Electron-correlated level calculations

The calculations at the electron correlation level do not reveal the unpaired spin in the Cu02 planes indicating the formation of the singlet spin state. This supports the surmise [54] that due to a strong Cu-O hybridization, all spins in the Cu02 planes are coupled (the, so-called, Zhang-Rice singlet). 

This question has been probed by much higher levels of calculation recently and it appears that the previous lower-level work was largely correct. More precisely, the bottom of the proton transfer potential appears to be only very slightly asymmetric if at all the barrier, if it exists, is less than 0.5 kcal/mol. As in the (HOH OH) anion, the character of the potential alternates from single to double well upon small changes in level of theory, the former being favored by electron correlation. The calculations, employing CCSD(T) treat-... 

A further problem of N chemical shift calculations is the influence of electron correlation. In calculations on the Hartree-Fock level the error is typically 20 ppm for isotropic nitrogen values. The observed range of backbone nitrogen chemical shifts is also about 20 ppm, hence only calculations on the MP2 level or better are suitable for structure elucidation or it must be assumed that the correlation effects are constant within the pool of studied structures. 

Our analysis is based on accurate calculations performed in Ref. [22] at the Moller-Plesset electron correlation level of the interaction energy and its many-body decomposition for Be , Mgn, and Ca (n= 2 and 3) clusters using a reasonably large basis set [6-311 + G (3df)]. All calculations were also carried out at the SCF level which allowed to study separately the SCF and electron correlation contributions and give a physical analysis of each term in the dimer and trimer energy decompositions. 

It is instructive to study the vacant atomic orbital population in dimers and trimers. As mentioned in the Introduction, in the 80 s Bauschlicher et al. [10,11] came to the conclusion that the promotion of ns-electrons to np-orbitals leading to sp-hybridization is the main mechanism responsible for binding in alkaline-earth clusters. This conclusion was based on a study of the SCF Mulliken population analysis for tetramers, which are stable at the SCF level. At present, we can perform more precise analysis using the Natural Bond Orbital Analysis and calculate it at the electron correlation level. 

It is important to check is the effect of a rather large population of vacant atomic orbitals at the electron correlation level specific for alkaline-earth atoms or it has a general character. In Table VII we present the results of net valence population calculations for noble-gas atoms performed by the Natural Bond Orbital Analysis at the MP4 level. We found non-negligible valence orbital population, especially for the d-orbitals. The results obtained for three different basis sets are quite close. Thus, the population of vacant orbitals in noble-gas atoms is not an artifact of the calculations. From this follows that elements traditionally assumed as closed-shell (noble gases) or closed-subshell (alkaline earths) atoms can to some extent manifest an anisotropic p-or d-symmetry behavior. It would be very interesting to obtain experimental evidence confirming this theoretical prediction. 

The density functional techniques that have been developed and significantly improved in the last decade have beeome a very tempting alternative to cluster-model calculations. They enable calculations to be performed at an electron-correlated level at a cost similar to that of the standard Hartree-Fock method. Some very recent studies performed in our laboratory by the application of DFT techniques to the calculation of the water-metal " and the ion-metal " " " interactions are summarized in Section 3.10.3. 

The PES of tetrasilacyclobutadiene, 144, the full silicon analogue of cyclobutadiene, was studied extensively using relatively high levels of theory which include the contributions of polarization functions and of electron correlation The calculations revealed a very complex Si4H4 PES. 

An ab initio MO calculation at electron correlated levels has been carried out on C3H3L1. A singlet cyclic structure (C ) was calculated as the most stable." ... 

Many potential energy surfaces have been proposed for the F + FI2 reaction. It is one of the first reactions for which a surface was generated by a high-level ab initio calculation including electron correlation [47]. The... 

Calculated transition structures may be very sensitive Lo the level of theory employed. Semi-empirical methods, since they are parametrized for energy miriimnm structures, may be less appropriate for transition state searching than ab initio methods are. Transition structures are norm ally characterized by weak partial" bonds, that is, being broken or formed. In these cases UHF calculations arc necessary, and sometimes even the inclusion of electron correlation effects. 

In addition to the mixed results in Table 10-1, the G2 calculation for H2 produces an energy that is lower than the experimental value, in contradiction to the rule that variational procedures reach a least upper bound on the energy. Some new factors are at work, and we must look into the stmcture of the G2 procedure in temis of high-level Gaussian basis sets and electron correlation. 

In the CI method, one usually attempts to realize a high-level treatment of electron correlation. A set of orthonormal molecular orbitals are first obtained from an SCF or MCSCF calculation (usually involving a small to moderate list of CSFs). The FCAO-MO... 

Cl calculations can be used to improve the quality of the wave-function and state energies. Self-consistent field (SCF) level calculations are based on the one-electron model, wherein each electron moves in the average field created by the other n-1 electrons in the molecule. Actually, electrons interact instantaneously and therefore have a natural tendency to avoid each other beyond the requirements of the Exclusion Principle. This correlation results in a lower average interelectronic repulsion and thus a lower state energy. The difference between electronic energies calculated at the SCF level versus the exact nonrelativistic energies is the correlation energy. 

The numerical value of hardness obtained by MNDO-level calculations correlates with the stability of aromatic compounds. The correlation can be extended to a wider range of compounds, including heterocyclic compounds, when hardness is determined experimentally on the basis of molar reffactivity. The relatively large HOMO-LUMO gap also indicates the absence of relatively high-energy, reactive electrons, in agreement with the reduced reactivity of aromatic compounds toward electrophilic reagents. 

Azulene does have an appreciable dipole moment (0.8 The essentially single-bond nature of the shared bond indicates, however, that the conjugation is principally around the periphery of the molecule. Several MO calculations have been applied to azulene. At the MNDO and STO-3G levels, structures with considerable bond alternation are found as the minimum-energy structures. Calculations which include electron correlation effects give a delocalized n system as the minimum-energy structure. ... 

Unlike reactive diatomic chalcogen-nitrogen species NE (E = S, Se) (Section 5.2.1), the prototypical chalcogenonitrosyls HNE (E = S, Se) have not been characterized spectroscopically, although HNS has been trapped as a bridging ligand in the complex (HNS)Fc2(CO)6 (Section 7.4). Ab initio molecular orbital calculations at the self-consistent field level, with inclusion of electron correlation, reveal that HNS is ca. 23 kcal mof more stable than the isomer NSH. There is no low-lying barrier that would allow thermal isomerization of HNS to occur in preference to dissociation into H -1- NS. The most common form of HNS is the cyclic tetramer (HNS)4 (Section 6.2.1). 

The parameterization of MNDO/AM1/PM3 is performed by adjusting the constants involved in the different methods so that the results of HF calculations fit experimental data as closely as possible. This is in a sense wrong. We know that the HF method cannot give the correct result, even in the limit of an infinite basis set and without approximations. The HF results lack electron correlation, as will be discussed in Chapter 4, but the experimental data of course include such effects. This may be viewed as an advantage, the electron correlation effects are implicitly taken into account in the parameterization, and we need not perform complicated calculations to improve deficiencies in fhe HF procedure. However, it becomes problematic when the HF wave function cannot describe the system even qualitatively correctly, as for example with biradicals and excited states. Additional flexibility can be introduced in the trial wave function by adding more Slater determinants, for example by means of a Cl procedure (see Chapter 4 for details). But electron cori elation is then taken into account twice, once in the parameterization at the HF level, and once explicitly by the Cl calculation. 

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