Modification of the indo method for calculating the characteristics of point defects in ionic crystals

Abstract

MODIFICATION OF THE INDO METHOD FOR CALCULATING THE CHARACTERISTICS OF POINT DEFECTS IN IONIC CRYSTALS A. L. Shlyuger and E. A. Kotomin UDC 541.128+539.192 At the present time, semiempirical methods of quantum chemistry have been widely used in the calculation of properties of perfect and imperfect crystals [1-3]. Two models are pre- dominantly used for this purpose: the molecular cluster model (MC) and the quasimolecular extended unit cell model (QEUC) [3]. As a rule, the use of both models requires calculation of fragments containing more than ten atoms. This is possible on the basis of semiempirical quantum-chemical methods. Some of the most correct methods are the zero differential over- lap (ZDO) methods -- CNDO, INDO [i, 4]. However, while these are effective for calculating properties of nonpolar molecules [4], within the framework of the standard calculation scheme and parametrization [4] they lead to unrealistic results for the electronic structure of ionic crystals [5, 6]. The goal of this work is a modification of the INDO method for calcu- lation of the electronic and spatial structure of point defects in ionic crystals. The nu- merical calculations were carried out for intrinsic hole H-, VK-, V2-, V3-centers in a KCI crystal. Comparison of the Results of Calculations with Experimental Data The predictive power of semiempirical quantum-chemical methods as a rule is apparent in the investigation of a number of similar systems (see, for example, [7]). In this case, we consider a perfect crystal and all possible intrinsic point defects in its crystal structure. The proposed approach is based on preliminary calibration of the parameters of the method for reproducing the experimental characteristics of the electronic structure of the perfect crys- tal MeX, the dissociation energies, and the equilibrium distances of the corresponding dia- tomic molecules (MeX, X2-, etc.), with the goal of using them further in calculations of in- trinsic defects. If the defect is an impurity defect (for example, T1 in KCI), its parame- ters are optimized in the calculation of the corresponding crystal (for example, TIC1) and the diatomic molecules. As follows from [8, 9], in order to compare the forbidden gap width of a perfect crystal calculated by the Hartree--Fock method within the framework of band or molecular models with the experimental data, we need to take into account correlation effects associated with the appearance of a hole in the valence band and an electron in the conduction band and leading to an increase in the (one-electron) energy of the top of the valence band and a lowering of the bottom of the conduction band by an amount equal to the so-called "correlation correc- tion," AE c. This leads to a decrease in the forbidden gap width, calculated from the dif- ference in the one-electron energies, by 4-10 eV. In principle, compensation of errors in the semiempirical method may reproduce some characteristics of the molecules and the crystals which may be impossible to obtain by nonempirical methods without taking correlation into account. Therefore it is not surprising that the difference between one-electron levels may be found to be in good agreement with the experimental forbidden gap width [i0, ii]. How- ever, in our opinion, the ZDO methods can successively take into account (upon optimization of parameters) only correlation effects between valence electrons and core electrons (the so-called shore-range correlation, which in fact has a one-center character [8]). The long-range correlation of valence electrons between themselves should additionally be taken into account, for example by the method in [8, 9]. This means that upon optimization of parameters, the for- bidden gap width obtained in the quasimolecular extended unit cell model (which most adequate- ly reproduces the characteristics of a perfect crystal) should be higher than the experimental value [5, 12] by the sum of the long-range correlations (~4-5 eV in alkali halide crystals [8, 9]). Latvian State University, Riga. Translated from Teoreticheskaya i Eksperimental'naya Khimiya, Vol. 19, No. 4, pp. 393-400, July-August, 1983. Original article submitted July 20, 1982. 0040-5760/83/1904-0363507.50 9 1984 Plenum Publishing Corporation 363