] 3 (s,p, d, and f) Ca+ atomic orbitals. An observed avoided crossing between the 14.19 2Σ+, υ = 1 and 14f ([Formula: see text] = –3), υ = 1 states implies that the previously identified 0.19 Σ+ core-penetrating series has 20–30% f 2υ+-character. The effective Hamiltonian approach accounts for much of the data, however, a complete accounting requires the use of multichannel quantum defect theory (MQDT). An MQDT analysis of the data presented here is provided in a companion paper by Jungen and Roche in this issue. The effective Hamiltonian model enabled derivation of electrostatic properties of the CaF+ core as well as the 0.14Δ series quantum defect derivative, [dδ/dR]Re+, which governs the exchange of energy between the Rydberg electron and the CaF+ ion-core. The CaF+ electric quadrupole moment, defined with the coordinate origin at the center-of-charge, is 11.3 ± 0.5 a.u. PACS Nos.: 33.40+f, 33.80Eh, 33.15Ry, 33.15Ta