Control aromaticity in the thermal decomposition of 2,5-dihydrofuran, 2,5-dihydrothiophene and...

Control aromaticity in the thermal decompositionof 2,5-dihydrofuran, 2,5-dihydrothiophene and3-pyrroline: a kinetic and thermodynamicstudy via DFT

Abolfazl Shiroudi • Ehsan Zahedi • Reza Zabihi

Received: 8 August 2010 / Accepted: 6 October 2010 / Published online: 3 November 2010

� Akademiai Kiado, Budapest, Hungary 2010

Abstract A theoretical study of the thermal decomposition kinetics of 2,5-dihy-

drofuran (1), 2,5-dihydrothiophene (2), and 3-pyrroline (3) has been carried out at

the B3LYP/6-31??G**, B3PW91/6-31??G** and MPW1PW91/6-31??G**

levels of theory. Our results show that the MPW1PW91/6-31??G** method is in

good agreement with the available experimental values. The nucleus independent

chemical shift (NICS) values of all reactants, TSs and products indicate that all

studied structures are aromatic and the studied reactions are controlled kinetically

and thermodynamically by the change of the aromaticity. Based on the optimized

ground state geometries using the MPW1PW91/6-31??G** method, the natural

bond orbital analysis (NBO) of donor–acceptor (bonding-antibonding) interactions

revealed that by the increase of electronegativity of atom X O; S; NHð Þ; LP

eð ÞX1! r�C2�H6resonance energies and also, the HOMO-LUMO energy-gaps in the

ground state structures increase. The results also suggest that in compounds 1–3, the

hydrogen elimination are controlled by LP(e) ? r* resonance energies.

Keywords DFT � Decomposition � NBO � NICS � GIAO

Introduction

The kinetics of thermal decomposition of several compounds of the general type

X.CH2.CH:CH.CH2have been previously studied using experimental techniques

A. Shiroudi � E. Zahedi (&)

Chemistry Department, Islamic Azad University, Shahrood Branch,

P.O.box 36155/133, Shahrood, Iran

e-mail: [email protected]; [email protected]

R. Zabihi

Chemistry Department, Islamic Azad University, Karaj Branch, Tehran, Iran

123

Reac Kinet Mech Cat (2011) 102:21–35

DOI 10.1007/s11144-010-0254-3

[1–4]. It has been shown that elimination of molecular hydrogen occurs in the cases

when X is O, S, or NH. In the case of 2,5-dihydrofuran [2], it has been suggested that

the mechanism of the reaction involves elimination of hydrogen atoms from the

2- and 5-positions in the ring by means of six-central transition states (Fig. 1). The

kinetics of the gas-phase decomposition of 2,5-dihydrofuran (1), 2,5-dihydrothioph-

ene (2) and 3-pyrroline (3) have been experimentally studied [2–4]. As an

experimental result, Wellington and coworkers [2, 4] studied the decomposition of

2,5-dihydrofuran (1) between 342 and 409 �C and 2,5-dihydrothiophene (2).

Wellington [2] showed that the addition of nitric oxide, propylene or toluene had

no effect upon the rate decomposition of 2,5-dihydrofuran and the rate constant was

calculated to be 5.3 ± 0.1 9 1012 exp(-24408/T) s-1. Also, Wellington [4] studied

the decomposition of 2,5-dihydrothiophene and the rate constant has been obtained

as 1.66 9 1013 exp(-27579.3 ± 1761.5/T) s-1. Thomas et al. [3] indicated that the

rate constant of the decomposition of 3-pyrroline (3) in the temperature range of

317–358 �C is 1.9 ± 0.4 9 1012 exp(-22445.9 ± 121.3/T) s-1. Thomas showed

that the addition of nitric oxide had no effect on the rate of decomposition but the rate

of the decomposition increased in heterogeneous processes. The results prove the

reaction to be homogeneous, unimolecular and to obey a first-order rate law. The

main goal of this work is to understand the influence of the affective factors on

the transition state structures of the kinetics of dehydrogenation reactions 1–3

(Fig. 1), involving the formation of molecular hydrogen and related diene hetero-

cyclic compounds using theoretical methods and comparison with those obtained

experimental data. The purpose is to investigate the kinetic and thermodynamic

parameters, pre-exponential factors, and barrier heights of these reactions, and

consideration of the nature of the molecular mechanism of these decomposition

reactions using natural bond orbital (NBO) analysis. The stabilization energies (E2)

associated with LP(e) ? r* delocalizations in compounds 1–3 were systematically

and quantitatively investigated by NBO analysis. We interpreted the kinetic and

thermodynamic results with nucleus independent chemical shift (NICS). Density

functional theory (DFT) has been found to be successful for determining activation

barriers, molecular energies, molecular geometries, electronic and magnetic prop-

erties [5–11]. Also, NBO analysis based density functional theory (DFT) provided a

useful picture for bonding and dynamic behavior of the compounds [12].

