Water Hexamers and Octamers: Tool to Study Hydrogen-Bonded Pattern in Liquid Water

Fourteen different structures of water hexamer found ab initio within a 6-311G** basis set in the interval of 1.7 kcal/mol above the global minimum represent an unprecedently wide range of conformational plasticity of liquid water. The present work also provides the first ab initio demonstration of the existence of pentacoordinated water clusters. cluster, " Dangling " bond, Ab initio HF 6-311 calculation


Introduction
Liquid water is the most mysterious substance for natural scientists because of its great importance in the Universe and its versatile abnormal properties are far from being completely understood.It is formed due to hydrogen or, shortly, Hbonds and it is, in fact, its H-bonded pattern with interconnectivity and tortuosity that always plays the role of the key starting point in numerous studies aimed at resolving water paradigm 1] (see also 2]).
It has been known for a long time that H-bonded patterns of liquid water and hexagonal ice Ih are tetrahedral 1(a)].They were also believed to have much more similarities between them.That is why ice was often chosen as a reasonable reference model for the study of an H-bonded water pattern.The aforementioned tetrahedrality originates, in fact, from the tetrahedral charge distribution around c E. Kryachko the oxygen atom in a water monomer possessing two positive partial charges at the positions of hydrogen atoms and two negative partial charges that refer to ear-like lone electron pair.This idea was expressed by Bernal-Fowler-Pauling and called ice rules 3]: (i) There are exactly two hydrogen atoms that belong to each oxygen atom with the O-H bond length of 1 A; (ii) There is exactly one hydrogen atom that occupies each O O bond between any pair of neighbouring oxygen atoms.
What might an H-bonded pattern of liquid water be like then?Well, obviously, like ice.Its \icelikeness" is manifested in the fact that each oxygen atom is involved in two covalent and two hydrogen bonds, or equivalently, that each water molecule is four-bonded and is surrounded by four nearest-neighbour water molecules.The latter ones compose its rst coordination shell.Within the Bernal-Fowler-Pauling H-bonded pattern, the oxygen atoms are arranged in such a way that all the O-O-O bond angles between the nearest-neighbour water molecules are tetrahedral, i. e., equal to circa 109:47 o .The hydrogen atoms decorate therein O-O \bonds", establishing the so-called \hydrogen bigamy".
Let us ask then the following question.Does this \icelikeness" adequately describe the whole H-bonded pattern of liquid water?Or, in other words.Does liquid water contain any \patches" in its pattern that in fact violate Bernal-Fowler-Pauling ice rules and are crucial for turning liquid water into what it actually is?The answers are certainly `no' and `yes', respectively.It is now apparently pretty hard to believe in resolving a liquid water paradigm denying the very existence of such non-icelikeness \patches".To put it simpler, water can be roughly described by a \two-state" model with one \state" obeying Bernal-Fowler-Pauling rules and another one violating them.The \two-state" model satis es either the energetical or geometrical criterion imposed on the H-bonded pattern 4-6].The former suggests that two water molecules are H-bonded if their interaction energy V < V HB .The negative threshold H-binding energy V HB plays the role of a model cuto parameter.It is allowed to take on a sequence of values, V HB = ?2n"with integer n from interval (10; 41) and " = 0.07575 kcal/mol.V HB varies then from -6.2115 to -1.5150 kcal/mol.
According to the geometrical criterion (for current references see 7]), two water molecules are H-bonded if the following three constraints are accomplished altogether.The rst one is the constraint on interoxygen separations that must be less than R thr = 3.5 -3.7 A 8]. R thr determines the position of the rst minimum of the g OO radial distribution function and de nes, in fact, the boundary of the rst coordination shell.The second constraint is imposed on the distance between the oxygen atom of the acceptor water molecule and the hydrogen atom of the donor one.It should be smaller than r thr = 2.45 A, that is, the distance at which the rst minimum of the radial distribution function g OH takes place 8].The third constraint limits angle H between the participating oxygen, the hydrogen of the donor molecule and the oxygen atom of the acceptor molecule: H > 160 o .This constraint seems to be quite fragile and is often omitted because a reasonable de-viation of H from 160 o to smaller angles indicates a stronger nonlinearity of an H-bond.These constraints are sometimes supplemented by another one imposed on the values of the lone pair-oxygen-oxygen angle.
