C‐H Transformation at Arenes

Rostovtsev, Vsevolod V.

doi:10.1002/9783527619450.ch5

Cited by 7 publications

(7 citation statements)

References 513 publications

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“…attosecond, laser technology allows searchers to obtain ultra-strong fields [39]. Interaction of such strong and broadband fields with a two-level atomic system, even under the action of a far-off resonance laser radiation is of current interest [27,28,[40][41][42]. Strong short laser pulses can excite remarkable coherence on high frequency transitions; and this coherence can be used for surprisingly efficient generation of XUV radiation [27,28,41,42].…”

Section: Discussionmentioning

confidence: 99%

“…For the function f (t), Eq. (4) yields the following Riccati Equation [28] f + iΩ * (t)e −i∆t f 2 − iΩ(t)e i∆t = 0. Then |C a (t| = |f (t)|/ 1 + |f (t)| 2 .…”

Section: Two-level Atom: Equation Of Motionmentioning

confidence: 99%

“…Several approximate solutions have also been proposed based on perturbation theory and the adiabatic approximation [25,26]. Recently, the topic has been in a focus of research related to generation of short wavelength radiation [27,28]. A two-level atomic system under the action of a far-off resonance strong pulse of laser radiation has been con-sidered and it has been shown that such pulses can excite remarkable coherence on high frequency far-detuned transitions; and this coherence can be used for efficient generation of UV and soft X-ray (XUV) radiation [28].…”

Section: Introductionmentioning

confidence: 99%

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Coherent excitation of a two-level atom driven by a far-off-resonant classical field: Analytical solutions

Jha

Rostovtsev

2010

Phys. Rev. A

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We present an analytical treatment of coherent excitation of a two-level atom driven by a far-off-resonant classical field. A class of pulse envelope is obtained for which this problem is exactly solvable. The solutions are given in terms of the Heun function, which is a generalization of the hypergeometric function. Degeneracy of the Heun to a hypergeometric equation can give all the exactly solvable pulse shapes of Gauss hypergeometric form from the generalized pulse shape obtained here. We discuss the application of the results obtained to the generation of soft x-ray and ultraviolet radiations.

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Section: Discussionmentioning

confidence: 99%

“…For the function f (t), Eq. (4) yields the following Riccati Equation [28] f + iΩ * (t)e −i∆t f 2 − iΩ(t)e i∆t = 0. Then |C a (t| = |f (t)|/ 1 + |f (t)| 2 .…”

Section: Two-level Atom: Equation Of Motionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Coherent excitation of a two-level atom driven by a far-off-resonant classical field: Analytical solutions

Jha

Rostovtsev

2010

Phys. Rev. A

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“…Coupled first order equations Eq. (27) can be transformed to Riccati equation for f = C a (t)/C b (t) [26,27] or to the second order differential equation [28,29] C a (t) − i∆ +Ω In the case of resonance ω = ν these equations Eq. (28) transforms tö…”

Section: B Position Dependent Mass Schrödinger Equation and Two-levementioning

confidence: 99%

Analytical solution to position dependent mass Schrödinger equation

Jha¹,

Eleuch²,

Rostovtsev³

2011

Journal of Modern Optics

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Using a recently developed technique to solve Schrödinger equation for constant mass, we studied the regime in which mass varies with position i.e position dependent mass Schrödinger equation(PDMSE). We obtained an analytical solution for the PDMSE and applied our approach to study a position dependent mass m(x) particle scattered by a potential V(x). We also studied the structural analogy between PDMSE and two-level atomic system interacting with a classical field. PACS numbers: 03.65.Ge; 03.65.Fd; 03.65.-w Schrödinger equation with position dependent mass is one of the areas of research which has gained great attention in the past decades. Position-dependent mass Schrödinger equation(PDMSE) has been applied to several physical systems. For example PDMSE is applied in electronic properties of semiconductors [1], quantum dots and quantum wells [2, 3], semiconductors heterostructures [4], supper-lattice band structures [5], He-Clusters [6] quantum liquids [7], the dependence of energy gap on magnetic field in semiconductor nano-scale rings [8], the solid state problem with Dirac equation [9]etc. One of the motivation behind investigating these system with position dependent mass is, how do these mass variation effects the dynamics of the quantum-mechanical system. In such systems the energy is described by a Hamiltonian which contains the kinetic energy and the potential energy opeators H = T + V , where special care is taken for the kinetic term.O. von Roos [10] was the first to suggest the following generalized form of the kinetic energy operator for position-dependent mass modelwhere m = m(r) is the position-dependent mass. The constants η, and ρ, which are also knows as the von Roos ambiguity parameters can be assumed to be arbitrary but they obey the constraint equation η + + ρ = −1. Before von Roos several forms of operator T has been used to solve this problem [11][12][13][14]. Different approaches have been used to find analytical solution to PDMSE like point-canonical transformation [15], Green's function [16], Heun equation [17, 18], Group-Theoretical method [19], potential algebra [20], Lie-algebraic [21] and supersymmetric [22] approach etc. In this Brief Report, we obtained an analytical solution for the position dependent mass Schrödinger equation with general mass variation m(x) by transforming the PDMSE to Riccati equation. Analytical solution for Schrödinger equation with constant mass, beyond adiabatic approximation, has been recently investigated extensively [23] where we applied our approach to 1-D [23] and 3-D [24] scattering problem and showed that our method gives better accuracy than the well-known JWKB method. Here in this article we have extended that approach to variable mass regime and obtained very accurate results for PDMSE. The main result of this paper is the analytical solution given by Eq. (19). To illustrate how well our method works we considered a position dependent mass m(x) particle scattered by potential V (x) and obtained the wave function for 1D case (which could easily be...

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“…Iridium-catalyzed direct C–H borylation was developed by Smith, Hartwig, Ishiyama, and Miyaura, − and this methodology has been employed for postfunctionalization to modify relatively simple and unfunctionalized porphyrins. Palladium-catalyzed C–H arylation − of porphyrins is also emerging as a direct method to install various aromatic substituents onto porphyrins.…”

Section: Introductionmentioning

confidence: 99%

Synthesis and Functionalization of Porphyrins through Organometallic Methodologies

2016

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This review focuses on the postfunctionalization of porphyrins and related compounds through catalytic and stoichiometric organometallic methodologies. The employment of organometallic reactions has become common in porphyrin synthesis. Palladium-catalyzed cross-coupling reactions are now standard techniques for constructing carbon-carbon bonds in porphyrin synthesis. In addition, iridium- or palladium-catalyzed direct C-H functionalization of porphyrins is emerging as an efficient way to install various substituents onto porphyrins. Furthermore, the copper-mediated Huisgen cycloaddition reaction has become a frequent strategy to incorporate porphyrin units into functional molecules. The use of these organometallic techniques, along with the traditional porphyrin synthesis, now allows chemists to construct a wide range of highly elaborated and complex porphyrin architectures.

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C‐H Transformation at Arenes

Cited by 7 publications

References 513 publications

Coherent excitation of a two-level atom driven by a far-off-resonant classical field: Analytical solutions

Coherent excitation of a two-level atom driven by a far-off-resonant classical field: Analytical solutions

Analytical solution to position dependent mass Schrödinger equation

Synthesis and Functionalization of Porphyrins through Organometallic Methodologies

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