Two-electron Excitation Research Articles

Exploration of the Two-Electron Excitation Space with Data-Driven Coupled Cluster.

Computational cost limits the applicability of post-Hartree-Fock methods such as coupled-cluster on larger molecular systems. The data-driven coupled-cluster (DDCC) method applies machine learning to predict the coupled-cluster two-electron amplitudes (t2) using data from second-order perturbation theory (MP2). One major limitation of the DDCC models is the size of training sets that increases exponentially with the system size. Effective sampling of the amplitude space can resolve this issue. Five different amplitude selection techniques that reduce the amount of data used for training were evaluated, an approach that also prevents model overfitting and increases the portability of data-driven coupled-cluster singles and doubles to more complex molecules or larger basis sets. In combination with a localized orbital formalism to predict the CCSD t2 amplitudes, we have achieved a 10-fold error reduction for energy calculations.

Differential Measurement of Electron Ejection after Two-Photon Two-Electron Excitation of Helium.

We report the measurement of the photoelectron angular distribution of two-photon single-ionization near the 2p^{2} ^{1}D^{e} double-excitation resonance in helium, benchmarking the fundamental nonlinear interaction of two photons with two correlated electrons. This observation is enabled by the unique combination of intense extreme ultraviolet pulses, delivered at the high-repetition-rate free-electron laser in Hamburg (FLASH), ionizing a jet of cryogenically cooled helium atoms in a reaction microscope. The spectral structure of the intense self-amplified spontaneous emission free-electron laser pulses has been resolved on a single-shot level to allow for post selection of pulses, leading to an enhanced spectral resolution, and introducing a new experimental method. The measured angular distribution is directly compared to state-of-the-art theory based on multichannel quantum defect theory and the streamlined R-matrix method. These results and experimental methodology open a promising route for exploring fundamental interactions of few photons with few electrons in general.

Neutral excitation density-functional theory: an efficient and variational first-principles method for simulating neutral excitations in molecules

We introduce neutral excitation density-functional theory (XDFT), a computationally light, generally applicable, first-principles technique for calculating neutral electronic excitations. The concept is to generalise constrained density functional theory to free it from any assumptions about the spatial confinement of electrons and holes, but to maintain all the advantages of a variational method. The task of calculating the lowest excited state of a given symmetry is thereby simplified to one of performing a simple, low-cost sequence of coupled DFT calculations. We demonstrate the efficacy of the method by calculating the lowest single-particle singlet and triplet excitation energies in the well-known Thiel molecular test set, with results which are in good agreement with linear-response time-dependent density functional theory (LR-TDDFT). Furthermore, we show that XDFT can successfully capture two-electron excitations, in principle, offering a flexible approach to target specific effects beyond state-of-the-art adiabatic-kernel LR-TDDFT. Overall the method makes optical gaps and electron-hole binding energies readily accessible at a computational cost and scaling comparable to that of standard density functional theory. Owing to its multiple qualities beneficial to high-throughput studies where the optical gap is of particular interest; namely broad applicability, low computational demand, and ease of implementation and automation, XDFT presents as a viable candidate for research within materials discovery and informatics frameworks.

Separation of electron-electron and electron-proton correlation in multicomponent orbital-optimized perturbation theory.

The multicomponent orbital-optimized second-order Møller-Plesset perturbation theory (OOMP2) method is the first multicomponent MP2 method that is able to calculate qualitatively accurate protonic densities, protonic affinities, and geometrical changes due to nuclear quantum effects in multicomponent systems. In this study, two approximations of the multicomponent OOMP2 method are introduced in an effort to demonstrate that, in orbital-optimized multicomponent methods, performing the orbital-optimization process with only electron-proton correlation is sufficient to obtain accurate protonic properties. Additionally, these approximations should reduce the computational expense of the multicomponent OOMP2 method. In the first approximation, the first-order wave function is written as a linear combination of one-electron one-proton excitations rather than as a linear combination of one-electron one-proton and two-electron excitations as in the original multicomponent OOMP2 method. Electron-electron correlation is included perturbatively after the orbital-optimization procedure has converged. In the second approach, the first approximation is further modified to neglect all terms in the orbital-rotation gradients that depend on the two-electron molecular-orbital integrals, which, assuming a fixed-sized protonic basis set, reduces the computational scaling for the orbital-optimization iterations to Ne 3, where Ne is a measure of the electronic system size, compared to the Ne 5 scaling of the original multicomponent OOMP2 method. The second approximation requires one Ne 5 step after orbital convergence to compute the electron-electron correlation energy. The accuracy of the calculated protonic densities, protonic affinities, and optimized geometries of these approximations is similar or improved relative to the original multicomponent OOMP2 method.

