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European	Journal	of	Chemistry	3	(3)	(2012)	340‐347	

European	Journal	of	Chemistry	
ISSN	2153‐2249	(Print)	/	ISSN	2153‐2257	(Online)		2012	EURJCHEM	

DOI:10.5155/eurjchem.3.3.340‐347.614	

	
	

	

	

European	Journal	of	Chemistry	
Journal	homepage:	www.eurjchem.com	

	 	 	

Theoretical	free	energies	of	electron	transfer,	electrochemical	properties,	
electron	transfer	kinetic	and	quantitative	structural	relationships	studies	of	
alkynyldihydrofullerene	in	[X‐UT‐Y][R‐C60–M+]	supramolecular	complexes	

Avat	Arman	Taherpour	a,*,	Masomeh	Tayebi‐Surakib	and	Nosratollah	Mahdizadeha	

a	Department	of	Organic	Chemistry,	Faculty	of	Chemistry,	Razi	University,	P.O.	Box:	67149‐67346,	Kermanshah,	Iran	
b	Chemistry	Department,	Faculty	of	Science,	Islamic	Azad	University,	38135‐567,	Arak,	Iran	

*Corresponding	author	at:	Department	of	Organic	Chemistry,	Faculty	of	Chemistry,	Razi	University,	P.O.	Box:	67149‐67346,	Kermanshah,	Iran.		
Tel.:	+98.831.4274559;	fax:	+98.831.4274559.	E‐mail	address:	avatarman.taherpour@gmail.com	(A.A.	Taherpour).	

	
	

	 	

	 	 	
ARTICLE	INFORMATION	 	 ABSTRACT	
Received:	13	April	2012	
Received	in	revised	form:	10	July	2012	
Accepted:	11	July	2012	
Online:	30	September	2012	

KEYWORDS	

	 The	 isolated	 pentagon	 rule	 (IPR)	 states	 that	 all	 pentagonal	 carbon	 rings	 are	 isolated	 in	 the
most	 stable	 fullerenes.	 Fullerenes	 (buckministerfullerene)	 are	 a	 class	 of	 spherical	 carbon
allotrope	 group	with	 unique	 properties.	 Electron	 transfer	 between	 fullerene	 C60	 derivatives
such	as	alkynyldihydrofullerene	(1‐alkynyl‐C60	carbanion)	and	other	molecules	are	thought	to
involve	the	transfer	of	electrons	between	molecules	surrounding	the	fullerene	cage.	One	class
of	 electron‐transfer	 molecules	 has	 introduced	 as	 [X‐UT‐Y][R‐C60–M+](R=tert‐Bu‐	 &	 H–C≡C‐;
M=Li	 &	 K).	 The	 supramolecular	 complexes	 [X‐UT‐Y]	 (1‐9)	 and	 [R‐C60–M+]	 (R=tert‐Bu‐	&	H–
C≡C‐;	 M=Li	 &	 K)	 are	 shown	 to	 possess	 a	 previously	 unreported	 host‐guest	 interaction	 for
electron	 transfer	 processes.	 The	 unsaturated,	 thiocrown	 ethers	 (1‐9,	 with	 cis‐geometry)
(described	 as	 [X‐UT‐Y],	 where	 X	 and	 Y	 indicate	 the	 numbers	 of	 carbon	 and	 sulfur	 atoms,
respectively)	are	a	group	of	crown	ethers	that	display	interesting	physiochemical	properties
in	light	of	their	conformational	restriction	compared	to	a	corresponding	saturated	system,	as
well	as	the	sizes	of	their	cavities.	Topological	indices	have	been	successfully	used	to	construct
mathematical	methods	 that	 relate	 the	 structural	 data	 to	 the	 various	 chemical	 and	 physical
properties.	To	establish	a	good	relationship	between	the	structures	of	1‐9	with	derivatives	of
alkynyldihydrofullerene	(1‐alkynyl‐C60	carbanion)	as	[R‐C60–M+]	(R=tert‐Bu‐	&	H–C≡C‐;	M=Li
&	K)	in	DMSO	and	THF	solvents	12‐38,	an	index	(cs)	is	utilized.	This	index	is	the	ratio	of	the
sum	of	the	number	of	carbon	atoms	(nc)	and	the	number	of	sulfur	atoms	(ns)	with	the	product
of	these	two	numbers	for	1‐9.	In	this	study,	were	investigated	the	relationships	between	this
index	and	the	first	to	third	free	energies	of	electron	transfer	(ΔGet(n);	n=1‐3,	which	is	given	by
the	Rehm‐Weller	equation)	between	1‐9	and	[R‐C60–M+]	(R=tert‐Bu‐	&	H–C≡C‐;	M=Li	&	K)	as
[X‐UT‐Y][R‐C60–M+](R=tert‐Bu‐	&	H–C≡C‐;	M=Li	&	K)	supramolecular	complexes	in	DMSO	and
THF	solvents.	The	first	to	third	free	energies	of	electron	transfer	and	the	kinetic	rate	constants
of	the	electron	transfers,	ΔG#et(n)	and	ket	(n=1‐3),	respectively,	were	also	calculated	for	[X‐UT‐
Y][R‐C60–M+]	 (R=tert‐Bu‐	 &	 H–C≡C‐;	 M=Li	 &	 K)	 in	 DMSO	 and	 THF,	 in	 accordance	 with	 the
Marcus	theory.	

Fullerenes	
Marcus	theory	
Non‐IPR	Carbon	Cage	
Rehm‐Weller	equation	
Unsaturated	thiocrown	ethers	
Alkynyldihydrofullerene	derivatives	

	
1.	Introduction	
	

In	 1985	 fullerenes	 were	 demonstrated	 as	 one	 of	 the	
uniquely	 stable	 molecular	 allotropic	 formsof	 carbon	 [1,2].	
Fullerenes	are	more	reactive	than	planar	aromatics,	acts	as	an	
important	 driving	 force	 for	 the	 additional	 reactions.	 This	
property	returns	to	the	reduction	of	the	strain	energies,	which	
results	from	pyramidalization	 in	the	sp2‐carbon	network	[3,4].	
One	of	the	simplest	compounds	in	the	huge	family	of	fullerenes	
is	 C60	 [3].	 Since	 1985,	metal‐containing	 endohedral	 fullerenes	
(EMFs)	 have	 attracted	 special	 attention	 as	 a	 new	 class	 of	
technologically	 relevant	 material	 due	 to	 their	 combined	
fullerene‐like	 and	 metallic	 properties.	 In	 most	 EMFs,	
introduction	 of	 metal	 atoms	 into	 carbon	 cages	 leads	 to	 an	
increase	 in	 the	 electron	 affinity	 relative	 to	 the	 corresponding	
empty‐cages	[2,5,6].	Endohedral	metallofullerenes	(EMFs)	have	
shown	 very	 interesting	 applications	 in	 optoelectronic	 devices	
since	 varying	 the	 encapsulated	 metal	 cluster	 can	 change	 the	
optical	 and	 electronic	 properties,	 without	 changing	 the	

structural	 features	 of	 the	 outer	 carbon	 shell.	 Enhancement	 of	
third‐order	 nonlinear	 optical	 susceptibility	 observed	 in	 EMFs	
further	establishes	 them	as	potential	 candidates	 for	nonlinear	
optical	devices	[2,3].	In	early	studies,	La@C60	was	examined	by	
Kroto	et	al.,	although	it	was	never	isolated	in	solid	form	[1,2].	A	
variety	 of	 endohedral	 metallofullerenes	 have	 been	 reported,	
but	 their	 investigations	 have	 been	 limited	 because	 they	were	
typically	formed	in	extremely	low	yields	[2].	Various	theoretical	
techniques	 have	 been	 employed	 to	 study	 the	 electronic,	
structural	 and	 vibrational	 properties	 of	 fullerenes	 and	 their	
derivatives	[2].	These	studies	have	revealed	the	structure	of	the	
fullerene	 cages,	 the	 electronic	 states	 of	 metal	 atoms	 and	
fullerene	cages,	and	how	the	electronic	properties	and	chemical	
reactivity	 of	 empty	 fullerene	 cages	 change	 upon	 endohedral	
metal	 doping	 [2].	 EMFs	 of	 carbon	 cage	 size	 in	 the	 range	
between	 C66	 and	 C84	 were	 shown	 to	 be	 stable	 structures	
although	 the	 corresponding	 empty	 fullerenes	 are	 either	 not	
stable	 or	 have	 been	 isolated	 only	 in	 minor	 quantities	 in	 the	
fullerene	soot	[2].		



