initially 
 restricted to atmospheric experimental studies , the study of water nucleation , namely the condensation 
 of water molecules around charged particles , has been extended in 
 recent years to the study of m metal 
 cations microhydration in clusters . indeed 
 understanding the bonding properties of a metal cation within its 
 first hydration shell or the organization of the solvent molecules 
 around the cation in ( [ m(h2o)n ] ) clusters can help to identify their 
 selectivity and to understand their involvement in complex biological 
 ( i.e. , metal poisoning ) and chemical ( catalytic 
 capacities ) processes . in this line , experiments 
 have been shown to be able to describe the nucleation of water molecules 
 around heavy metals such as gold thanks to collision induced dissociation 
 ( cid ) techniques . for quantum chemists , 
 such systems have been highly challenging for several decades as they raise the double problem of the inclusion 
 of both the electronic correlation and relativity effects within electronic 
 structure computations ( see refs ( 6b6d ) and references therein ) . from this perspective , electronic 
 structure studies are divided 
 into two categories : on the one hand , high level gas phase quantum 
 calculation , with accurate treatment of the relativistic and correlation 
 effects , on small size clusters , and on the other hand solvated cations treated at a hybrid quantum 
 mechanics / molecular mechanics ( qm / mm ) level to obtain condensed phase 
 results . in both cases , several experimental results allowed 
 the validation of those theoretical results . moreover , to understand the intrinsic importance of local 
 quantum 
 effects due to the metals , a new theoretical  interpretative strategy has been applied through the use of quantum chemical topological 
 ( qct ) analyses . indeed , de courcy et al . showed that the electron localization function ( elf ) topological analysis could define a topological criterion 
 to discriminate hard and soft metal cations in their local environment 
 providing new insights about physical phenomena at play . thus , a soft 
 ( polarizable ) cation is able to split / delocalize its outer - shell core 
 density ( denoted as core subvalence ) into different space domains 
 ( basins ) in order to accommodate the perturbing environment ( induction - like 
 effects ) . on the contrary , the electronic density of a hard ( and poorly 
 polarizable ) cation remains spherical under the same circumstances . such effects have been shown to be directly linked with observed increases 
 of second order metal energies such as polarization and charge transfer 
 ( induction terms ) in energy decomposition analysis approaches . in this contribution , we intend to follow up on theoretical studies devoted to gold in order to more 
 deeply understand the physical effects at play in water nucleation 
 around it and to extend it by comparing such microsolvation to hg which is isoelectronic to au . indeed , it should 
 allow us to illustrate the importance of the electronic correlation 
 vs relativity competition having in mind that if relativity is more 
 important for gold than for any other sixth row cations , hg should nevertheless exhibit smaller 
 but noticeable relativistic effects . to do so , we will study 
 the water molecules nucleation around these 
 two metal cations at a quantum mechanical level in clusters encompassing 
 a number of water molecules ranging from 1 to 16 ( denoted [ m(h2o)n ] or [ m]n where m is the metal name ( i.e. , 
 au or hg ) , n is the number of water molecules in 
 the complex , and p is the charge of the complex ( p = 1 for au and 2 for hg ) ) . in order to provide further 
 insights into the bonding properties of gold and mercury cations and 
 techniques to go beyond usual energetical studies , we will make extensive 
 use of quantum interpretative techniques such as elf or an energy 
 decomposition analysis ( eda ) scheme such as the constrained space 
 orbital variations ( csov ) approach . we 
 will also use the newly developed non - covalent interaction ( nci ) method to unravel weak interactions in clusters and quantify their strength . overall , each one of the obtained structures will be submitted to 
 a full cross - interpretative analysis scheme using combined analyses . for au and hg water complexes , 
 gaussian 09 geometry optimizations were 
 performed using density functional theory 
 ( dft ) at a b3lyp/6 - 31+g * * level on water molecules and 
 using the sdd pseudopotentials for the 
 metal cations . such a pseudopotential was found to give consistent 
 results for the [ au(h2o ) ] complex in comparison 
 with full electron , relativistic calculations using a four - component 
 hamiltonian that can not be performed 
 on the presently studied large systems . table 1 provides a short comparison of the agreement between scalar treatment 
 using sdd pseudopotentials and all - electrons fully relativistic ( four - component ) 
 results . moreover , it is important to point out that topological analyses 
