N-Electron rotation

Laser-Induced n-Electron Rotation in Aromatic Ring Molecules... 

When a circularly polarized laser pulse is applied to Mg porphyrin, the spin angular momentum of a photon selects Eu+) or -), and n electrons start to rotate in the clockwise or counterclockwise direction. In other words, a linearly polarized laser pulse, which has no spin angular momentum, cannot induce n-electron rotations in Mg porphyrin. In general, a linearly polarized pulse cannot rotate n electrons in an aromatic ring molecule with degenerate excited states. 

In the following, we take a chiral aromatic molecule as a target system to study laser-induced n-electron rotation, although chirality is not necessary to break the degeneracy of the relevant excited states. Ring current and nonadiabatically coupled molecular vibration in chiral aromatic molecules have interesting potential applications as will be shown in Sect. 6.4. 

Control of n-Electron Rotation in a Chiral Aromatic Molecule Within a Frozen-Nuclei Approximation... 

For quantitative evaluation of n-electron rotation in DCPH, we calculate the angular momentum expectation value L (t) = In n circular... 

Fig. 6.3 (a) Pump and dump pulses for clockwise n-electron rotation in an R enantiomer of DCPH. The polarization vectors of the pump and dump pulses are e+ and e, respectively, (b) Temporal behavior in the populations of G) (thick solid line), - -) (thin solid line), and —) (thin dotted line) denoted as Pg(0> P+ (0. andP (t), respectively, (c) Expectation value of angular momentum L (f). (d) Expectation value of rotational angle (t) (Reprinted from Ref. [15]. Copyright (2006) by John Wiley and Sons)... 

In the previous section, we treated rr-electron rotation within a frozen-nuclei approximation. However, the effects of nonadiabatic coupling should not be ignored when the duration of n-electron rotations becomes close to the period of molecular vibrations. Therefore, in this section, we explicitly take into account vibrational degrees of freedom and perform nuclear WP simulations in a model chiral aromatic molecule irradiated by a linearly polarized laser pulse. The potentials of the vibrational modes were determined by ab initio MO methods [12]. For reducing computational time, while maintaining properties of jt-electronic structures, we used 2,5-dichloropyrazine (DCP, Fig. 6.4) instead of 2,5-dichloro[n](3,6)pyrazinophane (DCPH), in which the ansa group is replaced by hydrogen atoms. 

In Fig. 6.5a, the initial direction of K-electron rotation depends on the photon polarization vector, that is, clockwise (counterclockwise) direction for e+ (e ) excitation, which has been described in Sect. 6.3. However, the amplitudes of mt) temporally vary for both cases, due to the decrease of the overlap between the nuclear WPs moving on the relevant two adiabatic PESs as depicted later in Fig. 6.6. This is one of the characteristic behaviors that are absent in a frozen-nuclei model. As for nuclear motions, DCP vibrates during n-electron rotation as seen in Fig. 6.5b, but the behavior of Q(f) differs only slightly between e+ and e excitations. 

Finally, let us consider molecules with identical nuclei that are subject to C (n > 2) rotations. For C2v molecules in which the C2 rotation exchanges two nuclei of half-integer spin, the nuclear statistical weights of the symmetric and antisymmetric rotational levels will be one and three, respectively. For molecules where C2 exchanges two spinless nuclei, one-half of the rotational levels (odd or even J values, depending on the vibrational and electronic states)... 

The progression of sections leads the reader from the principles of quantum mechanics and several model problems which illustrate these principles and relate to chemical phenomena, through atomic and molecular orbitals, N-electron configurations, states, and term symbols, vibrational and rotational energy levels, photon-induced transitions among various levels, and eventually to computational techniques for treating chemical bonding and reactivity. 

In this case the excited molecules produced on interaction with radiation undergo spin reversal to yield a triplet state with a much longer lifetime than that of the singlet excited state. One or more jt-bonds are broken in the triplet state since one of the n-electrons affected is in an antibonding n molecular orbital. This means that the o-bond is free to rotate and cis and trans isomers can be formed next to each other on recombination of the double bond. 

Bohr, N., Ibid., 26, 1913, (1, 476, 857). On p. 862 Bohr discusses the hypothesis that atoms may be held in combination by electrons rotating about the line j oining the positive nuclei of two atoms. This is similar to Ramsay s view mentioned below. 

Fig. 14 The experimental geometries of benzene- -HC1 and benzene- -ClF (to scale) and the n-electron model of benzene. See text for discussion of the motion of the C1F subunit, as inferred from an analysis of the rotational spectrum of benzene- -ClF. See Fig. 1 for key to the colour coding of atoms... 

It is also worthwhile to compare the ferrocenyl ethylene (vinylferrocene) anion-and cation-radicals. For the cyano vinylferrocene anion-radical, the strong delocalization of an unpaired electron was observed (see Section 1.2.2). This is accompanied with effective cis trans conversion (the barrier of rotation around the -C=C- bond is lowered). As for the cation-radicals of the vinylferrocene series, a single electron remains in the highest MO formerly occupied by two electrons. According to photoelectron spectroscopy and quantum mechanical calculations, the HOMO is mostly or even exclusively the orbital of iron (Todres et al. 1992). This orbital is formed without the participation of the ethylenic fragment. The situation is quite different from arylethylene radical cations in which all n orbitals overlap. After one-electron oxidation of ferrocenyl ethylene, an unpaired electron and a positive charge are centered on iron. The —C=C— bond does not share the n-electron cloud with the Fe center. As a result, no cis trans conversion occurs (Todres 2001). 

So far we have based the formalism on an N-electron basis built from Slater determinants. However, as shown above, both the Hamiltonian and the orbital rotations can be described in terms of the orbital excitation operators Ey. All... 

The stabilization of the vinyl cation by the a-cyclopropyl group was calculated to be significantly less than that by the phenyl group. The theoretical rotational barrier of the a-cyclopropylvinyl cation is less than that of the cyclopropylethyl cation, presumably due to the stabilization of the intermediate perpendicular conformation by the overlap of the ff-bonds with the n-electrons of the C=C bond72. 

If definite stoichiometry is maintained in the exciplex formation, an isoemissive point similar to isosbestic point in absorption may be observed. An interesting example of intra-molecular exciplex formation has been reported foi 9-methoxy-10-phenanthrenecarboxanil. The aniline group is not necessarily coplanar with the phenanthrene moiety but is oriented perpendicular to it. The n-electron located on its N-atom interacts with the excited -electron system and an intramolecular exciplex with T-bone type structure is formed in rigid glassy medium where rotation is restricted. Temperature dependence of fluorescence of this compound in methylcyclohexane-isopentane (3 1) solvent shows a definite isoemissive point (Figure 6.8). As the solvent melts and movement is restored to the molecule, structured fluorescence reappears. 

Pack, R. T. and Hirschfelder, J. O. Separation of rotational coordinates from the N-electron diatomic Schrodinger equation, J.Chem.Phys., 49 (1968) 4009-4020,... 

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