Thermal irreversibility study on the electrocyclic reaction ofdiaryl maleic anhydrides by density functional calculations
Yue Liu a,b,*, Qi Wang a, Ying Liu b, Xiao-Zhen Yang c
a National Key Laboratory of Tunable Laser Technology, Institute of Opto-Electronics, Harbin Institute of Technology,
Harbin 150001, PR Chinab Department of Chemistry, Harbin Normal University, Harbin, Heilongjiang Province, Harbin 150080, PR Chinac Polymer Physics Laboratory, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100080, PR China
Received 11 December 2002; in final form 14 April 2003
Abstract
Photochromic materials are now anticipated as promising candidates for erasable memory media of the next gen-
eration because organic materials are easy to tailor. Density Functional calculations at the B3LYP/6-311+G(d,p)//HF/
3-21G and partly at the B3LYP/6-311++G(3df,3pd)//B3LYP/6-31G(d) levels were carried out for thermal irreversibility
study of the titled compounds, a kind of photochromic materials which undergo cyclization and cycloreversion reac-
tions. Eighteen configurations were characterized for both the cis and the trans forms of three diarylethene-type
compounds. Among them, six were transition states. The results from the relative energy barriers and from the normal
coordinate analyses of the imaginary frequencies show that Woodward–Hoffman principle about disrotatory and
conrotatory mechanisms is valid for the thermal irreversibility study on the compounds. The thermal irreversibility of
changing phenyl to thiophenyl groups in stilbene, of introducing methyl groups on central carbons that were re-
sponsible for the electrocyclic reaction was discussed. The applicability of Irie�s rule was investigated.� 2003 Elsevier Science B.V. All rights reserved.
1. Introduction
Photochromism is a reversible transformation in
a chemical species between two forms by means ofphotoexcitation. One of the tasks to be achieved is
to design thermal irreversible photochromic com-
pounds. The diarylethene-type compound [1], such
as 2,3-diphenylmaleic anhydride (1o), 2,3-bis(4-
methylthiophen-3-yl)maleic anhydride (2o), 2,3-bis
(2,4-dimethylthiophen-3-yl)maleic anhydride (3o),
or 2,3-bis(2,4,5-trimethylthiophen-3-yl)maleic an-
hydride (4o), is the photochromic material that hastwo forms connected by the photocyclization re-
action shown in Scheme 1 (numerical number for
compound, o for open-ring form, and c for ring-
closed form).
Stilbene, a kind of photochromic material, can
undergo photocyclization reaction to produce di-
hydrophenanthrene. However the dihydrophe-
nanthrene returns to stilbene in the dark in adeaerated solution. In the presence of air the
Chemical Physics Letters 373 (2003) 338–343
www.elsevier.com/locate/cplett
* Corresponding author. Fax: +08604516416060.
E-mail address: [email protected] (Y. Liu).
0009-2614/03/$ - see front matter � 2003 Elsevier Science B.V. All rights reserved.
doi:10.1016/S0009-2614(03)00628-6
dihydrophenanthrene irreversibly converts to
phenanthrene by hydrogen-elimination reaction
with oxygen [2–4]. When the 2- and 6-positions of
the phenyl rings in stilbene are substituted with
methyl groups, the elimination reaction is sup-
pressed and the compound undergoes a reversiblephotocyclization reaction even in the presence of
oxygen. The lifetime of the colored dihydro-type
isomer of 2,3-dimesityl-2-butene is still very short.
Such a thermally unstable photochromic system is
not useful for optical memories and switches [1].
By replacing the phenyl rings of stilbene with
thiophene rings the lifetimes of the dihydro-type
intermediates are prolonged [5]. But their prop-erties have still not met the application needs for
photonic devices. Although there are many re-
searches in the field, little theoretical work was
carried out on the real photochromic compounds
at ab initio level. In order to get a guiding prin-
ciple for molecular design of thermally irreversible
photochromic compounds, Irie and Nakamura [6]
studied the cyclization of 1,2-bis(3-furyl)ethane(5), 1,2-bis(3-thienyl)ethane (6), 1,2-diphenyleth-
ene, and 1,2-bis(3-pyrrolyl)ethane (7) from Wood-
ward–Hoffman rule by MNDO semiempirical
calculations. Based on the analysis of the energy
difference between the ring-closed and the open-
ring forms among the compounds, they suggested
a rule that the energy barrier of the cycloreversion
reaction become small and the thermal reaction beexpected to take place readily if the colored ring-
closed form had an energy much higher than the
open-ring form; the energy barrier become large if
the energy difference of the two forms became
small.