 such as elf / qtaim / nci require to have access to the relaxed electron 
 density . all optimized structures 
 were characterized by a full vibrational 
 analysis as frequencies were calculated for each one of the optimized 
 geometries so as to ensure that the finally obtained geometry was 
 at least a local minimum . for gold , in addition , different 
 starting geometries were tested , such as octahedral geometries . for 
 mercury , we choose our gold optimized structures as guess geometries , 
 but other initial geometries were also considered . for mercury , 
 additional computations were performed . indeed , for 
 the [ hg(h2o)3 ] complex , different 
 dft functionals such as blyp , pbe0 , pw91pw91 , and ab initio methods such as hf , mp2 , ccsd , 
 and ccsd - t , as well as various basis sets ( 6 - 31+g * * , 6 - 311++g * * , aug - cc - pvdz , aug - cc - pvtz ) were 
 tested . several treatments of the relativistic effects including scalar 
 sdd pseudopotential and different levels of douglas kroll / aug - cc - pvtz 
 computations were performed for clusters up to seven water molecules . we also studied the competition between the linear and centered form 
 of mercury complexed with three ligands [ hg(x)3 ] , x = hf , nh3 , imidazole , nh2 , h2o , oh , h2s , hs , and ch3s and p being their respective charge . for these 
 systems , calculations were performed at the b3lyp / sdd/6 - 31+g * * level 
 of theory . the different ligands were chosen to be ranked from typically 
 hard ( hf ) to typically soft ( ch3s ) ligands . to compare to previous studies , various 
 charge analysis schemes have been used in order to discuss the evolution 
 ( and stability ) of the metal cation s charge as a function 
 of the number of water molecules of the complexes . the mulliken , natural bond orbital ( nbo ) , and atoms in molecules ( qtaim ) charges were 
 performed . the top_mod software was used for all 
 qtaim computations as well as for the distributed moment analysis 
 based on the qtaim partition . to study the effects 
 of the method / basis set choices , charges were also computed on the 
 previously optimized structures using other levels of theory : mp2 , 
 hf , blyp , b3lyp , pbe0 , pw91pw91 , and m06 - 2x  and using other basis sets : sto-3 g , 3 - 21 g , dzvp , 6 - 31+g * * , 6 - 31++g * * , 6 - 311++g * * , and aug - cc - pvtz . the basis sets range from minimal to double 
 or triple- basis sets with diffuse and polarization orbitals . the dzvp basis set was additionally used in order to compare our results 
 with those from reveles et al . it was later associated with a measure of the 
 pauli repulsion in the atomic or molecular space by silvi and savin . it also enables access to the probability of 
 finding two same spin electrons . elf values are restricted between 
 0 and 1 and can be interpreted as a signature of the electronic pair 
 distribution , but in contrast to pair functions , it can be easily 
 calculated and interpreted . the elf function can be partitioned into 
 an intuitive chemical scheme once it has been computed on a 3d grid 
 from a given ab initio method . indeed , core regions , denoted c(x ) , 
 can be determined for any atom . this is also the case for valence 
 regions associated with lone pairs , denoted v(x ) , and for chemical 
 bonds [ v(x , y ) ] . these elf regions , called basins ( denoted as x ) , match 
 closely the domains of gillespie and nyholm s valence shell 
 electron pair repulsion model . all computations 
 were performed using the top_mod package . in 
 a recent study , de courcy et al . showed 
 that some metal cations were able to split their inner shell core 
 electron density ( named subvalence ) in order to accommodate to the 
 environment ( see figure 1 ) . they also realized 
 that the ability of a cation to split its subvalence was directly 
 related to its hardness / softness properties : indeed , hard cations 
 never split their subvalence whereas soft cations ones are able to 
 split it . such a property was also demonstrated to have an important 
 implication in biomolecular systems such as enzymes . elf 
 topology of a soft cation such as ca that splits 
 its outer - shell density into subvalence domains vs a hard cation such 
 as mg that remains spherical . in addition to the usual topological analysis , it is possible 
 to 
 use elf theory to obtain properties such as the partial charge or 
 the different first moments integrated on the elf basin . as the equations are very general , these properties 
 can also be integrated on the qtaim basins so as to obtain the atomic 
 partial charges or first moments . recently , johnson 
 et al . introduced the reduced density gradient as a new scalar function 
 able to analyze noncovalent interactions , providing a rich representation of van der waals interactions , hydrogen 
 bonds , and steric repulsions . such a function is defined using the 
 electron density and its first derivatives : it is a dimensionless quantity used in dft 
 to describe the deviation from a homogeneous electron distribution . 
