Conformations of stilbene-like species and new method of energy partition

Article abstract of DOI:10.1021/jp9726605

To understand the nature of π-electron delocalization, while questioning the abnormally large twist angle of N-benzylideneaniline, we prepared four stilbene-like species, (4-X-Ph)-CH=N-Ar (Ar = 2-pyridyl, X = -Cl, -NO₂, -N(Me)₂; Ar =

Full text of DOI:10.1021/jp9726605

2016
J. Phys. Chem. A 1998, 102, 2016-2028
Conformations of Stilbene-like Species and New Method of Energy Partition
Zhong-Heng Yu,* Lin-Tong Li, Wei Fu, and Liang-Ping Li
Institute of Chemistry, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
ReceiVed: August 13, 1997; In Final Form: December 10, 1997
To understand the nature of π-electron delocalization, while questioning the abnormally large twist angle of
N-benzylideneaniline, we prepared four stilbene-like species, (4-X-Ph)-CHdN-Ar (Ar ) 2-pyridyl, X ) -Cl,
-
NO
2
, -N(Me)
2
; Ar ) 2-pyrimidyl, X ) -NO
2
), and four ketenimine derivatives, (4-X-Ph)
2
CdCdN-(Ph-Y-4)
(Y ) -H, X ) -H; Y ) -NO
2
, X ) -H; Y ) -NO
2
, X ) -OMe; Y ) -N(Me) , X ) -H), and determined their
2
crystal structures using X-ray diffraction. Our new procedure for constructing a complete fragment molecular
orbital (FMO) basis set is described in detail. Based on our procedure, the Morokuma’s energy partitioning
provides, in the framework of ab initio SCF-MO computation at the STO-3G level, the various π and σ
energies associated with the inter- and intrafragment interactions. The π-electron delocalization in the DPI
state of stilbene-like species is found to be destabilization. The DPI state is most destabilized at the coplanar
geometry, and its electronic energy is the highest of four hypothetical electronic states. The characteristics
of the quantum mechanical resonance energy (QMRE), including its role with regard to chemical reactivities
toward electrophile attack, depend upon the response of the σ framework to the π-electron delocalization. In
the case of stilbene-like species, the QMRE is destabilizing. Conversely, the QMRE of benzene is stabilizing.
However, it is the σ framework of benzene, rather than the π system itself, which is strongly stabilized by the
QMRE, revealing that benzene is σ aromatic. The driving forces for the out-of-plane twist of stilbene-like
species arise from the QMRE and the σ orbital interaction. The electron-withdrawing (-I) groups and the
ring-nitrogen atoms seem to have an obvious influence upon the twist angle.
Introduction
to be questioned by the angles φ of stilbene-like species,
especially by those (both up to 30°) of 1a and azobenzene (1d)
It has been recognized as a cornerstone of the classical
structure theory of organic chemistry that molecules with
conjugated double bonds have a higher thermodynamic stability
than isomeric compounds having isolated double bonds. The
7
in the gas state, and by those of the compounds listed in Table
. (The phrase “stilbene-like species listed in Table 1” or “the
1
molecules of type 1” is often, hereafter, shortened to “STB-
type 1”.)
standard textbook explanation for this stability is given in terms
of resonance interactions.1 It is also one of the fundamental
In order to discern whether conjugation effect depends on
conformation or results in a nonplanar geometry, we prepared
the following eight compounds with less nonbonded contact
such as that in NBA: (4-X-Ph)-CHdN-2-pyridyl (1e, X ) -Cl;
concepts that the maximum resonance energy results from the
planarity of the π system.1,2 However, the abnormally large
twist angle of stilbene-like species seems to challenge the
viewpoint of π resonance stabilization.
1
f, X ) -NO2; 1g, X ) (Me)2N-), 4-NO2-Ph-CHdN-2-
pyrimidyl (1i) and (4-X-Ph)2CdCdN-(Ph-Y-4) (2a, X ) -H,
Y ) -H; 2b, X ) -H, Y ) -NO2; 2c, X ) -MeO, Y ) -NO2;
The marked dissimilarity in the electronic spectra of stilbene
(STB, 1a) and N-benzylideneaniline (NBA) has led to many
2
d, X ) -H, Y ) -N(Me)2) and determined their crystal
theoretical and experimental studies and arguments in the past
two or three decades, including studies employing infrared (IR)
and a variety of nuclear magnetic resonance (NMR) studies,
X-ray crystallography, and molecular orbital calculations. The
resonance stabilization is always used to interpret the effects
structures using X-ray diffraction (see Table 1 and Figures 1-3).
T
The total molecular energies E , total electronic energies Ee,
3
and total nuclear repulsion energies E , occurring in seven
N
typical optimized geometries of each of seven STB-type 1 were
1
2
calculated using the AM1 method. In addition, the nuclear
of substituents on the conformations of NBA and its substituted
derivatives.4 Burgi and recent researchers ascribed the large
repulsion energies E between the aromatic ring and fragment
n
Ar-QdP- were obtained from the ab initio SCF-MO (self-
twist angle (φ ) 55°) of NBA to the contact of nonbonded atoms
such as the hydrogen on the -NdCH- and one of the ortho
hydrogens on the aniline ring. The loss of the π-electron energy
in the twisted geometry can be compensated for partly by the
intramolecular charge transfer (CT-2) from the bridge nitrogen
lone-pair electrons to the phenyl ring and by the decrease in
consistent field molecular orbital) program. The nonbonded
contact in 1e-1g and 1i (Figure 1) should be comparable to
that in 2a-2d (Figure 2), but the twist angles φ for the former
are generally larger than those for the latter. Of all the
molecules listed in Table 1, the theoretical angle (φ ) 50°) of
1i is largest and the experimental angle (φ ) 0.5°) of 2a is
smallest. The data in Table 2 are especially noteworthy. These
data show identically that the driving force for out-of-plane twist
of STB-type 1 arises from the electron interaction, expressed
in terms of Ee, rather than from the nuclear repulsion EN and
En. At the θ ) 30° geometry of 1h, for example, the absolute
5
steric hindrance; these researchers expected, therefore, that if
the nonbonded interaction was neglected, the π-electron transfer
(CT-1) between the conjugated fragments was found to favor
6
the planar conformation of NBA. Burgi’s conclusions appear
*
E-mail: yuzh@infoc3.icas.ac.cn. Fax: (10) 62569564 (Institute).
S1089-5639(97)02660-1 CCC: $15.00 © 1998 American Chemical Society
Published on Web 02/25/1998

