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David Beljonne - One of the best experts on this subject based on the ideXlab platform.
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The Singlet–Triplet Exchange Energy in Conjugated Polymers†
Advanced Functional Materials, 2004Co-Authors: Anna Kohler, David BeljonneAbstract:Electron–electron interactions in organic semiconductors split the lowest singlet and triplet states by the Exchange Energy, ΔEST. Measurement of singlet and triplet emission spectra in a large number of conjugated polymers yield an almost constant ΔEST value close to 0.7 eV. This is in contrast to the situation in molecules, where the Exchange Energy is found to depend on molecular size and to vary over a wide range. Quantum-chemical calculations are performed to address the origin of the constant Exchange Energy in phenylene-based conjugated polymers. The electron–hole separation in the lowest singlet and triplet excited states is found to be independent of the π-conjugated backbone, and saturates for chains longer than a few repeating units, resulting in a constant Exchange Energy. In shorter conjugated oligomers, confinement of the excitations destabilizes the singlet with respect to the triplet through Exchange interactions and leads to a larger and size-dependent singlet–triplet Energy separation.
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the singlet triplet Exchange Energy in conjugated polymers
Advanced Functional Materials, 2004Co-Authors: Anna Kohler, David BeljonneAbstract:Electron–electron interactions in organic semiconductors split the lowest singlet and triplet states by the Exchange Energy, ΔEST. Measurement of singlet and triplet emission spectra in a large number of conjugated polymers yield an almost constant ΔEST value close to 0.7 eV. This is in contrast to the situation in molecules, where the Exchange Energy is found to depend on molecular size and to vary over a wide range. Quantum-chemical calculations are performed to address the origin of the constant Exchange Energy in phenylene-based conjugated polymers. The electron–hole separation in the lowest singlet and triplet excited states is found to be independent of the π-conjugated backbone, and saturates for chains longer than a few repeating units, resulting in a constant Exchange Energy. In shorter conjugated oligomers, confinement of the excitations destabilizes the singlet with respect to the triplet through Exchange interactions and leads to a larger and size-dependent singlet–triplet Energy separation.
K. T. Tang - One of the best experts on this subject based on the ideXlab platform.
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Exchange Energy of Diatomic Systems
Asymptotic Methods in Quantum Mechanics, 2020Co-Authors: S. H. Patil, K. T. TangAbstract:The Exchange Energy is of fundamental importance for the understanding of interatomic potentials, charge Exchange processes as well as the theory of magnetism. The concept of an Exchange Energy was first introduced by Heitler and London in their theory of the H2 molecule. The interaction between the two hydrogen atoms leads to the triplet and singlet states of the H2 molecule, which degenerate into a single Energy level when the internuclear distance becomes very large. Half of the difference between these Energy levels is defined as the Exchange Energy. In the case of the H 2 + molecular ion, the Energy splitting is between the ungerade and gerade states. It turns out that this definition can be applied to all systems. In this chapter, we will show that the asymptotic wave function can be used in the surface integral method to generate the Exchange Energy at large internuclear separations. But first, we will use some simple examples to explain the method.
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New Insight into Exchange Energy of Covalent Chemical Bonds
Journal of The Chinese Chemical Society, 2001Co-Authors: K. T. Tang, J. P. ToenniesAbstract:The Exchange Energy for the H2 molecule is calculated for a wide range of inter nuclear distance R extending down to R = 0.5 a0 using the surface integral method. This method accounts for the physical Exchange of the two electrons between the two nuclei. The good agreement of the present results with the standard Heitler-London calculation demonstrates that the Exchange Energy can in deed be described in terms of electrons hop ping back and forth between the nuclei, an interpretation which has been frequently criticized in the past.
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Angular momentum coupling in the Exchange Energy of multielectron systems
Journal of Chemical Physics, 1995Co-Authors: Ulrich Kleinekathöfer, K. T. Tang, J. P. ToenniesAbstract:The Exchange Energy between two multielectron atomic systems is shown to be a product of an angular momentum factor and the Energy of the triplet‐singlet splitting of a single pair of electrons. The angular momentum factor accounts for the coupling of the angular momentum of the valence electrons and was first given by Duman and Smirnov [Opt. Spectrosc. (USSR) 29, 229 (1970)]. Here it is rederived and in the cases of interactions between hydrogen, rare gas, alkali and alkaline earth atomic systems the new corrected expressions are shown to reduce to a simple physical model. The angular momentum factors are listed for all these interacting systems. The important factors in the analytic expression for the distance dependent asymptotic Exchange energies are also given for all the homonuclear alkali, alkaline earth, and rare gas dimers.
