Effective Hamiltonian Parameters Research Articles

Submillimeter wave spectrum of methylene chloride, [formula omitted]CH[formula omitted]Cl[formula omitted], [formula omitted]CH[formula omitted]Cl[formula omitted]Cl and [formula omitted]CH[formula omitted]Cl[formula omitted] up to 1.1 THz

High resolution spectra of methylene chloride in natural abundance are recorded in wide spectral regions from 0.075 up to 1.090 THz. The 5095 multiplet center frequencies with the value of quantum number Jmax=107 and Kamax=20 were assigned to the 12CH235Cl2 species. A weighed fit of the experimental data allowed us to obtain a set of 20 rotational and centrifugal distortion parameters which reproduce the initial experimental data with the drms=19 kHz in the whole region. Comparison with the literature values from microwave and from far infrared measurements is made. An analogous analysis was carried out for the 12CH235Cl37Cl and 12CH237Cl2 species for which 4561 and 2465 transitions with Jmax=100, Kamax=19 and Jmax=88, Kamax=19 where assigned and analyzed. Sets of 20 fitted effective Hamiltonian parameters of 12CH235Cl37Cl and 15 fitted parameters of 12CH237Cl2 reproduce the assigned experimental transitions of the latter two isotopologues with the drms=20 kHz and drms=19 kHz, respectively and considerably improve the calculated line positions up to 1.1 THz in comparison with previous parameters.

The ν3 band of 16O14N18O: Line positions and intensities

The Fourier transform IR spectra of samples prepared by mixing two gaseous species 18O2/14N16O (1:2) have been recorded in the region of the ν3 band of nitrogen dioxide. The spectra contain the lines corresponding to the ν3 band of the 16O14N18O isotopologue within the 1540–1640 cm−1. In total 1795 lines of the ν3 band of this isotopologue were assigned with the rotational quantum numbers N and Ka up to 51 and 12, respectively, what corresponds to 3487 electron spin-rotation-vibration transitions. The overall measured set of the line positions was used to fit the effective Hamiltonian parameters. The fitted set of the parameters reproduces the observed line positions with an rms of 3.6 × 10−3 cm−1. A selected set of the measured line intensities was used to determine the effective dipole moment parameters describing the line intensities of the ν3 band. The rms deviation of the fit is 5.0%. It was found that the lines with the ΔKa = ±1 are very weak compared to those with the ΔKa =0. At attained sensitivity only few lines with the ΔKa = ±1 were assigned. The measured line intensities lead to the small value of the dipole moment derivatives ratio |(∂μx/∂q3)(∂μz/∂q3)|≈0.139.

Janus 2H-VSSe monolayer: two-dimensional valleytronic semiconductor with nonvolatile valley polarization

Valleytronic as a hot topic in recent years focuses on electrons’ valley degree of freedom as a quantum information carrier. Here, by combining two-band k.p model with high-throughput density functional theory (DFT) calculations, the valley states of Janus 2H-VSSe monolayer are studied which have spontaneous polarization. Nonvolatile valley polarization state is mainly arises from intrinsic ferromagnetism contributed by V-3d electronic configuration and not the spontaneous out-of-plane dipole moment of VSSe monolayer. The effective Hamiltonian model and DFT calculations both showed that the valley splitting mainly originates from the smaller spin splitting coming from the spin–orbit coupling effect rather than the spin splitting of magnetic exchange field. By using the effective Dirac Hamiltonian and Kubo formula, we further calculated the longitudinal and transversal conductivities and absorption spectra of VSSe monolayer which exhibits an anomalous valley Hall effect and clear valley-selective circular dichroism. Our calculations indicate that the modification of valley and spin splitting related to Berry curvature by applying an external strain is more noticeable than by the change of the magnetic moment orientation and electric field. We found that carriers accumulation with particular spin and valley label can be manipulated by tuning effective Hamiltonian parameters. The coexistence of robust in-plane magnetic ordering and spontaneous valley polarization of 2H-VSSe monolayer supports the possibility of applications in spintronics, valleytronics and optoelectronics devices.

