under ambient conditions , 
 almost all solid surfaces are covered 
 in a thin film of water . the ubiquitous 
 nature of water  solid interfaces means that they are relevant 
 to an almost endless list of everyday and technological phenomena , 
 ranging from the slipperiness of ice to electrochemical reactions 
 and from ice formation to water purification . as a result of this 
 widespread importance and the pressing need for clean water , renewable 
 energy , and deeper insight into environmental chemical processes , great strides have been made in rationalizing water at interfaces 
 from various perspectives , and the  field  of interfacial 
 water is now flourishing . one area that has been particularly instrumental in improving 
 understanding 
 of interfacial water is the study of water on clean well - defined solid 
 surfaces under ultrahigh vacuum conditions . in these studies , the full arsenal of surface science techniques has been applied to 
 interrogate interfacial water and obtain clear atomic and molecular - level 
 insight . this has shed light on the chemistry of interfacial water 
 and , in turn , on the balance between water  water and water  substrate 
 bonding , precise information that is otherwise rarely available . of 
 the various techniques employed , the application of low - temperature 
 scanning tunneling microscopy ( lt - stm ) has been particularly fruitful 
 as it provides direct real - space images of the structures that water 
 forms on surfaces . when used in conjunction with density functional theory ( dft ) , this 
 has exposed an incredible richness in the structures water can form 
 at the surfaces of materials at low temperatures . on metal surfaces , 
 for example , not only have structures comprising water hexamers ( the 
 building block of ice i ) been identified , but various other structures have been reported comprising pentamers , heptamers , and combinations thereof . some of these structures are built exclusively from intact ( non - dissociated ) 
 water molecules , whereas others contain mixtures of intact water molecules 
 and hydroxyl groups , sometimes with highly defective h - bonding networks . this body of work , along with 
 earlier studies , has been used to develop 
 a set of so - called 2d ice rules  , which have been successfully used to rationalize how water 
 bonds to certain metal surfaces ( notably pd and ru ) at low temperatures . pauling ice rules for 3d bulk ice , which do not go far enough to explain 
 water  ice structures at the interfaces of materials . however , 
 the paucity of data means that it is unclear how far such rules can 
 be extended . understanding these structures is not just of fundamental 
 interest , but it is an important first step in the rational design 
 of substrates with specific functionality , for example , for the control 
 of ice formation , the flow of water , or water oxidation . with 
 this in mind , we report measurements on the adsorption and 
 clustering of water at low coverages on cu(111 ) . ice adsorption , in part because of its relevance to ( electro)-catalysis and corrosion 
 but also because water molecules remain intact on this surface ( i.e. , 
 they do not dissociate ) even under 0.1 torr of h2o pressure . water 
 versus water  substrate interactions without the complications 
 of hydroxyl group formation . water coverage , sample preparation , and 
 imaging conditions were similar to previously reported experimental 
 settings , except for a higher annealing 
 temperature used in the present work . indeed , this higher annealing 
 temperature of 25 k ( compared to 17 k ) is crucial in that it leads to the formation of large ordered clusters 
 which have not been characterized before . these clusters ( shown in figure 1 ) appear in stm images 
 as bi- or trilobed entities , which with the help of dft are shown 
 to consist of interconnected hexamers and pentamers . interestingly , 
 we find that the oxygen skeletons of the structures identified resemble 
 the carbon skeletons of polycyclic aromatic hydrocarbons ( pahs ) , and 
 water superstructures corresponding to inene , naphthalene , phenalene , 
 anthracene , phenanthrene , and triphenylene have been observed . in 
 addition , the h - bonding networks suggested also bear some resemblance 
 to the resonance structures of pahs predicted by clar s rules . current models for 2d ice growth are not fully 
 compatible with the water nanoclusters identified here , and so in 
 rationalizing these structures , we revise the existing 2d ice rules , in a manner that we hope makes them more generally 
 applicable . high - resolution stm images of submonolayer coverage of water on 
