“This	document	is	the	Accepted	Manuscript	version	of	a	Published	
Work	that	appeared	in	final	form	in	Phys. Chem. Chem. Phys. 2017,
19, 5343,	copyright	©	Royal	Society	of	Chemistry	after	peer	review	
and	technical	editing	by	the	publisher.	To	access	the	final	edited	
and	published	work	see	DOI	10.1039/C6CP08511C.
	

Anions	coordinating	anions:	Analysis	of	the	interaction	between	
anionic	Keplerate	nanocapsules	and	their	anionic	ligands	
a,b

Dolores	Melgar, 	Nuno	A.	G.	Bandeira,

	a,c,d

b

	Josep	Bonet	Avalos, 	Carles	Bo*

a,e	

Keplerates	are	a	family	of	anionic	metal	oxide	spherical	capsules	containing	up	to	132	metal	atoms	and	some	hundreds	of	
oxygens.	These	capsules	holding	a	high	negative	charge	of	-12	coordinate	both	mono-anionic	and	di-anionic	ligands	thus	
raising	its	charge	till	-42	even	till	-72,	which	is	compensated	by	the	corresponding	counter-cations	in	X-Ray	structures.	We	
present	an	analysis	of	the	relative	importance	of	several	energy	terms	of	the	coordinate	bond	between	the	capsule	and	
ligands	 like	 carbonate,	 sulphate,	 sulphite,	 phosphinate,	 selenate,	 and	 a	 variety	 of	 carboxylates,	 of	 which	 the	 overriding	
component	is	the	contribution	due	to	solvation/de-solvation	effects.				

Introduction	
1,	2

During	the	last	decade,	polyoxometalate	(POM)	chemistry	enabled	growing	impressive	new	giant	molecular	metal	oxide	nanostructures. 	
In	some	cases,	the	shape	of	the	POM	framework	is	such	that	it	forms	inner	cavities,	which	are	usually	filled	with	other	molecular	species.	
These	 two	 characteristics	 are	 found	 in	 the	 unique	 family	 of	 compounds	 known	 as	 Keplerates,	 which	 are	 uniquely	 symmetric	 spherical	
3,	 4
capsules	containing	either	102	or	132	metal	atoms	(Fig.	1). 	The	first	discovered	and	most	relevant	member	of	this	family	is	known	as	
5
VI
VI
V
n(12+n)Mo132	and	it	was	reported	by	Müller	and	co-workers	in	1998. 	With	general	formula	[(Mo (Mo )5O21(H2O)6)12(Mo 2(µ-O)2O2(L ))30]
,	
nwhere	L 	is	a	bridging	anionic	ligand,	the	sphere	is	highly	negatively	charged,	holding	a	charge	of	-42	for	monovalent	anions	(L )	and	-72	for	
2VI
VI
divalent	anionic	ligands	(L ).	This	sort	of	capsule	is	built	from	twelve	pentagonal	Mo (Mo )5O21	units,	which	are	placed	at	the	vertices	of	
VI
nV
an	 icosahedron	 and	 contain	 six	 Mo 	 atoms.	 These	 units	 are	 connected	 by	 (Mo2(µ-O)2O2(L )	 dimers	 or	 linkers,	 holding	 Mo 	 atoms	 thus	
thirty	 of	 them	 are	 needed	 to	 complete	 the	 spherical	 capsule.	 This	 building-block	 combination	 is	 highlighted	 in	 Fig.	 1.	 In	 a	 simplified	
notation,	we	will	refer	to	this	species	as	Mo132	for	short.		
Since	the	initial	synthesis	of	Mo132,	Müller	and	co-workers	noticed	that	other	combinations	of	pentagons	and	linkers	could	be	possible,	and	
6
III
7
readily	discovered	Mo72Fe30, 	a	Keplerate	with	Mo(Mo)5	pentagonal	units	and	magnetic	Fe 	ions	as	linkers,	and	a	related	Mo75V20	capsule. 	
8
3The	Mo102	Keplerate	was	synthesised	next, 	which	is	formally	a	Mo72Mo30	Keplerate,	incorporating	MoO 	groups	as	linkers.	Using	the	same	
IV
9
III
10
strategy,	 the	 Mo72V30	 containing	 V O	 units	 as	 linkers 	 and	 the	 Mo72Cr30	 with	 Cr 	 linkers 	 were	 discovered.	 The	 next	 advance	 was	 the	
ability	 to	 generate	 pentagonal	 units	 with	 tungsten	 centres,	 i.e.,	 W(W)5	 building	 blocks,	 that	 were	 assembled	 using	 both	 dimeric	 and	
11
12
monoatomic	linkers.	Thus,	the	W72Mo60 	and	W72Fe30 	clusters	were	discovered.	Further	chemical	synthesis	enabled	replacing	μ-oxo	with	
V
13
14
μ-thio	 bridging	 ligands	 in	 the	 Mo 2(µ-S)2O2	 linker	 moiety	 within	 the	 frameworks	 of	 W72Mo60(µ-S)2 	 and	 Mo132(µ-S)2, 	 and	 the	 mixed	 μV
15
oxo/thio	bridges,	such	as	Mo 2(µ-O)(µ-S)O2	introduced	in	the	W72Mo60	cluster. 		

