Calculations of the EPR g-tensor using unrestricted two- and four-component relativistic approaches within the HF and DFT frameworks

ABSTRACT

Approaches and programs for calculations of the EPR g-tensor in the framework of the two- and four-component methods are still very rare. There are three main reasons for this: the wider community's unawareness of the importance of second- and higher order spin–orbit effects on the g-tensor, the methodological problems associated with performing such calculations and the lack of understanding of these problems. This paper reports on the implementation of a method for calculation of the g-tensor in the framework of the relativistic unrestricted two- and four-component Hartree–Fock and density functional theory approaches based on the Kramers pair formalism. This implementation allows us to analyse problems which arise when the g-tensor is calculated via Kramers pairs in the unrestricted framework.     

Excited-states and spectroscopic properties of superoxide anion: a theoretical study including spin–orbit coupling

ABSTRACT

The potential energy curves (PECs) of 24 Λ–S electronic states of superoxide anion (O₂^?), which correlated with the first dissociation channel, were calculated using a high-accuracy internally contracted multireference configuration interaction (icMRCI) methodology with the Davidson correction in conjunction with the correlation-consistent basis sets. The core electron correlation and scalar relativistic corrections as well as basis set extrapolation were included. The spin–orbit coupling was also taken into account by using the state interaction approach with the Breit–Pauli Hamiltonian. The PECs of 54 Ω states generated from the 24 Λ–S states were constructed and described in detail. The spectroscopic constants of the seventeen Λ–S and 37 Ω bound states were evaluated and the vibrational properties of some weakly bound states were predicted. Comparing with the available experimental and theoretical data shows that the computational strategy employed is suitable and highly accurate for this system.     

On the performance of DFT/MRCI-R and MR-MP2 in spin–orbit coupling calculations on diatomics and polyatomic organic molecules

ABSTRACT

We have investigated the performance of different multi-reference quantum chemical methods with regard to electronic excitation energies and spin–orbit matrix elements (SOMES). Among these methods are two variants of the combined density functional theory and multi-reference configuration interaction method (DFT/MRCI and DFT/MRCI-R) and a multi-reference second-order Møller–Plesset perturbation theory (MR-MP2) approach. Two variants of MR-MP2 have been tested based on either Hartree–Fock orbitals or Kohn–Sham orbitals of the BH-LYP density functional. In connection with the MR-MP2 approaches, the first-order perturbed wave functions have been employed in the evaluation of spin–orbit coupling. To validate our results, we assembled experimental excitation energies and SOMES of eight diatomic and fifteen polyatomic molecules. For some of the smaller molecules, we carried out calculations at the complete active space self-consistent field (CASSCF) level to obtain SOMEs to compare with. Excitation energies of the experimentally unknown states were assessed with respect to second-order perturbation theory corrected (CASPT2) values where available. Overall, we find a very satisfactory agreement between the excitation energies and the SOMEs obtained with the four approaches. For a few states, outliers with regard to the excitation energies and/or SOMEs are observed. These outliers are carefully analysed and traced back to the wave function composition.     

准一维半导体量子点中电偶极自旋共振的物理机理

半导体量子点中的电子自旋具有较长相干时间以及可扩展性的特点, 在近十几年来引起了人们的广泛兴趣. 人们常常利用电子自旋共振技术来对单个自旋进行操纵. 这样不但需要一个静磁场来使电子产生赛曼劈裂, 同时还需要一个与之垂直的局域振荡磁场. 但是, 在实验上产生足够强且具有固定频率的局域磁场是比较困难的. 后来人们发现, 局域的振荡电场也可以操纵单个电子自旋, 也就是所谓的电偶极自旋共振. 众所周知, 自旋只有自旋磁矩, 不会与电场有任何直接的相互作用. 所以, 电偶极自旋共振的发生必须依赖于某些媒质. 这些媒质包括：量子点材料中的自旋轨道耦合作用, 量子点中的局域磁场梯度, 以及量子点中电子自旋与核自旋的超精细相互作用. 这些媒质能诱导出自旋与电场之间间接的相互作用, 从而外电场操纵单个电子自旋得以实现. 本文总结归纳了目前半导体量子点系统中发生电偶极自旋共振的三种主要物理机理.     

