Exact Exchange Effects Research Articles

Understanding plasmon coupling in nanoparticle dimers using molecular orbitals and configuration interaction.

We perform a theoretical investigation of the electronic structure and optical properties of atomic nanowire and nanorod dimers using DFT and TDDFT. In both systems at separation distances larger than 0.75 nm, optical spectra show a single feature that resembles the bonding dipole plasmon (BDP) mode. A configuration interaction (CI) analysis shows that the BDP mode arises from constructive coupling of transitions, whereas the destructive coupling does not produce significant oscillator strength for such separation distances. At shorter separation distances, both constructive and destructive coupling produce oscillator strength due to wave-function overlap, which results in multiple features in the calculated spectra. Our analysis shows that a charge-transfer plasmon (CTP) mode arises from destructive coupling of transitions, whereas the BDP results from constructive coupling of the same transitions at shorter separation distances. Furthermore, the coupling elements between these transitions are shown to depend heavily on the amount of exact Hartree-Fock exchange (HFX) in the functional, which affects the splitting of CTP and BDP modes. With 50% HFX or more, the CTP and BDP modes mainly merge into a single feature in the spectra. These findings suggest that the effects of exact exchange must be assessed during the prediction of CTP modes in plasmonic systems.

The effects of exact exchange of density functionals on the evaluation of second hyperpolarizabilities of streptocyanines using sum-over-states method

TDDFT calculations are used to discuss the effects of the exact exchange (Ex) on the evaluation of second hyperpolarizabilities (γyyyy) of streptocyanines (3–9 carbons). The results confirm that TDDFT calculations are reliable on the reproduction of the first excitation energies (E01) compared with experiments (within 0.3eV deviations). The sum-over-states (SOS) calculations based on TDDFT suggest that the percentages of Ex determines the γyyyy. The nonlinear optical (NLO) active region of streptocyanines is the π-bridge conjugation where the bond length is between 2 and 3au. Within this area, the higher the percentage of Ex is, the lower the γyyyy is (γyyyy is normally negative for streptocyanines). The γyyyy can be decomposed into T and N contributions according to the three-level SOS method. The decomposition shows that the T term significantly decreases with the increasing percentages of Ex, while N term gradually increases. Therefore, hybrid generalized gradient approximation (hGGA), hybrid meta-generalized gradient approximation (hybrid meta-GGA) and long-range corrected (LRC) functionals tend to overestimate γyyyy. The functional tuning process can improve the results due to the decreasing of ω. This means the deviation of γyyyy do NOT corresponds to the delocalization error (DE). Consequently, the pure GGA, pure meta-GGA, and LRC with small ω can give qualitative correct results.

The individual and collective effects of exact exchange and dispersion interactions on the ab initio structure of liquid water.

In this work, we report the results of a series of density functional theory (DFT) based ab initio molecular dynamics (AIMD) simulations of ambient liquid water using a hierarchy of exchange-correlation (XC) functionals to investigate the individual and collective effects of exact exchange (Exx), via the PBE0 hybrid functional, non-local van der Waals/dispersion (vdW) interactions, via a fully self-consistent density-dependent dispersion correction, and an approximate treatment of nuclear quantum effects, via a 30 K increase in the simulation temperature, on the microscopic structure of liquid water. Based on these AIMD simulations, we found that the collective inclusion of Exx and vdW as resulting from a large-scale AIMD simulation of (H2O)128 significantly softens the structure of ambient liquid water and yields an oxygen-oxygen structure factor, SOO(Q), and corresponding oxygen-oxygen radial distribution function, gOO(r), that are now in quantitative agreement with the best available experimental data. This level of agreement between simulation and experiment demonstrated herein originates from an increase in the relative population of water molecules in the interstitial region between the first and second coordination shells, a collective reorganization in the liquid phase which is facilitated by a weakening of the hydrogen bond strength by the use of a hybrid XC functional, coupled with a relative stabilization of the resultant disordered liquid water configurations by the inclusion of non-local vdW/dispersion interactions. This increasingly more accurate description of the underlying hydrogen bond network in liquid water also yields higher-order correlation functions, such as the oxygen-oxygen-oxygen triplet angular distribution, POOO(θ), and therefore the degree of local tetrahedrality, as well as electrostatic properties, such as the effective molecular dipole moment, that are in much better agreement with experiment.

Short-range exact exchange effects in ultra-narrow zigzag silicon carbide nanoribbons

The hydrogen-passivated N chains zigzag silicon carbide nanoribbons (N-ZSiC NRs) are indexed by its width N (the number of zigzag Si–C chains across the nanoribbon). Using density-functional theory (DFT) with the Heyd–Scuseria–Ernzerh screened hybrid functional (HSE06) and the Perdew–Burke–Ernzerhof functional (PBE), we investigate the edge energy and electronic and magnetic properties of the ultra-narrow N-ZSiC NRs (2 6). Our calculated results reveal effects of short-range exact exchange on the edge energy, the band gap, and the magnetic properties of the ultra-narrow N-ZSiC NRs. It is noted that the inclusion of a portion of short-range exact exchange enhances the calculated band gap. HSE06 functional calculations confirm that the ultra-narrow N-ZSiC NRs (4 6) are ferrimagnetic semiconductors, and the 2-ZSiC and 3-ZSiC NRs are nonmagnetic semiconductors. Moreover, the calculated local magnetic moments at the edge carbon and silicon atoms (those connected to hydrogen). It is also found that the inclusion of a portion of short-range exact exchange always lower the calculated edge energy of the ultra-narrow N-ZSiC NRs. As a comparison we also used the HSE06 functional as well as the PBE functional to investigate the edge energy, as well as electronic and magnetic properties, of the hydrogen-passivated N chains zigzag graphene nanoribbon (N-ZG NRs, 2 4). It is noted that the short-range exact exchange corrections to the edge energy, band gap, and edge atom's local magnetic moment are more striking in the ultra-narrow N-ZG NRs than in the ultra-narrow N-ZSiC NRs. At lastly, we present the origin why when 3, the N-ZSiC NR has only a NM state, while all N-ZG NRs have AFM states.