		

	

	
Fig.	1	Polyhedral	representation	of	Mo132	(left)	with	formate	groups	acting	as	the	ligands	bound	to	the	interior	wall	of	the	linkers.	The	two	types	
VI
V
of	building	blocks	have	been	highlighted	(right):	blue	for	the	pentagonal	(Mo )	units	and	red	for	the	dimeric	(Mo )	linkers.		

	

V

n-

16-18

4,	5

In	Keplerates,	the	ligands	L	in	the	linker	units	[Mo 2(µ-X)2O2(L ),	X=O,	S]	are	bidentate	oxygen	donor	anions	such	as	formate,
	acetate, 	
18
4,	19,	20
21
6,	22
19
23
24
25
monochloroacetate, 	sulphate,
	sulphite, 	hipophosphite, 	hydrogen	phosphate, 	selenate, 	valerate, 	carbonate, 	carboxylates	
26-29
30
in	general,
	and	even	dicarboxylates. 	Some	of	these	can	undergo	rapid	exchange	with	others	either	internally	or	by	transiting	through	
31
the	pores	of	the	Keplerate. 	From	a	pure	electrostatic	point	of	view,	it	seems	non	rational	that	a	large	number	(30	units)	of	anionic	ligands	
VI
VI
V
12(charge	–1,	–2)	coordinate	to	an	anionic	capsule	[(Mo (Mo )5O21(H2O)6)12(Mo 2(µ-O)2O2)30] ,	which	formally	holds	a	high	negative	charge.	
The	 whole	 system	 raises	 then	 its	 charge	 from	 –12	 to	 –42,	 or	 even	 to	 –72	 upon	 ligand	 coordination,	 which	 is	 compensated	 by	 the	
corresponding	counter-cations	(either	inside	or	outside	the	capsule).		
For	 a	 series	 of	 similar	 carboxylates,	 it	 has	 been	 demonstrated	 that	 the	 exchange	 rate	 through	 the	 pores	 depends	 on	 the	 size	 of	 the	
26
27
carboxylate	substituent. 	The	hydrophobic	environment	generated	by	propionate	ligands	allowed	the	encapsulation	of	1-hexanol, 	and	
–
28
when	 longer	 carbon	 chains	 were	 introduced,	 as	 in	 n-Pr-CO2 	 carboxylates,	 they	 self-assemble	 step-wise	 inside	 the	 capsule. 	 Capsules	
internally	 decorated	 with	 propionate	 ligands	 can	 selectively	 distinguish	 hydrophobic	 domains	 by	 sequestering	 differently	 sized	 alkanes	
32
(from	n-heptane	to	methane). 		
The	dynamic	nature	of	Keplerate-ligand	interactions	from	this	inside/outside	exchange	of	molecular	species	suggested	the	possibility	that	
these	nanoclusters	could	purposefully	also	be	used	as	nanoreactors.	The	first	properly	identified	application	of	Mo132	as	a	nanoreactor	was	
V
found	in	the	hydrolysis	of	methyl	tert-butyl	ether,	a	reaction	that	takes	place	inside	the	capsule	and	it	is	mediated	by	the	Mo 2(µ-O)2O2	
33
linkers	 as	 DFT	 based	 studies	 by	 some	 of	 us	 and	 detailed	 NMR	 experiments	 demonstrated. 	 Mo132	 has	 shown	 to	 be	 also	 capable	 of	
34
25
modifying	 the	 regioselectivity	 of	 the	 Huisgen	 reaction, 	 and	 very	 remarkably,	 to	 uptake	 CO2	 and	 transform	 it	 to	 carbonate. 	 The	
35
mechanism	of	this	CO2	hydration	reaction	is	now	well	understood	and	is	mediated	by	the	linkers	too. 	Related	to	CO2	uptake,	Garai	et	al.	
221
recently	 reported	 the	 transformation	 of	 SO2	 gas	 into	 SO3 	 ligands. 	 Other	 examples	 of	 the	 catalytic	 activity	 of	 Keplerates	 all	 fall	 in	 the	
36-45
category	of	oxidation	reactions,	which	in	our	opinion	probably	occur	outside	the	capsule.	
	