 in density tails ( i.e. , regions far from the molecule , in which the 
 density is decaying to zero exponentially ) , the reduced gradient has 
 very large positive values . on the contrary , the s( ) function assumes values approaching zero for regions of 
 both covalent bonding and noncovalent interactions . these low s( ) areas are traced back to molecular space that 
 gives rise to isosurfaces , enabling the visualization of the weak 
 interactions of the system . in order to differentiate between the 
 different types of interactions , we will use the following color code:blue for the 
 highly attractive 
 weak interactions ( such as hydrogen bonds)green for the extremely weak 
 interactions ( such as dispersive - like van der waals)red for repulsive interactions 
 ( such as steric clashes ) blue for the 
 highly attractive 
 weak interactions ( such as hydrogen bonds ) green for the extremely weak 
 interactions ( such as dispersive - like van der waals ) red for repulsive interactions 
 ( such as steric clashes ) the synergetic 
 use of elf and nci enables the simultaneously 
 identification of regions of strong and weak electron pairing . initially 
 devoted to the study and the understanding of chemical reaction mechanisms , it has been recently applied to the understanding 
 of the role of metal for metalloenzymes reactivity . the interaction 
 energy between two or more fragments such as a cation and its ligands 
 can be decomposed into four different contributions : namely , coulomb / electrostatic energy ( ec ) , short - range exchange - repulsion energy ( eexch / rep ) in first - order ( e1 is the sum of ec and eexch / rep energies ) , polarization energy ( epol ) , and charge - transfer energy ( ect ) in second - order ( e2 is 
 the sum of the epol and ect energies , sometimes denoted as induction ) . all of these 
 four terms can only be computed at the dft level with the b3lyp functional 
 using the constrained space orbital variations ( csov ) procedure in a modified version of the hondo 95.3 software . computations 
 were performed on both gold and mercury complexes for clusters [ m]nn = 2 to 16 and m being 
 au or hg . table 2 shows the evolution of the 
 polarization and charge transfer energies ( kcal / mol ) for [ au]n . in this section , 
 we will first present the computed structures 
 and discuss their significance compared to previous experimental and 
 theoretical studies . we will then apply an extensive multimethod strategy 
 using various quantum interpretative techniques in order to deeper 
 study the present electronic effects . finally , we will discuss the 
 final charge on the au cation within the complexes . the basis set superposition error ( bsse ) and 
 zero point energy ( zpe ) corrected incremental binding energy of a 
 cluster ( [ au]n for example ) can be defined 
 as the difference between the bonding energy of the [ au]n and the [ au]n1 complexes . it therefore represents the change in energy due to the 
 bonding of the water number n. for the gold 
 cation , we compared our incremental bonding energies to other studies 
 including reference experimental gas phase bonding energies ( poisson 
 et al . ) and theoretical works ( lee et 
 al . , feller et al . , reveles et al . ) as shown in 
 figure 2 . they all reported that the two first 
 water molecule additions were at least twice as favorable ( around 
 35 to 45 kcal / mol ) as the following ones ( from 10 to 20 kcal / mol ) . this specificity of the gold cation has been attributed to the 
 large relativistic effects it undergoes . as shown in figure 2 , our 
 results agree with these previous studies and therefore state that 
 our optimized structures can be assimilated as reasonable global minima . bsse / zpe 
 corrected incremented bond energy ( in kcal mol ) for increasing the size of clusters from our study ( diamonds ) or 
 other experimental ( triangles , points and stars ) as well as theoretical 
 results ( squares ) . for ( [ au(h2o)2 ] ) and larger clusters , 
 only two water molecules remain linearly bonded to the cation with 
 an angle ranking between 170 and 178 , the others being 
 located in the second and third hydration shells . for medium size 
 clusters ( up to [ au]7 ) , hydrogen bonded water molecules 
 attempt to form rings on each side of the cation . for the largest 
 clusters ( eight or more water molecules ) , some water molecules are 
 bridging the two sides of the cation thanks to hydrogen bonds . they 
 are however localized too far from the cation ( around 4  instead 
 of 2  for the first solvation water molecules ) to be considered 
 bonded to it . the elf topological analysis shows 
 that gold s subvalence is divided into two half - sphere domains 
 pointing along the au  o bond ( figure 3 and figure s1 in supporting information for larger images of all the complexes ) . this subvalence is conserved 
 whatever the number of water molecules is , i.e. , from 1 to 16 water 
 molecules . indeed , it is already preorganized at the one water molecule 
 stage and will not be modified even with the apparition of bridging 
 water molecules and can be therefore considered as frozen . this preorganization 
 can be traced back to the importance of relativity which was shown 
 to dominate the au(h2o ) complex ( see ref ( 11 ) for the importance of 
 relativity vs correlation effects using all - electrons - dft 4-components 
 computations ) . this last part reinforces the fact that au only strongly interacts with the two first hydration shell water 
