Further insights in the ability of classical nonadditive potentials to model actinide ionwater ...

13 Pages·2012·0.56 MB·English

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Further Insights in the Ability of Classical Nonadditive
Potentials to Model Actinide Ion–Water Interactions
Florent R!eal,*[a] Michael Trumm,[b] Bernd Schimmelpfennig,[b] Michel Masella,[c]
and Val!erie Vallet[a]
Pursuing our efforts on the development of accurate classical reproduce high-level ab initio data concerning only hydrated
models to simulate radionuclides in complex environments ion species in gas phase. For the two types of cooperative
(R!eal et al., J. Phys. Chem. A 2010, 114, 15913; Trumm et al. J. charge-transfer models, we define two sets of parameters
Chem. Phys. 2012, 136, 044509), this article places a large allowing or not to cancel out possible errors inherent to the
emphasis on the discussion of the influence of models/ force field used to model water/water interactions at the ion
parameters uncertainties on the computed structural, vicinity. We define thus five different models to characterize
dynamical, and temporal properties. Two actinide test cases, the solvation of each ion. For both ions, our cooperative
trivalent curium and tetravalent thorium, have been studied charge-transfer models lead to close results in terms of
with three different potential energy functions, which allow us structure in solution: the coordination number is included
to account for the polarization and charge-transfer effects within 8 and 9, and the mean ion/water oxygen distances are
occurring in hydrated actinide ion systems. The first type of 2.45 and 2.49 A˚, respectively, for Th(IV) and Cm(III). VC 2012
models considers only an additive energy term for modeling WileyPeriodicals,Inc.
ion/water charge-transfer effects, whereas the other two treat
cooperative charge-transfer interactions with two different
analytical expressions. Model parameters are assigned to DOI:10.1002/jcc.23184
Introduction unreasonable,[2] since crystal structures containing a fully
hydrated Th(IV) have been reported, [Th(H O) ]Br , with a
2 10 4
Investigating at the molecular scale, the fundamental proc- mean Th/water oxygen distance of 2.50 A˚ in a dicapped
esses affecting the chemistry and the thermodynamics of acti- square antiprismatic configuration.[9] Asfar asdynamics is con-
nide ions in liquid phase is a major topic in the nuclear waste
cerned, the only estimate of residence time of the first-shell
and disposal research fields. Their rich chemistry and the
water molecules is less than 20 ns (obtained from the lower
statrlocnogndsietniosnitsiv(istuycohfatshethirepiroonpceortniecsenintrastoioluntioanndtotheexnpaetruimreeno-f value kex > 5 !107 S"1, for the rate constant of the exchange
between water solvent and the hydrated Th(IV)), as suggested
the counter ions considered) explain the difficulties to unam-
by12O NMRmeasurementsofFarkas etal.[10]
biguously define experimentally the main features of their
However, an overall experimental consensus prevails for
behavior(s) in aqueous phase. In particular, despite the fact
some actinide ions, such as the trivalent curium ion, Cm(III),
that most of the available experimental spectroscopic techni-
for which a nine-fold coordinated structure in an aqueous me-
ques [such as extended X-ray absorption fine spectroscopy
dium is usually reported. Indeed, Kimura and Choppin deter-
(EXAFS), high energy X-ray scattering (HEXS), nuclear magnetic
mined its CN to be 9.2 6 0.5 by luminescence,[11] agreeing
resonance (NMR), or time-resolved laser fluorescence spectros-
with the HEXS and EXAFS findings of Skanthakumar et al.,[12]
copy(TRLFS)]wereusedtoinvestigateactinideionsinsolution,
who also exhibited the Cm(III) first hydration shell to present
there are still many debates concerning their hydrated proper-
two characteristic Cm/water oxygen distances, namely, six-
ties, such as the structure of their first hydration shell, the resi-
short distances of 2.48 A˚ and three longer ones of 2.63A˚,
dencetimeoffirst-shellwatermoleculesandiontransportprop-
erties, for instance.[1] Thanks to the developments of both
computer power and theoretical approaches,numerical experi- [a] F.Re!al,V.Vallet
mentoffersanalternativetechniquetodeterminenewdataand Universite!Lille1(SciencesetTechnologies),LaboratoirePhLAM,CNRSUMR
8523,BaˆtP5,F-59655Villeneuved’AscqCedex,France
reducetheexperimentaluncertainties,providingthattheaccu-
[b] M.Trumm,B.Schimmelpfennig
racyandpredictioncapabilityofthemodelsareassessed.
Institutfu¨rNukleareEntsorgung(INE),KarlsruheInstituteofTechnology
A well-known example of the experimental uncertainties (KIT),Postfach3640,D-76021Karlsruhe,Germany
concerning the aqueous behavior of actinides is the case of [c] M.Masella
LaboratoiredeChimieduVivant,Serviced’inge!nieriemole!culairedes
the tetravalent thorium ion, Th(IV). The reported number of
prote!ines,InstitutdebiologieetdetechnologiesdeSaclay,CEASaclay,
water molecules involved in its hydration first shell [coordina-
F-91191GifsurYvetteCedex,France
tion number (CN)] ranges from 8 to 13.[2–8] However, the larg- E-mail:[email protected]
est CN values reported (ranging from 11.6 to 12.7) seem VC 2012WileyPeriodicals,Inc.
JournalofComputationalChemistry2012,000,000–000 1
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corresponding to a tricapped trigonal prismatic coordination set to reproduce ion/ligand properties in condensed phase.
geometry. However, one should note that EXAFS yields CNs For instance, Atta-Fynn et al.[36] recently adjusted the parame-
with an accuracy of 10–20%.[13,14] In line with the latter ters of a Lennard-Jones nonpolarizable potential to reproduce
authors, Lindqvist-Reis et al. used TRLFS to find a 9:1 ratio of EXAFS radial distribution functions (RDFs) of Cm(III) in aqueous
the nine-fold coordinated Cm(III) species to the eight-folded solution. Note that all the simulation results derived from the
one.[15,16] As far as we know, there is no experimental data on latter approaches agree well with the experimental data on
the first-shell water molecule dynamics around the Cm(III). The the CN (computed values are within 8 and 9), but exhibit a
only available measured quantity relatedto transport phenom- discrepancy on the Cm/water distance, since the range of
enon is the value 6 10"6 cm2 s"1 of the curium self-diffu- computed values (2.46–2.55 A˚), is about three times larger
!
