2146 Calculation of σ-, π-, and δ-Components of Quantum-Chemical Bond Orders O. V. Sizova, L. V. Skripnikov, and A. Yu. Sokolov St. Petersburg State University, Universitetskii pr. 25, St. Petersburg, 195298 Russia e-mail: ovsizova@mail.ru Received July 29, 2008 LETTERS TO THE EDITOR ISSN 1070-3632, Russian Journal of General Chemistry, 2008, Vol. 78, No. 11, pp. 2146–2147. © Pleiades Publishing, Ltd., 2008. Original Russian Text © O.V. Sizova, L.V. Skripnikov, A.Yu. Sokolov, 2008, published in Zhurnal Obshchei Khimii, 2008, Vol. 78, No. 11, pp. 1911–1912. Wiberg (W AB ) and Mayer (B АВ ) indexes introduced and theoretically proved in the 1960-80s [1–5] are widely used as quantum-chemical analogs of the chemical bond order or multiplicity. These indexes are cal-culated on the basis of a density matrix by a uniform algorithm for any molecules and types of bonds that allows analysis of chemical bonds in com- pounds of various compositions and structures. The indexes take the values close to 1, 2, or 3 in the cases when these values are assigned to the bonds by the classical structural theory. The concept of a multi- plicity of the chemical bond is inseparably linked to the isolation of its σ-, π-, and δ-components. These com- ponents are easy to find for linear molecules by sorting their МОs by irreducible representations of the C ∞v or D ∞h point groups [6]. Meanwhile, σ- and π-bonds be- tween atoms are discussed in the chemical literature also for molecules with different geometrical struc- tures, for which such classification of МОs is impossible. We offer a universal algorithm AOSB (atomic- orbital-symmetry based) of splitting diatomic indexes B АВ and W AB into σ-, π-, and δ-components. For its realization the MWBI-AOSBD program has been written, which takes coordinates of atoms and C matrix of the coefficients of МО expansion in basis functions as the input information. For each specified pair of atoms A and B of a polyatomic molecule the system of coordinates is displaced and turns so that atoms A and B are placed on a z axis. The C matrix and the density matrix are transformed in the appropriate way. The AOSB scheme uses a local cylindrical symmetry of an A-B fragment and is based on sorting matrix elements Р ȝȞ according to the AO symmetry ȝ € A and Ȟ € B defined by the quantum number m. Bond orders are calculated as sums of σ-contributions (m ȝ = m Ȟ = 0), π- contributions (m ȝ = ±1 and m Ȟ = ±1), δ-contributions (m ȝ = ±2 and m Ȟ = ±2), and “cross contributions” ∆ including Р ȝȞ elements with different symmetry of ȝ and Ȟ: W AB = W σ AB + W π AB + W δ AB + ∆ AB . 1 For each bond the reliability of AOSB decomposition is checked by calculating ∆ AB index, its non-negligible values indicating that the procedure is inapplicable. For linear molecules ∆ AB = 0. To calculate W AB indexes and their components, the transition to the orthogonal basis of natural atomic orbitals (NAO) is carried out in the program according to the procedure described in [7]. The AOSB scheme of bond orders decomposition has been preliminary tested by analyzing the electronic structure of nitrosyl complexes [8, 9]. Test calculations of diatomic molecules and organic compounds have shown that the results obtained completely correspond to classical notions of chemical bonds in “standard” compounds with bond multiplicity 1, 2, and 3, and also in the benzene molecule. A detailed pattern of decreasing bond order on passing from homonuclear diatomic molecules to isoelectronic heteronuclear molecules is clearly seen. The dependence on the oxidation state of compounds and the influence of surrounding groups are traced. For small cyclic fragments with a high degree of electronic density delocalization “cross contributions” ∆ AB appeared to be significant, which limits the application area of the model. DOI: 10.1134/S1070363208110273 1 Formulas are given for Wiberg indexes W AB , for В AB indexes they are similar.