Conformations of Stilbene-like Species
J. Phys. Chem. A, Vol. 102, No. 11, 1998 2017
TABLE 1: Experimental and Theoretical Values (deg) of Twist Angles O and r in Compounds of Types 1 and 2
twist angle φ
twist angle R
X-ray AM1
compd
P
Q
X
Y
Z
W
R
R′
X-ray
5a
AM1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
a
b
c
d
e
f
g
h
i
CH
N
N
N
N
N
N
N
N
N
CH
CH
CH
N
CH
CH
CH
CH
CH
CH
CH
CH
CH
CH
N
N
N
CH
N
CH
CH
CH
CH
CH
CH
CH
CH
CH
N
CH
CH
CH
CH
CH
CH
CH
N
C
C
C
C
C
C
C
C
C
N
H
N(Me)
NO
H
Cl
NO
N(Me)
H
H
NO
N(Me)
H
H
H
H
H
H
H
H
H
MeO
H
27
40
15
15
13
0
15
38
50
5
10
4
15
6
27
0
0
15
3
b
2
2
41
9
15
b
e
2
2
c
15
20
36
2
2
7
0.5
0
e
2
d
46
13.4
12
8
14
4.5
2
CH
CH
NO
2
26
d
e
j
CH
21
35
a
b
c
d
H
NO
NO
0.5
16
6.5
9.1
2
2
N(Me)
2
a
This value is from ref 8. b From ref 9. c From ref 10. d From ref 11. e Conformational space was sampled by varying θ in steps of 5°.
value (|-11 090.9611|eV) of Ee and value (9004.6837 eV) of
EN are greatest, and decrease as the molecular framework is
distorted away from this geometry. Therefore, we cannot
attribute the nonplanarity of STB-type 1 to the steric hindrance
or to the crystal lattice force.13 In molecule 2c (Figure 2), the
combination of the “pushing” and “pulling” actions, exerted by
an electron-releasing (+M) group MeO- and an electron-
withdrawing (-M) group -NO2, respectively, should greatly
benefit the CT-2 interaction between the nitrogen lone pair and
phenyl ring A, and its twist angle C8-N7-C1-C6 should be
larger than the angle (41°) in 1b. At the least, it should be
larger than that (16°) in 2b. Contrary to expectation, the actual
angle is only 9.2°. Nakai and collaborators found that the C1-
N7 distance in several molecules such as 1c (1.416 Å) and 1b
Methods and Computational Details
Based on the most common definitions of the resonance
1
6
energy (RE), the RE is essentially associated with the local
interaction between double bonds. Inevitably, this interaction
influences the original characteristics of the double bonds,
including the observed and calculable changes in their bond
lengths and bond orders, and also including the disturbance to
17
their original π energies. The geometric data in Figure 3, for
example, indicate that the lengths of the bonds N7-C8 and C1-
C6 are changed as the bond C1-N7 is lengthened from 1.405 to
1.411 Å with the rotation of fragment A about the C -N .
1
7
Accordingly, the fundamental problems in the energy partition-
ing are how to calculate, reasonably and directly, the π energies
occurring in a conjugated molecule and its corresponding
hypothetical structures with the localized π systems, and how
to evaluate the effects of the π-electron delocalization on the σ
framework. In this sense, the perturbation molecular orbital
(
1.398 Å) decreases with increasing CT-2 effect.9 Accordingly,
this distance should decrease in order of 1f, 1i, and 1g and of
d, 2a, 2b, and 2c, respectively. In fact, the bond length (1.439
2
(PMO) method should be more reasonable and valuable. It is
Å) in 1i is much longer than that (1.410 Å) in 1f, and the
experimental value (1.409 Å) in 1g is almost equal to that in 1f
prerequisite for the PMO analysis that the symmetric (σ) and
antisymmetric (π) FMOs are thoroughly separated. It is easy
when and only when the geometry of a molecule is planar.18
However, STB-type 1 are not planar. In this case, the M-SCF
method based on our new procedure becomes a useful instru-
ment for partitioning total electronic energy. Our procedure
provides a complete FMO basis set for the M-SCF partition.
(Figure 1); of the four ketenimine derivatives, the distance (1.436
Å) in 2a is longest and that (1.419 Å) in 2d is shortest (Figure
2
). Recently, our calculations have approximately shown that
1
4
in the aniline molecule, the CT-2 interaction is destabilizing.
Accordingly, the nonplanarity of STB-type 1 cannot be ex-
plained in terms of the CT-2.
1
9
According to the PMO theory and based on the fact that in
In this work, our procedure for constructing a complete
fragment molecular orbital (FMO) basis set is described in detail.
Morokuma’s partition of the intermolecular SCF interaction
energy,15 denoted as M-SCF partition, is introduced into the
intramolecular interaction, and it is used for analyzing the direct
and indirect effects of the π-electron delocalization, respectively,
on the π system itself and the σ frame in an effort to gain insight
into the nature of the π-electron delocalization. Meanwhile, it
is also applied to the σ interactions in order to search for the
unknown driving force and to probe the influence of the
electron-withdrawing (-I) effect upon the twist angle.
STB-type 1 both twist angles φ and R are not equal to 0° or
1
80°, we can consider a nonplanar molecule N-phenylmethyl-
ene-3-pyridineamine (1h), for example, as three planar opened-
shell fragments, phenyl fragment (A), imine group -CHdN- (B),
and 3-pyridyl fragment (C), i.e., A-B-C dissection as shown
in Figure 4.
Figure 5 displays a thermodynamic cycle for the orbital
interactions in STB-type 1. It shows the symbols for the π-
and σ-electronic energies in the following hypothetical states:
the full localized state denoted as FUL; the state, denoted as
DPI, with a delocalized π system and localized σ frameworks;

2018 J. Phys. Chem. A, Vol. 102, No. 11, 1998
Yu et al.
Figure 1. Experimental and theoretical geometric data of four stilbene-like molecules.
(
λ,F)
and ∆E (σ λ,F) arise from
the DSI state with delocalized σ frameworks and localized π
systems; the full delocalized state denoted as FUD. Figure 5
also contains a set of definitions of the various energy
differences that will be used consistently in this work. For
simplicity, these energy differences are expressed by the
following general formulas:
(λ,F) mean that the energy effects ∆E
π
the delocalization of the λ- and F-electrons; the characters π
and σ in super- and subscripts denote that the energy effects
are associated, respectively, with the π and σ orbital interactions.
When λ ) π and F ) π, eqs (1-1) and (1-2) become
(
π
π)
(π)-π
(π)-π
∆
E
E
) ∆E
+ ∆E
(2-1)
(2-2)
ab+bc+ca
a+b+c
(λ,F)
(λ,F)-π
ab+bc+ca
(λ,F)-π
a+b+c
∆
E
) ∆E
+ ∆E
(1-1)
(1-2)
π
(
σ
π)
(π)-σ
(π)-σ
∆
) ∆E
+ ∆E
ab+bc+ca
a+b+c
(
σ
λ,F)
(λ,F)-σ
ab+bc+ca
(λ,F)-σ
a+b+c
∆
E
) ∆E
+ ∆E
(
π
π)
(π)
where ∆E and ∆Eσ are the energy differences between the
where the characters λ and F (λ, F ) π, σ) in the superscript
DPI and FUL states. Two terms in the right side of eq (2-1)

Conformations of Stilbene-like Species
J. Phys. Chem. A, Vol. 102, No. 11, 1998 2019
Figure 2. Crystallographic data of four ketenimine derivatives.
are the energy components associated, respectively, with the
inter- and intrafragment interactions, and are given as
often written as
(
π)-π
(π)-π
(π)-π
∆
E
) ∆Eab + ∆Ebc
(2-6)
ab+bc
(
π)-π
(π)-π
(π)-π
(π)-π
∆
E
) ∆Eab + ∆Ebc + ∆Eca
(2-3)
(2-4)
ab+bc+cb
In this work, the energy components such as those in eqs
(π)-π
(π)-π
(π)-π
(π)-π
(π)-λ
∆
E
) ∆Ea
+ ∆Eb
+ ∆Ec
(2-3)-(2-6) are often written as the general forms ∆E
and
where p, q ) a, b, c; p * q; λ ) π, σ). In this case,
the subscript pq and the character λ in the superscript (π)-λ
a+b+c
pq
(
p
π)-λ
∆
E
where
(
π)-λ
pq
mean that the ∆E is associated with the λ orbital interac-
tions between fragment P and Q (P, Q ) A, B, C; P * Q), and
the subscript p denotes a energy effect ∆Ep
fragment P. In eq (2-5), the character o in the superscript (o)
(
a
π)
) E (a π)-π - E (a o)-π, ∆E
(π)
b
) E (b π)-π - E (b o)-π, ∆E
(π)
∆
E
)
c
(π)-π
(o)-π
(π)-λ
E
- Ec
(2-5)
occurring in
c
(π)-π
-3
(o)-λ
In the case of STB-type 1, |∆Eac | < 10 ; hence, eq (2-3) is
denotes that the Ep
(p ) a, b, c; λ ) π, σ) is a λ electronic