Taherpour	et	al.	/	European	Journal	of	Chemistry	3	(3)	(2012)	340‐347	 341	
 

Among	fullerenes,	many	of	them	do	not	follow	the	IPR	rule.	
There	are	 several	ways	 in	which	 the	 IPR	 can	be	violated;	 one	
way	is	to	generate	fused‐pentagons	in	which	the	pentagons	are	
adjacent	 to	 one	 another	 [2].	 All	 pentagonal	 carbon	 rings	 are	
isolated	 in	 the	most	 stable	 fullerenes,	 in	 accordance	with	 the	
isolated	 pentagon	 rule	 (IPR).	 The	 IPR	 has	 proved	 valuable	 in	
understanding	the	stability	of	cage	structures	of	fullerenes	and	
metallofullerenes	 [3].	 The	 most	 abundant	 fullerenes,	 C60	 and	
C70	and	all	pure	carbon	fullerenes	larger	than	C70	follow	the	IPR	
[8‐11].	 Non‐IPR	 fullerenes,	 which	 contain	 adjacent	 pentagons	
(APs),	have	been	stabilized	experimentally	in	cases	where	it	is	
topologically	 impossible	 to	 fully	 isolate	 all	 the	 pentagons,	 in	
accordance	with	Euler’s	theorem	[8].	Alcami	et	al.	have	shown	
that,	 apart	 from	 strain,	 the	most	 important	 physical	 property	
that	 governs	 the	 relative	 stabilities	 of	 fullerenes	 is	 the	 charge	
distribution	 within	 the	 cage	 [8].	 This	 charge	 distribution	 is	
controlled	 by	 the	 number	 and	 location	 of	 APs	 and	 pyrene	
motifs.	 Alcami	 et	al.	 have	 also	 shown	 that,	when	 these	motifs	
are	 uniformly	 distributed	 and	well‐separated	 from	 one	 other,	
stabilization	of	non‐IPR	endohedral	and	exohedral	derivatives,	
as	well	 as	 pure	 carbon	 fullerene	 anions	 and	 cations,	 becomes	
the	rule,	rather	than	the	exception.	This	suggests	that	non‐IPR	
derivatives	might	even	be	more	common	 than	 IPR	derivatives	
[8].	

Fullerenes	 violating	 the	 IPR	 are	 only	 obtained	 in	
derivatized	form,	since	the	[5,5]‐bond	carbons	readily	react	to	
release	 bond	 strain.	 However,	 non‐IPR	 fullerenes	 still	 have	
unsaturated	 sp2	 carbons	 at	 the	 [5,5]	 bond	 junctions,	 which	
allow	 their	 chemical	 properties	 to	 be	 probed	 [8‐11].	 It	 is	
concluded	 that	 although	 the	 fused‐pentagon	 sites	 are	 very	
reactive	 toward	 a	 carbene,	 the	 carbons	 forming	 the	 [5,5]	
junctions	are	less	reactive	than	the	adjacent	ones;	this	confirms	
that	 these	 carbons	 interact	 strongly	 with	 the	 encaged	metals	
and	are	stabilized	by	them	[11].		

For	 C60	 and	 C72,	 only	 one	 IPR	 structure	 is	 consistent	with	
their	symmetry.	Theoretical	studies	on	C60	and	C72	have	shown	
that	the	non‐IPR‐satisfying	structures	are	more	stable	than	the	
IPR‐satisfying	 structures	 [8‐15].	 It	 is	 believed	 that	 the	 fused‐
pentagon	 pairs	 in	 non‐IPR	 EMFs	 are	 stabilized	 by	 electron	
transfer	from	the	encapsulated	metals	to	the	carbon	cage	[16].	
Actually,	both	experimental	results	and	theoretical	calculations	
have	indicated	that	the	encaged	metals	are	associated	with	the	
fused‐pentagon	 pairs	 in	 non‐IPR	 EMFs,	 but	 more	 direct	
experimental	 proof	 is	 still	 lacking	 [16,17‐24].	 Furthermore,	
unlike	the	exohedrally	derivatized	non‐IPR	fullerenes,	non‐IPR	
EMFs	 still	 bear	 unsaturated	 sp2	 carbons	 at	 the	 [5,5]	 bond	
junctions,	 and	 thus,	 it	 is	 of	 special	 interest	 to	 elucidate	 the	
properties	 and	 chemical	 reactivities	 of	 the	 fused	 pentagons.	
However,	 little	 is	 known	 about	 the	 properties	 of	 non‐IPR	
fullerenes	and	non‐IPR	EMFs	 [16].	The	non‐IPR	 fullerenes	are	
always	 attractive	 not	 only	 because	 of	 their	 unique	 structures,	
which	 contain	 fused	 pentagons,	 but	 also	 because	 of	 their	
unusual	properties	 resulting	 from	 the	high	curvatures	 around	
the	adjacent	pentagons	[16,25,26].	

It	 is	 a	 well	 known	 fact	 that	 fullerene	 C60	 is	 a	 highly	
electronegative	molecule.	So,	 it	readily	undergoes	nucleophilic	
reactions	[27,28].	After	the	interesting	work	by	Wudl	et	al.	[29],	
Hirsch	 and	 co‐workers	 [30]	 studied	 the	 reaction	with	 various	
organolithium	 and	 Grignard	 reagents,	 which	 gave	monoalkyl‐
dihydrofullerenes	 with	 well‐defined	 structures	 after	
protonation.	 Fagan	 et	 al.	 [31]	 reported	 the	 synthesis	 and	
properties	 of	 tert‐butyl‐C60	 anion	 by	 means	 of	 nuclcophilic	
addition	of	 tert‐butyllithium	 to	C60	 [27].	 The	 fullerenyl	proton	
in	the	tert‐butyl	derivative	was	shown	to	be	highly	acidic	with	
the	pKa	value	of	5.7	[31].	Since	an	ethynyl	group	has	electron‐
withdrawing	 inductive	 effects	 [32]	 as	 compared	 with	 alkyl	
groups,	 it	was	 expected	 that	 C60	 bearing	 an	 ethynyl	 group,	 R‐
C≡C‐C60‐H,	would	 give	 even	more	 stable	 carbanion	 than	 tert‐
Bu‐C60–	 [27,33].	 However,	 these	 derivatives	 were	 not	 quite	
suitable	 for	 the	 study	of	 their	 anions,	 since	 the	phenylethynyl	
derivative	 was	 only	 soluble	 in	 common	 organic	 solvents	 and	

the	trimethylsilylethynyl	derivative	was	rather	unstable	under	
basic	conditions.	 In	1996,	Komatsu	et	al.	prepared	a	1‐octynyl	
derivative,	Hex‐C≡C‐C60‐H	(1),	which	was	expected	to	be	more	
soluble	 and	 chemically	 stable.	 The	 synthesis,	 properties,	 and	
reactions	of	1‐octynyl‐C60	anion	(2–)	bearing	60	π‐electrons	on	
the	 C60	 core,	 which	 was	 readily	 generated	 from	 1	 (R‐C60–M+;	
R=tert‐Bu‐	&	H–C≡C‐)	were	reported	by	Komatsu	et	al.	[27,33].	