Fig. 1 Thermal decomposition of compounds 1–3 (Structures and numbering system)

22 A. Shiroudi et al.

123

Computational details

Initial estimates of the geometries of reactants and products were obtained by a

molecular-mechanics program PC-MODEL (88.0) [13] followed by full minimi-

zation using semi-empirical PM3 in the MOPAC 6.0 computer program [14, 15].

Energy minimum molecular geometries were located by minimizing the energy,

with respect to all geometric coordinates, without imposing any symmetry

constraints. The initial structures of the transition state geometries were obtained

using the optimized geometries of the equilibrium structures according to the

procedure of Dewar et al. (keyword SADDLE) [16]. Then, all initial geometries of

reactants, transition states and products were re-optimized using the DFT method at

B3LYP/6-31??G**, B3PW91/6-31??G** and MPW1PW91/6-31??G** levels

of theory by means of the GAUSSIAN 98 program package [17].

The nature of the stationary points for species has been fixed by means of the

number of imaginary frequencies. For minimum state structure, only real frequency

values and, in the transition states, only a single imaginary frequency value (with

negative sign) was accepted [18, 19]. The vibrational frequencies of minimum state

structures were calculated by the FREQ subroutine. The first order rate coefficient

k(T) was computed using the transition state theory (TST) [20, 21] and assuming

that the transmission coefficient is equal to 1, as expressed in the following relation:

kðTÞ ¼ kBT

h

� �exp �DG6¼

RT

� �ð1Þ

where DG= is the Gibbs free energy change between the reactant and its corre-

sponding transition structure, k and h are the Boltzmann and Planck constants,

respectively. DG= was calculated as follows:

DG 6¼ ¼ DH 6¼ � TDS 6¼ ð2Þ

and

DH 6¼ ¼ V 6¼ þ DZPVE þ DE Tð Þ ð3Þ

where V= is the potential energy barrier and DZPVE and DE(T) are the difference

of ZPVE and temperature corrections between the TS and the corresponding

reactant, respectively [22]. Comparison with experimental values shows better

agreement at the MPW1PW91/6-31??G** level of theory. A NICS study and

NBO [23] analysis were also performed using the MPW1PW91/6-31??G** level

of theory on the optimized structures.

Results and discussion

Kinetic and thermodynamic parameters

The zero-point vibrational energies (ZPVE), total electronic (Eel) energies and total

internal energies at 0 K (E0 = Eel ? ZPVE) of compounds 1–3, as calculated by

Control aromaticity in thermal decomposition 23

123

B3LYP/6-31??G**, B3PW91/6-31??G** and MPW1PW91/6-31??G** levels

of theory, are summarized in Table 1. Considering a comparison of activation

energies (DE0 is equal to activation energy in 0 K) from the DFT methods, the

MPW1PW91/6-31??G** results are in good agreement with the experimental data

[2–4] and show that the barrier height of the decomposition of compounds 1–3 is

48.24, 58.48 and 43.96 kcal mol-1. The effect of the electronegativity of the X

atom (O, S, NH) may be an important factor in this study. Oxygen is the most

electronegative of these atoms. This electronegativity may have the effect of

facilitating the formation of the transition state and hence the value of the adjusted

activation energy for the decomposition of 2,5-dihydrofuran is low, and is in

agreement with experimental studies [4]. In these reactions, the X atom and its

adjacent carbon atoms may become puckered out of the plane of the ring thus

bringing hydrogen atoms in the 2 and 5 positions close enough to form a six-centre

transition state. This would result in a loss of some vibrational freedom, forming a

more rigid structure [1]. The energy profiles for the thermal decompositions of

compounds 1–3 are depicted in Fig. 2.

The comparative kinetic and thermodynamic parameters, i.e., enthalpies (DHr),

Gibbs free energies (DGr), enthalpies of activation (DH=), Gibbs activation free

energies (DG=), activation entropies (DS=), pre-exponential factors (A) and the

unimolecular rate coefficients (k) of the thermal decomposition of compounds 1–3are listed in Table 2. The thermal decomposition of compounds 1 and 2 are

endothermic processes. As can be seen, DS= values are relatively small, so that the

calculated DH= and DG= parameters are close to the DE0 values. According to the

experimental data, the decomposition rate constants at 400 �C for compounds 1–3are 9.48 9 10-4, 2.67 9 10-5 and 6.27 9 10-3 s-1 [2–4]; therefore the computed