2020 J. Phys. Chem. A, Vol. 102, No. 11, 1998
Yu et al.
T
TABLE 2: Total Molecular Energy E , Total Electronic Energy E
e
, Total Nuclear Repulsion E
N
, Nuclear Repulsion E
n
(
hartrees) between Fragments C and A + B, and Their Changes with Rotation of Fragment C (Energy in eV except for E
n
)a
θ ) 0°
θ ) 5°
θ ) 10°
θ ) 30°
θ ) 50°
θ ) 70°
θ ) 90°
1
a
ET
-1 956.3956
-10 866.6455
8 910.2499
-1 956.3965
-10 867.0250
8 910.6289
-1 956.3988
-10 868.0638
8 911.6649
-1 956.4010
-10 874.0003
8 917.5993
-1 956.3544
-10 871.0929
8 914.7384
E
E
E
e
N
n
229.3696
229.3942
229.4682
229.9104
229.8220
1
b
ET
-3 383.8153
-20 354.9945
16 971.1792
381.1377
-3 383.8150
-20 355.6694
16 971.8534
381.1843
-3 383.8191
-20 356.3679
16 972.5488
381.2470
-3 383.8376
-20 362.3796
16 978.5420
381.7394
-3 383.8378
-20 360.1906
16 976.3527
381.5754
-3 383.8211
-20 351.4668
16 967.6457
380.8868
E
E
E
e
N
n
1
d
ET
-2 085.5479
-11 110.8509
9 025.3029
-2 085.5481
-11 110.8661
9 025.3181
-2 085.5484
-11 110.9009
9 025.3525
-2 085.5425
-11 111.6857
9 026.1432
-2 085.5071
-11 111.8174
9 026.3103
-2 085.4587
-11 108.9611
9 023.5024
-2 085.4424
-11 107.4265
9 021.9545
E
E
E
e
N
n
237.0091
237.0092
237.0093
237.0371
237.0132
236.8095
236.6407
1
e
ET
-2 446.2838
-12 559.3338
10 113.0499
272.0361
-2 446.2839
-12 559.3430
10 113.0591
272.0402
-2 446.2841
-12 559.5186
10 113.2345
272.0553
-2 446.2803
-12 560.4603
10 114.1800
272.1561
-2 446.2559
-12 560.3311
10 114.0752
272.1461
-2 446.2068
-12 557.6144
10 111.4076
271.8893
E
E
E
e
N
n
1
f
ET
-2 917.0114
-15 549.8119
12 632.8005
284.5411
-2 917.0114
-15 549.8462
12 632.8348
284.5444
-2 917.0113
-15 549.9552
12 632.9439
284.5526
-2 917.0062
-15 551.1046
12 634.0984
284.6605
-2 916.9803
-15 551.0171
12 634.0368
284.6523
E
E
E
e
N
n
1
h
ET
-2 086.2632
-11 087.7973
9 001.5341
-2 086.2643
-11 087.8483
9 001.5840
-2 086.2665
-11 088.1340
9 001.8675
-2 086.2773
-11 090.9611
9 004.6837
2 086.2675
-11 089.0204
9 002.7529
-2 086.2417
-11 082.1533
8 995.9116
-2 086.2269
-11 078.3659
8 992.1390
E
E
E
e
N
n
235.6215
235.6290
235.6588
235.9209
235.7749
235.1954
234.8701
1
i
ET
-2 981.5947
-15 656.0401
12 674.4455
286.1286
-2 981.5953
-15 656.1216
12 674.5263
286.1398
-2 981.5982
-15 656.2985
12 674.6976
286.1591
-2 981.6182
-15 658.3358
12 676.7176
286.3514
-2 981.6315
-15 658.4500
12 676.8184
286.3859
E
E
E
e
N
n
a
The starting geometry of each molecular conformation was taken from its crystal structure. The conformational space was sampled by varying
θ in steps of 5° for 0° < θ < 90°. At each point a full optimization was carried out under the condition that all the ring atoms in each of two
aromatic ring were kept coplanar.
energy in the FUL state of fragment P. In eq (2-2), the energy
for the DPI state under the following conditions: in each SCF
iteration, all the elements Sij (the elements of the overlap integral
matrix S) and Fij (i * j) between the FMOs of the σ type are
set equal to zero except four elements, Fsa,sb1, Ssa,sb1, Fsc,sb2, and
Ssc,sb2. The subscripts sa and sb1 in Fsa,sb1 denote a pair of the
singly occupied FMOs belonging, respectively, to two bonded
fragments A and B, and the sc and sb2 (sb1 * sb2) a pair of
those belonging to fragments C and B. The conditional RHF
(π)
effect ∆E
is the response of the σ framework to the
σ
delocalization of the π-electrons and it arises from the effects
of the π-electron delocalization on the σ-π space interactions
expressed in terms of the Coulomb Jσπ and exchange Kσπ
integrals. In the M-SCF scheme, the energy components
(
pq
π)-λ
(π)-λ
∆E
and ∆Ep
are obtained from the following general
expressions:
π
computation, denoted as RHF -f, for the various elements in
λ
eq (3-3) was performed over the same complete FMO basis. In
this computation, all the elements Sij ) 0.0 and Fij ) 0.0 (i *
j) except the elements Fsa,sb1, Ssa,sb1, Fsc,sb2, and Ssc,sb2. In the
(
pq
π)-λ
(π)-λ
+ H (i jπ )-λ)D
(π)-λ
∆
E
)
(Fij
i ∈ P, j ∈ Q
(3-1)
∑
ij
i,j
σ
λ
conditional RHF computation, denoted as RHF -m, for the
(
p
π)-λ
(π)-λ
(π)-λ
(π)-λ
various elements in the DSI state, all the Fij and Sij (i * j)
between the FMOs of the π type are set equal to zero. The
E
)
)
(F
+ Hik )D
i, k ∈ P (3-2)
i, k ∈ P (3-3)
∑
ik
ik
i,k
(
ij
σ,π)-λ
RHF-T computation for the elements, such as F
,
λ
(σ,π)-λ
(σ,π)-λ
(
p
o)-λ
(o)-λ
(o)-λ
(o)-λ
ik
H
, and Dij
, in the FUD state was performed under
ij
E
(F
+ Hik )D
∑
ik
the constraint, a fundamental requirement for every type of
conditional RHF computation, that all the Fij and Sij between
the π and σ FMOs are set equal to zero. All the conditions
employed in each of four types of the conditional RHF
computations ensure that the molecular orbitals (MOs) of the
π type are thoroughly separated from those of the σ type.
i,k
where F, H, and D are Fock, Hamiltonian, and density
matrices respectively (a capital bold letter denotes, hereafter, a
(
ij
π)-λ
(π)-λ
matrix over the complete FMO basis set); F
, Hij
,
(π)-λ
D
et al. are their respective elements. The various ele-
ij
ments in eqs (3-1)-(3-2) are obtained from the RHF (restricted
The complete FMO basis set, in which all FMOs have correct
electron occupancies, consists of CDF-MOs (closed-shell de-
π
Hartree-Fock) computation, denoted as RHF -m in Figure 5,

Conformations of Stilbene-like Species
J. Phys. Chem. A, Vol. 102, No. 11, 1998 2021
Figure 3. The crystal structure of 1h, and its rotational geometries 1h-R0, 1h-R40, 1h-R90, 1h-PL, and 1h-VER obtained from AM1.
na
na+nb
N
localized FMOs) and singly occupied OLF-MOs (opened-shell
localized FMOs). The construction of this basis set is a three-
step procedure: (i) three basis sets from their respective planar
fragment molecules (PFM), (ii) transformation of the basis set
for the PFM into that for the corresponding nonplanar fragment
molecule, and (iii) the formation of a complete basis set for the
optimized geometry of a molecule by the superposition of three
basis sets belonging, respectively, to fragments A, B, and C.
Construction of a Complete FMO Basis Set. According
to the Whangbo-Schlegel-Wolfe-Kost (WSW-K) proce-
dure,20 i.e., a conditional UHF (unrestricted Hartree-Fock)
computation for the composite system such as 1h followed by
the Kost’s localization, three groups of OLF-MOs can be
characterized by the following expressions:
ψ
)
a
φ
+
a
φ
+
a
φ
(4-3)
cl
∑
kl
k
∑
ml
m
∑
nl
n
k)1
m)na+1
n)na+nb+1
where the atomic orbitals (AOs) φk (k ) 1, 2, ..., na) ∈ A, φm
m ) na + 1, ..., na + nb) ∈ B, and φn (n ) na + nb + 1, ..., N)
C; aki, ami, and ani are their coefficients. In our new procedure,
(
∈
the first sum term in eq (4-1) , i.e., a set of the OLF-MOs ψai
for the isolated fragment A, is obtained indirectly from a planar
fragment molecule, denoted as FM-A in Figure 4b, using the
WSW-K procedure. The FM-A resulted from the replacement
of the 3-pyridyl-NdCH- group (B + C) in 1h with a hydrogen
atom denoted as Hr while all the bond angles and bond lengths
were kept unchanged with the exceptions that the value of 1.0
Å was imposed on the length of the C9-Hr bond and the
dihedral angle Hr-C9-C10-C11 was set equal to 180°. The 1s
AO of the Hr, denoted as ψH, is an excellent singly occupied σ
FMO, and the formation of the FM-A simplifies the localization
procedure greatly. However, the dihedral angles, such as the
C8-C9-C10-C11 and N7-C1-C2-C3 in Figures 1 and 3, are
generally less than 180°. Therefore, it is necessary for the OLF-
MOs of the σ type to be localized once more. In the second
na
na+nb
N
ψ ) a φ +
a φ +
a φ (4-1)
ni n
ai
∑
ki
k
∑
mi
m
∑
k)1
m)na+1
n)na+nb+1
na
na+nb
N
ψ ) a φ +
a φ +
a φ (4-2)
nj n
bj
∑
kj
k
∑
mj
m
∑
k)1
m)na+1
n)na+nb+1

