Effective Hamiltonian Analysis Research Articles

An effective Hamiltonian analysis of a Franck-Condon-like pattern in the IR spectra of phenol-alkylsilane dihydrogen-bonded clusters in the S1 state.

Infrared (IR) spectra in a region of the OH stretch band of phenol (PhOH)-ethyldimethylsilane (EDMS), phenol (PhOH)-triethylsilane (TES), and phenol (PhOH)-t-butyldimethylsilane (BDMS) dihydrogen-bonded clusters in the S1 state were observed. All of the species exhibited unconventional band patterns in which many combination bands appeared with comparable intensities to those of allowed bands. Such a behavior is sometimes called a Franck-Condon-like pattern. In the case of the PhOH-BDMS, one intermolecular vibrational mode is involved in this behavior. The observed IR spectra were well reproduced based on the concept of the Franck-Condon-like behavior. As an alternative treatment, we analyzed the band patterns on the concept of intensity borrowing due to the vibrational anharmonic interaction. The analysis was based on an effective Hamiltonian involving an anharmonic interaction between the OH stretch and intermolecular vibrational modes. Two treatments provided the same results. Thus, it was confirmed that the Franck-Condon-like behavior originates from vibrational anharmonic interactions. In the cases of the PhOH-EDMS and PhOH-TES, we carried out a two-dimensional Franck-Condon and an effective Hamiltonian analysis to interpret the Franck-Condon-like patterns. We examined vibrational wave functions obtained by the latter analysis. Shapes of the wave functions suggest that a recombination of the intermolecular vibrational modes occurs during the excitation of OH stretch mode in these clusters, which is a similar behavior to the Duschinsky effect in the electronic transition.

Extended measurements and an experimental accuracy effective Hamiltonian model for the 3ν2 and ν4+ν2 states of ammonia

The infrared spectrum of ammonia has proven to be highly problematic for effective Hamiltonian analysis. The most complete previous study of the 3ν2 and ν4+ν2 bands achieved the accuracy of 0.0069 cm−1 as reflected by the root-mean-square error of their fit, which is slightly more than 10 times the experimental accuracy. In the present study, we performed a global fit of the existing 2141 literature data involving 3ν2, ν4+ν2, 3ν2-ν2, (ν4+ν2)-ν2 together with 1281 new data involving 3ν2-2ν2, 3ν2-3ν2 and (ν4+ν2)-(ν4+ν2) using an effective Hamiltonian together with the Pickett suite of program SPFIT/SPCAT. The new dataset consists of three spectra recorded at the SOLEIL synchrotron facility. The effective Hamiltonian model proposed for 3ν2/ν4+ν2 has achieved experimental accuracy. This success combined with our previous success of the 2ν2/ν4 analysis leads us to believe that the vibrational states higher than 3ν2/ν2+ν4 may be analyzed with effective Hamiltonians as well.

Precision spectroscopy and comprehensive analysis of perturbations in the A1∏(v = 0) state of 13C18O

ABSTRACTWe have reinvestigated the A level of 13C18O using new high-resolution spectra obtained via multi-photon laser excitation as well as with synchrotron-based Fourier-transform absorption spectroscopy of the A, e, d, a, and a bands. In addition, Fourier-transform emission spectroscopy in the visible range is performed on the band. Spectra of the B band are measured in order to tie information from the latter emission data to the level structure of A. The high pressures in the absorption cell at the synchrotron and the high temperatures in the emission discharge permitted monitoring of high rotational quantum levels in A up to J=43. All information, in total over 900 spectral lines, was included in an effective Hamiltonian analysis of the Alevels that are directly perturbed by the e, d, a, D, I close-lying levels and the e, d, a remote levels, as well being indirectly influenced by the a state. The influence of 9 further perturber levels and their interactions was investigated and are not significant for reproducing the present experimental data. This analysis leads to a much improved description in terms of molecular constants and interaction parameters, compared to previous studies of the same energy region for other CO isotopologues.