 cu(111 ) acquired at 5 k. insets are zoomed - in images showing the five 
 most prevalent ordered water clusters observed . ( a ) large - area image 
 of water clusters that form on cu(111 ) after a 25 k anneal . ( c ) smallest of the three 
 bilobed features , referred to as the symmetric dimer . what follows , we first report details of the experimental 
 and 
 simulation setup . we then present structural models for the new water 
 clusters identified in this study , followed by a discussion including 
 a new set of 2d ice rules . all stm experiments were performed 
 with an omicron nanotechnology low - temperature scanning tunneling 
 microscope . to clean the cu(111 ) single crystal , the sample was cleaned 
 in a separate preparation chamber by sputtering with ar for two cycles ( 14 a , 1 kv ) and annealing ( 1000 k ) . the sample 
 was then transferred to a precooled stm stage with a base temperature 
 of 5 k and base pressure of 1  10 mbar 
 or lower . deionized water was obtained from a nanopure water system 
 and was further purified by first boiling the water ( to reduce the 
 amount of dissolved gas in the liquid ) and then proceeding with freeze  pump  thaw 
 cycles . low coverages of water were deposited through a high - precision 
 leak valve onto the surface held at 5 k followed by a thermal anneal 
 to 25 k , which enabled the self - assembly of ordered clusters . the 
 sample was then cooled back down to 5 k to acquire high - resolution 
 images . stm images were obtained with omicron chemically etched w 
 tips at bias voltages between 10 and 50 mv and tunneling 
 currents between 50 and 100 pa . the optb86b - vdw functional was used 
 throughout for the optimization of the adsorbed structures and the 
 simulation of the stm images . the optb86b - vdw functional is a revised 
 version of the van der waals ( vdw ) density functional of dion et al . , which has shown good agreement with experimental 
 results in a variety of molecular adsorption systems . although not shown , several of the adsorption structures examined 
 in this study have been computed with two other vdw - inclusive functionals 
 ( vdw - df2 and the method of tkatchenko  scheffler applied on top of the perdew ernzerhof 
 ( pbe ) functional ) finding qualitatively 
 similar results in all three cases . for comparison , calculations on 
 the same range of structures were also performed with pbe , which does 
 not include vdw interactions . core electrons were replaced by projector - augmented 
 wave ( paw ) potentials , whereas the valence 
 states were expanded in planewaves with a cutoff energy of 500 ev . adsorption calculations of superstructures formed by 618 molecules 
 were carried out for water on four - layer ( 8  8) slabs separated 
 by 15  of vacuum . for one of the considered structures 
 ( the  long dimer  ) , a three - layer thick ( 9  9 ) 
 cu(111 ) slab was considered instead to minimize lateral interactions 
 between the periodic images of the water cluster . within such unit 
 cells , the shortest water  water interactions between periodic 
 replicas are always 7  or more . this is adequate for characterizing 
 the structures of the clusters observed in experiment , although the 
 absolute water coverage in our simulations is higher than the experimental 
 coverage of 0.05 monolayer ( ml ) . the metal atoms in the bottom layer 
 were fixed to the bulk optb86b - vdw ( or pbe ) optimal positions ( acuoptb86b - vdw = 3.623  , acupbe = 3.636  ) , whereas all other atoms 
 were allowed to relax . a monkhorst pack k - point 
 grid of ( 2  2  1 ) was used in all calculations . a dipole 
 correction along the direction perpendicular to the metal surface 
 was applied , and geometry optimizations were performed with a residual 
 force threshold of 0.01 ev /  . a stricter convergence criterion 
 ( 0.005 ev /  ) produced no noticeable difference in the structures 
 and adsorption energies . hamann 
 approach , with a voltage of 500 
 mv and at a height of 6.5  above the metal surface . simulated images for different voltages and tip height show similar 
 results , demonstrating that the conclusion does not depend on the 
 choice of parameters ( see supporting information ) . adsorption energies per molecule , eads , were computed with a standard definition : where the total energies of the n  water system , 
 relaxed bare metal slab , and an isolated gas 
 phase water molecule are , respectively , ewater / cu(111 ) , ecu(111 ) , and eh2o . it should be noted that 
 adsorption energy differences between different h2o / cu(111 ) 
 systems can be rather small , on the order of 15 mev . therefore , 
 to ensure that the quoted energy difference is meaningful , direct 
