Multi-electron States Research Articles

Modeling the doubly excited state with time-dependent Hartree–Fock and density functional theories

Multielectron excited states have become a hot topic in many cutting-edge research fields, such as the photophysics of polyenes and in the possibility of multiexciton generation in quantum dots for the purpose of increasing solar cell efficiency. However, obtaining multielectron excited states has been a major obstacle as it is often done with multiconfigurational methods, which involve formidable computational cost for large systems. Although they are computationally much cheaper than multiconfigurational wave function based methods, linear response adiabatic time-dependent Hartree-Fock (TDHF) and density functional theory (TDDFT) are generally considered incapable of obtaining multielectron excited states. We have developed a real-time TDHF and adiabatic TDDFT approach that is beyond the perturbative regime. We show that TDHF/TDDFT is able to simultaneously excite two electrons from the ground state to the doubly excited state and that the real-time TDHF/TDDFT implicitly includes double excitation within a superposition state. We also present a multireference linear response theory to show that the real-time electron density response corresponds to a superposition of perturbative linear responses of the S(0) and S(2) states. As a result, the energy of the two-electron doubly excited state can be obtained with several different approaches. This is done within the adiabatic approximation of TDDFT, a realm in which the doubly excited state has been deemed missing. We report results on simple two-electron systems, including the energies and dipole moments for the two-electron excited states of H(2) and HeH(+). These results are compared to those obtained with the full configuration interaction method.

Ab Initio Analysis of Exchange Interactions in [V2O(BIPY)4CL2]2+ Complex

In this work an ab initio analysis of the binuclear vanadium complex [V2O(bipy)4Cl2]2+ electronic structure is performed. The ground state was calculated to be a quintet, which means a ferromagnetic interaction between centers. The orbitals participating in exchange interaction according to ROHF+CI calculations are two molecular orbitals consisting of vanadium d-orbitals and two molecular orbitals with main contributions from p-orbitals of bipyridine ligands perpendicular to V-V axis, vanadium d- and p-orbitals and μ-oxygen p-orbital. Calculated energy values of the multielectronic states are placed in accordance with Lande rule. The value of magnetic moment at 293K calculated for the complex in vacuum taking into consideration the Boltzmann distribution and the energies of the excited states is 3.95BM which is in accordance with experimental value of 3.99BM (for complex in acetone).

A New Differential Formula About Product of Polynomials and ItsApplication in Multi-electron State Physics

We derive a new differential formula about a kind ofproduct of polynomials and then apply it to analyze some propertiesof multi-electron state ``related to Laughlin wave function". Theentangled state representation for describing electrons in uniform magneticfield is used.

Jahn–Teller Instability of Correlated C60 Anions

ABSTRACT The results of calculations on static Jahn-Teller ground state splittings inicosahedral fullerene anions with different types of electron-electron interaction are presented. Multielectron states of anions are determined within a quasy-π-electronic model configuration interaction (CI) method for two active spaces of t1u and t1u + t1g molecular orbitals. Electron–lattice interaction is taken into account over a linear dependence of the neighbor site resonance integrals on the correspondent length change. The results show that, in opposition to the case of short-range electron repulsion, long-range electron correlation can significantly change the features of the Jahn–Teller splitting.

Calculation of nonadiabatic couplings in density-functional theory

This paper proposes methods for calculating the derivative couplings between adiabatic states in density-functional theory (DFT) and compares them with each other and with multiconfigurational self-consistent field calculations. They are shown to be accurate and, as expected, the costs of their calculation scale more favorably with system size than post-Hartree-Fock calculations. The proposed methods are based on single-particle excitations and the associated Slater transition-state densities to overcome the problem of the unavailability of multielectron states in DFT which precludes a straightforward calculation of the matrix elements of the nuclear gradient operator. An iterative scheme employing linear-response theory was found to offer the best trade-off between accuracy and efficiency. The algorithms presented here have been implemented for doublet-doublet excitations within a plane-wave-basis and pseudopotential framework but are easily generalizable to other excitations and basis sets. Owing to their fundamental importance in cases where the Born-Oppenheimer separation of motions is not valid, these derivative couplings can facilitate, for example, the treatment of nonadiabatic charge transfers, of electron-phonon couplings, and of radiationless electronic transitions in DFT.

