Orbital bias

The electrons are divided into pairs, and each pair is given two orbitals. In the VB method, the inner-shell orbitals i and 4 are each assumed to be 1 AOs on carbon, the bonding orbital bia is assumed to be an 5p -hybridized carbon AO pointing toward Hi, and bu, is assumed to be a Is AO on hydrogen number 1. In the GVB method, no assumptions are made about the nature of the orbitals. One simply expands each of them in terms of the chosen basis set and solves the GVB equations until self-consistency is attained. 

The schematic model is depicted in Fig. 8. As the bias voltage increases, the number of the molecular orbitals available for conduction also increases (Fig. 8) and it results in the step-wise increase in the current. It was also found that the conductance peak plotted vs. the bias voltage decreases and broadens with increasing temperature to ca. 1 K. This fact supports the idea that transport of carriers from one electrode to another can take place through one molecular orbital delocalising over whole length of the CNT, or at least the distance between two electrodes (140 nm). In other words, individual CNTs work as coherent quantum wires. 

Fig. 8. Schematic illustration of the tunnelling in a CNT-based device (a) under no bias voltage, there are no orbitals available for conduction, (b) with small bias voltage, only one molecular orbital of a CNT contributes to the carrier transport and (c) when the next molecular orbital enters the bias window, current increases stepwise. Gate voltage can shift all the orbitals upward or downward. AE indicates the energy separation of molecular orbitals.

NXHOMO of the hydroxy-substituted dihydroanthracene is also symmetric in sign. Therefore, the antisymmetric orbital does not interact significantly with these vacant n orbitals of 36, resulting in an unperturbed n face of the carbonyl it orbital. This motif is regarded as an example of orbital non-interaction [105], Thus, the reduction of 2-methoxy and 3-methoxydibenzobicyclo[2.2.2]octadienones (34c and 34f) should intrinsically show little or no bias. 

The dibenzobicyclo[2.2.2]octatriene system (71) essentially involves interaction of three composite n orbitals, i.e., the olefinic n orbital as the reaction center, and two aromatic k orbitals. A simplified interaction network, i.e., two n component systems free from steric bias, is intriguing. In this context the facial selectivities of... 

Although there have been many experimental and theoretical studies on the behavior of facially perturbed dienes (see below), only a few systematic experiments have been carried out to characterize facially perturbed dienophiles. Dienophiles embedded in the norbomane or norbomene motif have been rather intensively studied [146-150]. In most cases, steric effect controls selectivity, but in some cases the reactions are considered to be free from steric bias, and the selectivity has been explained in terms of other factors, such as orbital effects [151, 152]. 

In this paper a method [11], which allows for an a priori BSSE removal at the SCF level, is for the first time applied to interaction densities studies. This computational protocol which has been called SCF-MI (Self-Consistent Field for Molecular Interactions) to highlight its relationship to the standard Roothaan equations and its special usefulness in the evaluation of molecular interactions, has recently been successfully used [11-13] for evaluating Eint in a number of intermolecular complexes. Comparison of standard SCF interaction densities with those obtained from the SCF-MI approach should shed light on the effects of BSSE removal. Such effects may then be compared with those deriving from the introduction of Coulomb correlation corrections. To this aim, we adopt a variational perturbative valence bond (VB) approach that uses orbitals derived from the SCF-MI step and thus maintains a BSSE-free picture. Finally, no bias should be introduced in our study by the particular approach chosen to analyze the observed charge density rearrangements. Therefore, not a model but a theory which is firmly rooted in Quantum Mechanics, applied directly to the electron density p and giving quantitative answers, is to be adopted. Bader s Quantum Theory of Atoms in Molecules (QTAM) [14, 15] meets nicely all these requirements. Such a theory has also been recently applied to molecular crystals as a valid tool to rationalize and quantitatively detect crystal field effects on the molecular densities [16-18]. 

Furthermore, it was shown the unpaired spin S = 1/2, which is delocalized over the two Pc rings, still remained in the Jt-orbitals after absorption on Au(lll). Consequently, STS measurements also provided direct observation ofthe S = 1/2 radical on the TbPc2 molecules on Au(lll) whereby the indicative Kondo-peak could be switched off by tunnelling current pulses [215]. Indeed the tunnelling conductance (dl/dV) was analysed from STS experiments of TbPc2 on Au(lll) near the Fermi level showed a zero-bias peak (ZBP) in the spectra, which could be assigned as a Kondo resonance. Clear Kondo features for the molecules with 9 = 45° were observed when the tip was positioned over one ofthe lobes of TbPc2. 

