Effective Hamiltonian Theory Research Articles

Sequential double photodetachment of He− in elliptically polarized laser fields

Four-photon double detachment of the helium negative ion is investigated experimentally and theoretically for photon energies where the transient helium atom is in the $1s2s\phantom{\rule{0.16em}{0ex}}^{3}S$ or $1s2p\phantom{\rule{0.16em}{0ex}}^{3}P^{\mathrm{o}}$ states, which subsequently ionize by absorption of three photons. Ionization is enhanced by intermediate resonances, giving rise to series of peaks in the ${\mathrm{He}}^{+}$ spectrum, which we study in detail. The ${\mathrm{He}}^{+}$ yield is measured in the wavelength ranges from 530 to 560 nm and from 685 to 730 nm and for various polarizations of the laser light. Double detachment is treated theoretically as a sequential process, within the framework of $R$-matrix theory for the first step and effective Hamiltonian theory for the second step. Experimental conditions are accurately modeled, and the measured and simulated yields are in good qualitative and, in some cases, quantitative agreement. Resonances in the double detachment spectra can be attributed to well-defined Rydberg states of the transient atom. The double detachment yield exhibits a strong dependence on the laser polarization which can be related to the magnetic quantum number of the intermediate atomic state. We also investigate the possibility of nonsequential double detachment with a two-color experiment but observe no evidence for it.

Effect of Second-Order Spin-Orbit Coupling on the Interaction between Spin States in Spin-Crossover Systems.

The second-order spin-orbit coupling is evaluated in two transition-metal complexes to establish the effect on the deactivation mechanism of the excited low-spin state in systems that undergo spin transitions under the influence of light. We compare the standard perturbational approach to calculate the second-order interaction with a variational strategy based on the effective Hamiltonian theory and show that the former one can only be applied in some special cases and even then gives results that largely overestimate the interaction. The combined effect of geometry distortions and second-order spin-orbit coupling leads to sizeable interactions for states that are nearly uncoupled in the symmetric (average) structure of the complex. This opens the possibility of a direct deactivation from the singlet and triplet states of the metal-to-ligand charge-transfer manifold to the final high-spin state as suggested from the interpretation of experimental data but so far not supported by theoretical descriptions of the light-induced spin crossover.

Study of the Electronic Structure of NiGa2S4 and Extraction of the Spin Hamiltonian Parameters from Ab Initio Calculations

The magnitude of the parameters of the various proposed model Hamiltonians used to model the macroscopic properties of NiGa2S4 and to interpret experimental observations has been the subject of controversy for more than a decade. Both the nature of the relevant operators (magnetic couplings, biquadratic exchange, and anisotropic terms) and the values of their corresponding interactions are far from settled. Through effective Hamiltonian theory and correlated relativistic ab initio calculations, theoretical chemistry can rigorously extract all the required operators and the magnitudes of their corresponding interactions. In this article, we report the values of all relevant interactions. Contrarily to what is often reported, it is shown that: (1) the biquadratic exchange is negligible and smaller than the three‐body terms, (2) the nearest‐neighbor interaction is ferromagnetic and dominant, (3) the next‐nearest‐neighbor coupling is ferromagnetic and small, (4) the next‐next‐nearest‐neighbor coupling is antiferromagnetic and three times smaller than the nearest‐neighbor interaction, and (5) the axial parameter for the local magnetic anisotropy is of the same order of magnitude as the nearest‐neighbor magnetic coupling.

Diabatic investigation for the NaRb molecule

AbstractAn extensive diabatic investigation of the NaRb species has been carried out for all excited states up to the ionic limit Na‐Rb+. An ab initio calculation founded on the pseudopotential, core polarization potential operators and full configuration interaction has been used with an efficient diabatization method involving a combination of variational effective hamiltonian theory and an effective overlap matrix. Diabatic potential energy curves and electric dipole moments (permanent and transition) for all the symmetries Σ+, Π, and Δ have been studied for the first time. Thanks to a unitary rotation matrix, the examination of the diabatic permanent dipole moment (PDM) has shown the ionic feature clearly seen in the diabatic 1Σ+ potential curves and confirming the high imprint of the Na‐Rb+ ionic state in the adiabatic representation. Diabatic transition dipole moments have also been computed. Real crossings have been shown for the diabatic PDM, locating the avoided crossings between the corresponding adiabatic energy curves.

