DFT schemes based on conventional exchange-correlation (XC) functionals have been employed to determine the dipole moment (μ), polarizability (α), and first (β) and second (γ) hyperpolarizabilities of push−pull π-conjugated systems. In addition to the failures already pointed out for α and γ in a recent study on polyacetylene chains [J. Chem. Phys. 1998, 109, 10489; Phys. Rev. Lett. 1999, 83, 694], these functionals are also unsuitable for the evaluation of μ and β. In the case of β, in particular, an almost catastrophic behavior with respect to increasing chain length is found. We show that the C functional has a negligible effect on the calculated μ, α, β, and γ whereas the X-part is responsible for the large property overestimations when the size of the system increases. The overly large μ values are associated with an overestimation of the charge transfer between the donor and the acceptor whereas for α, β, and γ, incomplete screening of the external electric field is responsible for the large discrepancies with respect to accurate values. Our results show that current XC functionals incorrectly describe the polarization of conjugated systems when the polarization is due to donor/acceptor substitution or an external field or both.

Density functional calculations on the (non)linear optical properties of conjugated molecular chains using currently popular exchange-correlation (xc) potentials give overestimations of several orders of magnitude. By analyzing "exact" and Krieger-Li-Iafrate xc potentials, the error is traced back to an incorrect electric field dependence of the "response part" of the xc potential in local and gradientcorrected density approximations, which lack a linear term counteracting the applied electric field.PACS numbers: 31.15. Ew, 42.65.An, 71.15.Mb, 77.22.Ej The nonlinear optical (NLO) properties of molecules are of considerable current interest, both from the fundamental and technological points of view [1][2][3]. Prototype systems exhibiting large NLO responses like the polyacetylene (PA) chains have been studied intensively with conventional, ab initio Hartree-Fock (HF) based theoretical techniques [2]. Because density functional theory (DFT) [4,5] usually provides clearly improved accuracy with respect to HF at similar or lower computational cost, it seems tempting to apply DFT to the prediction of the NLO properties of large, conjugated molecular chains.Our calculations on static hyperpolarizabilities (determining the NLO response in the static limit) of such chains show, both here and in Ref. [6], that the local density approximation (LDA) and generalized gradient approximations (GGAs) in DFT provide very poor results. Whereas previously reported LDA errors are typically 10% for dielectric constants, we find overestimations of several orders of magnitude for the second hyperpolarizability g. In view of the respectable accuracy which is usually obtained in DFT calculations, this is highly surprising and deserves a detailed analysis, as this error may be among the largest in the history of DFT calculations. Our analysis allows us to pinpoint the weakness of the LDA. It will be shown below that, if an electric field, E, is applied, the so-called response part of the exact exchange-correlation (xc) potential develops a global behavior counteracting the applied field. Such behavior is not present in the LDA or GGA potentials. Our results substantiate and further elucidate the findings of Gonze, Ghosez, and Godby [7] and others [8][9][10][11][12][13], who pointed out the existence of such a counteracting linear potential in the exact y xc and provided the first physical interpretation for it [10,13].Description of the problem.-For this work, extensive calculations have been performed on PA and hydrogen chains. The LDA results described below have been obtained in the same manner as earlier calculations on the polarizability (a) and second hyperpolarizability (g) of C 60 [14]. Details of the computational procedure, the geometries, etc., have been given in another paper [6], where several aspects of the LDA problem (size of electron correlation correction, effect of bond length alternation) are described more fully.From the HF-based ab initio studies [15] on the NLO properties of PA chains, it is known that even sim...

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The joint design of hybrid beamforming matrices is conceived for multiuser mmWave full-duplex (FD) multiple-input multiple-output (MIMO) relay-aided systems in the presence of realistic channel state information (CSI) errors. Specifically, considering a probabilistic CSI error model, we maximize the system's worst-case sum rate by jointly optimizing the base station's (BS) analog and digital beamforming matrices, plus the analog receive and transmit beamforming matrices of the relay station (RS) as well as its digital amplify-and-forward (AF) beamforming matrix under practical constraints. Explicitly, the transmit power constraints of the BS and RS, the residual selfinterference power constraint of the RS, the per-user quality of service constraints and the unit-modulus constraints on the analog beamforming matrix elements are all taken into account. Since the resultant optimization problem is very challenging due to its highly nonlinear objective function and nonconvex coupling constraints, we first transform it into a more tractable form. We then develop a novel joint optimization algorithm based on the penalty dual decomposition (PDD) technique to solve the resultant problem. The proposed PDD-based algorithm performs double-loop iterations: the inner loop updates the optimization variables in a block coordinate descent fashion, while the outer loop adjusts the Lagrange multipliers and penalty parameter, hence ensuring convergence to the set of stationary solutions of the original problem. Our simulations show that mmWave FD hybrid MIMO relay systems relying on our new algorithm significantly outperform both their non-robust FD and conventional half-duplex counterparts. Index Terms-Millimeter wave, full-duplex, multiuser MIMO relay, hybrid beamforming, robust transceiver design. I. INTRODUCTION Millimeter wave (mmWave) communications in the 30-300GHz band represent a salient next-generation technique