Regarding the O-O distribution function g OO of liquid water at 25 o C 8], its rst maximum is sharply peaked at 2.86 A and its integral from zero to R thr , which is interpreted as the mean number of water molecules within the rst coordination shell, is about 4.5.This implies that the H-bonded pattern of liquid water partly possesses ve-fold coordinated \patches".Their very existence unambiguously shows how far real liquid water is from that modelled by the Bernal-Fowler-Pauling rules.One may even insist that its natural perfection is, in fact, in its imperfection which makes water so anomalous and so mysterious for natural science.In terms of patterns, this imperfection might be explained by the fact that water possesses some sort of defects, namely, such \patches" in its H-bonded pattern where the Bernal-Fowler-Pauling rules are violated.It has been thought that these defects manifest themselves in many ways, for instance, in conductivity, in water restructuring resulting in a ow of water, in interpreting the Raman 9,10] and infrared spectra 1].They are usually divided into two types: ionic and orientational, depending on which the Bernal-Fowler-Pauling ice rule is violated.
In the present work we focus only on orientational defects which represent the violation of the second Bernal-Fowler-Pauling rule.The simplest model of an orientational defect was a long time ago suggested by Bjerrum 11(a)] (see also 1]).The Bjerrum orientational defects are of two types.One corresponds to the \empty" O O bond and is called L-defect 11 (b)].Another one, D-defect 11 (b)] is, in fact, a doubly occupied bond O -H H -O. This de nition of orientational defects is rather schematic and does not take into account the cooperative nature of H-bonding in liquid water.The progress towards understanding the nature of orientational defects was made due to the rst and in some sense semi-empirical calculations by Dunitz 12(a)], Cohan et al. 12(b)], and Eisenberg and Coulson 12(c)] (see also 12(d-h)]).These calculations show that an orientational defect is actually some area of the H-bonded pattern around an \empty" or doubly occupied H-bond that should include some distorted H-bonds around.Distortion is primarily thought in terms of H angle whose value in the range of 160 o ?130 o describes a leaned or nonlinear H-bond that converts to the so-called bifurcated H-bond when this angle approaches 120 o ? 100 o .A physical model of a solitonictype orientational defect where the central part is, in fact, a sort of a bifurcated H-bond was elaborated in 13] (for recent review see 14]).
A bifurcated H-bond is such a speci c type of H-bond where the hydrogen atom simultaneously participates in or donates two hydrogen bonds.In other words, the hydrogen atom is shared by a couple of oxygen atoms simultaneously 9].It is believed that these bonds contribute signi cantly to the Raman 10] and infrared 1] (see also 13(b)]) spectra of liquid water.It is also believed that they are important in mobility of water molecules.This view was supported experimentally 15] and by computer simulations 16,17].However, it should be stressed that all these Bjerrum-type defects rely on the tacit assumption of preserving a four-fold coordination.It has been recently suggested 17] that a ve-fold \patch" is a new type of an orientational defect with a bifurcated H-bond which appears as a result of approaching the fth water molecule (see also 10(b)]).As suggested in 17] as well, this \patch" facilitates a transition from one Bernal-Fowler-Pauling pattern to another through a lowered energy barrier.The similar model of a ve-fold \patch" was discussed in 18].There is still another very speci c feature of liquid water worth mentioning.It is the O-O-O bond angle distribution function that, according to the recent studies 19] (see also 17(b), 18]), reveals two maxima.One corresponds to the tetrahedral bond angle.Another one, peaked at \O-O-O = 60 o , demonstrates that the corresponding water molecules are settled in nontetrahedral directions.
In this context, pentacoordinated \patches" within an H-bonded pattern of liquid water are an appealing concept, since they constitute a simple and, to some extent, a rather universal principle of the underlying liquid water dynamics.The aim of the present paper is to reveal such \patches" in water clusters by means of performing ab initio search over their total potential energy surfaces and to study the properties of these defects.Section II deals with the computational GAUSSIAN-type methodology of this work.The next Section III starts with a brief description of the present status of ab initio water clusters and continues with the exhaustive search of the total potential energy surface of water hexamer cluster to reveal novel lower-lying water hexamer structures and in particular those of hexamers and octamers that possess pentacoordinated \patches".This is, in fact, the rst evidence of ab initio ve-fold coordinated water clusters.Section VI discusses and summarizes the present work.