2. Computational details
2.1. Principle
For the discussion on thermal aspects of the
cyclization and the cycloreversion reaction in di-
arylethene type compound, it is reasonable to refer
to the principle of Woodward–Hoffman. Accord-
ing to the principle, a conrotatory cyclization orcycloreversion reaction is brought about by light
and a disrotatory reaction by heat for hexatriene
or cyclohexadiene which is the central part of the
compound among 1 to 3 as shown in Scheme 1.
The conrotatory mechanism requires C2 symmetryfor each of the configuration involved, i.e., for the
configuration of the open-ring form, the ring-
closed form, and the transition state connecting
the two forms in the reaction (here after these
configurations are denoted as trans forms).
ðOpened formÞtrans �hm ðTSÞtrans �hm0 ðClosed formÞtrans
ð1ÞThere would involve symmetry breakage for the
conrotatory mechanism of hexatriene or cyclo-
hexadiene by thermal reaction. The difficult is
overcome by photon excitation from the principle
of Woodward–Hoffman. But this aspect of photon
excitation has not been investigated in the present
thermal irreversibility study. The disrotatory
mechanism requires mirror symmetry (Cs) of the
species concerned (the configurations involved aredenoted as cis forms). The focus would be on the
cis forms for thermal reactions.
ðOpened formÞcis �D ðTSÞcis �D ðClosed formÞcis
ð2Þ
2.2. Computational details
Thermal irreversibility for the cyclization andcycloreversion reactions of compounds 1–3 was
discussed. The study was carried out by GAUS-AUS-
SIANSIAN 98 [7]. A total of 18 configurations for both
cis and trans forms of compounds 1–3 had been
fully optimized without symmetry constraints,
though the initial structures for the optimizations
Scheme 1. The open- and the closed-ring forms of the bis(thi-
ophenyl)maleic anhydrides.
Y. Liu et al. / Chemical Physics Letters 373 (2003) 338–343 339
were adopted as cis or as trans configurations.
Among them, six were transition states. The ge-
ometries for the cis forms of compounds 2 and 3
were also optimized with strict Cs constraint. The
structures 2c(s), 3c(s), and 3o(s) of the cis forms,
which are corresponding to the cis forms of 2c, 3c,and 3o,respectively, are transition states obtained
by Berny optimization with strict Cs symmetry
constraint for local minimum searching at B3LYP/
6-31G(d) level. They are transition states obvi-
ously because of the congestion within each
structure. The less congested cis structure 2o(s) is a
local minimum and is not deviate from the cis
form of 2o very much. The corresponding vibra-tion frequencies of the two structures are also al-
most the same. And the energies of the two
structures are almost the same (Fig. 1). The
structures of the cis transition states 2TS(s) and
3TS(s) are almost the same as the cis 2TS and 3TS,
respectively. The energy differences for the cis
2TS(s) and 2TS, and 3TS(s) and 3TS are 0.0021
and 0.0033 kJ/mol at B3LYP/6-31G(d) level, re-spectively. The imaginary frequencies for the cis
2TS, 3TS, 2TS(s), 2c(s), 3TS(s), 3c(s), and 3o(s)
are 376i, 314i, 376i, 43i, 315i, 55i, and 37i cm�1 at
B3LYP/6-31G(d) level, for cis 1TS is 736i cm�1
and for the trans 1TS, 2TS, 3TS are at 3648i,
2038i, and 1596i cm�1 at HF/3-31G level, respec-
tively.
The cis transition states, 2c(s), 3c(s), and 3o(s),
screw to either side to break the Cs symmetry to
form the two geometrically degenerate forms of cis
2c, 3c, and 3o, respectively (Fig. 2).