values for compounds 1–3 at the MPW1PW91/6-31??G** level of theory are in

agreement with experimental data (1.02 9 10-3, 4.87 9 10-7, and 3.58 9

10-2 s-1). The MPW1PW91/6-31??G** level of theory shows that for compound

1, the rate constant, k1, can be represented as k1 = 4.7 9 1012 exp(-24280/T) s-1,

while rate constant for compound 2, k2, is 4.76 9 1012 exp(-29435/T) s-1 and for

compound 3, k3, is 6.76 9 1012 exp(-22128/T) s-1. Log A has been used to suggest

the type of transition state according to Benson [21, 24, 25]. The TS for the thermal

decomposition of compounds 1–3 is a cyclic six-membered structure, as suggested

by log A values from 12.67 to 12.83. The transition state geometric parameters

optimized at the MPW1PW91/6-31??G** theoretical level compared to the

reactants and are given in Table 3. The C2–H6 and C5–H11 bond distances increase,

which implies breaking of this bond (1.095–1.01–1.497–1.539 A) in the TSs. The

C2–C3 and C4–C5 bond distances reveal changes from single to double bond

character (1.498–1.508 to 1.429–1.438 A) in TSs. The H6–H11 bond is forming in

the TSs, and the C3–C4 bond distances reveal changes from single to double bond

character (1.33–1.333 to 1.367–1.372 A) in TSs [26]. The imaginary frequencies

characterized for the TS found for 2,5-dihydrofuran (1), 2,5-dihydrothiophene (2),

and 3-pyrroline (3) are 1590, 1622 and 1663 cm-1, respectively.

Hammond’s postulate can be interpreted in terms of the position of the transition

structure along the reaction coordinate, nT, as defined by Agmon [27]:


123

Ta

ble

1C

alcu

late

dze

ro-p

oin

tvib

rati

onal

ener

gie

s(Z

PV

E),

tota

lel

ectr

onic

(Eel)

ener

gie

s,to

tal

inte

rnal

ener

gie

sat

0K

(E0

=E

el

?Z

PV

E)

and

rela

tiv

een

erg

iesD

E0

(in

har

tree

)fo

rth

eg

rou

nd

stat

ean

dtr

ansi

tio

nst

ate

stru

ctu

res

of

the

ther

mal

dec

om

po

siti

on

of

2,5

-dih

yd

rofu

ran

(1),

2,5

-dih

yd

roth

iop

hen

e(2

)an

d3

-py

rro

lin

e(3

)at

the

var

ious

lev

els

of

theo

ry

Met

ho

dG

eom

etry

12

3

GS

TS

GS

TS

GS

TS

Ex

per

imen

tala

(kca

lm

ol-

1)

48

.55

4.8

44

.6

ZP

E0

.09

22

27

0.0

84

80

00

.089

36

90

.08

09

90

0.1

05

24

60

.097

41

0

Eel

-2

31

.23

573

9-

23

1.1

49

58

7-

55

4.2

19

88

4-

55

4.1

16

84

1-

21

1.3

71

11

4-

21

1.2

91

29

2

Eo

-2

31

.14

351

2-

23

1.0

64

78

8-

55

4.1

30

51

5-

55

4.0

35

85

1-

21

1.2

65

86

9-

21

1.1

93

88

2

DE

ob(B

3L

YP

/6-3

1?

?G

**

)0

.00

00

00

(0.0

)c0

.07

87

24

(49

.4)c

0.0

00

00

0(0

.0)c

0.0

94

66

4(5

9.4

)c0

.000

00

0(0

.0)c

0.0

71

98

7(4

5.1

)c

ZP

E0

.09

25

62

0.0

85

28

60

.089

67

90

.08

14

10

0.1

05

68

60

.097

95

5

Eel

-2

31

.14

674

5-

23

1.0

64

00

8-

55

4.1

11

96

0-

55

4.0

11

99

0-

21

1.2

91

88

8-

21

1.2

15

41

63

Eo

-2

31

.05

418

3-

23

0.9

78

72

3-

55

4.0

22

28

1-

55

3.9

30

58

1-

21

1.1

86

20

3-

21

1.1

17

46

2

DE

ob(B

3P

W9

1/6

-31?

?G

**

)0

.00

00

00

(0.0

)c0

.07

54

60

(47

.3)c

0.0

00

00

0(0

.00

00

00

)c0

.09

17

00

(57

.5)c

0.0

00

00

0(0

.0)c

0.0

68

74

1(4

3.1

)c

ZP

E0

.09

32

49

0.0

85

93

40

.090

31

80

.08

20

02

0.1

06

45

20

.098

66

9

Eel

-2

31

.17

536

1-

23

1.0

91

16

5-

55

4.1

84

61

7-

55

4.0

83

09

7-

21

1.3

17

99

0-

21

1.2

40

13

9

Eo

-2

31

.08

211

2-

23

1.0

05

23

1-

55

4.0

94

30

0-

55

4.0

01

09

6-

21

1.2

11

53

9-

21

1.1

41

47

0

DE

ob(M

PW

1P

W9

1/6

-31?