2022 J. Phys. Chem. A, Vol. 102, No. 11, 1998
Yu et al.
Results and Discussion
Geometry Optimization. In our practical calculations, the
rotational geometries of each of STB-type 1 were optimized
using the various semiempirical calculations such as AM1,
12
MNDO, MINDO/3, and PM3. Our practical calculations and
recent literature show that the AM1 method appears to be most
3
,21
suitable.
However, AM1 cannot treat correctly all the
molecules. In fact, the abnormal difference in the twist angle
φ between the experiment and AM1 calculation occurs in
molecule 1f. According to the energy data in Table 2, it may
result from its rather flat potential energy.
The starting geometry of each molecular conformation was
taken from the crystal structure, and the geometry optimizations
for the various rotational conformers were experimentally carried
out under the following two models: (i) the full optimization
(Model I); (ii) all the dihedral angles are kept to be 0° or 180°
(Model II). In addition, the H and ring atoms in each of two
aromatic rings were kept on same plane, and the twist angle θ
in a given rotational conformer was kept unchanged in above
two models. Our practical calculations show that of all the
dihedral angles, only the angle P-C1-X-Z has the greatest
effect on the preferential geometry, and a larger angle θ
corresponds generally to a larger deviation of the angle N7-
C1-X-Z (X, Z ) C, N) from 180° (see Figures 1-3).
Therefore, the whole aromatic ring with a substituent group such
as -NO2, -NH2, or -Cl can be considered approximately as a
planar fragment, which will greatly simplify our computational
procedure.
Figure 4. (a) The dissection way and the numbering system in
N-phenylmethylene-3-pyridineamine (1h). The A-B-C dissection of
1
h into a phenyl fragment (A), an imine group (B), and a 3-pyridyl
fragment (C). (b) Formation of the corresponding fragment molecules
denoted as FM-A, FM-B, and FM-C.
localization, all the π OLF-MOs are kept unchanged, and the
atomic overlap integral matrix s used in Kost’s localization is
from a nonplanar fragment molecule denoted as NFM-A. The
only difference in the geometry between the FM-A and the
NFM-A occurs in the angle Hr-C9-C10-C11. In the case of
the NFM-A, this angle is set equal to the C8-C9-C10-C11 in
the optimized geometry of 1h.
However, the Kost’s localization fails to ensure all the π OLF-
MOs correct electronic occupancies. A conditional RHF
computation, over the OLF-MOs basis set, for the NFM-A has
to be performed after the Kost’s localization. From this
computation, a set of the CDF-MOs æai is obtained under the
following conditions: first, all the elements Fij ) 0.0 and Sij )
When R * 0 and θ * 0, there should be eight types of the
FMO interactions. However, the σ-π interaction results in the
mixture of the σ and π FMOs and will not be considered here.
π-System Is Most Destabilized in the DPI State of
Coplanar Geometry. According to the definitions of the
Coulomb and exchange integral matrices J and K, we have the
following theoretical expressions for the elements in eqs (3-
2
2
1
)-(3-3).
(
ij
π)-λ
) H (i jπ )-λ
(π)-λ
F
+
+
+
D
[(ij,mn) - 1/2(im,jn)] (5-1)
[(ik,mn) - 1/2(im,kn)] (5-2)
[(ik,mn) - 1/2(im,kn)] (5-3)
∑
∑
mn
m
n
0
.0 (i ∈ A, j ∈ Hr) except two elements Fsa,H and Ssa,H between
a pair of singly occupied OLF-MO ψsa and ψH; second, all the
intrafragment elements Fsa,ai and Ssa,ai (sa * ai) and those
between the π and σ OLF-MOs are set equal to zero. A set of
the CDF-MOs and a singly occupied OLF-MO ψsa form a FMO
basis set Φai for fragment A. All Φai have now correct
electronic occupancies, and the π type of Φai has been
thoroughly separated from the σ type. A FMO basis set Φbj
for fragment B and that Φcl for fragment C are obtained in a
similar way. In the case of fragment B, there are two singly
occupied OLF-MOs ψsb1 and ψsb2. A singly occupied OLF-
MO for fragment C is denoted as ψsc. At last, according to the
characteristics as shown in eqs (4-1)-(4-3), a complete FMO
basis set is formed by the superposition of three basis sets, Φai,
Φbj, and Φcl. In the meantime, all the coefficients corresponding
to those ami, ani, akj, anj, akl, and aml in eqs (4-1)-(4-3) are set
equal to zero.
(
ik
π)-λ
(π)-λ
(π)-λ
F
F
) Hik
D
∑∑ mn
m
n
(
ik
o)-λ
(o)-λ
(o)-λ
∑∑ mn
) Hik
D
m n
π
π
The constrained conditions in the RHF -f and RHF -m ensure
(π)-σ
(o)-σ
all the Dmn and Dmn (m * n) are equal to zero except those
between two pairs of the single occupied FMOs. In these cases,
the effect of the σ-electron delocalization on the π system has
been eliminated as far as possible.
In order to get deeper insight into the conjugation effect on
(o)-π
(π)
the original energies Ep , the energy effect ∆E (θ) includ-
π
(π)-π
(π)-π
ing its components ∆E
(θ) and ∆Ep (θ) were calculated
pq
(
Tables 3 and 4). In accord with the classic viewpoint, the
(π)-π
conjugation energy ∆E
(θ) is most stabilizing at the co-
In the case of larger molecules such as 1a-1j, the calculations
involving larger basis sets such as 6-31G et al. are extremely
costly. In this work, the complete FMO basis set and the various
orbital interaction energies were constructed and calculated using
the ab initio SCF-MO computation program at the STO-3G
level. The various rotational geometries were optimized using
AM1. It should be stressed that during the period of any ab
initio SCF iteration, the geometries of a molecule, its fragments
and fragment molecules were no longer optimized.
ab+bc
planar geometry, and weakens with the rotation of fragment C
about the C1-N7 bond. The absolute value (|-1.1369|hartree)
(π)-π
of ∆Eab+bc in the coplanar geometry is greatest of all the
rotational geometries listed in Table 3, and its minimum value,
about |-0.000 99|hartree, occurs in the vertical geometry with
R ) θ ) 90°. However, as shown by the data in Tables 3 and
4, the conjugation reduces, without exception, the original π
(o)-π
energy Ep
of each of fragments, and, moreover, the energy

Conformations of Stilbene-like Species
J. Phys. Chem. A, Vol. 102, No. 11, 1998 2023
Figure 5. The thermodynamic cycle for the orbital interactions and the definitions of the various energy differences. The numbers in parentheses
are the values (hartrees) of the total electronic energies in four hypothetical states (FUL, DPI, DSI, and FUD) of the copolanar geometry of 1h.
(
pq
π)-π
, Energy Losses ∆E (p π)-π, Total π and σ Interaction Energies ∆E and ∆E (σ π), and Total
(π)
TABLE 3: Energy Gain ∆E
π
(π)
(π)
Electronic Energies E and Eσ in the DPI State of 1h, and Their Changes with the Rotation of Fragment C (Energy in
π
Hartrees)
angle (deg)
(
ab
π)-π
(π)-π
∆E (a π)-π
∆E (b π)-π ∆E (c π)-π
Model II of Optimizing
(π)
(π)
(π)
π
(π)
σ
θ
R
∆E
∆Ebc
∆Eπ
∆Eσ
E
E
0
0
0
0
0
0
-0.544 29
-0.542 14
-0.528 31
-0.504 27
-0.474 11
-0.000 30
-0.592 56
-0.574 64
-0.445 13
-0.248 88
-0.000 68
-0.000 69
0.550 15
0.549 37
0.544 42
0.532 71
0.516 63
0.000 34
0.433 80
0.420 35
0.321 17
0.158 33
-0.054 51
0.000 49
0.242 19
0.234 03
0.179 43
0.107 83
0.023 01
0.000 20
0.088 67
0.086 63
0.071 33
0.045 58
0.010 34
0.000 05
-0.076 47
-0.074 58
-0.060 44
-0.036 63
-0.003 35
-0.000 08
-134.7154
-134.7285
-134.8300
-134.9147
-134.9125
-135.0351
-1167.2741
-1167.3118
-1167.6070
-1167.6222
-1167.0489
-1167.1675
1
3
5
9
9
0
0
0
0
0
90
Model I of Optimizing
0
0
0
0
0
-0.541 44
-0.536 62
-0.526 65
-0.505 65
-0.473 32
-0.592 20
-0.574 43
-0.454 66
-0.271 93
-0.002 91
0.547 48
0.544 06
0.542 47
0.532 61
0.516 33
0.432 71
0.418 05
0.322 35
0.172 14
-0.056 07
0.242 36
0.235 70
0.188 71
0.121 31
0.025 67
0.088 54
0.086 40
0.071 89
0.048 31
0.009 68
-0.076 36
-0.074 40
-0.061 03
-0.039 10
-0.002 73
-134.7147
-134.7296
-134.8072
-134.8507
-134.8104
-1167.2647
-1167.3036
-1167.4844
-1167.3113
-1166.4864
1
3
5
9
(
π)-π
gain ∆E
(θ) is insufficient to compensate for the total
mixes the occupied FMO of one fragment with the vacant FMO
of the other and vice versa, and one of two exchange (EX)
energies is associated with the interaction between the occupied
ab+bc+ca
(π)-π
(π)
energy loss ∆E
(θ). The total π energy effect ∆E (θ) is
a+b+c
π
(π)
destabilizing. The ∆E (0°) of 1h is large up to 55.64 kcal/
mol. At the vertical geometry, there should be no π interactions
between fragments except the long distance interaction between
fragments A and C. The calculation results are ∆E
0.62 kcal/mol and ∆Eπ ) 0.031 kcal/mol (Table 3).
As shown by the data of ∆E (θ) in Tables 3 and 4, the σ
framework is stabilized owing to the σ-π space interactions,
while the π system itself is destabilized due to the π-electron
interactions between fragments. However, this energy gain
π
1
5
FMOs. According to the Morokuma definitions, these two
interactions cause π-electron delocalization between fragments.
Based on the PMO expression for two-electron interaction
(
π)-π
)
ab+bc
24
pq
(π)
energy, the CT energy ΣoV (Figure 6) can be defined as the
-
energy gain of fragment P, and it is associated with the
(
σ
π)
interaction which causes the delocalization of the π-electrons
2
from P to Q. Comparison of the values of the Σ and the net
p
(π)
π-electron charge DF (Table 5) and inspection of their signs
indicate that the quantity Σ , as defined by eqs (6-1)-(6-3),
can be used to measure, indirectly, the net charge transfer.
2
p
(
σ
π)
∆
E (θ) is still insufficient to compensate for the π energy
(
π
π)
(π)
π
(π)
σ
loss ∆E (θ). The total energy effect ∆E (θ) + ∆E (θ) is
destabilizing. At the coplanar geometry of 1h, for example,
its value (7.66 kcal/mol) is greatest, and the total electronic
energy (-1301.9895 hartrees) in the DPI state is the highest of
four hypothetical electronic states (see Figure 5). It might be
a reason why the symmetrization of the phenyl ring in 1h-VER
is better than that of 1h-R0 (Figure 3).
2
a
ba
oV
ab
oV
Σ ) Σ - Σ
(6-1)
(6-3)
(6-2)
2
bc
oV
cb
oV
Σ ) Σ - Σ
c
2
2
a
2
c
Σ
) -(Σ
+ Σ
)
b
Destabilization of the π-System in the DPI State Is Due
to π-Electron Delocalization. Electron delocalization is an
important concept in modern organic chemistry. One problem
is that “delocalization” is not directly measurable and there is
no single definition underlying the use of this concept throughout
whether fragment P is a +M or -M group depends upon the
2
(π)
2
sign of Σ . The signs of the D and Σ both are positive
p
a
a
without exception; fragment A is +M group as far as two-
electron interaction is concerned. On the other hand, it is
difficult to determine the contributions made by each of two
2
3
chemistry. As shown by Figure 6, the charge transfer (CT)