Computational methodology
All the calculations were performed with the Gaussian-94 suite of programs 20] at the Cherry L. Emerson Center for Scienti c Computation of Emory University in Atlanta.The ground-state geometry of water clusters was optimized at the Hartree-Fock level of computation with the triply split valence 6-311G** basis set of 180 basis functions that includes polarization functions on the oxygen and hydrogen atoms in particular 21].In all the computations, no constraints were imposed on the geometry of water clusters.Full geometrical optimization was performed for each water cluster structure, and the attainment of the energy minimum was veri ed by calculating the vibrational frequencies that result in the absence of negative eigenvalues.Default options were used for the SCF convergence and for the threshold limits determining the nal changes in the maximum forces and displacements in the geometry optimization.Vibrational modes and the corresponding frequences are based on a harmonic force eld.Empirical scaling factors were not used.For conciseness, the tables report only the most intensive infrared (IR) and Raman active bands for which IR intensity and Raman activity exceed 100 km/mol and 20 A 4 /amu, respectively.

Prelude: hexamer and octamer
Study of water clusters is one of promising ways to resolve the liquid water paradigm.It is trivial, on the one hand, that a larger cluster better mimics bulky water.On the other hand, it is also quite evident that a larger cluster possesses a richer potential energy surface picture.It is then a rather well-spread and reasonable belief that to grasp the water paradigm, it might be su cient to study those water cluster structures that occupy lower-lying energy minima on the potential energy surface.Should we be con dent with this belief?Apparently, `yes', if among lower-lying water cluster structures there are, in particular, those with ve-fold coordinated water molecules.Hexamer and octamer water clusters were the subject of a number of ab initio studies 22,23].It has been recently shown 22(d)] that at the HF/6-311G** level of the computational theory, the global minimum of the hexamer potential energy surface is attained by prism structure.There are also two lower-lying local minima, one of which, corresponding to the cyclic chair-type structure, is 0.84 kcal/mol.Another one occupied by the boat-like structure distances from the chair-type one by 1.08 kcal/mol.There is yet another global minimum found at the cagelike water hexamer cluster with 8 H-bonds 23(d-g)].To resolve this controversy, we have done an exhaustive search of the landscape of the total potential energy surfaces of water hexamer.The result of this search is reported in table 1 for energy, zero-point vibration energy (ZPVE) enthalpy and entropy, and in table 2 { for rotational constants and the total dipole moment and are displayed in gure 1.As it is seen in gure 1, three prism structures of (H 2 O) 6 are at the bottom of the total potential energy surface.Prism I occupies its global minimum, but two others lie very close, at 2.4 and 5.8 cm ?1 , taking the zero-point vibration energy into account.Five cage-type structures are followed by them.They are shown in gure 2. Table 2 demonstrates a good agreement of rotational constants for cages calculated in the present work and reported in 23(g)].Four lower-lying cages I -IV possess very particular geometries.Their interoxygen distances between O 3 and O 4 are 3.577, 3.577, 3.466, and 3.570 A, respectively.This implies that according to the rst geometrical constraint these are precisely \dangling" bonds because of the absence of a hydrogen atom between these oxygens.Furthermore, some O-O-O interbond angles move away from the tetrahedral values to lower angles.For example, in cage I, \O   With regard to water octamer, it is well known that the cubic structure Ca 23(a)] of D 2d is the most stable one on the water octamer potential energy surface computed at the HF/6-311G** level.The cubic structure of S 4 symmetry occupies the local minimum that lies 3.49 kcal/mol above the Ca structure.In addition, there have been found another twenty ve lower-lying octamer structures among which the ring structure R8a is energetically higher than the Ca one by 12.91 kcal/mol.At room temperature, their free energy di erence diminishes to 0.19 kcal/mol 23(a)].).The latter is less than R thr and thus, one might think of these molecules as bonded to each other by the so-called \dangling" bond.One, therefore, concludes that this water cluster with a \dangling" bond is a ve-folded \patch" that may appear among four-folded ones in an H-bonded pattern of liquid