Probing interactions between core-electron transitions by ultrafast two-dimensional x-ray coherent correlation spectroscopy.
14 May 2008-Journal of Chemical Physics (American Institute of Physics)-Vol. 128, Iss: 18, pp 184307-184307
TL;DR: Two-dimensional x-ray correlation spectra obtained by varying two delay periods in a time-resolved coherent all-x-ray four-wave-mixing measurement are simulated for the N 1s and O 1s transitions of aminophenol.
Abstract: Two-dimensional x-ray correlation spectra (2DXCS) obtained by varying two delay periods in a time-resolved coherent all-x-ray four-wave-mixing measurement are simulated for the N 1s and O 1s transitions of aminophenol. The necessary valence and core-excited states are calculated using singly and doubly substituted Kohn-Sham determinants within the equivalent-core approximation. Sum-over-states calculations of the 2DXCS signals of aminophenol isomers illustrate how novel information about electronic states can be extracted from the 2D spectra. Specific signatures of valence and core-excited states are identified in the diagonal and off-diagonal peaks arising from core transitions of the same and different types, respectively.
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TL;DR: A review of the areas in which ideas from coherent X-ray methods are contributing to methods for the neutron, electron and optical communities is presented in this article, along with associated experiments in materials science.
Abstract: X-ray sources are developing rapidly and their coherent output is growing correspondingly. The increased coherent flux from modern X-ray sources is being matched with an associated development in experimental methods. This article reviews the literature describing the ideas that utilize the increased brilliance from modern X-ray sources. It explores how ideas in coherent X-ray science are leading to developments in other areas, and vice versa. The article describes measurements of coherence properties and uses this discussion as a base from which to describe partially coherent diffraction and X-ray phase-contrast imaging, with applications in materials science, engineering and medicine. Coherent diffraction imaging methods are reviewed along with associated experiments in materials science. Proposals for experiments to be performed with the new X-ray free-electron lasers are briefly discussed. The literature on X-ray photon-correlation spectroscopy is described and the features it has in common with other coherent X-ray methods are identified. Many of the ideas used in the coherent X-ray literature have their origins in the optical and electron communities and these connections are explored. A review of the areas in which ideas from coherent X-ray methods are contributing to methods for the neutron, electron and optical communities is presented.
450 citations
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TL;DR: It is discussed possible experiments that employ attosecond X-ray pulses to probe the quantum coherence and correlations of valence electrons and holes, rather than the charge density alone, building on the analogy with existing studies of vibrational motions using femtosecond techniques in the visible regime.
Abstract: New free-electron laser and high-harmonic generation X-ray light sources are capable of supplying pulses short and intense enough to perform resonant nonlinear time-resolved experiments in molecules. Valence-electron motions can be triggered impulsively by core excitations and monitored with high temporal and spatial resolution. We discuss possible experiments that employ attosecond X-ray pulses to probe the quantum coherence and correlations of valence electrons and holes, rather than the charge density alone, building on the analogy with existing studies of vibrational motions using femtosecond techniques in the visible regime.
165 citations
TL;DR: Using some fundamental symmetries of pulse polarization configurations of nonlinear signals, the authors can construct superpositions of signals designed to better distinguish among various coherent and incoherent exciton transport pathways and amplify subtle variations among different species of the Fenna-Matthews-Olson antenna complex.