The	 unsaturated,	 cis‐thiocrown	 ethers	 (1‐9),	 comprise	 a	
group	 of	 compounds	 with	 interesting	 physiochemical	
properties,	 in	 light	 of	 their	 conformational	 restrictions	
compared	to	corresponding	saturated	systems	and	the	sizes	of	
their	 cavities.	 The	 presence	 of	 sulfur	 atoms	 gives	 rise	 to	 the	
unique	 properties	 of	 thiocrown	 ethers.	 The	 cis‐unsaturated	
thiocrown	 ethers	 (described	 as	 [X‐UT‐Y],	 where	 X	 and	 Y	
indicate	the	numbers	of	carbon	and	sulfur	atoms,	respectively),	
1‐9,	were	synthesized	and	their	structures	were	confirmed	[34‐
43].	1,4‐Dithiin	is	the	smallest	member	of	compounds	1‐9	that	
has	been	widely	studied	[44‐54].	In	2001,	the	structures	of	[X‐
UT‐Y]	(X	=	6,	9,	12,	15,	18,	21,	24	and	27	and	Y	=	2‐9)	1‐9	were	
reported	by	Tsuchiya	et	al.	 [34]	 In	 that	 report,	 the	 1H	and	 13C	
NMR	 spectra,	 x‐ray	 crystallographic	 data,	 ORTEP	 drawings,	
cavity	 size,	 and	 UV	 spectra	 of	 [X‐UT‐Y]	 1‐9	 were	 carefully	
considered	 [34].	 The	 x‐ray	 crystal	 structures	 and	 ORTEP	
drawings	for	some	members	of	1‐9	[X‐UT‐Y],	namely	X	=	15,	18,	
21,	24	and	27	and	Y	=	5‐9,	show	the	presence	of	cavities	and	a	
nearly	coplanar	arrangement	of	sulfur	atoms	[34].	The	average	
radii	 of	 the	 cavities	 for	4‐8	were	 found	 to	be	1.76,	2.34,	3.48,	
4.43	and	5.36	Å,	respectively	[34].	The	previously	reported	13C	
and	1H‐NMR	spectra	in	CDCl3	showed	that	compound	4	has	the	
highest	chemical	shifts.	The	electron	densities	of	the	C=C	bonds	
increase	with	the	increasing	ring	size	from	4	to	9	and	decrease	
from	4	 to	1	with	the	decreasing	ring	size	[34,35].	In	2006,	the	
oxidation	potential	 (oxE1),	 cyclic	voltammograms	 (Fc/Fc+),	 and	
free	 energies	 of	 electron	 transfer	 (Get)	 of	 supramolecular	
complexes	 of	 [X‐UT‐Y][C60]	 with	 cis‐unsaturated	 thiocrown	
ethers,	1‐9,	were	considered	by	Tsuchiya	et	al.	[35].	The	EMFs	
and	 their	 complexes	 with	 the	 thiocrown	 ethers	 have	 shown	
interesting	 properties	 for	 applications	 and	 basic	 research	
studies.	

The	 wide	 variety	 of	 useful	 applications	 of	 graph	 theory	
shows	 that	 this	 branch	 of	 discrete	 mathematics	 can	 benefit	
various	fields	of	sciences.	Graph	theory	has	been	found	to	be	an	
effective	 tool	 in	 QSAR	 and	 QSPR	 [55‐60].	 A	 graph	 is	 a	
topological	 concept	 rather	 than	 a	 geometrical	 concept,	 and	
hence	Euclidean	metric	 lengths,	 angles	 and	 three‐dimensional	
spatial	 configurations	 have	 no	 meaning.	 Numerous	 studies	
have	 related	 these	 fields	 using	 topological	 indices	 (TI)	 [60].	
Numerous	 applications	 have	 shown	 that	 one	 can	 utilize	 the	
topological	 index	as	a	very	useful	tool	for	molecular	structural	
studies,	 which	 can	 be	 used	 to	 describe	 and	 predict	 reactivity	
and	 structural	 properties,	 in	 addition	 to	 biological	 and	
toxicological	 characters	 of	 compounds.	 One	 group	 of	 TI	 was	
founded	 by	 Randic,	 who	 introduced	 the	 molecular	 branching	
index	 [61].	 In	1975,	Randic	proposed	 a	 topological	 index	 that	
has	 become	 one	 of	 the	 most	 widely	 used	 in	 both	 QSAR	 and	
QSPR	studies.	However,	the	most	important	contribution	of	this	
stage	 is	 probably	 the	 development	 of	 a	 great	 number	 of	
applications	 of	TIs	 in	 several	 fields	 of	 chemistry.	 The	TIs	 are	
based	 on	 Randic’s	 original	 idea	 of	 molecular	 branching,	 but	
have	been	extended	 to	account	 for	contributions	coming	 from	
path	clusters,	clusters,	and	chains	of	different	lengths	[62‐69].	A	
burst	 in	 the	 research	 into	TIs	 began	 during	 the	 1990s,	 and	 is	
marked	 by	 an	 increase	 in	 the	 number	 of	 studies	 and	
applications	of	TIs	 in	chemistry	 [70,78].	Among	 the	successful	
TIs	 in	 these	 applications,	 it	 is	 worth	 noting	 the	 molecular	
connectivity	 indices	 [70,71]	 (including	 the	Randic	 index	[61]),	
the	Randic	index	[61,	65‐69,79‐83],	the	Kier	indices	[73,74],	the	
elecro‐topological	 state	 indices	 [75],	 the	 Balaban	 index	 [75],	
and	 the	 Wiener	 index	 [72].	 Trinajstic	 and	 coworkers	 have	
reported	 that	39	 topological	 indices	are	presently	available	 in	
the	literature	[78,84,85].		



342	 Taherpour	et	al.	/	European	Journal	of	Chemistry	3	(3)	(2012)	340‐347	
	
	
Table	1.	The	reduction	potentials	redEn	(n=1‐3	in	Volt)	of	R‐C60–M+;	R=tert‐Bu‐	&	Hex–C≡C‐,	M=Li	&	K.a	
Compounds	 	 Solv. redE1 redE2 redE3	
Tert‐Bu‐C60–Li+	 THF ‐1.53 ‐2.04 ‐2.61	
Tert‐Bu‐C60–Li+	 DMSO	 ‐1.27	 ‐1.77	 ‐	
Hex‐C≡C‐C60–K+	 THF	 ‐1.55	 ‐2.08	 ‐2.75	
Hex‐C≡C‐C60–Li+	 DMSO	 ‐1.21	 ‐1.72	 ‐2.33	
	a	See	reference	[27].		

	

	

Estrada	has	performed	important	studies	of	generalized	TIs	
with	several	 topological	 indices	 in	 the	graph	 invariant	[79].	 In	
1993	and	1997,	the	Wiener	and	Harary	indices	were	applied	to	
studies	of	fullerenes	[85‐87].	The	use	of	effective	mathematical	
methods	 in	 making	 strong	 correlations	 between	 chemical	
properties	and	the	indices	has	been	reported	[80‐90],	which	is	
an	important	area	of	development.	The	ratio	of	the	sum	of	the	
number	of	carbon	atoms	(nc)	to	the	number	of	sulfur	atoms	(ns)	
to	 the	 product	 of	 these	 two	 numbers	 (cs)	 was	 a	 useful	
numerical	and	structural	value	in	the	studies	reported	here	on	
the	unsaturated	thiocrown	ethers	1‐9	[86‐90].	

Quantitative	structural	relationships	studies	of	the	cs	index	
with	 respect	 to	 the	 oxidation	 potentials	 (oxE1)	 of	 thiocrown	
ethers	 (1‐9),	 as	 well	 as	 the	 free	 energy	 of	 electron	 transfer	
(Get)	between	1‐9	with	fullerenes	and	some	of	the	EMFs	were	
previously	reported	[16,86‐91].	

Here,	 the	 relationships	 between	 this	 index	 and	 oxidation	
potential	 (oxE1)	 of	 1‐9,	 as	 well	 as	 the	 first	 and	 second	 free	
energies	of	electron	transfer	(Get(n),	 for	n=1,	2,	which	is	given	
by	 the	 Rehm‐Weller	 equation)	 between	 1‐9	 and	 [R‐C60–M+]	
(R=tert‐Bu‐	 &	 H–C≡C‐;	 M=Li	 &	 K)	 and	 their	 supramolecular	
complexes	derivatives	as	 [X‐UT‐Y][R‐C60–M+]	 (R=tert‐Bu‐	&	H–
C≡C‐;	M=Li	&	K)	in	DMSO	and	THF	solvents,	are	presented	and	
investigated.	The	first	to	third	free	energies	of	electron	transfer	
and	kinetic	rate	constants	of	the	electron	transfers,	G#et(n)	and	
ket	 (n=1‐3),	 respectively,	were	also	calculated	 in	 this	study	 for	
[X‐UT‐Y][R‐C60–M+]	(R=tert‐Bu‐	&	H–C≡C‐;	M=Li	&	K)	in	DMSO	
and	 THF	 solvents	 and	 in	 accordance	 with	 the	Marcus	 theory	
[16,88‐93],	Figure	1.		

	

 
	

Figure	1.	 The	 structures	 of	 unsaturated	 thiocrown	 ethers	1‐9 with	 [R‐C60–
M+]	(R=tert‐Bu‐	&	H–C≡C‐;	M=Li	&	K)	10	and	11,	to	produce	supramolecular	
complexes	[X‐UT‐Y][R‐C60–M+]	(R=tert‐Bu‐	&	Hex–C≡C‐;	M=Li	&	K)	12‐38.	
	