Magnetization of interacting electrons in anisotropic quantum dots with Rashba spin–orbit interaction

Magnetization of anisotropic quantum dots in the presence of the Rashba spin–orbit interaction has been studied for three and four interacting electrons in the dot for non-zero values of the applied magnetic field. We observe unique behaviors of magnetization that are direct reflections of the anisotropy and the spin–orbit interaction parameters independently or concurrently. In particular, there are saw-tooth structures in the magnetic field dependence of the magnetization, as caused by the electron–electron interaction, that are strongly modified in the presence of large anisotropy and high strength of the spin–orbit interactions. We also report the temperature dependence of magnetization that indicates the temperature beyond which these structures due to the interactions disappear. Additionally, we found the emergence of a weak sawtooth structure in magnetization for three electrons in the high anisotropy and large spin–orbit interaction limit that was explained as a result of merging of two low-energy curves when the level spacings evolve with increasing values of the anisotropy and the spin–orbit interaction strength.     

Theoretical studies on 14 Λ-S and 30 Ω states of BeBr molecule: potential energy curves,spectroscopic parameters and spin–orbit couplings

Using the complete active space self-consistent field (CASSCF) method followed by the internally contracted multi-reference configuration interaction (MRCI) approach in combination with the correlation-consistent basis sets, this paper studies the potential energy curves of X²Σ⁺, 2²Σ⁺, 3²Σ⁺, 1²Σ^?, A²Π, 2²Π, 3²Π, 1²Δ, 1⁴Σ⁺, 2⁴Σ⁺, 1⁴Σ^?, 1⁴Π, 2⁴Π and 1⁴Δ Λ-S states of BeBr molecule and the corresponding 30 Ω states for the first time. All the Λ-S states correlate to the first two dissociation channels, Be(¹S_g) + Br(²P_u) and Be(³P_u) + Br(²P_u), of BeBr molecule. Of these Λ-S states, the 3²Π and 2⁴Π are found to be repulsive without the spin–orbit coupling, whereas 1⁴Π, 2⁴Π, 3²Π and 2⁴Σ⁺ are found to be repulsive with the spin–orbit coupling included. A²Π and 2²Σ⁺ possess the double well whether the spin–orbit coupling effect is included or not. Only 1⁴Σ⁺, 1⁴Σ^?, 1²Π and 2²Π are found to be the inverted Λ-S states. The spin–orbit coupling is accounted for by the state interaction approach with Breit–Pauli Hamiltonian using the all-electron cc-pCVTZ basis set. The potential energy curves determined by the internally contracted MRCI method are corrected for size-extensivity errors by means of the Davidson correction. Core–valence correlation correction is calculated with a cc-pCVTZ basis set. Scalar relativistic correction is included using the third-order Douglas–Kroll Hamiltonian approximation at the level of cc-pVTZ basis set. The spectroscopic parameters of all the Λ-S and Ω bound states are evaluated. The spectroscopic parameters are compared with those reported in the literature. Fair agreement is found between the present results and available measurements. In particular, the energy splitting of 204.43 cm^?1 in the A²Π Λ-S state agrees well with the measurements of 201 cm^?1. Analyses demonstrate that the spectroscopic parameters reported here can be expected to be reliably predicted ones.     

Accurate spectroscopic calculations of the 12 Λ-S states and 27 Ω states of NF+ cation including the spin–orbit coupling effect

This paper studies the potential energy curves (PECs) of 27 Ω states generated from the 12 Λ-S states (X²Π, 1²Σ⁺, 1²Σ^?, 2²Σ^?, A²Π, 1²Δ, 1⁴Σ⁺, 1⁴Σ^?, 2⁴Σ^?, 1⁴Π, 2⁴Π and 1⁴Δ), which are attributed to the first dissociation channel of NF⁺ cation. Of these 12 states, only 2²Σ^? and 2⁴Π are the repulsive ones, which are very different from those reported by G.-S. Kim and D. M. Hirst, Mol. Phys. 86, 1183–1193 (1995) G.-S. Kim and D.M. Hirst, Mol. Phys. 86, 1183–1193 (1995).[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]. In addition, the 1²Δ and 1⁴Σ^? states are found to possess the double well. 1⁴Σ⁺, 1⁴Σ^? and 1⁴Δ are found to be the inverted states with the spin–orbit coupling effect taken into account, and 1²Σ⁺, 1²Σ^?, 1²Δ, 1⁴Σ⁺, 2⁴Σ^? and 1⁴Δ are found to be the weakly bound states. The PECs are calculated by the complete active space self-consistent field method, which is followed by the internally contracted multireference configuration interaction approach with Davidson correction. The convergent behaviour of the present calculations is discussed with respect to the basis set and level of theory. All the PECs are extrapolated to the complete basis set limit. Core–valence correlation and scalar relativistic corrections are included at the same time. The spin–orbit coupling effect is accounted for by the state interaction method with the Breit–Pauli Hamiltonian. The spectroscopic parameters are evaluated and compared with available measurements and other theoretical results. The effect of spin–orbit coupling on the spectroscopic parameters is discussed. The Franck–Condon factors and radiative lifetimes of the transitions from the 1⁴Π_3/2, 1⁴Σ^?_3/2, 1²Δ_3/2 and A²Π_1/2 states to the X²Π_1/2 state are calculated for several low vibrational levels and some necessary discussion is done. It shows that the spectroscopic results reported in this paper can be expected to be reliably predicted ones.     