Abstract: Linear-spectroscopy is one-dimensional (1D); the absorption spectrum provides information about excitation energies and transition dipoles as projected into a single frequency axis. In contrast, multidimensional optical spectroscopy uses sequences of laser pulses to perturb or label the electronic degrees of freedom and watch for correlated events taking place during several controlled time intervals. The resulting correlation plots can be interpreted in terms of multipoint correlation functions that carry considerably more detailed information on dynamical events than the two-point functions provided by 1D techniques1–7. Correlations between spins have been routinely used in NMR to study complex molecules. The Nobel prize was awarded to Richard Ernst8 for inventing the technique and to Kurt Wuthrich9 for developing pulse sequences suitable for large proteins. Optical analogues of 2D NMR techniques first designed to study vibrational dynamics by Raman or infrared pulses1 and later extended to resonant electronic excitations in chromophore aggregates10 have been made possible thanks to the development of stable femtosecond laser sources with controlled phases11. In an ideal heterodyne-detected 2D experiment (Fig. 1) 3 laser pulses with wavevectors k1, k2, k3 interact sequentially with the molecules in the sample to create a polarization with wavevector k4 given by one of the linear combinations ±k1 ±k2 ±k3. In all other directors the polarization vanishes due to the random phases of contributions from different molecules. The coherent signal is generated in directions close to the various possible k4. The missmatch caused by frequency variation of the index of refraction is optimized (“phase matched”) to generate an intense signal detected by interference with a 4th pulse at the desired wavevector k4. When the radiation field is described quantum mechanically the entire process can be viewed as a concerted 4 photon process. The signal S(t3,t2,t1) depends parametrically on the time intervals between pulses which constitute the primary control-parameters. Other parameters include the direction k4, pulse polarizations, envelope shapes, and even the phases.
Figure 1
Scheme of the time-resolved four-wave-mixing experiment. All calculations are given for the three-band scheme shown on the bottom left.
We shall illustrate the power of 2D techniques and how they work using the three-band model system shown in Fig. 1 which has a ground state (g), a singly excited manifold (e) and a doubly excited manifold (f ). The dipole operator can induce transitions between g to e and e to f . All transitions in the system are stimulated: spontaneous emission is neglected. This three-band model represents electronic excitations in the various physical systems covered in the this article.
Multidimensional signals monitor the dynamics of the system’s density matrix during the time intervals between pulses. Diagonal elements of this matrix ρnn represent populations of various states, while the off diagonal elements ρnm (n ≠ m), known as coherences, carry additional valuable phase information. These signals can be described intuitively using the Feynman diagrams shown in Fig. 2 which display the Liouville space pathways: sequences of interactions with the various fields and the relevant elements of the density matrix during the controlled intervals between interactions6. The two vertical lines represent the ket (left) and the bra (right) of the density-matrix.
Figure 2
Feynman diagrams for two 2D techniques with wavevectors kI and kIII. Incoming and outgoing arrows represent the interaction events, labels indicate states of the system during various intervals between interactions. ESA - excited state absorption, GSB ...
Time runs from bottom to top and the labels mark the density matrix elements during the evolution periods between interactions. The arrows represent interactions with photons and are labelled by their wavevectors. Photon absorption is accompanied by a molecular excitation (g to e or e to f transition) whereas photon emission induces deexcitation (e to g or f to e).
Our discussion will focus on two signals: the photon-echo SkI with kI = −k1+k2+k3 and the double-quantum-coherence SkIII with kIII =+k1+k2−k3. We first present the Feynman diagrams and the quantum pathways relevant for the two techniques for the generic exciton model of Fig. 1. Simulated signals are then presented for three different physical systems: Wannier excitons in semiconductor quantum wells12–15, Frenkel excitons in photosynthetic complexes6,7, and soft x-ray core excitons in molecules16–19. We demonstrate that both techniques provide new insights into the structure and exciton dynamics in semiconductor nanostructures and molecular aggregates and are highly sensitive to the separation between core-shells and the localization of the core-excited states.
The three contributions to the SkI signal depicted in Fig. 2 are known as ground state bleaching (GSB), excited state stimulated emission (ESE) and excited state absorption (ESA)6. In the GSB pathway the system returns to the ground state (and described by the density matrix element ρgg), during the second interval t2, after interacting with the first two pulses. The third interaction is affected by the decrease of the ground state population which reduces (bleaches) the subsequent photon absorption. In the ESE pathway, the system resides in the singly-excited (e) manifold during t2 and the third interaction brings it back to the ground state by stimulated emission. The ESA pathway shares the same t1 and t2 history of the ESE, however the third interaction now creates a doubly-excited state f . The SkI signal is usually displayed as a frequency/frequency correlation plot SkI (Ω3,t2,Ω1) obtained by a double Fourier transform with respect to the time delays t1 and t3, holding t2 fixed. Ω3 and Ω1 reveal the various resonance transitions, as can be anticipated from the diagrams. Only single-exciton ωeg resonances corresponding to optical coherences ρeg show up during t1 and are projected onto the Ω1 axis. The Ω3 axis shows either ωe′g resonances (ESE, GSB) or ωfe (ESA). The t2 evolution reflects exciton populations ρee and intra-band single-exciton coherences ρee′. Population transport, coherence oscillations and spectral diffusion dominate this interval in the ESE and ESA paths6.
