An entry from the Cambridge Structural Database, the world's repository for small molecule cr... more An entry from the Cambridge Structural Database, the world's repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
Access to metallobacteriochlorins is essential for investigation of a wide variety of fundamental... more Access to metallobacteriochlorins is essential for investigation of a wide variety of fundamental photochemical processes, yet relatively few synthetic metallobacteriochlorins have been prepared. Members of a set of synthetic bacteriochlorins bearing 0−4 carbonyl groups (1, 2, or 4 carboethoxy substituents, or an annulated imide moiety) were examined under two conditions: (i) standard conditions for zincation of porphyrins [Zn(OAc) 2 •2H 2 O in N,N-dimethylformamide (DMF) at 60−80°C], and (ii) treatment in tetrahydrofuran (THF) with a strong base [e.g., NaH or lithium diisopropylamide (LDA)] followed by a metal reagent MX n. Zincation of bacteriochlorins that bear 2−4 carbonyl groups proceeded under the former method whereas those with 0−2 carbonyl groups proceeded with NaH or LDA/THF followed by Zn(OTf) 2. The scope of metalation (via NaH or LDA in THF) is as follows: (a) for bacteriochlorins that bear two electron-releasing aryl groups, M = Cu, Zn, Pd, and InCl (but not Mg, Al, Ni, Sn, or Au); (b) for bacteriochlorins that bear two carboethoxy groups, M = Ni, Cu, Zn, Pd, Cd, InCl, and Sn (but not Mg, Al, or Au); and (c) a bacteriochlorin with four carboethoxy groups was metalated with Mg (other metals were not examined). Altogether, 15 metallobacteriochlorins were isolated and characterized. Single-crystal X-ray analysis of 8,8,18,18-tetramethylbacteriochlorin reveals the core geometry provided by the four nitrogen atoms is rectangular; the difference in length of the two sides is ∼0.08 Å. Electronic characteristics of (metal-free) bacteriochlorins were probed through electrochemical measurements along with density functional theory calculation of the energies of the frontier molecular orbitals. The photophysical properties (fluorescence yields, triplet yields, singlet and triplet excited-state lifetimes) of the zinc bacteriochlorins are generally similar to those of the metal-free analogues, and to those of the native chromophores bacteriochlorophyll a and bacteriopheophytin a. The availability of diverse metallobacteriochlorins should prove useful in a variety of fundamental photochemical studies and applications.
Journal of Nanoelectronics and Optoelectronics, 2009
The technology for preparing colloidal CdTe quantum dots (QDs) in an alcaline medium in the prese... more The technology for preparing colloidal CdTe quantum dots (QDs) in an alcaline medium in the presence of passivators thioglycolic acid (TGA) and L-cysteine (L-cys) as well as the technology for preparing colloidal CdSe QDs by method of the reverse micelles is presented. The CdTe QDs were synthesized at different technologic conditions in an aqua colloidal solutions as well as in a polymeric matrix of poly(diallydimethylammonium chloride). For synthesis of CdSe QDs in microemulsion system Triton X-100 and n-hexyl alcohol were used. Cyclohexane served as a non-polar phase, water and water solutions of cadmium acetate and sodium selenide were used as polar phase. The peculiarities of photoluminescence (PL) and optical absorption spectra of CdTe QDs in the 4.2 K-300 K temperature range were investigated. PL spectrum consist of relatively narrow exciton line with maximum at 2.1-2.4 eV for QDs synthesized at different content of thioglycolic acid (TGA) and L-cysteine (L-cys). It was shown that the Stokes shift in PL and optical absorption spectra monotonically increases from 170 meV to 200 meV at decreasing of QDs size from 3.1 nm to 1.8 nm that is caused by the increasing of the electron-phonon interaction. The dependence of the Huang-Rhys factor on QDs size was obtained.
Proceedings of the 12th International Conference on “Electronics, Communications and Computing"
The Schwinger's oscillator model of angular momentum is applied to define quantum logical ele... more The Schwinger's oscillator model of angular momentum is applied to define quantum logical elements in quantum circuits by means of wave functions of two independent harmonic oscillators. It is shown how four EPR entangled states can be determined based on this model.