Some	 issues	 regarding	 Keplerate	 chemistry	 were	 addressed	 computationally	 using	 both	 classical	 and	 quantum	 methods.	 Our	 group	
46
demonstrated 	that	the	layered	structure	of	encapsulated	water	could	be	reproduced	using	molecular	dynamics	simulations,	and	studied	
47,	48
49,	50
its	dynamic	behaviour.
	Other	authors	studied	the	assembly	of	Keplerates	in	sheet-like	structures	using	Monte	Carlo	methods.
	Our	
33,	35
group	used	DFT	methods	to	study	catalytic	reaction	mechanisms	by	considering	models	of	the	capsules,
	and	described	for	the	first	time	
25
51
the	electronic	structure	of	Mo132	and	W72Mo60. 		Kuepper	et	al.	discussed	the	electronic	structure	of	Mo72Fe30	and	W72Fe30. 	
Since	 anionic	 ligands	 coordinating	 to	 an	 already	 anionic	 Keplerate	 appears	 paradoxical,	 and	 given	 the	 key	 role	 that	 Keplerate-ligand	
interactions	play	in	tuning	the	chemical	properties	of	the	inner	surface	of	these	capsules,	in	this	manuscript	we	are	reporting	a	detailed	
study	of	the	interaction	between	the	Mo132	capsule	and	different	types	of	ligands.	The	analysis	relies	on	the	bonding	energy	decomposition	
52-58
analysis	(EDA).
	The	procedure	we	used	enables	decomposing	the	energy	changes	upon	bonding	of	two	molecular	fragments	in	several	
energy	terms,	namely	Pauli,	electrostatic,	orbital	interactions,	and	solvation	energy	balance.		
59,	60

The	EDA	procedure	has	been	widely	employed	to	analyse	the	nature	of	the	bonding	between	molecular	fragments	in	a	variety	of	cases,
	
61
including	interactions	between	transition	metal	atoms	and	ligands	of	a	varied	nature. 	In	most	of	these	examples,	a	non-charged	system	
60
was	divided	into	neutral	fragments,	and	the	analysis	did	not	take	into	consideration	any	sort	of	solvent	effects. 	Other	examples	can	be	
62,	 63
64,	 65
found	in	which	charged	fragments	interact	to	form	either	a	neutral
	or	a	charged	system,
	 but	in	these	cases	solvent	effects	were	

	

	
66

not	included	in	the	analysis	either.	De	Jong	and	Bickelhaupt 	introduced	for	the	first	time	the	EDA	analysis	in	solvent,	thus	we	followed	an	
equivalent	protocol.	In	a	very	recent	example	that	dealt	with	a	host-guest	charged	system,	supramolecular	interactions	including	solvent	
67	 	
effects	were	analysed	in	terms	of	EDA. Since	including	solvent	effects	within	the	EDA	framework	is	not	a	straightforward	protocol,		we	
describe	herein	a	general	procedure	for	extracting	the	relevant	data.		

	
VI

V

10-

Fig.	2	A	fragment	cut-out	of	the	[(Mo 6O21)2(Mo 2O4)] 	simplified	model	ion	used	in	the	calculations	(blue	for	pentagons	and	red	for	the	linker).	
	

In	this	paper,	we	consider	various	charged	fragments	that	form	a	charged	system,	taking	into	account	the	role	of	the	solvent	by	means	of	a	
continuum	 model.	 The	 relationship	 between	 the	 computed	 bonding	 energies	 and	 the	 pKb	 of	 anionic	 ligands	 sets	 up	 the	 basis	 to	
understanding	Keplerate-ligand	interactions.	

Computational	Details	and	Models	
52,	 68

69-71

All	 the	 results	 presented	 herein	 were	 obtained	 using	 the	 ADF2012	 program	 system.
	 The	 BP86
	 DFT	 GGA	 functional	
72,	 73
including	scalar	relativistic	ZORA
	approach	was	used	together	with	the	Slater	triple-ζ	plus	polarization	basis	sets	(TZP)	in	all	
atoms,	which	included	frozen	cores	up	to	4p	for	Mo	and	1s	for	O	and	C	atoms.	Solvent	effects	were	introduced	non-explicitly	by	
74,	 75
means	of	the	COSMO	model.
	The	values	of	the	atomic	radii	correspond	to	the	Van	der	Waals	radii	from	the	MM3	method	
76
77
78
developed	by	Allinger. 	A	data	set	collection	of	input	and	output	files	is	available	online 	in	the	ioChem-BD	repository.	 	
	The	energy	decomposition	analysis	(EDA)	as	implemented	in	ADF	was	applied	to	divide	the	bonding	energy	between	the	capsule	
and	its	ligands	into	four	parts:	the	Pauli	repulsion,	the	electrostatic	energy,	the	orbital	interaction	energy	and	finally	the	solvation	
energy	contribution.	Given	the	anionic	nature	of	both	the	capsule	and	the	ligands,	the	latter	plays	a	key	factor	in	balancing	out	
excessive	 electrostatic	 and	 bonding	 repulsions.	 The	 electrostatic	 interaction	 component	 yields	 the	 classical	 electrostatic	
contribution	between	the	unperturbed	fragments	and	the	Pauli	repulsion	term	is	the	anti-symmetrisation	energy	penalty	(always	
positive)	 between	 electrons	 of	 like	 spin	 upon	 assembling	 the	 two	 fragments.	 Neither	 of	 these	 components	 changes	 upon	
inclusion	 of	 implicit	 solvation	 models.	 Only	 the	 orbital	 interaction	 term,	 which	 is	 a	 consequence	 of	 the	 relaxation	 due	 to	
overlapping	the	two	fragment	densities,	is	different	with	the	use	of	COSMO	with	respect	to	the	in	vacuo	orbital	interaction	term,	
since	 there	 is	 an	 intrinsic	 change	 in	 electronic	 density	 due	 to	 the	 solvation	 potential.	 The	 deformation	 energies	 of	 the	 ligands	
were	computed	in	the	case	of	the	full	capsule	model,	and	taken	into	account	in	the	final	total	bonding	energy	value.			
	
