STRUCTURE OF THE ELECTRONIC ENERGY BANDS OF THE CHARGE TRANSFER COMPLEX MOLECULAR CRYSTAL TMPD.(TCNQ)_2 AND THE COMPARISON WITH THOSE OF NMP.TCNQ AND TTF.TCNQ

As a exanple,the total and partial and local density of states for the molecular crystal [C_0(H_2O)_4(NCS)_2]·(18-Crown-6)were calculated by CNDO/2 quantum chemical method based on a simpler cluster Con- formations of local interaction about this crystal have been obtained simply and clearly.

In this paper,by us ing the continued method,the exact energy eigenvalues(i.e.the exact values of the bi nding energy of molecular crystal)of the Hamiltonian operator of the molecu-la r crystal with the interaction potential between atoms in the molecular crystal V(r)=A 1 r-10-A 2 r-6 +A 3 r 2 (A 1 ,A 2 ,A 3 >0)is acquired.

STRUCTURE OF THE ELECTRONIC ENERGY BANDS OF THE CHARGE TRANSFER COMPLEX MOLECULAR CRYSTAL TMPD.(TCNQ)_2 AND THE COMPARISON WITH THOSE OF NMP.TCNQ AND TTF.TCNQ

As a exanple,the total and partial and local density of states for the molecular crystal [C_0(H_2O)_4(NCS)_2]·(18-Crown-6)were calculated by CNDO/2 quantum chemical method based on a simpler cluster Con- formations of local interaction about this crystal have been obtained simply and clearly.

In this paper,by us ing the continued method,the exact energy eigenvalues(i.e.the exact values of the bi nding energy of molecular crystal)of the Hamiltonian operator of the molecu-la r crystal with the interaction potential between atoms in the molecular crystal V(r)=A 1 r-10-A 2 r-6 +A 3 r 2 (A 1 ,A 2 ,A 3 >0)is acquired.

In this paper,by us ing the continued method,the exact energy eigenvalues(i.e.the exact values of the bi nding energy of molecular crystal)of the Hamiltonian operator of the molecu-la r crystal with the interaction potential between atoms in the molecular crystal V(r)=A 1 r-10-A 2 r-6 +A 3 r 2 (A 1 ,A 2 ,A 3 >0)is acquired.

STRUCTURE OF THE ELECTRONIC ENERGY BANDS OF THE CHARGE TRANSFER COMPLEX MOLECULAR CRYSTAL TMPD.(TCNQ)_2 AND THE COMPARISON WITH THOSE OF NMP.TCNQ AND TTF.TCNQ

As a exanple,the total and partial and local density of states for the molecular crystal [C_0(H_2O)_4(NCS)_2]·(18-Crown-6)were calculated by CNDO/2 quantum chemical method based on a simpler cluster Con- formations of local interaction about this crystal have been obtained simply and clearly.

In this paper,by us ing the continued method,the exact energy eigenvalues(i.e.the exact values of the bi nding energy of molecular crystal)of the Hamiltonian operator of the molecu-la r crystal with the interaction potential between atoms in the molecular crystal V(r)=A 1 r-10-A 2 r-6 +A 3 r 2 (A 1 ,A 2 ,A 3 >0)is acquired.

Using the Ewald method for different degrees of ionic character, we have calculated the Madelung energy of the Β phase of the donor-acceptor molecular crystal (BEDT-TTF)2I3 for pressures 1 bar and 9.5 kbar.

The intra- and inter-molecular H bonding modes in 3 were demonstrated both in molecular crystal structure and IR spectral characterization.

The saturation of a nonequidistant spin system is analyzed for the example of spin-5/2 nuclear quadrupole resonance in a molecular crystal; nonequilibrium states of the dipole-dipole reservoir are taken into account.

A method for the approximate computer calculation of the correlation functions for a molecular crystal with central interaction is developed on the basis of the statistical scheme of conditional distributions.