 molecules ( in agreement with pyykk et al . who proposed results in that direction ) . elf isosurfaces ( elf 
 = 0.78 ) for different [ au]n ( n = 1 , 2 , and 8) clusters . for each of them , 
 the distance between the closest water molecules and the cation are 
 added (  ) . for a better visibility , the pictures of the other 
 complexes studied can be found in figure s1 in the supporting information . all structures were computed at the 
 b3lyp / sdd/6 - 31+g * * level of theory . for small clusters , nci and elf give very similar results , 
 as interactions 
 between the cation and the two first hydration shell water molecules 
 can be found ( figure 4 and figure s2 in the supporting information for larger images of all 
 the complexes ) . for clusters of eight and more water molecules , however , 
 differences arise as weak interactions can be found between the bridging 
 water molecules and the cation . these interactions are weak ( van der 
 waals strength type ) as the density value associated is very small . the nci approach also explains the reason why cycles are formed between 
 hydrogen bonded water molecules . indeed , an attractive interaction 
 domain can be found in the center of those cycles of four water molecules 
 that corresponds to an additional stabilization due to their formation . nci analyses on mp2 single point relaxed densities on dft 
 structures displayed the same picture . nci analysis for several 
 [ au]n ( n = 1 , 2 , and 
 8) complexes . the colors range from blue for 
 strongly attractive interactions to red for repulsive ones . for more 
 visibility , the pictures of all the complexes studied can be found 
 in figure s2 in the supporting information . all structures were computed at the b3lyp / sdd/6 - 31+g * * level of 
 theory . finally , regarding the definition 
 of hardness / softness introduced 
 by de courcy et al . , au can not 
 be considered as a hard cation as it splits its subvalence into two 
 half - spheres , but neither can it be considered as a soft cation as 
 once its subvalence is split into two domains , the cation is strongly 
 polarized by the water molecules . moreover , it is important to note 
 that au appears impervious to any change in the external 
 field that is a characteristic of a hard cation . it will therefore 
 be designated as a o 
 bonds was very important ( 35 to 45 kcal / mol , see figure 2 ) . the elf analysis shows that an electron donation from the 
 ligand to the subvalence basins of the metal exists ( for example 0.06 
 e for the [ au]4 complex ) . back donation 
 from the metal into first solvation shell oxygen water lone pairs 
 also takes place in these systems ( 0.05 e out of 
 1.63 and 0.05 e out of 1.65 in the [ au]4 complex ) . to investigate it further , we performed decomposition 
 analysis on the different [ au]n , n = 2 to 10 , complexes . using csov energy decomposition , we found important charge transfer energies from the water molecules 
 to the cation and also from the cation to the water molecules ( see 
 results in table 3 ) , which is in agreement 
 with the elf results . therefore , the au  o bond appears as a 
 very strong metal ligand bond due to its partial covalence that mixes 
 metal and ligand electrons . finally , both polarization and charge transfer energies 
 appear 
 stable whatever the number of additional water molecules . this suggests 
 that the remaining interactions between the cation and its ligand 
 ( especially for bridging complexes ) are mainly due to other effects 
 such as electrostatics or dispersion . in a 
 previous study , reveles et al . computed 
 the evolution of gold mulliken charge as a function of the number 
 of water molecules of the complexes . they concluded that gold s 
 charge could decrease so much with the number of water molecules that 
 the cation finally appeared almost neutral ( charge less than + 0.10 
 e for [ au]n , n  5 ) . however , in agreement with lee et al . , they also showed that such a phenomenon was 
 more a trend than an actual neutralization of the gold cation , as 
 other charge analysis schemes such as nbo were finding far less electron 
 transfer to au . we propose here a detailed analysis of 
 the influence of the methodology on the gold charge . in agreement 
 with reveles et al . , we show similar trends as au exhibits 
 the capability to partially recover an electronic fraction . however , 
 our qtaim population analysis clearly shows that the au charge never decreases beyond + 0.6 e , preventing 
 any full neutralization of the gold cation . we therefore decided 
 to investigate more precisely the role of the charge population analysis 
 approach , the basis set , and the ab initio computational method used . nbo , qtaim , and mulliken population analysis were performed for 
 all complexes with cluster encompassing up to 10 water molecules ( [ au]n , n = 1 to 10 ) . the b3lyp 
 functional was used together with the 6 - 31+g * * basis set on the water 
 molecules and the sdd pseudopotential on gold . qtaim and nbo analyses 
 give relatively similar results showing a gold charge that never decreases 
 below + 0.6 e ( as shown in figure 5a and figure s3-a ) , whereas the 
 mulliken population , on the contrary , decreases up to + 0.4 e. this difference between mulliken and nbo charges had already been 
 noticed by reveles et al . and arises from the well - known unstabilities 
 of the mulliken approach ( see refs ( 45 ) , ( 46 ) , and ( 61 ) , for discussion ) evolutions 
 of gold charge for different [ au]n clusters : 
 ( a ) nbo , qtaim , and mulliken population analysis 
