“…Such linear transformed orbitals are defined as the natural orbitals, and their occupation numbers do not necessarily take integer values. 9,20 It should be noted, with much attention, that the occupation numbers of the π-and π*-CCOs only, indicated by dashed lines in Figure 4, are changed, and by the same amount, around k ) π/a.…”
Section: Resultsmentioning
confidence: 97%
“…The CCOs are given by the unitary transformation of the canonical COs as described in eq 14. Such linear transformed orbitals are defined as the natural orbitals, and their occupation numbers do not necessarily take integer values. , It should be noted, with much attention, that the occupation numbers of the π- and π*-CCOs only, indicated by dashed lines in Figure , are changed, and by the same amount, around k = π/ a . 4 The occupation numbers for the alternating t -PA calculated by our method, where the dashed lines indicate the occupation number derived from the π- and π*-CCOs.…”
Section: Resultsmentioning
confidence: 99%
“…7,8 In this work, we have tried to proceed by using those treatments which are based on our previous study. 9 The following procedure is derived from the electronic Hamiltonian H that is represented as a function of the crystal momentum k (i.e., λ ) k). The theory has been applied to pure (nondoped) alternating trans-polyacetylene (t-PA) to understand better the electronic structure from our new standpoint.…”
Section: Introductionmentioning
confidence: 99%
“…In this work, we have tried to proceed by using those treatments which are based on our previous study …”
Quasi-diabatic band theory has been developed by using the localized crystal orbital (LCO) transformation to study the electronic structure representing the diabatic behavior of electrons. The theory has been applied to nondoped alternating trans-polyacetylene (t-PA) to understand better the electronic structure from this new standpoint. The results show that the π-(π*-) band of the newly constructed crystal orbital becomes higher (lower) than that of the canonical crystal orbital. The occupation number analysis also indicates that the π-bands near the Fermi energy level play a significant role in the electron transport. These results have been discussed in terms of the LCOs representing the biradical and zwitterionic states.
“…Such linear transformed orbitals are defined as the natural orbitals, and their occupation numbers do not necessarily take integer values. 9,20 It should be noted, with much attention, that the occupation numbers of the π-and π*-CCOs only, indicated by dashed lines in Figure 4, are changed, and by the same amount, around k ) π/a.…”
Section: Resultsmentioning
confidence: 97%
“…The CCOs are given by the unitary transformation of the canonical COs as described in eq 14. Such linear transformed orbitals are defined as the natural orbitals, and their occupation numbers do not necessarily take integer values. , It should be noted, with much attention, that the occupation numbers of the π- and π*-CCOs only, indicated by dashed lines in Figure , are changed, and by the same amount, around k = π/ a . 4 The occupation numbers for the alternating t -PA calculated by our method, where the dashed lines indicate the occupation number derived from the π- and π*-CCOs.…”
Section: Resultsmentioning
confidence: 99%
“…7,8 In this work, we have tried to proceed by using those treatments which are based on our previous study. 9 The following procedure is derived from the electronic Hamiltonian H that is represented as a function of the crystal momentum k (i.e., λ ) k). The theory has been applied to pure (nondoped) alternating trans-polyacetylene (t-PA) to understand better the electronic structure from our new standpoint.…”
Section: Introductionmentioning
confidence: 99%
“…In this work, we have tried to proceed by using those treatments which are based on our previous study …”
Quasi-diabatic band theory has been developed by using the localized crystal orbital (LCO) transformation to study the electronic structure representing the diabatic behavior of electrons. The theory has been applied to nondoped alternating trans-polyacetylene (t-PA) to understand better the electronic structure from this new standpoint. The results show that the π-(π*-) band of the newly constructed crystal orbital becomes higher (lower) than that of the canonical crystal orbital. The occupation number analysis also indicates that the π-bands near the Fermi energy level play a significant role in the electron transport. These results have been discussed in terms of the LCOs representing the biradical and zwitterionic states.
“…They are something in between, depending on the type of coupling. Accordingly, the change of the occupation number ν j ( k ) of the CCO φ‘ j ( k ) can be a criterion of the degree of electron transport along k -space in the quasi-diabatic states. , Then, the energy dependence of the occupation and the unoccupation (hole) numbers, which we have called “the effective number of free carriers”, is given by and respectively, where E F stands for the Fermi energy level. The integration is taken over a first Brillouin zone (BZ).…”
A quasi-diabatic crystal orbital (CO) theory earlier developed has been applied to lithium heavily-doped trans-polyacetylene (t-PA) to study quasi-diabatic electronic effects in a metallic state. It has been shown that the quasi-diabatic electronic structure largely changes from the adiabatic electronic structure. This change arises from the strong interaction of the crystal momentum coupling between carbon π and lithium canonical COs. The coupling also leads to occurrence of a large spin-density-wave (biradical character) in the quasidiabatic electronic state. The occurrence has been analyzed to be due to a large electron-electron repulsive interaction. The quasi-diabatic electronic structure has been discussed with a focus on the electron-electron repulsion.
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