The validity of the Hartree–Fock (HF) approximation in bis(π-pentadienyl)dinickel (1) and in cyclopentadienyl-allyl-cyclobutadiene-dinickel (2) has been investigated by means of the Thouless instability conditions in the computational framework of a variable model Hamiltonian. Singlet, nonsinglet (triplet), and nonreal instabilities in 1 and 2 have been studied as a function of the one-electron resonance integral β and as a function of the one- and two-center elements of the electron–electron interaction. The one-center integrals of Coulomb (γ) and exchange-type (K) have been modified by a multiplicative factor; the two-center integrals (γ) have been calculated by means of an exponential interpolation formula with a variable decay amplitude. Additionally the Thouless conditions have been studied for nuclear deformations. The stability domain of the HF solution in the model space spanned by the variable INDO Hamiltonian has been analyzed. The nature of the many-body interactions in the unstable region depends strongly on the parametrization of the model operator. HF instabilities in the high-density region (long-range forces) of 1 have their origin in individual particle–hole fluctuations while negative roots for short-range forces (low-density region) are similar to collective excitations in many-body systems (strong off-diagonal coupling). The opposite behavior is encountered in the Ni complex 2. The physical origin of these different types of correlation processes are analyzed in a simple two-electron two-orbital model. The nature of the HF fluctuations in 1 and 2, the importance of spatial and spin correlation, and the coupling of symmetry breaking of the electronic wave function with nuclear deformations are compared with the nature of phase transitions in solid-state systems.

Symmetry breaking in the Hartree–Fock approximation for binuclear transition metal compounds—a theoretical investigation based on a variable model operator

The excited states of the π‐electron system of linear polyacenes are studied with the self‐consistent field–random phase approximation (SCF–RPA) scheme. The semiempirical Pariser–Parr–Pople (PPP) model is used. The parametrization is derived by fitting the benzene and it is held fixed throughout the polyacene series. Substantial improvement with respect to Tamm–Dancoff results [J. Chem. Phys. 24, 250 (1956)] for the singlet oscillator strengths is obtained. It is pointed out that the ratio between the experimental oscillator strength of the strong 1B3u transition and the total f‐sum rule strength shows a drastic drop for naphthacene and pentacene. It is argued that this behavior is associated with a deep modification of the π‐electron correlation structure of these two molecules with respect to the smaller ones. The calculated energies are compared with experimental and Tamm–Dancoff values. The assignments of Meyer et al. [J. Chem. Phys. 56, 801 (1972)] for the triplet excited states of naphthalene and an...

Electronic structure of linear polyacenes in the SCF–RPA method

In the framework of the SCF-RPA scheme and ppp approximation we studied the excitation spectrum of pyrene, coronene, ovalene, and hexabenzocoronene. The triplet stability matrix of the corresponding Hartree–Fock solution was also studied for each molecule. At variance with the case of long linear polyacenes [M. Baldo, G. Piccitto, R. Pucci, and P. Tomasello, Phys. Lett. 95A, 201 (1983)], all these molecules do not display Hartree–Fock triplet instability. Furthermore, the theoretical analysis indicates that the electronic structure of the molecular series can be characterized by a dimensionality intermediate between one and two, with a smooth transition between the two limits. The transition is essentially determined by the molecular shape. The analysis is supported by the fairly good agreement of the theoretical spectra with the available experimental data.

Dimensional and geometrical effects on the electronic structure of polycyclic hydrocarbons

In the framework of the PPP Hamiltonian, we have studied the low-lying spectra of all trans linear polyenes with the dielectirc function method. It is shown that higher order processes, not included in the RPA scheme as local field correction (LFC) and self-energy (SE) effects can be introduced in a effective way by a suitable parametrization of the residual coulomb interaction. This parametrization is fixed along the polyene series both for singlet and triplet states, at variance with previous RPA calculations. Comparison with the most refined CI calculations, as well as with the experimental findings shows very good agreement. Furthermore, chain length and geometry dependence of the electron–electron correlation is briefly discussed.

Excited states of linear polyenes in the SCF–RPA method

The many-body perturbation theory is reformulated within the dielectric function method presented in the preceding paper [12]. The self-energy effects are explicitly considered. These corrections turn out to be important and are calculated to the same level of approximation as the corresponding local-field terms. The method is at the moment applicable to π-electron systems within the zero differential overlap approximation. Explicit calculations of the excitation energies for the benzene molecule, using different parametrizations, are presented. Comparison is made with the results obtained in the random phase approximation (RPA) and other schemes.

Antonio Grassi

Papers

Toward a microscopic description of molecular electronic systems