Quantum Infrastructure of Attosecond Sensors and Actuators of Nonequilibrium Physical Media in Smart Materials

The advances in new smart materials are linked with attosecond subatomic technologies which can create entangled subatomic electron pairs by attosecond hard ultraviolet and soft X rays in addition to one-electron excitations by femtosecond optical pulses. The quantum infrastructure of nonequilibrium physical media in smart materials is provided by the Fermi and Bose gas of quasi-electron excitations, and the quantum infrastructure of their space-time scales is specified by the quantum mechanisms of two-electron attophysics and one-electron femtochemistry. The primary scale is subatomic (1.0 pm to 0.1 nm), and the next scale is supra-atomic (0.1 to 10.0 nm), being the scale of nanoelectromechanical systems of sensors and actuators that provide self-organization in the space-time hierarchy of nano-, micro-, meso-, and macroscopic dissipative structures of nonequilibrium physical media in smart materials. Here we show that any quantum nanoelectromechanical system can alternately be a sensor and an actuator of dissipative structures with a two-clock cycle: an attosecond sensor of entangled two-electron excitations and a femtosecond actuator of electromechanical motion modes in a nonequilibrium physical medium. For such nanoelectromechanical sensors-actuators, the motion rhythm is three orders of magnitude faster than for femtosecond nanomolecular sensors of one-electron excitations and nanomolecular actuators of vibrationrotation modes in nonequilibrium physical media.

Excitation Mechanisms in Moderate-Energy Li+–He Collisions

Excitation mechanisms in Li+–He collisions were studied at laboratory collision energies of 350 ≤ Elab ≤ 2000 eV by measuring double differential cross sections (DCSs) σ(Θ)k over a wide range of center-of-mass scattering angles, 2.5 ≤ Θ ≤ 175°. At Elab ≥ 500 eV, two-electron (2e) excitations were observed as well as one-electron (1e) excitations. At the higher collision energies, excitation probabilities P(Θ)k for the 1e and 2e excitations have characteristic angular dependences, i.e., at Elab = 1500 and 2000 eV, P(Θ)1e for the 1e excitations has double maxima around Θ = 20 and 120° and P(Θ)2e for the 2e excitations has a broad maximum around Θ = 60°. As a first analysis of the experimental data, P(Θ)k, σ(Θ)k, and the integral cross sections Sk(Elab) were calculated by assuming excitations from the 11Σ state into the 11Π and 11Δ states through rotational couplings using the model potentials and couplings. As the next step, ab initio potential energies for the ground and excited states were calculated by a...

Resonance enhanced electron impact excitation for P-like Cu XV**Project supported by the National Natural Science Foundation of China (Grant Nos. 11076009 and 11374062), the Chinese Association of Atomic and Molecular Data, the Chinese National Fusion Project for ITER (Grant No. 2015GB117000), and the Leading Academic Discipline Project of Shanghai, China (Grant No. B107).

Employing both the Dirac R-matrix and the relativistic distorted wave with independent process and isolated resonance approaches, we report resonance enhanced electron impact excitation data (specifically, effective collision strengths) among the lowest 41 levels from the n = 3 configurations of Cu XV. The results show that the latter approach can obtain resonance contributions reasonably well for most excitations of Cu XV, though a comparison between the two approaches shows that the close-coupling effects are truly significant for rather weak excitations, especially for two-electron excitations from the 3s3p4 to 3s23p23d configuration. Resonance contributions are significant (more than two orders of magnitude) for many excitations and dramatically influence the line intensity ratios associated with density diagnostics.

Singlet and triplet instability theorems.

A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree-Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree-Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree-Fock-theory-based explanations of Hund's rule, a singlet instability in Jahn-Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.

Benchmarking the completely renormalised equation-of-motion coupled-cluster approaches for vertical excitation energies

The vertical excitation energies for a comprehensive test set of about 150 singlet excited states of 28 medium-sized organic molecules computed using two variants of the completely renormalised (CR) equation-of-motion (EOM) coupled-cluster (CC) method with singles, doubles, and non-iterative triples, abbreviated as δ-CR-EOMCCSD(T), and the analogous two variants of the newer, left-eigenstate δ-CR-EOMCC(2,3) approach are benchmarked against the previously published CASPT2, CC3, and EOMCCSDT-3 results, as well as the suggested theoretical best estimate (TBE) values. The δ-CR-EOMCC approaches are also used to identify and characterise about 50 additional excited states, including several states having substantial two-electron excitation components, which have not been found in the previous work and which can be used in future benchmark studies. It is demonstrated that the non-iterative triples corrections to the EOMCCSD excitation energies defining the relatively inexpensive, single-reference, black-box δ-CR-EOMCC approaches provide significant improvements in the EOMCCSD data, while closely matching the results of the iterative and considerably more expensive CC3 and EOMCCSDT-3 calculations and their CASPT2 and TBE counterparts. It is also shown that the δ-CR-EOMCC methods, especially δ-CR-EOMCC(2,3), are capable of bringing the results of the CC3 and EOMCCSDT-3 calculations to a closer agreement with the CASPT2 and TBE data, demonstrating the utility of the cost-effective δ-CR-EOMCC methods in applications involving molecular electronic spectra. We show that there may exist a relationship between the magnitude of the triples corrections defining δ-CR-EOMCC approaches and the reduced excitation level diagnostic resulting from EOMCCSD.

