several attempts at ironing out rough spots, the question still appears partially
unsettled [15, 137, 138].
In particular, a common agreement about the notion of interatomic current has
not been reached and fundamental questions remain unanswered, e.g., are delocalized currents a distinguishing prerogative of planar unsaturated molecules, or
rather the ubiquitous feature [131, 132] of any molecule? To what extent are the
electrons of noncyclic compounds capable of sustaining delocalized flow in the
presence of a magnetic field? Are p- and r-electrons characterized by comparable
mobility? What about a practical intensity measure of the induced currents? Are
ring-shaped molecules carriers of stronger currents compared with noncyclic ones?
Is there an indisputable quantifier of current delocalization?
Delocalized r-electron currents were found in planar saturated molecules.
A paradigmatic example is provided by H 6 , the cyclic arrangement of three juxtaposed hydrogen molecules with D 6h symmetry [141–143], first studied by London
[144]. Noticeably, a delocalized pattern was observed also in ethylene, another
noncyclic system which sustains an annular current (with maximum modulus 0.075
au, for jBj ¼ 1 au) orthogonal to the molecular plane, see Fig. 7.10 and a recent
paper [103]. Delocalization of electron flow takes place on the plane of the hydrogen
nuclei of the CH 3 -group in D 3d or D 3h conformations of ethane in the presence of a
magnetic field parallel to the C 3 symmetry axis, see Figs. 7.15 and 7.17.
The existence of fairly large delocalized electron flow was demonstrated in H 2 O,
BH 3 , NH 3 , CH 4 , CH 3 –CH 3 , H 3 O
+ , CH
þ
3 , and NH
þ
4 , by plots of quantum
mechanical current density and by current susceptibilities, Eq. (7.55), calculated by
accurate ab initio methods [102, 145]. The latter, also referred to as “current
strengths” measured in nano ampère per tesla, are defined via flux integrals evaluated over suitably chosen molecular domains [76]. Simple procedures, allowing
for ideal current models based on the BS law [46], have been applied to predict the
ability of a certain molecule to support magnetic-field induced electron currents
flowing through an interatomic circuit [77, 141–143].
According to the conclusions expounded in a recent paper [145] one can reasonably claim that the delocalized patterns observed in the current density maps
actually prove the existence of “ring currents without a ring”. These results would
seem to lend support to the paradoxical statement made by Musher, “… the
hydrogen atom also… sustains a ring current.” [131]. Since electron currents
flowing over wide portions of a molecular domain are not the exclusive property of
cyclic conjugated systems, rigorous and comprehensive definitions of “delocalized
current’’ seem therefore to be necessary.
In the light of the findings discussed above, a definition of delocalized current was
tentatively proposed [145] as a current flowing along a closed loop containing three
or more atoms. It appears consistent with the IUPAC acceptation of delocalized
charge [126]. Such a definition would seem appropriate for CH
þ
3 and BH 3 , as well as
NH 3 , H 3 O
+ , and NH
þ
4 . However, the intriguing case of H 2 O in a field B parallel to the
C 2 axis shows that only two atoms may be sufficient to give rise to an intense
delocalized current, moving around in a loop of sufficiently large size [145].
218
P. Lazzeretti
unsettled [15, 137, 138].
In particular, a common agreement about the notion of interatomic current has
not been reached and fundamental questions remain unanswered, e.g., are delocalized currents a distinguishing prerogative of planar unsaturated molecules, or
rather the ubiquitous feature [131, 132] of any molecule? To what extent are the
electrons of noncyclic compounds capable of sustaining delocalized flow in the
presence of a magnetic field? Are p- and r-electrons characterized by comparable
mobility? What about a practical intensity measure of the induced currents? Are
ring-shaped molecules carriers of stronger currents compared with noncyclic ones?
Is there an indisputable quantifier of current delocalization?
Delocalized r-electron currents were found in planar saturated molecules.
A paradigmatic example is provided by H 6 , the cyclic arrangement of three juxtaposed hydrogen molecules with D 6h symmetry [141–143], first studied by London
[144]. Noticeably, a delocalized pattern was observed also in ethylene, another
noncyclic system which sustains an annular current (with maximum modulus 0.075
au, for jBj ¼ 1 au) orthogonal to the molecular plane, see Fig. 7.10 and a recent
paper [103]. Delocalization of electron flow takes place on the plane of the hydrogen
nuclei of the CH 3 -group in D 3d or D 3h conformations of ethane in the presence of a
magnetic field parallel to the C 3 symmetry axis, see Figs. 7.15 and 7.17.
The existence of fairly large delocalized electron flow was demonstrated in H 2 O,
BH 3 , NH 3 , CH 4 , CH 3 –CH 3 , H 3 O
+ , CH
þ
3 , and NH
þ
4 , by plots of quantum
mechanical current density and by current susceptibilities, Eq. (7.55), calculated by
accurate ab initio methods [102, 145]. The latter, also referred to as “current
strengths” measured in nano ampère per tesla, are defined via flux integrals evaluated over suitably chosen molecular domains [76]. Simple procedures, allowing
for ideal current models based on the BS law [46], have been applied to predict the
ability of a certain molecule to support magnetic-field induced electron currents
flowing through an interatomic circuit [77, 141–143].
According to the conclusions expounded in a recent paper [145] one can reasonably claim that the delocalized patterns observed in the current density maps
actually prove the existence of “ring currents without a ring”. These results would
seem to lend support to the paradoxical statement made by Musher, “… the
hydrogen atom also… sustains a ring current.” [131]. Since electron currents
flowing over wide portions of a molecular domain are not the exclusive property of
cyclic conjugated systems, rigorous and comprehensive definitions of “delocalized
current’’ seem therefore to be necessary.
In the light of the findings discussed above, a definition of delocalized current was
tentatively proposed [145] as a current flowing along a closed loop containing three
or more atoms. It appears consistent with the IUPAC acceptation of delocalized
charge [126]. Such a definition would seem appropriate for CH
þ
3 and BH 3 , as well as
NH 3 , H 3 O
+ , and NH
þ
4 . However, the intriguing case of H 2 O in a field B parallel to the
C 2 axis shows that only two atoms may be sufficient to give rise to an intense
delocalized current, moving around in a loop of sufficiently large size [145].
218
P. Lazzeretti