Global modeling of the 12C32S2 line positions within the framework of the non-polyad model of effective Hamiltonian

The global modeling of 12C32S2 line positions in the 240 – 12 000 cm−1 region has been performed using the non-polyad model of effective Hamiltonian. The effective Hamiltonian parameters were fitted to the measured line positions collected from the literature. The fitted set of 99 effective Hamiltonian parameters allowed reproduction of more than 13 000 measured line positions with the dimensionless weighted standard deviation of 1.65. The root-mean-square of errors of the fitted high-resolution rotation-vibration line positions in the 240 - 466 cm−1 range is 0.0013 cm−1. A comparison of the calculated line positions based on the fitted model with HITRAN2020 is presented and discussed.

Спектроскопия высокого разрешения сильно резонирующих полос ν-=SUB=-4-=/SUB=-, ν-=SUB=-6-=/SUB=-, ν-=SUB=-7-=/SUB=-, ν-=SUB=-8-=/SUB=- и ν-=SUB=-10-=/SUB=- дейтерированного этилена C-=SUB=-2-=/SUB=-H-=SUB=-3-=/SUB=-D

Rotational structure of strongly interacting bands v4,v6,v7,v8, and v10 of the C2H3D molecule is spectroscopically studied. Spectra were recorded by Fourier spectrometer Brucker IFD 125HR in the laboratory of physical and theoretical chemistry of Technical University of Braunschweig. 27950 transitions with maximum values of J=40 and Ka=20 were assigned to the studied bands. The effective Hamiltonian parameters were determined in the model including the v3 resonating state. The 4028 upper energy levels were used as incoming data. They are reproduced with root mean square deviation of drms = 1.7.10-4 cm-1. Corresponding value for more than 24000 line positions is drms = 2.1.10-4 cm-1.

High resolution spectroscopy of strongly interacting bands ν-=SUB=-4-=/SUB=-, ν-=SUB=-6-=/SUB=-, ν-=SUB=-7-=/SUB=-, ν-=SUB=-8-=/SUB=-, and ν-=SUB=-10-=/SUB=- of deuterated ethylene, C-=SUB=-2-=/SUB=-H-=SUB=-3-=/SUB=-D

Rotational structure of strongly interacting bands ν4, ν6, ν7, ν8, and ν10 of the C2H3D molecule is spectroscopically studied. Spectra were recorded by Fourier spectrometer Brucker 125HR in the laboratory of physical and theoretical chemistry of Technical University of Braunschweig. 27950 transitions with maximum values of Jmax = 40 and Kmaxa= 20 were assigned to the studied bands. The effective Hamiltonian parameters were determined in the model including the ν3 resonating state. The 4028 upper energy levels were used as incoming data. They are reproduced with root mean square deviation of drms =1.7· 10-4 cm-1. Corresponding value for more than 24000 line positions is drms = 2.1 · 10-4 cm-1. Keywords: ethylene, high resolution spectroscopy, strongly interacting bands, Fourier-spectroscopy.

Neutron scattering investigation of proposed Kosterlitz-Thouless transitions in the triangular-lattice Ising antiferromagnet TmMgGaO4

The transverse-field Ising model on the triangular lattice is expected to host an intermediate finite-temperature Kosterlitz-Thouless (KT) phase through a mapping of the spins on each triangular unit to a complex order parameter. TmMgGaO$_4$ is a candidate material to realize such physics due to the non-Kramers nature of Tm$^{3+}$ ion and the resulting two-singlet single-ion ground state. Using inelastic neutron scattering, we confirm this picture by determining the leading parameters of the low-energy effective Hamiltonian of TmMgGaO$_4$. Subsequently, we track the predicted KT phase and related transitions by inspecting the field and temperature dependence of the ac susceptibility. We further probe the spin correlations in both reciprocal space and real space via single crystal neutron diffraction and magnetic total scattering techniques, respectively. Magnetic pair distribution function analysis provides evidence for the formation of vortex-antivortex pairs that characterize the proposed KT phase around 5~K. Although structural disorder influences the field-induced behavior of TmMgGaO$_4$, the magnetism in zero field appears relatively free from these effects. These results position TmMgGaO$_4$ as a strong candidate for a solid-state realization of KT physics in a dense spin system.