Photoionization cross sections for O-like S IX: a Breit–Pauli R-matrix calculation

In this paper we present photoionization cross sections for the lowest five states of O-like S IX (1s22s22p4 3P0,1,2, 1D2, 1S0). The relativistic Breit–Pauli R-matrix codes were utilized including all terms of the 2s22p3, 2s2p4, 2p5, 2s22p23s, 3p, 3d and 2s2p33s, 3p, 3d configurations in the expansion of the collision wavefunction for S X. It was also found that to achieve convergence of the low-lying energy separations of the target levels, an additional 21 configuration functions needed to be included in the configuration interaction expansion, incorporating two-electron excitations from the 2s and 2p shells to the 3s, 3p and 3d shells. The present work thus constitutes the most sophisticated photoionization evaluation for ground and metastable levels of the S IX ion. Direct comparisons have been made with the only available data found on the OPEN-ADAS database between level resolved contributions of the spectrum. This comparison for the background cross section exhibits excellent agreement at all photon energies for each partial photoionization cross section contribution investigated. Finally, the autoionizing bound states arising from numerous open channels have also been investigated and identified using the QB approach, a procedure for analyzing resonances in atomic and molecular collision theory which exploits the analytic properties of R-matrix theory. Major Rydberg resonance series are also presented and tabulated for the dominant linewidths considered.

Construction of the energy matrix for complex atoms Part III: Excitation of two equivalent electrons from a closed shell into an open shell or an empty shell

The effects of the second-order configuration interaction perturbations on the energy-level structure of nl N , $$nl^N n_1 l_1^{N_1 }$$ and $$nl^N n_1 l_1^{N_1 } n_2 l_2$$ configurations have been studied. In the previous works (see Part I and II) we presented a method, which allows to analyse complex electronic systems composed of configurations including up to four open shells and the formulae for the first-order electrostatic interaction between sophisticated configurations. In the present paper we consider two-electron core excitations for and between the configurations under study. They constitute the basis for the design of an efficient computer program package allowing large-scale calculations providing accurate wave functions.

Excitation Mechanisms in Moderate-Energy Na+–He and K+–He Collisions

Excitation mechanisms in Na + –He and K + –He collisions were studied at laboratory collision energies of 1000 ¯ Elab ¯ 1500eV by differential scattering spectroscopy. Extensive measurements were performed at Elab = 1500eV. Double differential cross sections ·(©)k were measured over a wide range of center-of-mass scattering angles, 7.3 ¯ © ¯ 173°, by detecting all the scattered particles (Na + , Na, K + ,K , He + , and He), where the subscript k denotes the number of exit channels in the reactions. At the collision energy of Elab = 1500eV, one- and two-electron excitations were observed appreciably for the Na + –He collisions, while only one-electron excitations were observed in the K + –He collisions. The analyses of the experimental results for these collision systems indicate that the electronic transitions in the Na + –He and K + –He collisions take place at the internuclear distances of R 49eV] and R 36eV], respectively. For these asymmetric systems, at Elab= 1500eV, the electronic transition probabilities around the threshold angles are so small that the integral excitation cross sections have small values of Sex < 1.2 © 10 ¹21 m 2 .

Spectroscopic Diagnostics of Laser Plasma Plume of Aluminum

The emission of aluminum Al laser ablated plasma has been investigated in the 200-600 nm spectral range. The most intensive spectral lines were 308.2; 309.3; 394.4 and 396.2 nm Al I. The highest levels of neutral atoms, responsible for the detected spectral lines, correspond to the two-electron excitation with 8.3-9.06 eV energy. The time average value of electron temperature on the 1 and 7 mm distances from the target was calculated. It is 0.43 eV for 1 mm and 0.51 eV for 7 mm distance from the target. The experimentally obtained time of recombination (29 ns) have been used to extract the electron number density at 1 mm from the target which is 9.4×1015 cm-3. The time-resolved emission of atomic spectral lines at 1 mm distance from the target was studied. The maximums of aluminum spectral lines emission have appeared in times of 8-20 ns, which correspond to atom velocities of (0.05-0.13)106 m/s.

