Magnetic breakdown - Effective Hamiltonian and de Haas-van Alphen effect.
Magnetic breakdown on usual effective Hamiltonian theory for Bloch electrons in magnetic field, using simple two-dimensional rectangular model
SOLID STATE PHYSICS↗
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An EPR investigation of the dynamic Jahn-Teller effect in SrCl2:y(2 plus) and SrCl2:Sc(2 plus)
EPR spectra have been observed for SrCl2:Y(2+) and SrCl2:Sc(2+) at liquid helium temperatures. At 1.2 K the spectra were dominated by anisotropic hyperfine patterns whose lineshapes and angular dependences were explained using second order solutions of the effective Hamiltonian for an isolated 2Eg state split by large random internal strains. Pronounced asymmetries in some of the strin produced lineshapes for Srcl2:Sc(2+) are shown to result from second order terms in the solution of the effective Hamiltonian. Coexisting with the anisotropic hyperfine patterns are weak nearly isotropic hyperfine patterns with typical lineshapes. Variations in the apparent intensity of lines in these weak hyperfine patterns as functions of the applied magnetic field direction and temperature imply that these lines result from averaging by vibronic relaxation of a portion of the anisotropic pattern. The effective Hamiltonian parameters for SrCl2:La(2+), SrCl2:y(2+), and SrCl2:SC(2+) are analyzed in terms of crystal field theory modified to include a dynamic Jahn-Teller effect.
Herrington, J. R.↗
Preliminary Modeling of CH3D From 4000 to 4550 cm (exp-1)
A new study of 12CH3D line positions and intensities was performed for the upper portion of the Enneadecad polyad between 4000 and 4550/cm. For this, FTIR spectra were recorded with D-enriched methane samples (at 80 K with a Bruker 125 IFS at 0.005/cm resolution and at 291 K with the McMath-Pierce FTS at 0.011/cm resolution, respectively). Line positions and intensities were retrieved by least square curve-fitting procedures and analyzed using the effective Hamiltonian and the effective dipole moment expressed in terms of irreducible tensor operators adapted to symmetric top molecules. Initially, only the cold spectrum was used to identify quantum assignments and predict 12CH3D relative intensities in this region. To assign higher quanta up to J equal 14, additional line positions and intensities were obtained from two room temperature spectra. In the final stage, measured intensities from both the cold and the room temperature data were normalized to corresponding values at 296 K and then averaged. Combining the two temperature datasets confirmed the assumed quantum assignments and also demonstrated the relative accuracies to be better than 70.0002/cm for line positions and at least +/-6% for intensities so that approx.1160 features were selected. Including additional assignments from the room temperature spectra alone permitted 1362 line intensities of 11 bands (involving 23 vibrational symmetry components) to be reproduced with an RMS of 9%. Over 4085 selected positions for 12 bands were modeled to 0.008/cm. Nevertheless a number of known assignments could not be modeled to within our experimental precisions. More work is needed to obtain a complete characterization of this complex polyad.
Nikitin, A. V.↗
Experimental and Ab Initio Studies of the HDO Absorption Spectrum in the 13165-13500 1/cm Spectral Region
The HDO absorption spectrum has been recorded in the 13165 - 13500 cm(exp-1) spectral region by Intracavity Laser Absorption Spectroscopy. The spectrum (615 lines), dominated by the 2n2 + 3n3 and n1+3n3 bands was assigned and modeled leading to the derivation of 196 accurate energy levels of the (103) and (023) vibrational states. Finally, 150 of these levels have been reproduced by an effective Hamiltonian involving two vibrational dark states interacting with the (023) and ( 103) bright states. The rms deviation achieved by variation of 28 parameters is 0.05-1 cm, compared to an averaged experimental uncertainty of 0.007-1 cm, indicating the limit of validity of the effective Hamiltonian approach for HDO at high vibrational excitation. The predictions of previous ab initio calculations of the HDO spectrum were extensively used in the assignment process. The particular spectral region under consideration has been used to test and discuss the improvements of new ab initio calculations recently performed on the basis of the same potential energy surface but with an improved dipole moment surface. The improvements concern both the energy levels and the line intensities. In particular, the strong hybrid character of the n1+3n3 band is very well accounted for by the the new ab initio calculations.