The pseudo Jahn–Teller (PJT) origin of the proton transfer barrier in the Zundel cation at differ... more The pseudo Jahn–Teller (PJT) origin of the proton transfer barrier in the Zundel cation at different O–O distances and in an H5O2+(H2O)4 cluster is revealed by means of ab initio calculations of their electronic structures and the adiabatic potential energy curves. The vibronic constants in this approach were estimated by fitting the ab initio calculated adiabatic potential to its analytical expression. It is shown also that the high-symmetry nuclear configurations ofproton-centered water clusters of the type H+(H2O)n (n = 6, 4, 3) are unstable with respect to the low-symmetry nuclear distortions leading to forming the dihydronium cation H5O2+ and the appropriate number of water molecules: H2n + 1On+ → (n – 2)H2O + H5O2+. The reason for this instability and the subsequent decay is the PJT coupling between the ground and excited electronic states.
Semiconductor Physics, Quantum Electronics and Optoelectronics, 2018
The method for transforming antiferromagnetic exchange interaction into the ferromagnetic one has... more The method for transforming antiferromagnetic exchange interaction into the ferromagnetic one has been proposed for binuclear coordination compounds, which contain dimers consisting of iron or rare earth ions with arbitrary spins and having identical electronic configurations. The method is based on the time-reversal symmetry violation at isomorphic substitution of one of dimer's ions by a "time-reversed" ion, when the spin projection operators of only one of dimer's ions are reversed. Restoration of broken symmetry accompanied by its transformation into combined time-reversal symmetry is caused by sign reversing of exchange interaction constant J at isomorphic substitution. Experimental data confirm the proposed way of inverting the sign of J. The method for controlled synthesis of binuclear coordination compounds using specific isomorphic substitutions with "time-reversed" ions allows extending the class of coordination compounds characterized by ferromagnetic exchange interaction.
Proceedings of the 11th International Conference on “Electronics, Communications and Computing (IC|ECCO-2021)”, Apr 1, 2022
An alternative approach to superdense coding of information in quantum computing is proposed on t... more An alternative approach to superdense coding of information in quantum computing is proposed on the basis of Schwinger's two-boson representation of angular momentum. Since the effective spin S = 2 n-1-1/2 corresponds to the n-qubit system, this representation can be used in the quantum computing. Operators of the logical elements of the quantum circuit were found, performing superdense coding of information in the paired bosons representation. It is shown that for superdense coding of information, the results obtained in the spinor representation and in the representation of paired bosons coincide. For one-qubit systems, one of the two representations cannot be favored. In the case of n-qubit systems for n >> 1, the representation of paired bosons is probably more convenient for applications, since in this representation the explicit form of the Pauli operators X, Y, and Z does not depend on n.
Proceedings of the 11th International Conference on “Electronics, Communications and Computing (IC|ECCO-2021)”, Apr 1, 2022
An alternative approach to superdense coding of information in quantum computing is proposed on t... more An alternative approach to superdense coding of information in quantum computing is proposed on the basis of Schwinger's two-boson representation of angular momentum. Since the effective spin S = 2 n-1-1/2 corresponds to the n-qubit system, this representation can be used in the quantum computing. Operators of the logical elements of the quantum circuit were found, performing superdense coding of information in the paired bosons representation. It is shown that for superdense coding of information, the results obtained in the spinor representation and in the representation of paired bosons coincide. For one-qubit systems, one of the two representations cannot be favored. In the case of n-qubit systems for n >> 1, the representation of paired bosons is probably more convenient for applications, since in this representation the explicit form of the Pauli operators X, Y, and Z does not depend on n.
The time-reversal symmetry violation is the most mysterious phenomenon that allows explaining the... more The time-reversal symmetry violation is the most mysterious phenomenon that allows explaining the matter–antimatter asymmetry in the present Universe. This is due to the fact that the CP-symmetry violation (Lee and Yang, Phys. Rev. 106:340, 1957, [458]), which causes the asymmetry of matter–antimatter, also leads to a violation of T-symmetry due to the CPT theorem. According to Sakharov (JETP Lett. 5:24, 1967, [478]), this asymmetry could have arisen from CP-violating (and consequently, T-violating) interactions at an early stage of the Big Bang. In the course of further evolution, this led to the present structure of the Universe. The most important motivation for studying the time-reversal symmetry breaking is the fact that its origin is not completely understood.