High-resolution x-ray-emission study of1s4pand1s3dtwo-electron photoexcitations in Kr

photoexcitation spectra. Both two-electron excitation spectra are well described by a model spectrum builtofconsecutivebound-bounddiscretetransitionsandshake-upandshake-offchannelsgivingpreciseenergiesandintensitiesofthecorrespondingcontributions.Theobtainedresultsarecomparedwithotherexistingexperimentalvalues based on x-ray-absorption measurements and theoretical predictions.DOI: 10.1103/PhysRevA.90.022513 PACS number(s): 32

Excitation of autoionizing states of helium-like ions by high-energy electron scattering

We have evaluated the cross sections for two-electron excitations of helium-like ions into the autoionizing ( 2 s 2 p ) 1 P states by high-energy electron scattering. The problem is solved to leading orders of non-relativistic perturbation theory. The analytical formulas for cross sections are deduced in the form of universal scaling. The resonant electron-emission yield is calculated with taking into account the interference between direct and sequential ionization channels. A comparison between the present results and the experimental data for helium atom is made.

Electron-hole spin flip-flop in semiconductor quantum dots

We use temporally resolved intensity cross-correlation measurements to identify the biexciton-exciton radiative cascades in a negatively charged QD. The polarization sensitive correlation measurements show unambiguously that the excited two-electron triplet states relax nonradiatively to their singlet ground state via a spin nonconserving flip-flop with the ground state heavy hole. We explain this mechanism in terms of resonant coupling between the confined electron states and an LO phonon. This resonant interaction together with the electron-hole exchange interaction provides an efficient mechanism for this otherwise spin-blockaded, electronic relaxation.

Two-electron photoionization processes in He@C60 using the R-matrix with pseudostates and time-dependent close-coupling methods

The R-matrix with pseudostates method is applied to the case of two-electron excitation and ionization processes in He@C60. A finite spherical-well potential, which simulates the effect of the fullerene enclosing cage, is incorporated into the Hamiltonian using a modified R-matrix method, as recently applied to similar single photoionization studies of Xe@C60 and Ca@C60. Comparison is made with time-dependent close-coupling results for two-electron processes in He and He@C60, and excellent agreement is found in the respective descriptions of confinement resonances. Earlier findings are confirmed that the cage potential causes a redistribution between the n = 2 and n = 3 photoionization–excitation cross sections. The R-matrix with pseudostates method, in particular, is well-suited for treating atomic Feshbach resonances and studying multi-electron systems.

Comparison of low-rank tensor expansions for the acceleration of quantum chemistry computations

Low-rank spectral expansion and tensor hypercontraction are two promising techniques for reducing the size of the two-electron excitation tensor by factorizing it into products of smaller tensors. Both methods can potentially realize an O(r(4)) quantum chemistry method where r is the number of one-electron orbitals. We compare the two factorizations in this paper by applying them to the parametric 2-electron reduced density matrix method with the M functional [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)]. We study several inorganic molecules, alkane chains, and potential curves as well as reaction and dissociation energies. The low-rank spectral expansion, we find, is typically more efficient than tensor hypercontraction due to a faster convergence of the energy and a smaller constant prefactor in the energy optimization. Both factorizations are applicable to the acceleration of a wide range of wavefunction and reduced-density-matrix methods.

Excitation of autoionizing states of helium-like ions by scattering of high-energy particles

The cross sections for two-electron excitations of helium-like atomic systems into the autoionizing 2s 2 (1 S)- and 2p 2 (1 S)-states by collisions with high-energy electrons and photons are deduced. The evaluations are performed to the leading order of non-relativistic perturbation theory. The analytical formulas for cross sections are obtained in the form of universal scalings. A comparison of our theoretical predictions with available theoretical and experimental results for the helium atom is made.

Theoretical study of level structure and transitions of configurations 3d94s2 3d94s4p, 3d94p2 for Nb XIII

Fine-structure energy levels of two-electron excitation configurations 3d94s2, 3d94s4p, 3d94p2 are calculated by Hartree-Fock method, which includes the configuration interaction, relativistic correction and approximate Breit correction, for copper-like Nb XIII. More accurate levels are obtained by the least-square-fit technique. The wavelengths and transition probabilities of 3d94s4p-3d104s, 3d94s2-3d104p, 3d94p2-3d104p, 3d94s4p-3d94s2 transition array are obtained, and some unknown results are predicted. Computing research shows that the 40.92 nm line should belong to 3d94s(1D)4p2F7/2-3d9(2D)4s2 2D5/2 transition, but not to the 3d94s(1D)4p4D7/2-3d9(2D)4s2 2D5/2 transition, and the upper term level should be 2F7/2, but not 4D7/2.