Use Of Many-body Perturbation Theory Research Articles

Electronic Properties of III-V Semiconductor Photocathode-Water Interfaces: Predictions from First-Principles Calculations

Photoelectrochemical (PEC) cells based on III-V semiconductor photocathodes offer a promising avenue for hydrogen production from water and sunlight. The efficiency of these devices depends on the electronic structure of the interface between the photocathode and liquid water, including the alignment between the semiconductor band edges and the water redox potential. Accurate theoretical predictions of this quantity remain a challenging task, as conventional electronic structure methods such as density functional theory (DFT) often yield substantial errors [1]. In this talk, we present calculations of the electronic properties of two representative III-V semiconductor electrodes, i.e. GaP and InP, at the interface with water using a combination of first-principles molecular dynamics simulations and many-body perturbation theory (MBPT). We show that the use of MBPT is key to obtain band alignments in agreement with experimental measurements. In addition, we describe the relationship between interfacial structure, electronic properties of semiconductors and their reactivity in aqueous solutions. 1. T. A. Pham, D. Lee, E. Schwegler and G. Galli, J. Am. Chem. Soc. in press (2014). This work was supported by the U.S. Department of Energy at the Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Interfacial effects on the band edges of functionalized si surfaces in liquid water.

By combining ab initio molecular dynamics simulations and many-body perturbation theory calculations of electronic energy levels, we determined the band edge positions of functionalized Si(111) surfaces in the presence of liquid water, with respect to vacuum and to water redox potentials. We considered surface terminations commonly used for Si photoelectrodes in water splitting experiments. We found that, when exposed to water, the semiconductor band edges were shifted by approximately 0.5 eV in the case of hydrophobic surfaces, irrespective of the termination. The effect of the liquid on band edge positions of hydrophilic surfaces was much more significant and determined by a complex combination of structural and electronic effects. These include structural rearrangements of the semiconductor surfaces in the presence of water, changes in the orientation of interfacial water molecules with respect to the bulk liquid, and charge transfer at the interfaces, between the solid and the liquid. Our results showed that the use of many-body perturbation theory is key to obtain results in agreement with experiments; they also showed that the use of simple computational schemes that neglect the detailed microscopic structure of the solid-liquid interface may lead to substantial errors in predicting the alignment between the solid band edges and water redox potentials.

Probing the electronic structure of liquid water with many-body perturbation theory

We present a first-principles investigation of the electronic structure of liquid water based on many-body perturbation theory (MBPT), within the ${G}_{0}{W}_{0}$ approximation. The liquid quasiparticle band gap and the position of its valence band maximum and conduction band minimum with respect to vacuum were computed and it is shown that the use of MBPT is crucial to obtain results that are in good agreement with experiment. We found that the level of theory chosen to generate molecular dynamics trajectories may substantially affect the electronic structure of the liquid, in particular, the relative position of its band edges and redox potentials. Our results represent an essential step in establishing a predictive framework for computing the relative position of water redox potentials and the band edges of semiconductors and insulators.

Combined Theoretical and Experimental Study of Band-Edge Control of Si through Surface Functionalization

The band-edge positions of H-, Cl-, Br-, methyl-, and ethyl-terminated Si(111) surfaces were investigated through a combination of density functional theory (DFT) and many-body perturbation theory, as well as by photoelectron spectroscopy and electrical device measurements. The calculated trends in surface potential shifts as a function of the adsorbate type and coverage are consistent with the calculated strength and direction of the dipole moment of the adsorbate radicals in conjunction with simple electronegativity-based expectations. The quasi-particle energies, such as the ionization potential (IP), that were calculated by use of many-body perturbation theory were in good agreement with experiment. The IP values that were calculated by DFT exhibited substantial errors, but nevertheless, the IP differences, i.e., IPR–Si(111)–IPH–Si(111), computed using DFT were in good agreement with spectroscopic and electrical measurements.

Atomic properties calculated by many-body theory

The use of many-body perturbation theory to calculate atomic properties is discussed. Results are given for correlation energies, hyperfine constants, frequency-dependent polarizabilities, and London dispersion forces.

Effective operators in nuclear-structure calculations

A brief review of the history of the use of many-body perturbation theory to determine effective operators for shell-model calculations, i.e., for calculations in truncated model spaces, is given, starting with the ground-breaking work of Arima and Horie for electromagnetic moments. The problems encountered in utilizing this approach are discussed. New methods based on unitary-transformation approaches are introduced and analyzed. The old problems persist, but the new methods allow us to obtain a better insight into the nature of the physics involved in these processes.

