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1,4-Benzokinin, 2-Metil-1,4-Benzokinin ve Tetrametil-1,4- Benzokinin Moleküllerinin Moleküler Elektronik Spektroskopi Yöntemiyle ncelenmesi
(Selçuk Üniversitesi Fen-Edebiyat Fakültesi, 2004) Yakar, Yusuf; Karabıyık, Mevlüt; Çakır, Bekir; Akın, Erhan; Güleç, Atilla; Yüksel, Hüseyin
Bu çalışmada, 1,4-benzokinin, 2-metil-1,4-benzokinin ve tetrametil-1,4-benzokinin bileşiklerinin mor ötesi-görünür bölge spektrumları Beer-Lambert konsantrasyon bölgesinde farklı çözücüler ve değişik konsantrasyonlarda deneysel olarak incelendi. Organik bileşiklerin mor ötesi-görünür bölge spektrumlarında görülen elektronik geçişlerin etkin elektronik yapısı ve bu geçişlere etki eden faktörler belirlendi. Spektral kaymaların çözücülerin dielektrik sabitlerine bağlılığı incelendi. Ana moleküle eklenen metil gruplarının ve molekül içi hidrojen balarının soğurma piklerine etkisi tartışıldı.
Binom Katsayıları Kullanarak Tek Merkezli Overlap, Potansiyel Enerji ve Kinetik Enerji İntegrallerinin Slater-Tipi Orbitaller Üzerinden Hesaplanması
(Selçuk Üniversitesi Fen-Edebiyat Fakültesi, 2001) Özmen, Ayhan; Yakar, Yusuf; Sezer, Mahmut Özgür; Atav, Ülfet; Yüksel, Hüseyin
Slater tipi orbitaller kullanılarak tek-merkez overlap, potansiyel enerji ve kinetik enerji integralleri binom katsayıları cinsinden analitik ifadeler olarak elde edilmiştir. Bu Integraller farklı kuantum sayıları ve farklı perdeleme sabitleri için hesaplanmış, hesaplarda merkezi işlem birimi (CPU) zamanlarının faktöriyelli ifadelere göre küçük olduğu tespit edilmiştir.
Birinci Sıra Atomlarda Aşırı İnce Yapı Çiftlenim Sabitlerinin Binom Katsayıları Kullanılarak Hesaplanması
(Selçuk Üniversitesi Fen-Edebiyat Fakültesi, 2002) Yakar, Yusuf; Özmen, Ayhan
Bu çalışmada birinci sıra atomların(B-F) literatürde verilen spin sınırlı Hartre-Fock dalga fonksiyonları(ROHF) kullanılarak, taban durumlarının spin yoğunlukları ve aşırı ince yapı çiftlenim sabitleri hesaplanmıştır. Elde edilen sonuçların literatürde verilenlerle uyum içinde olduğu görülmüştür.
Calculation of electronic structure of a spherical quantum dot using a combination of quantum genetic algorithm and Hartree-Fock-Roothaan method
(WORLD SCIENTIFIC PUBL CO PTE LTD, 2008) Cakir, Bekir; Oezmen, Ayhan; Atav, Uelfet; Yueksel, Hueseyin; Yakar, Yusuf
The electronic structure of Quantum Dot (QD), GaAs/AlxGa1-xAs, has been investigated by using a combination of Quantum Genetic Algorithm (QGA) and Hartree-Fock-Roothaan (HFR) method. One-electron system with an on-center impurity is considered by assuming a spherically symmetric confining potential of finite depth. The ground and excited state energies of one-electron QD were calculated depending on the dot radius and stoichiometric ratio. Expectation values of energy were determined by using the HFR method along with Slater-Type Orbitals (STOs) and QGA was used for the wave-functions optimization. In addition, the effect of the size of the basis set on the energy of QD was investigated. We also calculated the binding energy for a dot with finite confining potential. We found that the impurity binding energy increases for the finite potential well when the dot radius decreases. For the finite potential well, the binding energy reaches a peak value and then diminishes to a limiting value corresponding to the radius for which there are no bound states in the well. Whereas in previous study, in Ref. 40, for the infinite potential well, we found that the impurity binding energy increases as the dot radius decreases.