Line intensities of the 01111–00001 magnetic dipole absorption band of 12C16O2: Laboratory measurements

The spectra of carbon dioxide in the 3.3 µm region were recorded at three pressures using Bruker IFS 125 HR Fourier transform spectrometer and a 30 m base multipass gas cell of V.E. Zuev Institute of Atmospheric Optics SB RAS. Several lines of the 01111–00001 (ν2 + ν3) magnetic dipole band of 12C16O2 were detected and their line intensities were measured. The vibrational transition magnetic dipole moment was fitted to the observed line intensities. The fitted value of the vibrational transition magnetic dipole moment of 0.71(1)µN is substantially smaller than the value of 0.96µN obtained in the result of the analysis of the Martian atmosphere spectra (here µN is the nuclear magneton). Using the known set of the effective Hamiltonian parameters and fitted value of the vibrational transition magnetic dipole moment the list of the line parameters of this band was generated for the HITRAN database. In addition the line intensities of the R-branch of the electric dipole 01111–00001 band of the 16O12C18O isotopologue were measured for the first time.

Analysis of thirteen absorption bands of 16O18O18O ozone isotopomer in the 950–3500 cm−1 infrared spectral range

Thirteen bands of the CS symmetry 16O18O18O ozone isotopic species were observed in spectra generated from 16O2/18O2 mixtures recorded between 950 and 3500 cm−1. Experimentally and theoretically this work is similar to the one on the 16O16O18O isotopologue analysis, recently published [Barbe A, et al. J. Quant. Spectrosc. Radiat. Transfer, 2018;218;231–247]. In total 11402 rovibrational transitions (corresponding to 8784 upper state energy levels) were assigned. The line positions are modelled with the root mean squares deviations varying from 0.001 to 0.002 cm−1. The final comparisons show a good agreement between experimental and theoretical band centres and rotational constants predicted from ab initio potential energy surface. Effective dipole transition moment parameters were either fitted or estimated from a comparison between observed and simulated spectra. The line lists built using effective Hamiltonian and transition moment parameters containing 61194 transitions are provided in Supplementary Materials.

Exploring the limits of the Data-Model-Theory synergy: “Hot” MW transitions for rovibrational IR studies

In order to further improve the accuracy of rovibrational IR line lists generated from the “Best Theory + Reliable High-resolution Experiment” (BTRHE) strategy from 0.01 to 0.05 cm−1, or 300–1500 MHz, to ∼10 MHz, we explore the current limits of the Data-Model-Theory synergy by examining the accuracy and consistency of existing data, then propose that “hot” bands in microwave (MW) spectra is the solution we need for future enhancements. The Ames SO2J = 0–20 rovibrational energy levels computed on the semi-empirically refined Ames-2 potential energy surface (PES) are fit to the Effective Hamiltonian (EH) model regularly used in the experimental infrared (IR) analysis for SO2 isotopologues. In the fitted EH(Ames) model, the rotational constants A/B/C and all 5 quartic centrifugal distortion constants display clear, systematic, and consistent patterns along the vibrational state energy or quanta. Such consistent patterns may facilitate the vibrational assignments for MW hot bands and extract more information from high temperature MW spectra. Some EH(Expt) analyses were carried out with the lowest order Coriolis Coupling term, C1. Their constants should not be directly compared with other EH(Expt) and EH(Ames) results. After excluding them, our δ = EH(Ames)- EH(Expt) analyses for 5 isotopologues (626, 636, 646, 628 and 828) indicates some loss of accuracy and consistency starting from vibrational states as low as 2ν2 or 1000 cm−1. Some EH parameters, e.g. δK, may have relative deviations as large as 50–100% and totally lose any recognizable patterns. This simply means that current EH(Expt) models do not have the system-wide consistency we need to further refine the EH(Ames) and Ames rovibrational IR line lists. A large part of such defects are probably inherited from the limited precision of experimental line positions, i.e. 1E-3 ∼ 1E-4 cm−1, or 3–30 MHz. This is confirmed in a series of truncation tests using the Ames data. Although the EH(Ames) consistency may help identify unreliable rovibrational EH(Expt) parameters, and make reliable predictions for minor isotopologues and unobserved vibrational bands, we believe only the highly accurate “hot” MW transitions can provide real enhancements for EH(Expt) accuracy and consistency. “Hot” MW spectra should play a more significant role in the future synergy of Data, Model, and Theory in the field of rovibrational IR studies.

