"This	is	the	peer	reviewed	version	of	the	following	article:	[Chem. Eur. J. 2017, 23 (22), 5338],	which	
has	been	published	in	final	form	at	[DOI	10.1039/c0dt00166j].	This	article	may	be	used	for	noncommercial	purposes	in	accordance	with	Wiley	Terms	and	Conditions	for	Self-Archiving."		

	

Electronic	Structure	Studies	on	the	Whole	Keplerate	Family:	Predicting	New	
Members	
Dolores	Melgar,a	Nuno	A.	G.	Bandeira,a	Carles	Boa,b,*	
a.	Institute	of	Chemical	Research	of	Catalonia	(ICIQ),	The	Barcelona	Institute	of	Science	and	Technology,	Av.	
dels	Països	Catalans,	16,	43007	Tarragona,	Spain.	
b.	Departament	de	Química	Física	i	Inorgànica,	Universitat	Rovira	i	Virgili,	Av.	dels	Països	Catalans,	26,	43007	
Tarragona,	Spain.	

	
	
Abstract	
The	 present	 paper	 presents	 a	 comprehensive	 study	 of	 the	 electronic	 structure	 of	 nano-scale	
molecular	oxide	capsules	of	the	type	[{MVI(MVI)5O21}12{M'V2O2(µ-X)(µ-Y)(Ln-)}30](12+n)-,	where	M,M’=Mo,	
W,	and	the	bridging	ligands	X,Y=O,S,	carried	out	by	means	of	density	functional	theory.	Discussion	of	
the	electronic	structure	of	these	derivatives	is	focused	on	the	thermodynamic	stability	of	each	of	the	
structures,	 the	 one	 having	 the	 highest	 gap	 being	 M=W,	 M’=Mo,	 X=Y=S.	 For	 the	 most	 well	 known	
structure	 M=M’=Mo,	 X=Y=O,	 [Mo132O372]12-,	 the	 chemical	 of	 several	 ligands	 to	 the	 {MoV2O2(μ-O)2}	
linker	 moiety	 produces	 negligible	 effects	 on	 its	 stability	 which	 is	 evidence	 of	 a	 strong	 ionic	
component	 in	 these	 bonds.	 The	 existence	 of	 hitherto	 unknown	 species,	 namely	 W132	 with	 both	
bridging	alternatives	is	discussed	and	put	into	context	with	our	findings.			
	
Introduction	
In	 the	 last	 years,	 new	 molecular	 nano-clusters	 have	 emerged	 in	 the	 context	 of	 polyoxometalate	
(POM)	science.[1]	A	good	example	of	these	nano-systems	is	the	so-called	Keplerates	family.	The	term	
Keplerate	stands	for	a	family	of	POMs	with	nanometric	size	and	an	internal	cavity	that	makes	these	
nano-capsules	 an	 excellent	 environment	 to	 study	 the	 effect	 of	 confinement	 on	 the	 encapsulated	
species.[2]	Keplerates	can	be	considered	thus	as	spherical	nano-containers,	the	vast	majority	of	them	
holding	102	or	132	metal	atoms	(Figure	1),[2-3]	although	recently	an	icosidodecahedral	structure	was	
identified	 containing	 just	 42	 titanium	 atoms.[4]	 The	 difference	 between	 the	 102	 or	 the	 132	 atoms	
systems	 lays	 on	 the	 building	 blocks	 that	 form	 the	 Keplerate	 structure.	 The	 most	 characteristic	
building	 block	 that	 can	 be	 found	 over	 all	 the	 Keplerate	 family	 is	 the	 pentagonal	 unit.	 From	 Euler's	
theorem,	12	of	these	pentagonal	motifs	are	needed	in	order	to	build	a	spherical	structure.	These	12	
pentagonal	pieces	are	joined	together	by	30	linker	units.	The	size	of	these	linkers	(that	can	be	either	
1	
	

	