water.The assignment of harmonic vibrations of the Defect I \patch" is shown in table 5. Harmonic frequencies computed for inter-and intra-molecular modes of the Defect I structure are listed in the second column of this table.Its third and fourth columns report the corresponding theoretical IR intensity and Raman activity.First of all, before studying table 5, it should be mentioned that the theoretical spectra of the chair and boat water hexamers 22(d)] do not have vibrations in the range 4000-4200 cm ?1 .It implies that the hydrogen atoms in these structures are solely of two sorts: the hydrogens involved in forming H-bond, and \free" hydrogens participating in unbonded OH groups.On the contrary, the prism hexamers and Defect I do have H-stretching vibrations in this region.The most intensive IR band of Defect I is the librational one centered at 663.5 (IR intensity 564 km/mol, Raman activity 0.5 A 4 /amu) comparing with the most IR intensive ones for the prism, chair, and boat hexamers that fall into the region of H-stretching vibrations.
The band at 663.5 cm ?1 is assigned to the composed libration of the O 4 ?H       The second grouping of bands lies in the interval from 4085 to 4180 cm ?1 and is primarily contributed by nonlinear or bent H-bonded hydrogens.The last one consists of bands from 4183 to 4221 cm ?1 .They are assigned to the stretching vibrations of \free" hydrogen atoms.These bands are slightly blueshifted and mainly twice enhanced comparing with the stretching mode 3 of a water monomer.Regarding the intramolecular or scissor modes of our defect hexamer structure, it has to be mentioned rst that the harmonic mode (monomer) 2 of a water monomer calculated at the HF/6-311G** level is 1750.3cm ?1 .Its IR absorption and Raman activity constitute 79.2 km/mol and 6.4 A 4 /amu, respectively.Two intra-molecular modes of Defect I are redshifted comparing with (monomer)   2 and more pronounced.Their normal vibration assignment is also shown.For instance, the rst intramolecular mode of Defect I with frequency 1756.8 cm ?1 describes the composed scissor vibrations of water molecules H 2 H 3 O 1 and H 11 H 12 O 10 bonded to each other via a \dangling" bond.The dipole moment of the Defect II \patch" is very low and equal to 0.87 D. Energetically, it is situated 12.30 kcal/mol above the Ca structure.At room temperature, their di erence in free energy is just 5.47 kcal/mol.Regarding the spectrum of this \patch", it is worth noting that the spectrum of Defect II possesses rather strong IR intensive bands.Namely, its most IR intensive and Raman active bands fall only in the region of stretching vibrations.This is the band H Comparing with the stretching modes of a water monomer, these bands are slightly redshifted, which indicates their weakness.This grouping of bands borders another one falling to 4205-4215 cm ?1 and describing the stretching vibrations of unbonded or \free" O-H groups.
Table 8 also lists the most intensive vibrations of fully deuterated Defect II calculated at the HF/6-311G** level of computation.Its zero-point vibrational energy is 87.961 kcal/mol and entropy { 178.571 cal/mol K.For the deuterium Defect II, the band D 2 O 20 = 2880.0cm ?1 becomes most IR and most Raman active, simultaneously being contrary to the protium Defect II.We should also mention the behaviour of 27 assigned to the coupled asymmetric stretching vibrations of O 11 ?H 14 and O 5 ?H 9 bonds under isotopic substitution.For the protium Defect II this band possesses IR intensity equal to 48.8 km/mol while it becomes ve times more pronounced than its deuterated isotopomer.Analyzing the second and sixth columns of table 8 one nds that the calculated harmonic frequencies and reduced masses of the protium and deuterium Defect II do not show the known isotopic relationships connecting the ratio of frequencies of translational and bending modes H 2 O = D 2 O with the square root of the ratio of the corresponding moments of inertia or masses, respectively.This is perhaps the common situation with computing harmonic vibrational frequencies 27], although, in our case with larger water clusters this deviation appears more pronounced than with water dimer.From table 8 it follows that, rst, for H 2 O 1 = 167.5 cm ?1 , the ratio  8, the isotopic frequency ratios behave rather regularly around 1.37-1.38 with the exception for the 13th and 15th modes when they are 1.40 and 1.39, respectively.The isotopic reduced mass ratio does not reveal such a simple regularity, although it is largerly clustered near 1.44-1.45.Altogether, this isotopic analysis emphasizes a very anharmonic picture of the total potential energy surface of water clusters.