Multi-electron strong field theory

We develop a multi-electron strong field theory that takes into account the fully correlated dynamics of bound electrons. The theory is applied to investigate the reconfiguration dynamics of matter during optical field ionization. We obtain analytical results which identify the parameter ranges where multi-electron bound state dynamics plays an important role.

Computational formulas for symmetry-forbidden vibronic spectra and their application to n–π* transition in neat acetone

In this study theoretical expressions are derived to investigate the non-Condon effect for symmetry-forbidden optical transition using displaced–distorted harmonic potential energy surfaces. These expressions can efficiently cope with multipromoting modes and multielectronic states involved in the non-Condon effect at a finite temperature. Ab initio and molecular dynamics calculation results can be directly invoked into the formulas. Based on the proposed formulas, the temperature dependence of the interference effects of multipromoting modes on the non-Condon optical linear spectra is investigated. To demonstrate the computational formulas, the optical absorption and dispersion fluorescence spectra for the forbidden transition of neat acetone, A11–A21(n–π*), are also studied. Simulation results indicate that the vibrational frequency of CH3 torsion mode of acetone plays an important role in the optical spectra. Moreover, the electronic energy gap (adiabatic transition), the Stokes shift caused by environmental interaction, and the average Huang–Rhys factor for intermolecular modes in neat acetone are obtained as 29 900 cm−1, 5400 cm−1, and 0.607, respectively.

Product of Projective Representations in Description of Multi-Electron States in An External Magnetic Field

In this paper all inequivalent irreducible projective representations of the two-dimensional translation group for a given factor system are determined. A normalized, i.e. corresponding to the Landau gauge, factor system is considered. Obtained representations directly lead to concept of magnetic cells and to periodicity with respect to the charge of a moving particle. It is also shown that the quantization condition is imposed on the product qH of the charge q and the magnitude of magnetic field H. The Kronecker product of such representations is considered and it is proven that the multiplication of representations corresponds to the addition of charges of particles moving in a given external magnetic field. In general, coupling of d representations corresponds to d-particle states. Presented results can be applied in any problem related to two-dimensional electron gas in a magnetic field, for example in the fractional quantum Hall effect or high temperature superconductivity. PACS numbers: 03.65.Fd, 02.10.Sp, 71.70.Di

An Investigation of the Electron Transfer and Repulsive Coulomb Interactions in the One-, Two-, Three-Dimensional Isotropic Hubbard Models I: Eigenfunctions and Eigenvalues

In this paper we investigate the Hubbard model, with S-orbits on each site, for one-, two- and three-dimensional isotropic lattices with arbitrary values of transfer and on-site repulsion parameters. The method of diagonalization is based on equivalences due to Stevens for number conserving operators and a unitary transformation utilizing permutational symmetries of the problem. We obtained simple analytical formulas for single particle eigenstates and somewhat more involved expression for determinantal multi-electron states. Numerical calculations have been performed which demonstrate the boundaries of the lowest band for various filling factors using examples in one- and two-dimensions. The states within the band have also been identified and degeneracies evaluated numerically. These computations were based on a Monté Carlo technique in conjunction with particle conservation requirements. Agreement with some well-known limiting cases has been found.