monomers	 or	 dimers)	 constitutes	 the	 main	 difference	 between	 the	 M132	 and	 M102	 Keplerates.	 This	
paper	 aims	 at	 studying	 the	 electronic	 properties	 of	 Keplerate	 systems	 with	 dimeric	 linkers,	 with	
general	 formula	 [{MVI(MVI)5O21}12{M'V2O2(µ-X)(µ-Y)(Ln-)}30](12+n)-,	 where	 M	 and	 M'	 are	 the	 metal	
positions	that	can	be	Mo	or	W	atoms).	X	and	Y	stand	for	the	bridging	sites	in	the	linkers	and	can	be	
both	O	or	S	atoms.	Using	a	simplified	notation,	we	will	address	to	Keplerate	systems	as	M72M'60(µX)(µ-Y),	 depending	 on	 the	 particular	 composition	 of	 each	 system.	 In	 some	 cases,	 when	 the	 linkers	
present	only	oxo-bridges	the	description	of	such	positions	is	omitted.	
In	the	general	formula	of	Keplerates,	L	represents	a	bidentate	ligand	that	can	be	coordinated	to	the	
inner	surface	of	the	capsule.	These	ligands	are	usually	bidentate	oxygen	donor	anions,	as	formate,[5]	
acetate,[2b]	 monochloroacetate,[5c]	 sulfate,[2b,	 6]	 sulfite,[7]	 hypophosphite,[8]	 hydrogen	 phosphate,[9]	 ,	
selenate,[10]	 valerate,[11],	 carbonate,[8]	 carboxylates	 in	 general,[12]	 or	 even	 dicarboxylates.[13]	 These	
ligands	are	labilely	bonded	to	the	inner	surface	of	the	capsule.	Therefore,	they	are	able	to	exchange	
their	positions	inside	of	the	Keplerate	or	even	with	solvated	anions	from	the	outer	medium	through	
the	 pores.[14]	 The	 particularities	 of	 the	 coordinated	 anions	 alter	 the	 capsule's	 properties,	 as	 the	
charge,	 the	 hydrophobic	 character	 of	 the	 inner	 surface,	 and	 the	 size	 of	 the	 internal	 cavity.		
Therefore,	 the	 exchange	 of	 ligands	 allows	 the	 tuneability	 of	 the	 Keplerate	 capsules	 for	 different	
purposes.	

	
Figure	 1:	 Polyhedral	 representation	 of	 two	 typical	 Keplerate	 structures:	 M132	 (a)	 and	 M102	 (b).	 Pentagonal	 motifs	 are	
represented	in	blue	and	equivalent	for	both	systems.	In	contrast,	linker	units	(red	polyhedra)	are	monomeric	in	the	case	of	
M102	and	dimeric	for	M132	systems.	

Historically,	 the	 first	 Keplerate	 is	 the	 Mo132(µ-O)2	 and	 it	 was	 synthesized	 in	 1998	 by	 Müller	 and	
collaborators.[15]	 After	 this	 amazing	 discovery,	 Müller's	 group	 realized	 that	 the	 composition	 of	
building	blocks	could	be	altered,	giving	rise	to	several	interesting	structures.	For	instance,	instead	of	
the	 original	 MoV2O2(µ-O)2,	 different	 linker	 units	 were	 used	 introducing	 new	 metal	 ions	 as	 FeIII	 in	
Mo72Fe30,[16]	monomeric	MoV		in	Mo102,[16]	VIV	in	Mo72V30,[17]		and	CrIII	in	Mo72Cr30.[18]	The	composition	
of	the	pentagonal	building	blocks	can	also	be	altered	changing	the	Mo	metal	centers	by	W	atoms.	
Examples	of	these	W-based	pentagons	can	be	found	in	W72Mo60	 [19]	and	in	W72Fe30.[19]	Moreover,	in	
2	
	

	