?G

**

)0

.00

00

00

(0.0

)c0

.07

68

81

(48

.2)c

0.0

00

00

0(0

.0)c

0.0

93

20

4(5

8.4

)c0

.000

00

0(0

.0)c

0.0

70

06

9(4

3.9

)c

aR

ef.

[2–4]

bR

elat

ive

toth

eb

est

con

fig

ura

tio

nc

Nu

mb

ers

inp

aren

thes

isar

eth

eco

rres

po

ndin

gD

E0

val

ues

ink

cal

mo

l-1


123

nT ¼1

2� ðDGr=DG 6¼Þ ð4Þ

The magnitudes of nT, indicate the degree of similarity between the transition

structure and the product. According to this equation, the position of the transition

state along the reaction coordinate is determined solely by DGr� (a thermodynamic

quantity) and DG= (a kinetic quantity). The values of nT for the thermal

decomposition of compounds 1–3, are 0.5042, 0.5144 and 0.4543. In fact the

transition state structures in the reactions 1 and 2 are more similar to the products

than to its reactants and the similarity between transition states and products

increases in the order of R2 [ R1 [ R3.

The nucleus independent chemical shift (NICS) study

In the NICS study, the gauge-invariant atomic orbital (GIAO) theory with the

MPW1PW91/6-31??G** method was applied to estimate the diamagnetic ring

current intensity on the optimized geometries of diene ring-heterocyclic reactants,

products and TSs in the gas phase. Magnetic properties of organic molecules arise

from the diamagnetic ring current of aromatic systems [28]. The nucleus

independent chemical shift (NICS) is defined as the negative value of the absolute

magnetic shielding in centers of rings or 1 A above or below the molecular plane

[29]. NICS at an empty point in space equals to zero and in principle does not

require reference molecules and calibrating (homodesmotic) equations for

Fig. 2 Energy profile for the unimolecular thermal decomposition of compounds 1–3


123

Tab

le2

Kin

etic

and

ther

modynam

icpar

amet

ers

of

the

deh

ydro

gen

atio

nof

2,5

-dih

ydro

fura

n(1

),2

,5-d

ihy

dro

thio

phen

e(2

),an

d3

-py

rro

lin

e(3

)at

the

var

ious

lev

els

of

theo

ry

Par

amet

erM

ethod

B3L

YP

/6-3

1?

?G

**

B3P

W91/6

-31

??

G**

MP

W1P

W91/6

-31

??

G**

C1

C2

C3

C1

C2

C3

C1

C2

C3

k(s

-1)

4.6

99

10

-4

(9.4

89

10

-4)

2.6

79

10

-7

(2.6

79

10

-5)

1.3

39

10

-2

(6.2

79

10

-3)

2.0

79

10

-3

(9.4

89

10

-4)

1.0

19

10

-6

(2.6

79

10

-5)

6.4

99

10

-2

(6.2

79

10

-3)

1.0

29

10

-3

(9.4

89

10

-4)

4.8

70 1

0-

7

(2.6

79

10

-5)

3.5

89

10

-2

(6.2

79

10

-3)

A(s

ec-

1)

5.1

49

10

12

(5.3

910

12)

5.1

79

10

12

(1.6

69

10

13)

6.2

910

12

(1.9

910

12)

4.8

99

10

12

(5.3

910

12)

4.8

69

10

12

(1.6

69

10

13)

6.5

89

10

12

(1.9

910

12)

4.7

910

12

(5.3

910

12)

4.7

69

10

12

(1.6

69

10

13)

6.7

69

10

12

(1.9

910

12)

Ea (k

cal

mol-

1)

49.4

(48.5

)59.4

(54.8

)45.1

(44.6

)47.3

(48.5

)57.5

(54.8

)43.1

(44.6

)48.2

(48.5

)58.4

(54.8

)43.9

(44.6

)

DH=

(kca

lm

ol-

1)

48.8

(47.1

)58.9

(53.4

)44.7

(43.2

)46.8

(47.1

)57.0

(53.4

)42.6

(43.2

)47.7

(47.1

)57.9

(53.4

)43.5

(43.2

)

DS= (cal

mol-

1

K-

1)

-3.9

(-3.9

)-

3.9

(-1.6

)-

3.6

(-5.9

)-

4.0

(-3.9

)-

4.0

(-1.6

)-

3.4

(-5.9

)-

4.1

(-3.9

)-

4.1

(-1.6

)-

3.4

(-5.9

)