	

2.	Graphing	and	mathematical	method	
	

All	mathematical	and	graphing	operations	were	performed	
using	MATLAB‐7.4.0	 (R2007a)	 and	Microsoft	Office	 Excel‐2003	
programs.	The	ratio	of	the	sum	of	the	number	of	carbon	atoms	
(nc)	and	the	number	of	sulfur	atoms	(ns)	to	the	product	of	these	
two	numbers	(cs)	is	a	useful	numerical	and	structural	value	for	
the	 unsaturated	 thiocrown	 ethers	1‐9	 that	 were	 investigated	
[75,76,86‐90].		
	
cs	=	ns	+	nc	/	(ns	.	nc)	 	 	 	 (1)	
	

If	nc	=	2ns,	the	coefficient	of	cs	is	given	by		
	
cs	=	3/(2ns)	 	 	 	 	 (2)	
	

For	 modeling,	 both	 linear	 (MLR:	 Multiple	 Linear	
Regressions)	 and	 nonlinear	 (ANN:	 Artificial	 Neural	 Network)	
models	were	examined.	Other	 indices	were	examined	and	 the	
best	 results	 and	 equations	 for	 extending	 the	 physicochemical	
and	electrochemical	data	were	chosen.	
	

The	Rehm‐Weller	equation	estimates	the	free	energy	change	
between	an	electron	donor	(D)	and	an	acceptor	(A)	as:	[92]		
	
ΔGet	=	e[ED−	EA]	−	ΔE*	+	ω1	 	 	 	 (3)	
	

where	 “e”	 is	 the	unit	 electrical	 charge,	EDo	 and	EAo	 are	 the	
reduction	 potentials	 of	 the	 electron	 donor	 and	 acceptor,	
respectively,	 ΔE*	 is	 the	 energy	 of	 the	 singlet	 or	 triplet	 excited	
state,	 and	 ω1	 is	 the	 work	 required	 to	 bring	 the	 donor	 and	
acceptor	within	 the	 electron	 transfer	 (ET)	 distance.	 The	work	
term	in	this	expression	can	be	considered	to	be	 ‘0’	 in	so	far	as	
an	 electrostatic	 complex	 exists	 before	 the	 electron	 transfer	
[92].	

The	Marcus	theory	of	electron	transfer	implies	rather	weak	
(<0.05eV)	 electronic	 coupling	 between	 the	 initial	 (locally	
excited,	 LE)	 and	 final	 (electron	 transfer,	 CT)	 states	 and	
presumes	that	the	transition	state	is	close	to	the	crossing	point	
of	 the	 LE	 and	 CT	 terms	 [93‐100].	 The	 value	 of	 the	 electron	
transfer	 rate	 constant	 ket	 is	 controlled	 by	 the	 activation	 free	
energy	ΔG#et,	which	 is	 a	 function	of	 the	 reorganization	energy	
(l/4)	and	the	electron	transfer	driving	force	ΔGet	[93‐100].		
	
ΔG#et	=	(l/4)(1+ΔGet/l)2	 	 	 	 (4)		
	
ket	=	k0	exp(‐ΔG#et/RT)	 	 	 	 (5)		
	

The	 reorganization	 energy	 of	 organic	 molecules	 ranges	
from	0.1‐0.3	eV.	 In	 this	study,	was	used	the	minimum	amount	
of	reorganization	energy	[93‐100].	
	
3.	Discussion	
	

The	 reduction	potentials	and	redox	behavior	of	1‐octynyl‐
C60	 anion	 (2‐)	 were	 examined	 before	 by	 the	 use	 of	 cyclic	
voltammetry	 in	 THF	 and	 DMSO	 solvents	 [27].	 Characteristic	
voltammogram	 results	 were	 observed	 by	 Komatsu	 et	 al.	 and	
their	 data	 were	 presented	 in	 Table	 1,	 together	 with	 those	
reported	for	tert‐Bu‐C60	anion	[27].		

	
	



Taherpour	et	al.	/	European	Journal	of	Chemistry	3	(3)	(2012)	340‐347	 343	
 

	
Table	2.	Structural	coefficients	of	unsaturated	thiocrown	ethers	[X‐UT‐Y]	1‐9	and	the	values	of	the	free	energy	of	electron	transfer	(Get(n),	n=1‐3),	in	kcal	mol‐1,	
between	unsaturated	thiocrown	ethers,	1‐9,	with	[R‐C60–M+](R=tert‐Bu‐	&	Hex–C≡C‐;	M=Li	&	K)	10‐11	in	supramolecular	[[X‐UT‐Y][R‐C60–M+](R=tert‐Bu‐	&	Hex–
C≡C‐;	M=Li	&	K)	12‐38	complexes	a	[27].	
No	 Formula	of		

[X‐UT‐Y]	
cs	 oxE1	

(Volt)	
[X‐UT‐Y][tert‐Bu‐C60–Li+]	12‐20 solved	in	THF [X‐UT‐Y][tert‐Bu‐C60–Li+]	12‐20	solved	in	DMSO	

Get(1)	 Get(2)	 Get(3)	 Get(1)	 Get(2)	 Get(3)	
1	 6‐UT‐2(1,4‐dithiin)	 0.7500	 1.02	 58.05	

(58.11)	
69.82
(69.87)	

82.96
(83.02)	

52.06
(52.12)	

63.59	
(63.65)	

_	

2	 9‐UT‐3	 0.5000	 0.97	 57.11	
(56.96)	

68.87
(68.72)	

82.01
(81.86)	

51.11
(50.96)	

62.64	
(62.49)	

_	

3	 12‐UT‐4	 0.3750	 0.89	 55.20	
(55.11)	

66.96
(66.87)	

80.10
(80.02)	

49.20
(49.12)	

60.73	
(60.65)	

_	

4	 15‐UT‐5	 0.3000	 0.82	 53.60	
(53.50)	

65.35	
(65.26)	

78.49	
(78.40)	

47.59	
(47.50)	

59.12	
(59.03)	

_	

5	 18‐UT‐6	 0.2500	 0.79	 52.33	
(52.81)	

64.08	
(64.57)	

77.29	
(77.71)	

46.33	
(46.81)	

57.86	
(58.34)	

_	

6	 21‐UT‐7	 0.2143	 0.73	 51.34	
(51.48)	

63.09
(63.18)	

76.23
(76.33)	

45.33
(45.43)	

56.86	
(56.96)	

_	

7	 24‐UT‐8	 0.1875	 0.69	 50.54	
(50.50)	

62.29
(62.26)	

75.43
(75.41)	

44.53
(44.51)	

56.06	
(56.04)	

_	

8	 27‐UT‐9	 0.1667	 0.66	 49.89	
(49.81)	

61.64
(61.57)

74.78
(74.71)

43.88
(43.81)

55.41	
(55.34)	

_	

9	 30‐UT‐10	 0.1500	 0.63	 49.35	
(49.12)	

61.10	
(60.88)	

74.24	
(74.02)	

43.33	
(43.12)	

54.87	
(54.65)	

_	

	 	 	 	 	 	 	 	 	
No	 Formula	of	

[X‐UT‐Y]	
cs	
	

oxE1	
(Volt)	

[X‐UT‐Y][Hex‐C≡C‐C60–Li+]	21‐29 solved	in	DMSO [X‐UT‐Y][Hex‐C≡C‐C60–K+]	30‐38	solved	in	THF

Get(1)	 Get(2)	 Get(3)	 Get(1)	 Get(2)	 Get(3)	
1	 6‐UT‐2(1,4‐dithiin)	 0.7500	 1.02	 50.68	

(50.73)	
62.43
(62.49)	

76.50
(76.56)	

58.51
(58.57)	

70.74	
(70.79)	

86.18
(86.24)	

2	 9‐UT‐3	 0.5000	 0.97	 49.73	
(49.58)	

61.49
(61.34)	

75.56
(75.41)	

57.57
(57.42)	

69.79	
(69.64)	

85.24
(85.09)	

3	 12‐UT‐4	 0.3750	 0.89	 47.82	
(47.73)	

59.58
(59.50)	

73.64
(73.56)	

55.66
(55.58)	

67.88	
(67.80)	

83.33
(83.25)	

4	 15‐UT‐5	 0.3000	 0.82	 46.20	
(46.12)	

57.97	
(57.88)	

72.03	
(71.95)	

54.05	
(53.96)	

66.27	
(66.18)	

81.72	
(81.63)	

5	 18‐UT‐6	 0.2500	 0.79	 44.94	
(45.43)	