some	cases	the	characteristic	icosahedral	symmetry	of	these	systems	can	be	somehow	distorted,	as	
in	 the	 Mo75V20	 capsule.[20]	 The	 latest	 modification	 introduced	 in	 Keplerates	 composition	 was	
regarding	the	bridging	positions	in	the	linker	units.	Sulfur	atoms,	as	in	Mo132(µ-S)2	[21]	and	W72Mo60(µS)2	 [22]	 can	 substitute	 the	 traditional	 oxo-bridges.	 Furthermore,	 a	 mixed-bridges	 possibility	 has	 also	
been	reported	as	in	W72Mo60(µ-O)(µ-S).[23]		
Although	the	Keplerate	family	is	short	and	young,	it	is	revealing	promising	properties.	Mo72Fe30	was	
reported	as	an	active	catalyst	for	the	selective	oxidation	of	sulfides,[24]	and	also	used	to	form	hybrid	
films	for	building	electro-catalytic	electrodes.[25]	Of	most	interest	are	those	cases	reporting	catalysis	
occurring	 inside	 the	 Keplerate.	 In	 the	 first	 example	 of	 such	 a	 kind	 of	 nano-reactor	 the	 authors	
demonstrated,	both	experimentally	and	computationally,	the	mechanism	of	the	hydrolysis	of	methyl	
tert-butyl	ether	inside	the	Mo132	capsule.[26]	Also,	it	has	been	proved	that	the	Mo132	Keplerate	is	able	
to	 modify	 the	 regioselectivity	 of	 the	 Huisgen	 reaction.[27]	 Other	 examples	 refer	 to	 the	 uptake	 and	
oxidation	 of	 simple	 gases	 such	 CO2	 [8,	 28]	 and	 SO2	 ,[7]	 inside	 the	 Mo132	 capsule:	 in	 both	 cases	 the	
products	 were	 characterized	 by	 X-Ray.	 Several	 other	 catalytic	 oxidation	 processes	 have	 been	
reported,	 which	 in	 our	 opinion	 probably	 occur	 outside	 the	 capsule.[29]	 Besides	 their	 catalytic	
applications,	 new	 materials	 a	 being	 prepared	 employing	 Keplerates.	 For	 instance,	 they	 have	 been	
combined	with	surfactants,[30]	ionic	liquids,[31]	ionic	crystals,[32]	and	gold	nanoparticles.[33]	Last	but	not	
least,	Mo132	showed	activity	for	disrupting	peptides	aggregation	related	with	Alzheimer's	disease.[34]	
This	paper	presents	a	DFT	study	on	the	whole	Keplerate	family,	which	includes	those	known	species	
described	above	incremented	with	unsynthesized	yet	potential	members,	such	as	the	full	tungsten	
analogs	 W132,	 W132(µ-S)2	 and	 W132(µ-O)(µ-S),	 and	 Mo132(µ-O)(µ-S).	 We	 aimed	 at	 complementing	 a	
preliminary	 study[35]	 on	 Mo132(µ-O)2	 	 and	 W72Mo60(µ-O)2	 empty	 capsules,	 but	 also	 at	 analyzing	 the	
effect	 of	 the	 30	 ligands	 coordinated	 at	 the	 bridging	 metal	 atoms,	 and	 the	 effect	 of	 the	 72	 water	
molecules	in	the	pentagonal	motifs.	Ligands	include	mono-anionic	species	hypophosphite,	formate,	
acetate,	 acrylate,	 bisulfate	 and	 bicarbonate,	 as	 well	 as	 di-anionic	 carbonate,	 selenate,	 sulfate	 and	
sulfite.		
Electronic	 structure	 studies	 on	 Keplerates	 are	 scarce.	 In	 addition	 to	 our	 preliminary	 report,	 [35]	
Kuepper	 et	 al.[36]	 characterized	 the	 electronic	 structure	 of	 the	 Mo72Fe30	 and	 W72Fe30	 systems	 using	
plane-wave	DFT	methods.	On	the	other	hand	classical	molecular	dynamics	allowed	us	to	study	the	
layered	structures	that	encapsulated	water	molecules	form	inside	Mo132,[37]	and	more	recently,	the	
influence	 of	 the	 hydrophobic	 character	 of	 the	 counter-cations	 on	 the	 interactions	 with	 the	
Keplerates	in	aqueous	solution.[38]	Other	groups	have	used	Monte	Carlo	methods	to	shed	some	light	
on	 the	 assembly	 of	 Keplerates.[39]	 In	 this	 context,	 we	 hope	 that	 the	 results	 derived	 in	 the	 present	
study	will	be	useful	for	developing	parameters	for	molecular	simulations.	
	
Computational	Details	
All	results	presented	herein	correspond	to	full	geometry	optimizations	carried	out	by	means	of	the	
Amsterdam	Density	Functional	package	ADF.[40]	The	GGA	BP86	functional[41]	was	used	together	with	
a	 Slater	 triple-ζ	 plus	 polarization	 basis	 set	 in	 all	 atoms.	 Relativistic	 corrections	 were	 introduced	 by	
the	 scalar-relativistic	 zero-order	 regular	 approximation	 (ZORA).[40a,	42]	 Solvent	 effects	 were	 included	
by	using	the	continuum	model	COSMO.[43]	For	constructing	the	solvent	cavity,	the	atomic	radii	values	
3	
	

	

chosen	 were	 those	 Van	 der	 Waals	 radii	 from	 Allinger[44]	 divided	 by	 1.2.	 The	 numerical	 integration	
parameter	that	controls	the	precision	of	numerical	integrals	was	set	to	4.5.	Geometry	optimization	
at	the	LDA	VWN[45]	level	with	the	same	basis	sets,	with	and	without	implicit	solvent	were	also	carried	
out.	The	reader	is	addressed	to	the	Supporting	Information	for	further	details.	A	data	set	collection	
which	includes	input	files,	and	selected	results	is	available	online[46]	in	the	ioChem-BD	repository.[47]	
	
