One-electron property

It is usual to consider the following factors in discussions of one-electron properties ... 

Density Matrices One-electron density matrices of initial and final states should be related to the orbitals used to mterpret electron binding energies. Their eigenvalues should lie between zero and unity and their traces should equal the number of electrons in each state. One-electron properties should be size-extensive. 

Details of the extended triple zeta basis set used can be found in previous papers [7,8]. It contains 86 cartesian Gaussian functions with several d- and f-type polarisation functions and s,p diffuse functions. All cartesian components of the d- and f-type polarization functions were used. Cl wave functions were obtained with the MELDF suite of programs [9]. Second order perturbation theory was employed to select the most energetically double excitations, since these are typically too numerous to otherwise handle. All single excitations, which are known to be important for describing certain one-electron properties, were automatically included. Excitations were permitted among all electrons and the full range of virtuals. 

Potential energy curve one-electron properties spectroscopic constants... 

Table 1. Calculated and measured one-electron properties of the PN X + state...

Potential energy curvesfor the K U.and Astates. Selected one-electron properties. Spectroscopic constants... 

Table 5. Calculated one-electron properties of the PN A FI state at the experimental...

Quantitative similarities of molecules can easily be recognized if it is possible to define quantities for molecular parts which are additive as well as transferable. Such quantities can be derived from transferable molecular orbitals because any one-electron property, such as dipole moment, quadrupole moment, kinetic energy, is a sum of the corresponding contributions from all molecular orbitals in a system, if such orbitals are chosen mutually orthogonal. Thus, for each transferable orthogonal molecular orbital there exists, e.g., a transferable orbital dipole moment. Since chemists appreciate additive decompositions of... 

Ab initio one-electron property calculations. II Molecular oxetane, cyclobutanone, and thietane. °... 

Although 1 is one of the best investigated molecules, there is, apart from data concerning its electron density distribution, very little information available on its one-electron properties. In principle, accurate data could be obtained by correlation-corrected ab initio methods, but almost nothing has been done in this direction, which of course has to do with the fact that experimental data on one-electron properties of 1 are also rare, and therefore, it is difficult to assess the accuracy and usefulness of calculated one-electron properties such as higher multipole moments, electric field gradients, etc. 

The one-electron properties such as the deuteron quadrupole coupling constant have been less studied until recently, but Dixon et al33 have recently reported the results for this property and also values of the diamagnetic shielding and susceptibility computed with a medium-size basis set. Moderate agreement with experiment was obtained. 

A second paper117 computed localized orbitals, one-electron properties, and detailed populations and gave a detailed discussion of the bonding in this species and in hydroxylamine. 

The remaining error in the dipole moment Green8 attributes to lack of highly excited configurations. For open-shell molecules it is probable that Hartree-Fock results will be unreliable (see above) and a limited amount of Cl will be essential. Thus even for a Hartree-Fock function the calculated one-electron properties may not agree well with experiment (it should be remembered that, in the most favourable cases where the substance can be studied in a molecular-beam spectrometer and the dipole moment obtained from Stark effect measurements, the experimental error is much less than 0.001 D).28... 

For any variational wavefunction which is not near the Hartree-Fock limit the Brillouin theorem is irrelevant, and even for those of Hartree-Fock accuracy low-lying important excited states may invalidate the conclusions drawn from it. The statement that values of one-electron properties are expected to be good because of the Brillouin theorem should therefore be regarded with caution. 

To summarize the discussion in this section, it is fair to state that the Hartree-Fock approximation is adequate in many cases and that the importance of correlation effects is sometimes overestimated. It appears that the basis set effects may be larger than the correlation effects and that the errors in theoretical heats of formation may be mainly due to the limited basis set used30,31. Very instructive discussions on this problem were reported for the inversion barrier in ammonia6,20,32 and the barrier to rotation20 in H2O2. Finally, it should be noted that the Hartree-Fock approximation is also justifiable for the one-electron properties because the latter do not depend explicitly on relative positions of electrons (electron correlation), but rather on the overall distribution of electronic charge. 

T. Korona, B. Jeziorski, One-electron properties and electrostatic interaction energies from the expectation value expression and wave function of singles and doubles coupled cluster theory. 

DFT calculation starts from an assumed value of E p. The socalled Kohn-Sham orbitals tpi are expanded in a reasonably selected truncated set of Gaussian functions representing atomic orbitals [58]. After iteration between pir) and e to self-consistency the final values of the parameters are used to calculate E0 and other one-electron properties. 

In addition to the energies, the values predicted by these SCF calculations for a number of the one-electron properties of the water molecule are also compared by Kern and Karplus.6 As anticipated, the values predicted for these properties by the near Hartree-Fock functions are in good agreement with the experimental values. The molecular dipole moment, for example is calculated to be 2.054 D by the best STO set compared with an experimental value of 1.884 D.57 (Hartree-Fock estimates of molecular dipole moments are generally too large by ca. 0.2 D.)... 

The recent developments in generalized Valence Bond (GVB) theory have been reviewed by Goddard and co-workers,13 and also the use of natural orbitals in theoretical chemistry,14 15 and the accuracy of computed one-electron properties.18 The Xa method has been reviewed by Johnson,17 and Hurley has discussed high-accuracy calculations on small molecules.18 Several other reviews of interest have appeared in Advances in Quantum Chemistry.17 Localized orbital theory has been reviewed by England, Salmon, and Ruedenberg,19 and the bonding in transition-metal complexes discussed by Brown et a/.20 Finally, the recent developments in computational quantum chemistry have been reviewed by Hall.21... 

This work was carried out in order to be used for calculations of electron-impact cross-sections, and P.E. curves and some one-electron properties were calculated. 

Goddard, and compare with the experimental values of 4.9064 and 4.494 bohr for AlH+ and B1 . The calculated values of De, one-electron properties, and transition moments were in reasonable agreement with experimental values where these were known. 

More accurate calculations by Lie et a/.166 have also been reported, with bigger basis sets and more configurations. A variety of Cl calculations were compared, and the X2U and C2S+ states were also considered. 4147 Configurations were included in the most extensive calculation. Results in essentially quantitative agreement with experiment were obtained, but it should be noted that only the most extended Cl predicts, correctly, the bound B21r state, whereas the less extensive Cl calculations did not predict this. A further paper167 dealt with one-electron properties. Table 3... 

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