2024 J. Phys. Chem. A, Vol. 102, No. 11, 1998
Yu et al.
(
π)-π
(π)-π
cb
(π)
(π)
TABLE 4: Energy Gain ∆E
, Energy Losses ∆Ep , CT Energy Σ , Total π and σ Interaction Energies ∆E and ∆Eσ ,
oW π
ab+bc
(
π)
(π)
Total Electronic Energies E and Eσ in the DPI State of Stilbene-like Species, and the Changes with the Rotation of Fragment
π
C (Energy in Hartrees)
angle (deg)
(
π)-π
∆E (a π)-π
∆E (b π)-π
∆E (c π)-π
cba
oV
(π)
(π)
(π)
π
(π)
σ
θ
R
∆E
Σ
∆Eπ
∆Eσ
E
E
model
ab+bc
Compound 1a
0
5
0
0
5
20
-1.156 54 0.392 98 0.463 76 0.391 81 -0.469 82 0.091 47 -0.077 24 -132.1603 -1131.6589
-1.146 70 0.390 12 0.458 76 0.389 18 -0.466 52 0.090 83 -0.076 71 -132.1687 -1131.6866
-1.010 44 0.351 21 0.390 41 0.350 51 -0.419 28 0.081 69 -0.068 87 -132.2658 -1131.9565
II
I
I
2
2
Compound 1j
0
5
0
0
-1.086 10 0.370 63 0.443 10 0.359 74 -0.424 78 0.087 06 -0.074 61 -134.5834 -1166.7678
-1.081 24 0.370 70 0.440 27 0.357 19 -0.421 71 0.086 61 -0.074 22 -134.5856 -1166.7696
-1.015 04 0.373 17 0.403 28 0.319 36 -0.376 72 0.080 48 -0.068 61 -134.6308 -1166.9018
II
I
I
Compound 1h
0
5
0
0
-1.136 85 0.550 15 0.433 80 0.242 19 -0.401 70 0.088 68 -0.076 62 -134.7154 -1167.2741
-1.129 79 0.548 20 0.429 52 0.240 48 -0.398 80 0.088 06 -0.075 98 -134.7182 -1167.2761
II
I
Compound 1f
0
5
0
-1.187 51 0.436 23 0.604 73 0.232 78 -0.399 47 0.085 97 -0.075 19 -193.9805 -1588.3054
-1.182 36 0.435 96 0.601 38 0.230 87 -0.396 55 0.085 61 -0.074 82 -193.9824 -1588.3087
-1.115 67 0.435 65 0.554 78 0.205 94 -0.356 36 0.080 50 -0.069 99 -194.0056 -1588.3379
II
I
I
2
2
2
2
Compound 1e
0
5
0
0
0
0
-1.178 91 0.538 06 0.547 58 0.180 87 -0.382 01 0.087 32 -0.076 22 -168.3976 -1754.1825
-1.171 11 0.534 28 0.544 25 0.179 57 -0.378 47 0.086 74 -0.075 76 -168.3997 -1754.1976
-1.104 93 0.530 53 0.495 18 0.160 74 -0.340 69 0.081 28 -0.070 68 -168.4250 -1754.2161
II
I
I
Compound 1gb
0
5
0
-1.236 37 0.823 43 0.431 83 0.056 22 -0.345 69 0.074 71 -0.064 45 -158.8848 -1292.3778
-1.231 94 0.822 73 0.427 97 0.055 95 -0.343 45 0.074 31 -0.064 10 -158.8863 -1292.3785
-1.163 73 0.812 81 0.369 94 0.049 61 -0.308 33 0.068 28 -0.058 35 -158.9106 -1292.4070
II
I
I
Compound 1i
0
5
0
-1.175 75 0.493 97 0.716 34 0.048 37 -0.333 22 0.082 75 -0.072 86 -195.1525 -1605.7806
-1.170 04 0.492 91 0.711 34 0.048 27 -0.330 88 0.082 29 -0.072 37 -195.1545 -1605.7823
-1.105 63 0.488 24 0.649 97 0.044 36 -0.297 89 0.076 76 -0.067 37 -195.1867 -1605.8563
II
I
I
a
The energy effect Σ will be defined and used in the next section. b -N(Me)
cb
oV
2
group in 1g has been replaced with a planar -NH
2
.
A comparison of the data in Table 5 with the corresponding
(
p
π)-π
∆
∆
E
E
(θ) in Table 3 shows that the energy losses
(
b
π)-π
(π)-π
(θ) and ∆E
(θ) become larger while the absolute
c
bc
ba
cb
values of the Σ (θ) + Σ (θ) and the Σ (θ) increase with the
oV
oV
oV
geometry of 1h getting flatter. At the coplanar geometry, for
bc
oV
ba
oV
example, the Σ (0°) + Σ (0°) (-0.874 72 hartree) and
cb
Σ (0°) (-0.401 87) are most stabilizing, and the correspond-
ing ∆Eb (0°) (0.242 36) and ∆Ec (0°) (0.432 71) both are
oV
(π)-π
(π)-π
most destabilizing. In Table 4, there are seven sets of the data
cb
oV
listed in increasing order of the value of Σ (0°) in each of
seven compounds. Table 4 shows further that from compound
(
c
π)-π
1
a to 1i, the value of the ∆E
(0°) decreases as the absolute
cb
value of the Σ (0°) decreases. In molecule 1a, for example,
oV
cb
oV
the absolute value (|-0.4698|hartree) of the Σ (0°) and the
(
c
π)-π
value (0.3918 hartree) of the corresponding ∆E
(0°) both
are greatest, and the smallest values (|-0.3332| and 0.0484
hartree) of these two energies both occur in 1i. This comparison
also indicates that in a given geometry with the θ * 50°, a
(
p
π)-π
larger energy loss ∆E
(θ) corresponds to a larger value of
2
the Σ (θ). In the θ ) 0° geometry (Model I) of 1h, for
example, the value of the Σ (0°) decreases in the sequence:
Σ (0°) ) 0.135 70 hartree > Σ (0°) ) -0.017 46 > Σ (0°) )
0.118 24, and the value of the corresponding ∆E
p
2
p
2
a
2
2
b
c
Figure 6. Morokuma’s definitions of the FMO interactions between
fragments P and Q (P, Q ) A, B, C).
(π)-π
-
(0°)
p
(
a
π)-π
decreases in the same sequence: ∆E
(0°) ) 0.547 48
(0°) ) 0.242 36.
pq
fragments to the EX energy Σ . Referring to the method
(π)-π
(π)-π
c
oo
hartree > ∆Eb
(0°) ) 0.432 71 > ∆E
25
for calculating the gross AO’s charge, the EX energy might
oV
pq
pq
oo
pq
oo
Every π system with Σ (θ) < 0.0 is destabilized (except
(90°)), and which one is most destabilized depends
upon their values of Σ (θ).
p
be able to be divided evenly into two parts Σ ) (1/2)Σ
+
qp
(π)-π
b
(
1/2)Σ (Table 5); still we cannot say which fragment is a -M
group as far as the four-electron interaction is concerned.
∆E
oo
2