Summary
The fourteen di erent structures in the interval of 1.7 kcal/mol represent an unprecedentedly wide range of conformational excursions for water hexamer cluster.They illustrate how rich the picture of the total potential energy surface of liquid water might be.
The present work also provides the rst ab initio demonstration of the pentacoordinated water hexamer structure.This structure is not, in fact, a defective one in the common sense of defects in the H-bonded pattern that violates the Bernal-Fowler-Pauling rules nor those structures that involve a bifurcated H-bond.It actually represents a novel structure of H-bonds where the approaching fth water molecule forms a \dangling" bond with the central water molecule generating in such a way a pentacoordinated \patch" of higher density.This \patch", being incorporated into an H-bonded pattern of liquid water, on the one hand, partly contributes to nontetrahedral con gurations and to the known blurred maximum of the O-O-O bond angle distribution function in the interval 60 o ?80 o , in particular.On the other hand, it contributes to tetrahedral con gurations as well.Notwithstanding that such hexamer and octamer ve-fold coordinated \patches" occupy lower-lying local energetic minima on the total potential energy surfaces, they become energetically accessible at room temperature.27.We analyze the ratio H 2 O = D 2 O for the harmonic vibrational frequencies of water dimer calculated in 28] at the HF/6-31G* and MP2 levels.Following Tables 1 and 2 of 28], one easily derives that this ratio spans the range 1.16-1.18for all listed modes.28.Scheiner S., Cuma M. Relative stability of hydrogen and deuterium bonds.//J.Am.

Figure 2 .
Figure 2. Five lowest cage structures of six molecules of water.

3. 2 .Figure 3 .
Figure 3. Opened prism water hexamer.A novel lower-energy local-minimum structure of (H 2 O) 6 water cluster is revealed on the water hexamer potential energy surface at the HF/6-311G** level.It is shown in gure 6 and hereafter is named Defect I. Its total dipole is equal to 2.47 D. It lies above prism VI and chair water hexamers by 2.88 and 2.04 kcal/mol, respectively, and the distances from the prism I structure by 4.40 kcal/mol which reduces to 3.19 kcal/mol with taking ZPVE into acccount.The zero-point vibrational energy, enthalpy, free energy of Defect I and their di erences with respect to the corresponding quantities for the prism and chair structures tabulated in22(d)] are listed in table 3.One readily gures out that at room temperature, the energy of formation of Defect I is 1.49 kcal/mol with respect to that of prism I.It is worth mentioning that Defect I and prism VI are almost isoenergetical at room temperature (see also gure 7).

Figure 4 .
Figure 4. Cage VI cluster of six water molecules.

Figure 7 .
Figure 7. Phase-like diagram of Defect I and some lower-lying water hexamers.from3967 to 4069 cm ?1 and possesses the dominant character of stretching the H-bonded hydrogen atoms.The band 3967.5 cm ?1 (79.7; 162.6) describes the composed symmetric stretching vibration of O 4 ?H 6 , O 14 ?H 13 bonds and is, in fact, the strongest Raman active one.The aforementioned band 4002.0 cm ?1 corresponds to asymmetric stretching vibration.Comparing with the stretching bands of a single water molecule, the latter are both redshifted, considerably enhanced, and become closer to each other by 60 cm ?1 .The second grouping of bands lies in the interval from 4085 to 4180 cm ?1 and is primarily contributed by nonlinear or bent H-bonded hydrogens.The last one consists of bands from 4183 to 4221 cm ?1 .They are assigned to the stretching vibrations of \free" hydrogen atoms.These bands are slightly blueshifted and mainly twice enhanced comparing with the stretching mode 3 of a water monomer.Regarding the intramolecular or scissor modes of our defect hexamer structure, it has to be mentioned rst that the harmonic mode(monomer)

3. 3 .Figure 8 .
Figure 8 displays a pentacoordinated water octamer.Its distinction is that it has formed 3 H-bonds and looks identical to the structure R6c found in 23(a)], although a slight deviation in their properies is revealed 25].Energy, enthalpy, = 63:95 o shows, in particular, a loss of tetrahedrality in this area of the pentacoordinated \patch".It seems worth discussing right now the distribution of oxygen-oxygen separations beyond the rst coordination shell.They are quite well clustered around 4.65 A and take the values: R(O 4 ?O 10 ) = 4.32 A, R(O 5 ?O 19 ) = 4.54 A, R(O 4 ?O 18 ) = 4.62 A, R(O 19 ?O 21 ) = 4.71 A, R(O 10 ?O 21 ) = 4.84 A, R(O 5 ?O 21 ) = 4.92 A, and R(O 1 ?O 11 ) = 4.94 A. The oxygen atom is placed in a particularly privileged position because it stays very close to O 5 and O 19 , namely, by 3.58 and 3.86 A, respectively.