Since the molecular frequencies during t1 (ωge) are negative and during t3 (ωeg and ωfe) are positive, the Ω1 frequency axis is reversed in the 2D plots. With this convention uncoupled excitons only show diagonal peaks. Off diagonal cross-peaks are markers of some kind of communication between various excitations which causes their resonance frequency to be different during t1 and t3. This can be attributed either to exciton delocalization or to population transport. A simple interpretation of the signals is possible by using a basis of states localized on the various chromophores. Since the dipole is localized on each chromophore and can only excite one chromophore at a time, cross peaks only appear when the chromophores are coupled. NMR spectra are similarly interpreted in terms of the couplings of localized spin states8. The couplings of chromophores can always be formally eliminated by diagonalizing the single-exciton Hamiltonian and switching to the delocalized exciton basis. However in this representation the dipole operator matrix elements will depend on the details of the eigenstates, which prevents the simple intuitive interpretation of the signal.
The SkIII technique has two ESA-type contributions (Fig. 2). 2D spectra is obtained by either correlating t1 → Ω1 with t2 → Ω2, SkIII (Ω1, Ω2, t3), or t2 → Ω2 with t3 → Ω3, SkIII (t1,Ω2,Ω3). The density matrix evolution during t1 and t2 is identical for the ESA1 and ESA2 diagrams: single-exciton resonances corresponding to ρeg show up during t1. During t2 the system is in a coherent superposition (coherence) ρfg between the doubly-excited state f and the ground-state g. Two-exciton double-quantum-coherence resonances corresponding to the different doubly excited states f are then projected onto Ω2. The t3 evolution is very different: In ESA1 the system is in a coherence between f and e′ (ρfe′) which results in resonances at Ω3 = ωfe′, corresponding to all possible transitions between doubly- and singly- excited states. For ESA2 the system is in a coherence between e′ and g (ρe′g) and reveals single- exciton resonances at Ω3 = ωe′g as t3 is scanned. When the single-exciton states e and e′ do not interact (e.g. when they belong to two uncoupled chromophores), the corresponding two-exciton state is given by a direct product |f〉 = |ee′〉 and the double-excitation energy is the sum ef = ee + ee. In that case ωeg =ωfe′ =ee, the two diagrams exactly cancel and the signal vanishes! The entire SkIII signal is thus induced by correlations and its peak pattern provides a characteristic fingerprint for the correlated doubly excited wavefunctions. This conclusion goes beyond the present simple model. SkIII vanishes for uncorrelated many electron systems described by the Hartree Fock wavefunction and thus provides an excellent background-free probe for electron correlations12,20. The (Ω2,Ω3) correlation plots spread the two-exciton (f state) information along both axes, thus improving the resolution of the two-exciton manifold.
86 citations
TL;DR: Comparison of the simulated XANES signals with experiment shows that the restricted window time-dependent density functional theory is more accurate and computationally less expensive than the static exchange method.
Abstract: We report simulations of X-ray absorption near edge structure (XANES), resonant inelastic X-ray scattering (RIXS) and 1D stimulated X-ray Raman spectroscopy (SXRS) signals of cysteine at the oxygen, nitrogen, and sulfur K and L2,3 edges. Comparison of the simulated XANES signals with experiment shows that the restricted window time-dependent density functional theory is more accurate and computationally less expensive than the static exchange method. Simulated RIXS and 1D SXRS signals give some insights into the correlation of different excitations in the molecule.