Prediction of high-temperature quantum anomalous Hall effect in two-dimensional transition-metal oxides

Quantum anomalous Hall (QAH) insulator is a topological phase which exhibits chiral edge states in the absence of magnetic field. The celebrated Haldane model is the first example of QAH effect, but difficult to realize. Here, we predict the two-dimensional single-atomic-layer V2O3 with a honeycomb-Kagome structure is a QAH insulator with a large band gap (large than 0.1 eV) and a high ferromagnetic Curie temperature (about 900 K). Combining the first-principle calculations with the effective Hamiltonian analysis, we find that the spin-majority dxy and dyz orbitals of V atoms on the honeycomb lattice form a massless Dirac cone near the Fermi level which becomes massive when the on-site spin-orbit coupling is included. Interestingly, we find that the large band gap is caused by a cooperative effect of electron correlation and spin-orbit coupling. Both first-principle calculations and the effective Hamiltonian analysis confirm that 2D V2O3 has a non-zero Chern number (i.e., one). Our work paves a new direction towards realizing the QAH effect at room temperature.

Topological nodal-line semimetals in alkaline-earth stannides, germanides, and silicides

Based on first-principles calculations and an effective Hamiltonian analysis, we systematically investigate the electronic and topological properties of alkaline-earth compounds $AX_2$ ($A$=Ca, Sr, Ba; $X$=Si, Ge, Sn). Taking BaSn$_2$ as an example, we find that when spin-orbit coupling is ignored, these materials are three-dimensional topological nodal-line semimetals characterized by a snake-like nodal loop in three-dimensional momentum space. Drumhead-like surface states emerge either inside or outside the loop circle on the (001) surface depending on surface termination, while complicated double-drumhead-like surface states appear on the (010) surface. When spin-orbit coupling is included, the nodal line is gapped and the system becomes a topological insulator with Z$_2$ topological invariants (1;001). Since spin-orbit coupling effects are weak in light elements, the nodal-line semimetal phase is expected to be achievable in some alkaline-earth germanides and silicides.

Theory of Anomalous Optical Properties of Bulk Rashba Conductor

The Rashba interaction induced when inversion symmetry is broken in solids is a key interaction connecting spin and charge for realizing novel magnetoelectric cross-correlation effects. Here, we theoretically explore the optical properties of a bulk Rashba conductor by calculating the transport coefficients at finite frequencies. It is demonstrated that the combination of direct and inverse Edelstein effects leads to a softening of the plasma frequency for the electric field perpendicular to the Rashba field, resulting in a hyperbolic electromagnetic metamaterial. In the presence of magnetization, a significant enhancement of anisotropic propagation (directional dichroism) is predicted because of interband transition edge singularity.Based on an effective Hamiltonian analysis, the dichroism is demonstrated to be driven by toroidal and quadratic moments of the magnetic Rashba system. The effective theory of the cross-correlation effects has the same mathematical structure as that of insulating multiferroics.

Survey of the high resolution infrared spectrum of methane ((12)CH4 and (13)CH4): partial vibrational assignment extended towards 12,000 cm(-1.).

We have recorded the complete infrared spectrum of methane (12)CH4 and its second most abundant isotopomer (13)CH4 extending from the fundamental range starting at 1000 cm(-1) up to the overtone region near 12,000 cm(-1) in the near infrared at the limit towards the visible range, at temperatures of about 80 K and also at 298 K with Doppler limited resolution in the gas phase by means of interferometric Fourier transform spectroscopy using the Bruker IFS 125 HR prototype (ZP 2001) of the ETH Zürich laboratory. This provides the so far most complete data set on methane spectra in this range at high resolution. In the present work we report in particular those results, where the partial rovibrational analysis allows for the direct assignment of pure (J = 0) vibrational levels including high excitation. These results substantially extend the accurate knowledge of vibrational band centers to higher energies and provide a benchmark for both the comparison with theoretical results on the one hand and atmospheric spectroscopy on the other hand. We also present a simple effective Hamiltonian analysis, which is discussed in terms of vibrational level assignments and (13)C isotope effects.

Formation of quantum spin Hall state on Si surface and energy gap scaling with strength of spin orbit coupling.

For potential applications in spintronics and quantum computing, it is desirable to place a quantum spin Hall insulator [i.e., a 2D topological insulator (TI)] on a substrate while maintaining a large energy gap. Here, we demonstrate a unique approach to create the large-gap 2D TI state on a semiconductor surface, based on first-principles calculations and effective Hamiltonian analysis. We show that when heavy elements with strong spin orbit coupling (SOC) such as Bi and Pb atoms are deposited on a patterned H-Si(111) surface into a hexagonal lattice, they exhibit a 2D TI state with a large energy gap of ≥0.5 eV. The TI state arises from an intriguing substrate orbital filtering effect that selects a suitable orbital composition around the Fermi level, so that the system can be matched onto a four-band effective model Hamiltonian. Furthermore, it is found that within this model, the SOC gap does not increase monotonically with the increasing strength of SOC. These interesting results may shed new light in future design and fabrication of large-gap topological quantum states.