The	 outcome	 of	 EDA	 is	 largely	 dependent	 on	 how	 fragments	 are	 defined.	 In	 the	 present	 case,	 and	 following	 our	 successful	
33,	 35
previous	 experience	 in	 studying	 chemical	 reactions	 catalysed	 by	 Mo132,
	 a	 first	 choice	 would	 be	 one	 linker	 unit	 and	 two	
capping	 pentagon	 moieties,	 highlighted	 in	 Fig.	 2,	 as	 a	 model	 of	 the	 whole	 capsule.	 This	 would	 be	 justified	 as	 a	 compromise	
between	 accurate	 chemical	 description	 and	 computational	 cost.	 But	 doing	 that,	 the	 degree	 of	 protonation	 to	 saturate	 the	
dangling	 bonds	 introduces	 additional	 uncertainties,	 since	 this	 model	 system	 might	 be	 fully	 protonated	 as	 in	
VI
V
6+
VI
V
10-	
[(H8Mo 6O21)2(Mo 2O4)] ,	 or	 fully	 deprotonated	 as	 in	 the	 [(Mo 6O21)2(Mo 2O4)] anionic	 fragment.	 Although	 both	 models	
retain	 the	 main	 characteristics	 of	 the	 linker’s	 chemical	 environment,	 the	 presence	 or	 lack	 of	 protons	 in	 the	 pentagon	 motifs	
make	 the	 whole	 model	 either	 highly	 positively	 or	 highly	 negatively	 charged.	 Actually,	 the	 anionic	 model	 is	 closer	 to	 the	actual	
VI
V
12charge	if	we	consider	the	whole	capsule	[(Mo 6O21)12(Mo 2O4)30] .	We	considered	notwithstanding	these	three	models:	the	two	
models	of	the	linker	unit	interacting	with	one	ligand,	and	the	entire	thirty	ligands	being	bound	onto	the	capsule	walls.	We	are	

	

	
presenting	 herein	 the	 results	 for	 the	 anionic	 model	 and	 the	 whole	 capsules,	 whereas	 the	 results	 for	 the	 cationic	 model	 are	
included	in	the	Supporting	Information.		
	
Since	 the	 EDA	 implementation	 requires	 the	 fragments	 to	 be	 in	 the	 gas-phase,	 the	 energy	 that	 ADF	 provides	 in	 such	 kind	 of	
!"#$
analysis	is	∆𝐸!"# ,	as	indicated	in	the	thermodynamic	cycle	in	Scheme	1.	

	
Scheme	1	Definition	and	notation	of	the	different	energies	terms	in	the	thermodynamic	cycle.		
!
To	compute	the	Bonding	Energy,	which	we	label	as	∆𝐸!"# 	in	Scheme	1,	we	could	use	Equation	1.		
R
syst
capsule
lig
ΔEsol = Esol − Esol − Esol 																								(1)	

!"#$

When	the	EDA	is	carried	out	using	ADF,	the	magnitude	∆𝐸!"# 	is	obtained	(Equation	2).	
frag
syst
capsule
lig
ΔEsol = Esol − Egas − Egas =
syst
syst
syst
capsule
lig
= ( Esol − Egas ) + ( Egas − Egas − Egas ) = 													(2)	
syst
R
= ΔEsol + ΔEgas

!
!
The	combination	of	(1)	and	(2)	give	Equation	3.	Note	that	𝐸!"# − 𝐸!"# 	is	the	solvation	energy	of	species	i.	
R
frag
capsule
capsule
lig
lig
ΔEsol = ΔEsol + ( Egas − Esol ) + ( Egas − Esol ) 							(3)	

!
Of	course,	we	can	also	compute	∆𝐸!"# 	directly,	just	evaluating	the	energy	in	solution	of	the	whole	system	and	of	the	fragments	to	know	
!"!

!"#$%&'

𝐸!"# , 𝐸!"#

!"#

and	𝐸!"# 	as	in	Equation	1.	But	since	we	aim	at	decomposing	the	interaction	energy	between	the	two	fragments	under	the	

EDA	framework,	we	used	the	fragment	based	approach	leading	thus	to	Equation	4.	
R
R
syst
capsule
lig
ΔEsol = ΔEgas + ΔEsol − ΔEsol − ΔEsol 												(4)	

The	two	approaches	give	fully	equivalent	results.	The	reader	can	find	a	detailed	numerical	example	in	the	Supporting	Information.	