Results	
Keplerates	are	discrete	molecules	but	containing	a	huge	number	of	atoms	and	electrons.	This	makes	
their	electronic	structure	closer	to	bands	in	solids	than	to	discrete	and	well-separated	energy	levels	
as	 found	 in	 small	 molecules.	 Therefore,	 we	 chose	 the	 Density	 of	 States	 (DOS),	 which	 is	 a	 function	
that	represents	the	number	of	electronic	levels	per	energy	unit,	to	plot	and	analyze	the	electronic	
structure	 of	 these	 thousands	 of	 electrons	 systems.	 	 The	 Total	 Density	 of	 States	 (TDOS)	 includes	 all	
the	existing	energy	levels.	In	contrast,	the	Partial	Density	of	States	(PDOS)	gives	the	contribution	to	
the	TDOS	of	a	specific	atom	type.	
We	have	chosen	the	Mo132(µ-O)2	molecule	to	illustrate	the	typical	DOS	profile	of	Keplerates.	Figure	2	
shows	the	DOS	of	Mo132,	from	-30	eV	to	10	eV.	The	deepest	band	in	Figure	2	corresponds	to	the	2s	
orbitals	 from	 the	 oxygen	 atoms	 (Figure	 3a).	 Figure	 2	 also	 shows	 the	 characteristic	 oxo-band	 of	
polyoxometalates.	The	oxo-band	includes	the	p	orbitals	of	the	different	oxygen	atom	types	present	
on	Mo132	(Figure	3b,	c,	d,	and	e).	The	HOMO	band	comprises	30	doubly	occupied	orbitals,	including	
mainly	contributions	of	60	MoV	atoms	in	the	30	linkers.	Those	electrons	form	the	metal-metal	bonds	
between	the	metal	centers	in	the	linker	units	(Figure	3f).	Finally,	the	LUMO	band	includes	all	the	d	
orbitals	from	the	Mo	atoms	in	the	pentagonal	units	(Figure	3g).	
	

	

4	
	

	

Figure	 2:	 Plot	 of	 the	 DOS	 function	 for	 Mo132.	 The	 energy	 range	 comprises	 from	 -30	 eV	 to	 10	 eV.	 Total	 Density	 of	 States	
(TDOS,	black)	and	Partial	Density	of	States	(PDOS,	red	for	Mo	and	grey	for	O).	

	
Figure	3:	Examples	of	different	types	of	Kohn-Sham	orbitals	for	the	Mo132	Keplerate.	a)	s	oxygen	orbitals,	corresponding	to	
the	deepest	band	on	Figure	2.	b,	c,	d,	e)	p	oxygen	orbitals	belonging	to	the	oxo-band.	f)	HOMO	band	orbital,	corresponding	
to	the	metal-metal	bond,	which	involves	the	d	orbitals	of	the	linker	Mo	atoms.	g)	LUMO	orbital	related	to	the	d	orbitals	of	
the	pentagonal	Mo	atoms.	Note	that	for	the	LUMO	orbital	different	colors	were	used	to	highlight	the	fact	that	this	is	a	nonoccupied	orbital.	

While	 Mo132(µ-O)2	 is	 the	 most	 well-known	 Keplerate,[15]	 W72Mo60(µ-O)(µ-S)	 mixed-bridges	 is	 the	
latest	 discovered.[48]	 The	 X-ray	 data	 of	 this	 compound	 presents	 crystallographic	 disorder	 in	 the	
bridging	 positions,	 while	 the	 metal-metal	 bond	 distance	 is	 the	 same	 for	 all	 the	 linkers.	 In	 other	
words:	 all	 the	 linkers	 hold	 one	 thio-	 and	 one	 oxo-bridge.	 This	 inherent	 disorder	 leads	 to	 different	
isomeric	possibilities.	Geometries	of	several	isomers	were	thus	studied	and	found	that	their	relative	
energies	 fall	 within	 the	 1	 kcal/mol	 range.	 We	 thus	 conclude	 that	 the	 different	 isomers	 with	 mixed	
sulfur-oxo	 bridges	 are	 almost	 degenerate	 in	 terms	 of	 stability.	 The	 reader	 is	 addressed	 to	 the	
Supporting	 Information	 for	 further	 details	 on	 these	 isomeric	 possibilities.	 To	 compare	 the	 mixed	
bridge	Keplerate	with	the	other	members	of	the	family,	we	have	chosen	the	most	stable	isomer	as	
the	reference	structure.	

	
5	
	

	

Figure	 4:	 HOMO	 (pink)	 and	 LUMO	 (violet)	 energy	 levels	 (in	 eV)	 and	 its	 corresponding	 gap	 value	 for	 the	 whole	 Keplerate	
family.	