Calculation of hyperfine interaction in spherical quantum dot
(ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, 2015) Yakar, Yusuf; Cakir, Bekir; Ozmen, Ayhan
In this study, we have calculated the unperturbed wavefunctions and energy eigenvalues of the ground and excited states of a spherical quantum dot, GaAs/AlxGa1-xAs, by using quantum genetic algorithm and Hartree-Fock Roothaan method. Hyperfine coupling constant and hyperfine energy of is, 2p, 3d and 4f levels are carried out as a function of dot radius. The results show that the hyperfine constant and hyperfine energy varies rapidly in the strong and medium confining regions as dot radius decreases. It is worth pointing out that dot radius, impurity charge and angular momentum have a strong influence on the hyperfine energy. It is also found that hyperfine energy and hyperfine splitting vary with aluminium concentration ratio x. (C) 2015 Elsevier Ltd. All rights reserved.
Calculation of Linear and Nonlinear Optical Absorption Coefficients of a Spherical Quantum Dot with Parabolic Potential
(ELSEVIER, 2010) Yakar, Yusuf; Çakır, Bekir; Özmen, Ayhan
In the effective mass approximation, we calculated the binding energy and wave function for the 1s-, 1p-, 1d- and 1f-states of a spherical quantum dot (QD) with parabolic potential by using a combination of quantum genetic algorithm (QGA) and Hartree-Fock-Roothaan (HFR) method. In addition, we also investigated the linear and the third-order nonlinear optical absorption coefficients as a function of the incident photon energy for the 1s-1p, 1p-1d and 1d-1f transitions. Our results are shown that the existence of impurity has great influence on optical absorption coefficients. Moreover, the optical absorption coefficients are strongly affected by the incident optical intensity, relaxation time, parabolic potential and dot radius.
Calculation of oscillator strength. and the effects of electric field on energy states, static and dynamic polarizabilities of the confined hydrogen atom
(ELSEVIER, 2014) Cakir, Bekir; Yakar, Yusuf; Ozmen, Ayhan
In this study, we investigate the effect of an electric field on energy states of a spherical quantum dot with infinite confining potential using the perturbation method. We also perform the static dipole and dynamic dipole polarizabilities. In addition, the oscillator strengths have been calculated for the dipole transitions between higher unperturbed states. The results show that impurity and dot radius have an important effect on the Stark shift, and the effect of electric field is insensitive in small dot radii. For the excited states the Stark shift from the first-order increases linearly with the increase of electric field strength. On the other hand, the Stark shift from the first-order decreases with increasing of the magnetic quantum number. A very important future is that, for dot radius region 1.8 a(B) <= R <= 7a(B), the static dipole polarizabilities change very quickly. In addition, it is found that as the dot radius increases, the photon energy corresponding to the singularity of dynamic dipole polarizability decreases. (C) 2013 Elsevier B.V. All rights reserved.
Calculation of Zeeman splitting and Zeeman transition energies of spherical quantum dot in uniform magnetic field
(ELSEVIER SCIENCE BV, 2016) Cakir, Bekir; Atav, Ufet; Yakar, Yusuf; Ozmen, Ayhan
In this study we report a detailed theoretical investigation of the effect of an external magnetic field on the 1s-, 2p-, 3d- and 4f-energy states of a spherical quantum dot. We treat the contribution of the diamagnetic term as a perturbation and discuss the effect of the diamagnetic term on the 1s-, 2p-, 3d- and 4f-energy states. We also have calculated the Zeeman transition energies between 2p -> 1s and 3d -> 2p states with m = 0, +/- 1 and 0, +/- 1, +/- 2 as a function of dot radius and the magnetic field strength. The results show that the magnetic field, impurity charge and dot radius have a strong influence on the energy states and the Zeeman transitions. It is found that the energies of the electronic states with m < 0 addition of the diamagnetic term firstly decrease toward a minimum, and then increase with the increasing magnetic field strength. We have seen that as magnetic field intensity is adjusted, frequency of the emitted light can be changed for Zeeman transitions. (C) 2016 Elsevier B.V. All rights reserved.
Computation of hyperfine energies of hydrogen, deuterium and tritium quantum dots
(ELSEVIER SCIENCE BV, 2016) Cakir, Bekir; Ozmen, Ayhan; Yakar, Yusuf
The hyperfine energies and hyperfine constants of the ground and excited states of hydrogen, deuterium and tritium quantum dots(QDs) are calculated. Quantum genetic algorithm (QGA) and Hartree-Fock-Roothaan (HFR) methods are employed to calculate the unperturbed wave functions and energy eigenvalues. The results show that in the medium and strong confinement regions the hyperfine energy and hyperfine constant are strongly affected by dot radius, impurity charge, electron spin orientation, impurity spin and impurity magnetic moment. Besides, in all dot radii, the hyperfine splitting and hyperfine constant of the confined hydrogen and tritium atoms are approximately equivalent to each other and they are greater than the confined deuterium atom. (C) 2015 Elsevier B.V. All rights reserved.