The novel bis(µ 3-oxo) tetranuclear trichloracetate cluster, [Fe 4 O 2 (CCl 3 COO) 8 (THF) 2 (DMF... more The novel bis(µ 3-oxo) tetranuclear trichloracetate cluster, [Fe 4 O 2 (CCl 3 COO) 8 (THF) 2 (DMF)(H 2 O)]⋅THF (1), has been synthesised and subsequently characterised by X-ray structure analysis, magnetic measurements and infra red (IR). The structure of cluster is "butterfly" type. The Fe•••Fe separation has the value of 2.883(1)-3.441(7) Å. The coordination number of iron (III) is 6. Magnetic studies reveal the presence of an antiferromagnetic exchange in the parallelogram skeletons of the tetranuclear species. Using the spin Hamiltonian H =-2J wb (Ŝ 1 Ŝ 2 + Ŝ 2 Ŝ 3 + Ŝ 3 Ŝ 4 + Ŝ 4 Ŝ 1)-2J bb Ŝ 2 Ŝ 4v + gµ β (Ŝ 1z + Ŝ 2z +Ŝ 3z + Ŝ 4z)B, the fitting parameters J bb =-14.3 cm-1 , J wb =-32.1 cm-1 , g = 2.07, ρ param. impur. = 4.2 %, Θ Curie-Weiss const. =-0.5 K and R = 6.8•10-5 were obtained.
A novel hexanuclear iron-calcium-oxo complex has been synthesized and characterized by different ... more A novel hexanuclear iron-calcium-oxo complex has been synthesized and characterized by different physicochemical methods and X-ray single crystal structural analysis: [Fe 4 Ca 2 O 2 (μ 2-HCCl 2 COO) 10 (μ 3-HCCl 2 COO) 2 (THF) 6 ]. The molecular structure shows that there are two types of coordination for COOanions: bidentate and tridentate. The corresponding variable temperature susceptibility measurement shows that in the complex there exists an antiferromagnetic interaction (|J 12 | = |J 34 | =-71.86 cm-1). The iron(III) high spin state (5/2) is proved by Mössbauer spectroscopy. High magnetic EPR measurements of 1 indicates the presence of S=0 ground state with low-lying S=1 excited state centred around g = 2.0054 ±0.0001.
In this chapter we discuss the properties of the time-reversal operator (introduced into quantum ... more In this chapter we discuss the properties of the time-reversal operator (introduced into quantum mechanics by Wigner in 1932) for particles without spin, as well as taking into account the spin. There are given Wigner criteria (a), (b), and (c) concerning the absence or presence of an additional degeneracy of energy levels due to the symmetry with respect to time reversal, both in the case when the spin of particles that form the quantum system is taken into account and in the case it is not. Wigner corepresentations of symmetry groups associated with the presence of time-reversal symmetry are also discussed.
In this section, it will be shown how the wave function of a non-stationary state of a quantum sy... more In this section, it will be shown how the wave function of a non-stationary state of a quantum system is transformed under the action of the time reversal operator \(\mathbf {T}\). Despite the fact that in the case of non-stationary states the total energy of the system is uncertain, it does not mean violating the law of energy conservation, since the average energy is conserved. It is found that the wave functions \(\Psi \left( \xi , t\right) \) and \(\mathbf {T}\Psi \left( \xi , t\right) \), on average, belong to the same energy level and are linearly dependent, if \(\mathbf {T}^{2}=\mathbf {1}\). However, if \(\mathbf {T}^{\mathbf {2}}\mathbf {=}-\mathbf {1}\), then the wave functions \(\Psi \left( \xi , t\right) \) and \(\mathbf {T}\Psi \left( \xi , t\right) \) belonging in average to the same level, are orthogonal (quasi-degeneracy of energy levels due to time-reversal symmetry).
Excitons and Biexcitons in Semiconductors.- Paramagnetic and Paraelectric Resonances of Excitons.... more Excitons and Biexcitons in Semiconductors.- Paramagnetic and Paraelectric Resonances of Excitons.- Exciton Acoustical Resonance.- Double Resonances.- Investigations of Excitons by Means of NMR Spectroscopy.- Interaction of Excitons with Paramagnetic Centers.- Effects of Deep Saturation.