Figure	4	shows	how	the	ratio	of	W/Mo	in	the	pentagonal	units	and	S	and/or	O	bridges	in	the	linkers	
affect	the	HOMO-LUMO	gap:	the	gap	increases	with	the	presence	of	W	and	S.	The	HOMO-LUMO	gap	
is	 an	 important	 measure	 of	 stability	 since	 it	 is	 directly	 related	 to	 quantities	 such	 as	 the	 chemical	
potential	and	chemical	hardness.	From	the	principle	of	maximum	hardness	as	expounded	by	Pearson	
the	most	stable	substances	will	have	a	higher	gap.	
The	presence	of	W	drives	the	LUMO	level	higher,	because	this	level	is	related	to	the	5d	orbitals	of	
the	metal	centers	on	the	pentagon	(Figure	3g).	The	existence	of	sulfur-bridges	in	the	linkers	makes	
the	HOMO	level	decrease	in	energy,	because	the	HOMO	level	is	related	to	the	metal-metal	bonds	in	
these	units.	When	sulfur	atoms	populate	the	bridges,	the	distances	between	the	two	metal	centers	
change	from	2.64	Å	to	2.91	Å,	making	the	Mo-Mo	metal-metal	bond	weaker.	As	seen	in	Figure	3f	the	
bridging	 lobes	 are	 out	 of	 phase	 with	 the	 central	 Mo-Mo	 bonding	 region.	 Since	 the	 3p	 orbitals	 of	
sulfur	 are	 radially	 more	 external	 these	 will	 introduce	 more	 anti-bonding	 repulsion	 with	 the	 metal	
lobes	 resulting	 in	 an	 increased	 metal-metal	 bond	 distance	 to	 minimize	 this	 and	 also	 tighten	 the	
bridging	angle.	It	is	apparent	that	the	energy	of	the	HOMO	level	is	a	consequence	of	the	influence	of	
the	 bridging	 sites	 to	 the	 metal-metal	 bond.	 Summing	 up,	 regarding	 the	 HOMO-LUMO	 gap,	
W72Mo60(µ-S)2	is	the	most	stable	system	among	the	experimentally	synthesized	Keplerates.		

	
Figure	5:	DOS	for	different	Keplerates,	including	TDOS	(black)	and	PDOS	(red	for	Mo,	yellow	for	W,	grey	for	O	and	dark	blue	
for	S).	Black	arrows	highlight	the	corresponding	HOMO	level	for	each	system.		

6	
	

	

Figure	 5	 compares	 the	 DOS	 for	 the	 set	 of	 Keplerates	 whose	 HOMO-LUMO	 gap	 was	 represented	 in	
Figure	4.	Starting	from	the	left,	the	first	system	Mo132(µ-O)2	has	already	been	analyzed	above	(Figure	
2).	Figure	5	shows	that	the	DOS	of	all	the	Keplerate	family	are	quite	similar,	in	terms	of	the	HOMO	
and	LUMO	levels	and	the	presence	of	the	oxo-band.	Nevertheless,	there	are	some	differences.	The	
most	distinctive	feature	is	the	appearance	of	new	peaks	associated	with	the	sulfur	electrons	(Figure	
5b,	 d,	 and	 e)	 in	 the	 case	 of	 thio-Keplerates.	 The	 3s	 sulfur	 orbitals	 are	 located	 between	 the	 2s	 O	
orbitals	band	and	the	oxo-band.	Also,	p	orbitals	related	to	these	sulfur-bridges	are	found	between	
the	oxo-band	and	the	HOMO	band.	It	is	worth	noting	that	in	the	case	of	pure	sulfur-bridges,	the	3s	
sulfur	 orbitals	 form	 two	 peaks	 (Figures	 5c,	 5f	 and	 5i),	 while	 only	 one	 peak	 appears	 in	 the	 case	 of	
mixed-bridges	(Figures	5b,	5e,	and	5h).	This	is	due	to	the	differences	in	energy	of	the	bonding	and	
antibonding	orbitals	of	the	sulfur	atoms	located	at	the	bridges.		

	
Figure	 6:	 Top:	 Molecular	 Electrostatic	 Maps	 (MEP).	 Red	 color	 indicates	 negative	 MEP	 regions,	 while	 blue	 represents	
positive	MEP	areas.	Bottom:	Representations	of	the	fragments	represented	in	the	MEP	plots.	In	this	case,	purple	and	grey	
spheres	 stand	 for	 Mo	 and	 W	 atoms,	 respectively.	 Red	 and	 yellow	 spheres	 are	 reserved	 for	 oxygen	 and	 sulfur	 atoms.	 	 a)	
Comparison	between	the	Mo	(left)	and	W	(right)	based	pentagonal	units.	b)	Comparison	between	the	pores	of	oxo-	(left)	
and	thio-Keplerates	(right).	