Empirical rovibrational energy levels of ammonia up to 7500 cm[formula omitted

The most recent version of the MARVEL (Measured Active Rotational-Vibrational Energy Levels) protocol and code is used to update and extend the list of accurately known empirical rovibrational energy levels of 14NH3 falling in the range of 0−7500 cm−1. Compared to an earlier similar study covering all the measured transitions of 14NH3 [22], the present investigation is limited to transitions with an upper energy level below 7500 cm−1, considers 82 sources (28 new) of transitions data, corrects several older assignments, and utilizes an improved validation procedure based partially on high-quality first-principles rovibrational energies. This study yields 4936 uniquely labelled empirical rovibrational energy levels, the set is complete up to 2413 cm−1. We confirm the overall high accuracy of the most recent “spectroscopic” (fitted) 14NH3 potential energy surface, C2018, up to 7500 cm−1. Investigation of energy values resulting from previous effective-Hamiltonian fits forms an important part of this study. It is established that previous effective-Hamiltonian fits, using high expansion orders in the Hamiltonian, are inaccurate for certain high rotational excitations of all vibrational parents considered. Employing the ground vibrational state as a test case, it is shown that the origin of the problem is that the observed 14NH3 spectroscopic network formed by rotational transitions and used for the effective-Hamiltonian fit contains floating components. A much improved effective-Hamiltonian fit is presented whereby the floating components are connected to the principal components of the spectroscopic network by carefully selected first-principles links. It is recommended that for all molecules the experimental set of transitions employed for an effective Hamiltonian fit should be checked for floating components and extra care be exercised if they exist, as in these cases the adequate reproduction of the transitions does not automatically mean that the energies derived from the effective-Hamiltonian parameters are correct as well. The connectivity problem of measured spectroscopic networks becomes more and more pronounced as the order of the Hamiltonian is increased.

High resolution infrared spectrum of 16O3: The 3600–4300 cm−1 range reinvestigated

The spectral range from 3600 to 4300 cm−1 of ozone was reinvestigated, leading to a large improvement of the analysis of the strongest ν1+3ν3 band, visible in atmospheric spectra. Recent progress, particularly in the theoretical predictions and observation of the hot band 4ν3-ν3 has allowed identify the strong anharmonic resonance with the dark 3ν1+ν2 band. As the (310) state is also in interaction with the (211), it was necessary to include seven vibration states to correctly reproduce 3389 transitions with the root mean square deviation of 3.54 × 10−3 cm−1 for line positions and 1295 intensities within 8.6%. We report the Effective Hamiltonian parameters and the band transition moments with the corresponding statistics as well as two line lists of the vibration-rotation transitions, and associated figures of the comparisons between observed and calculated spectra. The first line list containing 15,731 transitions is directly obtained from the fitted parameters. In the second one, the calculated line positions were replaced by the observed ones, for the cases where the (νobs - νcalc) differences were larger than the experimental uncertainty. New improved information on the energy levels and transitions can be used to extend the non-LTE models of the atmospheric ozone towards the energy range above 3500 cm−1.