84 citations
TL;DR: Bennett et al. as mentioned in this paper survey various possible types of multidimensional x-ray spectroscopy techniques and demonstrate the novel information they can provide about molecules, such as core-electronic structure and couplings, real-time tracking of impulsively created valence-electronics wavepackets and electronic coherences, and monitoring ultrafast processes such as nonadiabatic electron-nuclear dynamics near conical-intersection crossings.
Abstract: Author(s): Bennett, K; Zhang, Y; Kowalewski, M; Hua, W; Mukamel, S | Abstract: New x-ray free electron laser (XFEL) and high harmonic generation (HHG) light sources are capable of generating short and intense pulses that make x-ray nonlinear spectroscopy possible. Multidimensional spectroscopic techniques, which have long been used in the nuclear magnetic resonance, infrared, and optical regimes to probe the electronic structure and nuclear dynamics of molecules by sequences of short pulses with variable delays, can thus be extended to the attosecond x-ray regime. This opens up the possibility of probing core-electronic structure and couplings, the real-time tracking of impulsively created valence-electronic wavepackets and electronic coherences, and monitoring ultrafast processes such as nonadiabatic electron-nuclear dynamics near conical-intersection crossings. We survey various possible types of multidimensional x-ray spectroscopy techniques and demonstrate the novel information they can provide about molecules.
33 citations
References
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TL;DR: In this article, a semi-empirical exchange correlation functional with local spin density, gradient, and exact exchange terms was proposed. But this functional performed significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.
Abstract: Despite the remarkable thermochemical accuracy of Kohn–Sham density‐functional theories with gradient corrections for exchange‐correlation [see, for example, A. D. Becke, J. Chem. Phys. 96, 2155 (1992)], we believe that further improvements are unlikely unless exact‐exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange‐correlation functional containing local‐spin‐density, gradient, and exact‐exchange terms is tested on 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total atomic energies of first‐ and second‐row systems. This functional performs significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.
87,732 citations
TL;DR: In this article, two extended basis sets (termed 5-31G and 6 -31G) consisting of atomic orbitals expressed as fixed linear combinations of Gaussian functions are presented for the first row atoms carbon to fluorine.
Abstract: Two extended basis sets (termed 5–31G and 6–31G) consisting of atomic orbitals expressed as fixed linear combinations of Gaussian functions are presented for the first row atoms carbon to fluorine. These basis functions are similar to the 4–31G set [J. Chem. Phys. 54, 724 (1971)] in that each valence shell is split into inner and outer parts described by three and one Gaussian function, respectively. Inner shells are represented by a single basis function taken as a sum of five (5–31G) or six (6–31G) Gaussians. Studies with a number of polyatomic molecules indicate a substantial lowering of calculated total energies over the 4–31G set. Calculated relative energies and equilibrium geometries do not appear to be altered significantly.
13,036 citations
Book•
01 Jan 1981
TL;DR: In this article, the authors present a model for the second quantization of a particle and show that it can be used to construct a pair distribution function with respect to a pair of spinless fermions.
