Negative orbit

Mulliken also noted another disturbing tendency in this population anal-ysis. - The gross atomic orbital population could have a value less than zero or greater than 2. A population greater than 2 appears to violate at least the spirit of the Pauli exclusion principle. A negative orbital population is even more difficult to interpret. Mulliken s examples all had very small negative values and were thus discounted as unimportant. However, the atomic population can be very negative—a population of —0.7 e for a sulfur d orbital in SFg... 

The ionization potential of thiophene is 8.87 eV which is, according to Koopman s theorem, equal to the negative orbital energy of (see Fig. 5.2c, p 53). Because of the lower electronegativity of sulfur compared with oxygen, the dipole moment of 0.52 D is even smaller than that of furan. The chemical shifts in the NMR spectrum lie in the typical aromatic regions, as is the case with furan ... 

Pe spectra are usually interpreted in terms of Koopmans approximation which relates the vertical ionization energy / (/) to the negative orbital energy / of the MO / from an SCF procedure. 

Fig. 4 GVB oibitals and overlaps for the N( D) and P( D) states. A red line means that the eleetrons in these singly occupied orbitals are singlet coupled the values of the orbital overlaps are given above the line. Contours are 0.10, 0.15, 0.20 and 0.25. Red contour represents positive, and blue contour represents negative orbital phase...

Here, the columns of the matrix describe the one-electron molecular orbitals (technically the spin orbitals the spatial orbitals described above are combined with an a or a (3 spin function), and the electrons are assigned to N rows. By using a matrix, we have taken care of the requirement highlighted in Section 3.2.1 that the wavefunction we construct must be antisymmetric. This follows since the value of the determinant shown in Eq. 3.5, when written out in full, includes positive and negative orbital contributions of the type shown in Eq. 3.3. Thus, should any electronic configuration attempt to include two electrons with the same spin in the same orbital, the determinant (and therefore the wavefunction) will vanish. 

Guest Orbital Negative orbital energy -e [eV] -Ae [eV] in vacuo in endohedral complex... 

Theoretical calculations of oxidation potentials ox are based on a linear correlation of the first ionization potential Ip to the electrochemical oxidation potential Eox [274]. From a theoretical point of view, the linear correlation of the ionization potentials to oxidation potentials qx is based on Koopmans theorem [275], which states that the negative orbital energy Iihomo of the highest occupied molecular orbital (HOMO) equals the first ionization potential Ip. But this is only valid at H F... 

To summarize, we have found that the IPs and EAs of a closed-shell molecular system may be identified with the negative orbital energies of the canonical orbitals ... 

According to Koopmans theorem, we may identify the negative orbital energies with IPs ... 

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