Results	and	discussion	
[(MoVI6O21)2(MoV2O4)]10-	Model.	By	following	the	procedure	described	above,	we	considered	a	model	of	the	capsule,	i.e.	the	
VI

V

10-

negatively	 charged	 fragment	 [(Mo 6O21)2(Mo 2O4)] .	 The	 two	 pentagonal	 moieties	 are	 joined	 together	 with	 a	 linker	 unit,	
without	any	additional	protons,	exactly	as	highlighted	in	Fig.	2.	Note	that	the	model	holds	a	high	negative	charge,	which	is	much	
larger	than	in	the	real	system.	Table	1	collects	the	decomposition	of	the	energy	bonding	terms	obtained	from	the	EDA	analysis	
and	the	differences	in	solvation	energy.	
	
VI

V

10-

Table	1	Bonding	energy	decomposition	in	eV	of	the	interaction	between	the	[(Mo 6O21)2(Mo 2O4)] 	model	and	various	ligands.	
	
2-

	
		SeO4 	
Pauli	Repulsion	
8.04	
Electrost.	Int.	
24.95	
Orbital	Int.	
-5.65	

	

2-

SO4 	
7.49	
25.63	
-5.59	

2-

SO3 	
9.47	
24.29	
-7.18	

-

HSO4 	
4.43	
12.73	
-2.33	

2-

CO3 	
11.96	
21.97	
-9.52	

	
Diff.	Solvation		
Energy	
Bonding		
Energy	

-28.25	

-28.33	 -28.29	 -15.00	 -26.88	

-0.91	

-0.79	

-1.71	

-0.18	

-2.47	

	
-

-

-

-

	
HCO3 	 HCOO 	 CH3COO 	 H2PO2 	
Pauli	Repulsion	 5.79	
5.96	
6.36	
6.99	
Electrost.	Int.	
11.91	 11.74	
11.33	
11.19	
Orbital	Int.	
-3.15	
-3.22	
-3.30	
-3.55	
Diff.	Solvation		
-15.40	 -15.47	
-15.53	
-15.66	
Energy	
Bonding		
-0.85	
-0.99	
-1.16	
-1.03	
Energy	
	
As	 expected,	 the	 electrostatic	 energy	 between	 the	 unperturbed	 charge	 densities	 of	 the	 two	 anions	 (model	 and	 ligand)	 shows	 positive	
values	in	all	the	cases.	The	magnitude	of	the	electrostatic	term	follows	a	clear	trend	dictated	by	the	charge	of	the	ligand,	di-anionic	ligands	
roughly	doubling	the	repulsion	computed	for	mono-anionic	ligands.	The	difference	in	solvation	energy	follows	a	very	similar	trend	dictated	
by	 the	 ligand	 charge,	 although	 this	 term	 is	 clearly	 stabilizing.	 This	 is	 because	 the	 total	 charge	 of	 the	 system	 increases	 upon	 bonding.	
Actually,	the	whole	system	is	more	charged	(-11	or	-12)	than	its	fragments	(-1	or	-2,	and	-10),	so	solvation	energy	differences	contribute	to	
bonding.	Since	the	Pauli	repulsion	term	is	positive	in	all	cases,	it	is	the	balance	between	the	orbital	interactions	and	the	solvation	energy,	
compared	to	the	repulsive	terms,	which	makes	the	total	bonding	energies	negative.	It	is	worth	noting	that	although	individual	terms	afford	
high	numbers	in	absolute	value,	the	total	bonding	energies	are	negative	in	all	the	cases	and	relatively	small.	Again,	mono-anionic	ligands	
22are	less	strongly	bound	to	the	linker	unit	than	di-anionic	ligands,	apart	from	SO4 	and	SeO4 .	We	will	discuss	this	apparently	wrong	trend	
below.	A	close	look	at	the	values	in	Table	1	reveals	that	it	is	not	only	the	charge	of	the	ligand	what	determines	the	bonding	strength,	but	
2the	 chemical	 nature	 of	 the	 different	 ligands.	 At	 this	 point,	 it	 is	 worth	 noting	 that	 the	 most	 strongly	 bound	 ligand,	 carbonate	 CO3 	 and	
221,	25,	35
sulphite	SO3 ,	are	precisely	the	products	obtained	in	the	related	catalytic	transformations	reported	recently.
	
We	carried	out	the	same	analysis	for	a	series	of	carboxylate	ligands	as	shown	in	Fig.	3.	The	results	we	obtained	are	collected	in	Table	2.	As	
expected,	no	surprises	arise	from	these	results,	just	confirming	the	similarity	between	the	bonding	properties	of	these	ligands.	Differences	
are	really	small	in	all	cases,	so	in	line	with	ligand	exchange	experiments.	Note	that	despite	the	high	negative	charge	of	the	model	we	chose	
for	the	cluster,	bonding	energies	of	anionic	ligands	are	negative	in	all	the	cases	resulting	in	favourable	bonding.	