Abstract: 1. Introductory Material.- 1.1. Harmonic Oscillators and Phonons.- 1.2. Second Quantization for Particles.- 1.3. Electron - Phonon Interactions.- A. Interaction Hamiltonian.- B. Localized Electron.- C. Deformation Potential.- D. Piezoelectric Interaction.- E. Polar Coupling.- 1.4. Spin Hamiltonians.- A. Homogeneous Spin Systems.- B. Impurity Spin Models.- 1.5. Photons.- A. Gauges.- B. Lagrangian.- C. Hamiltonian.- 1.6. Pair Distribution Function.- Problems.- 2. Green's Functions at Zero Temperature.- 2.1. Interaction Representation.- A. Schrodinger.- B. Heisenberg.- C. Interaction.- 2.2. S Matrix.- 2.3. Green's Functions.- 2.4. Wick's Theorem.- 2.5. Feynman Diagrams.- 2.6. Vacuum Polarization Graphs.- 2.7. Dyson's Equation.- 2.8. Rules for Constructing Diagrams.- 2.9. Time-Loop S Matrix.- A. Six Green's Functions.- B. Dyson's Equation.- 2.10. Photon Green's Functions.- Problems.- 3. Green's Functions at Finite Temperatures.- 3.1. Introduction.- 3.2. Matsubara Green's Functions.- 3.3. Retarded and Advanced Green's Functions.- 3.4. Dyson's Equation.- 3.5. Frequency Summations.- 3.6. Linked Cluster Expansions.- A. Thermodynamic Potential.- B. Green's Functions.- 3.7. Real Time Green's Functions.- Wigner Distribution Function.- 3.8. Kubo Formula for Electrical Conductivity.- A. Transverse Fields, Zero Temperature.- B. Finite Temperatures.- C. Zero Frequency.- D. Photon Self-Energy.- 3.9. Other Kubo Formulas.- A. Pauli Paramagnetic Susceptibility.- B. Thermal Currents and Onsager Relations.- C. Correlation Functions.- Problems.- 4. Exactly Solvable Models.- 4.1. Potential Scattering.- A. Reaction Matrix.- B. T Matrix.- C. Friedel's Theorem.- D. Phase Shifts.- E. Impurity Scattering.- F. Ground State Energy.- 4.2. Localized State in the Continuum.- 4.3. Independent Boson Models.- A. Solution by Canonical Transformation.- B. Feynman Disentangling of Operators.- C. Einstein Model.- D. Optical Absorption and Emission.- E. Sudden Switching.- F. Linked Cluster Expansion.- 4.4. Tomonaga Model.- A. Tomonaga Model.- B. Spin Waves.- C. Luttinger Model.- D. Single-Particle Properties.- E. Interacting System of Spinless Fermions.- F. Electron Exchange.- 4.5. Polaritons.- A. Semiclassical Discussion.- B. Phonon-Photon Coupling.- C. Exciton-Photon Coupling.- Problems.- 5. Electron Gas.- 5.1. Exchange and Correlation.- A. Kinetic Energy.- B. Direct Coulomb.- C. Exchange.- D. Seitz' Theorem.- E. ?(2a).- F. ?(2b).- G. ?(2c).- H. High-Density Limit.- I. Pair Distribution Function.- 5.2. Wigner Lattice and Metallic Hydrogen.- Metallic Hydrogen.- 5.3. Cohesive Energy of Metals.- 5.4. Linear Screening.- 5.5. Model Dielectric Functions.- A. Thomas-Fermi.- B. Lindhard, or RPA.- C. Hubbard.- D. Singwi-Sjolander.- 5.6. Properties of the Electron Gas.- A. Pair Distribution Function.- B. Screening Charge.- C. Correlation Energies.- D. Compressibility.- 5.7. Sum Rules.- 5.8. One-Electron Properties.- A. Renormalization Constant ZF.- B. Effective Mass.- C. Pauli Paramagnetic Susceptibility.- D. Mean Free Path.- Problems.- 6. Electron-Phonon Interaction.- 6.1 Frohlich Hamiltonian.- A. Brillouin-Wigner Perturbation Theory.- B. Rayleigh-Schrodinger Perturbation Theory.- C. Strong Coupling Theory.- D. Linked Cluster Theory.- 6.2 Small Polaron Theory.- A. Large Polarons.- B. Small Polarons.- C. Diagonal Transitions.- D. Nondiagonal Transitions.- E. Dispersive Phonons.- F. Einstein Model.- G. Kubo Formula.- 6.3 Heavily Doped Semiconductors.- A. Screened Interaction.- B. Experimental Verifications.- C. Electron Self-Energies.- 6.4 Metals.- A. Phonons in Metals.- B. Electron Self-Energies.- Problems.- 7. dc Conductivities.