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

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* Corresponding author. Fax: +08604516416060.

E-mail address: yuesd@0451.com (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.

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