The localized and the canonical variants of the many-body perturbation theory are used to calculate the energy corrections through fourth order for C14H14 in Pariser--Parr--Pople approximation, for a wide range of the coupling constant/]. The behaviour of the iocalization terms is examined. It is shown how the nonlocal cont¡ to the correlation energy can be gradually separated. The strictly local contribution left behind is surprisingly large: more than 50% of the total correlation energy. IntrodnctionAs is well known the wavefunctions determined by the Hartree---Fock (HF) method are not suitable to calculate acr values for the energy quantities of the valence shell (elr affinities, ionization and binding energies, etc.). In the last two decades various procedures have been developed which go beyond the independent particle seheme. One of the most straightforward approaches for taking into ar correlation effects is the diagrammatic many-body perturbation theory [1--3]. Ir can be used routinely for small molecules through third order in the energy (including some fourth order temas) [4 6]. Recently, with moderately sized basis sets the evaluation of ail fourth order temas has become feasible [7,8]. Except for some model systems, the calculation of all temas o f a given order lª than the fourth is out of question at present. There exist procedures, however, in which certain types of terms ate summed over to infinite order (CPMET [9,10], CEPA [11,12], and the method of Green's functions [13,14]).Previously it was conjectured that local and nonlocal r can be clr separated and that the former predominate [15]. One.of the authors of the present article (E.K.) developed a perturbation theory whose zeroeth order wavefunction is the APSG ground state [16]

Recent experimental and theoretical studies reporting remarkable monobridged structures for Si2H2, A12H2, and Ga2H2 have motivated us to re-investigate the singlet potential energy surface of Ge2H2 using the self-consistentfield (SCF), single and double excitation configuration interaction (CISD), and single and double excitation coupled cluster (CCSD) methods in conjunction with a double-£ plus polarization basis set (DZP). In addition to the dibridged (or butterfly) ground state and the low-lying vinylidene-like minimum reported earlier by Grev and DeLeeuw, our study predicts the existence of a monobridged isomer, which is characterized as a minimum by means of harmonic vibrational frequency analyses. Relative energies of the above structures were also predicted with use of the coupled cluster single, double, and (perturbative) triple excitation method (CCSD(T)), which employed a triple-£ plus polarization basis set augmented with a set of f functions on the germanium atoms (TZP+f). Final energetic predictions suggest that the monobridged structure is the second most stable isomer of Ge2H2, lying 8.9 kcal mol-1 above the butterfly ground state and 2.1 kcal mol-1 below the branched (vinylidene-like) minimum.

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Diagrammatic formulation of the MBPT is applied when the occupied and the virtual canonical orbitals are separately localized by unitary transformations. In this localized representation, due to the off‐diagonal Fock matrix elements, the perturbation operator contains extra terms generating the so‐called localization corrections. These corrections enter the perturbation energy in third and higher orders. Their magnitude depends on the type of localization, but they represent only a small fraction of the canonical corrections. The calculation of the localization corrections, however, does not need a significant amount of extra computer time. It is shown that by introducing an “order of neighborhood” local and nonlocal effects of the electron correlation can be separated and the contribution of the nonlocal effects can be neglected to a good approximation. Ab initio calculations have been carried out for the normal saturated hydrocarbons: C2n+1H4n+4 and for the all‐trans conjugated polyenes C2n+2H2n+4. As to the ratio of the local and nonlocal corrections, it is shown that there is only a quantitative difference for these two kinds of systems (strongly or weakly localizable). Neglecting nonlocal effects, considerable amount of computer time can be saved.

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