sioncoefficient withanopenend-capillarymethod.[17] thantheexperimentalone(2.45–2.48A˚).[33,36,37]Thisraisesfirst
As mentioned above, an alternative route to investigate at the question of the accuracy of the models proposed so far to
the molecular scale the structural, dynamical, and transport simulate aqueous media. In addition, it is not clear whether
properties of actinide ions in large and complex chemical envi- implicitly accounting for nonadditive effects makes the models
ronments consists in simulating them using computational mo- robust enough to investigate the thermodynamics of actinide
lecular modeling techniques.[1,18] Beside theoretical protocols ion dehydration processes at interfaces, and even of basic
based on quantum numerical techniques, such as the Density ligand competition reactions in solution, for instance. Never-
Functional Theory (DFT) Car–Parinello method (see for instance theless, we may quote a recent attempt to develop an ad hoc
Refs. [19,20]) and hybrid quantum/molecular mechanics (QM/ three-body potential to investigate the solvation of Cm(III).[36]
MM) approaches (see for instance Refs. [21,22]), classical models However, the total potential energy function used in that case
based on empirical force fields allow one to simulate much does not correspond to a polarizable one, which prevents
larger molecular systems on significantly longer simulation from clearly defining to which physical interaction such a
times (usually, at the ns scale and above). Hence, they provide three-bodytermistied.
statistically relevant sampled sets of data, which may then be Recently, we proposed a new polarizable force-field includ-
postprocessed to estimate specific properties. However, the ing a specific nonadditive charge-transfer term well suited to
study of the ligand coordination dynamics around ions requires theoretically investigate the hydration process of the actinide
the use of sophisticated force fields accounting for in particular ion Th(IV).[25] In that approach, the nonadditive component of
polarization phenomena, as well as for the charge-transfer the charge-transfer term handling a specific ion/water interac-
effects affecting ion/ligand interactions, which are shown to be tion is based on an estimate of the local water density in the
significantinseveralheavyelementsystems.[23–25] first hydration shell of the cation. Moreover, the force-field pa-
Many approaches have been proposed to account for polar- rameters are set to reproduce accurate high-level quantum ab
ization effects in molecular simulations (see the recent review initio results in gas phase which encompass the geometries
Ref. [26] and the references mentioned therein). Among them, andenergiesofalargesetofhydratedTh(IV)clusters(contain-
several recent studies exhibited that physical models based on ing up to 10 water molecules), using a least square-based
induced dipole moments used in conjunction with Thole-like assignment procedure. We took care of defining parameters
damping functions (which are inferred to account for short corresponding to ion/water interactions by considering only
range repulsive Pauli effects) are particularly well suited to ion/water total binding energies (BE) from which the water/
model ion/ligand polarization interactions.[27–31] However, the water interaction energies was subtracted (such BEs are called
developmentsofmodelsabletohandlethe‘‘covalent’’ character reduced BEs and are labeled hereafter BE’s). Our model ion/
of ion/ligand interactions in molecular simulations are still in water parameters are thus tied only to ion/water interactions
their first stage. Most of the models developed so far are com- andtheydonotthuscorrectforpossiblefforce-fielddrawbacks
monly based on a two-body exponential radial decaying term, indescribing water/waterinteractions.
whichisshowntoaccuratelymodelcharge-transferphenomena Despite its sophistication, our force-field approach allows us
occurring in ion/water hetero dimer systems.[24,25,30,32,33] How- to generate several molecular dynamics (MD) trajectories at
ever, charge-transfer effects are nonadditive in nature. In partic- the 10 ns scale of Th(IV) embedded in a large water box (con-
ular, it is now well accepted that they are anticooperative in taining about 1000 molecules) at ambient conditions, using
large ion/ligand systems: their intensity between the ionic cen- periodic boundary conditions and Ewald summation techni-
ter and the surrounding ligand molecules tends to decrease as ques. Note that the simulation conditions correspond to a
thesizeoftheion/ligandsystemincreases.[34] very dilute solution, about 0.05M, far more dilute than the sol-
Until now, the nonadditive nature of ion/ligand charge- utions reported in experimental conditions, and no counter
transfer effects is usually not explicitly accounted for in force- ion is explicitly considered. Hence, we may not expect a one-
field based models,but rather implicitly, as,for instance,in the to-onematchofsimulatedandexperimentalresults,butrather
recentworksofBeuchatetal.[35]andofHagbergetal.[33]deal- expect fair to good agreements. Nevertheless, along the
ing with simulations of trivalent lanthanide(III)/chloride salt hydrated trajectories, the Th/water oxygen average distance
and of Cm(III) in aqueous phase. The two-body exponential was found to be 2.45 A˚, in excellent agreement with the
decaying charge-transfer term was adjusted to ion/ligand clus- recent EXAFS and large angle x-ray scattering (LAXS) experi-
ters and not to ion/ligand hetero dimers. We may also quote mental estimates of Torapava et al.[8] Concerning the Th(IV)
model force-field approaches for which the parameters were CN, we showed it to be included within 8 and 9, which
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corresponds to the lower bound of the experimental esti- results in bulk water are tied only to the nonadditive compo-
mates. It also appeared to be sensitive to the parameters of nent of our charge-transfer term and to the possible defect of
the charge-transfer nonadditive component. In particular, the theforcefieldhandlingthewater/water interactions.
smaller is the radius of the sphere from which the local water The details of the force-field model, the quantum reference
density within the ion is computed, the smaller is the corre- ab initio data, as well as the procedure we follow to adjust the
sponding CN (8.45 and 8.05 with a sphere radii of 7 and 4 A˚, model parameters are presented in Section Models and Meth-
respectively). However, the latter conclusion was drawn by ods. Note the current sets of Th(IV) parameters may differ from
considering only two different model parameter sets, and may that reported in our earlier study[25] because we extended our
not be considered as definitive. One may also wonder about reference data set by adding BE of clusters along the dissocia-
the reliability of accounting for nonadditive charge-transfer tion curve of one water molecule from the 10-coordinated
effects by using an isotropic term rather than by using an hydrated compound. The Results and Discussion section dis-
explicit anisotropic term, as the one proposed by Atta-Fynn cussestheresultsobtainedwithour force-fieldmodels.
etal.[36]
We have identified another possible source of model uncer-
Models and Methods
tainty, which may affect the resulting MD trajectory averages,
that is, the ability of the force field handling the water/water Quantummechanical referencecalculations
interactions to accurately describe the energetic of water mol-
For both the Cm(III) and Th(IV) ions, the quantum reference
eculesasinteracting inIonicFirstHydrationShells(IFHS).Com-
dataused toassignthemodelparametersare:
pared to other available force fields, the water model TCPEp
1The energy dissociation curve of the actinide ion with
considered in our Th(IV) study provides fairly accurate interac-
tion energies for water molecules in IFHS geometry.[25] How- one water molecule in C2v symmetry. In the case of Cm(III),
the water geometry is relaxed for each fixed ion/water oxygen
ever, we exhibited that the TCPEp total interaction energies
distance. However, in the case of the tetravalent Th(IV), the
for IFHS water molecules surrounding Th(IV) still differ from
quantum RI-MP2 ones by about 10–30 kcal mol"1, which rep- water geometry was kept fixed to its geometry found at the
resentsabout40%ofsuchwaterclusterBEs.Theoverallinabil- Th4þAOH2 equilibrium geometry, because the appearance of
electron/charge transfer from water to the highly positively
ity of water-force fields to accurately describe the energetic of
charged Th(IV) ion lead to severe convergence problems in
water molecules at a close distance from an ion originates
the Hartree–Fockcalculation step.