 comparison of adsorption energies of different structures will be 
 presented only for overlayer structures which have been optimized 
 on the same slab and with the same parameters . the adsorption energy 
 difference between the same structure optimized on the two different 
 slabs was estimated to be 7 mev . a low 
 coverage of water ( 0.05 ml ) was deposited on cu(111 ) , 
 and lt - stm was used to image the pre - equilibrated sample . mobile monomers , 
 stable hexamers , and metastable aggregates were observed ( see figure s1 ) , and these small water clusters match 
 those previously reported for water on cu(111 ) in ref ( 30 ) . moreover , a number of 
 discrete , ordered clusters form at these conditions . and they are 
 shown in figure 1 , 
 with panel a showing a typical stm image of the surface after annealing 
 to 25 k. the five most common cluster types are shown in panels b  f , 
 and they exhibit either two or three bright lobes at subtly different 
 distances and alignments with respect to the substrate . we will show 
 in the following , through the combination of high - resolution stm data 
 and dft calculations , that several of the observed clusters have novel 
 structures and resemble pahs of ever - increasing size . the 
 first cluster that we discuss appears as a bilobed entity , with one 
 lobe significantly brighter than the other . we therefore refer to 
 this structure as an  asymmetric dimer  ; the terminology 
 here relates simply to the stm observation of two lobes and should 
 not be confused with a dimer of two water molecules , which when imaged 
 on metals is significantly smaller than the structures being discussed 
 here . the asymmetric dimer appeared in six different 
 orientations , as shown in high - resolution stm images in figure 2a , with the long axis of the 
 cluster oriented in the 3 direction of cu(111 ) . ( a ) high - resolution 
 stm images , acquired at 5 k , of asymmetric 
 dimers on cu(111 ) . an image of the underlying cu(111 ) lattice is included 
 ( inset ) to show the orientation of the symmetry axes of the cu crystal 
 used to perform all experiments . the asymmetric dimers are found in 
 six different orientations and are aligned with the 3 direction 
 of the underlying cu surface . ( b ) top panel is a dft - calculated structure 
 proposed for the asymmetric dimer , which is composed of nine water 
 molecules ( n = 9 ) arranged as a h - bonded pentamer 
 and hexamer . the bottom panel shows an alternate and equally stable 
 structure that consists of two h - bonded hexamers , composed of 10 water 
 molecules ( n = 10 ) . the side views for both proposed 
 structures show that water molecules common to both rings in each 
 cluster lie flat on the surface while the outer portion of each ring 
 is buckled . dft - calculated stm images for each structure are shown 
 on the far right , which match well with experimental results . in order to arrive at plausible 
 structural models for this adsorbed 
 water aggregate however , the large body of previous work for water 
 on metals suggests that h - bonded structures built out of six- or five - membered 
 water rings with most water molecules bonded directly above metal 
 atoms of the substrate are most likely . indeed , from our dft calculations , two low - energy 
 structures ( eads = 635 mev for 
 both ) of this type emerged as likely candidates for the experimentally 
 observed cluster . the first dft - calculated structure consists 
 of nine water molecules 
 arranged in a double - looped configuration with a water hexamer h - bonded 
 to a pentamer ring ( top panel of figure 2b ) . as expected , most molecules in this cluster 
 both accept and donate h - bonds and are bonded directly above metal 
 atoms of the substrate . there is one molecule , however , in the pentamer 
 ring which is exclusively a h - bond acceptor . we refer to this water 
 molecule which sits upright in the plane of the surface normal and 
 accepts two h - bonds and donates none as a double acceptor ( da ) . unlike 
 the other water molecules , the molecules in the cluster sit at different heights 
 above the surface , with the lowest molecules at 2.15  and the 
 highest - lying ( da ) molecule at 3.20  . ignoring this buckling 
 for now and just considering the 2d projection of the oxygen , 
 this water cluster is an analogue of the carbon skeleton in the indene 
 ( c9h8 ) molecule . the simulated stm image of 
 this nine - molecule cluster is shown in figure 2b , and similar to the experimental image , 
 it is bilobed with one lobe noticeably brighter than the other . the 
 brighter contrast of one of the rings arises from the high - lying da 