Effective Hamiltonian theory for nonreciprocal light propagation in magnetic Rashba conductor

Rashba spin-orbit interaction leads to a number of electromagnetic cross-correlation effects by inducing a mixing of electric and magnetic degrees of freedom. In this study, we investigate the optical properties of a magnetic Rashba conductor by deriving an effective Hamiltonian based on an imaginary-time path-integral formalism. We show that the effective Hamiltonian can be described in terms of toroidal and quadrupole moments, as has been argued in the case of insulator multiferroics. The toroidal moment turns out to coincide with the spin gauge field induced by the Rashba field. It causes Doppler shift by inducing intrinsic spin current, resulting in anisotropic light propagation (directional dichroism) irrespective of the polarization. The quadrupole moment on the other hand results in a magneto-optical phenomenon such as a Faraday effect for circularly-polarized waves.

Adiabatic and quasi-diabatic investigation of the strontium hydride cation SrH+: structure, spectroscopy, and dipole moments

Ab initio investigation has been performed for the strontium hydride cation SrH + using a standard quantum chemistry approach. It is based on the pseudopotentials for atomic core representations, Gaussian basis sets, as well as with full configuration interaction calculations. A diabatisation procedure based on the effective hamiltonian theory and an effective metric is used to produce the quasi-diabatic potential energy. Adiabatic and quasi-diabatic potential energy curves and their spectroscopic parameters for the ground and many excited electronic states of 1,3Σ+, 1,3Π, and 1,3Δ symmetries have been determined. Their predicted accuracy is discussed by comparing our well depths and equilibrium positions with the available experimental and theoretical results. Moreover, we localized and analyzed numerous avoided crossings between the electronic states of 1,3Σ+ and 1,3Π symmetries. The correction of the electron affinity of the H atom is also considered, for the 1–101Σ+ electronic states, to improve the accuracy of the adiabatic potential energies of these states. In addition, we calculated the dipole moments, for a wide range of internuclear distances in both diabatic and quasi-diabatic representations. The adiabatic permanent dipole moments for the 101Σ+ electronic states revealed ionic characters related to electron transfer and yields both SrH(+) and Sr(+)H arrangements. The transition dipole moments between neighbor electronic states revealed many peaks around the avoided crossing positions.

Dzyaloshinskii-Moriya Interaction as a Consequence of a Doppler Shift due to Spin-Orbit-Induced Intrinsic Spin Current.

We present a physical picture for the emergence of the Dzyaloshinskii-Moriya (DM) interaction based on the idea of the Doppler shift by an intrinsic spin current induced by spin-orbit interaction under broken inversion symmetry. The picture is confirmed by a rigorous effective Hamiltonian theory, which reveals that the DM coefficient is given by the magnitude of the intrinsic spin current. Our approach is directly applicable to first principles calculations and clarifies the relation between the interaction and the electronic band structures. Quantitative agreement with experimental results is obtained for the skyrmion compounds Mn_{1-x}Fe_{x}Ge and Fe_{1-x}Co_{x}Ge.

Magnetic Coupling Constants in Three Electrons Three Centers Problems from Effective Hamiltonian Theory and Validation of Broken Symmetry-Based Approaches.

In the most general case of three electrons in three symmetry unrelated centers with Ŝ1 = Ŝ2 = Ŝ3 = 1/2 localized magnetic moments, the low energy spectrum consists of one quartet (Q) and two doublet (D1, D2) pure spin states. The energy splitting between these spin states can be described with the well-known Heisenberg-Dirac-Van Vleck (HDVV) model spin Hamiltonian, and their corresponding energy expressions are expressed in terms of the three different two-body magnetic coupling constants J12, J23, and J13. However, the values of all three magnetic coupling constants cannot be extracted using the calculated energy of the three spin-adapted states since only two linearly independent energy differences between pure spin states exist. This problem has been recently investigated by Reta et al. (J. Chem. Theory Comput. 2015, 11, 3650), resulting in an alternative proposal to the original Noodleman's broken symmetry mapping approach. In the present work, this proposal is validated by means of ab initio effective Hamiltonian theory, which allows a direct extraction of all three J values from the one-to-one correspondence between the matrix elements of both effective and HDVV Hamiltonian. The effective Hamiltonian matrix representation has been constructed from configuration interaction wave functions for the three spin states obtained for two model systems showing a different degree of delocalization of the unpaired electrons. These encompass a trinuclear Cu(II) complex and a π-conjugated purely organic triradical.