56.70	
(57.19)	

70.77	
(71.25)	

52.78	
(53.27)	

65.01	
(65.49)	

80.46	
(80.94)	

6	 21‐UT‐7	 0.2143	 0.73	 43.95	
(44.05)	

55.71	
(55.80)	

69.78	
(69.87)	

51.79	
(51.88)	

64.01	
(64.11)	

79.46	
(79.56)	

7	 24‐UT‐8	 0.1875	 0.69	 43.15	
(43.12)	

54.91
(54.88)	

68.98
(68.95)	

50.99
(50.96)	

63.21	
(63.18)	

78.66
(78.64)	

8	 27‐UT‐9	 0.1667	 0.66	 42.50	
(42.43)	

54.26
(54.19)	

68.33
(68.26)	

50.34
(50.27)	

62.56	
(62.49)	

78.09
(77.94)	

9	 30‐UT‐10	 0.1500	 0.63	 41.96	
(41.74)	

53.71
(53.50)

67.78
(67.57)

49.79
(49.58)

62.02	
(61.80)	

77.47
(77.25)

a	The	data	for	the	compounds	and	their	complexes	have	not	been	previously	reported.	The	supramolecular	[X‐UT‐Y][R‐C60–M+]	(R=tert‐Bu‐&	Hex–C≡C‐;	M=Li	&	
K)	12‐38	complexes	have	not	been	synthesized	nor	reported	previously.	
	
	
	
They	 reported	 that	 the	 anion	 2‐	 in	 THF	 was	 oxidized	 to	 its	
radical	 at	 ‐0.39	 V	 vs	 ferrocene/ferrocenium	 (Fc/Fc+:	 0.1	 V/s;	
supporting	 electrolyte,	 Bu4NBF4;	 0.1	 M),	 the	 corresponding	
reduction	 was	 shifted	 to	 ‐1.20	 V,	 the	 difference	 of	 peak	
potentials	 being	 0.81	V	 [27].	 They	 investigated	 that	 this	 large	
negative	 shift	 of	 the	 cathodic	 peak	 was	 ascribed	 to	 some	
chemical	process	associated	with	the	electron	transfer,	which	is	
most	 probably	 a	 very	 rapid	 dimerization	 of	 the	 1‐octynyl‐C60	
radical	 [27].	 The	 reduction	 of	 the	 dimer	 to	 the	 original	
monomeric	anion	2‐	required	extra	energy	for	dissociation	and	
also	for	structural	change	 in	C60	 framework,	which	could	have	
caused	 the	cathodic	shift	as	has	been	observed	by	Komatsu	et	
al.	[27].	The	second	and	third	reductions	were	nearly	reversible	
as	observed	in	individual	redox	waves	[27].	In	order	to	examine	
the	 structure	 and	 properties	 of	 anion	 2‐,	 semiempirical	 MO	
calculations	(AM1)	were	conducted	as	has	been	done	by	Hirsch	
and	 co‐workers	 for	 tert‐Bu‐C60	 anion	 [27,30]	 (0.1	 V/s;	
supporting	electrolyte,	Bu4NBF4;	0.1	M).		

The	 reduction	 potentials	 of	 1‐9,	 shown	 in	 Table	 2,	
demonstrate	 that	 the	cs	 index	 decreases	 with	 increasing	 the	
molecular	 size.	 In	 Table	 2,	 related	 values	 for	 the	
supramolecular	 complexes	 of	 [X‐UT‐Y]	 1‐9	 with	 R‐C60–M+;	
R=tert‐Bu‐	&	H–C≡C‐	 (M=Li	and	K)	 (10‐12)	were	also	shown.	
Table	2	shows	the	values	of	oxidation	potential	(oxE1),	as	well	as	
the	 calculated	 first	 and	 second	 free	 energies	 of	 electron	
transfer	(Get(n),	n=1‐3)	between	some	of	the	[X‐UT‐Y]	and	the	
complexes	 10‐12	 for	 supramolecular	 13‐15	 complexes.	 The	

RedEn	 (n=1‐3)	data	 for	10,	11	 and	12	 are	presented	 in	Table	1	
[16].		

The	oxidation	potentials	(oxE1)	of	4‐7	were	found	to	be	0.82,	
0.79,	 0.73	 and	 0.69	 V,	 respectively	 [34,35,86‐90].	 The	 free	
energies	 of	 electron	 transfer	 (Get(n),	 n=1‐3)	 between	1‐9	 and	
10‐12	 for	 making	 [X‐UT‐Y][R‐C60–M+]	 (R=tert‐Bu‐	 &	 H–C≡C‐;	
M=Li	&	K)	(complexes	13‐15)	were	calculated	using	the	Rehm‐
Weller	equation	[86‐90].	

In	Figure	1	supramolecular	[X‐UT‐Y][R‐C60–M+]	(R=tert‐Bu‐	
&	Hex–C≡C‐;	M=Li	&	K)	complexes	were	shown	as	groups	12‐
38	in	THF	and	DMSO	solvents.	

Table	3	 shows	 the	equations	of	 the	 relationships	between	
the	 cs	 index	 and	 the	 first,	 second	 and	 third	 free	 energies	 of	
electron	 transfer	 (Get(n),	 n=1‐3)	 between	 1‐9	 with	 the	
molecules	[R‐C60–M+]	(R=tert‐Bu‐	&	H–C≡C‐;	M=Li	&	K)	10	and	
11	 to	 produce	 [X‐UT‐Y][R‐C60–M+]	 (R=tert‐Bu‐	 &	 Hex–C≡C‐;	
M=Li	&	K)	in	THF	and	DMSO	solvents.		

Figure	 2	 shows	 the	 plots	 of	 the	 relationship	 between	 cs	
and	 the	 three	 free	 energies	 (Get(n)	 n=1‐3	 in	 kcal	 mol‐1)	 for	
electron	transfer	between	1‐9	and	[tert‐But‐C60–Li+]	to	produce	
supramolecular	 [X‐UT‐Y][tert‐But‐C60–Li+]	 (compounds	12‐20)	
solved	 in	THF.	The	 related	 curves	 for	other	 complexes	 [X‐UT‐
Y][R‐C60–M+]	(R=tert‐Bu‐	&	Hex–C≡C‐;	M=Li	&	K)	21‐38	which	
they	solved	in	THF	and	DMSO	have	similar	structures	to	Figure	
2.	The	calculated	values	and	the	related	equations	of	the	three	
free	energies	of	electron	transfer	(Get(n)	n=1‐3)	were	shown	in	
Table	2	and	3.		



344	 Taherpour	et	al.	/	European	Journal	of	Chemistry	3	(3)	(2012)	340‐347	
	

	
Table	3.	Second	order	polynomial	equations	(4‐16)	that	indicate	the	relationship	between	the	index	cs	and	the	first	and	second	free	energies	of	electron	transfer	
(Get(n),	n=1,2)	between	unsaturated	thiocrown	ethers	1‐9	with	10	and	11	in	the	structures	[X‐UT‐Y][R‐C60–M+]	(R=tert‐Bu‐	&	Hex–C≡C‐;	M=Li	&	K)	12‐38.		
Complexes	[X‐UT‐Y][R‐C60–	M+]	(R=tert‐Bu‐	&	Hex–C≡C‐;	M=Li	&	K)	

Equations	 R2	
Get(n)	=	a(cs)2	+	b(cs)	+	c	

Number	of	complexes	 	 	 a	 b	 c	
12‐20	 THF 1 Eq.‐6 0.995 ‐30.691	 42.137	 43.716
12‐20	 THF 2 Eq.‐7 0.995 ‐30.707	 42.172	 55.460
12‐20	 THF 3 Eq.‐8 0.995 ‐30.683	 42.158	 68.606
12‐20	 DMSO 1 Eq.‐9 0.995 ‐30.683	 42.158	 37.706
12‐20	 DMSO	 2	 Eq.‐10	 0.996	 ‐30.683	 42.158	 49.236	
21‐29	 DMSO	 1	 Eq.‐11	 0.996	 ‐30.754	 42.214	 44.154	
21‐29	 DMSO	 2	 Eq.‐12	 0.996	 ‐30.751	 42.208	 53.377	
21‐29	 DMSO 3 Eq.‐13 0.996 ‐30.735	 42.190	 71.831
30‐38	 THF	 1	 Eq.‐14	 0.996	 ‐30.705	 42.166	 36.323	
30‐38	 THF 2 Eq.‐15 0.996 ‐30.754	 42.214	 48.074
30‐38	 THF 3 Eq.‐16 0.996 ‐30.694	 42.163	 62.150
	

	
The	values	were	obtained	using	the	Rehm‐Weller	equation	

[92],	 for	other	complexes	of	1‐9	with	[R‐C60–M+]	(R=tert‐Bu‐	&	
Hex–C≡C‐;	M=Li	&	K)	10‐11	as	[X‐UT‐Y][R‐C60–M+]	(R=tert‐Bu‐	
&	Hex–C≡C‐;	M=Li	&	K)	12‐38.		