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Exchange Energy of H2 calculated by the surface integral method in zeroth order approximation
Journal of Chemical Physics, 1993Co-Authors: K. T. Tang, J. Peter ToenniesAbstract:The surface integral method of Holstein and Herring is applied to the calculation of the Exchange Energy of the H2 molecule. This theory provides a means for calculating the Exchange Energy by taking into account the physical Exchange of the two electrons with respect to the nuclei. Problems associated with symmetrization of the polarized wave functions which have encumbered previous attempts at developing a perturbation theory of the chemical bond are circumvented. Whereas the previous calculations using this method by Gor’kov and Pitaevski and Herring and Flicker were restricted to the asymptotic (R→∞) limit, in the present calculation we have used an extended formula to examine the validity also for the short range region down to R=0.5 a.u. In order to compare with the results of Heitler–London theory we have used the undisturbed zeroth order wave function of the H atoms in the calculations. An analytic expression is obtained for the Exchange Energy and the numerical results are found to be in good agr...
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The Exchange Energy of H+2 calculated from the exact first-order wavefunction of polarization perturbation theory
Chemical Physics Letters, 1993Co-Authors: K. T. TangAbstract:Abstract The exact analytic first-order wavefunction of an H atom in the field of a proton obtained from the unsymmetrized perturbation theory as calculated in 1957 by Dalgarno and Lynn is used to calculate the Exchange Energy of H + 2 with the Holstein-Herring method. The asymptotic Exchange Energy obtained from the exact wavefunction is term-by-term identical with that obtained from the 1/ R expanded wavefunction and is within 5% of the exact Exchange Energy from large R down to R = 5 a 0 .
Anna Kohler - One of the best experts on this subject based on the ideXlab platform.
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The Singlet–Triplet Exchange Energy in Conjugated Polymers†
Advanced Functional Materials, 2004Co-Authors: Anna Kohler, David BeljonneAbstract:Electron–electron interactions in organic semiconductors split the lowest singlet and triplet states by the Exchange Energy, ΔEST. Measurement of singlet and triplet emission spectra in a large number of conjugated polymers yield an almost constant ΔEST value close to 0.7 eV. This is in contrast to the situation in molecules, where the Exchange Energy is found to depend on molecular size and to vary over a wide range. Quantum-chemical calculations are performed to address the origin of the constant Exchange Energy in phenylene-based conjugated polymers. The electron–hole separation in the lowest singlet and triplet excited states is found to be independent of the π-conjugated backbone, and saturates for chains longer than a few repeating units, resulting in a constant Exchange Energy. In shorter conjugated oligomers, confinement of the excitations destabilizes the singlet with respect to the triplet through Exchange interactions and leads to a larger and size-dependent singlet–triplet Energy separation.
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the singlet triplet Exchange Energy in conjugated polymers
Advanced Functional Materials, 2004Co-Authors: Anna Kohler, David BeljonneAbstract:Electron–electron interactions in organic semiconductors split the lowest singlet and triplet states by the Exchange Energy, ΔEST. Measurement of singlet and triplet emission spectra in a large number of conjugated polymers yield an almost constant ΔEST value close to 0.7 eV. This is in contrast to the situation in molecules, where the Exchange Energy is found to depend on molecular size and to vary over a wide range. Quantum-chemical calculations are performed to address the origin of the constant Exchange Energy in phenylene-based conjugated polymers. The electron–hole separation in the lowest singlet and triplet excited states is found to be independent of the π-conjugated backbone, and saturates for chains longer than a few repeating units, resulting in a constant Exchange Energy. In shorter conjugated oligomers, confinement of the excitations destabilizes the singlet with respect to the triplet through Exchange interactions and leads to a larger and size-dependent singlet–triplet Energy separation.
Junji Kido - One of the best experts on this subject based on the ideXlab platform.