Conformations of Stilbene-like Species
J. Phys. Chem. A, Vol. 102, No. 11, 1998 2025
pq
oW
2
P
pq
oo
TABLE 5: CT Energies Σ , Net CT Energies Σ , EX Energies Σ Occurring in Five Typical Geometries (Model I) of 1h, and
(π)
the Net π-Electron Charge Dp on Each of Three Fragments (Energy in Hartrees)
θ ) 0°
θ ) 10°
θ ) 30°
θ ) 50°
θ ) 90°
Fragment A
ab
Σ
Σ
0
-0.490 32
0.135 70
0.162 41
-0.488 31
0.136 46
0.162 10
0.026 14
-0.495 35
0.147 20
0.166 66
0.026 60
-0.500 18
0.160 95
0.171 87
0.026 81
-0.503 93
0.180 64
0.177 42
0.027 03
oV
2
a
ab
oo
.5Σ
(
a
π)
0.026 22
D
Fragment B
ba
bc
oV
Σ
Σ
0
+ Σ
-0.874 72
-0.017 46
0.350 36
-0.856 96
-0.021 43
0.345 03
-0.749 94
-0.052 91
0.313 19
-0.580 52
-0.103 12
0.260 89
-0.325 57
-0.180 62
0.178 05
oV
2
b
ba
oo
bc
oo
.5(Σ + Σ )
(
b
π)
-0.013 49
-0.013 78
-0.016 43
-0.020 58
-0.027 12
D
Fragment C
cb
Σ
-0.401 87
-0.118 24
0.187 95
-0.390 08
-0.115 03
0.182 93
-0.307 50
-0.094 29
0.146 53
-0.183 46
-0.057 84
0.089 02
-0.002 27
0.000 60
0.000 63
0.000 09
oV
2
Σc
cb
oo
0
.5Σ
(
c
π)
-0.012 73
-0.012 36
-0.010 17
-0.006 23
D
Q
Q
σ
(π,σ)
π
and E (σ π,σ) in the
TABLE 6: QMRE of 1h, Its π and σ Components ∆Eπ and ∆E , Total π and σ Electronic Energies E
FUD State, and Their Changes with the Rotation of Fragment C (Energy in Hartrees)
angle (deg)
Q
Q
(π,σ)
π
(π,σ)
σ
θ
R
QMRE
∆Eπ
∆Eσ
E
E
0
0
0
0
0
0
0.008 44
0.008 23
0.006 94
0.004 89
0.002 87
-0.083 13
-0.084 98
-0.099 35
-0.125 24
-0.161 32
0.091 57
0.093 21
0.106 29
0.130 13
0.164 19
-134.661 80
-134.674 40
-134.772 34
-134.854 25
-134.851 51
-1167.965 79
-1168.006 13
-1168.319 01
-1168.357 51
-1167.805 82
3
3
3
2
50
30
10
70
a
a
a
Maximal absolute values.
TABLE 7: QMRE of Stilbene-like Species, and Their π and
occurring in six typical dSH geometries were calculated (Table
8). The dSH distortion was previously investigated by Shaik
and Hiberty. The geometries dSH * 0.0 Å arise from variations
Q
Q
σ Components ∆E and ∆Eσ at the Planar Geometry
π
(Hartrees)
28
Q
Q
in alternating CC bond lengths within the constraint that the
contribution of the nuclear repulsion to the total energy remains
constant, equal to that of the dSH ) 0.0 Å geometry. The dSH
) 0.1644 Å geometry resembles an idealized cyclohexatriene
structure of alternating single and double CC bond lengths
R′cc and Rcc (see Table 8). In our PMO calculation, a distorted
benzene molecule was dissected into three ethylenic fragments
A, B, and C. In each of three fragments, the length of the CC
compds
QMRE
∆Eπ
∆Eσ
1
1
1
1
1
1
1
a
j
h
e
f
i
g
0.014 10
0.009 41
0.008 44
0.007 77
0.007 70
0.006 84
0.006 30
0.009 27
-0.065 70
-0.083 13
-0.049 56
-0.055 59
-0.041 25
-0.083 24
0.004 83
0.075 11
0.091 57
0.057 37
0.063 29
0.048 09
0.089 54
The Quantum Mechanical Resonance Energy (QMRE) of
Stilbene-like Species Is Destabilizing. According to the
double bond was equal to that of the shorter R in the composite
system. Table 8 shows that the QMRE is most stabilizing at
the dSH ) 0.0 Å geometry and monotonically weakens as the
carbon framework is increasingly distorted away from the dSH
) 0.0 Å. At the dSH ) 0.0 Å geometry, for example, the QMRE
is -43.28 kcal/mol, and it is the average of the spectroscopy
cc
2
6
original definition, the QMRE of a delocalized system in a
given geometry of benzene is the difference between the energy
of the true ground state and the energy of a single Kekule
structure. In this work, it is defined as the difference in the
electronic energy between the FUD and DSI states. As shown
by Tables 6 and 7, the QMRE of each of STB-type 1 is
destabilizing. The QMRE (0.008 44 hartree) of 1h, for example,
is most destabilizing at its planar geometry (Table 6), and its
value monotonically decreases with the rotation of fragment C.
A comparison of the data in Table 7 with those in Table 4 and
Table 1 shows that of all molecules listed in the tables, a larger
QMRE (>0.008 hartree), such as those 0.0141, 0.0094, and
2
9a
29b
value (-50 kcal/mol) and that (-36 kcal/mol) suggested
by thermochemical measures. However, the detail energy
partition shows that the QMRE is a sum of two components
Q
(π,σ)
(σ)
Q
(π,σ)
(σ)
∆
Eσ ) Eσ - Eσ and ∆Eπ ) Eπ - E . Whether the
QMRE is stabilizing or destabilizing depends upon the response,
expressed in terms of the ∆E (dSH) and ∆E (θ), respectively,
π
Q
σ
Q
σ
of the σ frameworks to the delocalization of the π-electrons. In
Q
σ
the case of STB-type 1, ∆E (θ) is always destabilizing and its
0
.0084 hartree, respectively, in 1a, 1j, and 1h (Table 7)
cb
value is slightly larger than the absolute value of the corre-
corresponds generally to a larger Σ (0°) and to a larger sum
oV
Q
sponding ∆E (θ) which is generally stabilizing except for that
π
(
φ + R > 35°) (Table 1).
Q
σ
27
in 1a. Conversely, the ∆E (dSH), as shown by the data in
Table 8, is always stabilizing, and the ∆E (dSH) is generally
It is known that benzene is strongly stabilized by the QMRE.
Q
π
In order to make a comparison between the QMREs of benzene
and molecules of type 1, and to understand the role of the
QMRE with regard to molecular geometry and chemical
reactivity, the distortion of the benzene geometry, denoted as
dSH, is considered in this work, and the various energies
destabilizing except that in the dSH ) 0.0 Å geometry
of benzene. Particularly, the absolute value (|-0.0533|hartree)
Q
σ
of the ∆E
(dSH ) 0.0) is about three time larger than that
Q
(|-0.0177|hartree) of the ∆E (0.0). Therefore, it is the σ
π