All of the calculations for the trans and cis
structures optimized without symmetry constraintwere given first at the B3LYP/6-311+G(d, p)//HF/
3-21G level. And then for the cis species of com-
pounds 2 and 3 calculations were also carried
out at the B3LYP/6-311++G(3df,3pd)//B3LYP/
6-31G(d) level to confirm the results obtained at
the above lower level. Frequency and intrinsic re-
action coordinate (IRC) analyses were carried out
to verify that there is one and only one imaginaryfrequency for each transition state and that the
desired reactant and product are connected by the
transition state concerned. The normal coordi-
nates of the imaginary frequencies for the cis 2TS
and 3TS show that the cis 2TS and 3TS are re-
sponsible for the disrotatory reaction. And the
normal coordinates of the imaginary frequencies
for the trans 2TS and 3TS show that the trans 2TSand 3TS are responsible for conrotatory reaction.
If the trans TS can be reached by some ways, the
reaction would be proceeded by conrotatory
mechanism. The vibration corresponding to the
imaginary frequency for both the cis and the trans
transition state of any diarylethene type com-
pound studied is similar to the resonance between
the open and the close ring forms of the cis or thetrans structures, respectively, or to the resonance
between the central hexatriene moiety and the
central cyclohexadiene moiety of the cis or the
Fig. 1. The relative energies, respectively, to the cis 2o or 3o for
various cis species corresponding to the cis forms of 2 or 3 at the
B3LYP/6-31G(d) level.
Fig. 2. The sketched reaction path involved in the cis forms of
species 3.
340 Y. Liu et al. / Chemical Physics Letters 373 (2003) 338–343
trans compound, respectively. The result of fre-
quency analyses for the imaginary frequencies is
the main evidence that the principle of Wood-
ward–Hoffman could be applied approximately to
the cyclization and cycloreversion reaction of di-
arylethene type compound.
2.3. Transition state optimizations
From the initial HF/3-21G geometries of the
products, the reactants, and the TSs [8] the TS
geometries for the cis 2TS and 3TS at the B3LYP/
6-31G(d) level were obtained by Synchronous
Transit-Guided Quasi-Newton approach with thecalculations for the force constants at every point
in the optimization. The optimizations that started
with an initial guess for the second derivative
matrix derived from a simple valence force field
and the approximate matrix is improved at each
step of the optimization using the computed first
derivatives were proved unsuccessful.
3. Results and discussion
The energy differences (Table 1) between the cis
and the trans configurations optimized without
symmetry constraint for the open-forms of 1o, 2o,
and 3o are 15.9, 6.2, and 1.2 kJ/mol at the B3LYP/
6-311+G(d,p)//HF/3-21G level, respectively. Thismeans that the cis and the trans configurations,
which are responsible, respectively, for the heat and
the light initiated reaction, of compounds 1o, 2o,
and 3o can be converted easily between the cis and
the trans by rotation around the C2–C30 and the
C3–C300 bonds in the open-ring forms (Scheme 1)
ðOpened formÞcis � ðOpened formÞtrans ð3Þ
When the cis form is consumed by the thermal
reaction the trans form will be converted partially
to the cis form. Whether the reaction takes a dis-
rotatory or a conrotatory mechanism is decided
entirely by whether heat or light is applied, con-firming Woodward–Hoffman principle.
The result about disrotatory and conrotatory
gotten from the energy barriers with no symmetry
constraint optimization for diarylethene type
compound is equivalent to the result gotten from
Woodward–Hoffman principle for triene or cyclo-
diene. The disrotatory reaction mode for each of
the cis compounds 1–3 has a smaller energy barrierthan the conrotatory reaction mode for the trans
form (Table 1), conforming Woodward–Hoffman
principle from the energy barriers that the thermal
reaction is undergone by a disrotatory mechanism.