from the strategy used to develop them: only water/water
hydrogen bonded structures are usually taken into account
2The BEs and geometries (in terms of ion/water oxygen
and not the unstable structures observed at the close vicinity
distances) of three different ion/water decamer clusters (see
of an ion. As far as we know, the possible incidence of such a
Fig. 1; the Cartesian coordinated are listed in the Supporting
drawback on simulated hydrated ionic structures has never
Information), with 8, 9, and 10 CNs in the range of the
been discussed. Usually, in the case of parameter assignment
expectedvaluesreportedbyeither experimentor theory.
strategies based on the use of quantum data sets, ion/water
parameters are assigned to reproduce the total quantum BEs 3The potential energy curves C and C corresponding
9/1 8/1
of ion/water clusters. Hence, ion/water parameters are to the dissociation of one water molecule from the Th(IV) 10-
assumed to implicitly cancel out the errors arising from the coordinated cluster andfromthe Cm(III) 9-coordinated one.
water/waterinteractionenergies.
The aim of the present study is to determine how the sour- The details on the QM calculations for Th(IV) complexes
cesofuncertaintiesinthemodel,suchastheform ofthenon- werealready presented in ourprevious study.[25] We used size-
additive term and the water/water interaction description, extensive Davidson corrected multireference configuration
influence the computed properties of actinide ions interacting interaction method (MRCI-DC) to compute correctly the dia-
with bulk water. We will here focus our study on the Cm(III) batic Th(IV)/water hetero dimer interaction curve (see details
and Th(IV) ions. For each ion, we built up five models, all of the diabatisation procedure in our previous article[25]). The
based on the water TCPEp force field. The first kind of models diabatisation step could be avoided in the case of Cm(III),
considers only a classical additive exponential term to model because we managed to avoid charge-transfer problems along
the charge-transfer phenomena occurring in actinide ion/water the Cm(III)/water hetero dimer curve using level shifts in the
systems. The four other models differ in the nature of the Hartree–Fock step. The latter curve was computed at the sec-
quantum data used to assign the model parameters (i.e., full ond-order Mo€ller–Plesset perturbation theory (MP2) level of
BEs or reduced BE’s), and from the analytical form used to calculation, since we provedin our previous study[25] that MP2
account for nonadditive nature of ion/water charge-transfer
effects. For all mfodels, the adjustment of the nonadditive
charge-transfer contributions is carried out by using a com-
mon set of parameter values for the two-body energy compo-
nents (i.e., the repulsive one and the additive part of the
charge-transfer term), as well as for the polarization term. This
ensures that the possible differences among our simulation Figure 1. Definitionof8-,9-,and10-coordinatedion/waterdecamerclusters.
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yields as good BE as coupled-cluster singles and doubles with where r is the distance from the atomic center and j is an ad-
perturbative triples, CCSD(T), and MRCI-DC. We also used the justable parameter (note that a five-order polynomial function
MP2 method to optimize and compute the ion/water clusters. is applied to switch off the damping to zero between 4.5 and
In all calculations, we used the aug-cc-pVTZ basis sets[38] on 5.0A˚).
oxygen and hydrogen atoms and the small-core relativistic In the present study, we consider three different types of
pseudopotentials[39] (ECP60MWB) with the corresponding basis ion/water models corresponding to three different definitions
sets on the actinide ions.[40] The 1s oxygen atomic orbitals, of the term U , which is introduced to account for the partial
ct
and the 5d and lower energy ones for Th or Cm are kept fro- ‘‘covalent’’ character of the actinide/water interactions. All our
zen. Finally, the ground-state of the open-shell Cm(III) is modelsconsidera classicalexponentialenergycomponent
treatedwithintheunrestrictedapproach.
The potential energy dissociation curves for dimers were Uct ¼ Dictexpð"bict!rÞ: (4)
i
computed using the MOLPRO quantum chemistry package,[41] X
whereas larger systems were computed with the TURBOMOLE Here, the sum runs over all possible ion/water pairs, r is the
programpackage,[42]usingtheMP2methodwiththeresolution ion/water oxygen distance, and bct i is an adjustable parame-
oftheidentityapproximation.[43,44]AllMP2optimizedstructures ter. Dict is used as a parameter in the additive charge-transfer
are shown to be true minima by checking their vibrational fre- model, Mnocoop. Among the two models corresponding to a
quency modes. Spin-orbit effects were ignored for both Th(IV) nonadditive charge-transfer term, the first one, Mdens, corre-
andCm(III)systems.Th(IV)havingaclosed-shellelectronicconfig- sponds to the one we proposed in our previous study:[25] the
urationinitsground-state,spin-orbitcouplingisexpectedtobe parameterDict ofthemodelMnocoop isalteredasfollows:
negligibleasshownforotherclosed-shellactinidecomplexes.[45]
IonnthtehecacsuerioufmCma(tIoIIm),,thaereoptehne-rsehfoelrle5fwoerabkitlyalspaerretuvrebreydlobcayliztehde DictðrÞ¼dct 1"nctXj6¼i FcjtðrÞ!: (5)
ligand field of the surrounding water molecules. We have dct and nct are two adjustable parameters, whereas Fcjt is a
checkedthattheenergeticcontributionofspin-orbitcouplingis function quantifying the effect of a given water molecule j on
identical along the curium-water interaction curve. Spin-orbit the charge-transfer effect taking place between the ion and a
couplingcanthusbeneglectedwhencomputingBE.AllBEsare water molecule i = j. As we chose the functions Fj so that
ct
correctedforbasissetsuperpositionerrors(BSSE)estimatedfrom their values are included within 0 and 1, the sum occurring in
thecounterpoisemethod,[46]consideringtheionandthecluster the above equation may be considered as providing an esti-
ofwatermoleculesastwodistinctfragments. mate of the local water density the ion first hydration shell.