Topological phase transition and unexpected mass acquisition of Dirac fermion in TlBi(S1−xSex)2

Based on first-principles calculations and effective Hamiltonian analysis, we predict a topological phase transition from normal to topological insulators and the opening of a gap without breaking the time-reversal symmetry in TlBi(S1−xSex)2. The transition can be driven by modulating the Se concentration, and the rescaled spin-orbit coupling and lattice parameters are the key ingredients for the transition. For topological surface states, the Dirac cone evolves differently as the explicit breaking of inversion symmetry and the energy band can be opened under asymmetry surface. Our results present theoretical evidence for experimental observations [Xu et al., Science 332, 560 (2011); Sato et al., Nat. Phys. 7, 840 (2011)].

Microwave electronic spectrum of the Ne···Ne+ long-range complex

We have used an ion beam method to observe 276 transitions in the microwave electronic spectrum of the long-range Ne···Ne+ ionic complex, involving levels which lie within 10.2 cm-1 of the lowest dissociation limit. An electric field dissociation technique has been used to access directly levels with binding energies of up to 6.8 cm-1 and we have been able to construct an experimental energy level pattern for at least 17 vibration–rotation progressions in this region of the potential. Microwave–microwave double resonance and Zeeman effect measurements have been crucial in establishing this energy level pattern. The levels are populated by the vertical electron impact ionisation of the neutral neon dimer, produced by means of a nozzle beam, with some population of higher rotational levels of the dimer ion probably resulting from larger cluster fragmentation. A case (c) effective Hamiltonian analysis has been successful in describing the levels in six of the progressions but a full theoretical analysis requires a coupled-states calculation. Analysis of Zeeman splittings for the microwave lines identifies the J values of the levels involved. The observed g-factors provide information about the transition from case (c) to case (e) coupling as both the rotational quantum number increases and the energy levels become more weakly bound.

Effective Hamiltonian analysis of fluid criticality and application to the square–well fluid

The critical behavior of fluids is analyzed in terms of an effective Hamiltonian which is obtained by a Hubbard–Schofield transformation that maps the fluid Hamiltonian onto a Wilson–Fisher Ising–type Hamiltonian. Within this approach we find an approximate relation between critical temperature and critical density, depending on the parameters of the interaction potential, and compare it with simulation results. In the framework of the effective Hamiltonian we examine the critical data for the square–well fluid obtained using thermodynamic-scaling Monte Carlo and discuss the impact of finite–size effects on the Monte Carlo studies of the fluid criticality.

The algebra of effective Hamiltonians and operators: Truncated operators and computational aspects

We extend to finite orders of perturbation theory our previous analysis of effective Hamiltonians h and effective operators a which produce, respectively, exact energies and matrix elements of a time-independent operator A for a finite number of eigenstates of a time-independent Hamiltonian H. The validity of various properties is examined here for perturbatively truncated h and a, particularly, the preservation upon transformation to effective operators of commutation relations involving H and/or constants of the motion, of symmetries, and of the equivalence between dipole length and velocity transition moments. We compare formal and computational features of all a definitions and of the more limited Hellmann–Feynman theorem based ‘‘effective operators,’’ which provide only diagonal matrix elements of A in special cases. Norm-preserving transformations to effective operators are found to yield a simpler effective operator formalism from both formal and computational viewpoints.

Further analysis of effective Hamiltonians for triply degenerate fundamentals of tetrahedral molecules: Unambiguous fit of q2J5 and q2J6 terms for ν4 of 12CH 4

The further study of ambiguities among q 2 J 5 and q 2 J 6 terms in effective Hamiltonians for triply degenerate fundamentals of tetrahedral molecules is presented. It is shown that, in agreement with theory, q 2 J 5 and q 2 J 6 diagonal coupling parameters cannot be considered as constants having definite values for a given F 2 vibrational state, just like q 2 J 4 terms previously studied [Vl. G. Tyuterev, J. P. Champion, G. Pierre, and V. I. Perevalov, J. Mol. Spectrosc. 105, 113–138 (1984)]. The use of reduced Hamiltonians containing fewer (but unambiguous) parameters is suggested and applied to the ν 4 band of 12CH 4.