Papers by Herbert H H Homeier
It is described how the Hermite-Padé polynomials corresponding to an algebraic approximant for a ... more It is described how the Hermite-Padé polynomials corresponding to an algebraic approximant for a power series may be used to predict coefficients of the power series that have not been used to compute the Hermite-Padé polynomials. A recursive algorithm is derived, and some numerical examples are given.
ISRN Applied Mathematics
ISRN Applied Mathematics (Print), Oct 25, 2012
ARInternet Corporation, 1994
The evaluation of functions of square matrices can be based on either the Taylor series of the fu... more The evaluation of functions of square matrices can be based on either the Taylor series of the function, or on diagonalization techniques. In the present contribution it is shown that suitable extrapolation techniques enhance the efficiency of the Taylor series approach. As an important example, the exponential of a matrix can be obtained via this method. The exponential of matrices has to be calculated frequently in recursive methods for the solution of linear systems of ordinary differential equations, as occur in the solution of evolution equations, and also in the solution of the heat-conduction equation or the time-dependent Schrödinger equation after suitable discretization [Yung-Ya Lin and Lian-Pin Hwang, Computers Chem. 16 (1992), 285]. Several extrapolation methods will be compared. It is discussed whether these methods may also be useful for the extrapolation of vector sequences which occur for instance in iterative solutions of nonlinear equations. Examples for the latter are for instance ab initio SCF and MCSCF equations.
Extrapolationsverfahren ... (Habilitation thesis)
Journal of Molecular Structure: THEOCHEM, 1996
Some methods for the convergence acceleration of the Møller-Plesset perturbation series for the c... more Some methods for the convergence acceleration of the Møller-Plesset perturbation series for the correlation energy are discussed. The order-by-order summation is less effective than the Feenberg series. The latter is obtained by renormalizing the unperturbed Hamilton operator by a constant factor that is optimized for the third order energy. In the fifth order case, the Feenberg series can be improved by order-dependent optimization of the parameter. Alternatively, one may use Padé approximants or a further method based on effective characteristic polynomials to accelerate the convergence of the perturbation series. Numerical evidence is presented that, besides the Feenberg-type approaches, suitable Padé approximants, and also the effective second order characteristic polynomial, are excellent tools for correlation energy estimation.
CCDC 1894261: Experimental Crystal Structure Determination
CCDC 1894739: Experimental Crystal Structure Determination
Some methods for the convergence acceleration of the Møller-Plesset perturbation series for the c... more Some methods for the convergence acceleration of the Møller-Plesset perturbation series for the correlation energy are discussed. The order-by-order summation is less effective than the Feenberg series. The latter is obtained by renormalizing the unperturbed Hamilton operator by a constant factor that is optimized for the third order energy. In the fifth order case, the Feenberg series can be improved by orderdependent optimization of the parameter. Alternatively, one may use Padé approximants or a further method based on effective characteristic polynomials to accelerate the convergence of the perturbation series. Numerical evidence is presented that, besides the Feenberg-type approaches, suitable Padé approximants, and also the effective second order characteristic polynomial, are excellent tools for correlation energy estimation. Key words: Many-body perturbation theory, convergence acceleration, extrapolation, Møller-Plesset series, Feenberg series, Padé approximants, effective ...
Zur Konvergenzverbesserung der Møller-Plesset Störungsreihe (Engl.: On Convergence Acceleration of the Møller-Plesset Perturbation Series)
Inspired by molecular crystal theory of coupling symmetry-related transition dipole moments, we d... more Inspired by molecular crystal theory of coupling symmetry-related transition dipole moments, we develop a model for rational design of Cu(I) complexes to achieve short TADF (thermally activated delayed fluorescence) decay times. This is, for example, important to reduce OLED stability problems and roll-off effects. Guided by the model, we design a new class of Cu(I) dimers focusing on Cu 2 (tppb)(PPh 3) 2 Cl 2 2 (tppb(PPh 3) 2 = 1,2,4,5-tetrakis(diphenylphosphino)benzene). Indeed, this class of compounds shows particularly short TADF decay times as evidenced by luminescence studies over a temperature range of 1.5 K ≤ T ≤ 300 K and, thus, supports the proposed design strategy. The model is further supported by TD-DFT calculations. A key property of the strategy is that the new dimer(s) exhibit a drastically faster radiative rate of the transition between the lowest excited singlet state and the ground state than the related monomer, Cu(dppb)(PPh 3)Cl 1 (dppb = 1,2bis(diphenylphosphino)benzene). This is even valid at a small singlet−triplet energy gap of ΔE(S 1 −T 1) = 390 cm −1 (48 meV). Accordingly, we find a benchmark TADF decay time for the Cu(I) dimer 2 of only 1.2 μs (radiative decay: 1.5 μs). This is a factor of about three times shorter than found so far for any other Cu(I) complex with a similarly small energy gap. The presented design strategy seems to be of general validity.
