Parametrization of the MNDO Quantum-Chemical Method for the Numerical Analysis of Adsorption on Transition Metals

Abstract

For studying the influence of environment on deformed metals and alloys, semiempirical quantum-chemical methods of computation are widely used in the computer simulation of adsorption processes [1] with different kinds of parameterization (i.e., replacement of certain calculated integrals by empirical parameters). For example, such a parameterization was carried out for zinc and aluminum [2]. However, in software for the simulation of adsorption interactions of metals and alloys with their environment, the quantum-chemical parameters of the most widespread semiempirical modified method of neglecting diatomic differential overlap (MNDO) are absent for practically important systems with elements of the fourth to sixth periods (iron, chromium, nickel, molybdenum, tungsten, palladium, and platinum) [3]. Practical experience shows that studying adsorption interactions on the surface of metals and alloys with the use of quantum-chemical methods, on which the software mentioned above is based, requires too much machine time for efficient computations of complex polyatomic systems. To extend the MNDO quantum-chemical method to transition metals, we carried out a systematic search for the optimal empirical parameters of their atoms. We optimized 22 parameters (spd-basis), namely: Us s , Up p , and Ud d (one-centered single-electron energies), βs , βp , and βd (resonance integrals), gs , gss , gp , gpp , gd , gdd , gp2 , and hsp (two-centered two-electron integrals), dd, qq, am, and ad (the integrals of interelectronic interactions), and Eisol (the energy of an isolated atom). As the basis of parameterization, we took the system of parameters of a chromium atom, which is developing at present and is used in the GAMESS quantum-chemical computational complex (subroutine MOPAC) [4]. To refine the parameters of a chromium atom and to find the parameters of iron, nickel, molybdenum, tungsten, palladium, and platinum atoms, we systematically computed the energy (the heat of formation of molecules and the energy of interatomic bonds) and geometric (interatomic distances and valence angles) characteristics of simple compounds formed from atoms of a transition metal and atoms of elements of the second and third periods, namely, oxides, carbides, chalcogenides, and halogenides. As the criterion of optimality of these parameters, we took the maximum approach of the computed characteristics to the experimental ones borrowed from [5]. For each quantum-chemical parameter, we gradually approximated these characteristics. The behavior of geometric and energy characteristics of simple compounds containing one or several atoms of transition metals, for the given set of parameters (Table 1) is the following: For oxides, carbides, chalcogenides, and halogenides, the computed heat of formation of molecules in the equilibrium state constitutes 60 – 70%, 55 – 65%, 50 – 60%, and 60 – 75%, respectively, of the experimental value (Table 2). The computed equilibrium distances between an atom of a transition element and an electronegative atom (oxygen, carbon, chalcogen, or halogen) are equal to 80 – 85%, 75 – 80%, 70 – 80%, and 80 – 90% as compared with the experimental values. The obtained empirical parameters enable one to study adsorption interactions on the surface of metals and alloys with a speed several times higher than that using the widespread ZINDO/1 quantum-chemical method, on which numerous computer programs are based. In addition, having introduced the computed empirical parameters of transition metals into the GAMESS quantum-chemical computational complex (subroutine MOPAC), one