 ( in e ) for [ au]nn = 1 , 10 clusters computed at the b3lyp / sdd/6 - 31+g * * level 
 of theory . ( b ) nbo charge for [ au]n complexes 
 ( n = 1 to 16 ) using sto-3 g , 3 - 21 g , dzvp , 6 - 31+g * * , 
 6 - 31++g * * , 6 - 311++g * * , and aug - cc - pvtz . ( c ) nbo charge for the different 
 [ au]n clusters ( n = 1 
 to 16 ) using hf , mp2 , b3lyp , blyp , pbe0 , pw91pw91 , and m06 - 2x . for 
 more visibility , the pictures of the other complexes studied can be 
 found in figure s3 in the supporting information . indeed , as expected , the basis 
 set has a strong influence on the 
 results ( see figure 5b and figure s3-b ) . it appears that the charge is stable for relatively 
 large basis sets ( at least dzvp or 6 - 31+g * * ) , but very important variations 
 can however be seen for small basis sets . for example , the use of 
 a minimal basis set such as sto-3 g will even lead to a negatively 
 charged gold . consequently , it seems mandatory to use , at least , a 
 double- with polarization and diffuse functions basis sets 
 to accurately model such systems to avoid an unphysical description 
 of the electronic structure . finally , we investigated the influence 
 of the ab initio or dft 
 computational approach on the gold population analysis . the cation charge is slightly modified with the ab 
 initio or dft method used . if we compare to the mp2 charges , hf ones 
 appear always too important , whereas dft ones are usually smaller . these results are in good agreement with the delocalization error 
 described in refs ( 58 ) , ( 62 ) , and ( 63 ) . in addition , it 
 is interesting to notice that all the hybrid functionals 
 reproduce better mp2 charges probably due to the addition of a part 
 of exact hf exchange . among the others , finally , our results are also in good agreement 
 with the fact that the dft delocalization error is decreasing with 
 the size of the cluster while the hf one is not . overall , all the results gathered here show that the charge 
 of 
 gold is method- and basis - dependent , as could have been anticipated . moreover , it seems necessary to use nbo or qtaim population analysis 
 with hybrid dft calculation and a basis set larger or equal to dzvp . nevertheless , if au tends to recover a fraction of an 
 electron , it seems far from an actual neutralization of its + 1 charge 
 that was discussed by reveles et al . to complement 
 our results and following the same computational 
 protocol , we extended our water nucleation study to hg , which is isoelectronic to au . for complexes 
 with up to eight water molecules , the mercury behaves similarly to 
 gold : it only bonds to two water molecules , with the remaining going 
 to the second or third hydration shell . its subvalence splits also 
 into two half - spheres directed toward the hg  o bond . this property is eager 
 to be due to the higher charge transfer and therefore more important 
 covalent character of the hg o bonds ( see table 4 ) . in order to reduce electrostatic repulsion , the created 
 protons will then be transferred as far as possible from the cation . this induces a second difference as , in mercury , water molecules tend 
 then to create hydrogen bonded water strings instead of rings in gold 
 clusters . for more than eight water molecules , the mercury switches from 
 its  gold type  or solvation 
 to a  centered  one where hg accepts more 
 than two water molecules in its first solvation shell . this transition 
 can be characterized looking at its elf subvalence basins that move 
 from the two half - spheres to a more divided form characteristic of 
 soft cations ( figure 6 and figure s4 in the supporting information for larger images of all 
 the complexes ) . this topological transition explains why , for small 
 clusters , the mercury has a gold type solvation structure , whereas 
 once solvated , mercury binds seven water molecules . elf representation ( elf = 0.775 ) for complexes 
 [ hg]n , n = 4 , 8 , 9 , or 
 10 . specific attention 
 was paid to the subvalence domain of the cation for each cluster . 
 for more visibility , the pictures of all the complexes studied can 
 be found in figure s4 in the supporting information . all structures were computed at the b3lyp / sdd/6 - 31+g * * level of 
 theory . the nci analysis ( figure 7 and figure s5 
 in the supporting information for larger 
 images of all the complexes ) shows that hg  o bond strength 
 is decreasing when mercury accepts more than two water molecules in 
 its first hydration shell . these modifications induce the loss of 
 the mercury ability to deprotonate the water molecules . indeed , as 
 the bond gets weaker , the acidity gets smaller . despite the increasing 
 number of water molecules in its first hydration shell , the mercury 
 still binds more strongly two opposed water molecules just as in smaller 
 clusters ( the angle o  hg  o ranks between 148 and 
 180 ) indeed , the density characteristic of these interactions 
 is higher than those of other cation / water molecule interactions ( for 
 example , 0.063 and 0.061 compared to 0.049 , 0.044 , 0.040 , and 0.028 
 in [ hg]16 ) . therefore , even if its coordination increases , 
 the mercury remains more strongly bonded to two water molecules presenting 
 a  gold type  geometry . nci analysis for several [ hg]n complexes 
 ( n = 4 , 8 , 9 , 10 , 16 ) . in [ hg]n complexes , only the two most important interactions between 
 mercury and water molecules are represented . the colors range from 
 blue for strongly attractive interactions to red for repulsive ones . 