As discussed in Introduction, we consider two sets of quan- Many analytical forms are possible for Fj . Here, we choose
ct
tum data, which differ only by the kind of quantum BEs used. againa Fermi-likeone
The first set is made of the so-called full cluster BE, BE s,
computed as discussed above, whereas the second set cBoSrSrEe- Fj r exp 2 r"rmax 1 "1 P r ; (6)
ctð Þ¼ r r þ ! 5ð Þ
sponds to the so-called reduced BE, BEBSSE’s, which result from % # max" min$ &
the subtraction of the water interaction energy (i.e., the BE of where r is the ion/water distance, and r and r are two
min max
the water cluster in its ion/water clufster geometry), from the adjustable parameters (r >r ) that roughly represent the
max min
totalBEBEBSSEs: range of the first hydration shell. P5 is a five-order polynomial
function allowing to zero the cooperative contribution of a
BE BE BE : (1)
BSSE¼ BSSE" water water molecule whose distance r from the ion is beyond a
chosencutoff valuer (setto4 A˚ in thisstudy).Hence,we
Modelingion/waterfinteractions smooth
consider that only first hydration shell water molecules have
As in our previous study,[25] the force field used to model ion/ anincidenceonthecharge-transfernonadditivity.
water interactions is based on the following decomposition of The latter approach is based on altering the two-body
thetotalpotentialenergy charge-transfer term of eq. (4) into a many-body one. More-
over, we consider here ion/water nonadditive charge-transfer
U U U U U : (2)
¼ repþ qq0 þ polþ ct effects to depend mostly on ion/water distances. Other
The different terms correspond to a repulsive, a classical approaches have been proposed to account explicitly for the
charge-charge electrostatic, a polarization, and a specific many-body character of ion/water interactions. A popular one
charge-transfer term, respectively. The first two terms are com- consists in introducing a specific three-body energy compo-
mon additive potentials (U being a radial exponential term). nent, which allows one to account forangular dependences of
rep
The polarization term U is based on a many-body induced ion/watercooperativeeffects
pol
dipole moment approach. The dipolar tensor, we consider U3b f r f r f r : (7)
includes Thole-like short range damping functions, derived ct ¼ 1ðiÞ! 2ðjÞ! 3ðijÞ
i>j
X
fromthe followingchargedensitydistribution
Thesumrunsover thesetof(i,j)watermoleculessurround-
3j ing the ion, r and r are the corresponding ion/water distan-
q r exp jr3 ; (3) i j
ð Þ¼4p! " ces, and r is the distance between the set of water molecules
ij
! "
4 JournalofComputationalChemistry2012,000,000–000 WWW.CHEMISTRYVIEWS.COM
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(i, j). Such a term was used since 1991 by Dang et al.[47] to
investigate the hydration of Naþ and Cl", for instance, with
thefollowinganalyticalform
U3ctb ¼A3ctb expð"b3ctb’riÞ!expð"b3ctb’rjÞ!expð"c3ctb’rijÞ:
i>j
X
(8)
Notethatthelatterauthorsusedsuchaterminconjunction
with an induced dipole moment polarization term. A similar
term was used by Schwenk et al.[48] to investigate the solva-
tion of Ca(II) and more recently by Atta-Fynn et al.[36] to inves-
tigatethesolvationofCm(III). However,both thelatterauthors
didnotconsider apolarizableapproach.
Our thirdmodel type,M , is basedon a similar approach
3body
asthelatterones.Weaddtothetwo-bodyenergy component
U defined eq. (4) a three body one U3b, whose analytical
ct ct
form corresponds to that of eq.(7). However, the function f is
3
takenasa linear functionofthedistancer
ij
U3ctb¼ expð"b3ctb’riÞ!expð"b3ctb’rjÞ!ða1’rijþa2Þ: (9)
i>j
X
This choice arises from our own quantum study of the
three-body energy contribution in the hetero trimer
[Cm (H2O)2]3þ.Fordifferention/waterdistancesri ¼rj, we plot
in Figure 2 the energy difference DE between quantum
3body
results and those derived from our nonadditive charge-transfer
model M for a set of water/water distances r corre-
nocoop ij
sponding to angles OACmAO included within 60 and 180
(
(the model parameters are assigned as follows, concerning the
quantum level used, see above). A linear dependence of
DE3body on the water/water distance rij is shown, especially for
distancescorrespondingtoanglesOACmAOsmaller than150(,
irrespective from the distances (ri, rj). Moreover, the DE3body lin-
ear interpolation parameters (a , a ) both decrease exponen- Figure 2. Cooperative charger transfer energy in hetero trimer
1 2
tiallyasthedistancesri;rj increase,sothattheyarealmostneg- [Cm(H2O)2]3þ. (a) Energy difference between ab initio and model Mnocoop
ligible for distances (r,r) greater than 4 A˚. This supports the results vs. the oxygen/oxygen distance fordifferent Cm/water oxygen dis-
i j tances (shown in bold character, dashed lines: linear regression fits). (b)
analytical form proposed eq. (9), and clearly suggests that only 3body charge-transfer energy linear fit coefficient a (black circles, in kcal
1
water molecules in ionic first hydration shell are involved in co- mol"1A˚"1)anda2(emptycircles,inkcalmol"1)plotted vs.theCm/water
operativecharge-transfereffectsaffectingion/waterinteractions. oxygendistance(indashedlines,correspondingexponentialfits).
This is our working hypothesis for the adjustment of both ana-
lyticalformsofthenoncooperativecharge-transfercomponent.
set of parameters is derived from the both sets of quantum
As a result, we define three kinds of ion/water interaction
referencedatafora givenactinideion.
models, corresponding to an additive M , a many-body
nocoop
and a three-body charge-transfer energy term. Comparing
Modelingwater/water interactions
among them, the model results concerning the solvation of
Th(IV) and Cm(III) will allow us, on one hand, to evaluate the The TCPEp model for water is based on a decomposition of the
importance of accounting for the nonadditive character of systemtotalenergyUincludingthefirstthreetermsofeq.(2)to
ion/water charge-transfer effects and, conversely, to evaluate which are added an intramolecular relaxation term U (sum of
rel
the incidence of the analytical form chosen to handle them in OHstretchingandHOHbendingharmonicpotentials)andaspe-
classical modeling approaches. Lastly, we define forboth Mdens cifichydrogen bond(HB) term UHB. Thelatter term is introduced
and M3body models two sets of parameters, the first derived to reproduce small water cluster potential energy surfaces in
from BEBSSE -based quantum reference data and the second vacuo.Itcorrespondstoashort-rangeanisotropicfunction
from BE -based ones. The models corresponding to the lat-
BSSE UHB f r g /;w : (10)
tercase arelabeled BE and BE . Comparing the results of ¼ ð Þ ð Þ
BSSE BSSE
models M to BE , one leads to evaluate the incidence of the The sum runs over all thXe water HB pairs, r corresponds to
BSSE
water/water force-field defects in classical simulations of the HB length, / may be interpreted as the angle between
hydrated actinide ions. Note for the model Mnocoop, the same one water lone pair and the OAH bond of the second water
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molecule participating to the HB. Lastly, w is the O H -O
ff ’’’ Table1. QuantumandTCPEpmodelwater/waterinteractionenergies
angle. f and g are Gaussian functions of the latter geometrical correspondingtoclusters{[An(HO) ]31,(HO) } .