																											

	

Fig.	3	A	series	of	carboxylate	ligands:	acrylate,	isobutyrate,	propionate,	butyrate,	pivalate,	and	pentanoeate.	We	will	refer	to	these	species	
as	A,	B,	C,	D,	E,	and	F	for	short.	
VI

V

10-

Table	2	Bonding	energy	decomposition	in	eV	of	the	interaction	between	the	[(Mo 6O21)2(Mo 2O4)] 	model	and	various	ligands	with	different	carbon	chains.	
Labels	meanings	are	indicated	on	Fig.	3.	
	
Pauli	Repulsion	
Electrost.	Int.	
Orbital	Int.	
Diff.	Solv.	Energy	
Bonding	Energy	

A	
6.43	
11.27	
-3.16	
-15.64	
-1.11	

B	
6.69	
10.92	
-3.28	
-15.43	
-1.10	

C	
6.36	
11.24	
-3.24	
-15.52	
-1.17	

D	
6.53	
11.03	
-3.23	
-15.49	
-1.16	

E	
6.73	
10.84	
-3.26	
-15.36	
-1.04	

F	
6.50	
10.97	
-3.14	
-15.50	
-1.17	

	

We	refer	the	reader	to	the	Supporting	Information	section	where	we	included	the	results	of	a	similar	analysis	on	a	model	of	the	capsule	
VI
V
6+
which	is	a	fully	protonated	and	positively	charged	fragment	[(H8Mo 6O21)2(Mo 2O4)] .	As	expected,	for	such	a	model,	the	total	bonding	

	

	
VI

V

10-	

energies	values	are	much	more	negative	than	for	the	[(Mo 6O21)2(Mo 2O4)] model	since	the	electrostatic	term	predominates.	Solvation	
energy	differences,	however,	play	an	opposite	role.	From	the	results	here	gathered	it	is	clearly	revealed	that	the	EDA	is	strongly	dependent	
on	 the	 model,	 the	 sign	 of	 electrostatic	 and	 the	 solvation	 energy	 terms	 being	 highly	 dependent	 on	 the	 charge	 of	 the	 fragment	 chosen.	
However,	it	is	worth	mentioning	that	the	same	trends	amongst	the	ligands	are	obtained,	independently	of	the	model.		

[(MoVI6O21)12(MoV2O4)30]12-	 Capsule.	 To	 eliminate	 ambiguities,	 we	 applied	 the	 same	 procedure	 as	 described	 above	 and	
considered	the	full	capsule	coordinating	30	ligands,	in	order	to	compare	with	the	results	provided	by	the	two	aforementioned	
smaller	models.	Instead	of	taking	into	account	just	a	Mo132	fragment,	we	dealt	with	the	whole	Mo132	capsule	and	computed	and	
decomposed	 the	 total	 bonding	 energy	 between	 the	 Keplerate	 and	 its	 30	 ligands	 decorating	 the	 inner	 surface	 of	 the	 capsule.	
Results	are	collected	in	Table	3	and	Fig.	4.	In	this	case	we	have	also	accounted	for	the	ligands	deformation	energy,	which	is	the	
energy	needed	to	bring	a	ligand	from	solution	to	coordinating	to	the	linkers	within	the	capsule.		
	
Table	3	Bonding	energy	decomposition	in	eV	of	the	interaction	between	the	Mo132	capsule	and	the	30	inner	ligands.	Values	for	the	whole	system	and	per	
ligand.	
	
Pauli	Repulsion	
Pauli	Rep.	/	ligand	
Electrost.	Interaction		
Electrost.	Int.	/	ligand	
Orbital	Interaction	
Orbital	Int.	/	ligand	
Diff.	Solvation	Energy	
Diff.	Solv.	E	/	ligand	
Bonding	Energy	
BE	/	ligand	
Deform.	E	/	ligand	
Total	BE	/	ligand	

2-

SeO4 	
275.84	
9.19	
262.16	
8.74	
-420.87	
-14.03	
-129.91	
-4.33	
-12.78	
-0.43	
0.27	
-0.15	

2-

SO4 	
235.17	
7.84	
298.54	
9.95	
-379.79	
-12.66	
-141.00	
-4.70	
-5.17	
-0.17	
0.08	
-0.09	

2-

SO3 	
289.10	
9.64	
239.14	
7.97	
-461.25	
-15.37	
-98.71	
-3.29	
-31.72	
-1.06	
0.09	
-0.96	

-

2-

HSO4 	
110.10	
3.67	
182.34	
6.08	
-139.92	
-4.66	
-145.69	
-4.86	
6.83	
0.23	
0.03	
0.26	

CO3 	
295.09	
9.84	
232.79	
7.76	
-442.13	
-14.74	
-116.46	
-3.88	
-30.71	
-1.02	
0.04	
-0.98	

	