 for more visibility , the pictures of all the complexes studied can 
 be found in figure s5 in the supporting information . all structures were computed at the b3lyp / sdd/6 - 31+g * * level of 
 theory . in a previous paper , cox and stace studied the reasons leading to the gas phase s 
 unusual acidity 
 of mercury on small hydrated clusters ( [ hg(h2o)2 ] and [ hg(h2o)4 ] ) . 
 for these small complexes , our results are similar : they found that 
 mercury was able to deprotonate bonded water molecules . this property 
 was said to lead to its unusually important acidity in water . however , 
 our calculations showed that , for large clusters ( [ hg]nn = 9 , 10 , and 16 ) , the mercury 
 loses this ability but remains more strongly bonded to two water molecules 
 ( as shown in nci analysis ) . therefore , hg will enhance 
 the acidity of these two water molecules , and it will consequently 
 increase its solvated acidity . the study of the qtaim charge 
 and a distributed moments analysis 
 ( first and second moments ) on the mercury ( the first moment is a dipolar 
 level contribution as the second moment is related to the quadrupole 
 on the cation ) gives additional information about the topological 
 transition ( see table 3 ) . although the charge 
 analysis remains unchanged , the first and second moments , on the contrary , 
 show important differences before and after the transition . indeed , 
 the first moment , which fluctuates between 0.07 and 0.13 au from one 
 to eight water molecules , reaches 0.32 au for [ hg]9 and 
 then decreases to 0.06 au for [ hg]16 . the second moment 
 increases slowly from 1.95 to 3.21 between [ hg]2 and [ hg]8 and starts decreasing rapidly after . it is finally divided 
 by 6 between [ hg]8 and [ hg]16 water molecules 
 due to the greater symmetry of the set . the qtaim moments ( m1 and m2 ) appear therefore 
 to be good descriptors of the topological transition , whereas a charge 
 analysis would not have noticed any differences . it appears then important 
 to look at higher moments than the charge that can provide information 
 on more complex events . table 4 shows 
 that the cation polarization 
 increases up to 21.4 kcal / mol for [ hg]8 but suddenly 
 decreases for nine water molecules ( 17.1 kcal / mol ) and finishes 
 divided by 10 for [ hg]10 ( 2.70 kcal mol ) . this transition is also visible in the charge transfer energies 
 from cation to water and from water to cation that are both divided 
 by 2 when going from 8 to 10 water molecules . the polarization of 
 the solvent keeps going up as it is not concerned by the transition . the energy decomposition analysis shows also that charge transfer 
 from the ligands to the cation is almost twice as important in mercury 
 than in gold cations , whereas it is the contrary for the charge transfer 
 from the cation to the ligand . this could be understood as an increase 
 of the donation of the ligands in the cation orbitals going together 
 with a decrease of the back - donation . indeed , relativistic effects 
 on gold induce a contraction of the gold empty 6s orbital and an expansion 
 of the full 5d one . as these effects are less important in mercury 
 than in gold , their consequences will be smaller too . if previous four - component / b3lyp all electrons computations clearly demonstrated a lower influence of relativity 
 on the monoligated hg complex compared to the au one , it should be informative to interest ourselves in clusters . we should highlight here that the structures we optimized are different 
 from those of afaneh et al . however , 
 their goal differed from ours by the fact that they tried to reproduce 
 the structure of the solvated mercury but with a limited number of 
 water molecules . therefore they started from a mercury cation solvated by 30 water molecules , 
 optimized the structure , and then kept only water from the first or 
 second solvation shell . if this approach allows getting a good idea 
 of the mercury solvated structures , it presupposes that the mercury 
 geometry is purely centered and that the mercury will accept as many 
 waters as possible in its first hydration shell ( up to 6 ) . the transition 
 we observed is therefore totally ignored . to assess the existence 
 of the transition of [ hg]n complexes , 
 we compared the energy of different [ hg]6 complexes ( the 
 results are exposed in figure s6 and table s1 in 
 the supporting information ) . more importantly , 
 we studied the relative stability of a centered form against a linear 
 (  gold type  ) form for the [ hg]3 complex 
 ( see figure 8a and b ) at several levels of 
 theory . if the linear form is more stable than the centered one ( meaning 
 e negative ) , then there will necessarily be 
 a transition from a gold type ( linear ) form to a more centered one , 
 as it is known that the solvated hg is seven - folded . if the centered form is already 
 the most stable one , then we can assess that there will not be any 