Assignment and modeling of the 13CH4 cold absorption spectrum in the 5471–5852 cm−1 spectral range

This work continues our investigation on the high resolution infrared 13C-enriched spectrum of methane recorded on a Bruker IFS-125HR Fourier transform spectrometer at 80 K in the 4970–6200 cm−1 range. In this paper we report the results of assignment and modelling of the line positions and intensities of 13CH4 in the range between 5471 and 5852 cm−1, corresponding to the middle part of Tetradecad. The analysis was performed using a non-empirical effective Hamiltonian (EH) derived from the ab initio potential energy surface (PES) by high-order Contact Transformations (CT). The EH parameters were empirically optimized during the treatment of experimental data. In total, 3297 lines belonging to nine cold bands of the Tetradecad of 13CH4 were assigned in the 5471–5852 cm−1 range up to Jmax = 11. The 3297 lines included correspond to 91% of the total line number in the region. Among them, 3251 line positions were fitted with an rms deviation of 1.33×10−3 cm−1. Measured line intensities for 1624 transitions were modeled using the effective dipole transition moments approach with an rms deviation of about 9%. Finally, the observed transitions were incorporated to fit simultaneously the 13CH4 Hamiltonian parameters for the {Ground state/Dyad/Pentad/Octad/Tetradecad} system and the dipole moment parameters for the {Ground state - Tetradecad} system.

The ν3 bands of 17O17O18O and 17O18O17O ozone isotopomers

This work continues the investigation of high resolution infrared spectra of 17O and 18O enriched ozone isotopomers in the 10 µm spectral range. Spectra are recorded by the Reims Fourier Transform Spectrometer. In a mixture of 18 isotopic species of ozone including 17O, 16O and 18O oxygen atoms, two ν3 bands are analyzed for the first time: those of 17O17O18O and 17O18O17O species. The analyses, performed accounting for interactions between the (100) and (001) states, permitted to assign 769 transitions for 17O18O17O and 1290 for 17O17O18O. The resulting sets of effective Hamiltonian parameters allow reproducing observed transitions within experimental accuracies and calculating synthetic spectra in excellent agreement with the observed ones. We also report here the comparison of main fitted parameters with recent theoretical predictions.

Cavity ring-down spectroscopy of 15N enriched N2O near 1.56 µm

The absorption spectrum of nitrous oxide around 1.56 µm has been recorded with Doppler limited resolution by a continuous-wave cavity ring-down spectrometer at room temperature using 15N-enriched samples. The typical sensitivity was at the level of 2 × 10−10 cm−1. In total, 3389 transitions were observed and ro-vibrationally assigned on the basis of the global effective Hamiltonian model for six nitrous oxide isotopologues (14N15N16O, 15N14N16O, 14N15N18O, 15N14N18O, 14N15N17O and 15N14N17O). The band-by-band analysis led to the determination of ro-vibrational parameters of 47 bands, 36 of them were newly observed, and the rotational analysis of 11 others were significantly extended and improved. New sets of the effective Hamiltonian parameters were determined for the 14N15N16O and 15N14N16O isotopic species.