2026 J. Phys. Chem. A, Vol. 102, No. 11, 1998
Yu et al.
TABLE 8: QMRE (kcal/mol) of Benzene, Its Components ∆E and ∆E , Electronic Energies E and E (σ σ) in the DSI State,
Q
π
Q
σ
(σ)
π
(π,σ)
(π,σ)
Those Eπ and Eσ in the FUD State, and Their Changes along the dSH Distortion (Energy in Hartrees except for QMRE)
d
SH (Å)
0.0
0.0403
0.0811
0.1224
0.1644
0.2070
R
R
cc (short)
cc (long)
1.40 Å
1.40 Å
-43.281 875
-0.017 645
-0.051 329
39.744 438
391.040 527
1.38
1.4203
1.36
1.4411
1.34
1.4624
1.32
1.4844
1.30
1.5070
QMRE
∆
∆
E
E
E
E
-31.083 080
0.001 388
-0.050 922
-39.765 388
-391.036 011
-39.764 000
-391.086 914
-20.865 963
0.015 810
-0.049 062
-39.786 453
-391.029 022
-39.770 645
-391.078 094
-12.554 593
0.026 050
-0.046 057
-39.807 735
-391.020 599
-39.781 689
-391.066 681
-5.868 474
0.0328 05
-0.042 157
-39.827 721
-391.001 709
-39.794 918
-391.043 884
-0.626 882
0.036 767
-0.037 766
-39.847 374
-390.978 485
-39.810 608
-391.016 266
Q
E
E
π
Q
σ
(
σ)
-
-
-
-
π
(
σ)
σ
(
π,σ)
39.762 085
391.091 858
π
(
π,σ)
σ
TABLE 9: Occupied π MOs and Energy Changes along the dSH Distortion (Energy in Hartrees)a
d
SH (Å)
0.0
0.0403
0.0811
0.1224
0.1644
0.2070
DSI State
-0.339 77
2
1st (HOMO)
-0.331 63
-0.335 56
-0.344 28
-0.349 04
-0.354 10
FUD State
-0.281 37
-0.453 27
2
1
1st (HOMO)
7th
-0.278 24
-0.453 21
-0.279 02
-0.453 21
-0.285 13
-0.453 44
-0.290 10
-0.453 75
-0.296 09
-0.454 29
a
In the DSI state, three occupied π MOs, 21st, 20th, and 19th, are degenerate. There are doubly degenerate levels, 21st and 20th, in the FUD
state.
T
(π)
(σ)
e W
σ
TABLE 10: Total Electronic Energy E , Nuclear Repulsion E , Total Molecular Energy E , Potential Energies REπ and RE ,
(σ)
(σ)
and Electronic Energies E and Eσ in the DSI State of Five Typical Geometries of 1h (Energy in Hartrees)
π
(
π
π)
RE (σ σ)
(σ)
π
(σ)
σ
ET
θ (deg)
RE
E
E
E
e
RE
e
E
V
Model I of Optimizing
0a
0.0000
-0.0149
-0.0827
-0.1360
-0.0957
0.0000
-0.0434
-0.2531
-0.1243
0.6393
-134.5778
-134.5902
-134.6510
-134.6682
-134.5876
-1168.0484
-1168.0918
-1168.3015
-1168.1727
-1167.4091
-1302.6175
-1302.6718
-1302.9333
-1302.8076
-1301.9436
0.0000
-0.0543
-0.3158
-0.1901
0.6739
740.5334
740.5874
740.8477
740.7220
739.8610
-562.0842
-562.0844
-562.0855
-562.0856
-562.0826
3
3
3
2
50
30
10
70
a
T
The referential geometry for the calculations of the potential energies. The energies E
V
, E
e
, and E were obtained from full SCF computation
at the STO-3G level.
(
π
π,σ)
framework for the dSH ) 0.0 Å geometry to be strongly
the E (θ) in Table 6, is in accordance with the chemical
30
stabilized by the QMRE. Benzene is σ aromatic. On the other
feature that the π systems of benzene and STB-type 1 both are
reactive toward electronphilic attack. However, the high
stability of benzene due to the ∆E (0.0) < 0.0 (-32.21 kcal/
mol) is getting weaker while its π-system is increasingly
localized under the electrophile attacking. In the transition state,
the σ-framework of benzene is reluctant to undergo addition
reaction and has to opt for “aromatic” substitution instead in
order to maintain its original σ-aromaticity. On the other hand,
STB-type 1 are willing to undergo addition reaction owing to
their ∆E (θ) > 0.0. During the period of preparing 1i, we
(
π
π,σ)
(π,σ)
hand, the π potential energy RE (0.0) ) Eπ (0.0) -
(π,σ)
Q
σ
E
(0.1644) is large, up to 20.6 kcal/mol (Table 8), revealing
π
that the π-system of benzene is destabilized, and it prefers a
31
distorted geometry.
In the DSI state of benzene, the differences dE (dSH) )
(
σ)
σ
(
σ)
(σ)
o
SH
(σ)
(σ)
E (dSH) - E (d ) < 0.0, dE (dSH) ) E (dSH) -
σ
σ
π
π
(
π
σ)
o
o
E (d SH) > 0.0 when dSH < d , and the absolute value of the
SH
(σ)
(σ)
π
(σ)
dE (dSH) is less than that of the dE (dSH). The dE (dSH)
σ
σ
Q
σ
between the dSH ) 0.0 and 0.1644 Å geometries is, for example,
(
π
σ)
-
24.359 kcal/mol, and the corresponding dE (dSH) is large up
found that the -CHdN- double bond is very unstable in its
alcohol solution; the addition product is 2-ethoxyl-2-(4-nitro-
phenyl)-N-(2-pyrimidyl)ethylamine.
to 52.261 kcal/mol. The σ-framework in the DSI state only
possesses a distortive tendency. It is the π delocalization to
make this tendency become an effective driving force, expressed
σ Interaction Is a Main Driving Force for Out-of-Plane
Twist. The electronic energy of the DSI state is the lowest of
four hypothetical states. In this state, all the elements, such as
(
σ
π,σ)
(π,σ)
(π,σ)
o
in terms of the dE (dSH) ) [Eσ (dSH) - Eσ (d )] whose
SH
(
π,σ)
absolute value is now larger than that of the dE (dSH) )
π
(
π
π,σ)
(π,σ)
o
SH
E
(dSH) - Eπ (d ), for distorting the dSH * 0.0 Å toward
the symmetrical geometry. The dEσ (dSH ) 0.0) between
the dSH ) 0.0 and 0.1644 Å geometries is, for example, -30.104
kcal/mol, and the corresponding dEπ (0.0) ) 20.603 kcal/
mol.
(σ)-π
(σ)-π
(σ)-π
F
, Hij , and Dij
(i * j) corresponding to those in eqs
(π,σ)
ij
31
(3-1)-(3-2), are equal to zero. Therefore, the potential energy,
denoted as RE (θ) ) E (θ) - E (0°), is useful for analyz-
ing the molecular conformation. In the region of the θ from 0
to about 40°, the absolute values of the various energies in 1h,
(σ)
σ
(σ)
σ
(σ)
σ
(π,σ)
Table 9 shows further that in a given dSH geometry, the energy
of the highest occupied MO (HOMO) of the π type in the FUD
state is always higher than that in the DSI state. Along the dSH
distortion, the energy, about -0.278 24 hartree, of the HOMO
is highest at the dSH ) 0.0 Å geometry. This energy character,
(
σ
σ)
(π)
π
such as the E (θ), Ee(θ) (Table 10), and E (θ) (Table 3),
increase concurrently as the nuclear repulsion EV (Table 10)
becomes larger. In a given conformer, the absolute value of
(
σ)
RE (θ) is generally three times larger than that of the
RE (θ), and it is very close to that of the REe(θ). The
σ
(
π
π,σ)
(π)
together with those indicated by the E (dSH) in Table 8 and
π