The Wigner time-reversal operator \(\mathbf T \) is represented as the product of two or three so... more The Wigner time-reversal operator \(\mathbf T \) is represented as the product of two or three so-called operators of incomplete time-reversal, under the action of which not all the angular momentum projection operators change sign. It is shown that when the symmetry of time reversal is violated (reduced) in systems with Kramers degeneracy of energy levels, a violation of the Kramers theorem occurs, with the exception of one case when such reducing is insufficient to remove the Kramers degeneracy. The commutation and anticommutation relations between operators of incomplete time reversal, as well as between these operators and the operator \(\mathbf T \), are found. It is shown that these relations are different for Kramers and non-Kramers systems.
The symmetry of time reversal is one of the basic symmetries considered in the natural sciences. ... more The symmetry of time reversal is one of the basic symmetries considered in the natural sciences. It occurs in many physical dynamic systems, in particular, in classical and relativistic mechanics and electrodynamics. These consider the time conception, time translation invariance, and time-reversal symmetry. It was shown that the symmetry under time translation, which is a manifestation of the time homogeneity, is stipulated by the law of conservation of total energy of a closed system. This is proved in the Lagrange formalism of classical mechanics, as well as on the basis of Noether’s theorem in the case of Einstein’s special relativity.
On the basis of the group-theoretic approach, the existence of six new time reversal operators is... more On the basis of the group-theoretic approach, the existence of six new time reversal operators is proved, along with the well-known anti-unitary time-reversal operator introduced into quantum mechanics by Wigner. Among the new time-reversal operators, three are anti-unitary and three are unitary. A characteristic feature of the new time-reversal operators is that under their action the signs do not change for all three spin projection operators, but only for two or only for one of them. For this reason, such operators should be called operators of incomplete time reversal, in contrast to the Wigner operator, which in this context is an operator of complete time reversal.
The molecules and molecular clusters of high symmetry with orbital degeneracy of the ground state... more The molecules and molecular clusters of high symmetry with orbital degeneracy of the ground state are unstable with respect to a weak structural deformation due to Jahn-Teller effect. In the Sect. 7.1 is discussed the possibility for existence of an analogical effect of instability of spin populations of the trihomonuclear magnetic cluster with respect to a weak structural deformation (the Kahn’s instability) in the case when each of three ions of the cluster has the spin \(S=1/2\).
An entry from the Cambridge Structural Database, the world's repository for small molecule cr... more An entry from the Cambridge Structural Database, the world's repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
Access to metallobacteriochlorins is essential for investigation of a wide variety of fundamental... more Access to metallobacteriochlorins is essential for investigation of a wide variety of fundamental photochemical processes, yet relatively few synthetic metallobacteriochlorins have been prepared. Members of a set of synthetic bacteriochlorins bearing 0−4 carbonyl groups (1, 2, or 4 carboethoxy substituents, or an annulated imide moiety) were examined under two conditions: (i) standard conditions for zincation of porphyrins [Zn(OAc) 2 •2H 2 O in N,N-dimethylformamide (DMF) at 60−80°C], and (ii) treatment in tetrahydrofuran (THF) with a strong base [e.g., NaH or lithium diisopropylamide (LDA)] followed by a metal reagent MX n. Zincation of bacteriochlorins that bear 2−4 carbonyl groups proceeded under the former method whereas those with 0−2 carbonyl groups proceeded with NaH or LDA/THF followed by Zn(OTf) 2. The scope of metalation (via NaH or LDA in THF) is as follows: (a) for bacteriochlorins that bear two electron-releasing aryl groups, M = Cu, Zn, Pd, and InCl (but not Mg, Al, Ni, Sn, or Au); (b) for bacteriochlorins that bear two carboethoxy groups, M = Ni, Cu, Zn, Pd, Cd, InCl, and Sn (but not Mg, Al, or Au); and (c) a bacteriochlorin with four carboethoxy groups was metalated with Mg (other metals were not examined). Altogether, 15 metallobacteriochlorins were isolated and characterized. Single-crystal X-ray analysis of 8,8,18,18-tetramethylbacteriochlorin reveals the core geometry provided by the four nitrogen atoms is rectangular; the difference in length of the two sides is ∼0.08 Å. Electronic characteristics of (metal-free) bacteriochlorins were probed through electrochemical measurements along with density functional theory calculation of the energies of the frontier molecular orbitals. The photophysical properties (fluorescence yields, triplet yields, singlet and triplet excited-state lifetimes) of the zinc bacteriochlorins are generally similar to those of the metal-free analogues, and to those of the native chromophores bacteriochlorophyll a and bacteriopheophytin a. The availability of diverse metallobacteriochlorins should prove useful in a variety of fundamental photochemical studies and applications.