Cross-modulation coupling of incoherent soliton modes in photorefractive crystals

A problem of nonlinear wave propagation through a photorefractive crystal (PRC) with drift nonlinearity has been evaluated. A class of spatially localized solitonlike solutions with finite energy has been found. Solutions of this class can be considered as multicomponent solitons, combined by two or more mutually incoherent self-consistent components bonded by cross-modulation coupling. Light field spatial distributions of the components look like zero and higher order modes of their common waveguide formed in PRC due to its nonlinearity. We have shown such a soliton is stable on distances of several diffraction lengths and its spatial structure is robust to collisions and appreciable (more than 10% in intensity) stochastic perturbations of the intensity distributions. With taking into account saturation of PRC nonlinearity, parameters of all the soliton components (their amplitudes and widths) change quasiperiodically as the soliton propagates. The components do not exchange energy while a small fraction of the energy is emitted on few diffraction lengths. We discuss also a possibility of excitation of incoherent solitonlike multielectron states in conjugated polymers, ferromagnetics, and superconductors. These states could correspond to some mutually incoherent and self-consistent wave packets composed of electronic wave functions and propagating along conjugated chains or prominent atomic planes.

A REMPI study of the correlation of internal excitations and substrate-adsorbate coupling for CO molecules desorbed by electron impact

We compare vibrational, translational and rotational excitations of CO molecules desorbed by electron impact, and the yield of oxygen and carbon atoms from electron-induced fragmentation of CO molecules for: (1) CO monolayers on bare transition metals [Ru(001) and Pt(111)]; (2) CO monolayers coadsorbed with well-ordered oxygen atoms; (3) weakly bound CO monolayers on epitaxially grown silver films; and (4) CO monolayers decoupled from the metallic substrate by mono-atomic xenon spacer layers. For all but the last system, we find CO molecules which are vibrationally extremely hot. This is explained by the excitation of strongly antibonding multi-electron states which are quenched in the vicinity of the metal surface before enough translational energy is acquired by the nuclei to complete dissociation. For CO/Xe/Ag(111), vibrationally hot CO molecules are missing among the desorbing particles, whereas strong fragment signals persist. Because of the isolating Xe layer, the substrate-adsorbate coupling is too weak to terminate the dissociation reaction which is induced by the electron impact before the rupture of the molecular bond.

Correlated electrons in coupled quantum dots and related phenomena

Three topics related to correlated electrons in coupled quantum dots are discussed. The first is quasi-resonance between multi-electron states, which causes hitherto unremarked types of resonant absorption in coupled quantum dots. The second is electron tunneling through a Hubbard gap, which is induced by an increase in the density of electrons in a quantum-dot chain under an overall confining potential. The third is Mott transition in a two-dimensional quantum-dot array induced by an external electric field. In this system, the metal-insulator transition goes through a heavy electron phase in which the density of correlated electrons fluctuates.

Coherent transport through a coupled-quantum-dot system with strong intradot interaction.

The coherent transport through a coupled-quantum-dot system with strong intradot interaction is investigated by the nonequilibrium Green's-functions method. The conductance as a function of the chemical potential, and the I-V curves are presented. Both of them display oscillation structures, and the number of peaks depends on the energy spectrum of the dots. All the phenomena can be understood on the basis of the coupling between the multielectron states in the two dots. When the temperature is higher than the Kondo temperature, the coupling between the two dots is equivalent to the coupling between several renormalized resonant levels. The density of states of each level displays an unsymmetrical structure, and the coupling coefficients are modified by the electron occupancy in the dots.

Electronic Spaces and Classification of Multielectron States in Multicentre Systems

Electronic Spaces and Classification of Multielectron States in Multicentre Systems

Observation of the formation of N+ and ArN+ in the collisions of Ar+(2P3/2,1/2) with N2