	

	
Figure	2.	Plots	of	 the	 relationship	between	 the	cs	 index	versus	 the	 first	 to	
third	 free	energies	of	electron	transfer	(Get(n)	n=1‐3	in	kcal	mol‐1)	between	
1‐9	 with	 [tert‐But‐C60–Li+]	 (compounds	12‐20)	 to	 produce	 supramolecular	
[X‐UT‐Y][tert‐But‐C60–Li+]	 solved	 in	 THF.	 The	 related	 curves	 for	 other	
complexes	 [X‐UT‐Y][R‐C60–M+]	 (R=tert‐Bu‐	 &	 Hex–C≡C‐;	 M=Li	 &	 K)	 21‐38	
which	they	solved	in	THF	and	DMSO	have	similar	structures	to	Figure	2.	

	
Using	equations	6‐16	(Table	3),	it	is	possible	to	obtain	good	

approximations	for	the	Get(n)	of	supramolecular	complexes	12‐
20,	 21‐29	 and	 30‐38	 groups,	 in	 the	 first	 to	 third	 reduction	
potential	states	of	[X‐UT‐Y][R‐C60–M+]	(R=tert‐Bu‐	&	Hex–C≡C‐;	
M=Li	 &	 K)	 12‐38	 complexes,	 in	 THF	 and	 DMSO	 solvents.	
Equations	 6‐8	 describe	 Figure	 2.	 They	 show	 a	 quadratic	
relationship	 between	Get(n)	 (n=1‐3)	 and	cs	 for	 [X‐UT‐Y][tert‐
But‐C60–Li+]	(compounds	12‐20)	solved	in	THF.	In	the	complex	
groups,	 the	R2	 values	 for	 the	 graphs	 (Figure	2)	 are	0.995	 and	
the	appropriate	 equations	are	given	 in	Table	3.	 In	 light	of	 the	
good	correlations	between	cs	and	the	free	energies	of	electron	
transfer,	it	is	possible	to	use	cs	to	calculate	the	Get(n)	of	12‐38.	
The	values	of	the	Get	decrease	with	increasing	group	size	(1‐9)	
and	 decreasing	 cs	 indices,	 as	 indicated	 in	 Table	 2	 and	 3.	
Equations	 9	 and	 10	 return	 to	 the	 quadratic	 second	 order	
relationship	 between	 Get(n)	 (n=1	 and	 2)	 and	 cs	 for	 [X‐UT‐
Y][tert‐But‐C60–Li+]	 (compounds	 12‐20)	 solved	 in	 DMSO.	 In	
accordance	with	the	data	of	Table	1,	there	was	not	any	reported	
result	for	the	third	reduction	potential	(redE3)	of	tert‐Bu‐C60–Li+	
in	DMSO.		

The	values	of	the	first	to	third	free	energies	were	shown	in	
Table	2	for	the	electron	transfer	process	between	unsaturated	
thiocrown	ethers	1‐9	and	the	reduction	potential	of	10	and	11	
as	 the	 complexes	 [X‐UT‐Y][Hex–C≡C‐C60–Li+]	 (in	 THF	 and	
DMSO	solvents)	(groups	21‐29).	The	predicted	values	of	Get(n)	
for	the	complexes	21‐29	and	other	complexes	were	calculated	
using	 the	 Rehm‐Weller	 equation.	 The	 equations	 of	 the	
relationship	 between	 values	 of	 cs	 and	 the	 free	 energies	 of	

electron	 transfer	 Get(n)	 of	 21‐29	 were	 shown	 in	 Table	 3.	
Equations	11	to	13	show	quadratic	polynomial	structures.	The	
R2	 values	 that	 indicate	 correlation	 between	 cs	 and	 the	 free	
energies	of	electron	transfer	of	21‐29	(in	redEn	(n=1‐3)	state	of	
11	 in	 DMSO	 solvent)	 are	 all	 equal	 to	 0.996.	 These	 good	
correlations	 between	 cs	 and	 the	 free	 energies	 of	 electron	
transfer	 suggest	 that	 it	 is	 possible	 to	 use	 cs	 to	 calculate	 the	
Get(n)	 for	 [X‐UT‐Y][Hex–C≡C‐C60–Li+]	 (in	 DMSO	 solvents)	
(groups	 21‐29)	 by	 the	 equations	 of	 this	 model.	 This	 case	 is	
found	to	be	similar	to	the	other	complexes,	in	which	the	values	
of	 the	 Get(n)	 decrease	 with	 the	 increasing	 size	 (1‐9)	 and	
decreasing	cs	indices	(see	Table	2).		

Equations	 14‐16	 (Table	 3)	 demonstrate	 the	 relationships	
between	the	free	energies	of	electron	transfer	between	1‐9	and	
11	 in	 [X‐UT‐Y][Hex–C≡C‐C60–K+](in	 THF	 solvent)	 (groups	30‐
38)	 complexes	 with	 the	 cs	 indices	 for	 the	 unsaturated	
thiocrown	ethers,	1‐9.	These	data	were	fitted	using	regression	
with	a	second‐order	polynomial.	The	amounts	of	R2	values	for	
these	 graphs	 are	 0.996.	 Using	 Equations	 3	 and	 14‐16,	 it	 is	
possible	 to	 calculate	 the	 values	 of	 Get(1)	 to	 Get(3)	 of	 [X‐UT‐
Y][Hex–C≡C‐C60–K+]	complexes	(groups	30‐38)	in	THF	solvent.	
As	shown	in	Table	2,	similar	to	complexes	12‐20	and	21‐29	(in	
THF	and	DMSO	solvents)	the	values	of	Get(n)	in	the	complexes	
decrease	 with	 increasing	 the	 size	 of	 1‐9	 and	 decreasing	 cs	
indices.	 In	 THF	 solvent	 the	 values	 of	 Get(1)	 to	 Get(3)	 show	
greater	amounts	than	DMSO	in	each	group	of	12‐20,	21‐29	and	
30‐38	 complexes.	 It	 may	 returns	 back	 to	 the	 greater	 dipole	
moment	and	structural	properties	of	DMSO	than	THF.	It	seems	
that	 these	 properties	 were	 susceptible	 the	 HOMO	 and	 LUMO	
level	 energies	 and	 the	 HOMO‐LUMO	 energy	 gaps	 of	 the	
complexes	in	the	groups	12‐20,	21‐29	and	30‐38.		

The	 ratio	 of	 sum	of	 the	number	 of	 carbon	 atoms	 (nc)	 and	
the	 number	 of	 sulfur	 atoms	 (ns)	 to	 the	 product	 of	 these	 two	
numbers,	given	by	the	index	cs,	shows	a	good	relationship	with	
structural	 values	 of	 the	 unsaturated	 thiocrown	 ethers,	 1‐9.	
These	results	show	the	calculated	values	of	the	free	energies	of	
electron	 transfer	 Get(1)	 to	Get(3).	 On	 the	 basis	 of	 the	 first	 to	
third	reduction	potentials	(redE1	to	redE3	states)	the	free	energies	
of	electron	transfer	were	calculated	for	the	supramolecular	[X‐
UT‐Y][R‐C60–M+]	(R=tert‐Bu‐	&	Hex–C≡C‐;	M=Li	&	K)	complexes	
as	groups	12‐38	in	THF	and	DMSO	solvents.		

The	 Marcus	 theory	 is	 currently	 the	 dominant	 theory	 of	
electron	 transfer	 in	 chemistry.	 The	 Marcus	 theory	 is	 widely	
accepted	because	it	accurately	predicts	electron	transfer	rates.	
The	 most	 significant	 prediction	 is	 that	 the	 rate	 of	 electron	
transfer	will	increase	as	the	electron	transfer	reaction	becomes	
more	exergonic,	but	only	to	a	point	[94‐100].	

