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.     

Spin-polarized electron emission from magnetic and non-magnetic solids

The use of spin-polarization analysis in electron spectroscopy of magnetic and non-magnetic surfaces is demonstrated with a few examples. The existence and properties of spin-dependent transmission of electrons through the solid-vacuum interface is shown. The influence of surface reconstruction of Pt(110) on spin polarization and energy distribution curves in photoemission with circularly polarized light is studied. The polarization of secondary electrons from Fe(110) is observed to depend on the spin polarization of primary electrons at low energies. The temperature dependence of the exchange splitting in Ni is studied by means of spin-polarized electron energy loss spectroscopy and found to be at variance with the assumptions of the Stoner-Wohlfarth theory.     

Collective state of electrons and impurities with a spin

The problem of states of an electron system interacting with impurities that have a spin of 1/2 is considered. It is shown that in the calculation of the energy of the system, the electron spin-flip processes and the formation of electron–hole–impurity flip spin (hole against the background of electrons with another spin projection) play the major role. Such complexes are accumulated in the system (a sort of Bose condensate of complexes is formed); this reduces the energy of the system, which is a linear function of the initial interaction of an electron with the impurity spin (in contrast, for example, to the result obtained in perturbation theory). The hole-type excitation and the spin excitation have a gap in the spectrum. Small parameters of the problem are the interaction of electrons with impurity spins and the number of impurities. The electron–electron interaction is not taken into account. Impurities are assumed to be distributed at random, and calculations are performed using the known averaging over the positions of impurities.     

Lowest Π–Π* electronic transitions in linear and two-dimensional polycyclic aromatic hydrocarbons: enhanced electron density edge effect

Polycyclic aromatic hydrocarbons (PAHs) form an important class of molecules as they are ubiquitous, pollute air and cause severe health problems. Lowest vertical π–π* singlet–singlet or triplet–triplet excitation energies and corresponding oscillator strengths were studied for several linear and two-dimensional PAHs employing time-dependent density functional theory. Excited-state electron density, molecular electrostatic potential (MEP) and spin density distributions in the PAHs, along with ground-state chemical hardness, were also studied. It has been found that, generally, excitation energies and oscillator strengths decrease with increase in PAH size, and excitation energies and chemical hardness are strongly linearly correlated. Enhanced electron density edge effect, which was found to occur in the ground states of the molecules, continues to hold in their excited states also. A strong similarity between the ground and π–π* excited-state MEP maps suggests that σ electrons are the main contributors to the enhanced electron density at the edges. Due to their strong electronic absorption transitions in the visible and infrared regions, the PAHs can be used for harnessing solar energy efficiently.     

Specific features of the electronic structure and spectral characteristics of the Gd<Subscript>5</Subscript>Si<Subscript>3</Subscript> compound

The electronic structure and optical properties of the hexagonal intermetallic compound Gd₅Si₃ are investigated. The spin-polarization calculation of the band spectrum is performed in the local spin density approximation, taking account for the strong electron correlations in the 4 f shell of a Gd ion (LSDA + U method). Optical constants of the compound in the wavelength range of 0.22–15 μm are determined by the ellipsometry technique and some spectral characteristics are calculated. The frequency dependence of optical conductivity in the light quantum absorption region is analyzed on the basis of the calculated electron density of states.     

From spin flip excitations to the spin susceptibility enhancement of a two-dimensional electron gas

The g-factor enhancement of the spin-polarized two-dimensional electron gas was measured directly over a wide range of spin polarizations, using spin flip resonant Raman scattering spectroscopy on two-dimensional electron gases embedded in Cd(1-x)Mn(x)Te semimagnetic quantum wells. At zero Raman transferred momentum, the single-particle spin flip excitation, energy Z*, coexists in the Raman spectrum with the spin flip wave of energy Z, the bare giant Zeeman splitting. We compare the measured g-factor enhancement with recent spin-susceptibility enhancement theories and deduce the spin-polarization dependence of the mass renormalization.     

Optical spectroscopy and electronic structure of the Er5Ge3 compound

The results of the study of the optical properties and electronic structure of the Er₅Ge₃ compound have been presented. In the wavelength range of 0.22–15 μm (0.083–5.64 eV), the optical constants have been measured, and the spectral and electronic characteristics have been determined. The spin-polarization calculations of the band spectrum have been performed in the local electron spin density approximation (LSDA) with a correction for strong correlations in the 4f shell of the rare-earth atom (LSDA + U method). The main features of the experimental dispersion dependence of the optical conductivity in the region of quantum light absorption have been interpreted based on the results of calculations of the electron density of states.     