Besides	 DOS,	 Molecular	 Electrostatic	 Potential	 maps	 (MEP)	 are	 also	 a	 good	 tool	 for	 assessing	 the	
effects	of	chemical	composition	on	the	electronic	properties	of	the	systems.	With	this	purpose,	the	
electrostatic	 potential	 is	 projected	 onto	 the	 electronic	 density	 (see	 Supporting	 Information	 to	 see	
the	 complete	 graphical	 representation).	 All	 the	 five	 systems	 studied	 showed	 a	 very	 similar	 MEP	
pattern,	which	means	that	they	should	have	a	similar	self-assembly	behavior	such	as	that	found	in	
blackberries.[49]	In	spite	of	the	very	similar	MEP	patterns,	there	are	some	differences	on	the	systems	
studied.	When	W	atoms	form	the	pentagonal	units,	the	oxygen	atoms	that	link	those	metal	centers	
are	 slightly	 less	 negatively	 charged	 than	 when	 Mo	 is	 present.	 This	 effect	 is	 due	 to	 the	 different	
properties	of	Mo-O	and	W-O	bond,	resulting	in	less	basic	oxygens.	The	most	remarkable	difference	
between	 the	 MEP	 patterns	 is	 the	 change	 of	 the	 electrostatic	 potential	 when	 sulfur-bridges	 are	
present	(Figure	6b).	This	change	in	the	electrostatic	potential	in	the	vicinity	of	the	pore	together	with	
the	change	in	pore	size,	will	lead	to	different	pore-cation	interactions	in	solution.	The	change	in	the	
7	
	

	

electrostatic	potential	of	the	pore	framework	can	also	be	observed	when	the	electrostatic	charges	of	
the	 oxo-	 and	 sulfur-bridges	 are	 analyzed.	 For	 instance,	 in	 the	 case	 of	 the	 Mo132	 capsule,	 when	 the	
bridging	positions	are	occupied	by	O	atoms	they	have	a	VDD	charge	of	-0.38	whereas	when	they	are	
occupied	by	S	atoms,	their	charge	decreases	to	-0.26.	
Not	Empty	Capsules:	Presence	of	Ligands	and	Coordination	Water	Molecules	
All	 the	 systems	 described	 in	 the	 previous	 section	 are	 experimentally	 characterized	 Keplerates	 that	
have	 been	 considered	 as	 empty	 capsules,	 which	 means	 that	 the	 POM	 has	 been	 treated	 as	 a	
polyanion	with	a	charge	of	-12	since	only	the	metal-oxo	framework	has	been	taken	into	account.	To	
improve	this	model	and	check	the	effect	of	a	more	realistic	description,	different	bidentate	ligands	
were	 added	 as	 decoration	 of	 the	 inner	 surface	 of	 the	 Mo132(µ-O)2	 capsule.	 Those	 ligands	 are	
experimentally	known	to	be	weakly	attached	to	the	linkers	and	they	make	these	capsules	even	more	
negatively	charged.	The	geometry	optimizations	performed	for	the	system	composed	of	Mo132(µ-O)2	
and	30	ligands	were	carried	out	at	the	standard	DFT	level.	To	reduce	the	computational	cost,	these	
optimizations	were	carried	out	under	the	constraints	of	a	Ci	molecular	symmetry	point	group	,	with	
the	 exception	 of	 formate,	 carbonate,	 selenate,	 hypophosphite,	 and	 sulfate	 ligands.	 The	 fact	 that	
these	ligands	present	a	plane	of	symmetry,	allows	keeping	the	D5d	point	group	symmetry.	
In	the	presence	of	ligands,	the	electronic	levels	of	the	Mo132	Keplerate	are	upshifted	because	of	the	
increase	 in	 total	 charge	 (from	 -12	 to	 -42	 or	 -72,	 depending	 on	 the	 ligand	 charge).	 The	 higher	 the	
ligand	charge,	the	larger	the	shifting:	for	the	-42	systems	the	DOS	displacement	is	around	1	eV,	while	
for	-72	systems	it	is	about	1.5	eV.	The	different	shifts	depending	on	the	charge	can	be	observed	on	
the	 DOS	 as	 well	 as	 the	 new	 electronic	 levels	 due	 to	 the	 presence	 of	 the	 new	 ligands	 (The	
corresponding	figures	can	be	found	in	Supporting	Information).		

	

8	
	

	