Under +1 V of forward bias (Fig. lid), there is no pathway for current flow. At +2 V, however, the orbitals have adjusted to give a downhill path from MA to acceptor to donor to MD, and Aviram-Ratner current flows. On the reverse bias side, however, two pathways exist for current flow at —1 V (Fig. 1 lb) as well as —2 V (Fig. 11a). These pathways (Fig. 11a, b) are asymmetric rectification via HOMO and via LUMO, and they are in the anti-Aviram-Ratner direction, i.e., from donor to acceptor. This could allow for anti-Aviram-Ratner rectification under moderate biases. Note, however, that the electrons in Fig. 11a, b must tunnel over longer distances than those in Fig. lie, because there is only one way-station, instead of two. The Aviram-Ratner current flow under the higher bias of Fig. lie could therefore be much more intense than the reverse flow of Fig. 1 lb or 1 la. 

Elastic tunneling spectroscopy is discussed in the context of processes involving molecular ionization and electron affinity states, a technique we call orbital mediated tunneling spectroscopy, or OMTS. OMTS can be applied readily to M-I-A-M and M-I-A-I -M systems, but application to M-A-M junctions is problematic. Spectra can be obtained from single molecules. Ionization state results correlate well with UPS spectra obtained from the same systems in the same environment. Both ionization and affinity levels measured by OMTS can usually be correlated with one electron oxidation and reduction potentials for the molecular species in solution. OMTS can be identified by peaks in dl/dV vs bias voltage plots that do not occur at the same position in either bias polarity. Because of the intrinsic... 

Fig. 3 Energy diagram for an M-A-M diode showing elastic and inelastic tunneling processes (top). The HOMO (n) and LUMO (71 ) orbital energies and a few vibrational levels are indicated. Applied bias energy (eV) is just sufficient to allow inelastic tunneling with excitation of the first vibrational level, eV = hv. Also shown (bottom) are the I(V) curve, conductance- / curve, and the IETS spectrum that would result from both elastic processes and the first inelastic channel. (Reproduced by permission of the American Chemical Society from [19])...

When the sample is biased positively (Ub > 0) with respect to the tip, as in Fig. 9c, and assuming that the molecular potential is essentially that of the substrate [85], only the normal elastic current flows at low bias (<1.5 V). As the bias increases, electrons at the Fermi surface of the tip approach, and eventually surpass, the absolute energy of an unoccupied molecular orbital (the LUMO at +1.78 V in Fig. 9c). OMT through the LUMO at — 1.78 V below the vacuum level produces a peak in dl/dV, seen in the actual STM based OMTS data for nickel(II) octaethyl-porphyrin (NiOEP). If the bias is increased further, higher unoccupied orbitals produce additional peaks in the OMTS. Thus, the positive sample bias portion of the OMTS is associated with electron affinity levels (transient reductions). In reverse (opposite) bias, as in Fig. 9b, the LUMO never comes into resonance with the Fermi energy, and no peak due to unoccupied orbitals is seen. However, occupied orbitals are probed in reverse bias. In the NiOEP case, the HOMO at... 

Fig. 9 OMT bands for NiOEP, associated with transient reduction (1.78 V) and transient oxidation (—1.18 V). Data obtained from a single molecule in a UHV STM. The ultraviolet photoelectron spectrum is also shown, with the energy origin shifted (by the work function of the sample, as discussed in [25]) in order to allow direct comparison. The highest occupied molecular orbital, n, and the lowest unoccupied molecular orbital, %, are shown at their correct energy, relative to the Fermi level of the substrate. As in previous diagrams,

P + 1.18 V below the vacuum level produces a peak in dl/dV at —1.18 V sample bias. It is also clear from Fig. 9 that there are other occupied MOs, with one near + 1.70 V giving a well-defined shoulder. Note that peaks are observed in dl/dV (and not /). This is because, once current starts to flow through orbital-mediated channels, increasing the bias doesn t turn it off. On the other hand, the probability... 

In contrast, the NBO and NRT methods make no use of molecular geometry information (experimental or theoretical), but instead provide optimal descriptions of orbital composition or electron-density distributions based directly on the first-order density operator. For this reason the NBO/NRT indices have predictive utility for a broad range of chemical phenomena, without bias toward geometry or other particular empirical properties. 

The characteristics of s/p-orbital chemistry are associated, above all, with the atoms H, C, N, and O that dominate organic and biochemical phenomena. Hence, the discussion of bonding in s/p-block elements inevitably carries a bias toward organic chemistry, and toward the issues and controversies that continue to animate this most mature and advanced area of chemistry. Indeed, organic chemistry may be considered the cradle of covalency, where many principles of chemical bonding were first grasped and exploited. 

An important result, found for the SDTQ[N/N] wavefiinctions of all molecules considered, is that the split-localized molecular orbitals yield a considerably faster convergence for truncated expansions than the natural orbitals. For example, for NCCN SDTQ[18/18], millihartree accuracy is achieved by about 50,000 determinants of the ordering based on split-localized orbitals whereas about 150,000 determinants are needed for the natural-orbital-based ordering. This observation calls for the revision of a widely held bias in favor of natural orbitals. 

---