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a host material with a small singlet triplet Exchange Energy for phosphorescent organic light emitting diodes guest host and exciplex emission
Organic Electronics, 2012Co-Authors: Shijian Su, Junichi Takamatsu, Junji KidoAbstract:Abstract A host material containing a triazine core and three phenylcarbazole arms, called 2,4,6-tris(3-(carbazol-9-yl)phenyl)-triazine (TCPZ), was developed for phosphorescent organic light-emitting diodes (OLEDs). Ultra-low driving voltages were achieved by utilizing TCPZ as the host due to its decreased singlet–triplet Exchange Energy (Δ E ST ) and low-lying lowest unoccupied molecular orbital (LUMO) Energy level. Interaction between the RGB triplet emitters and TCPZ were studied in both photoluminescent and electroluminescent processes. Transient photoluminescence (PL) measurement of the co-deposited film of fac -tris(2-phenylpyridine) iridium (Ir(PPy) 3 ):TCPZ exhibits a shoulder at 565 nm whose lifetime is about two times longer than that of the Ir(PPy) 3 triplet excitons and can be attributed to the triplet exciplex formed between Ir(PPy) 3 and TCPZ. Such exciplex was also found for the green phosphorescent OLED, giving the most efficient phosphorescent OLED with triplet exciplex emission hitherto. Different from the PL process, a broad featureless band with a maximum at 535 nm was found for the OLED based on an EML of iridium(III) bis(4,6-(di-fluorophenyl)pyridinato- N , C 2 ′)picolinate (FIrpic):TCPZ, which can be attributed to the emission from the singlet excited state of TCPZ formed by direct hole-electron recombination. A multi-emitting-layer white OLED was also fabricated by utilizing FIrpic and tris(1-phenylisoquinolinolato- C 2 , N )iridium(III) (Ir(piq) 3 ) as the complementary triplet emitters and TCPZ as the host. Different from most of ever reported white OLEDs fabricated with blue/red complementary triplet emitters that exhibit color rendering index (CRI) lower than 70, a high CRI of 82 is achieved due to the combination of blue and red phosphorescence emissions from FIrpic and Ir(piq) 3 , and the emerging green fluorescence emission from TCPZ.
J. P. Toennies - One of the best experts on this subject based on the ideXlab platform.
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New Insight into Exchange Energy of Covalent Chemical Bonds
Journal of The Chinese Chemical Society, 2001Co-Authors: K. T. Tang, J. P. ToenniesAbstract:The Exchange Energy for the H2 molecule is calculated for a wide range of inter nuclear distance R extending down to R = 0.5 a0 using the surface integral method. This method accounts for the physical Exchange of the two electrons between the two nuclei. The good agreement of the present results with the standard Heitler-London calculation demonstrates that the Exchange Energy can in deed be described in terms of electrons hop ping back and forth between the nuclei, an interpretation which has been frequently criticized in the past.
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Angular momentum coupling in the Exchange Energy of multielectron systems
Journal of Chemical Physics, 1995Co-Authors: Ulrich Kleinekathöfer, K. T. Tang, J. P. ToenniesAbstract:The Exchange Energy between two multielectron atomic systems is shown to be a product of an angular momentum factor and the Energy of the triplet‐singlet splitting of a single pair of electrons. The angular momentum factor accounts for the coupling of the angular momentum of the valence electrons and was first given by Duman and Smirnov [Opt. Spectrosc. (USSR) 29, 229 (1970)]. Here it is rederived and in the cases of interactions between hydrogen, rare gas, alkali and alkaline earth atomic systems the new corrected expressions are shown to reduce to a simple physical model. The angular momentum factors are listed for all these interacting systems. The important factors in the analytic expression for the distance dependent asymptotic Exchange energies are also given for all the homonuclear alkali, alkaline earth, and rare gas dimers.
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Exchange Energy of alkali-metal dimer cations calculated from the atomic polarizability with the Holstein-Herring method.
Physical Review A, 1992Co-Authors: K. T. Tang, J. P. Toennies, M WanschuraAbstract:A formula relating the dipole polarizability and the Exchange Energy is derived for alkali-metal dimer cations. The theory is based on the fact that the unsymmetrized polarized wave function gives both the polarizability and the Exchange Energy through the Holstein-Herring integral. The results are seen to be remarkably accurate for large ineratomic distances
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The Exchange Energy of H+2 calculated from polarization perturbation theory
Journal of Chemical Physics, 1991Co-Authors: K. T. Tang, J. P. ToenniesAbstract:The Rayleigh–Schrodinger (polarization) perturbation theory without symmetrization is used to calculate the Exchange Energy of H+2 through the surface integral of Holstein–Herring. It is mathematically proven that the Exchange Energy series so obtained is exact in the same sense as Herring’s result is exact. It is shown that the contributions to the leading term of the Exchange Energy series from all orders of polarized wave functions can be calculated exactly. Furthermore, it is explicitly demonstrated that the sum of these contributions converges to the exact value. The rate of convergence is relatively fast. With the first four orders of wave function, virtually 100% of the asymptotic Exchange Energy is recovered. With the present theory, terms other than the leading one can also be calculated systematically. This is demonstrated by the calculation of the first three terms of the Exchange Energy series from the first‐ and second‐order wave functions.