Adiabatic and quasi-diabatic study of FrRb: structure, spectroscopy and dipole moments

Ab initio investigations are performed for the FrRb using a standard quantum chemistry approach based on pseudopotentials for atomic core representations, Gaussian basis sets and full configuration interaction calculations. A diabatisation procedure based on the effective Hamiltonian theory and an effective metric is used to produce the quasi-diabatic potential energy. Firstly, we determine the adiabatic and quasi-diabatic potential energies and the spectroscopic constants for the ground and several excited states of 1,3Σ+, 1,3Π and 1,3Δ symmetries. Their predicted accuracy is discussed by comparing our well depths and equilibrium positions with the available theoretical results. Secondly, we calculate the permanent dipole moments for a wide range of internuclear distances. The adiabatic permanent dipole moments for the 151Σ+ electronic states have revealed ionic characters related to electron transfer and yielding both Fr−Rb+ and Fr+Rb− arrangements. Finally, the transition dipole moments between neighbor electronic states revealed many peaks around the avoided crossing positions.

Influence of intermolecular forces at critical-point wedge filling.

We use microscopic density functional theory to study filling transitions in systems with long-ranged wall-fluid and short-ranged fluid-fluid forces occurring in a right-angle wedge. By changing the strength of the wall-fluid interaction we can induce both wetting and filling transitions over a wide range of temperatures and study the order of these transitions. At low temperatures we find that both wetting and filling transitions are first order in keeping with predictions of simple local effective Hamiltonian models. However close to the bulk critical point the filling transition is observed to be continuous even though the wetting transition remains first order and the wetting binding potential still exhibits a small activation barrier. The critical singularities for adsorption for the continuous filling transitions depend on whether retarded or nonretarded wall-fluid forces are present and are in excellent agreement with predictions of effective Hamiltonian theory even though the change in the order of the transition was not anticipated.

Effective Hamiltonian and Dynamics of Edge States in Two-Dimensional Topological Insulators under Magnetic Fields

The magnetic field opens a gap in the edge state spectrum of two-dimensional topological insulators, thereby destroying the protection of these states against backscattering. To relate properties of this gap to parameters of the system and to study the dynamics of electrons in edge states in the presence of inhomogeneous potentials, the effective Hamiltonian theory is developed. Using this analytical theory, the quantum-mechanical problems of edge-state electron transmission through potential steps and barriers and of motion in a constant electric field are considered. The influence of a magnetic field on the resistance of two-dimensional topological insulators based on HgTe quantum wells is discussed together with comparison to experimental data.

Calculating Effective Wilson Coefficients for Kaon Decays in Renormalization Scale <i>μ=1 GeV</i>

The decay rates of <i>K and ̅K</i> mesons, consisting of a quark-anti quark, as a weak decay in the presence of strong interactions have been studied by means of the Effective Hamiltonian Theory. One of the most important key factors for calculating Effective Hamiltonian is Wilson coefficients. In this paper, effective Wilson coefficients in renormalization scale <i>μ=1GeV</i> are calculated.