 molecule in the pentamer ring . indeed , we will see throughout that 
 it is the presence of upright da molecule in a ring that gives the 
 ring a particularly bright contrast . as we will discuss below , simply 
 by satisfying the existing 2d ice rules , da molecules must always 
 be present in structures containing more than one hexagonal or pentagonal 
 ring . we note in passing that we have considered the possibility that 
 the bright features in the stm simulations assigned here to da water 
 molecules might be oh groups . however , the agreement with the experimental 
 stm image is significantly worse if a da water molecule is replaced 
 with an oh . in particular , oh images less brightly than water , mainly 
 because it resides much closer to the surface than the water molecules . the absence of oh groups in the structures is consistent with earlier 
 studies which show that water does not dissociate on cu(111 ) and the lack of any detectable hydrogen on our surface . the 
 second structure , which also agrees well with the size and 
 rotational orientation measurements of the experimentally observed 
 asymmetric dimer , consists of 10 water molecules on atop sites , arranged 
 as two h - bonded water hexamers ( figure 2b , bottom panel ) . this superstructure is a water cluster 
 analogue of naphthalene ( c10h8 ) . as with the 
 nine - molecule cluster , this structure contains one da molecule in 
 one of the two rings , and it is the presence of this high - lying molecule 
 ( do  cu = 3.21  ) that creates 
 the asymmetric contrast , as shown in the simulated stm image of this 
 structure at the bottom of figure 2b . overall both nine- and 10-molecule structures offer 
 a similar level of agreement with experiment , and they are equally 
 plausible models for the observed clusters . before moving on 
 to the larger structures , we note that , previously , another n = 9 cluster , a water 
 nonamer , was proposed . this water cluster comprises a central water 
 hexamer with three additional molecules bonded at the periphery to 
 every other molecule of the hexamer ( see figure s3 in the supporting information ) . interestingly , in our 
 study , the calculated n = 9 structure composed of 
 a pentamer h - bonded to a hexamer is ever so slightly ( 16 mev ) more 
 stable than this previously reported water nonamer . when postulating 
 the 2d ice rules to describe water growth on pd(111 ) and ru(0001 ) 
 surfaces , we found that the most energetically stable clusters consisted 
 of water molecules that were able to form as many h - bonds as possible . this suggests that , in our study , the added 
 stability found in the proposed n = 9 structure is 
 due to the  closed - loop  because four additional h - bonds 
 are formed ( with respect to the hexamer ) , relative to the three h - bonds 
 formed with under - coordinated water molecules in the nonamer . this 
 preference for closed - loop structures also explains why binding to 
 a hollow site is energetically favorable for the da molecule in the 
 pentameric loop of the n = 9 structure as binding 
 to an atop site would result in an opened ring system with under - coordinated 
 molecules that have unsatisfied h - bonds . the next 
 nanocluster we discuss , shown in figure 3 , is imaged as two lobes of equal brightness . the dft calculations show that an ordered cluster composed of three 
 h - bonded water hexamers ( figure 3d ) , comprising 13 water molecules , is the most energetically 
 stable cluster ( with eads = 645 
 mev ) that is consistent with the size and rotational orientation measurements 
 of the observed symmetric bilobes in figure 3a  c . this water cluster is analogous 
 to the phenalene ( c13h10 ) molecule . in figure 3d , the side view 
 of the proposed n = 13 water cluster shows that , 
 while all water molecules sit on preferred atop sites , they have different 
 o  cu distances ; two of the hexamer loops contain a da molecule 
 at the periphery of each ring , and each da lies 3.2  
 above the surface . also , consistent with predictions for the n = 13 structure , the da - containing rings can be found in 
 two of the three high - symmetry directions of the cu surface , resulting 
 in three possible orientations , all of which are experimentally observed 
 ( figure 3a  c ) . ( a  c ) 
 high - resolution stm image of a bilobed feature , referred 
 to as the symmetric dimer , in the three possible orientations . ( d ) 
 dft - calculated structure proposed for the symmetric dimer , which consists 
 of 13 water molecules arranged as three interconnected h - bonded hexamers . ( e ) dft - calculated stm image of the proposed n = 
 13 water cluster , which matches well with experimental data . the distance separating the 