2 n 2 102nn58,9,10
parameters. U is a cooperative energy term, whose analytical
HB
form is close to that described for the nonadditive charge- [An(H2O)8]3þ,(H2O)2 [An(H2O)9]3þ,(H2O) [An(H2O)10]3þ
transfercomponentoftheion/watermodelMdens.[49,50] Cm(III)
TCPEp considers only one point dipole per water molecule. MP2 24 31 40
TCPEp 34 47 60
It is located at the oxygen nucleus, and its polarizability is set
to that of a water molecule in gas phase, 1.45 A˚3. The TCPEp Th(IV)
water static electrostatic charges (used for U0 ) are set to MP2 33 34 41
qq TCPEp 46 56 70
reproduce the dipole moment of water in gas phase, 1.85
Debye.This model has beenshown to provide accurate results
concerning water clusters in gas phase,[49] as well as liquid
watermolecules.TheNewtonianequationsofmotionaresolved
wateratambientconditions.[51] using the multiple time steps r-RESPAp algorithm,[54] with two
timesteps:1fsforintramolecularandshort-rangeintermolecu-
Procedurefor theadjustmentof theactinide/water force-
lar interactions and 5 fs for electrostatic and polarization long-
fieldmodel
range interactions. The water OAH bonds and HAOAH angles
Theionelectricdipolepolarizabilityisrequiredbythepolariza- werebothconstrained usingtheiterativeRATTLEprocedureto
tiontermU .ForTh(IV),weusethevalue1.142A˚3computed their value in gas phase. The induced dipole moments are
pol
at the relativistic coupled-cluster level,[52] avalue which can be solvedusinganiterativescheme,untilanaveragedconvergence
reproduced within 2% with relativistic effective-core-potential criterionof10"6Debyeisreached(however,forasingledipole,
(RECP)s at the MP2 level.[37] For Cm(III), we compute a value the maximum deviation between two successive iterations has
1.165 A˚3 at the MP2 level, slightly lower than the MP2 value alsotobesmallerthan5!10"6Debye).
reportedbyDuvailetal.,[37]1.238A˚3.However,suchasmalldis- The trajectory last 9 ns segments are sampled each 500 fs
to compute the statistical averages. The water structure
crepancyhasanegligibleinfluenceontheresultingpolarization
around actinide ions is investigated by computing the stand-
contributiontoforce-fieldBE.
ard ion/water-oxygen RDFs as well as by computing the
We adjust all the remaining ion/water model parameters
OAionAO angulardistributionfunctions(ADFs).
accordingtoatwo-stepprocedure,usingtheModel-Independ-
ent Parameter Estimation software package.[53] Unlike in our Ion diffusion coefficients Dsim are computed by integrating
previous study,[25] we constrained here both the water OAH the ionic velocity auto-correlation (VACs) functions. VACs are
estimated by sampling 200 ps trajectory segments each 5 fs
bonds and the HAOAH angles to their values in gas phase
(0.96 A˚ and 104.5 ), respectively. This choice arises from the (those segments correspondto a restart ofthe10 ns trajecto-
(
ries). The D values correspond to the averages of the VAC
water geometry constrains used in our MD simulations (see sim
integralvalues included between 3 and4 ps (i.e., the first pla-
below). In the first step of the fitting procedure, we adjust the
teau of the VAC integral functions, as proposed by Zeebe,
parameters of U , of the U two-body component, and of
rep ct
see Ref. [55]). For a reliable comparison with experiment, D
the U damping functions to accurately reproduce the ab ini- sim
pol
values have to be corrected to account for the finite size L3
tio ion/water hetero dimer dissociation energy curves. These
of the simulated system, as well as for the difference
parameters are the sole needed to define the models M .
nocoop
between our water model and experimental data concerning
For models M and M , the latter parameters are kept
dens 3body
the molecular diffusion Dwater in pure water. Here, we follow
frozen and the parameters of the cooperative charge-transfer
again the correction scheme proposed by Zeebe allowing the
component are adjusted alone in a second step to reproduce
compute the theoretical corrected coefficient of diffusion
the quantum data concerning the ion/water decamer clusters
Dc
and the C9/1 (Th(IV)) or C8/1 (Cm(III)) dissociation curves. The sim
parameters of models Mdens and M3body are derived from Dc D nkBT Dwexapter: (11)
BEBSSE -based quantum data sets, whereas those of models sim¼ð simþ6pgLÞ!Dwsimater
M~ and M~ from BE ones. The resulting parameters
dens 3body BSSE where g is the water viscosity and n is the parameter
for thefivemodelsaresummarizedin Table1.
2.837297 corresponding to cubic unit cells.[56] In the present
f
study, we consider the TCPEp estimates for both the water
MD simulations andtrajectory analysis details
viscosity (about 7 10"4 kg m"1 s"1) and the water diffu-
!
MD simulations were performed using the same protocol as in sion coefficient Dswimater ¼ 2.9 ’ 10-5 cm 2 s -1, which leads to
our previous study dealing about the solvation of Th(IV).[25] correction formula Dscim¼0.79 !(Dsim þ0.29).
For each actinide ion and each parameter set, we generate The mean residence time (mrtk) of water molecules in ion
three 10 ns NVT trajectories corresponding to a 0.05 M dilute kthhydration shell is computed accordingto theprotocol pro-
solution at ambient conditions (T 300 K, water density posed by Impey et al.[57] Based on the probability survival
¼ ¼
0.997 g cm"3). The starting points of each trajectory corre- function pi(t0,t0 þ t;s*) of the ith water molecule, which is
spond to 8-, 9-, and 10-coordinated ion/water clusters embed- equal to 1 if that molecule is present in the kth shell at both
ded in a water cubic box of volume (30.94 A˚)3 containing 999 time steps t0 and t0 þ t and does not leave the coordination
6 JournalofComputationalChemistry2012,000,000–000 WWW.CHEMISTRYVIEWS.COM
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shell for any continuous period longer than s* (it takes the
Table2. Adjustedion/waterparametersformodelsM ,M ,and
valuezerootherwise),wecomputethecorrelation function nocoop dens
M .ParametersA andB correspondtotherepulsiveterm
3body ij ij
1 nkðt0Þ (UAiroenp/h¼ydrogeni,>BjiAonij/heydxrpogðe"n,Bjiijon’/rhiyjdÞr.oFgeonr)ipoanr/ahmydertoegresnetaitsotmhepsaairms,ethe
CkðtÞ¼ CN piðt0;t0þt;s*Þ : (12) regardlesPsoftheion,thatis(75000kcalmol21,7.0A˚21,0.5A˚21).For
’ k Xi¼1 (t0 additivecharge-transfermodelsMnoncoop,‘‘allmodels’’parametersapply,
however,withn ,a anda allequaltozero.