 transition because the mercury will always try to have more than two 
 water molecules in its first hydration shell . visualization of elf 
 basins for  linear  or  gold 
 type  complex ( a ) and the  centered  one ( b ) . a variety of dft functionals ( blyp , 
 pw91pw91 , b3lyp , pbe0 , and 
 m06 ) and ab initio methods ( hf , mp2 , ccsd , ccsd(t ) ) were used , as 
 well as different treatments of the relativistic effects : scalar treatment 
 with sdd pseudopotential and two - component treatment with douglass  kroll hess 
 theory ( dkh2 and dkh4 ) , as described in the theoretical 
 and computational methods section . if modifying the basis 
 sets ( figure 9a ) 
 does not influence the existence of a transition , the nature of the 
 method used appears to be very important ( figure 9b ) . indeed , except for m06 that reproduces well mp2 relative 
 energy , dft functionals stabilize more the linear form contrary to 
 ab initio methods that prefer rather the centered one . this is due 
 to the correlation and dispersion treatments that are different in 
 these two sets of methods . as no nondynamical correlation is to taken 
 into account , we can consider the ccsd(t ) method as a reference , and 
 then no transition should be considered at this level of theory . difference 
 of energy , energy + bsse , and free energy between the 
 linear and the centered complexes : e = elinear  form ( a ) using different basis sets and 
 b3lyp ; ( b ) using various levels of theory and the 6 - 31+g * * basis set ; 
 ( c ) using various functionals and ab initio methods and for different 
 treatments of relativistic effects . the use of the douglas  kroll level of theory that 
 improves 
 the treatment of the relativistic effects leads however to a stabilization 
 of the linear form ( figure 9c ) . the latter 
 appears finally more stable than the centered one , and the topological 
 transition needs to be invoked again . the geometry of the solvated 
 mercury cation appears therefore as a fragile equilibrium between 
 correlation and relativity effects . the interactions between 
 the various mercury ligands were studied 
 so as to understand better the nature of the different forms of the 
 mercury . figure 10 shows that the hardest ligand regarding the hsab theory ( hf , nh3 , or h2o ) are binding preferentially in a linear 
 form corresponding to the pseudosoft complexed form of mercury . on 
 the contrary , the softest ones ( h2s , hs , ch3s , oh ... ) form 
 preferentially centered ( soft ) complexes . the pseudosoft geometries 
 exhibit a strong polarization and charge transfer effect : e1/e2 < 1 ( see theoretical and computational methods section for 
 a definition of e1 and e2 and table s2 for energy decomposition 
 values ) . these properties had already been linked by gourlaouen et 
 al . to the reduction of the energy of 
 the ( n + 1)s orbital of the cation due 
 to the relativistic effects . on the contrary , the soft centered form 
 has e1/e2 > 
 1 , which is characteristic of a state where relativistic effects play 
 a minor role and , thus , correlation effects are predominant . energy and 
 free energy differences between the linear and centered 
 forms for the nine different ligands ( hf , nh3 , imidazole , 
 nh2 , h2o , oh , h2s , hs , and ch3s ) computed at the b3lyp / sdd/6 - 31+g * * level of theory . then , the transition observed 
 in mercury solvation structures appears 
 to be dependent on the nature of the ligand considered . for a hard 
 ligand , the pseudosoft form will be preferred and the transition will 
 be observed , whereas for a soft one , the soft form will be adopted 
 from the beginning . finally , the differences between mercury 
 and gold cations 
 microsolvated geometries and , particularly , the existence of a transition 
 in the solvation structure can now be explained in terms of importance 
 of the relativistic effects . relativity freezes the metal cation in 
 a linear geometry ( for gold and mercury ) . in gold , relativity is so 
 important that correlation effects do not manage to reach the importance 
 of relativistic ones , and the clusters remain in the linear type geometry 
 whatever the number of water molecules . on the contrary , as relativity 
 is smaller in mercury , correlation effects manage to reach the importance 
 of relativistic ones . when they get higher , the geometry is then driven 
 by correlation effects and the cation manages to accept more than 
 two water molecules in its first hydration shell , which induces the 
 topological transition . . however , it appears 
 that , if one should use a ccsd(t)/4-component reference level , the 
 simpler b3lyp / sdd level gives fairly good results . the study of microsolvated 
 complexes appears as a powerful model 
 to understand the physics of the nucleation of water molecules around 
 metal cations such as gold and mercury . in this contribution , we proposed 
 an in depth study of such complexes using quantum interpretative techniques . 