Analysis of the rovibrational spectrum of 13CH4 in the Octad range

We have measured the infrared spectrum of methane 13CH4 from 1100cm−1 (33THz), below the fundamental range, to about 12000cm−1 (360THz) in the high overtone region at temperatures ranging from 80K to 300K by high resolution Fourier transform infrared (FTIR) spectroscopy. With instrumental bandwidths between 0.0027cm−1 (80MHz) and 0.01cm−1 (300MHz) this provides close to Doppler-limited spectra, using the Zürich prototype spectrometer (ZP2001, Bruker 125HR) combined with a multipath collisional cooling cell. Using perturbation theory and an accurate empirically adjusted potential we have computed ro-vibrational energy levels of 13CH4 and 12CH4 in the same energy range. Exploiting the synergy between theory and experiment, we analyze here specifically the experimental spectra in the Octad range (∼3700–4700cm−1, or 110 to 140THz), using the theoretical results to guide the fitting of parameters of a Dijon effective Hamiltonian theory. With the aid of the theoretical results it is possible to analyse the Octad of 13CH4 with much less effort than without such information. In the end 1144 purely experimental line positions were fitted with root mean square deviations drms⩽2.6×10−3cm−1 (5548 data including theoretical results, with similar drms).

Emergence of fluctuating traveling front solutions in macroscopic theory of noisy invasion fronts

The position of an invasion front, propagating into an unstable state, fluctuates because of the shot noise coming from the discreteness of reacting particles and stochastic character of the reactions and diffusion. A recent macroscopic theory [Meerson and Sasorov, Phys. Rev. E 84, 030101(R) (2011)] yields the probability of observing, during a long time, an unusually slow front. The theory is formulated as an effective Hamiltonian mechanics which operates with the density field and the conjugate "momentum" field. Further, the theory assumes that the most probable density field history of an unusually slow front represents, up to small corrections, a traveling front solution of the Hamilton equations. Here we verify this assumption by solving the Hamilton equations numerically for models belonging to the directed percolation universality class.

Magnetic interactions in LiCu2O2: Single-chain versus double-chain models

The possible origin of the spiral spin structure in multiferroic LiCu2O2 is studied by calculating all relevant isotropic and anisotropic magnetic interactions in the material. The coupling constants are extracted from accurate ab initio quantum chemical calculations with an effective Hamiltonian theory. First, the anisotropic or Dzyaloshinskii-Moriya interactions are found to be negligible. Secondly, we obtain small isotropic interactions of the spin moments located on different chains, which classifies the material as a quasi-one-dimensional magnetic system. The intrachain isotropic interactions between nearest neighbors are relatively large and ferromagnetic, while second-neighbor interactions along the chain have antiferromagnetic character and are about half the magnitude of the former. This frustration leads to a spiral spin structure, which can be subjected to electric polarization.

High-Order Noise Filtering in Nontrivial Quantum Logic Gates

Treating the effects of a time-dependent classical dephasing environment during quantum logic operations poses a theoretical challenge, as the application of noncommuting control operations gives rise to both dephasing and depolarization errors that must be accounted for in order to understand total average error rates. We develop a treatment based on effective Hamiltonian theory that allows us to efficiently model the effect of classical noise on nontrivial single-bit quantum logic operations composed of arbitrary control sequences. We present a general method to calculate the ensemble-averaged entanglement fidelity to arbitrary order in terms of noise filter functions, and provide explicit expressions to fourth order in the noise strength. In the weak noise limit we derive explicit filter functions for a broad class of piecewise-constant control sequences, and use them to study the performance of dynamically corrected gates, yielding good agreement with brute-force numerics.

Rationalization of the behavior of M2(CH3CS2)4I (M = Ni, Pt) chains at room temperature from periodic density functional theory and ab initio cluster calculations