	
Pauli	Repulsion	
Pauli	Rep.	/	ligand	
Electrost.	Interaction	
Electrost.	Int.	/	ligand	
Orbital	Interaction	
Orbital	Int.	/	ligand	
Diff.	Solvation	Energy	
Diff.	Solv.	E	/	ligand	
Bonding	Energy	
BE	/	ligand	
Deform.	E	/	ligand	
Total	BE	/	ligand	

-

HCO3 	
148.79	
4.96	
136.14	
4.54	
-65.34	
-2.18	
-139.02	
-4.63	
-25.09	
-0.84	
0.01	
-0.82	

-

HCOO 	
152.05	
5.07	
134.62	
4.49	
-158.27	
-5.28	
-144.52	
-4.82	
-16.12	
-0.54	
0.00	
-0.53	

-

CH3COO 	
172.67	
5.76	
113.77	
3.79	
-168.89	
-5.63	
-136.25	
-4.54	
-18.70	
-0.62	
0.01	
-0.62	

-

CH2CHCOO 	
186.02	
6.20	
102.33	
3.41	
-172.87	
-5.76	
-131.70	
-4.39	
-16.23	
-0.54	
0.01	
-0.53	

-

H2PO2 	
167.25	
5.58	
118.50	
3.95	
-164.61	
-5.49	
-139.05	
-4.64	
-17.91	
-0.60	
0.01	
-0.59	

	

	

Fig.	 4	 Bonding	 energies	 per	 ligand	 in	 eV	 with	 its	 decomposition	 into	 the	 different	 energy	 terms	 for	 the	 interaction	 of	 the	 Mo132	 capsule	 with	 a	 set	 of	
bidentate	ligands.	

Results	in	Table	3	and	Fig.	4	show	that	the	sign	of	each	individual	contribution	to	the	total	bonding	energy	is	equivalent	to	those	obtained	
VI
V
10when	we	analysed	the	negatively	charged	model	[(Mo 6O21)2(Mo 2O4)] ,	namely,	negative	value	for	the	difference	in	solvation	energy	and	
positive	 value	 for	 the	 electrostatic	 interaction	 term.	 Note	 that	 the	 Pauli	 repulsion	 term	 almost	 matches	 the	 values	 obtained	 with	 the	
smaller	models,	being	the	origin	of	the	differences	tiny	changes	in	the	geometrical	parameters	upon	bonding.	A	remarkable	result	from	
Table	3	is	that	the	difference	in	solvation	energy	depends	on	the	charge	of	the	ligand	in	a	lesser	extend	than	in	the	smaller	models.	This	is	

	

	
because	of	the	smaller	charge	density	in	the	entire	capsule	compared	to	smaller	model.	Although	the	total	charge	of	the	former	is	-12,	the	
much	larger	molecular	surface	of	the	capsule	with	respect	to	the	smaller	models	attenuates	the	differences	per	ligand	upon	bonding,	which	
was	 responsible	 for	 the	 large	 solvation	 effects	 observed	 in	 the	 models.	 Being	 electrostatic	 interactions	 much	 smaller	 and	 solvation/desolvation	effects	almost	constant	along	the	ligand	series,	the	orbital	interaction	term	plays	the	main	role	in	the	bonding.		
Regarding	the	deformation	energy	of	the	ligands,	in	most	of	the	cases	this	term	contributes	less	than	10%	to	the	bonding	energy.	Only	for	
selenate	and	sulphate,	the	deformation	contribution	represents	a	large	percentage	of	the	bonding	energy,	63%	and	47%	respectively.	The	
deformation	energy	can	be	understood	in	terms	of	the	geometrical	changes	of	the	ligands	upon	coordination.	For	instance,	the	geometry	
of	 the	 free	 carbonate	 ligand	 (which	 has	 a	 deformation	 energy	 contribution	 of	 only	 4%)	 is	 almost	 exactly	 the	 same	 than	 when	 it	 is	
coordinated	within	the	capsule.	The	distance	between	the	oxygen	atoms	of	an	acetate	ligand	increases	less	than	0.01	Å	upon	coordination.	
In	contrast,	the	changes	upon	bonding	for	sulphate	and	selenate	are	much	larger.	Particularly	the	O-O	distance	between	the	coordinated	
oxygen	atoms	in	the	selenate	ligand	increases	from	2.766	Å	(free)	to	2.920	Å	(coordinated).	This	change	justifies	the	largest	deformation	
energy	of	the	selenate	ligand,	and	also	the	multiple	bonding	modes	found	in	the	X-Ray	structures.		
The	total	bonding	energy	values	are	smaller	in	absolute	value,	which	is	in	agreement	with	experimental	evidence.	The	equilibrium	observed	
between	 ligands	 inside/outside	 must	 be	 originated	 by	 relatively	 small	 bonding	 energies,	 so	 the	 values	 in	 Table	 3	 are	 in	 line	 with	 this.	
-	
Sulphite	and	carbonate	are	the	most	strongly	bound	ligands,	and,	according	to	the	results	in	Table	3,	HSO4 would	not	even	coordinate	to	
the	capsule.	All	the	tested	di-anionic	ligands	but	sulphate	are	definitively	more	tightly	bound	to	the	capsule	than	mono-ionic	ligands.	Again,	
we	 obtained	 an	 apparently	 wrong	 behaviour	 for	 the	 sulphate	 and	 selenate	 anion.	 However,	 this	 trend	 retains	 the	 chemical	 nature	 of	
sulphate	anion	being	a	weak	base	or	a	weak	coordinating	ligand.	Actually	if	we	plot	the	computed	bonding	energy	per	ligand	together	with	
the	ligands’	experimental	pKb	values,	some	degree	of	correlation	emerges	(see	Fig.	5).	Although	EDA	provides	very	large	values	for	some	
individual	 components	 (Pauli	 repulsion,	 electrostatic	 energy)	 and	 the	 balance	 of	 solvation	 effects	 upon	 bonding	 are	 not	 negligible,	 the	
bonding	between	the	Keplerate	capsule	and	its	ligands	is	mainly	dominated	by	the	intrinsic	nature	of	the	ligands,	hence	by	their	acid/base	
properties.	