DG=

(kca

lm

ol-

1)

50.0

(49.8

)60.0

(54.5

)45.7

(43.2

)48.0

(49.8

)58.2

(54.5

)43.7

(43.2

)48.9

(49.8

)59.2

(54.5

)44.5

(43.2

)

DH

r

(kca

lm

ol-

1)

5.5

8.0

-3.8

6.8

9.4

-2.4

8.7

11.2

-0.6

DG

r

(kca

lm

ol-

1)

-2.4

-0.0

-12.0

-1.1

1.4

-10.7

0.8

3.3

-8.9

Exper

imen

tal

val

ues

are

show

nin

par

enth

eses

[Ref

.2

–4

]


123

the evaluation of aromaticity. Negative values of NICS indicate a shielding effect

resulting from the induced diatropic ring current understood as aromaticity at a

specific point. On the contrary, its positive values are interpreted as the deshielded-

paratropic ring current and thus antiaromaticity. Schleyer and coworkers, based on

studies on an extensive set of heterocyclic compounds, proved that there are very

good linear correlations among the geometric, energetic, and magnetic properties

providing straightforward interpretation of the electronic structures and properties

of five-membered heterocycles with one heteroatom [30].

For all the reactants, TSs and products, the sets of points lying below and above

the rings’ geometric centers were used. Their locations correspond to distances from

0 to 1 A with 0.5 A steps. The NICS 0 A values calculated at the center of the ring

were influenced by r bonds, whereas the NICS 1 A values calculated at 1 A above

the plane were more affected by the p-system [31]. From Table 4, one may

conclude that all the studied reactants and products are aromatic. The structures

exhibit characteristic decreasing of the NICS values from the point located in the

geometric center of the ring to the 1 A above of it. The NICS values are the

isotropic chemical shifts of the respective bq’s, and the eigenvalues of the chemical

shift tensors were used to separate the isotropic NICS values into their in-plane and

out-of-plane components. Since the NICS values are distance-dependent, the

symbol ‘N@r’ will be used in this article to denote the NICS value (ppm) at distance

r(A) from the molecular plane. The magnitudes of the isotropic chemical shifts

for the products are very different; the minimal values are -12.3@0, -13.1@0 and

-14.3@0 for furan, thiophene and pyrrole. The strongest aromatic character in the

products was found for pyrrole, and the aromatic character is in the order

P3 [ P2 [ P1. Minimal values of the isotropic chemical shifts for the reactants are

-4.5@0, -6.0@0 and -3.6@0 for 2,5-dihydrofuran, 2,5-dihydrothiophene, and

3-pyrroline. The strongest aromatic character in the reactants was found for

2,5-dihydrothiophene, and the aromatic character is in the order: R2 [ R1 [ R3.

The transition states are not planar; therefore, the ring center in the C2–C3–C4–C5

Table 3 Structural parameters for the ground state and transition state structures of the thermal

decomposition of 2,5-dihydrofuran (1), 2,5-dihydrothiophene (2) and 3-pyrroline (3) at the MPW1PW91/

6-31??G** level of theory

State Compound

1 2 3

GS TS GS TS GS TS

Bond lengths (A)

r C2–H6 1.099 1.506 1.095 1.539 1.010 1.497

r C5–H11 1.099 1.506 1.095 1.539 1.010 1.497

r C2–C3 1.498 1.429 1.498 1.429 1.508 1.438

r C3–C4 1.330 1.371 1.331 1.372 1.333 1.367

d H6–H11 3.551 1.011 3.955 0.987 3.285 1.058

TS imaginary frequency (cm-1) 1590 1622 1663

Bond lengths are in angstroms (A)


123

Ta

ble

4N

ICS

val

ues

asa

fun

ctio

no

fd

ista

nce

(an

gst

rom

)fo

rth

ere

acta

nts

,pro

duct

san

dT

Ss:

isotr

opic

chem

ical

shif

t,in

-pla

ne

com

ponen

tan

dout-

of-

pla

ne

com

ponen

t

Sp

ecie

sN

ICS

(0)

(pp

m)

NIC

S(0

.5)

(pp

m)

NIC

S(1

)(p

pm

)