Absolute total cross sections for the reactions, Ar+(2P3/2,1/2)+N2→N++N+Ar [reaction (1)] and ArN++N [reaction (2)], have been measured in the center-of-mass collision energy (Ec.m.) range of 6.2–123.5 eV. The appearance energy for the formation of N+ (Ec.m.=8.65±0.21 eV) is in agreement with the thermochemical threshold for reaction (1). The comparison of the collision energy dependence of the N+ cross section with the photoionization efficiency spectrum of N+ from N2 suggests that the predissociative multielectron states of N+2, C̃ 2Σ+u, F̃ 2Σ+g, G̃ 2Σ+g, and 2Σ+g (2σg)−1, which are responsible for the dissociative photoionization of N2, also play a role in the formation of N+ via reaction (1). Product ArN+ ions of reaction (2) are only observed in the Ec.m. range of 8.2–41.2 eV. At Ec.m. slightly above the thermochemical thresholds of reactions (1) and (2), the majority of ArN+ and N+ ions are scattered backward and forward with respect to the center-of-mass velocity of reactant Ar+, respectively. This observation is rationalized by a charge transfer predissociation mechanism which involves the formation of ArN+ and N+ ions via nearly collinear Ar+-N-N collision configurations at Ec.m. near the thresholds of reactions (1) and (2). At Ec.m.≥11 eV, more than 92% of the charge transfer product N+2 ions are found to be slow ions formed mostly by the long-range electron jump mechanism.

Soliton and Polaron Dynamics in Conducting Polymers

Solitons and polarons in conducting polymers are strongly coupled electron-lattice excitations. The lattice relaxation theory generalized by us to include the self-consistency of multi-electron states with lattice symmetry-breaking is summarized. The discrete symmetries and corresponding selection rules for both radiative and nonradiative processes are discussed. Theoretically calculated probability of nonradiative decay of an electron-hole pair into a soliton pair and that of electron (hole) into polaron as well as the probability of soliton pair photo-generation is compared with results of numerical and laboratory experiments. The resonance Raman scattering data of cis-polyacetylene are interpreted in terms of a bipolaron model. The parameters involved are determined directly from experimental data. Other applications of lattice relaxation theory to conducting polymers are briefly mentioned.

Soliton and polaron generation in polyacetylene

Abstract The nonradiative decay of an e-h pair into soliton pair and that of an electron (hole) into polaron as well as the photoproduction of solitonpairs are considered using the lattice relaxation theory generalized to include the self-consistency of multi-electron states with the lattice symmetry breaking. The branching ratio of the photogenarated neutral to charged soliton pairs is estimated. The recent related experiments are discussed.

Theory of Soliton Generation and Lattice Relaxation in Polyacetylene (II) Non-Radiative Transitions

This is the second paper in a series devoted to the theory of soliton and polaron generation in polyacetylene by both radiative and non-radiative processes. The general formalism presented in the first paper of this series which combines the lattice relaxatipn theory of multiphonon processes with the adiabatic self-consistency condition in terms of the Bogoliubovde Gennes equation and the gap equation, is applied in this paper to explicit calculation of the non-radiative decay rate of an electron(ho1e) into a plaron and that of an electron-hole pair into a soliton pair in polyacetylene. A heuristic derivation for the formula of non-radiative decay rate is given to elucidate the physical meaning of the approximation involved in the case of low temperature and strong coupling. The matrix elements between multi-electron states are estimated in the Hartree approximation using the single electron states obtained as solutions of the Bogoliubov-de Gennes equation. The result obtained is compared with the numerical calculations on a discrete model.

Theory of Soliton Generation and Lattice Relaxation in Polyacetylene (I) General Formalism

This series of papers is devoted to the theory of soliton and polaron generation in polyacetylene by both radiative and non-radiative processes. In the first paper of this series a general formalism is presented which combines the Lattice relaxation approach for the multiphonon process developed by Huang and many others with the consistency condition in terms of the Bogoliubov-de Gennes equation and the gap equation. The exact adiabatic electron wave functions consistent with the different lattice symmetry breaking in the initial and final states are used to calculate the transition probability between these multi-electron states. The formalism presented is illustrated by deriving a general expression for the non-radiative decay rate using the steepest descent method in the case of strong coupling. The theory developed here can be applied to treating the quantum transitions between states of differnet symmetry breaking when the multi-electron background effect and the consistency condition are essential. The applications of the general formalism to polyacetylene and the comparison with numerical results and the recent experiments wi11 be given in the succeeding papers.