- 7.1. Electron Scattering by Impurities.- A. Boltzmann Equation.- B. Kubo Formula: Approximate Solution.- C. Kubo Formula: Rigorous Solution.- D. Ward Identities.- 7.2. Mobility of Frohlich Polarons.- A. Single-Particle Properties.- B. ??1 Term in the Mobility.- 7.3. Electron-Phonon Interactions in Metals.- A. Force-Force Correlation Function.- B. Kubo Formula.- C. Mass Enhancement.- D. Thermoelectric Power.- 7.4. Quantum Boltzmann Equation.- A. Derivation of the Quantum Boltzmann Equation.- B. Gradient Expansion.- C. Electron Scattering by Impurities.- D. T2 Contribution to the Electrical Resistivity.- Problems.- 8. Optical Properties of Solids.- 8.1. Nearly Free-Electron System.- A. General Properties.- B. Force-Force Correlation Functions.- C. Frohlich Polarons.- D. Interband Transitions.- E. Phonons.- 8.2. Wannier Excitons.- A. The Model.- B. Solution by Green's Functions.- C. Core-Level Spectra.- 8.3. X-Ray Spectra in Metals.- A. Physical Model.- B. Edge Singularities.- C. Orthogonality Catastrophe.- D. MND Theory.- E. XPS Spectra.- Problems.- 9. Superconductivity.- 9.1. Cooper Instability.- 9.2. BCS Theory.- 9.3. Electron Tunneling.- A. Tunneling Hamiltonian.- B. Normal Metals.- C. Normal-Superconductor.- D. Two Superconductors.- E. Josephson Tunneling.- 9.4. Infrared Absorption.- 9.5. Acoustic Attenuation.- 9.6. Excitons in Superconductors.- 9.7. Strong Coupling Theory.- Problems.- 10. Liquid Helium.- 10.1. Pairing Theory.- A. Hartree and Exchange.- B. Bogoliubov Theory of 4He.- 10.2. 4He: Ground State Properties.- A. Off-Diagonal Long-Range Order.- B. Correlated Basis Functions.- C. Experiments on nk.- 10.3. 4He: Excitation Spectrum.- A. Bijl-Feynman Theory.- B. Improved Excitation Spectra.- C. Superfluidity.- 10.4. 3He: Normal Liquid.- A. Fermi Liquid Theory.- B. Experiments and Microscopic Theories.- C. Interaction between Quasiparticles: Excitations.- D. Quasiparticle Transport.- 10.5. Superfluid 3He.- A. Triplet Pairing.- B. Equal Spin Pairing.- Problems.- 11. Spin Fluctuations.- 11.1. Kondo Model.- A. High-Temperature Scattering.- B. Low-Temperature State.- C. Kondo Temperature.- 11.2. Anderson Model.- A. Collective States.- B. Green's Functions.- C. Spectroscopies.- Problems.- References.- Author Index.
5,888 citations
Book•
01 Jan 1987
TL;DR: In this paper, the dynamics of nuclear spin systems were studied by two-dimensional exchange spectroscopy and nuclear magnetic resonance imaging (NEMI) imaging, and two different correlation methods based on coherence transfer were proposed.
Abstract: List of notation Introduction The dynamics of nuclear spin systems Manipulation of nuclear spin Hamiltonians One-dimensional Fourier spectroscopy Multiple-quantum transitions Two-dimensional Fourier spectroscopy Two-dimensional separation of interactions Two-dimensional correlation methods based on coherence transfer Dynamic processes studied by two-dimensional exchange spectroscopy Nuclear magnetic resonance imaging References Index.
4,977 citations
TL;DR: In this paper, a general technique for the investigation of exchange processes in molecular systems is proposed and demonstrated and applications include the study of chemical exchange, of magnetization transfer by inter-and intramolecular relaxation in liquids, and of spin diffusion and cross-relaxation processes in solids.
Abstract: A new general technique for the investigation of exchange processes in molecular systems is proposed and demonstrated. Applications comprise the study of chemical exchange, of magnetization transfer by inter‐ and intramolecular relaxation in liquids, and of spin diffusion and cross‐relaxation processes in solids.
4,534 citations