Schwenke, David↗
Quantitative validation of Ames IR intensity and new line lists for (32/33/34)S(16)O2, (32)S(18)O2 and (16)O(32)S(18)O
The quality of Ames-296K SO2 Infrared (IR) line list intensities is first validated by quantitative exploration of several dipole moment surfaces (DMSs) and partition sum convergence. The DMSs are computed with several of Dunning’s correlation-consistent basis sets and their vibrational dependence are compared to the empirical model derived from Stark effect experiments reported by D. Patel, D. Margolese, and T.R. Dykea [J.Chem.Phys. 70, 2740 (1979)]. The effective dipole deviations from the DMS adopted in the Ames IR lists is 0.2-0.4% for vibrational states up to 3v3. The vibrational dependence of the dipole moment is also in good agreement, except for nv1. Partition sum convergence at 296K is confirmed by new calculations with rotational quantum number J up to 150 and upper state E’ up to 8000 cm-1. The isotopologue consistency of the Ames IR line lists is superior relative to the regular Effective Hamiltonian (EH) models and Effective Dipole Moment (EDM) models. The v1+v2 and v2+v3 intensity consistency check reveals the recently reported experimental intensities need significant improvement or re-analysis. After the accuracy, convergence, and isotopologue consistency have been confirmed, the theoretical Ames-296K intensities are combined with the experimental line positions or EH models that experimental spectroscopists published after 2009. Three high-resolution IR line sets are reported for the (32/33/34)S(16)O2, (32)S(18)O2 and (16)O(32)S(18)O isotopologues: (1) the “New Lines Sets” include experimentally measured line positions; (2) the “Expanded Line Sets” include possible transitions among new rovibrational levels assigned in experiments and ground state (GS) levels predicted by reliable EH models; (3) the “Ames + MARVEL Sets” include possible transitions among all those levels reported in a recent MARVEL analysis. [Tóbiás et al, JQSRT 208, 152 (2018)]. Compared to the limited data in High-resolution TRANsmission molecular absorption database (HITRAN), these line sets have significantly improved the data coverage up to 4000 cm-1. Some missing bands can be traced to the unpublished experimental data. The isotopologue consistency of these line sets will help identify the uncertainties and defects in the experimental EH and EDM models. These line sets are good candidates for the next HITRAN update, if line shape parameters are available. The line sets can be downloaded from supplementary files or from the Ames Molecular Spectroscopic Database at http://huang.seti.org.
Xinchuan Huang↗
Evolution of wave function in a dissipative system
For a dissipative system with Ohmic friction, we obtain a simple and exact solution for the wave function of the system plus the bath. It is described by the direct product in two independent Hilbert space. One of them is described by an effective Hamiltonian, the other represents the effect of the bath, i.e., the Brownian motion, thus clarifying the structure of the wave function of the system whose energy is dissipated by its interaction with the bath. No path integral technology is needed in this treatment. The derivation of the Weisskopf-Wigner line width theory follows easily.
Yu, Li-Hua↗
Isotopologue Consistency of Semi-Empirically Computed InfraRed Line Lists and Further Improvement for Rare Isotopologues: CO2 and SO2 Case Studies.