Electron	 transfer	 (ET)	 is	 one	 of	 the	 most	 important	
chemical	processes	 in	nature	and	plays	a	central	 role	 in	many	
biological,	 physical	and	chemical	 (both	organic	and	 inorganic)	
systems.	 Solid‐state	 electronics	 depends	 on	 controlling	 ET	 in	
semiconductors.	 Current	 molecular	 electronics	 depends	
critically	 on	 understanding	 and	 controlling	 the	 transfer	 of	
electrons	in	and	between	molecules	and	nanostructures.		

	



Taherpour	et	al.	/	European	Journal	of	Chemistry	3	(3)	(2012)	340‐347	 345	
 

	
Table	4.	Structural	coefficients	of	unsaturated	thiocrown	ethers	[X‐UT‐Y]	1‐9	and	the	values	of	the	free	energy	of	electron	transfer	(G#et(n),	n=1‐3),	in	kcal	mol‐1,	
between	unsaturated	thiocrown	ethers,	1‐9,	with	[R‐C60–M+](R=tert‐Bu‐	&	Hex–C≡C‐;	M=Li	&	K)	10	and	11)	in	supramolecular	[X‐UT‐Y][R‐C60–M+](R=tert‐Bu‐	&	
Hex–C≡C‐;	M=Li	&	K)	12‐38	a	[27].	
No	 Formula	of	*		

[X‐UT‐Y]	
[X‐UT‐Y][tert‐Bu‐C60–Li+]	12‐20 solved	in	THF [X‐UT‐Y][tert‐Bu‐C60–Li+]	12‐20	solved	in	DMSO	b

G#et(1)	 G#et(2)	 G#et(3)	 G#et(1)	 G#et(2)	 G#et(3)	
1	 6‐UT‐2(1,4‐dithiin)	 122.88	 169.55	 230.62	 101.99	 143.94	 _	
2	 9‐UT‐3	 118.72	 164.66	 224.86	 98.17	 139.39	 _	
3	 12‐UT‐4	 112.18	 156.94	 215.86	 92.26	 132.33	 _	
4	 15‐UT‐5	 106.63	 150.36 208.10 87.21 126.26	 _	
5	 18‐UT‐6	 104.30	 147.59 204.83 85.10 123.72	 _	
6	 21‐UT‐7	 99.88	 142.08 198.38 80.96 118.72	 _	
7	 24‐UT‐8	 96.68	 138.50 194.14 78.26 115.44	 _	
8	 27‐UT‐9	 94.45	 135.84 190.94 76.24 112.98	 _	
9	 30‐UT‐10	 92.26	 133.20 187.81 74.26 110.58	 _	

	 	 	 	 	 	 	
No	 Formula	of		

[X‐UT‐Y]	
[X‐UT‐Y][Hex‐C≡C‐C60–Li+]	21‐29 solved	in	DMSO [X‐UT‐Y][Hex‐C≡C‐C60–K+]	30‐38	solved	in	THF
G#et(1)	 G#et(2)	 G#et(3)	 G#et(1)	 G#et(2)	 G#et(3)	

1	 6‐UT‐2(1,4‐dithiin)	 97.42	 139.39	 199.45	 124.57	 173.52	 247.00	
2	 9‐UT‐3	 93.72	 134.95	 194.14	 120.38	 168.57	 241.09	
3	 12‐UT‐4	 87.92	 128.01	 185.74	 113.82	 160.79	 231.77	
4	 15‐UT‐5	 83.02	 122.04 178.59 108.20 154.10	 223.72
5	 18‐UT‐6	 80.96	 119.55 175.52 105.85 151.29	 220.34
6	 21‐UT‐7	 76.92	 114.60 169.55 101.19 145.76	 213.64
7	 24‐UT‐8	 74.26	 111.38 165.63 98.17 142.08	 209.64
8	 27‐UT‐9	 72.31	 108.99 162.72 95.93 139.39	 205.24
9	 30‐UT‐10	 70.40	 106.63 159.84 93.72 136.72	 202.67
a	The	data	for	the	compounds	and	their	complexes	were	not	reported,	previously.	The	compounds	[X‐UT‐Y][R‐C60–M+]	(R=tert‐Bu‐	&	Hex–C≡C‐;	M=Li	&	K)	12‐38	
complexes	were	neither	synthesized	nor	reported	previously.	
b	This	derivative	has	not	ket(3)	and	G#et(3)	in	DMSO.	
	
Table	5.	The	values	of	the	first	to	third	free	activation	energies	of	electron	transfer	rate	constants	(ket(n),	n=1‐3)	of	[X‐UT‐Y][R‐C60–M+](R=tert‐Bu‐	&	Hex–C≡C‐;	
M=Li	&	K)	12‐38	supramolecular	complexes	between	1‐9	and	10	and	11.	
No	 Formula	of		

[X‐UT‐Y]	
[X‐UT‐Y][tert‐Bu‐C60–Li+]	12‐20 solved	in	THF [X‐UT‐Y][tert‐Bu‐C60–Li+]	12‐20	solved	in	DMSO	a
ket(1)	 ket	(2) ket(3) ket(1) ket	(2)	 ket(3)

1	 6‐UT‐2(1,4‐dithiin)	 4.32×10‐78	 2.54×10‐112	 4.12×10‐157	 9.07×	10‐63	 1.57×10‐93	 _	
2	 9‐UT‐3	 4.87×10‐75	 9.87×10‐109	 6.96×10‐153	 5.76×10‐60	 3.38×10‐90	 _	
3	 12‐UT‐4	 3.07×10‐70	 4.56×10‐103	 2.75×10‐146	 1.25×10‐55	 5.10×10‐85	 _	
4	 15‐UT‐5	 3.58×10‐66	 3.01×10‐98 1.36×10‐140 6.33×10‐52 1.43×10‐80	 _	
5	 18‐UT‐6	 1.84×10‐64	 3.25×10‐96 3.38×10‐138 2.23×10‐50 1.04×10‐78	 _	
6	 21‐UT‐7	 3.24×10‐61	 3.56×10‐92 1.82×10‐133 2.42×10‐47 4.88×10‐75	 _	
7	 24‐UT‐8	 7.19×10‐59	 1.52×10‐89 2.36×10‐130 2.32×10‐45 1.23×10‐72	 _	
8	 27‐UT‐9	 3.06×10‐57	 1.36×10‐87 5.23×10‐128 7.11×10‐44 7.91×10‐71	 _	
9	 30‐UT‐10	 1.25×10‐55	 1.17×10‐85 1.03×10‐125 1.98×10‐42 4.57×10‐69	 _	
	 	 	 	 	 	 	 	

No	 Formula	of		
[X‐UT‐Y]	

[X‐UT‐Y][Hex‐C≡C‐C60–Li+]	21‐29 solved	in	DMSO [X‐UT‐Y][Hex‐C≡C‐C60–K+]	30‐38	solved	in	THF
ket(1)	 ket	(2) ket(3) ket(1) ket	(2)	 ket(3)

1	 6‐UT‐2(1,4‐dithiin)	 2.04×10‐59	 3.38×	10‐90	 3.00×10‐134	 2.51×10‐79	 3.12×10‐115	 3.98×10‐169	
2	 9‐UT‐3	 1.06×10‐56	 6.04×10‐87 2.36×10‐130 2.97×10‐76 1.34×10‐111	 8.68×10‐165
3	 12‐UT‐4	 1.91×10‐52	 7.51×10‐82	 3.39×10‐124	 1.91×10‐71	 6.73×10‐106	 5.90×10‐158	
4	 15‐UT‐5	 7.51×10‐49	 1.78×10‐77 5.99×10‐119 2.53×10‐67 5.46×10‐101	 4.73×10‐152
5	 18‐UT‐6	 2.42×10‐47	 1.21×10‐75 1.06×10‐116 1.34×10‐65 6.25×10‐99	 1.44×10‐149
6	 21‐UT‐7	 2.21×10‐44	 5.17×10‐72 2.54×10‐112 3.48×10‐62 7.20×10‐95	 1.17×10‐144
7	 24‐UT‐8	 1.98×10‐42	 1.19×10‐69 1.91×10‐109 5.76×10‐60 3.56×10‐92	 1.98×10‐141
8	 27‐UT‐9	 5.30×10‐41	 6.67×10‐68 2.60×10‐107 2.52×10‐58 3.33×10‐90	 5.40×10‐139
9	 30‐UT‐10	 1.35×10‐39	 3.58×10‐66 3.40×10‐105 1.06×10‐56 3.06×10‐88	 1.30×10‐136
a	This	derivative	has	not	ket(3)	and	G#et(3)	in	DMSO.	