The ν1 + 3ν3 absorption band of nitrogen dioxide (14N16O2) by CRDS near 6000 cm−1

The high resolution absorption spectrum of the NO2 molecule is recorded between 5855 and 6006 cm−1 by high sensitivity cavity ring down spectroscopy (CRDS). Positions and intensities in the 5 × 10−27 − 4 × 10−23 cm/molecule range are derived from the profile fitting of more than 6900 lines. The absorption is dominated by the transitions of the (103)–(000) vibrational band centered at 5984.704 cm−1. The spectrum is assigned and modeled using an effective Hamiltonian (EH) which explicitly takes into account a spin–rotational interaction and interaction of the (103) bright state with three “dark” states: (122), (080) and (410). The ν1 + 3ν3 band was already analyzed by Fourier transform spectroscopy (FTS) in Miljanic S., Perrin A., Orphal J., Fellows C.E., Chélin, J. Mol. Spectrosc. 2008, V. 251, P. 9–15, where resonance interactions between the (103) state and the (122) and (080) “dark” states were taken into account. More than 3000 lines are presently assigned with rotational quantum numbers N and Ka up to 59 and 13, respectively, while 1147 transitions with maximum N and Ka values of 47 and 8, respectively, were previously identified by FTS. The measured line positions are reproduced with an (obs.-calc.) rms of 0.0023 cm−1 by variation of 41 EH parameters. About 80 transitions reaching the (080) highly excited bending upper state and borrowing their intensity from the resonance coupling with the (103)–(000) band were assigned for the first time. The main parameter in the transition moment series of the ν1 + 3ν3 band is determined from the fitting of the measured intensities.

High resolution infrared spectra of 17O enriched ozone isotopic species in the 5 µm range: The ν1 + ν3 bands of 17O3, 17O16O17O, 16O17O17O and 17O17O18O

In a mixture of 18 isotopic species of ozone including 17O, 16O and 18O oxygen atoms, four ν1+ν3 bands of 17O3, 17O17O18O, 16O17O17O, 17O16O17O in the 5 µm range are analyzed for the first time. The analyses, accounting for interactions between (101) with (002) and (200) states permitted to assign respectively 747 transitions for 17O17O18O, 705 transitions for 17O16O17O, 889 transitions for 16O17O17O and 1404 transitions for 17O3. The results of fits of effective Hamiltonian and transition moment parameters permit reproducing observed transitions within experimental accuracy. They allow to calculate synthetic spectra in excellent agreement with the observed ones. The band centers and rotational constants derived from experimental spectra are in good agreement with recent theoretical predictions from potential energy surfaces.

Global modeling of the 14N216O line positions within the framework of the non-polyad model of effective Hamiltonian

The global modeling of 14N216O line positions in the 0.8–14,917 cm−1 region has been performed using the non-polyad model of effective Hamiltonian. The effective Hamiltonian parameters were fitted to the measured line positions collected from the literature. The dimensionless weighted standard deviation of the fit is 1.71. The fitted set of 195 effective Hamiltonian parameters allowed reproduction 56,888 measured line positions with an RMS value of 0.006 cm−1. Comparisons of the calculated line positions based on the fitted model with HITRAN2016 and a recent line list by Bertin et al. (J Quant Spectrosc Radiat Transf 2019;229:40–9) are presented and discussed.

Coupled-mode theory for stationary and nonstationary resonant sound propagation

In this paper, we present a complete analytical derivation of the equations used for stationary and nonstationary wave systems regarding resonant sound transmission and reflection described by the phenomenological coupled-mode theory. We calculate the propagating and coupling parameters used in coupled-mode theory directly by utilizing the generalized eigenwave-eigenvalue problem from the Hamiltonian of the sound wave equations for the problem of a one-dimensional isolated on-channel resonance. This Hamiltonian formalization could be beneficial and could potentially model and parameterize a broad range of acoustic wave phenomena. We demonstrate how to use this theory as a basis for perturbation analysis of complex resonant scattering scenarios. In particular, we form the effective Hamiltonian and coupled-mode parameters for the study of sound resonators with background moving media. Finally, we provide a comparison between coupled-mode theory and full-wave numerical examples, which validate the Hamiltonian approach as a relevant model to compute the scattering characteristics of waves by complex resonant systems.

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-296 K 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. A microwave (MW) line set consisting of 644,636 strong transitions (at 296K) 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.