The reaction barriers for the thermal cycloreversion
reactions (52.6 and 77.7 kJ/mol at the B3LYP/
6-311+G(d,p)//HF/3-21G level) of the cis forms 2o
and 3o are higher than that of the cis 1o, confirmingthe experimental result that the thermal irreversible
property is improved when the phenyl rings of
stilbene is replaced by thiophenyl rings. The cy-
cloreversion energy barrier for the cis compound 3
has a higher value for disrotatory reaction than that
of for the cis compound 2 (Table 1 at the B3LYP/
6-311+G(d,p)//HF/3-21G level, Table 2 and Fig. 1
at the B3LYP/6-31G(d) level, and Table 2 at theB3LYP/6-311++G (3df,3pd)//B3LYP/6-31G(d) le-
vel), conforming the fact that changing R (as shown
in Scheme 1) from the hydrogen atom to the methyl
group would give a more thermal irreversible
compound.
Table 1
Relative energies calculated for the optimized species without symmetry constraint at the B3LYP/6-311+G(d,p)//HF/3-21G level
(kJ/mol)
1 2 3
Cis Trans Cis Trans Cis Trans
E[o(cis)])E[o(trans)] 15.92 6.16 1.24
E(c))E(o) 186.08 171.76 65.66 25.55 114.61 60.55
E(ts))E(o) 207.98 295.49 118.24 211.03 192.34 239.97
E(ts))E(c) 21.90 123.73 52.58 185.48 77.72 179.41
Y. Liu et al. / Chemical Physics Letters 373 (2003) 338–343 341
From the consideration of orbital symmetry bytaking the central moiety of diarylethene type
compound as an isolated hexatriene, the conrota-
tory mechanism is impossible for thermal reaction.
As the trans species were optimized with no sym-
metry constraint at the HF/3-21G level, it is diffi-
cult to assign symmetry to orbital. In fact the
reaction may take place deviate from C2 symmetry
along the reaction path for the trans species. Forspecies without symmetry the orbital is a mixing of
the A and the B symmetry. The Woodward–
Hoffman forbidden rule could thus be weakened
just as the forbidden transition was lifted in a
spectrum. Apart from the orbital symmetry con-
sideration, it could also be concluded that the
conrotatory mechanism is disfavored by compar-
ing the energy barriers if the thermal reaction waspossible via conrotatory mechanism by some
ways, e.g., substituent effect. As the p conjugated
system extends to the thiophenyl and the anhy-
dride groups, the orbital symmetry for the central
hexatriene moiety is altered. Since the whole
molecule of each specie do not in one plane, some
p orbitals are a hybrid of the s and p orbitals(Scheme 2).Despite of all these effects, the number of oc-
cupied orbitals, respectively, with the symmetry A0
and the symmetry A00 is invariant within the whole
path from o(s) through TS(s) to c(s) for cis species
of 2 and 3 under strict Cs symmetry.
If the Woodward–Hoffman thermal forbidden
rule could be lifted for the trans diaryl maleic an-
hydrides by some asymmetry reaction path, thenIrie�s rule could be discussed also by comparingthe relative energies involving the cis and the trans
forms, since Irie�s rule only involves the relativeenergy of the closed and the opened forms in
speculating reaction barriers. From Table 1 of the
relative energies calculated, it could be concluded
that Irie�s rule holds true for comparing the pro-cesses involving the cis and the trans forms withineach compound 1, 2, or 3, respectively. That is,
within each compound the higher the energy of the
ring-closed form, c, the lower the energy barrier
for cycloreversion reaction. Compared with the
energies of their opened form, the ring-closed
forms have lower energies, 171.8, 25.6, and 60.6
kJ/mol for the trans forms (comparable if the
thermal reactons could also be via the conrotatorymechanism) than those for the cis forms, 186.1,
Scheme 2. The reaction path for the electrocyclic reaction of the cis 3.
Table 2
Relative energies calculated for cis form of compounds 2 and 3
optimized without symmetry constraint at higher levels (kJ/
mol)
2a 3a 2b 3b
E(c))E(o) 54.61 109.79 78.20 121.45
E(ts))E(o) 117.23 195.49 132.99 208.69
E(ts))E(c) 62.62 85.70 54.80 87.24
aValue calculated at the B3LYP/6-31G(d) level.b Value calculated at the B3LYP/6-311++G(3df,3pd)//
B3LYP/6-31G(d) level.