Figure	7:	HOMO	(pink),	LUMO	(violet)	and	the	corresponding	gap	for	the	Mo132(µ-O)2	systems	empty	
and	coordinated	with	different	bidentate	ligands.	The	label	"+H2O"	indicates	that,	in	addition	of	the	
mentioned	ligands,	72	water	molecules	have	been	considered	coordinated	to	the	motifs.		
Figure	7	shows	that	there	is	almost	no	change	in	the	HOMO-LUMO	gap	when	different	inner	ligands	
are	 considered.	 For	 instance,	 the	 empty	 Mo132	 capsule	 has	 a	 gap	 of	 1.1	 eV.	 When	 acetate,	
bicarbonate,	 bisulfate,	 acrylate,	 hypophosphite,	 and	 formate	 groups	 are	 acting	 as	 internal	 ligands	
the	 system	 presents	 almost	 the	 same	 gap	 (1.1	 eV	 for	 all	 the	 mentioned	 systems	 except	 for	 the	
bisulfate	case,	for	which	the	computed	gap	is	1.0	eV).	A	very	similar	behavior	is	found	when	divalent	
ligands	 are	 considered.	 SO42-	 and	 SO32-	 systems	 have	 a	 gap	 about	 1.1	 eV.	 A	 slight	 increase	 of	 the	
HOMO-LUMO	gap	is	found	for	the	case	of	carbonate	and	selenate	ligands	(1.2	eV).	The	fact	that	the	
Mo132	 capsule	 keeps	 almost	 constant	 its	 HOMO-LUMO	 gap	 upon	 changing	 the	 inner	 surface	
decoration	means	that	the	system's	electronic	stability	is	given	by	its	inherent	scaffold	and	is	almost	
independent	of	the	particular	features	of	the	specific	ligands	considered.	In	addition,	in	the	case	of	
formate	and	carbonate	ligands	the	presence	of	coordination	water	molecules	has	been	considered.	
The	inclusion	of	such	water	molecules	does	not	affect	the	HOMO-LUMO	gap,	but	does	shift	the	DOS	
(less	than	1	eV).		
Predicting	New	Members:	Mo132(µ-O)(µ-S),	and	W132	,	W132(µ-O)(µ-S)	and	W132(µ-S)2	
The	 majority	 of	 the	 structures	 presented	 in	 the	 previous	 sections	 were	 already	 characterized	 by	
means	 of	 X-ray	 experiments	 reported	 in	 the	 literature.	 Nevertheless,	 there	 are	 more	 composition	
variants	that	can	be	envisaged	and	these	were	studied	from	a	theoretical	point	of	view.	This	section	
aims	 at	 evaluating	 the	 theoretical	 stability	 of	 these	 new	 systems	 in	 terms	 of	 their	 electronic	
structure,	i.e.	the	HOMO-LUMO	gap.	Predicted	new	members	of	the	Keplerate	family	are	described	
in	the	following	paragraphs,	including	Mo132	systems	with	different	bridges	compositions	(sulfur-	and	
mixed	bridges)	and	full	W132	systems	(with	oxo-,	sulfur-,	and	mixed	bridges).		
Keplerates	 with	 W	 atoms	 hitherto	 introduced	 present	 W	 atoms	 only	 at	 the	 pentagonal	 motifs.	 So,	
the	 question	 that	 naturally	 arises	 is	 what	 would	 happen	 when	 W	 instead	 of	 Mo	 occupied	 the	 132	
metal	 centers.	 Also,	 as	 the	 W72Mo60	 Keplerate	 has	 been	 synthesized	 with	 oxo-,	 thio-	 and	 mixed	
brides,	it	seems	natural	to	analyze	these	possibilities	both	for	the	Mo132	and	W132	molecules.	
Figure	 4	 collects	 the	 HOMO	 and	 LUMO	 results	 for	 these	 new	 systems	 together	 with	 the	 systems	
presented	in	a	previous	section,	and	Figure	5	collects	the	DOS	representation	for	these	new	systems	
(Figures	5b,	c,	g,	h,	i).	The	most	remarkable	result	is	that	the	HOMO	level	is	not	constant	anymore	for	
the	W132	systems.	This	is	because	of	the	fact	that	the	HOMO	level	is	related	to	the	metal-metal	bond	
that	 involves	 the	 metal	 centers	 in	 the	 linkers	 (Figure	 3f).	 Hence,	 changing	 from	 Mo	 linkers	 to	 W	
linkers	strongly	affects	bond	properties,	making	the	HOMO	level	higher	in	energy.	Nevertheless,	the	
LUMO	 level,	 related	 to	 the	 pentagonal	 metal	 centers	 (Figure	 3g),	 is	 also	 higher	 in	 the	 case	 of	 W	
pentagons.	 Consequently,	 the	 HOMO-LUMO	 gap	 for	 the	 W132	 systems	 is	 the	 same	 that	 for	 Mo132	
systems.	The	comparatively	high	energy	of	the	W132	HOMO	also	brings	into	question	the	stability	of	
these	bonded	electrons	with	respect	to	external	oxidating	agents	or	electrophiles.	It	is	known	that	
while	 dinuclear	 complexes	 dominate	 the	 oxo	 chemistry	 of	 MoV	 complexes,	 few	 analogous	
complexes	are	known	to	exist	for	WV.	These	calculations	provide	a	hint	at	explaining	the	difficulty	in	
obtaining	 WV	 linkers.	 Two	 distinct	 chemical	 processes	 sourced	 from	 template	 libraries	 need	 to	
operate	 to	 form	 the	 Keplerate	 sphere:	 one	 is	 the	 formation	 of	 the	 star	 shaped	 moieties	 and	 the	
9	
	