 two lobes is comparable in the two structures ( 0.75 nm for 
 the structure in figure 3a  c and 0.81 nm for the octamer ) , but the present 
 cluster shows an additional dimmer central lobe . in the current study , 
 the most common bilobed feature is the proposed n = 13 structure , whereas the smaller octamer was less common . this 
 is again consistent with the finding that closed - looped structures 
 are energetically more stable and therefore more prevalent on this 
 surface after annealing to 25 k. in figure 4a  c , our high - resolution 
 stm images show another set of bilobed structures , referred to as 
  long dimers  , which are found in three different orientations . while these dimers are oriented in the 3 direction of the 
 underlying substrate , lateral size measurements show , however , that 
 the average lobe  lobe distance is 1.20  0.08 nm , which 
 is significantly longer than the distance measured for the symmetric 
 ( n = 13 ) dimer in figure 3a  c . indeed , dft calculations reveal 
 that the most stable cluster ( with eads = 645 mev ) that agrees with experimental size and rotation 
 measurements consists of three connected hexamers ( n = 14 ) arranged in a linear configuration , resembling the carbon 
 analog anthracene ( c14h10 ) , as illustrated in figure 4d . the central ring 
 is not buckled , being composed solely of low - lying ( do  cu  2.30  ) water molecules . in 
 contrast , the outer rings contain one da water molecule each and are 
 further composed of low - lying ( do  cu  2.35  ) and high - lying ( do  cu  3.05 similar to the n = 13 symmetric dimer , the n = 14 linear dimer images as two bright protrusions , with 
 the brightness being attributed to the da water molecules that are 
 sitting the highest above the surface with an o dft calculations predict that the energetically preferred 
 position of the da water molecules is at the periphery of the ring 
 structures , as illustrated in the side view of the dft - calculated 
 structure in figure 4d . this prediction is consistent with experimental data as only bilobes 
 with equal brightness at the ends of the structures have been imaged 
 with stm . ( a  c ) high - resolution stm image , acquired at 5 k , of the 
 bilobed structure referred to as the long dimer , which is found in 
 three different orientations on the cu surface . the inset is an atomic - scale 
 image of the cu(111 ) single - crystal substrate upon which the clusters 
 are adsorbed . ( d ) dft - calculated structure proposed for the experimentally 
 observed long dimer , which is composed of three h - bonded water hexamers 
 ( 14 water molecules ) arranged in a linear configuration . the side 
 view shows that the predicted structure consists of a central flat 
 hexamer flanked by two buckled water hexamers . ( e ) dft - simulated stm 
 image of the proposed n = 14 water cluster , indicating 
 that the da water molecules image as two bright protrusions . high - resolution 
 images of the fourth set of observed bilobed structures , which we 
 refer to as  bent dimers lobe 
 distance is 1.11  0.04 nm , and they have a central , dimmer region . the higher - lying features or the two brightest protrusions run almost 
 parallel to the close - packed direction of the underlying cu surface 
 and exist in at least five different orientations . the proposed dft 
 structure for the bent dimer ( figure 5 g , eads = 643 mev ) 
 is an isomer of the long dimer , as it is composed of 14 water molecules 
 ( n = 14 ) , or three water hexamers , arranged in a 
 bent formation . this is structurally comparable to the carbon - based 
 compound phenanthrene ( c14h10 ) . as shown in figure 5b  f , the bent 
 dimers appear as two bright protrusions flanking a dimmer , lower - lying 
 portion of the water adstructure . this is consistent with the dft - predicted 
 model of outer buckled rings containing one da water molecule each 
 ( at do cu  3.22  ) , 
 as well as alternating low - lying and high - lying molecules , all sitting 
 higher above the cu(111 ) surface than the water molecules in the partially 
 flat central water hexamer ( whose molecules are at do cu = 2.18  ) . based on the bent structure 
 predicted by dft , and due to the three - fold symmetry of the cu(111 ) surface , the bent dimer is expected to exist in three different configurations 
 with each having an  up  and  down  orientation , 
 resulting in a total of six clusters . experimentally , we observe five , 
 which is reasonable given poisson statistics and the total area searched . high - resolution 
 stm images acquired at 5 k. ( a ) atomic - scale image 
 of the cu(111 ) single crystal used to perform all experiments . ( b  f ) 
