Theor Chem Acc (2015) 134:147
1 3
single- and double-bond lengths [ 48 ]. For a π-conjugation
path containing N carbon–carbon bonds, it reads
where l i is the length of bond i . For an aromatic structure,
BLA > 0, and for quinonoid ones, BLA < 0 starting with a
short bond along the conjugation path. Signifi cant changes
in BLA due to oxidation or reduction indicate signifi cant
(4)
BLA =
1
N − 1
N−1
j=1
l j+1 − l j
(−1)
j
electronic structure changes. We note that due to a relatively large exact exchange contribution in the M05-2X
functional, the computed BLA values are expected to be
somewhat overestimated [ 49 ].
Considering a CT of adding electrons to the lowest
unoccupied molecular orbital, LUMO, or removing them
from the highest occupied molecular orbital, HOMO, two
major effects should be considered. The orbital effect can
lead to both positive and negative strain depending on the
bonding or antibonding nature of the frontier orbital in
Fig. 4 a Top and b side view of 1b with the numbering of the carbons of the inner part. Hydrogens were omitted for clarity. Carbons are in yellow , and oxygens in red
Fig. 5 a Top and b side view of 2b with the numbering of the carbons of the inner part. Hydrogens were omitted for clarity. The green bonds are
shorter than the yellow ones , indicating a bond length alternation pattern
50
Reprinted from the journal
1 3
single- and double-bond lengths [ 48 ]. For a π-conjugation
path containing N carbon–carbon bonds, it reads
where l i is the length of bond i . For an aromatic structure,
BLA > 0, and for quinonoid ones, BLA < 0 starting with a
short bond along the conjugation path. Signifi cant changes
in BLA due to oxidation or reduction indicate signifi cant
(4)
BLA =
1
N − 1
N−1
j=1
l j+1 − l j
(−1)
j
electronic structure changes. We note that due to a relatively large exact exchange contribution in the M05-2X
functional, the computed BLA values are expected to be
somewhat overestimated [ 49 ].
Considering a CT of adding electrons to the lowest
unoccupied molecular orbital, LUMO, or removing them
from the highest occupied molecular orbital, HOMO, two
major effects should be considered. The orbital effect can
lead to both positive and negative strain depending on the
bonding or antibonding nature of the frontier orbital in
Fig. 4 a Top and b side view of 1b with the numbering of the carbons of the inner part. Hydrogens were omitted for clarity. Carbons are in yellow , and oxygens in red
Fig. 5 a Top and b side view of 2b with the numbering of the carbons of the inner part. Hydrogens were omitted for clarity. The green bonds are
shorter than the yellow ones , indicating a bond length alternation pattern
50
Reprinted from the journal