	

other	is	the	co-existence	of	the	pentavalent	dimer	at	that	narrow	pH	window	to	successfully	follow	
through	 the	 condensation	 process.	 A	 WV	 oxo-dimer	 is	 less	 likely	 to	 form	 with	 such	 high	 energy	
electron	 pairs.	 A	 W132(μ-S)2	 Keplerate	 does	 however	 show	 to	 be	 a	 more	 promising	 candidate	 for	 a	
realizable	synthetic	procedure.				
Furthermore,	it	is	worth	noting	that	the	trend	observed	on	the	previous	systems,	i.e,	HOMO-LUMO	
gap	increase	by	introducing	sulfur-bridges,	is	still	present	and	the	mixed-bridges	Keplerates	have	an	
intermediate	gap	with	respect	to	the	pure	oxo-	and	thio-cases.	
	
	
Conclusions	
Summing	 up,	 we	 have	 proven	 that	 all	 the	 members	 of	 the	 Keplerate	 family	 present	 very	 similar	
electronic	 structure	 profiles,	 regarding	 both	 the	 DOS	 and	 the	 values	 of	 the	 HOMO-LUMO	 gap.	
Moreover,	we	have	shown	that	the	presence	of	W	in	the	pentagons	and	S	in	the	bridging	sites	of	the	
linkers	increase	the	HOMO-LUMO	gap,	and,	thus,	the	system's	electronic	stability.	The	inclusion	of	
bidentate	ligands	and	coordination	water	molecules	in	our	model	does	not	affect	the	HOMO-LUMO	
trend.	 Therefore,	 the	 capsule's	 stability	 is	 what	 determines	 the	 system's	 electronic	 stability,	
independently	 on	 the	 particularities	 of	 the	 internal	 decoration.	 We	 have	 also	 demonstrated	 that	
new	Keplerates	not	synthesized	yet,	as	the	W132	with	the	different	bridges	possibilities	and	the	Mo132	
with	mixed	bridges,	are	stable	from	an	electronic	and	theoretical	point	of	view.		
The	 results	 of	 this	 study	 suggest	 that	 the	 W132(μ-S)2	 Keplerate,	 i.e.,	 [W132O312(μ-S)60]12-	 is	 the	 most	
promising	 candidate	 to	 be	 synthesized	 next.	 Since	 the	 ligands	 L	 in	 the	 linkers	 does	 not	 affect	 the	
stability	 of	 the	 whole	 Keplerate	 in	 a	 significant	 extend,	 the	 choice	 of	 a	 suitable	 ligand	 for	 such	
synthesis	should	focus	on	increasing	the	stability	of	the	dimeric	species	[W2O2(μ-S)2]2+,	since	when	it	
combines	with	the	corresponding	and	already	available	(W6O21)	pentagonal	building	blocks,	the	full	
tungsten	Keplerate	should	be	readily	formed.		
	
Acknowledgements	
The	authors	acknowledge	the	Spanish	Ministerio	de	Economía	y	Competitividad	(MINECO)	through	
project	 CTQ2014-52824-R	 and	 the	 Severo	 Ochoa	 Excellence	 Accreditation	 2014-2018	 (SEV-20130319),	 and	 the	 AGAUR	 of	 Generalitat	 de	 Catalunya	 through	 project	 2014-SGR-409	 for	 financial	
support,	 and	 through	 the	 CERCA	 Programme.	 DM	 gratefully	 acknowledges	 URV-ICIQ	 fellowship.	
NAGB	gratefully	a	Fundação	para	a	Ciência	e	Tecnologia	(grant	SFRH/BPD/110419/2015)	for	funding.	
	
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a)F.	Haso,	X.	Fang,	P.	Yin,	D.	Li,	J.	L.	Ross,	T.	Liu,	Chem.	Commun.	2013,	49,	609-611;	bP.	Yin,	
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2010,	39,	6143-6152.	

	
	
For	the	Table	of	contents	
	
	
Which	 one	 is	 next?	 The	 electronic	 structure	 of	 metal	 oxide	 molecular	 nanocapsules	 known	 as	
Keplerates	was	described	at	the	DFT	level.	This	study	considered	several	combinations	of	the	metal	
atoms	(Mo	/	W),	of	the	bridging	atoms	(O	/	S)	and	also	of	internal	ligands,	discusses	stability	trends,	
and	 predicts	 the	 stability	 of	 not	 synthesized	 yet	 species:	 [W132O312(μ-S)60]12-	 is	 the	 most	 promising	
candidate	to	be	synthesized	next.	

	

	

	

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