 high - resolution stm image of the observed bilobe structure , with a 
 dimmer central protrusion , referred to as the bent dimer . ( g ) dft - calculated 
 structure proposed for the bent dimer , which is an isomer of the dft 
 structure proposed for the long dimer in figure 4 , as it also consists of three interconnected 
 hexamers , or 14 water molecules , but in a bent arrangement . the side 
 view shows that the predicted configuration involves a central partially 
 flat hexamer flanked by two buckled water hexamers . ( h ) dft - simulated 
 stm of the proposed n = 14 bent dimer , which matches 
 well with experimental observations . once again , the stm image 
 of this structure resembles a previously reported nine - water molecule 
 trilobe structure ; however , further experimental 
 measurements reveal major features indicating that these complexes 
 are larger than the previously reported nonamer . the first observation 
 is that there are two different types of trilobed features that exist 
 in  up  and  down  orientations , resulting 
 in four structures instead of the two expected for the water nonamer . this suggests that the rotational orientations for these trilobed 
 features are due to actual rotations of the structure relative to 
 the close - packed direction of the cu(111 ) lattice and not the migration 
 of monomeric units of water , as predicted and observed for the smaller 
 water nonamers . the second observation is that the rotations of the 
 trilobed structures are aligned almost parallel to the high - symmetry 
 axis of the underlying surface and not with the 3 direction 
 as predicted and observed for the water nonamer . experimental measurements 
 indicate that one type of trilobe structure is rotated + 4 from 
 the close - packed direction of the cu(111 ) surface whereas the second 
 is orientated 4 , making these structures chiral . ( a ) high - resolution 
 stm images acquired at 5 k of two chiral trilobed 
 structures , with each chiral conformer found in an up and down orientation . ( b ) ( top ) dft - simulated image of the proposed trilobed structure , 
 indicating that the three da water molecules image as three bright 
 protrusions . because the positions of da molecules can alternate within 
 their respective hexamer rings , the trilobed clusters are chiral as 
 they are rotated slightly from the high symmetry axes of the cu(111 ) 
 surface . ( bottom ) dft - calculated structure proposed for the trilobed 
 structures , which consist of four h - bonded hexamers or of 18 water 
 molecules . dft calculations predict that 
 the most stable cluster for this 
 trilobed structure ( with eads = 650 
 mev ) is composed of four h - bonded hexamers , or 18 water molecules 
 ( n = 18 ) , with three buckled hexamers arranged around 
 a flat central water hexamer ( figure 6b ) . the 
 dft - calculated structure in figure 6b shows that all water molecules sit on preferred atop 
 sites , and each outer hexagonal ring contains one da water molecule . 
 as with all the other proposed structures , dft calculations show that 
 the o  cu distance in the da molecules is 3.20  , 
 whereas the o atoms in the central flat hexamer lie much closer to 
 the surface with o  cu distances of 2.20  . the 
 three bright lobes observed in the stm images and the lack of resolution 
 of the central flat hexamer are consistent with this structural prediction . furthermore , the highest - lying molecules , the das , can iso - energetically 
 h - bond in two different positions at the periphery of their respective 
 buckled hexamer , giving rise to conformational isomers of the structure . we finally note that even more complex supramolecular 
 water structures 
 can be obtained at higher annealing temperatures . indeed , we find 
 that annealing to 40 k results in the formation of 3d water 
 clusters , indicating that these supramolecular assemblies discussed 
 here are metastable structures . we show some of these 3d structures in figure s1 , but these structures remain outside the scope of this work 
 and will not be analyzed in detail . having 
 identified a new set of structures for water nanoclusters 
 on cu , we now place these results in a somewhat broader context . the 
 structures identified here for water clusters comprising 918 
 molecules differ significantly from gas phase water clusters in this 
 size regime . this difference arises from 
 the interaction with the substrate , and we now look into this issue 
 in more detail focusing , in particular , on the subtle balance of water  water 
 and water  metal bonding . following this , we discuss how the 
 new structures identified and insight obtained relate to the so - called 