Electronic computer calculation of the correlation functions of a molecular crystal

Most of organio metals are formed from molecular crystals. The electronic structure of the molecular crystals consists of two levels. The principal one is the electronic structure of monomer molecules; and the second one corresponds to the interaction between monomers in orystal and may be considered as a perturbation. Starting from this point of view, the effect of the electronic structure of monomer molecules on the electrical conductivity of organic metals is investigated. We have pointed out...

Most of organio metals are formed from molecular crystals. The electronic structure of the molecular crystals consists of two levels. The principal one is the electronic structure of monomer molecules; and the second one corresponds to the interaction between monomers in orystal and may be considered as a perturbation. Starting from this point of view, the effect of the electronic structure of monomer molecules on the electrical conductivity of organic metals is investigated. We have pointed out that the creation and migration of the charge-carriers in crystals are closely related to the electronic structure of monomer molecules in crystals. If the conditions of energy correlation, symmetry match and overlap between the frontier orbitals of the corresponding monomer molecules are satisfied well in both creation and migration processes of charge-carriers, then it is possible for crystals to have a good electrical conductivity. That is, the above three conditions are necessary for organic metals in order to become good conductors. The corresponding logical graphs are shown in Pig. 1 and 2. Thus, by knowing the electrcnic structure and the packing condition of monomers in crystal, it is possible to get some qualitative informations about the electrical conductivity of organic metals.The energy spectra and the LCAO-MO coefficients of more than fifty electron donors and acceptors have been calculated (see Table 1). By using these results and the three necessary conditions mentioned above, for examples, the electrical conductivities of TTF-TCNQ, NMP-TCNQ, Q-TCNQ, TMPD-TONQ and C_(19)H_(19)N_2S_2-TCNQ complex crystals have been disoussed(see Fig. 6～13). In the first three orystals, the three necessary conditions are satisfied well, and they have higher electrioal conductivity (at room temp.,σ=500,143, 100Ω~(-1)cm~(-1) respecetively).According to the symmetry rules as defined in Fig. 5, in the process of the creation of charge-carriers the common symmetry element of TTF and TCNQ molecules is the ZX plane, and from Fig. 6 it can be seen that the two molecules are in symmetry match condition; and in the process of the migration of charge-carriers the ZX plane is the common symmetry element of the adjacent molecules in both TTF and TONQ column, and it can be seen that they are both in symmetry match conditions as expressed in Pig. 8. The conditions of energy correlation, symmetry match and overlap between the corresponding frontier orbitals in the processes of creation and migration of charge-carriers in TTFTCNQ system may be seen in Fig. 7. On the contrary, in the fourth crystal, the three necessary conditions are not well satisfied, and it has low electrical conductivity (at room temp., σ=10~(13)Ω~(-1)cm~(-1))and in the last crystal, the three necessary conditions are not satisfied, and so it has much poorer electrical conductivity (at room temp.,Finally, the structure of an organio metal whioh possesses the desired electrioal conductivity is proposed. That is, by. means of manually arranging energy, symmetry. and overlap of the frontier orbitals of the monomer moleoules and their packing situation in crystal, we may control its electrical condutivity (see Fig. 14).

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.

Using the HMO theory and Chang's reduction of the Huckel graph as well as the calibration valble of the resonance integrals of the non-coplanar σ-Plane, the energy level graph of the it-molecular orbit and the total energy graph of the π-electron for the various configurations of 1, 3,5-Triphenylbenzene have been calculated. Based on the energy level graph and the total energy graph of the π-electron,the plot method is used to find that the angle between benzene rings for the most possible configuration is 38°....

Using the HMO theory and Chang's reduction of the Huckel graph as well as the calibration valble of the resonance integrals of the non-coplanar σ-Plane, the energy level graph of the it-molecular orbit and the total energy graph of the π-electron for the various configurations of 1, 3,5-Triphenylbenzene have been calculated. Based on the energy level graph and the total energy graph of the π-electron,the plot method is used to find that the angle between benzene rings for the most possible configuration is 38°. The calculated value is found to agree with the Ultraviolet spectrum data and the X-ray diffraction data for the molecular crystal.