Journal of Nanoelectronics and Optoelectronics, 2009
The technology for preparing colloidal CdTe quantum dots (QDs) in an alcaline medium in the prese... more The technology for preparing colloidal CdTe quantum dots (QDs) in an alcaline medium in the presence of passivators thioglycolic acid (TGA) and L-cysteine (L-cys) as well as the technology for preparing colloidal CdSe QDs by method of the reverse micelles is presented. The CdTe QDs were synthesized at different technologic conditions in an aqua colloidal solutions as well as in a polymeric matrix of poly(diallydimethylammonium chloride). For synthesis of CdSe QDs in microemulsion system Triton X-100 and n-hexyl alcohol were used. Cyclohexane served as a non-polar phase, water and water solutions of cadmium acetate and sodium selenide were used as polar phase. The peculiarities of photoluminescence (PL) and optical absorption spectra of CdTe QDs in the 4.2 K-300 K temperature range were investigated. PL spectrum consist of relatively narrow exciton line with maximum at 2.1-2.4 eV for QDs synthesized at different content of thioglycolic acid (TGA) and L-cysteine (L-cys). It was shown that the Stokes shift in PL and optical absorption spectra monotonically increases from 170 meV to 200 meV at decreasing of QDs size from 3.1 nm to 1.8 nm that is caused by the increasing of the electron-phonon interaction. The dependence of the Huang-Rhys factor on QDs size was obtained.
Proceedings of the 12th International Conference on “Electronics, Communications and Computing"
The Schwinger's oscillator model of angular momentum is applied to define quantum logical ele... more The Schwinger's oscillator model of angular momentum is applied to define quantum logical elements in quantum circuits by means of wave functions of two independent harmonic oscillators. It is shown how four EPR entangled states can be determined based on this model.
The pseudo Jahn–Teller (PJT) origin of the proton transfer barrier in the Zundel cation at differ... more The pseudo Jahn–Teller (PJT) origin of the proton transfer barrier in the Zundel cation at different O–O distances and in an H5O2+(H2O)4 cluster is revealed by means of ab initio calculations of their electronic structures and the adiabatic potential energy curves. The vibronic constants in this approach were estimated by fitting the ab initio calculated adiabatic potential to its analytical expression. It is shown also that the high-symmetry nuclear configurations ofproton-centered water clusters of the type H+(H2O)n (n = 6, 4, 3) are unstable with respect to the low-symmetry nuclear distortions leading to forming the dihydronium cation H5O2+ and the appropriate number of water molecules: H2n + 1On+ → (n – 2)H2O + H5O2+. The reason for this instability and the subsequent decay is the PJT coupling between the ground and excited electronic states.
Semiconductor Physics, Quantum Electronics and Optoelectronics, 2018
The method for transforming antiferromagnetic exchange interaction into the ferromagnetic one has... more The method for transforming antiferromagnetic exchange interaction into the ferromagnetic one has been proposed for binuclear coordination compounds, which contain dimers consisting of iron or rare earth ions with arbitrary spins and having identical electronic configurations. The method is based on the time-reversal symmetry violation at isomorphic substitution of one of dimer's ions by a "time-reversed" ion, when the spin projection operators of only one of dimer's ions are reversed. Restoration of broken symmetry accompanied by its transformation into combined time-reversal symmetry is caused by sign reversing of exchange interaction constant J at isomorphic substitution. Experimental data confirm the proposed way of inverting the sign of J. The method for controlled synthesis of binuclear coordination compounds using specific isomorphic substitutions with "time-reversed" ions allows extending the class of coordination compounds characterized by ferromagnetic exchange interaction.
Proceedings of the 11th International Conference on “Electronics, Communications and Computing (IC|ECCO-2021)”, Apr 1, 2022
An alternative approach to superdense coding of information in quantum computing is proposed on t... more An alternative approach to superdense coding of information in quantum computing is proposed on the basis of Schwinger's two-boson representation of angular momentum. Since the effective spin S = 2 n-1-1/2 corresponds to the n-qubit system, this representation can be used in the quantum computing. Operators of the logical elements of the quantum circuit were found, performing superdense coding of information in the paired bosons representation. It is shown that for superdense coding of information, the results obtained in the spinor representation and in the representation of paired bosons coincide. For one-qubit systems, one of the two representations cannot be favored. In the case of n-qubit systems for n >> 1, the representation of paired bosons is probably more convenient for applications, since in this representation the explicit form of the Pauli operators X, Y, and Z does not depend on n.