	

	
Electron	transfer	is	a	very	simple	chemical	reaction,	which	can	
be	 used	 to	 gain	 insight	 into	 other	 kinds	 of	 chemistry	 and	
biochemistry.	 Electron	 transfer	 is	 fundamental	 in	 chemistry	
[93‐100].	

The	 free	 energy	 of	 electron	 transfer	Get	 is	 the	 difference	
between	 the	 reactants	 and	 the	 products,	 and	 Get#	 is	 the	
activation	 energy.	 The	 reorganization	 energy	 is	 the	 energy	
required	 to	 force	 the	 reactants	 to	 have	 the	 same	 nuclear	
configuration	 as	 the	products	without	permitting	 the	 electron	
transfer.	 If	 the	 entropy	 changes	 are	 ignored,	 the	 free	 energy	
becomes	energy	or	potential	energy	[93‐100].		

Using	 Equations	 4	 and	 5,	 it	 is	 possible	 to	 calculate	 the	
activate	 free	 energies	 of	 electron	 transfer	 and	 kinetic	 rate	
constants	 of	 the	 electron	 transfers,	 G#et(n)	 and	 ket(n)	 (n=1‐3),	
respectively,	 for	 12‐38	 in	 accordance	 with	 Marcus	 theory.	
Figure	 3	 shows	 the	 surfaces	 of	 the	 free	 energies	 of	 electron	
transfer	Get(n)	and	Get(n)#	 (n=1‐3)	 between	 [X‐UT‐Y]	1‐9	 and	
[R‐C60–M+]	 (R=tert‐Bu‐	 &	 Hex–C≡C‐;	 M=Li	 &	 K)	 10‐11	 in	
supramolecular	 [X‐UT‐Y][R‐C60–M+]	 (R=tert‐Bu‐	 &	 Hex–C≡C‐;	
M=Li	 &	 K)	 12‐38	 complexes.	 The	 values	 of	 the	 first	 to	 third	
activation	free	energies	of	electron	transfer,	G#et(n)	(n=1‐3)	for	

12‐20	 and	 21‐29	 in	 THF	 and	 DMSO	 solvents,	 decrease	 with	
Get(n)	and	cs	descriptor,	while	the	kinetic	rate	constants	of	the	
electron	transfers	ket(n)	(n=1‐3),	increase	with	decreasing	Get(n)	
and	Get(n)#	(n=1‐3)	for	12‐38.	See	Tables	4	and	5	and	Figure	3.	
In	 THF	 solvent	 the	 values	 of	Get(1)	 #	 to	Get(3)	 #	 show	 greater	
amounts	than	DMSO	in	each	group	of	12‐20,	21‐29	and	30‐38	
complexes.	 In	 notice	 to	 the	 reported	 results	 of	 the	 electron	
transfer	 rate	 constant	 ket(n)	 (n=1‐3)	 in	 Table	 5,	 the	 rate	 of	
electron	transfer	in	DMSO	is	greater	than	THF.		

Figure	3	shows	the	surfaces	of	the	free	energies	of	electron	
transfer	Get(n)	 and	Get(n)#	 (n=1	 to	 3)	 between	1‐9	 with	 10	
and	 11	 in	 the	 structures	 12‐38	 complexes.	 The	 values	 were	
calculated	by	equations	1‐16,	which	 they	are	shown	 in	Tables	
2‐5.	 With	 the	 appropriate	 equations	 and	 in	 light	 of	 the	 good	
correlations	(see	Figures	1‐3	and	equations	1‐16),	it	is	possible	
to	 calculate	 the	 values	 of	 the	 first	 to	 third	 free	 energies	 of	
electron	transfer	(Get	in	kcal/mol),	the	first	to	third	activation	
free	energies	of	electron	transfer	and	kinetic	rate	constants	of	
the	 electron	 transfers,	 G#et(n)	 and	 ket(n)	 (n=1‐3),	 respectively,	
for	 12‐38	 in	 THF	 and	 DMSO,	 in	 close	 accordance	 with	 the	
results	of	Marcus	theory.		



346	 Taherpour	et	al.	/	European	Journal	of	Chemistry	3	(3)	(2012)	340‐347	
	

	

Get(1)
#

Get(2)
#

Get(1)

Get(2)

[X-UT-Y] 1-9

with [R-C60
-M+] 10 and 11

R=tert-Bu- & 

Hex-C     C-; M=Li & K, 

in DMSO & THF Solvents

[TS]1

[TS]2

First step of electron transfer 
in 12-38

[TS]3

Get(3)
#

Get(3)

Second step of electron transfer 
in 12-38

[X-UT-Y][R-C60
-M+]

R=tert-Bu- & 

Hex-C     C-; M=Li & K,

12-38 

in DMSO & THF Solvents  
	

Figure	3.	The	surfaces	of	the	free	energies	of	electron	transfer	Get(n)	and	Get(n)# (n=1‐3)	between	1‐9,	10	and	11	in	12‐38.	
	
	
The	 supramolecular	 complexes	 of	 unsaturated	 thiocrown	

ethers	 1‐9	with	 10	 and	 11	 as	 [X‐UT‐Y][Hex–C≡C‐C60–Li+]	 (in	
THF	 and	 DMSO	 solvents)	 (groups	 21‐29)	 and	 their	
electrochemical	 data	 Get(n),	 G#et(n)	 and	 ket(n)	 (n=1‐3)	 have	
neither	been	synthesized	nor	reported	before.	
	
4.	Conclusion	
	

There	 have	 been	 three	 reduction	potentials	 (redE1	 to	 redE3)	
states	reported	for	[R‐C60–M+]	(R=tert‐Bu‐	&	Hex–C≡C‐;	M=Li	&	
K)	 10‐11	 in	 THF	 and	 DMSO	 solvents	 before.	 The	 cis‐
unsaturated	 thiocrown	 ethers	 1‐9	 have	 important	
physicochemical	 properties.	 Here,	 were	 reported	 the	 first	 to	
third	 free	 energies	 of	 electron	 transfer	Get(n)	 (n=1‐3)	 on	 the	
basis	of	the	electrochemical	data	of	[X‐UT‐Y]	1‐9	and	the	first	to	
third	 reduction	 potential	 (redE1	 to	 redE3)	 of	 the	 [R‐C60–M+]	
(R=tert‐Bu‐	 &	 Hex–C≡C‐;	 M=Li	 &	 K)	 10‐11,	 first	 and	 second	
activate	 free	 energies	 of	 electron	 transfer	 and	 kinetic	 rate	
constants	 of	 the	 electron	 transfers,	 G#et(n)	 and	 ket(n)	 (n=1‐3),	
respectively,	 in	 the	 supramolecular	 complexes	 12‐38.	 The	
predicted	 values	 of	Get(n)	 (n=1‐3)	 were	 calculated	 for	 12‐38	
groups	 in	 THF	 and	 DMSO	 solvents	 using	 the	 Rehm‐Weller	
equation.	Using	the	ratio	of	sum	of	the	number	of	carbon	atoms	
(nc)	 and	 the	 number	 of	 sulfur	 atoms	 (ns)	 and	 the	 product	 of	
these	 two	 values,	cs,	 equations	were	 derived	 that	 yield	 good	
structural	 relationships	 with	 the	 aforementioned	 physic‐
chemical	 data.	 These	 equations	 allow	 one	 to	 calculate	 Get(n)	
(n=1‐3),	G#et(n)	 and	ket(n)	 (n=1‐3)	on	 the	basis	of	 the	 first	and	
second	reduction	potential	 (redE1	 and	 redE2)	of	10	&	11	 for	 the	
12‐38	 supramolecular	 complex	 groups.	 The	 values	 were	
calculated	 using	 the	Rehm‐Weller	 equation	 and	 equations	 2‐3	

concern	 to	 the	Marcus	 theory.	 The	 group	 of	 supramolecular	
complexes	[X‐UT‐Y][R‐C60–M+]	(R=tert‐Bu‐	&	Hex–C≡C‐;	M=Li	&	
K)	12‐38	were	neither	synthesized	nor	previously	reported.	
	
Acknowledgments	
	

The	 corresponding	 author	 gratefully	 acknowledges	 the	
colleagues	 in	 the	 Chemistry	 Department	 of	 The	 University	 of	
Queensland	(UQ)‐Australia,	for	their	useful	suggestions.		
	
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