On the use of many-body perturbation theory and quantum-electrodynamics in molecular electronic structure theory

Many-body perturbation theory is firmly established in molecular electronic structure studies both as a method of calculation in its own right and in underpinning other approaches to the electron correlation problem, such as coupled electron pair approximations and various cluster expansions. The central pillar of the many-body perturbation theory is the linked diagram theorem obtained by Goldstone using the method of Feynman graphs to enumerate the terms of the perturbation series. Feynman had introduced his graphs in his formulation of quantum electrodynamics. Goldstone restricted his analysis to the non-relativistic many-body problem, so that interactions were taken to be instantaneous and the effects of relativity were ignored. In recent years, the growing interest in the treatment of relativistic and quantum electrodynamic effects in atoms and molecules has necessitated the re-introduction of physics that has been known for over forty years. A key to this development for molecular systems is a rigorous and robust implementation of the algebraic approximation for Dirac and Dirac-like equations. The algebraic approximation provides a representation of both the positive-energy and the negative-energy branches of the Dirac spectrum. Relativistic many-body perturbation theory, relativistic coupled pair approximations and relativistic coupled cluster theories can be formulated within the ‘no-virtual-pair’ approximation. Such formulations are restricted to the positive energy branch of the spectrum. However, the negative energy states make an essential contribution to the description of atomic and molecular electronic structure. The investigation of this contribution is facilitated by proper implementation of the algebraic approximation using formulations which are amenable to systematic refinement.

Affinities and photodetachment cross sections for the negative ions Si- and Ge-

Affinities and photodetachment cross sections are computed for the negative atomic ions Si- and Ge- by use of many-body perturbation theory. The computed ground-state affinities are 1.350 and 1.227 eV for Si- and Ge-, respectively, in reasonable agreement with the respective experimental values which are 1.389 51(20) and 1.232 712(15) eV. Photodetachment cross sections were obtained by inverting computed (real) dynamic polarizabilities (i) on the imaginary frequency axis by use of a simple dispersion relation. In the inversion process the general Fano-profile formula was used in an explicit manner, treating the cross sections and parameters of the Fano formula as frequency-dependent quantities that were determined from the dispersion relation. The present inversion procedure was carried out in several steps, enabling separate studies of various contributions to the total cross section, i.e. resonance, interference and background terms. The many-body approach used to derive the cross section is complete to second order, i.e. with two interactions with the electronic repulsion operator. This is important if the Fano profile is to be recovered, as only background contributions are obtained in an independent-particle model. The present results are compared with experiment for Si-, and with other theories.

The ACES II program system

ACES II, a new program system for ab initio electronic structure calculations is described. The strengths of ACES II involve the use of many-body perturbation theory (MBPT) and coupled-cluster (CC) theory for calculating the energy, geometry, spectra, and properties of small- to medium-sized molecules. This paper gives a brief overview of the ACES II project, describes many features of the program system, and documents a number of benchmark calculations. © 1992 John Wiley & Sons, Inc.

An a b i n i t i o study of the structure and infrared spectrum of Si2C

The Si2C ground state has been reinvestigated using various basis sets at the Hartree–Fock level as well as with the use of many-body perturbation theory to second order. In agreement with previous theoretical investigations, the ground state is found to be a closed-shell C2v symmetry structure, whereas a linear D∞h structure is a transition state. Vibrational frequencies, infrared intensities, and isotopic shifts are presented and found to be in excellent agreement with recent experimental results, supporting a reinterpretation of the infrared spectrum of Si2C.

Resonance structure due to the 4d104f7-->4d94f8 transition in the photoionization cross section of atomic europium.

Photoionization cross sections for the 4d, 4f, 5s, 5p, and 6s electrons and angular-distribution asymmetry parameters for the 4d, 4f, and 5p electrons of atomic europium at photon energies near the 4${\mathit{d}}^{10}$4${\mathit{f}}^{7}$\ensuremath{\rightarrow}4${\mathit{d}}^{9}$4${\mathit{f}}^{8}$ resonance have been calculated by use of many-body perturbation theory. Interactions among ionization channels were included in the calculation, and the results are compared with experiments and other calculations.

Ab initio calculation of the isotope shift in the fine structure of C II and N II.

The nuclear-motion fine-structure isotope shifts in the ground states of C ii and N ii are computed by use of many-body perturbation theory. There are three different kinds of nuclear motion corrections to the atomic fine structure: normal mass effects on the spin-orbit and spin-spin interactions, electron-nucleus relativistic interactions, and higher-order cross terms between the specific-mass-shift operator and spin-dependent interactions. All three types of corrections have been considered and computed to third order in the many-body perturbation expansion. The computed results are in excellent agreement with recent accurate experimental values.

Many-body calculations of hyperfine constants in diatomic molecules. II. First-row hydrides

Magnetic hyperfine parameters (Frosch and Foley parameters) have been computed for first-row diatomic hydrides by use of many-body perturbation theory. The computations are complete to third order in the many-body expansion, which means that core polarization corrections are included through second and thrid order, and correlation effects by their leading third-order corrections. Computed results are presented for the ground states, and in addition for the three excited states A 2Δ, A Π, and A 2Σ in CH, NH, and OH, respectively. The vibrational dependencies of the hyperfine parameters were also predicted, and even a hyperfine centrifugal distortion constant observed for CH was computed, in good agreement with experiment. Good agreements between computed and experimental parameters were generally obtained, in particular for the ground states, where the errors in the computed values are at most a few percent.