Proceedings of the 11th International Conference on “Electronics, Communications and Computing (IC|ECCO-2021)”, Apr 1, 2022
An alternative approach to superdense coding of information in quantum computing is proposed on t... more An alternative approach to superdense coding of information in quantum computing is proposed on the basis of Schwinger's two-boson representation of angular momentum. Since the effective spin S = 2 n-1-1/2 corresponds to the n-qubit system, this representation can be used in the quantum computing. Operators of the logical elements of the quantum circuit were found, performing superdense coding of information in the paired bosons representation. It is shown that for superdense coding of information, the results obtained in the spinor representation and in the representation of paired bosons coincide. For one-qubit systems, one of the two representations cannot be favored. In the case of n-qubit systems for n >> 1, the representation of paired bosons is probably more convenient for applications, since in this representation the explicit form of the Pauli operators X, Y, and Z does not depend on n.
The time-reversal symmetry violation is the most mysterious phenomenon that allows explaining the... more The time-reversal symmetry violation is the most mysterious phenomenon that allows explaining the matter–antimatter asymmetry in the present Universe. This is due to the fact that the CP-symmetry violation (Lee and Yang, Phys. Rev. 106:340, 1957, [458]), which causes the asymmetry of matter–antimatter, also leads to a violation of T-symmetry due to the CPT theorem. According to Sakharov (JETP Lett. 5:24, 1967, [478]), this asymmetry could have arisen from CP-violating (and consequently, T-violating) interactions at an early stage of the Big Bang. In the course of further evolution, this led to the present structure of the Universe. The most important motivation for studying the time-reversal symmetry breaking is the fact that its origin is not completely understood.
The novel bis(µ 3-oxo) tetranuclear trichloracetate cluster, [Fe 4 O 2 (CCl 3 COO) 8 (THF) 2 (DMF... more The novel bis(µ 3-oxo) tetranuclear trichloracetate cluster, [Fe 4 O 2 (CCl 3 COO) 8 (THF) 2 (DMF)(H 2 O)]⋅THF (1), has been synthesised and subsequently characterised by X-ray structure analysis, magnetic measurements and infra red (IR). The structure of cluster is "butterfly" type. The Fe•••Fe separation has the value of 2.883(1)-3.441(7) Å. The coordination number of iron (III) is 6. Magnetic studies reveal the presence of an antiferromagnetic exchange in the parallelogram skeletons of the tetranuclear species. Using the spin Hamiltonian H =-2J wb (Ŝ 1 Ŝ 2 + Ŝ 2 Ŝ 3 + Ŝ 3 Ŝ 4 + Ŝ 4 Ŝ 1)-2J bb Ŝ 2 Ŝ 4v + gµ β (Ŝ 1z + Ŝ 2z +Ŝ 3z + Ŝ 4z)B, the fitting parameters J bb =-14.3 cm-1 , J wb =-32.1 cm-1 , g = 2.07, ρ param. impur. = 4.2 %, Θ Curie-Weiss const. =-0.5 K and R = 6.8•10-5 were obtained.
A novel hexanuclear iron-calcium-oxo complex has been synthesized and characterized by different ... more A novel hexanuclear iron-calcium-oxo complex has been synthesized and characterized by different physicochemical methods and X-ray single crystal structural analysis: [Fe 4 Ca 2 O 2 (μ 2-HCCl 2 COO) 10 (μ 3-HCCl 2 COO) 2 (THF) 6 ]. The molecular structure shows that there are two types of coordination for COOanions: bidentate and tridentate. The corresponding variable temperature susceptibility measurement shows that in the complex there exists an antiferromagnetic interaction (|J 12 | = |J 34 | =-71.86 cm-1). The iron(III) high spin state (5/2) is proved by Mössbauer spectroscopy. High magnetic EPR measurements of 1 indicates the presence of S=0 ground state with low-lying S=1 excited state centred around g = 2.0054 ±0.0001.