Kink-like breathers in Bose–Einstein condensates with helicoidal spin–orbit coupling

We report a kind of kink-like breathers in one-dimensional Bose–Einstein condensates (BECs) with helicoidal spin–orbit coupling (SOC), on whose two sides the background densities manifest obvious difference (called kink amplitude). The kink amplitude and shape of breather can be adjusted by the strength and period of helicoidal SOC, and its atomic number in two components exchanges periodically with time. The SOC has similar influence on the kink amplitude and the exchanged atomic number, especially when the background wave number is fixed. It indicates that the oscillating intensity of breather can be controlled by adjusting initial kink amplitude. Our work showcases the great potential of realizing novel types of breathers through SOC, and deepens our understanding on the formation mechanisms of breathers in BECs.     

Gate control of quantum dot-based electron spin–orbit qubits

We investigate theoretically the coherent spin dynamics of gate control of quantum dot-based electron spin–orbit qubits subjected to a tilted magnetic field under electric-dipole spin resonance (EDSR). Our results reveal that Rabi oscillation of qubit states can be manipulated electrically based on rapid gate control of SOC strength. The Rabi frequency is strongly dependent on the gate-induced electric field, the strength and orientation of the applied magnetic field. There are two major EDSR mechanisms. One arises from electric field-induced spin–orbit hybridization, and the other arises from magnetic field-induced energy-level crossing. The SOC introduced by the gate-induced electric field allows AC electric fields to drive coherent Rabi oscillations between spin-up and -down states. After the crossing of the energy-levels with the magnetic field, the spin-transfer crossing results in Rabi oscillation irrespective of whether or not the external electric field is present. The spin–orbit qubit is transferred into the orbit qubit. Rabi oscillation is anisotropic and periodic with respect to the tilted and in-plane orientation of the magnetic field originating from the interplay of the SOC, orbital, and Zeeman effects. The strong electrically-controlled SOC strength suggests the possibility for scalable applications of gate-controllable spin–orbit qubits.     

Influence of spin–orbit interactions on the polaron properties in wurtzite semiconductor quantum well

We have study the simultaneous effect of Rashba and Dresselhaus spin–orbit interactions on the polaron properties in wurtzite semiconductor quantum wells. The linear and cubic contributions of the bulk Dresselhaus spin–orbit coupling and the effects of phonon confinement on electron–optical-phonon interaction Hamiltonians are taken into account. We have found analytical solutions for the polaron energies as well as polaron effective mass within the range of validity of perturbation theory. It is shown that the polaron energy and effective mass correction are both significantly enhanced by the spin–orbit coupling. Wave number dependent phonon contribution on the electron energy has minima and varies differently of the spin-up and spin-down states. Polaron self-energy due to interface optical phonon modes has larger values than of the confined optical phonon modes ones. The polaron effective mass exhibits anisotropy and the contribution of the Dresselhaus spin–orbit coupling term on the polaron effective mass is dominated by Rashba one.     

On the photophysics of four heteroleptic iridium(III) phenylpyridyl complexes investigated by relativistic multi-configuration methods

ABSTRACT

In this work, we present a detailed analysis of the photophysical properties of four phosphorescent iridium(III) complexes, i.e. trans-N,N- and cis-N,N-(ppy)₂Ir^III(acac) as well as their fluorinated derivatives trans-N,N- and cis-N,N-(F₂ppy)₂Ir^III(acac). These properties include absorption and emission characteristics, intersystem crossing rates from the lowest singlet excited state, phosphorescence lifetimes of the individual triplet sublevels as well as the orientations of the transition dipole vectors. To this end, we have carried out combined density functional theory and multi-reference configuration interaction studies including spin–orbit coupling by perturbational as well as variational procedures. For the experimentally known complexes, we observe excellent agreement between our computed data and literature data. Also the blueshifts of the emission maxima occurring upon fluorination of the (ppy)₂Ir(acac) compounds are well reproduced. To our surprise, we find the experimentally not yet investigated cis-N,N-(F₂ppy)₂Ir(acac) isomer to be thermodynamically more stable than the well-known blue phosphorescent emitter trans-N,N-(F₂ppy)₂Ir(acac).