Many-body calculations of hyperfine constants in diatomic molecules. I. The ground state of 16OH

Magnetic hyperfine parameters (Frosch and Foley parameters) have been computed for the 2Π ground state of 16OH by use of many-body perturbation theory. The computations are complete to third order in the many-body expansion, and they were repeated for a series of internuclear distances around re to reproduce the vibrational dependencies of the parameters. Parameters were computed for the three lowest vibrational levels, and were found to be within 1%–2% of the very accurate experimental values. The rather strong vibrational dependencies of the parameters were reproduced with accuracies of 80%–90%. Finally, centrifugal distortion corrections to the magnetic hyperfine parameters were also computed, and for the one parameter (dD) observed, the error was about 5%. The vibrational wave functions needed were obtained from a published accurate CI potential curve. Thus, no empirical results are incorporated in the present ab initio calculations.

Isotopic shift in atomic fine structure.

Nuclear-motion corrections to the atomic fine-structure isotopic shift are computed by use of many-body perturbation theory. The corrections are of three different types: normal mass effects (change of length scale), electron-nucleus relativistic interactions, and higher-order cross terms between the specific-mass operator and spin-dependent interactions. Numerical results are reported and compared with experiments for the ground states of Br, ${\mathrm{Ar}}^{+}$, Cl, ${\mathrm{Ne}}^{+}$, and C. Except for ${\mathrm{Ne}}^{+}$, reasonable agreements are obtained. For the best investigated case of Cl, the theoretical and experimental shifts are, respectively, -25.4 MHz and -24.9(1.0) MHz. In all cases the electron-nucleus relativistic interaction and the cross term between the specific mass-shift Hamiltonian and the spin-orbit interaction are found to yield large and counteracting contributions. The nuclear field-shift contribution to the fine-structure isotopic effect is also investigated for ${\mathrm{Ar}}^{+}$ and found to be of minor importance.

Photoionization cross section and resonance structure of atomic sodium.

The cross section of neutral sodium has been calculated from threshold at 5.14 eV to 250 eV with use of many-body perturbation theory. The calculations use LS coupling and include resonance effects due to single excitations of 2p and 2s electrons. Near threshold the results are very sensitive to electron correlations. Our results are compared with previous theoretical calculations and experimental measurements.

Diagrammatic many-body perturbation theory of atomic and molecular electronic structure

The diagrammatic many-body perturbation theory of atomic and molecular electronic structure is reviewed. Attention is centred on the formulation of the method within the algebraic approximation (that is, using finite basis sets) which allows applications to be made to atoms and molecules within a unified framework. The second section is devoted to the basic formalism of the diagrammatic many-body perturbation theory of atoms and molecules. The diagrammatic expansion of both the energy and the wavefunction are considered, the latter being more compact than the former. Section 3 is concerned with aspects of the truncation of the perturbation expansion and the use of many-body perturbation theory in the analysis and comparison of many contemporary approaches to the correlation problem is briefly outlined. The fourth section is devoted to computational aspects of many-body perturbation theory calculations. Some applications are very briefly discussed in section 5.

Photoionization cross sections with excitation to Ca+3d and

Photoionization cross sections of neutral calcium with excitation to ${\mathrm{Ca}}^{+}$ 3d and 4p levels have been calculated from threshold to 50 eV by use of many-body perturbation theory. The cross section for leaving ${\mathrm{Ca}}^{+}$ in the 4s ground level is also presented in this energy range and compared with the 3d and 4p cross sections which at their thresholds are larger than the 4s cross section. All three cross sections show interesting structure near 31 eV due to the 3p\ensuremath{\rightarrow}3d resonance.

Influence of electronic correlation effects on the photoionization of sodium and potassium

Various electronic correlation effects associated with the photoionization of alkalis are examined in detail by the use of many-body perturbation theory. With the inclusion of all important correlation effects, in particular, the effect of virtual excitation of inner shell electrons, the author removed most of the existing discrepancies between experimental observations and theoretical calculation.

Photoionization Cross Section of the Neutral Iron Atom

Calculations are presented for the photoionization cross section of the neutral iron atom for photon energies from threshold to 10 keV. Our results are based upon the use of nonrelativistic wave functions and the dipole approximation. Correlations are included to low orders by the use of many-body perturbation theory; and the cross section including correlations is found to differ greatly from that obtained from the Hartree-Fock approximation. Hartree-Fock results are also presented for comparison. We roughly estimate our cross section, including correlations near threshold, to be accurate to within a factor of 2 when integrated over a few eV.