Computation of Ionization and Various Excited State Energies of Helium and Helium-Like Quantum Dots
(WILEY-BLACKWELL, 2011) Yakar, Yusuf; Cakir, Bekir; Ozmen, Ayhan
In the effective mass approximation, we calculated the wave functions and some energy states of helium and helium-like quantum dots (QDs) with impurity charges Z = 0, 1, 2, 3, and 4. In addition, we carried out the ionization energies of these QDs as a function of dot radius, and we investigated the influence of impurity on the ionization energy. We utilized the method that is a combination of quantum genetic algorithm (QGA) and Hartree-Fock Roothaan (HFR). The results are in a good agreement with literature results. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem 111: 4139-4149, 2011
Computation of relativistic terms in a spherical quantum dot
(ELSEVIER, 2013) Yakar, Yusuf; Cakir, Bekir; Ozmen, Ayhan
We studied a hydrogenic impurity located at the center of a spherical quantum dot with an infinite spherical confining potential and calculated energy levels and wavefunctions using Quantum Genetic Algorithm(QGA) and Hartree-Fock Roothaan (HFR) method. In addition, we investigated the first-order relativistic terms such as the relativistic correction to the kinetic energy, Darwin and spin-orbit interaction term. These terms were calculated using the first-order perturbation theory. The electronic charge density for the Darwin term was carried out from a global operator defined by Hiller, Sucher and Feinberg. The results revealed that the relativistic corrections are important in small dot radii and they should not be neglected to improve the accuracy of calculations. Crown Copyright (c) 2012 Published by Elsevier B.V. All rights reserved.
Computation of relativistic terms in a spherical quantum dot (vol 134, pg 778, 2013)
(ELSEVIER SCIENCE BV, 2013) Yakar, Yusuf; Cakir, Bekir; Ozmen, Ayhan
[Abstract not Available]
Computation of rotation matrices making lined-up to the local Cartesian coordinates
(CHINESE CHEMICAL SOC, 2007) Yakar, Yusuf; Oezmen, Ayhan; Cakir, Bekir; Yueksel, Hueseyin
Rotation matrices were expressed in terms of Gaunt coefficients and complex spherical harmonics. The rotation matrices were calculated using two different ways. In the first, Gaunt coefficients and normalized complex spherical harmonics were directly calculated using binomial coefficients; in the second, Gaunt coefficients and complex spherical harmonics were recursively calculated. The methods were compared with respect to accuracy and computation time (CPU) for low and very high quantum numbers.
Computation of the oscillator strength and absorption coefficients for the intersubband transitions of the spherical quantum dot
(ELSEVIER SCIENCE BV, 2009) Ozmen, Ayhan; Yakar, Yusuf; Cakir, Bekir; Atav, Uelfet
The electronic structure and optical properties of one-electron Quantum Dot (QD) with and without an on-center impurity were investigated by assuming a spherically symmetric confining potential of finite depth. The energy eigenvalues and the state functions of QD were calculated by using a combination of Quantum Genetic Algorithm (QGA) and Hartree-Fock Roothan (HFR) method. We have calculated the binding energy for the states 1s,1p,1d,1f, oscillator strengths, the linear and third-order nonlinear optical absorption coefficients as a function of the incident photon energy and incident optical intensity for the 1s-1p, 1p-1d and id-If transitions. The existence of the impurity has great influence on the optical absorption spectra and the oscillator strengths. Also we found that the magnitudes of the total absorption coefficients of the spherical QD increase for transitions between higher states. (C) 2009 Elsevier B.V. All rights reserved.
Computation of Two-Center Coulomb Integrals Over Slater-Type Orbitals Using Elliptical Coordinates
(John Wiley & Sons Inc, 2003) Özmen, Ayhan; Karakaş, Aslı; Atav, Ülfet; Yakar, Yusuf
A general analytic formula is obtained for the two-center Coulomb integrals over Slater-type orbitals in elliptical coordinates. Finite series expansions are used in the evaluation of the radial part of the integrals. The analytic formula is expressed in terms of a product of the well-known auxiliary functions A,(p) and B,(p) and incomplete gamma functions. Recursive relations for the computer evaluation of these functions are given as well. The recursive relations are stable and our computer results are in good agreement with the benchmark values given in the literature.