342 Y. Liu et al. / Chemical Physics Letters 373 (2003) 338–343
65.7, and 114.6 kJ/mol, respectively, of 1, 2, and 3.
The energies barriers responsible for the processes
involving the trans forms, 123.7, 185.5, and 179.4
kJ/mol, are higher than those involving the cis
forms, 21.9, 52.9, and 77.7 kJ/mol, respectively.
From Irie�s rule of relative energy for diarylethenetype compound and from Woodward–Hoffman
principle of orbital symmetry for isolated triene
and cyclodiene with strict symmetry constraint, the
equivalent result that the thermal reaction is ex-
clusively via disrotatory mechanism could be ob-
tained. But when the comparisons are made for the
cis and the trans forms among compounds 1–3,
Irie�s rule is not always true from the B3LYP/6-311+G(d,p)//HF/3-21G calculations (Table 1)
and from the higher level calculations (Table 2).
For example, compared, respectively, with their
own open-ring forms the ring-closed form of
compound 2 is lower in energy than that of com-
pound 3 for the cis configurations of thermal
reactions by the disrotatory mechanism (65.7 vs.
114.6 kJ/mol in Table 1, or similar data in Table 2and Fig. 1), but the cycloreversion energy barrier
of 2 is not higher than that of 3 (52.6 vs. 77.7 kJ/
mol in Table 1, or similar data in Table 2 and Fig.
1). This result is also consistent with the result
at the HF/3-21G level but contrary to Irie�s rule.The order of the cycloreversion energy barriers
of the trans forms for 2 and 3 at the B3LYP/
6-311+G(d,p)//HF/3-21G level is in contrary withthe result for the trans forms at the HF/3-21G le-
vel, the latter is also contrary to Irie�s rule. But itshould be noticed that the difference between the
energy barriers of the trans forms is small (185.5
vs. 179.4 kJ/mol) and the energy calculated and the
geometry optimized are not at the same level for
the B3LYP/6-311+G(d,p)//HF/3-21G calcula-
tions. We have not carried out higher level calcu-lations for the trans forms. The above results
confirms with chemical intuition. For example,
when two atomic orbitals combined to give a
molecule orbital within a molecule, the closer the
two atomic orbitals are in energy, the more effec-
tive the bonding for the molecular orbital is. But
when different molecules are compared, the state-
ment may not be true. That is, there should be
cases that the molecular orbital from atomic or-bitals with smaller energy difference in one mole-
cule may be not as effective as the molecular
orbital from atomic orbitals with larger energy
difference in another molecule. Each ring- closed
form have smaller energy gap between LUMO and
HOMO than that for its open-ring form from ei-
ther the lower or the higher level calculations, in-
dicating longer wavelength absorption for thering-closed form. The result is also conformed by
experiment result that the closed form absorb
longer wavelength than its opened form.
Acknowledgements
We thank the Science and Technology ResearchFoundation of Heilongjiang Educational Com-
mittee of PR China (Project Nos. 10531081 and
10511033) for its support of this research.
References
[1] M. Irie, M. Mohri, J. Org. Chem 53 (1988) 803.
[2] D.H. Waldeck, Chem. Rev. (1991) 415.
[3] J. Saltiel, Y.P. Sun, in: H. Durr, H. Bouas-Laurent (Eds.),
Photochromism: Molecules and Systems, Amsterdam, 1990,
p. 64.
[4] F.B. Mallory, C.W. Mallory, Org. React. 30 (1984) 1.
[5] R.M. Kellogg, M.B. Groen, H.J. Wynberg, Org. Chem. 32
(1967) 3093.
[6] S. Nakamura, M. Irie, J. Org. Chem. 53 (1988) 6136.
[7] M.J. Frisch, G.W. Trucks, H.B. Schlegel, et al., GAUSSIANAUSSIAN
98, Revision-A.11.2, Gaussian, Inc., Pittsburgh, PA,
1998.
[8] Yue Liu, Q. Wang, Ying Liu, J. Mol. Sci. 19 (2) (2003) 108
(in Chinese).
Y. Liu et al. / Chemical Physics Letters 373 (2003) 338–343 343
Top Related