 2d ice rules . the novel structures presented 
 in this work previous 
 dft calculations found that in isolated water hexamers on cu(111 ) , 
 the constitutive molecules were at two distinct heights above the 
 surface ( i.e. , the clusters were buckled ) . specifically , every second 
 molecule in the hexamer was 0.76  further from the surface 
 than the other three molecules . the buckled configuration was explained in terms 
 of the competition between h - bonding between adjacent h2o molecules and h2o  metal interactions . the two 
 compete because the same orbital is involved in both accepting a h - bond 
 and in bonding with the metal surface . in addition , it was shown that 
 as one moved from cu to more reactive metals such as pd and ru , the 
 hexamers flattened because of the increased interaction strength of 
 water with this substrates . consistent with the earlier work , 
 we find that an isolated water hexamer on cu(111 ) is indeed buckled 
 with the distances from the surface being 2.35 and 3.30  . however , interestingly , we find that as the nanoclusters 
 get larger , there is a tendency for their structure to flatten as 
 the central or internal water molecules get closer to the surface . the hexamers in the center of the long dimer and the trilobed structure , 
 for example , have flat central cores , with all molecules in the central 
 hexamer of each 2.15  from the surface . in contrast , 
 the hexamers on the periphery of these structures , which contain the 
 high - lying da molecules , are buckled . detailed analysis of the various 
 structures , including decompositions of the total adsorption energies 
 into water water and water  substrate contributions ( available 
 in the supporting information ) , reveals 
 that the flattening arises from a weakening of the h - bonding network 
 and a subsequent greater water  substrate bonding in the larger 
 water clusters . thus , we see here that in addition to altering the 
 adsorbate  substrate interaction strength and subsequent adsorption 
 structure upon moving from one metal to the next , simply by changing 
 the size of the water nanocluster , the interaction strength and structure 
 of the water cluster is modified . the 
 results presented so far highlight 
 the complexity of ice formation on metal surfaces . ice formation is 
 shown , in this and previous studies , to be driven by the balance between 
 intermolecular h - bonding and water  surface interactions . it 
 is therefore influenced by the particular surface on which water is 
 deposited . the 2d ice rules , formulated for submonolayer ice growth 
 on pd(111 ) and ru(0001 ) below 130 k , have established that ( i ) h2o molecules bind on atop sites of metal atoms through the 
 oxygen lone pair in a flat orientation ; ( ii ) h2o molecules 
 form as many h - bonds as possible ; and ( iii ) h2o cluster 
 growth is terminated when condition ( ii ) can not be satisfied , restricting 
 the unsatisfied or nondonor bond to the periphery of the water cluster . whereas these established ice rules can be loosely 
 applied to this system , they do not adequately explain all the structures 
 observed . for example , our study reveals that the most stable nine - molecule 
 structure on cu(111 ) is a closed - ring system ( figure 2 ) containing a hexamer and a pentamer . this 
 is in violation of rule ( i ) because one h2o in the pentamer 
 is not on an atop site , whereas all molecules in the nonamer of refs ( 30 ) and ( 31 ) are . it , however , satisfies 
 rule ( ii ) as the closed - loop structure maximizes the number of h - bonds 
 in the system . in addition the observation of buckled structures , 
 most notably a buckled hexamer , is in violation of rule ( i ) because 
 certain h2o molecules in this structure do not bond in 
 a flat orientation . while recognizing the success of the 2d 
 ice rules , upon slight revision , we find that they can be extended 
 to structures identified here on cu(111 ) . we therefore propose the 
 following reformulated rules : ( i ) water molecules preferentially 
 form closed - loop structures 
 comprising five or more water molecules . expanding upon this , we further 
 suggest that the water molecules within these loops preferentially 
 donate and accept a single h - bond . at a ( ii ) water molecules preferably bind to metal atoms 
 at the atop 
 position as long as that leads to the formation of closed - loop structures , 
 that is , as long as rule ( i ) is followed . ( iii ) there are as 
 few double acceptors as possible in a superstructure . 
 for finite clusters , this implies that there are n  1 das ( n being the number of closed loops ) . 