The semi-empirical molecular rovibrational IR line lists, such as ExoMol, TheoReTs, and Ames, combine the experimental accuracy and theoretical power to reach better than 0.1 cm-1 accuracy for line positions and better than 80-90% agreement for line intensities. The quality of these existing semi-empirical IR lists allows further improvements of intensity and line positions for those unobserved minor isotopologues. This paper presents our new BTRHE (Best Theory + Reliable High-resolution Experiment) strategy implementation. For line intensity, the isotopologue consistency and the patterns of mass dependence in the Ames-296K SO2 and CO2 IR lists are quantitatively presented along the mass-inverse coordinates. The consistency and patterns are better than those in existing experimental data. The methodology proposed here can be used to identify inconsistencies, outliers, and mistakes in intensities, and help improve Effective Dipole Model (EDM) and molecular IR databases. We call for an experimental study on the 50006 and 60007 bands of CO2 628. For line position predictions, a simple approach combining the variational IR line lists with Effective Hamiltonian (EH) model may refine the effective rotational constants A0/B0/C0 and quartic centrifugal distortion constants of minor isotopologues. The prediction accuracy may be improved by two orders of magnitude, i.e. reaching 0-5 MHz prediction accuracy in the range of J<20-30, Ka<10-20, and 0.01-0.02 MHz accuracy for A0/B0/C0. Several important factors have been systematically investigated and discussed, e.g. convergence, uncertainties, higher order terms, fixing EH parameters, mass coordinates, etc. Amicrowave (MW) line set consisting of 644,636 strong transitions for all 30 isotopologues and corresponding refined EH(Ames) parameters are reported in the supplementary material. This approach may be easily extended to rovibrational bands, hot bands, and other molecular systems.
Xinchuan Huang↗
Utilizing Experimental-based Line Positions for Semi-empirical IR Line Lists
Molecular IR line lists computed from semi-empirically refined ab initio potential energy surface and high quality ab initio dipole moment surface may have line position accuracy typically within 0.01 - 0.05 cm−1. For high resolution spectroscopy databases, it is necessary to integrate the computed theoretical IR intensities with the line positions accurately determined from experiments and (or) reliably derived from Effective Hamiltonian models. However, it is not a trivial task, and the choices in reality are heavily contingent upon the coverage, consistency, and accuracy of the data available for a specific molecule or isotopologue. We will present several approaches applied to recent Ames IR line lists of CO 2 1, N 2 O 2 , and OCS to demonstrate how challenging such integration may become, and what we have learned From these projects. Discussions will focus on the relation between each different scenario and the corresponding choice or solution, including their advantages and limits, how the semi-empirical IR line lists can help, and what else may be needed for future improvements. We will emphasize that the “Theory+Experiment” synergy may still play significant role in the determination of the best line positions.
Effective Hamiltonian models↗
Boson mapping techniques applied to constant gauge fields in QCD
Pairs of coordinates and derivatives of the constant gluon modes are mapped to new gluon-pair fields and their derivatives. Applying this mapping to the Hamiltonian of constant gluon fields results for large coupling constants into an effective Hamiltonian which separates into one describing a scalar field and another one for a field with spin two. The ground state is dominated by pairs of gluons coupled to color and spin zero with slight admixtures of color zero and spin two pairs. As color group we used SU(2).
Hess, Peter Otto↗
The electronic Hamiltonian for cuprates
A realistic many-body Hamiltonian for the cuprate superconductors should include both copper d and oxygen p states, hopping matrix elements between them, and Coulomb energies, both on-site and inter-site. We have developed a novel computational scheme for deriving the relevant parameters ab initio from a constrained occupation local density functional. The scheme includes numerical calculation of appropriate Wannier functions for the copper and oxygen states. Explicit parameter values are given for La2CuO4. These parameters are generally consistent with other estimates and with the observed superexchange energy. Secondly, we address whether this complicated multi-band Hamiltonian can be reduced to a simpler one with fewer basis states per unit cell. We propose a mapping onto a new two-band effective Hamiltonian with one copper d and one oxygen p derived state per unit cell. This mapping takes into account the large oxygen-oxygen hopping given by the ab initio calculations.
Annett, James F.↗
Realizations of magnetic-monopole gauge fields - Diatoms and spin precession
It is found that the effective Hamiltonian for nuclear rotation in a diatom is equivalent to that of a charged particle in a background magnetic-monopole field. In certain cases, half-integer orbital angular momentum or non-Abelian fields occur. Furthermore, the effects of magnetic-monopole-like gauge fields can be experimentally observed in spin-resonance experiments with variable magnetic fields.
Moody, J.↗
The hyperfine splitting of the interaction energy of two hydrogen atoms.