ct 1 2
where n (t ) is the number of water molecules in the kth shell
k 0
at time t and CN the ion CN corresponding to that shell. The MTh M~Th MCm M~Cm
0 k
mrt sarethencomputedbyassuming
k Allmodels
Aion/hydrogen(kcalmol"1) 57497 88839
CkðtÞ¼CNk’expð"t=mrtkÞ: (13) jBiioonn//hhyyddrrooggeenn((AA˚˚""13)) 03.1.1184 03.1.6041
For the ion first hydration shell, the expected mrts for both dct(kcalmol"1) 718 300.8
ions havetobeabove100ps.Hence,thevalueofs*isexpected bct(A˚"1) 0.727 0.807
to have a weak incidence on the resulting mrts, this is why we ModelsM
dens
useinthatcasethestandardvalue2ps,asrecentlydiscussedby nct 0.066 0.061 0.090 0.116
r (A˚) 2.39 2.94 2.13 2.05
Laage and Hynes.[58] For the second hydration shell, the corre- rmin (A˚) 2.86 3.60 2.73 2.89
max
spondingmrtshavetobemuchsmallerthan100ps.Weconsider
ModelsM
in that case a weaker value for s*, for example, 0.5 ps, as pro- b3ctb (A˚"1)3body 2.73 2.97 0.86 0.90
posedbyHoferetal.[59]Notethat10nsscaletrajectoriesprovide a1(kcalmol"1A˚"1) 5.07 5.77 236.00 236.78
largeenoughdatasettocomputestaticallyrelevantmrtslyingin a2(kcalmol"1) 5.05 3.90 "16.66 "16.62
therange0.1–1.0ns,whereastheyonlyprovideatbesttheorder
ofmagnitudeformrtvalueslyingabove1ns.Lastly,thefunctions
Classical models (force fields) are based on a given mathe-
C(t)areaveragedalongthetrajectoriesgeneratedfromaparticu-
k
matical representation depending on parameters, which are
lar model. Comparing the mrts obtained from the average C(t)
k
calibrated here to reproduce a large enough set of ab initio
functions to those derived from single trajectories allows us to
reference data. The quality of a such models is tied to the
evaluatethesamplinguncertaintyaffectingsuchvalues.
level of precision their adjusted parameters are able to repro-
duce the reference data set. For all cooperative charge-transfer
Results and Discussion terms and quantum data sets, we obtain a very good agree-
ment between our adjusted models and the quantum data.
Parameterreliability ingasphase
From the results summarized in Table 2 concerning coopera-
Ion/water cluster geometries. The mean ion/water oxygen dis- tive models, the dissociation curves are reproduced within a
tances, for water molecules in ion first hydration shell, derived mean error of 2.3 (Th) and 1.0 kcal mol"1 (Cm), and the mean
from ab initio MP2 computations and from our cooperative errors on the cluster BE are 2.9 (Th) and 3.7 kcal mol"1 (Cm).
models (once their parameters assigned according to our Hence, assuming the worst case where no cancellation of
model development strategy) in gas phase are compared in errors occurs, we estimate the global uncertainty of our force-
Table 2. Our models are able to reproduce the MP2 data field models to be about 5 kcal mol"1. The latter model error
within about 0.03 and 0.02 A˚ on average, for Cm(III) and estimate has to be compared with the BEs of ion/water deca-
Th(IV), respectively. Moreover, if we consider one particular co- mer clusters, about 550 and 840 kcal mol"1 for Cm(III) and
operative charge-transfer model, our parameters allow us to Th(IV), respectively. The model uncertainties appear thus to be
reproduce both the increasing trend of ion/water oxygen dis- negligible, percentage wise. However, we must keep in mind
tances in {[An (H2O)n]4þ, (H2O)10-n} clusters as n increases from that an intrinsic model error of 5 kcal mol"1 may not allow an
8 to 10, and the overall shorter distances occurring in Cm(III) unambiguous prediction of the hydration number of metal
clusterscomparedtoTh(IV)ones. ions, in particular when different ion/water clusters are
expectedto co-exist in solution, as theyobey a Boltzmann dis-
Intrinsic uncertainties of cooperative models concerning cluster
tributionlaw.
energies. For a classical model built from quantum reference
data, two generic sources of uncertainties have to be taken Influence of cooperative charge-transfer effects on cluster
into account. The first one is related to the intrinsic accuracy energies. The cluster BEs computed from the M models
nocoop
of the reference ab initio data and the second one is tied to are also provided in Table 2. Comparing the latter energies to
the parameter adjustment procedure. We estimate the accu- those computed from cooperative models allows one to esti-
racyofabinitioBEsfor thegasphasesystemshereconsidered mate the energetic incidence of cooperative charge-transfer
to be about 2 kcal mol"1, namely because, for heavy element effects,whichareherestronglydestabilizing.Mnocoopmodelspre-
systems, current computational capacities do not allow us to dict cluster BE much lower than cooperative models, by 60–120
push quantum chemical models to their limits in all compo- kcal mol"1 for Cm(III) and by 80–160 kcal mol"1 for Th(IV). As
nents, treatment of relativistic effects, basis set and treatment expected from our parameter assignment strategy, the mean dif-
ofelectroncorrelation.[60] ferenceinBEbetweenmodelsM andcooperativeM~ ones is
nocoop
JournalofComputationalChemistry2012,000,000–000 7
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such cooperative effects
appears thus to be manda-
tory for an accurate descrip-
tion of actinide Cm(III) and
Th(IV) ion/water clusters, at
leastingasphase.
Actinideions inbulk water
from cooperativecharge-
transfer models
For each model and param-
eter sets, and for all MD
startingpoints,thedifferen-
ces in averages among the
hydrated trajectories are
negligible. Hence, the three
different trajectories corre-
sponding to each model
and parameter set are ana-
lyzed as being a single one
oftotallength27ns.
Ionhydrationstructures. The
RDFs corresponding to ion/
water oxygen distances,
RDF(O)s, and their inte-
grated counterparts are
plotted in Figure 3. In all
cases, the RDF(O)s are char-
acterized by two well-
defined peaks correspond-
ing to water molecules in
ion first and second hydra-
tion shells, respectively. The
position of those peaks,
their corresponding CN
numbers, and the results of
ion/water cluster popula-
tion analysis in solution are
reported in Table 3 for
bothions.