	
Fig.	5	Correlation	between	the	total	bonding	energies	per	ligand	and	the	pKb	values

79,	80

	for	the	set	of	ligands	collected	in	Table	3.	

Conclusions	
In	summary,	we	carried	out	studies	on	the	interaction	between	the	Mo132	capsule	and	its	inner	ligands	by	considering	two	models	of	the	
linker	with	different	protonation	states,	and	also	the	whole	capsule	as	it	is.	The	three	models	provide	similar	trends	regarding	the	bonding	
energy	 of	 the	 ligands,	 although	 the	 results	 obtained	 with	 a	 negatively	 charged	 model	 are	 more	 consistent	 with	 the	 results	 for	 the	 full	
system.	The	trends	in	Keplerate-ligands	bond	strength	are	the	same	for	both	cases,	being	carbonate	and	sulphite	the	most	strongly	bound	
2-	
2- 	
ligands,	followed	by	CH3COO ,	H2PO2 ,	CH2CHCOO ,	HCOO ,	HCO3 ,	SeO4 and	finally	SO4 . This	order	is	in	good	agreement	with	experimental	
observations,	and	it	shows	some	correlation	with	the	pKb	values	of	the	ligands.		
The	 bonding	 energy	 including	 solvent	 effects	 was	 decomposed	 by	 means	 of	 EDA	 method	 and	 has	 been	 analysed	 for	 the	 three	 models	
VI
V
6+
VI
V
10proposed	 ([(H8Mo 6O21)2(Mo 2O4)] ,	 [(Mo 6O21)2(Mo 2O4)] 	 and	 the	 complete	 Mo132	 capsule).	 The	 decomposition	 energy	 analysis	 is	
VI
V
6+
strongly	 dependent	 on	 the	 model	 used.	 In	 the	 case	 of	 the	 [(H8Mo 6O21)2(Mo 2O4)] 	 model,	 the	 bonding	 energy	 trends	 observed	 were	
dominated	by	the	electrostatic	interaction	and	the	favourable	orbital	interaction	term,	because	the	whole	system	(model	+	ligand)	is	less	
VI
V
10charged	that	its	fragments.	For	the	[(Mo 6O21)2(Mo 2O4)] 	model,	the	electrostatic	interaction	and	the	difference	on	solvation	energies	

	

	
has	an	opposing	sign	compared	with	the	positively	charged	model,	because	in	this	case,	the	whole	system	(model	+	ligand)	is	more	charged	
than	its	fragments.	In	the	case	of	the	negatively	charged	model,	it	has	been	shown	that	even	for	such	a	high	negative	charge	cluster,	the	
bonding	energies	for	the	set	of	ligands	studied	are	negative	as	well.	
Finally,	we	have	shown	that	even	the	capsule	being	a	large	macro-anion,	it	interacts	favourably	with	negatively	charged	ligands,	and	forms	
not	very	strong	bonds,	which	are	labile	in	all	cases.		The	interaction	of	the	ligands	and	the	Mo(V)	centers	in	the	linker	units	is	dominated	by	
orbital	 interactions	 that	 reflect	 the	 chemical	 nature	 of	 the	 ligands.	 The	 pKb	 of	 the	 ligands	 correlates	 almost	 linearly	 with	 the	 bonding	
energy.	
	

Acknowledgements	
The	authors	acknowledge	the	ICIQ	Foundation,	the	Spanish	Ministerio	de	Economía	y	Competitividad	(MINECO)	through	project	
CTQ2014-52824-R	and	the	Severo	Ochoa	Excellence	Accreditation	2014-2018	(SEV-2013-0319),	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.	

Notes	and	references	
	
	
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