Polaronic origin of the isotope effect on the London penetration depth in high-temperature superconducting oxides

Direct measurements of the in-plane London penetration depth λ _L have recently been performed on high-temperature superconducting copper oxides by a new low-energy muon spin rotation technique. The results show that λ _L is isotope dependent, evidencing unconventional electron–phonon interactions as its source. The data are interpreted here in terms of polaronic effects on the single-particle energies, which leads to level shifts and exponential band narrowing. Good agreement with the experimental data is obtained.     

Molecular properties in the Tamm–Dancoff approximation: indirect nuclear spin–spin coupling constants

The Tamm–Dancoff approximation (TDA) can be applied to the computation of excitation energies using time-dependent Hartree–Fock (TD-HF) and time-dependent density-functional theory (TD-DFT). In addition to simplifying the resulting response equations, the TDA has been shown to significantly improve the calculation of triplet excitation energies in these theories, largely overcoming issues associated with triplet instabilities of the underlying reference wave functions. Here, we examine the application of the TDA to the calculation of another response property involving triplet perturbations, namely the indirect nuclear spin–spin coupling constant. Particular attention is paid to the accuracy of the triplet spin–dipole and Fermi-contact components. The application of the TDA in HF calculations leads to vastly improved results. For DFT calculations, the TDA delivers improved stability with respect to geometrical variations but does not deliver higher accuracy close to equilibrium geometries. These observations are rationalised in terms of the ground- and excited-state potential energy surfaces and, in particular, the severity of the triplet instabilities associated with each method. A notable feature of the DFT results within the TDA is their similarity across a wide range of different functionals. The uniformity of the TDA results suggests that some conventional evaluations may exploit error cancellations between approximations in the functional forms and those arising from triplet instabilities. The importance of an accurate treatment of correlation for evaluating spin–spin coupling constants is highlighted by this comparison.     

Energy relaxation and thermalization of hot electrons in quantum wires

We develop a theory of energy relaxation and thermalization of hot carriers in clean quantum wires. Our theory is based on a controlled perturbative approach for large excitation energies and emphasizes the important roles of the electron spin and finite temperature. Unlike in higher dimensions, relaxation in one-dimensional electron liquids requires three-body collisions and is much faster for particles than holes which relax at nonzero temperatures only. Moreover, comoving carriers thermalize more rapidly than counterpropagating carriers. Our results are quantitatively consistent with a recent experiment.     

New correlation potential for the local-spin-density functional formalism I. Total energies and ionization potentials in free atoms

Based on the recently proposed Vosko-Wilk-Nusair interpolation formulae for the correlation energy density of the spin-polarized homogeneous electron liquid, a new parametrized form for the correlation potential for the self-consistent local-spin-density calculations of atoms, molecules and solids is proposed. The total energies and first ionization potentials for a few light atoms are calculated. The influence of the improved spin-polarization dependence on the calculated quantities is investigated, too. The calculated ionization potentials are in good agreement with observed values and are better (in average by 0.3 eV) than the values predicted by the hitherto most commonly used correlation potentials within the local spin density approximation.     

A spin-polarized scheme for obtaining quasi-particle energies within the density functional theory

We discuss an efficient scheme for obtaining spin-polarized quasi-particle excitation energies within the general framework of the density functional theory (DFT). Our approach is to correct the DFT eigenvalues via the electrostatic energy of a majority or minority spin electron resulting from its interaction with the associated exchange and correlation holes by using appropriate spin-resolved pair correlation functions. A version of the method for treating systems with localized orbitals, including the case of partially filled metallic bands, is considered. Illustrative results on Cu are presented.     

Modeling the effect of spin polarization of magnetic moments of electrons on crossover formation

We present the results from investigations of the effect of spin polarization on crossover formation in electron microscopes. Spatial distributions of magnetic states of electrons for the electron beams in the crossover of the electron gun are analyzed by the example of a self-consistent spin-polarization field. The factors able to affect the spatial resolving ability and sensitivity of scanning microscopy are evaluated.     

