Theoretical analysis of magnetic and electric hyperfine interactions on 1H and 2H nuclei of bis(acetylacetonato) copper (II)

The INDO method has been used in calculating the tensors of hyperfine structure and the electric field gradient on the ¹H and ²H nuclei in Cu(acac)₂. The procedure used in calculating the magnetic resonance parameters (MRPs) is based on an accounting for one-center and two-center Coulomb integrals of dipole-dipole interaction. The influence of out-of-plane step distortion of the complex on the MRPs is examined critically.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 24, No. 2, pp. 149–155, March–April, 1988.The authors wish to express their appreciation to P. V. Schastnev and S. A. Mustafaev for valuable discussion and for assistance in the work.     

Vector coupling coefficients for calculations of transition-metal atoms and ions by the SCF coupling operator method

We derived the necessary conditions to which the vector coupling coefficients (VCC ) a and b describing atomic L,S-multiplets of the configurations d^N (1 ≤ N ≤ 9), should satisfy. Special attention is paid to the states of non-Roothaan type for which VCC depend on the choice of degenerate d-orbitals basis set determined within the accuracy up to an orthogonal transformation u. It is shown that for such states the direct sum of matrices ‖a‖ and ‖b‖ must be the non-symmetric matrix. Obtained VCC were used for the ab initio calculations (basis set (14s9p5d)/[8s4p2d] from [15]) on first-row transition atoms (from Sc to Cu) to compare to similar calculations [16], in which the Peterson's VCC have been used, and with calculations [15] carried out by the atomic SCF program [4] as well.     

Coupling coefficients “symmetry dilemma” in the restricted open‐shell Hartree–Fock method

Two opposite conclusions are known on the symmetry of the vector coupling coefficients (VCCs), a_mn and b_mn, in the restricted open-shell Hartree-Fock (ROHF) method. The first one states that the VCCs are symmetric for all spectroscopic terms, i.e., a_mn = a_nm and b_mn = b_nm. An opposing statement is that the "non-Roothaan" terms, arising from the degenerate open-shell electronic configuration γ^N, can be characterized by non-symmetric VCCs matrices only: ‖a_mn‖ ≠ ‖a_nm,‖ ‖b_mn‖ ≠ ‖b_nm‖. This article presents a detailed analysis of the VCCs symmetry problem. A general approach to the VCCs determination has been developed leading to non‐symmetric VCCs for γ^N systems with γ ≥ 3. The main purpose of this work is to eliminate the contradiction arising in the ROHF theory when the latter is applied to highly symmetric open‐shell molecules and atoms. This revised version was published online in July 2006 with corrections to the Cover Date.     

Anomalous values of 〈Ŝ2〉 before and after annihilation of the first spin contaminant in UHF wave function

We present a number of molecular systems for which the average values 〈?²〉 before and after annihilation of the first spin contaminant in the wave function of the unrestricted Hartree-Fock method are anomalously large (they substantially exceed the expected value S (S + 1)). An example of such systems is N@C₂₀, for the doublet state of which the 〈?²〉 values are equal to 4.2595 before and 13.1390 after annihilation, respectively (calculated by UHF/6-31G* method). We show that four, at the least, spin multiplets (S′ = S, S + 1, S + 2, S + 3) contribute comparatively to the wave function of such systems. The relations are derived allowing one to estimate the contributions of the highest multiplets basing on the average values of 〈?²〉 before and after annihilation of the first spin contaminant.     

Integral invariants for high-symmetry open-shell molecules

A method for calculating the energies of electronic states arising from a degenerate open shellγ ^N in terms of integral invariants H^k(γ,γ) is presented. The calculation proceeds from expansions for the electron repulsion integrals 〈mm/nn〉 on degenerate orbitals ofγ symmetry in terms of H^k(γ,γ). The energies of states for theγ ^N electronic configurations with dimγ≤3 (e^N and t^N configurations) are tabulated. Institute of Catalysis, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 2, pp. 183–195, March–April, 1998. This work was supported by RFFR grants No. 96-03-01167 and 96-03-34035.     

Spectrum of states in icosahedral structures of the electronic configuration gn (N = 1–7). 1. Invariant expansion for integrals and energies

The energy spectrum of the states that appear in structures of icosahedral (I,I_h symmetry with open electronic shells g^N (dim g = 4; N = 1–7) is reported. The energies are obtained in terms of integral invariants (reduced matrix elements of electron-electron interaction) H^k (g, g). The latter are analogs of the Slater-Condon parameters F^k(l,l) for atoms with the l^N electronic configuration. A similar representation is proposed for the integrals mm’≨’) of electron-electron interaction on the 4-fold degenerate g orbitals in the “standard” representation. The relation between the terms of the g^N(I,I_h) configuration and the parent states of the orthogonal group O⁺(4) is discussed. Translated fromZhurnal Strukturnoi Khimii, Vol. 38, No. 1, pp. 3–13, January–February, 1997.