Iso

tro

pic

Ou

to

fp

lane

In-p

lane

Iso

trop

icO

ut

of

pla

ne

In-p

lane

Iso

trop

icO

ut

of

pla

ne

In-p

lan

e

2,5

-dih

yd

rofu

ran

-4

.5-

20

.87

.0-

3.7

-1

3.5

2.2

-2

.0-

5.6

-0

.6

Fu

ran

-1

2.3

-1

9.1

-1

7.9

-1

2.0

-2

1.2

-1

4.9

-9

.6-

27

.8-

1.1

TS

-2

4.1

-4

3.5

-2

8.9

––

––

––

2,5

-dih

yd

roth

iop

hen

e-

6.0

-2

2.8

4.6

-5

.1-

17

.01

.5-

3.0

-7

.9-

1.0

Th

iop

hen

e-

13

.1-

21

.3-

18

.0-

12

.8-

21

.2-

17

.2-

10

.5-

28

.9-

2.6

TS

-2

3.0

-4

2.8

-2

6.3

––

––

––

3-p

yrr

oli

ne

-3

.6-

17

.16

.2-

3.6

-9

.9-

0.8

-2

.1-

5.7

-0

.6

Py

rro

le-

14

.3-

18

.5-

24

.4-

13

.4-

25

.2-

15

.2-

10

.4-

31

.50

.0

TS

-2

4.4

-4

2.0

-3

1.2

––

––

––


123

plane is considered (Fig. 1). Minimal values of the isotropic chemical shifts for the

transition states are -24.1@0, -23.0@0 and -24.4@0 for 2,5-dihydrofuran,

2,5-dihydrothiophene, and 3-pyrroline. The strongest aromatic character in the

transition states was found for 3-pyrroline, and the aromatic character is in the order

TS3 [ TS1 [ TS2. The aromaticity on the ring center increased from reactants to

TSs and then decreases from TSs to products and the aromatic character of products

are higher than for reactants. The separation of the isotropic values into in-plane and

out-of plane contributions indicates that aromaticities of structures are controlled by

the out-of-plane component, with the exception of pyrrole, where it is in the ring

center. A quick look at the results reveals that the highest increases in the

aromaticity of ring along the dehydrogenation reaction (from reactant to TS and

from reactant to product) was found for 3-pyrroline, and the lowest increases was

found for 2,5-dihydrothiophene. These results indicated that the studied reactions

are controlled kinetically and thermodynamically by the changes of the aromaticity.

Bond order analysis

A more balanced measure of the extent of bond formation or bond breaking along a

reaction pathway is provided by the concept of bond order (B). This theoretical

technique has been used to investigate the molecular mechanism of chemical

reactions [32]. To follow the nature of the decomposition process, the Wiberg bond

indices have been computed by using the NBO [33, 34] analysis as implemented in

GAUSSIAN 98. There are several bond breaking/forming processes along the

fragmentation process and the global nature of the decomposition reaction can be

monitored by means of the synchronicity (Sy) concept [35], defined by the following

expression:

Sy ¼ 1�Pn

i¼1dBi�dBavj j

dBav

2n� 2ð5Þ

In this equation, n is the number of bonds directly involved in the reaction and the

relative variation of the bond index (dBi) for a bond i at the TS is given as a

percentage by:

dBi ¼BTS

i � BRi

BPi � BR

i

ð6Þ

where the superscripts R, TS, and P, refer to the reactant, transition state and

product. The evolution in bond change is calculated as:

%EV ¼ dBi � 100 ð7Þ

and average value is calculated from:

dBav ¼1

n

Xn

i¼1

dBi ð8Þ

Bond indices were calculated for those bonds changed in the reaction pathway, i.e.:

X1–C2, C2–C3, C3–C4, C4–C5, C5–X1, C2–H6, C5–H11 and H6–H11 bonds (Fig. 1);


123

all other bonds remain practically unaltered during the processes. The calculated

Wiberg indexes Bi for reactants, transition states and products for compounds 1–3,

enable us to examine the progress of the reactions (Table 5).

Reaction 1 leads to the cleavage of the C2–H6 and C5–H11 bonds through TS1 to

produce furan ? H2 located at 8.76 kcal mol-1 above the reactant at the

MPW1PW91/6-31??G** level. TS1 results from a simple elongation of the

breaking C2–H6 and C5–H11 bond lengths and the simultaneous shrinkage of

the H6–H11 distance as a result of the forming hydrogen molecule. The C2–H6 and

C5–H11 bonds are elongated by 1.506 A, and the forming H6–H11 bond is longer

than the equilibrium bond length in hydrogen molecule. Wiberg indeces show more

progress in the C2–X1 and C5–X1 bond breaking (about 55.38%) and less progress is

observed in the C2–C3 and C4–C5 single bond formation (39.28%). TS1 has an

imaginary frequency of 1590i cm-1 that indicates a well-defined transition state

geometry and the associated energy barrier located 48.24 kcal mol-1 above the

reactant at the MPW1PW91/6-31??G** level.

