Density functional theory (DFT), in its current local, gradient corrected, and hybrid implementations and their extensions, is approaching an impasse. To continue to progress toward the quality of results demanded by today's ab initio quantum chemistry encourages a new direction. We believe ab initio DFT is a promising route to pursue. Whereas conventional DFT cannot describe weak interactions, photoelectron spectra, or many potential energy surfaces, ab initio DFT, even in its initial, optimized effective potential, second-order many-body perturbation theory form [OEP (2)-semi canonical], is shown to do all well. In fact, we obtain accuracy that frequently exceeds MP2, being competitive with coupled-cluster theory in some cases. Furthermore, this is accomplished within a relatively fast computational procedure that scales like iterative second order. We illustrate our results with several molecular examples including Ne2,Be2,F2, and benzene.

We demonstrate how dynamic correlations of heavy-hole and light-hole excitons in semiconductor quantum wells may be investigated by two dimensional correlation spectroscopy (2DCS). The coherent response to three femtosecond optical pulses is predicted to yield cross (off-diagonal) peaks that contain direct signatures of manybody two-exciton correlations. Signals generated at various phase-matching directions are compared. I. INTRODUCTIONUnderstanding the signatures of many-body interactions in the nonlinear optical response of semiconductors is an important fundamental problem with implications to all-optical and electro-optical device applications. 1 The linear response to a weak optical field is well described by a model of non-interacting quasiparticles. However, residual interactions, not accounted for by these quasiparticles, can considerably affect the nonlinear response.Similar to Frenkel excitons in molecular crystals and aggregates, 2 Coulomb correlations among quasiparticles can dominate the nonlinear optical response of semiconductors, in marked contrast to the behavior of atomic systems. 3,4,5,6,7,8,9,10,11,12,13 The coherent ultrafast response and many-body correlations in semiconductor heterostructures have been studied extensively in the past two decades. 5,14,15,16,17,18,19,20,21,22,23,24,25 Due to various dephasing and relaxation mechanisms, the coherent response usually persists only on the tens of picosecond time scale.Optical spectra such as the linear absorption, pump-probe and Four-wave mixing (FWM) are commonly displayed as a function of a single (time or frequency) variable, and hence provide a one-dimensional (1D) projection of the microscopic information. 1D spectra are hard to interpret in systems with many congested energy levels. The spectroscopic signatures of complex many-body dynamics projected on a 1D spectral plot strongly overlap and may not be easily identified. For example, when 1D techniques are employed in III-V semiconductor quantum wells (QWs), it is difficult to pinpoint the signatures of. (11) Eq. (11) has various diagonal peaks (Ω 1 = Ω 3 ) and cross-peaks (Ω 1 = Ω 3 ). The relative contributions of different terms may be controlled by the carrier frequencies, ω 1 , ω 2 , and ω 3 .Spreading the signal in an extra frequency dimension enhances the resolving power of the 2DCS, compared to 1D techniques. 2 We can further improve the resolution by controlling other parameters such as the pulse polarization directions, carrier frequencies and envelopes.Other 2D techniques generated in different phase-matching directions and using different pairs of time variables (e.g. t 2 and t 3 ) provide complementary information 2,34,57 through different projections of the response, as will be discussed in Section III. Closed expressions for the other 2D signals S II and S III are given in Appendix A.

IntroductionLinear-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 techniques [1][2][3][4][5][6][7] . Correlations between spins have been routinely used in NMR to study complex molecules. The Nobel prize was awarded to Richard Ernst 8 for inventing the technique and to Kurt Wüthrich 9 for developing pulse sequences suitable for large proteins. Optical analogues of 2D NMR techniques first designed to study vibrational dynamics by Raman or infrared pulses 1 and later extended to resonant electronic excitations in chromophore aggregates 10 have been made possible thanks to the development of stable femtosecond laser sources with controlled phases 11 . In an ideal heterodyne-detected 2D experiment ( Fig. 1) 3 laser pulses with wavevectors k 1 , k 2 , k 3 interact sequentially with the molecules in the sample to create a polarization with wavevector k 4 given by one of the linear combinations ±k 1 ±k 2 ±k 3 . 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 k 4 . 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 k 4 . When the radiation field is described quantum mechanically the entire process can be viewed as a concerted 4 photon process. The signal S(t 3 ,t 2 ,t 1 ) depends parametrically on the time intervals between pulses which constitute the primary control-parameters. Other parameters include the direction k 4 , pulse polarizations, envelope shapes, and even the phases.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 ρ nn represent populations of various states, while the off diagonal elements ρ nm (n ≠ m), known as coherences, carry additional valuable phase information. These signals can be descr...

We propose two-dimensional x-ray coherent correlation spectroscopy for the study of interactions between core-electron and valence transitions. This technique may find experimental applications in the future when very high intensity x-ray sources become available. Spectra obtained by varying two delay periods between pulses show off-diagonal crosspeaks induced by coupling of core transitions of two different types. Calculations of the N1s and O1s signals of aminophenol isomers illustrate how novel information about many-body effects in electronic structure and excitations of molecules can be extracted from these spectra. X-ray absorption spectroscopy (XANES, EXAFS) [1] and its time-resolved extensions [2 -4] provide a direct probe for electronic structure of molecules with subatomic and subfemtosecond resolution. Novel ultrabright x-ray sources such as future free-electron laser (XFEL) [5] or high-harmonic generation (HHG) [6] may make it possible to perform nonlinear experiments with multiple x-ray pulses. All-x-ray nonlinear signals could provide more detailed information on the electronic structure and dynamics than is available from time-resolved XANES, by probing states with multiple core electrons excited. Many proposed applications of the new sources make use of their ultrashort temporal resolution and high intensity to monitor dynamical processes in real time. Two-photon absorption [7] and x-ray driven molecular dynamics [8] have been demonstrated using HHG. Techniques such as diffraction or pump probe do not rely on the coherence properties of the beams. The technique considered in this Letter, in contrast, depends also on pulse coherence in an essential way, and should become feasible once high intensity, attosecond [9-12] transform-limited pulses become available. Such pulses should allow one to control and manipulate the coherence of core excitations and use it as a window into correlations between different regions of the molecule. Similar ideas are effectively used in multidimensional NMR spectroscopy [13] to probe correlations between spin dynamics in controlled time periods using elaborate pulse sequences. The signals are interpreted in terms of multiple correlation functions which provide fundamentally new types of information compared to onedimensional techniques. The same ideas were recently extended to the infrared and optical regimes [14 -17].In this Letter we propose a new class of two-dimensional x-ray coherent correlation spectroscopy (2DXCS) techniques and demonstrate how they could provide a unique probe for interactions between the core transitions and electronic states that mediate these interactions. Infrared femtosecond 2D techniques can excite molecular vibrations impulsively and probe the subsequent correlated dynamics of nuclear wave packets. Similarly, attosecond x-ray pulses resonant with core transitions can excite valence electrons impulsively and probe correlations in dynamical events of resulting electron wave packets. Since core transitions are highly localized to the abso...