A first remark concerns
the general shortening
Figure 3. Trajectory results in solution for Cm(III) and Th(IV), respectively, on left and right columns. Black, violet,
green,andblueplotscorrespond,respectively,tomodelsM~dens,M~3body,Mdens,andM3body.(a),(b),and(c)cor- (included within 0.02 and
respond,respectively,toion/water RDFs (leftaxis)and integrated RDFfunctions (right axis),toADFs,andto water 0.10 A˚) of the ion/water ox-
dipole moment distributions. In the ADFs plots (b), ideal ADFs for8-coordinated structureseither with abicapped ygen distances in solution
trigonal prism or square antiprismatic coordination, and for 9-coordinated structures either with a capped square
as compared with gas
prismaticoratricappedtrigonalprismgeometryaredisplayedwithgraybars.
phase; this is independent
of the ion and the cluster
smaller than in the case of cooperative models M, by 30 kcal coordination favored along the trajectories. Such distance
mol"1,forbothcations.Lastly,noteourresultsexhibitcooperative shortenings from gas phase to aqueous solution have been al-
charge-transfereffectstoberesponsiblefortheenergyorderingof readyreportedfor awideset ofmonoatomicions.[30,36]
thethreedecamerion/waterclustersshowninFigure1.Forboth Concerning Cm(III), RDF(O) first peak positions are predicted
ions,theM modelspredictthe10-coordinatedclustertobe by all cooperative charge-transfer models to be 2.49 A˚. The
nocoop
morestablethan8-and9-coordinatedones,whereasabinitioand first peak spreads appear to be smaller for models M
3body
thus ourcooperativemodels predict thecontrary.Accountingfor compared with models M , by about 20%. However, as
dens
8 JournalofComputationalChemistry2012,000,000–000 WWW.CHEMISTRYVIEWS.COM
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Table3. Comparisonofabinitioandmodelresultsingasphaseconcerning8-,9-,and10-coordinatedclusters,intermsofbindingenergies(in
brackets,themeanion/oxygendistancesforwatermoleculesinionfirsthydrationshell).RMS:root-mean-squaredeviationbetweenquantumandmodel
dataconcerningthedissociativecurvesC9=1andC8=1.Energyresultsinkcalmol(1,distancesinA˚.
BE BE
BSSE BSSE
MP2 Mdens M3body MP2 M~dfens M~3body Mnocoop
R½½½CCCMmmmS(ðððCHHH8222=1OOO)ÞÞÞ8910,,33,þþ3þððHH22OOÞÞ2 """555654062...687[[[222...556151]]] """5555547220...590.6[[[222...566304]]] """5555539381...207.1[[[222...556172]]] """‘555888472...773 """5557879081...425.3[[[222...566126]]] """5558880330...045.9[[[222...566104]]] """666455399...619
R½½½TTTMhhhSððð(HHHC9222=OOO1ÞÞÞ)8910,,44,þþ4þððHH22OOÞÞ2 """888443631...072[[[222...455938]]] """8884424062...839.6[[[222...556062]]] """8884426251...249.8[[[222...455535]]] """888777981...238 """8887879161...817.8[[[222...455838]]] """‘8887774962...538.8[[[222...455615]]] """999689634...527
the first peak heights are smaller for models M com- Cm(III) ones, as they range from 8 to 9. As for Cm(III),
dens
pared with models M , the CN values are close for all Th(IV) models based on a three-body or on a local water
3body
cooperative charge-transfer models: they span from 8.2 to density cooperative charge-transfer component lead to the
8.9. However, note: (1) models based on a three-body or on same CN values. However, we note two major differences
a local water density charge-transfer component and whose betweenourmodelpredictionsconcerningtheCm(III)andTh(IV)
parameters are assigned from the same quantum reference first hydration shells. First, compared to models M~, models M
data set lead to very close CN values (within 0.2); (2) the lead to larger CN values for Th(IV) (by 1 molecule) and to
CN estimates from models M~ (8.85 6 0.05) are larger by smaller ones for Cm(III) (by 0.5 molecule). In the case of Th(IV),
about 0.5 molecule compared with models M (CN 8.30 6 a single coordination pattern is observed in solution, namely,
¼
0.10). The ADF profiles shown in Figure 3 are in line with the more than 95% of the Th(IV)/water clusters observed along
latter results. For models M~, they match the ideal angular dis- models M~ trajectories are 8-coordinated, whereas they are 9-
tribution expected in crystals for a 9-coordinated ion in a tri- coordinated along M trajectories. Unlike Th(IV), in the Cm(III)
gonal-tricapped prism (TTP) conformation, whereas they case, all cooperative models predict a hydration pattern that
match for models M the ideal square antiprism (SAP) one corresponds to an equilibrium between 8- and 9-coordinated
expectedfora 8-coordinatedion. clusters. The ADF profiles for Th(IV) are in line with the latter
In all models, the main hydrated Cm(III) clusters to be results, see Figure 3 and we compare them to ideal 8- and 9-
observed in solution are made of 8 and 9 water molecules. As coordinated structures, for which the ADFs are displayed in Fig-
discussed above, models M favor 8-coordinated clusters, ure3b.FormodelsM~,the8-coordinatedspeciesobservedalong
whereas models M~ favor 9-coordinated ones. However, the dif- the trajectories appear to in a SAP conformation, whereas for
ferences in free energy DG between the 8- and 9-coordi- model M , the corresponding 9-coordinated species are in
8/9 3body
nated cluster populations along the solvated trajectories are essentiallyinTTPone.Lastly,formodelM ,themainconfigu-
dens
small. According to a Boltzmann relation, DG is about 0.9 ration resembles the TTP one with possible contributions from
8/9 þ
6 0.2 and 0.5 6 0.2 kcal mol"1 for models M and M~, thecappedsquareantiprismone.
"
respectively. As for the RDF(O) first peaks, the second ones for Th(IV) are
The Cm(III) RDF(O) second peak properties are also close for centered at shorter distances for models M~ than for models M,
all cooperative models, in terms of position, height, and by about 0.1 A˚ on average. However, the second shell CN esti-
spread.The corresponding second hydrationshell CNs are pre- mates appear to be tied to the analytical form of the coopera-
dicted to be 20 6 0.5 molecules, larger than the sole experi- tive charge-transfer component: models M lead to the
dens
mental estimate reported so far from HEXS measurements, 13 same CN value (20.6 6 0.6), larger by 4.6 molecules compared
6 4[12] [note that the latter value represents a lower bound withmodels M (15.4 60.8). As far as we know, no experi-
3body
since the HEXS data analysis does not account for contribu- mental data have been reported for the Th(IV) second hydra-
tions from solvent dynamics correlations (L. Soderholm, private tionshellin solution.