PAMELA: An open-source software package for calculating nonlocal exact exchange effects on electron gases in core-shell nanowires

We present a new pseudospectral approach for incorporating many-body, nonlocal exact exchange interactions to understand the formation of electron gases in core-shell nanowires. Our approach is efficiently implemented in the open-source software package PAMELA (Pseudospectral Analysis Method with Exchange & Local Approximations) that can calculate electronic energies, densities, wavefunctions, and band-bending diagrams within a self-consistent Schrödinger-Poisson formalism. The implementation of both local and nonlocal electronic effects using pseudospectral methods is key to PAMELA's efficiency, resulting in significantly reduced computational effort compared to finite-element methods. In contrast to the new nonlocal exchange formalism implemented in this work, we find that the simple, conventional Schrödinger-Poisson approaches commonly used in the literature (1) considerably overestimate the number of occupied electron levels, (2) overdelocalize electrons in nanowires, and (3) significantly underestimate the relative energy separation between electronic subbands. In addition, we perform several calculations in the high-doping regime that show a critical tunneling depth exists in these nanosystems where tunneling from the core-shell interface to the nanowire edge becomes the dominant mechanism of electron gas formation. Finally, in order to present a general-purpose set of tools that both experimentalists and theorists can easily use to predict electron gas formation in core-shell nanowires, we document and provide our efficient and user-friendly PAMELA source code that is freely available at http://alum.mit.edu/www/usagi.

Studies on the vibrational excitation differential cross sections of non-resonant e-N2 scattering using augmented polarization potentials

Distributed spherical Gaussian (DSG) correlation-polarization model potentials with higher-order terms and exact exchange effects in single-configuration Slater determinant are taken into account for low-energy vibrational excitation e-N2 scattering system. The integrodifferential coupled channel equations are solved using a combination of linear-algebraic and R-matrix-propagator algorithms. Analytic Born completion is used to calculate high-order scattering matrix elements in order to obtain convergent differential cross sections. The energy range is set to 4–15 eV which is not tested by the present theoretical method before. The overall agreement of theoretical results with the latest experiments emphasizes the importance of higher-order correlation-polarization potentials and rigorous exchange effects in vibrational excitation scattering.

Integral and Momentum Cross Sections for Electron Elastic and Vibrational Excitation Scattering with Nitrogen in the Energy Range 5–30 eV

Integral and momentum transfer cross sections are calculated in the energy range from 5 to 30 eV and compared with other calculated and measured data. The overall agreement between our present results and various theoretical and experimental results are obtained. The present results are obtained by solving integrodifferential body-frame vibrational close-coupling equations. Distributed spherical Gaussian correlation-polarization model potentials with high-order terms and exact exchange effects in a single-configuration Slater determinant are used. The analytic Born completion method is also used to calculate high-order scattering matrix elements.

Practical failures from the inclusion of exact exchange: how much exact exchange is appropriate?

The influence of exact exchange incorporated into exchange—correlation functionals on the predictions of relative energies, structures, electronic states, and vibrational spectra is examined numerically. Failures of widely used hybrid exchange—correlation functionals due to either the physical unacceptability of including exact exchange or an unbalanced mixing of exact exchange are considered. One set of examples involves tetraatomic chalcogen clusters and charge transfer complexes between diatomic chalcogens and diatomic oxygen. Poor energetic predictions from Hartree-Fock rule against the inclusion of exact exchange into the exchange—correlation functionals for these systems with significant left—right electron correlation effects. The energies of the conformers of [10]annulene are considered from an unusual viewpoint, namely, the empirical adjustment of the admixture of exact exchange to match the predictions of very high level theoretical methods. For this annulene with insignificant left-right electron correlation effects, a greater (50%) percentage of exact exchange should be included. The relationship of symmetry breaking to the inclusion of exact exchange is examined for seven linear radicals, OXO (X = B, Al, Ga, In, TI). AIOS, and OAIS. exchange—correlation functionals generate symmetry adapted solutions at the expense of an unusual ordering of the Kohn-Sham orbitals, which can cause uncharacteristic electronic states, incorrect vibrational spectra, and poorer predictions of energetics. These effects are greater when exact exchange is included. In all the examples considered, the appropriate focus for a detailed discussion of molecular properties involves consideration of the effects of exact exchange.

Exact exchange effects on vibrational excitation ofH2by electron impact

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Implementation of nonseparable exact exchange effects in the first-order nondegenerate adiabatic theory.

We have implemented nonlocal exchange effects rigorously in the first-order nondegenerate adiabatic (FONDA) theory. This implementation requires solving integrodifferential equations that involve double integrals. Separable and model exchange approximations that simplify the inclusion of exchange in the scattering calculations have been previously implemented in the FONDA theory. The discrepancy between the exact exchange FONDA cross sections and the separable and model exchange results suggests that one needs to include exchange rigorously to obtain accurate results over a wide range of energies. Specifically, a difference of up to 30% is observed between the exact and separable exchange FONDA cross sections at near-threshold energies. At higher energies the FONDA results from the rigorous and model exchange implementations disagree by as much as 10%.