The electrical conductivities and plausible charge-ordering states in the room temperature (r.t.) phase for MMX chains [Ni(2)(dta)(4)I](∞) and [Pt(2)(dta)(4)I](∞) (dta = CH(3)CS(2)(-)) have been analyzed with periodic density functional theory (DFT) and correlated ab initio calculations combined with the effective Hamiltonian theory. Periodic DFT calculations show a more delocalized nature of the ground state in [Pt(2)(dta)(4)I](∞) compared to [Ni(2)(dta)(4)I](∞), which features a rather large energy gap between the occupied and empty bands, and charge polarized dimer units. A larger electrical conductivity for the Pt chain can be expected, especially because the Fermi level lies within a band with contributions from Pt and I orbitals. Electronic structure parameters extracted from ab initio cluster calculations show that the large difference between the observed conductivities at 300 K for Ni and Pt compounds, of 3 orders of magnitude, cannot be explained from the parameters extracted from an embedded M(2)(dta)(4)I(2) dimer fragment alone. When tetramer fragments are considered, we observe that the interdimer transfer integral (t) between neighboring M(2) units connected by an iodine atom at correlated level is comparable in both chains. On the other hand, the energy to transfer an electron from a dimer to the neighboring one (Coulomb repulsion U) is three times larger in the Ni compound with respect to the Pt chain, in line with the poor conductivity of the former. The electronic structure of the M(4)(dta)(8)I(3) fragment points to an alternate charge-polarization state for Ni and an average valence state for Pt when the r.t. X-ray structure is considered.

The order of filling transitions in acute wedges

Using a square-gradient density functional model we test the prediction that the filling transition for a fluid in a wedge geometry changes from continuous to first-order as the wedge becomes more acute. Our numerical findings confirm such a change of order, but the value of the tilt angle at which it occurs, α* ≈ 45°, is considerably smaller than the original theoretical prediction. We critically reassess this work, which was based on allowing for the self-interaction of the fluid interface, and argue that the interfacial curvature and effective wavevector dependent surface tension can further lower the predicted value of α*, in keeping with our numerical findings. Interfacial fluctuation effects, occurring beyond mean-field level, are also discussed using effective Hamiltonian theory and are shown to substantially increase the value of α*.

Structural and Spectroscopic Study of the LiRb Molecule beyond the Born–Oppenheimer Approximation

Adiabatic and diabatic potential energy curves and the permanent and transition dipole moments of the low-lying electronic states of the LiRb molecule dissociating into Rb(5s, 5p, 4d, 6s, 6p, 5d, 7s, 6d) + Li(2s, 2p) have been investigated. The molecular calculations are performed with an ab initio approach based on nonempirical pseudopotentials for Rb(+) and Li(+) cores, parametrized l-dependent core polarization potentials and full configuration interaction calculations. The derived spectroscopic constants (R(e), D(e), T(e), ω(e), ω(e)x(e), and B(e)) of the ground state and lower excited states are in good agreement with the available theoretical works. However, the 8-10(1)Σ(+), 8-10(3)Σ(+), 6(1,3)Π, and 3(1,3)Δ excited states are studied for the first time. In addition, to the potential energy, accurate permanent and transition dipole moments have been determined for a wide interval of internuclear distances. The permanent dipole moment of LiRb has revealed ionic characters both relating to electron transfer and yielding Li(-)Rb(+) and Li(+)Rb(-) arrangements. The diabatic potential energy for the (1,3)Σ(+), (1,3)Π, and (1,3)Δ symmetries has been performed for this molecule for the first time. The diabatization method is based on variational effective Hamiltonian theory and effective metric, where the adiabatic and diabatic states are connected by an appropriate unitary transformation.

First-principles study of magnetic interactions in cupric oxide

Cupric oxide (CuO) has been described as belonging to the quasi-one-dimensional antiferromagnetic compounds. It has also been suggested that cupric oxide possesses strong magnetic anisotropy, which is possibly related to the observed ferroelectricity in this material. In this paper, the magnetic interactions of CuO are investigated using the embedded cluster approach. Accurate wave-function-based methods have been employed to describe the interactions along all copper-oxygen chain directions. Both two-center and three-center clusters are considered in our calculations. The antisymmetric anisotropic interaction parameters are also calculated for the two-center clusters by applying an effective Hamiltonian theory. Our results show that the magnetic interactions are dominated by the antiferromagnetic coupling between copper ions along the chain of largest Cu-O-Cu angles in agreement with experiment. The results for the interplane magnetic interactions reveal competition between nearest-neighbor ferromagnetic coupling and second-nearest-neighbor antiferromagnetic interaction along the direction where two copper ions are connected via doubly bridged oxygen ligands. We also find nonnegligible Dzyaloshinskii-Moriya interactions with magnitude comparable to the weak isotropic interchain interactions.