In reaction 2, the mechanism involves the simultaneous breaking of the C2–H6

and C5–H11 bonds and shrinkage of the H6–H11 distance through TS2 to produce

thiophene ? H2 located at 11.29 kcal mol-1 above the reactant at the MPW1PW91/

6-31??G** level. TS2 results from a simple elongation of the breaking C2–H6 and

C5–H11 bond lengths and the simultaneous shrinkage of the H6–H11 distance as a

result of the formation of a hydrogen molecule. The C2–H6 and C5–H11 bonds are

elongated by 1.539 A, and the forming H6–H11 bond is longer than the equilibrium

bond length in the hydrogen molecule. The changes of C2–H6 and C5–H11 bonds,

and the formation of the H6–H11 single bond are advanced considerably by 55.54,

55.54 and 48.79%. The structure of TS2 possesses an imaginary frequency at

1622i cm-1 and the associated energy barrier located 58.48 kcal mol-1 above the

reactant at the MPW1PW91/6-31??G** level.

Reaction 3 leads to the cleavage of the C2–H6 and C5–H11 bonds through TS3

to produce pyrrole ? H2 located at 0.68 kcal mol-1 below the reactant at the

MPW1PW91/6-31??G** level. TS3 results from a simple elongation of

the breaking C2–H6 and C5–H11 bond lengths and the simultaneous shrinkage of

the H6–H11 distance as a result of the forming H6–H11 bond. The C2–H6 and C5–H11

bonds are elongated by 1.497 A, and the forming H6–H11 bond is longer than the

equilibrium bond length in the hydrogen molecule. Moreover, the evolution in bond

changes for the breaking of C2–H6 and C5–H11 bonds is 49.92% in this reaction, and

the formation of the H6–H11 single bond is 43.36%. The imaginary frequency of

1663i cm-1 indicates a well-defined transition state geometry and the associated

energy barrier, located 43.96 kcal mol-1 above the reactant at the MPW1PW91/

6-31??G** level. The synchronicity values of the thermal decomposition of

compounds 1–3 are 0.93, 0.96 and 0.95, which revealed that the reaction pathways

can be described as concerted and slightly asynchronous.

Natural bond orbital analysis

Delocalization of electron density between the filled (bonding or lone pair) Lewis

type NBOs and the empty (antibonding and Rydberg) non-Lewis NBOs leads to


123

Tab

le5

Bo

nd

ord

eran

alysi

sfo

rth

eth

erm

ald

eco

mp

osi

tio

no

fth

e2

,5-d

ihy

dro

fura

n(1

),2

,5-d

ihy

dro

thio

ph

ene

(2),

and

3-p

yrr

oli

ne

(3)

atth

eM

PW

1P

W9

1/6

-31?

?G

**

lev

elu

sin

gN

BO

anal

ysi

s

Com

po

und

C2–

H6

C2–

X1

C2–

C3

C3–

C4

C4–

C5

C5–

X1

C5–

H11

H6–

H11

dBav

Sy

C1

Bi(

R)

0.9

02

40

.918

01

.031

61

.917

41

.03

16

0.9

18

00

.902

40

.001

80

.483

90

.932

2

Bi(

TS

)0

.425

90

.990

51

.277

11

.606

91

.27

71

0.9

90

70

.425

90

.456

2

Bi(

P)

0.0

00

01

.048

91

.656

61

.250

11

.65

66

1.0

48

90

.000

01

.000

0

%E

V5

2.8

05

5.3

83

9.2

84

6.5

33

9.2

85

5.3

85

2.8

04

5.5

2

Bi(

R)

0.8

91

71

.003

91

.037

81

.923

51

.03

78

1.0

03

90

.891

70

.000

90

.490

70

.960

0

C2

Bi(

TS

)0

.396

41

.105

41

.295

91

.599

81

.29

58

1.1

05

60

.396

50

.488

4

Bi(

P)

0.0

00

01

.216

91

.628

21

.274

31

.62

82

1.2

16

90

.000

01

.000

0

%E

V5

5.5

44

7.6

54

3.7

14

9.8

64

3.7

14

7.6

55

5.5

44

8.7

9

Bi(

R)

0.8

93

60

.994

91

.022

51

.923

61

.02

25

0.9

94

90

.893

60

.002

80

.459

90

.952

5

C3

Bi(

TS

)0

.447

51

.090

81

.237

51

.645

51

.23

74

1.0

91

10

.447

50

.435

2

Bi(

P)

