In this paper, we calculate the energy band structure of the phononic crystal by making use of the method of plane wave expansion and investigate the influence of crystal structure, the properties of elastic units and the filling and shape of scatterer on the band gaps in an attempt to provide theoretical guidance to the preparation of phononic crystals.

The ab initio method, which is theoretically accurate, is applied to calculate the energy band structure of diamond. The results obtained is in good agreement with the experimental values.

The simple coherent potential approximation(SCPA) is developed to calculate the energy band gap Eg of the ternary mixed crystal(TMC) InGaN in group Ⅲ-Ⅴ.

The pseudopotential method is used to calculate the energy band structures of four

A mixed tight-binding, pseudopotential method is proposed to calculate the energy band structure of large-gap crystals and is tested here on LiF, NaF and KF.

The empirical tight-binding method has been used to calculate the energy band structure of semiconductors.

The ab initio method, which is theoretically accurate, is applied to calculate the energy band structure of diamond. The results obtained is in good agreement with the experimental values. And also studied is the saturator passivating the dangling bonds on the clustersurface-one of the methods for solving boundary condition at present. It was found that the exact results could hardly be obtained using hydrogen or virtual carbon (Cv) as a saturator because these bond lengths was not ia correspondence with...

The ab initio method, which is theoretically accurate, is applied to calculate the energy band structure of diamond. The results obtained is in good agreement with the experimental values. And also studied is the saturator passivating the dangling bonds on the clustersurface-one of the methods for solving boundary condition at present. It was found that the exact results could hardly be obtained using hydrogen or virtual carbon (Cv) as a saturator because these bond lengths was not ia correspondence with the minimum of total energy of the system and the optimum band gap, but the best bond length corresponding to them lay between C-H and C-Cv, e.g. it ranged from 1.25 to 1.26 A.

There are two levels in the structure of molecular crystals.The first level is molecule forming from atoms due to chemical bonds. The second level is crystal forming from molecules due to van der Waals forces. The structure characteristics of molecular crystals determine the characteristics of electronic energy bands. The band positions of the crystal orbitals are determined by the energy levels of the molecular orbitals; the widths of the bands and the state-densities are determined...

There are two levels in the structure of molecular crystals.The first level is molecule forming from atoms due to chemical bonds. The second level is crystal forming from molecules due to van der Waals forces. The structure characteristics of molecular crystals determine the characteristics of electronic energy bands. The band positions of the crystal orbitals are determined by the energy levels of the molecular orbitals; the widths of the bands and the state-densities are determined by the mutual action between the molecular orbitals belonging to the different molecules in the crystal. The relations between the energy bands of the crystal orbitals and the energy levels of the molecular orbitals and the atomic orbitals are shown in Fig. 1. (All of the equations, tables and figures can be found in the Chinese Text). According to Bloch's theorem and Born-von Kármán boundary condition, the one-electron crystal orbital may be expressed as Eq. 3. The meanings of the symbols in Eq. 3 are as follows: c—crystal orbitals, a—atomic orbitals, α—wave number,b—band index, A—normal coefficient, l—order number of the molecule in the crystal, n—number of atomic orbitals in the molecule, C—coefficient of linear combination and j—order number of the atomic orbital in the molecule. Substitute Eq. 3 into Schrodinger equation (Eq. 4). By means of a series of calculations, this problem is changed into a complex generalized eigenvalue problem as Eq. 24. If we denote "R" as real components and "I" as imaginary components, the relation between Eq. 24 and Eq. 6 may be obtained from Eq. 23. Their matrix elements are expressed as Eq. 7. This method is called direct method using linear combination of the atomic orbitals to the crystal orbitals, i. e. LCAO·CO method calculating energy bands of crystal orbitals. In the molecular crystal, the mutual action of the atomic orbitals between the molecules is much weaker than that within the molecule. (α_1,α_2,α_3) reflects the mutual action between the molecules in the crystal, so we may suppose that the coefficients of the linear combination C_j~h (α_1, α_2,α_3) are not connected with (α_1,α_2,α_3), then Eq. 15 is obtained. |l_1,l_2,l_3,b>m denotes the bth molecular orbital in (l_1,l_2,l_3) th molecule within the crystal. Then, the crystal orbital may be expressed by Eq. 16. Substitute Eq. 16 into Eq. 4. By a series of calculations, Eq. 17 is obtained to calculate the energy bands of the crystal orbitals. This method is called the method of using linear combination of the molecular orbitals to the crystal orbitals, i. e. LCAO-MO-LCMAO·CO method calculating energy bands of the crystal orbitals, Eq. 17 is much simpler than Eq. 24 in calculation. Using the concrete results calculated, we have proved that Eq. 17 gives the same energy bands as Eq. 6 or Eq. 24 for the molecular crystal. In the case of molecular crystals, the second term in the denominator of Eq. 17 is much less than one, so Eq. 17 can be expanded to obtain Eq. 19. It results in the conclusion about the structure characteristics of the electronic energy bands which has been pointed out in the previous section. For verifying the viewpoint given in the previous section with concrete data, We set up two one-dimensional models of molecular crystals, namely, Model in Series Type and Model in Parallel Type (see Figs. 3 and 4). There are two is atomic orbitals in every molecule. The distance between two adjacent molecules is d and that between two ls atomic orbitals in the molecule is r. If EHMO is applied to caloulate the energy bands of these two kinds of molecular crystals of onedimensional model, then Eqs. 17 and 7 are changed into Eqs. 20 and 25 respectively. The results calculated are shown in.Tables 2 and 3 and Figs. 5 and 6. From the tables and figures mentioned above, it can be seen that the energy bands calculated with Eq. 20 approaoh those calculated with Eq. 24 when d inereases. The more d inoreases, the more the width of the energy bands deoreases. At last, the energy bands ohange into energy levels belonging to the isolated molecule (4.254 and—17.567eV).When d is twice as large as r, the results calculated from Eq. 20 are already the same as those calculated from Eq. 24. In addition, comparing these results with the data in Table 4, we can see that the condition for approaching the calculation using LCMO·CO method to the ealoulation using LCAO·CO method is nearly the same as the condition for S_m《1 in Eq. 19 or 20. One-dimensional model molecules have been investigated in this paper, the results agree with the theoretical d eduotion. TTF-TCNQ, as an example of molecular crystals of one-dimensional model, has an intermolecular distance of 3.819 A. It is more than four times of the size of the interatomic distance in the molcoule (<1 A). So, according to the result given in this paper, we may use the method of the linear combination of the molecular orbitals to calculate the energy bands in a convenient manner.

We have used the perturbation theory to calculate the energy bands of the bipolaron and the free-polaron, in order to investigate the stabilities of the singlet and the triplet bipolaron states. By analyzing the specific heat and the magnetic susceptibility, we illustrate the importance of the triplet bipolaron state in understanding the experimental data.