Dipole and quadrupole polarizabilities and oscillator strengths of spherical quantum dot
(ELSEVIER SCIENCE BV, 2018) Yakar, Yusuf; Cakir, Bekir; Ozmen, Ayhan
In this study, the energy eigenvalues and eigenfunctions of the ground and excited states of a spherical quantum dot are calculated by using the Quantum Genetic algorithm (QGA) and Hartree-Eock Roothaan (HFR) method. Based on the calculated energies and wave functions, the static and dynamic dipole polarizabilities, the quadrupole polarizability, dipole and quadrupole oscillator strengths of spherical quantum dot are carried out as a function of dot size and the confining potential as perturbative. The results show that dot size and confining potential have a great influence on the polarizability and oscillator strength. It is found that the polarizability increases due to the spatial confinement effect in the strong confinement region. In the weak confinement region, the polarizability increases again until it reaches the saturation value. In addition, the peak positions of the dipole and quadrupole oscillator strengths shift toward smaller dot radii with the increases of the potential well depth.
Electronic structure and relativistic terms of one-electron spherical quantum dot
(ELSEVIER SCIENCE BV, 2013) Ozmen, Ayhan; Cakir, Bekir; Yakar, Yusuf
We calculated the energy eigenvalues and eigenfunctions of the ground and excited states of a hydrogenic impurity located at the center of a spherical quantum dot using the Quantum Genetic Algorithm (QGA) and Hartree-Fock Roothaan (HFR) method. In addition, we carried out the relativistic effects such as the relativistic correction to the kinetic energy, spin-orbit and Darwin terms by using the perturbation method. The electronic charge density for the Darwin term is computed from the Hiller, Sucher and Feinberg formulation instead of the traditional delta function operator. The results show that impurity, dot radius and confining potential have a great influence on the relativistic effects. In addition, as the absolute value of confining potential increases, the peak values of relativistic corrections increase and move toward lower dot radii. (C) 2013 Elsevier B.V. All rights reserved.
Electronic structure of two-electron quantum dot with parabolic potential
(TAYLOR & FRANCIS LTD, 2015) Yakar, Yusuf; Cakir, Bekir; Ozmen, Ayhan
In this study, we investigate the parabolic potential effects on the ground and excited energy states of two-electron quantum dot with impurity inside an infinite spherical confining potential well. The wave function and energy eigenvalues were calculated using a modified variational optimization procedure based mainly on quantum genetic algorithm and Hartree-Fock-Roothaan method. The results show that the parabolic potential and impurity charge have a strong effect on the energy states and ionization energies. It is worth pointing out that as impurity charge increases, the ionization energy rises, but the ionization dot radius decreases. On the other hand, as parabolic potential increases, the ionization energy decreases, but the ionization dot radius increases.
Evaluation of Two-Center One- and Two-electron Integrals Over Slater Type Orbitals
(Wiley-V C H Verlag Gmbh, 2006) Yakar, Yusuf; Özmen, Ayhan; Atav, Ülfet
A formulation previously presented by the authors for coulomb integrals was generalized to other two-center integrals, except exchange integral. Within this frame, molecular integrals were expressed in terms of some new functions closely related to the well-known incomplete gamma functions and these functions recursively evaluated. Special issues arising in the case of hybrid integrals were addressed, and the results were compared with the ones found in the literature.
Fenol, p-Bromfenol ve p-Nitrofenol Moleküllerinin Moleküler Elektronik Spektroskopi Yöntemiyle İncelenmesi
(Selçuk Üniversitesi Fen Fakültesi, 2001) Çakır, Bekir; Özmen, Ayhan; Yakar, Yusuf; Sezer, Mahmut Özgür; Yüksel, Hüseyin
Bu çalışmada fenol, p-bromfenol ve p-nitrofenol organik bileşiklerinin farklı çözücüler içinde değişik konsantrasyonlarda alman mor ötesi-görüniir bölge spektrumları incelendi. Bileşiklerin geçişlerdeki etkin elektronik yapısı belirlendi. Beer-Lambert konsantrasyon bölgesi sınırları içinde kalarak alınan spektrumlarda çözücünün, moleküllerin geçiş dalga boyu piklerine olan etkileri incelendi, çözücünün polarlığına göre dalga boyunun kırmızıya kaydığı ve spektrum şiddetinin çözücü konsantrasyonuyla orantılı olarak değiştiği belirlendi.

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