0.0

00

01

.188

61

.564

51

.322

51

.56

45

1.1

88

60

.000

01

.000

0

%E

V4

9.9

24

9.6

63

9.6

44

6.2

63

9.6

44

9.6

64

9.9

24

3.3

6

Wib

erg

bo

nd

indec

es(B

i),

%ev

olu

tion

thro

ugh

the

reac

tion

coord

inat

e(%

EV

),av

erag

ebond

index

var

iati

on

(dB

av)

and

syn

chro

nic

ity

par

amet

er(S

y)ar

esh

ow

n


123

transfer of occupancy from the localized NBOs of the idealized Lewis structure into

the empty non-Lewis orbitals (and thus, departure from the idealized Lewis

structure description). It is referred to as ‘delocalization’ correction to the zeroth-

order natural Lewis structure to a stabilizing donor–acceptor interaction. The

energies of these interactions can be estimated by the second order perturbation

theory [36, 37]. For each donor NBO (i) and acceptor NBO (j), the stabilization

energy (E2) associated with i ? j delocalization, is explicitly estimated by the

following equation [37, 38]:

E2 ¼ DEij ¼ qi½F2ði;jÞ=ðei � ejÞ� ð9Þ

where qi is the donor orbital occupancy, ei and ej, are diagonal elements (orbital

energies) and F(i,j) is the off-diagonal NBO Fock matrix elements.

Based on the optimized ground state geometries using the MPW1PW91/6-

31??G** method, the NBO analysis of donor–acceptor interactions revealed that

the stabilization energies associated with the electronic delocalization from non-

bonding Lone-Pair orbitals LP eð ÞX1

� �to r�C1�H2

antibonding orbitals of compounds

1–3. The LP eð ÞX1! r�C2�H6resonance energies for compounds 1–3 are 5.32, 3.10

and 4.14 kcal mol-1, while the LP(e)x1 occupancies in compounds 1–3 are 1.93418,

1.95132 and 1.93516 (Table 6). Also, the LP eð ÞX1! r�C2�H6delocalizations could

fairly explain the decrease of occupancies of LP(e)x1 nonbonding orbitals in the

rings of compounds 1–3 (1 \ 3 \ 2). The results revealed that by the increase of

electronegativity of atom X (O, S, N), LP eð ÞX1! r�C2�H6resonance energies

increase and the HOMO-LUMO energy-gaps in the ground state structures increase.

The results also suggest that in compounds 1–3, the hydrogen elimination are

controlled by LP(e) ? r* resonance energies.

Table 6 NBO calculated resonance energies (E2) (kcal mol-1), based on the MPW1PW91/6-31??G**

level calculated geometries, for LP eð ÞX1! r�C2�H6delocalization, and rC2�H6

bonding and r�C2�H6anti-

bonding orbitals occupancies, HOMO energies, LUMO energies and HOMO-LUMO gaps in the 2,5-

dihydrofuran (1), 2,5-dihydrothiophene (2), and 3-pyrroline (3)

MPW1PW91/6-31??G**

1 2 3

Occupancies

rC2�H61.97819 1.97960 1.97522

r�C2�H60.02751 0.02194 0.02838

LP(e)91 1.93418 1.95132 1.93516

Stabilization energy (E2)

LP eð ÞX1! r�C2�H65.32 3.10 4.14

HOMO,LUMO energies (a.u.)

HOMO -0.24885 -0.22859 -0.23773

LUMO -0.00260 -0.00507 -0.00494

HOMO–LUMO gap 0.24625 0.22352 0.23279


123

Conclusion

The decomposition of the 2,5-dihydrofuran (1), 2,5-dihydrothiophene (2), and 3-

pyrroline (3) has been studied at the B3LYP/6-31??G**, B3PW91/6-31??G**

and MPW1PW91/6-31??G** levels of theory. The MPW1PW91/6-31??G**

level of theory gives activation energies very close to the experimental values and

the decomposition barrier height of compound 3 is the lowest. The values of nT for

the decomposition compounds 1–3, are 0.5042, 0.5144 and 0.4543; therefore, the

similarity between transition states and products increase with respect to reactions in

the order of R2 [ R1 [ R3. In the NICS study, separation of the isotropic values

into in-plane and out-of-plane contributions indicates that aromaticities of products

are controlled by the out-of-plane component, with the exception of the pyrrole in

the ring centre. The strongest aromatic character in the products and TSs was found

for pyrrole and the studied reactions are controlled kinetically and thermodynam-

ically by change of the aromaticity. The NBO analysis revealed that the activation

energies for hydrogen elimination in compounds 1–3 are controlled by LP eð ÞX1

� �!

r�C2�H6resonance energies. Also, NBO results show that the synchronicity values of

decomposition reaction of compounds 1–3 are about 0.93–0.96; therefore, these

reactions are concerted and slightly asynchronous.

Acknowledgment The authors would like to thank Dr D. Tahmassebi for his help on the operation of

the Gaussian 98 programs in this study.

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Control aromaticity in the thermal decomposition of 2,5-dihydrofuran, 2,5-dihydrothiophene and...

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