 in the pentagonal linear chains that form on cu(110 ) , there are n das , and in the lace - like 
 structure on pd , there are n + 1 das . ( iv ) for finite clusters , the da molecules reside 
 preferentially 
 in closed loops at the periphery of a structure . as a final 
 comment , we note that our revised ice rules have an 
 analogy with clar s rule formulated in 1972 for predicting 
 the aromatic character of pahs . specifically , 
 clar s rule predicts that the most stable structure of pahs 
 has the maximum number of aromatic sextets , which can not be neighbors , 
 with the constraint that a kekul structure must be written 
 for the rest of the pah . maximizing the number of non - neighboring 
 sextets has the implication that these sextets are generally positioned 
 at the periphery of the pah structure ( e.g. , see structures in ref ( 56 ) ) . similarly , here , we 
 see that the water nanoclusters that form on cu(111 ) maximize the 
 number of h - bonds , thus preferring looped structures and penalizing 
 structures with single acceptors  zero donors . moreover , das 
 are found as far away from each other as possible , on non - neighboring 
 hexamers , and therefore in the outer rings of the water clusters . the only exception here is the case of the symmetric dimer ( composed 
 of three neighboring rings ) where two of the das are on adjacent rings 
 because , otherwise , rule ( iii ) would be violated and there would be 
 fewer than n  1 das . clar s rules 
 have been employed to help interpret experimental results and characterize 
 a large number of pahs . in the same way , 
 the proposed ice rules can guide future research on clusters on metal 
 substrates and help interpret experimental results . whereas the shape 
 of the cluster itself ( e.g. , whether it is formed of hexagons or pentagons , 
 whether it is buckled or flat ) will depend strongly on the strength 
 of the water substrate interaction and on the packing of the 
 substrate , the interpretation of experimental results should favor 
 structures with a h - bonding network compatible with the presently 
 stated rules . in this work , a number 
 of new features for water nanocluster formation 
 on cu(111 ) have been predicted and observed , thereby providing a greater 
 understanding of how ordered water structures form and grow on metal 
 surfaces . a combination of lt - stm and dft calculations was used to 
 characterize a set of ordered water clusters that formed when a submonolayer 
 concentration of water was deposited on a cu surface , annealed to 
 25 k , and imaged at 5 k. we confirmed that ice nucleation 
 commences with the formation of a stable buckled water hexamer , and 
 further cluster growth is stabilized by the  flattening  
 of the central portion of the superstructure . the desire to maximize the number of h - bonds is a key characteristic of the structures observed ; 
 on this particular surface , closed - loop structures , with interconnected 
 rings h - bonded via flat , low - lying molecules , are more stable than 
 opened - ring systems . furthermore , molecules will deviate from preferred 
 atop binding sites in order to form the more stable closed - ring structures . based on these findings , we have proposed a set of new conditions 
 that expand on the existing 2d ice rules for submonolayer coverages of water . these rules still describe 
 ice growth on other metal surfaces while accounting for the emergence 
 and stability of these larger , ordered water clusters observed on 
 cu(111 ) .
water has an incredible ability to 
 form a rich variety of structures , 
 with 16 bulk ice phases identified , for example , as well as numerous 
 distinct structures for water at interfaces or under confinement . 
 many of these structures are built from hexagonal motifs of water 
 molecules , and indeed , for water on metal surfaces , individual hexamers 
 of just six water molecules have been observed . 
 here , we report the 
 results of low - temperature scanning tunneling microscopy experiments 
 and density functional theory calculations which reveal a host of 
 new structures for water 
 ice nanoclusters when adsorbed on 
 an atomically flat cu surface . 
 the h - bonding networks within the nanoclusters 
 resemble the resonance structures of polycyclic aromatic hydrocarbons , 
 and water 
 ice analogues of inene , naphthalene , phenalene , anthracene , 
 phenanthrene , and triphenylene have been observed . 
 the specific structures 
 identified and the h - bonding patterns within them reveal new insight 
 about water on metals that allows us to refine the so - called 
 2d 
 ice rules  , which have so far proved useful in understanding 
 water 
 ice structures at solid surfaces .