Inspired by molecular crystal theory of coupling symmetry-related transition dipole moments, we d... more Inspired by molecular crystal theory of coupling symmetry-related transition dipole moments, we develop a model for rational design of Cu(I) complexes to achieve short TADF (thermally activated delayed fluorescence) decay times. This is, for example, important to reduce OLED stability problems and roll-off effects. Guided by the model, we design a new class of Cu(I) dimers focusing on Cu 2 (tppb)(PPh 3) 2 Cl 2 2 (tppb(PPh 3) 2 = 1,2,4,5-tetrakis(diphenylphosphino)benzene). Indeed, this class of compounds shows particularly short TADF decay times as evidenced by luminescence studies over a temperature range of 1.5 K ≤ T ≤ 300 K and, thus, supports the proposed design strategy. The model is further supported by TD-DFT calculations. A key property of the strategy is that the new dimer(s) exhibit a drastically faster radiative rate of the transition between the lowest excited singlet state and the ground state than the related monomer, Cu(dppb)(PPh 3)Cl 1 (dppb = 1,2bis(diphenylphosphino)benzene). This is even valid at a small singlet−triplet energy gap of ΔE(S 1 −T 1) = 390 cm −1 (48 meV). Accordingly, we find a benchmark TADF decay time for the Cu(I) dimer 2 of only 1.2 μs (radiative decay: 1.5 μs). This is a factor of about three times shorter than found so far for any other Cu(I) complex with a similarly small energy gap. The presented design strategy seems to be of general validity.
セクハラ論争は第2の 赤狩り か
文芸春秋, Dec 1, 1991
CCDC 1894259: Experimental Crystal Structure Determination
Chemistry of Materials, 2019
Inspired by molecular crystal theory of coupling symmetry-related transition dipole moments, we d... more Inspired by molecular crystal theory of coupling symmetry-related transition dipole moments, we develop a model for rational design of Cu(I) complexes to achieve short TADF (thermally activated delayed fluorescence) decay times. This is, for example, important to reduce OLED stability problems and roll-off effects. Guided by the model, we design a new class of Cu(I) dimers focusing on Cu 2 (tppb)(PPh 3) 2 Cl 2 2 (tppb(PPh 3) 2 = 1,2,4,5tetrakis(diphenylphosphino)benzene). Indeed, this class of compounds shows particularly short TADF decay times as evidenced by luminescence studies over a temperature range of 1.5 K ≤ T ≤ 300 K and thus, supports the proposed design strategy. The model is further supported by TD-DFT calculations. A key property of the strategy is that the new dimer(s) exhibit a drastically faster radiative rate of the transition between the lowest excited singlet state and the ground state than the related monomer, Cu(dppb)(PPh 3)Cl 1 (dppb = 1,2bis(diphenylphosphino)benzene). This is even valid at a small singlet-triplet energy gap of E(S 1-T 1) = 390 cm-1 (48 meV). Accordingly, we find a benchmark TADF decay time for the Cu(I) dimer 2 of only 1.2 s (radiative decay: 1.5 s). This a factor of about three times shorter than found so far for any other Cu(I) complex with similarly small energy gap. The presented design strategy seems to be of general validity.
The journal of physical chemistry letters, Jan 22, 2018
A highly potent donor-acceptor biaryl thermally activated delayed fluorescence (TADF) dye is acce... more A highly potent donor-acceptor biaryl thermally activated delayed fluorescence (TADF) dye is accessible by a concise two-step sequence employing two-fold Ullmann arylation and a sequentially Pd-catalyzed Masuda borylation-Suzuki arylation (MBSA). Photophysical investigations show efficient TADF at ambient temperature due to the sterical hindrance between the donor and acceptor moieties. The photoluminescence quantum yield amounts to Φ = 80% in toluene and 90% in PMMA arising from prompt and delayed fluorescence with decay times of 21 ns and 30 μs, respectively. From an Arrhenius plot, the energy gap Δ E(S - T) between the lowest excited singlet S and triplet T state was determined to be 980 cm (120 meV). A new procedure is proposed that allows us to estimate the intersystem crossing time to ∼10 ns.
Journal of Computational and Applied Mathematics, 2009
We introduce two families of Newton-type methods for multiple roots with cubic convergence. A fur... more We introduce two families of Newton-type methods for multiple roots with cubic convergence. A further Newton-type method for multiple roots with cubic convergence is presented that is related to quadrature. We also provide numerical tests that show that these new methods are competitive to other known methods for multiple roots.
We discuss certain special cases of algebraic approximants that are given as zeroes of so-called ... more We discuss certain special cases of algebraic approximants that are given as zeroes of so-called "effective characteristic polynomials" and their generalization to a multiseries setting. These approximants are useful for the convergence acceleration or summation of quantum mechanical perturbation series. Examples will be given and some properties will be discussed.
Vector extrapolation processes can be used for the acceleration of fixed point iterations. A larg... more Vector extrapolation processes can be used for the acceleration of fixed point iterations. A large variety of new methods is obtained by generalizations of a rather general scalar extrapolation method, the J transformation [1, 2, 3] that contains many wellknown extrapolation methods as special cases. The J transformation is constructed on the basis of the concept of hierarchical consistency. Suitable variants of the J transformation belong to the most powerful convergence accelerators for sequences of number sequences that are currently known. Here, we discuss how to generalize the J transformation to vector and matrix sequences in relation to the concept of hierarchical consistency using pseudoinverses. For this, several possibilities exist, and thus, a number of new transformations are obtained. Some applications will be discussed.
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Papers by Herbert H H Homeier