In this chapter we discuss the properties of the time-reversal operator (introduced into quantum ... more In this chapter we discuss the properties of the time-reversal operator (introduced into quantum mechanics by Wigner in 1932) for particles without spin, as well as taking into account the spin. There are given Wigner criteria (a), (b), and (c) concerning the absence or presence of an additional degeneracy of energy levels due to the symmetry with respect to time reversal, both in the case when the spin of particles that form the quantum system is taken into account and in the case it is not. Wigner corepresentations of symmetry groups associated with the presence of time-reversal symmetry are also discussed.
In this section, it will be shown how the wave function of a non-stationary state of a quantum sy... more In this section, it will be shown how the wave function of a non-stationary state of a quantum system is transformed under the action of the time reversal operator \(\mathbf {T}\). Despite the fact that in the case of non-stationary states the total energy of the system is uncertain, it does not mean violating the law of energy conservation, since the average energy is conserved. It is found that the wave functions \(\Psi \left( \xi , t\right) \) and \(\mathbf {T}\Psi \left( \xi , t\right) \), on average, belong to the same energy level and are linearly dependent, if \(\mathbf {T}^{2}=\mathbf {1}\). However, if \(\mathbf {T}^{\mathbf {2}}\mathbf {=}-\mathbf {1}\), then the wave functions \(\Psi \left( \xi , t\right) \) and \(\mathbf {T}\Psi \left( \xi , t\right) \) belonging in average to the same level, are orthogonal (quasi-degeneracy of energy levels due to time-reversal symmetry).
Excitons and Biexcitons in Semiconductors.- Paramagnetic and Paraelectric Resonances of Excitons.... more Excitons and Biexcitons in Semiconductors.- Paramagnetic and Paraelectric Resonances of Excitons.- Exciton Acoustical Resonance.- Double Resonances.- Investigations of Excitons by Means of NMR Spectroscopy.- Interaction of Excitons with Paramagnetic Centers.- Effects of Deep Saturation.
The Wigner time-reversal operator \(\mathbf T \) is represented as the product of two or three so... more The Wigner time-reversal operator \(\mathbf T \) is represented as the product of two or three so-called operators of incomplete time-reversal, under the action of which not all the angular momentum projection operators change sign. It is shown that when the symmetry of time reversal is violated (reduced) in systems with Kramers degeneracy of energy levels, a violation of the Kramers theorem occurs, with the exception of one case when such reducing is insufficient to remove the Kramers degeneracy. The commutation and anticommutation relations between operators of incomplete time reversal, as well as between these operators and the operator \(\mathbf T \), are found. It is shown that these relations are different for Kramers and non-Kramers systems.
The symmetry of time reversal is one of the basic symmetries considered in the natural sciences. ... more The symmetry of time reversal is one of the basic symmetries considered in the natural sciences. It occurs in many physical dynamic systems, in particular, in classical and relativistic mechanics and electrodynamics. These consider the time conception, time translation invariance, and time-reversal symmetry. It was shown that the symmetry under time translation, which is a manifestation of the time homogeneity, is stipulated by the law of conservation of total energy of a closed system. This is proved in the Lagrange formalism of classical mechanics, as well as on the basis of Noether’s theorem in the case of Einstein’s special relativity.
On the basis of the group-theoretic approach, the existence of six new time reversal operators is... more On the basis of the group-theoretic approach, the existence of six new time reversal operators is proved, along with the well-known anti-unitary time-reversal operator introduced into quantum mechanics by Wigner. Among the new time-reversal operators, three are anti-unitary and three are unitary. A characteristic feature of the new time-reversal operators is that under their action the signs do not change for all three spin projection operators, but only for two or only for one of them. For this reason, such operators should be called operators of incomplete time reversal, in contrast to the Wigner operator, which in this context is an operator of complete time reversal.
The molecules and molecular clusters of high symmetry with orbital degeneracy of the ground state... more The molecules and molecular clusters of high symmetry with orbital degeneracy of the ground state are unstable with respect to a weak structural deformation due to Jahn-Teller effect. In the Sect. 7.1 is discussed the possibility for existence of an analogical effect of instability of spin populations of the trihomonuclear magnetic cluster with respect to a weak structural deformation (the Kahn’s instability) in the case when each of three ions of the cluster has the spin \(S=1/2\).
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