 solvated structures as well as elf topological analysis confirmed 
 that the au only accepts two water molecules in its first 
 hydration shell . however , it also interacts with other water molecules , 
 further away , through weak interactions , as shown by nci . thus , the 
 elf analysis of au shows a peculiar aspect of its electronic 
 structure in that the cation exhibits the capability of preorganizing 
 its outer - shell core electrons ( subvalence ) into two half - spheres 
 directed toward au o bonds and will then never modify it whatever 
 the number of water molecules added . this behavior is not characteristic 
 of a hard cation that splits its subvalence nor of a soft cation as 
 it keeps it unchanged . we therefore decided to extend the usual description 
 and to refer to au as a pseudosoft cation . a population 
 analysis of the gold cation was also carried out on the [ au]n cluster using several levels of theories and methods . it seems necessary to use nbo or qtaim population analysis with hybrid 
 dft calculation and at least a double- basis set to model , 
 accurately enough , gold charge . in such a case , gold can recover up 
 to 0.4 e and therefore have a charge of + 0.6 e. hg microsolvation was shown to 
 be similar to the au one for small clusters ( less than 
 eight water molecules ) ; 
 it only binds to two water molecules , and its subvalence is also two 
 half - spheres directed toward hg  o bonds . however , for larger 
 clusters , a geometric and topological transition appears inducing 
 the arrival of more than two water molecules in the first hydration 
 shell of the cation and the modification of its subvalence topology . this transition can be followed looking at the different qtaim distributed 
 moments on the mercury or at the polarization and charge transfer 
 energies as obtained from eda computations . nci analysis shows however 
 that despite the fact that more than two water molecules bond the 
 cation , it will still keep a  gold type  geometry as 
 two of them , situated on each part of the cation , will remain more 
 strongly bonded to it . the existence of the transition was studied 
 at several levels of 
 treatment of the electronic correlation ( hf , post - hf , and dft methods ) 
 and relativistic effects ( pseudopotential , dkh2 , and dkh4 ) , and the 
 results point out their antagonist effects : if relativistic effects 
 are predominant , then the mercury will behave like gold and have a 
 similar subvalence ; otherwise when electronic correlation effects 
 are predominant , hg behaves more like a soft cation , 
 splitting additionally its subvalence . the results presented 
 here also highlight the interest of the synergetic 
 use of several interpretative methods to study complex systems under 
 the same philosophy as that for the results some of us presented for 
 the reaction mechanism . all of the different 
 schemes used here ( elf , qtaim , nci , eda ... ) have exposed different 
 properties of the two cations that , gathered together , allowed a more 
 detailed description of the systems that could be , for example , used 
 for the design of next generation force fields , allowing larger systems 
 to be tackled .
in this contribution , 
 we propose a deeper understanding of the 
 electronic effects affecting the nucleation of water around the au+ and hg2 + metal cations using quantum chemistry . 
 to do so , and in order to go beyond usual energetical studies , we 
 make extensive use of state of the art quantum interpretative techniques 
 combining elf / nci / qtaim / eda computations to capture all ranges of 
 interactions stabilizing the well characterized microhydrated structures . 
 the electron localization function ( elf ) topological analysis reveals 
 the peculiar role of the au+ outer - shell core electrons ( subvalence ) 
 that appear already spatially preorganized once the addition of the 
 first water molecule occurs . 
 thus , despite the addition of other water 
 molecules , the electronic structure of au(h2o)+ appears frozen due to relativistic effects leading to a maximal 
 acceptation of only two waters in gold s first hydration shell . 
 as the values of the qtaim ( quantum theory of atoms in molecules ) 
 cations s charge is discussed , the non covalent interactions 
 ( nci ) analysis showed that au+ appears still able to interact 
 through longer range van der waals interaction with the third or fourth 
 hydration shell water molecules . as these types of interaction are 
 not characteristic of either a hard or soft metal cation , we introduced 
 the concept of a 
 pseudo - soft  cation to define au+ behavior . then , extending the study , we performed the same 
 computations replacing au+ with hg2 + , an isoelectronic 
 cation . 
 if hg2 + behaves like au+ for small water 
 clusters , a topological , geometrical , and energetical transition appears 
 when the number of water molecules increases . 
 regarding the hsab theory , 
 this transition is characteristic of a shift of hg2 + from 
 a pseudosoft form to a soft ion and appears to be due to a competition 
 between the relativistic and correlation effects . 
 indeed , if relativistic 
 effects are predominant , then mercury will behave like gold and have 
 a similar subvalence / geometry ; otherwise when correlation effects 
 are predominant , hg2 + behaves like a soft cation .