communication)]. The origin of the different trend between models M~ and M
Compared to Cm(III), the Th(IV) RDF(O) first peaks are more concerning the first hydration shell CNs for the two actinide
sharpened and we note a larger spread in their positions ions is not obvious, as a complex interplay among ion/water
among the cooperative models (the peak positions vary from charge-transfer effects, polarization phenomena, and water/
2.42 to 2.47 A˚). On average, models M predict for Th(IV) a water interactions occurs in solution. Nevertheless, if we con-
slightly larger first peak positions compared with models M~ sider the difference in water interaction energies DE between
8/9
(2.475 6 0.005 and 2.43 6 0.01 A˚, respectively). Altogether, 8-and9-coordinatedion/waterclustersingasphase(computed
the cooperative models predict a mean first peak position from the data of Table 4), we note a large difference in those
of 2.45 6 0.02 A˚ for Th(IV), smaller by 0.05 A˚ than for values for Th(IV) clusters between quantum MP2 computations
Cm(III). Th(IV) first hydration shell CNs are close to the and our water model TCPEp results: about 10 kcal mol"1. For
JournalofComputationalChemistry2012,000,000–000 9
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except for Th(IV) and the two
Table4. TrajectoryaveragesforCm(III)andTh(IV)inaqueoussolution.CNk:coordinationnumber
correspondingtothekthhydrationshell.Rk:ionkthhydrationshellposition,inA˚.p(n):relativeabundance models M3body. In that case, the
ofn-coordinatedclusters,inpercent.DUpot:differenceintotalpotentialenergyalongthesolvated over polarization may reach 0.3
trajectoriesbetweentheadditivecharge-transfermodelandcooperativeones,inkcalmol21.Theoretical Debye for water molecules
averagesandRMSDvaluesarecomputedfromtheM~An ,M~An ,MAn ,andMAn simulationresults.
dens 3body dens 3body whose distance to Th(IV) is
close to 4.1 A˚. However, the
Model CN1 R1 p(8) p(9) p(10) CN2 R2 DUpot
magnitudes of Th(IV) RDF(O)s
MCm 9.0 2.41 0.1 98.8 1.2 20.9 4.67 –
nocoop within that distance are very
M~Cm 8.9 2.49 13.9 85.3 0.8 19.7 4.83 68.9
dens weak, which may lead to large
M~Cm 8.8 2.49 26.4 73.5 0.1 18.8 4.81 65.2
3body statisticaluncertainties.
MCm 8.4 2.49 62.0 36.9 1.1 20.4 4.81 86.7
dens ConcerningCm(III),ourresults
MCm 8.2 2.49 80.8 19.2 0.0 20.3 4.84 80.9
3body are in line with the quantum
Average 8.6 2.49 19.8 4.82
RMSD 0.3 – 0.6 0.02 data reported recently by Atta-
Averageexp.8 8–9 2.45–2.48 13(4) 4.65 Fynn et al.[36] From simulations
ofCm(III)embeddedin64water
MTh 10.0 2.43 0.0 2.1 97.9 17.5 4.72 –
nocoop boxes, the latter authors exhib-
M~Th 8.0 2.42 96.3 3.7 0.0 20.0 4.74 131.3
dens ited l# values to range from 3.2
M~Th 8.0 2.44 99.7 0.3 0.0 14.6 4.77 123.0
3body to 3.6 Debye for first hydration
MTh 9.0 2.48 0.5 98.6 0.9 21.2 4.79 171.7
dens shell molecules, in agreement
MTh 9.0 2.47 5.0 95.0 0.0 16.3 4.86 204.9
3body with the water dipole moments
Average – 2.45 18.0 4.79
they computed for 8- and 9-
RMSD – 0.02 2.0 0.04
Averageexp.8 8–10 2.45–2.46 coordinated Cm(III) clusters in
gas phase (about 3.5 Debye). In
the case of IV charged ions, a
þ
l# value as high as 4.2 Debye
Cm(III) clusters, that difference is twice as small, about 5 kcal has been recently reported for U(IV) in aqueous solution,[61] in
mol"1. That may be at the origin of the above-mentioned dif- agreementwithour Th(IV)estimate. In all cases, the rangeand
ferent trend between models M and M~, and that may also the magnitude of ion induced water polarization in the first
explain the less accented difference in first shell CN values and second hydration shells clearly questions the appropriate-
betweenthelattermodelsforCm(III)ascomparedwithTh(IV). ness of nonpolarizable models, and instead fully justifies the
Overall, our simulations exhibit that all cooperative charge- developmentofpolarizableforce-fieldmodels.
transfer models provide a very close picture for the solvation We recently proposed a new model to theoretically investi-
of both ions. Averaging the model results for Cm(III) leads to a gate the solvation of halide ions F", Cl", and Br".[30] That
first hydration shell CN of 8.6 6 0.3 and to a mean ion/water model is also based on the TCPEp force field to describe
oxygen distance in solution of 2.49 A˚. For Th(IV), the models water/water interactions, and we showed its ability in accu-
predict an almost pure 8- or 9-coordinated hydration pattern rately reproducing quantum estimates of l# for water mole-
and a mean ion/water oxygen distance of 2.45 6 0.02 A˚. All cules surrounding halide ions in aqueous solution (in particu-
those data agree with experimental ones in aqueous media. lar, the usually weaker values l# for halide first hydration shell
Our CN values are included within the experimental estimates molecules as compared to pure water). Hence, together with
[ranging from 8 to 9 for Cm(III) and from 8 to 10 for Th(IV)], the present results, it appears that modeling the water
and, for Cm(III), the mean first shell ion/oxygen distance is
shown to be about 2.45–2.48 A˚ from both EXAFS and TRFLS
experiments,[12]whereasitis about2.45–2.46A˚[8,9]forTh(IV).
Table5. Temporalpropertiesinsolution.Dc :coefficientofdiffusion,
sim
Water electrostatic properties near the actinide ions. The aver- in1025cm2s21.mrtk:watermeanresidencetimeinkthionhydration
age total water dipole moment M~ is plotted as a function of shell,innsforthefirsthydrationshell,andpsforthesecondhydration
the ion/water oxygen distanceR forboth ions and all coop- shell.Modelaverage:meanvaluesfromcooperativecharge-transfer
MW
models.
erativemodelsinFigure3.InbothCm(III)andTh(IV),l# reaches its
vreapluoertiendpfuorrehwaalitdeerbioenyos,n[2d7,3t0h]efodrisitnasntcaencReM.WFi¼rst6:h5ydA˚r,aatsioanlresahdeyll Mdens M3body M~dens M~3body Modelaverage Mnocoop
Cm(III)
water molecules that are in direct contact with the actinide ions
Dc 0.59 0.53 0.52 0.58 0.5560.03 0.53
are over polarized compared to the bulk value: l# increases line- sim
arlyasR decreasesfrom3.5to2.5A˚,toreachvaluesofabout mrt1[ns] 0.14 0.51 0.24 0.67 0.5260.20 5.17
MW mrt2[ps] 7.7 8.7 7.5 9.9 8.561.1 10.6
3.6and4.4DebyeforCm(III)andTh(IV),respectively.
Th(IV)
Water molecules belonging to the second hydration shell
Dc 0.70 0.54 0.58 0.59 0.6060.05 0.55
are also over polarized, however, to a lesser extent thanin first sim
hydration shell. The corresponding water over polarization is mrt1[ns] >10 >10 1.8 >10 – >10
mrt2 [ps] 17.7 15.6 18.6 29.6 20.464.7
usually smaller than 0.2 Debye, as compared to pure water,
10 JournalofComputationalChemistry2012,000,000–000 WWW.CHEMISTRYVIEWS.COM