Conformations of Stilbene-like Species
TABLE 11: Total σ-Electronic Energy E in the DSI
J. Phys. Chem. A, Vol. 102, No. 11, 1998 2027
(
σ
σ)
Summary
(σ)
States, Net σ-Electron Charge D and the Ratio, de/dW, of
c
We have been successful in separating σ from π FMOs based
on our new procedure. Besides the well-known resonance
interaction between fragments, the σ-electron interaction, arising
from the effect of the π-electron delocalization on the σ-π space
interactions, is also stabilization. However, the delocalization
of the π-electrons in the DPI state not only reduces the original
π energies in fragments, but also the energy gains are insufficient
to compensate for the energy loss. The π-electron delocalization
in the DPI state is found to be destabilization. As a result, the
DPI state is most destabilized at a coplanar geometry, and, in
a given geometry, its electronic energy is highest of four
hypothetical states. The characteristic of the QMRE depends
upon the response of the σ framework to the π delocalization.
In the case of stilbene-like species, the QMRE is destabilizing.
On the other hand, the QMRE of benzene is stabilizing.
However, it is the σ framework, rather than the π system itself,
which is strongly stabilized by the QMRE, revealing that
benzene is σ aromatic.
(
σ
σ)
the dE to dE
W
(Energy in Hartrees)
(
σ
σ)
(σ)
θ (deg)
E
Dc
de/dV
-0.82
-0.80
-0.78
-0.82
-0.74
-0.69
1
h
0
5
-1168.0484
-1168.0606
0.109 37
0.109 51
1
i
0
5
-1606.5901
-1606.5965
0.091 59
0.091 74
1
g
0
5
-1293.1949
-1293.1985
0.101 49
0.101 58
1
j
f
0
5
-1167.5517
-1167.5543
0.125 02
0.125 15
1
0
5
-1589.1171
-1589.1206
0.112 83
0.112 95
1
e
Contrary to the viewpoints in the literature, the driving forces
for the out-of-plane twist of stilbene-like species are due to the
σ orbital interaction and the QMRE. It seems that the electron-
withdrawing (-I) groups on the aromatic ring and the ring-
nitrogen atoms, has an obvious influence on the twist angle.
0
5
-1754.9791
-1754.9830
0.109 45
0.109 56
(
σ
σ)
RE plays a predominant role in determining the preferential
geometry of 1h.
In flexible molecules such as STB-type 1, it is difficult to
determine which pair of the atoms makes the greatest contribu-
tion to the driving force. According to the definition EV ) ΣiΣj-
Experimental Section
General Methods. All starting materials were obtained
commercially as reagent grade. Melting points were determined
on a Nagoya apparatus and are uncollected. H NMR spectra
were recorded on a Varian Unity 200 NMR spectrometer.
Crystal structures of molecules were determined by a Nicolet
R3WE X-ray diffractometer. The crystal data of each of the
following eight compounds are listed in Table 12.
(
eiej/rij), EV can be, indirectly, used to characterize the interaction
distance between fragments, and the quantity de/dV in eq 7 can
be defined as a generalized driving force for the out-of-plane
twist.
1
(
σ
σ)
(σ)
σ
de/dV ) [E (5°) - E (0°)]/[E (5°) - E (0°)]
(7)
V
V
N-(4-Chlorophenyl)methylene-2-pyridineamine (1e) was
32
Comparison of the values of de/dV in Table 11 and those of the
angle φ in Table 1 shows that a larger absolute value (>0.80)
of the de/dV corresponds to a larger twist angles φ (>30°). The
prepared from 4-chlorobenzaldehyde and 2-pyridineamine: mp
1
96-99 °C; H NMR (CDCl ) 9.12 (s, 1H), 8.56 (d, 1H), 7.18-
3
7.92 (m, 7H).
(σ)
calculations for the net σ electronic charge D (θ) of fragment
N-(4-Nitrophenyl)methylene-2-pyridineamine (1f) was pre-
pared from 4-nitrobenzaldehyde and N-(triphenylphosphora-
c
C (Table 11) show that, in the three typical molecules, the values
(
c
σ)
(σ)
(σ)
32
1
of the dD ) D (5°) - D (0°) are in the sequence: 1.5 ×
nylidene)-2-pyridineamine: mp 147-148 °C; H NMR (CDCl3)
c
c
-
4
1
0
(1i with a -NO2 group and two ring-nitrogen atoms) >1.4
9.27 (s, 1H), 8.58 (d, 1H), 8.38-7.25 (m, 7H).
-
4
×
10 (1h with a ring-nitrogen atom on fragment C) >1.3 ×
N-(4-N,N-Dimethylaminophenyl)methylene-2-pyridine-
amine (1g) was prepared from 4-N,N-dimethylbenzaldehyde and
-
4
1
0
(1j with a ring-nitrogen atom on fragment A), and their
respective values of the angle φ are 50 (1i) > 38 (1h) > 35°
1j). It seems that the electron-withdrawing (-I) groups and
3
2
1
2-pyridineamine: mp 123-124 °C; H NMR (CDCl3) 9.1 (s,
(
1H), 8.50 (d, 1H), 7.9-6.8 (m, 7H), 3.2 (s, 6H).
the ring-nitrogen atoms have an obvious influence upon the twist
angle.
N-(4-Nitrophenyl)methylene-2-pyrimidineamine (1i) was
prepared from 4-nitrobenzaldehyde and N-(triphenylphospho-
TABLE 12: Crystal Data of Four Stilbene-like Molecules 1 and Four Ketenimine Derivatives 2a
1f 1g 1i 2a 2b
1e
2c
2d
formula
C
12
H
9
ClN
2
C
12
H
9
N
O
3 2
C
14
H
15
N
3
C
11
H
8
N
4
O
2
C
20
H
15
N
C
20
H
14
N
2
O
2
C
22
H
18
N
2
O
4
22 20 2
C H N
fw
color
a
b
c
216.66
colorless
6.509
227.220
yellow
7.096
28.754
10.969
90.000
106.500
90.000
2145.9
1.407
225.290
yellow
11.923
17.914
12.059
90.000
103.990
90.000
228.210
yellow
6.015
13.393
25.572
90.000
90.000
90.000
269.00
yellow
20.594
8.753
17.471
90.000
101.698
90.000
3083.900
1.158
314.330
red
7.972
374.380
312.400
yellow
9.919
12.838
14.010
90.000
90.000
90.000
13.439
9.429
15.099
90.000
93.171
90.000
1910.400
1.302
4
8.005
18.951
11.062
90.000
106.911
90.000
1598.900
1.306
4
20.383
90.000
98.270
90.000
1051.000
1.369
R
â
γ
U
2499.300
1.197
8
2060.100
1.472
8
1785.000
1.162
4
D
Z
x
4
8
8
absorp coeff
space group
0.328
0.100
0.073
0.086
0.091
0.064
P2 2 2
1 1 1
P2
1
/n
P2
1
P2
, g/cm ; absorption coefficient, cm-1.
x
1
/c
C2/c
P2
1
/n
P2
1
/n
a
3
3
Units: R, â, and γ, deg; U, Å ; D

2028 J. Phys. Chem. A, Vol. 102, No. 11, 1998
Yu et al.
ranylidene)-2-pyrimidineamine:32 mp 236-238 °C; H NMR
1
(10) Brown, C. J. Acta Crystallogr. 1966, 21, 146.
(
(
11) Wiebcke, M.; Mootz, D. Acta Crystallogr. 1982, B38, 2008.
12) Stewart, J, J. P. MOPAC; Frank J. Seiler Research Laboratory, U.S.
(
CDCl3) 9.33 (s, H), 8.84 (d, 2H), 7.29-8.40 (m, 6H).
N-(Diphenylethenylidene)benzeneamine (2a) was obtained
Air Force Academy, 1990; Version 6.
as bright yellow crystalline from phenyl isocyanate and (diphe-
(13) (a) Bernstein, J.; Schmidt, G. M. J. Chem. Soc., Perkin Trans. 2
1972, 951. (b) Bernstein, J.; Anderson,T. E.; Eckhardt, C. J. J. Am. Chem.
Soc. 1979, 101, 541.
nylmethylene)triphenylphosphorane:33 mp 55-56 °C; 1H NMR
(CDCl3) 7.32-7.40 (m, Ar-H).
(
14) Yu, Z. H. Comput. Chem. 1994, 18, 95.
N-(Diphenylethenylidene)-4-nitrobenzeneamine (2b) was
(15) Kitaura, K.; Morokuma, K, Int. J. Quantum Chem. 1976, 10, 325.
obtained as a red crystal from triphenylphosphine, bromine,
(16) (a) Dewar, M. J. S.; Harget, A. J.; Trinajstic, N.; Worley, S. D.
Tetrahedron 1970, 26, 4505. (b) Hess, B. S. A.; Schaad, L. S.; Holyoke,
C. W. Tetrahedron 1975, 31, 295. (c) Katritzky, A. R.; Barczynski, P.;
Musumarra, G.; Pisano, D.; Szafran, M. J. Am. Chem. Soc. 1989, 111, 7.
(17) Libit, L; Hoffmann, R. J. Am. Chem. Soc. 1974, 96, 1370.
(18) Kollmar, H. J. Am. Chem. Soc. 1979, 101, 4832.
3
4
triethylamine, and N-(4-nitrophenyl)diphenylacetamide: mp
1
8
7
4-86 °C; H NMR (CDCl3) 8.27 (d, 2H), 7.45 (d, 2H), 7.28-
.40 (m, 10H).
N-(Bis(4-methoxyphenyl)ethenylidene)-4-nitrobenzene-
(
19) Dewar, M. J. S.; Dougherty, R. C. The PMO Theory of Organic
Chemistry; Plenum Press: New York and London, 1975.
20) (a) Cszmadia, I. G. Molecular Structure and Conformation,
amine (2c) was obtained using the same procedure for preparing
1
2
a. It was obtained as red crystals: mp 103.5-105.5 °C; H
(
NMR (CDCl3) 6.92, 7.24 (2d, 8H), 7.44, 8.26 (2d, 4H), 3.82
Progress in Theoretical Organic Chemistry; Elsevier: Amsterdam, 1982;
Vol. 3. (b) Whangbo, M. H.; Schlegel, H. B.; Wolfe, S. J. Am. Chem. Soc.
(s, 6H).
1
977, 99, 1296. (c) Kost, D.; Schlegel, H. B.; Mitchell, D. J.; Wolfe, S.
Can. J. Chem. 1979, 57, 729.
21) M u¨ ller, M.; Hohlneicher, G. J. Am. Chem. Soc. 1990, 112, 1273.
N-(Diphenylethenylidene)-4-(N,N-dimethylamino)benzene-
amine (2d) was obtained using the same procedure for preparing
(
1
2
(
a. It was obtained as yellow crystals: mp 90-92 °C; H NMR
(22) Dewar, M. J. S. The Molecular Orbital Theory of Organic
Chemistry; McGraw-Hill: New York, 1969; p 70.
CDCl3) 6.69 (d, 2H), 7.20-7.36 (12H, m), 2.98 (s, 6H).
(23) Bader, R. F. W.; Streitwieser, A.; Neuhaus, A.; Laidig, K. E.;
Acknowledgment. This work was supported by the National
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