Dynamic spin-polarized shot noise in a quantum dot coupled to ferromagnetic terminals under the perturbation of ac fields

We have investigated the shot noise in the mesoscopic system composed of a quantum dot (QD) coupled to ferromagnetic terminals under the perturbation of ac fields. The shot noise has been derived using the nonequilibrium Green's function (NGF) technique to describe the spin polarization effect along with photon absorption and emission processes in the Coulomb blockade regime. We have examined the influence of spin polarization on the shot noise under the perturbation of ac fields in the nonadiabatic regime. The Coulomb blockade effect results in the modification of shot noise compared with the noninteracting case. The spin orientation contributes a spin valve effect for controlling electron tunnelling through this QD, and different resonant forms appear around the Coulomb blockade channel. The photon-assisted spin-splitting and spin-polarization effect contributes a photon-assisted spin valve to adjust the electron tunnelling current and shot noise. The spin-polarization effect varies the value of the Fano factor. However, it does not change the noise type from sub-Poissonian to super-Poissonian.     

Surface magnetism of iron on W(110)

Ultrathin bcc iron films grown epitaxially on W(110) have been investigated by means of angle and spin resolving photoelectron spectroscopy. The electron spin polarization, spin resolved intensities and corresponding band structure have been experimentally investigated in dependence of the film thickness, exciting photon energy and variation of the photoelectron detection angle. Additionally, photoemission calculations for bulk iron have been performed in the framework of a relativistic one-step formalism. The comparison between measured and calculated spectra turns out to be in very good agreement for different excitation energies as well as for different angles of emission.     

Spin waves in Hubbard model

Gutzwiller's variational method has been used to study the spin waves in the ferromagnetic state of a narrow band. The spin wave energies are investigated in both the nondegenerate and the doubly degenerate bands. The electron correlation restricts the spin excitations and so improves the RPA solutions of the magnon energies. It is found that the bare intra-atomic interaction energies in the RPA solutions are replaced by smaller effective ones. In the case of a degenerate band model, contrary to the constant value as predicted by RPA, the Stoner gap parameter is reduced by the correlation effect.     

Light scattering observations of spin reversal excitations in the fractional quantum Hall regime

Resonant inelastic light scattering experiments access the low lying excitations of electron liquids in the fractional quantum Hall regime in the range 2/5≥ν≥1/3. Modes associated with changes in the charge and spin degrees of freedom are measured. Spectra of spin reversed excitations at filling factor ν?1/3 and at ν?2/5 identify a structure of lowest spin-split Landau levels of composite fermions (CFs) that is similar to that of electrons. Observations of spin wave excitations enable determinations of energies required to reverse spin. The spin reversal energies obtained from the spectra illustrate the significant residual interactions of composite fermions. At ν=1/3 energies of spin reversal modes are larger but relatively close to spin conserving excitations that are linked to activated transport. Predictions of composite fermion theory are in good quantitative agreement with experimental results.     

Effect of atomic disorder and temperature on incommensurate helical spin waves in the Anderson–Hubbard model

Based on the single-band t–t' Anderson–Hubbard model, the effect of disorder on the parameters and ranges of existence of incommensurate helical spin waves is studied. The problem is solved within the functional integration theory in static approximation, taking into account longitudinal fluctuations of the magnetic moment. Magnetic phase diagrams and parameters of incommensurate helical spin waves are obtained as functions of temperatures and electron and impurity concentrations. It is shown that disorder can lead to the first-order transition from the antiferromagnetic phase to the (Q, π) phase and the metal–dielectric transition from antiferromagnetic metal to antiferromagnetic dielectric far from the half-filled band. The results obtained are used to explain the incommensurate magnetic order observed in cuprates in the overdoped mode.     

自旋极化度对GaAs量子阱中吸收饱和效应与载流子复合动力学的影响研究

本文研究了(001) GaAs量子阱薄膜中重空穴激子近共振抽运-探测的载流子自旋弛豫动力学, 发现载流子的自旋极化对传统的线偏振光吸收饱和效应和载流子复合动力学都有影响. 进一步的抽运流依赖的自旋弛豫和复合动力学研究表明, 自旋极化对线偏振光的吸收饱和效应的影响随抽运流降低而变弱. 在低激发流时, 自旋极化对线偏振吸收饱和效应的影响才可忽略. 然而, 又显现出自旋极化对复合动力学的影响. 分析表明复合动力学的自旋极化依赖性起源于重空穴激子形成浓度的自旋极化依赖性. 复合动力学的自旋极化依赖性表明自旋弛豫时间计算中所涉及的复合时间应该使用自旋极化载流子的复合时间. 基于二维质量作用定律的激子浓度计算表明, 库仑屏蔽效应对激子形成的影响在较低激发载流子浓度下可以忽略.