Hyperfine splitting of spin interaction energy of two hydrogen atoms, determining eigenfunctions for effective Hamiltonian
HYPERFINE STRUCTURE↗
Study of diatomic molecules. 2: Intensities
The theory of perturbations, giving the diatomic effective Hamiltonian, is used for calculating actual molecular wave functions and intensity factors involved in transitions between states arising from Hund's coupling cases a,b, intermediate a-b, and c tendency. The Herman and Wallis corrections are derived, without any knowledge of the analytical expressions of the wave functions, and generalized to transitions between electronic states with whatever symmetry and multiplicity. A general method for studying perturbed intensities is presented using primarily modern spectroscopic numerical approaches. The method is used in the study of the ScO optical emission spectrum.
Femenias, J. L.↗
The B/K/ method - Application to methylene
The B(K) method is compared with conventional Configuration Interaction (CI) and other perturbation methods for the 3B1 and 1A1 states of methylene. Use of Rayleigh-Schroedinger perturbation theory for construction of an effective Hamiltonian is seen to be more accurate for estimating the full CI energy limit.
Davidson, E. R.↗
The far-infrared laser magnetic resonance spectrum of the SiH radical and determination of ground state parameters
The far-infrared laser magnetic resonance spectrum of the SiH radical in the v = O level of its X2Pi state has been recorded. The signals are rather weak. The molecules were generated in the reaction between fluorine atoms and SiH4. Rotational transitions have been detected in both 2Pi1/2 and 2Pi3/2 spin components but no fine structure transitions between the spin components were observed. Proton hyperfine splittings were resolved on some lines. The measurements have been analyzed, subjected to a least-squares fit using an effective Hamiltonian, and the appropriate molecular parameters determined. The weakness of the spectrum and the failure of attempts to power saturate favorable lines are both consistent with a small value for the electric dipole moment for SiH.
Brown, J. M.↗
Infrared and far-infrared laser magnetic resonance spectroscopy of the GeH radical - Determination of ground state parameters
The GeH radical has been detected in its ground 2 Pi state in the gas phase reaction of fluorine atoms with GeH4 by laser magnetic resonance techniques. Rotational transitions within both 2 Pi 1/2 and 2 Pi 3/2 manifolds have been observed at far-infrared wavelengths and rotational transitions between the two fine structure components have been detected at infrared wavelengths (10 microns). Signals have been observed for all five naturally occurring isotopes of germanium. Nuclear hyperfine structure for H-1 and Ge-73 has also been observed. The data for the dominant isotope (/Ge-74/H) have been fitted to within experimental error by an effective Hamiltonian to give a set of molecular parameters for the X 2 Pi state which is very nearly complete. In addition, the dipole moment of GeH in its ground state has been estimated from the relative intensities of electric and magnetic dipole transitions in the 10 micron spectrum to be 1.24(+ or - 0.10) D.
Brown, J. M.↗
The microwave and far-infrared spectra of the O-(18)H radical
Far-infrared laser magnetic resonance (LMR) spectroscopy was used to calculate the frequencies, wavelengths, and line strengths for transitions of O-(18)H molecules at microwave and far-infrared frequencies. In this experiment, a molecular transition frequency is tuned into coincidence with that of a fixed frequency laser by the application of a variable magnetic field. The O-(18)H radicals, detected in natural abundance (0.20 percent), were produced by the reaction of hydrogen atoms with nitrogen dioxide. These data together with microwave frequencies ascertained by Gottlieb, Redford, and Smith (1974) were used to determine the parameters of an effective Hamiltonian. Rotational levels up to J = 5.5 were involved. Results are indicated schematically and the low-lying energy levels of O-(18)H are shown. It is concluded that the frequencies of transitions between levels studied directly in the LMR experiment are reliable.
Comben, E. R.↗
A quantum theoretical study of polyimides
One of the most important contributions of theoretical chemistry is the correct prediction of properties of materials before any costly experimental work begins. This is especially true in the field of electrically conducting polymers. Development of the Valence Effective Hamiltonian (VEH) technique for the calculation of the band structure of polymers was initiated. The necessary VEH potentials were developed for the sulfur and oxygen atoms within the particular molecular environments and the explanation explored for the success of this approximate method in predicting the optical properties of conducting polymers.
Burke, Luke A.↗