Table 1 .
3 ?O 14 ?O 4 = 75:86 o ; in cage II, \O 3 ?O 14 ?O 4 = 75:85 o ; in cage III, \O 3 ?O 15 ?O 4 = 70:99 o ; in cage IV, \O 3 ?O 14 ?O 4 = 75:49 o ; and nally, in cage VI, \O 1 ?O 15 ?O 4 = 75:52 o .The cage structure of water hexamer mimics the basic unit of one of the high-density polymorphs of ice, ice VI (compare with 1(a)], gure 3.8).Proceding to the next structures, it is worth mentioning that prism VI is exactly the one found in 22(d)] at the global minimum.It is interesting that the open prism structure shown in gure 3 with a very high dipole moment of 4.38 D appears in the present list of lower-lying structures of water hexamer.Another cage structure, cage VI displayed in gure 4, is followed by an open prism and also possesses a rather high dipole moment equal to 3.45 D. Chair-or ring-type structure with Energy, enthalpy H, entropy S, and zero-point vibrational energy ZPVE of lower-lying water hexamers.Table1also reports the calculated thermodynamic properties of the aforementioned structures.As it is seen there, the chair structure is characterized by the highest entropy of 132.51 cal/mol T. Entropies of cage VI and the open prism are larger than those of the prism I structure.This implies that despite the fact that the latter is at the global minimum at T=0 K, the energy ordering might change with raising the temperature.In gure 5 we display a phase-like diagram of some water hexamer structures.It is seen that prism I remains at the global minimum at T < 130 K.If T> 130 K, the ring structure becomes the lowest one by free energy.At room temperature, cages I-IV compete with prism I.It is interesting that at T> 300 K the open prism becomes more energetically favourable than prism I.
a zero total dipole moment concludes the present list.

Table 2 .
Rotational constants and total dipole moment of lower-lying water hexamer structures.Calculated rotational constants from 23(g)] are in parentheses.

Table 3 .
Energy E, enthalpy H, entropy S, zero-point vibrational energy ZPVE, and free energy of defect water hexamer.Prisms I and VI and chair hexamers are chosen as the reference ones.prismI o ; prismVI p ; chair c .x X in kcal/mol, X = E, H, and G (at room T=298.15K); x S in cal/mol K, x = o; p; c.E (hartree) H (hartree) S (cal/mol K) ZPVE (kcal/mol) o

Table 5 .
Continued from the previous page.

Table 6 .
Energy E, enthalpy H, entropy S, zero-point vibrational energy ZPVE, and free energy of defect water octamer.Cubic octamer Ca is chosen as the reference one.For other notations see caption of table 3. the approaching fth water molecule is bonded to the central water molecule by a \dangling" bond.Defect II portrayed in gure 8 is referred to an absolutely di erent type of pentacoordinated water clusters.It is seen there that the oxygen atom O 4 has three elongated and rather weak H-bonds with the oxygen atoms O 1 ; O 5 , and O 11 separated from it by circa 3 A (table 7).Despite the fact that the angle \H 6 ?O 5 ?H 7 = 107:13 o remains unchanged comparing with the water monomer.However, the lone-pair angular distribution su ers drastic changes, which is revealed in the calculated values of the corresponding angles: \H 3 ?O 4 ?H 9 = 69:19 o , \H 9 ?O 4 ?H 14 = 70:54 o , and \H 3 ?O 4 ?O 14 = 115:65 o .Its arrangement relative to the H 6 ?O 4 ?H 7 plane is determined by the anlges \H 3 ?O 4 ?H 7 = 88:91 o , \H 6 ?O 4 ?H 14 = 79:56 o , and \H 6 ?O 4 ?H 9 = 125:61 o .

Table 7 .
Internal coordinates of defect water octamer. 1 ?H 3 ?O 4 O 4 ?H 9 ?O 5 O 5 ?H 8 ?O 11 O 1 ?H 13 ?O 10 O 4 ?H 14 ?O 10 O 1 ?H 2 ?O 18 O 5 ?H 16 ?O 18 O 4 ?H 6 ?O 19 O 10 ?H 17 ?O 19 O 4 ?H 7 ?O 21 O 11 ?H 22 ?O 19 O 1 ?H 24 ?O 21 1 ?O 18 ?O 5 O 4 ?O 5 ?O 18 O 10 ?O 1 ?O 18 O 11 ?O 5 ?O 18 O 5 ?O 4 ?O 19 O 1 ?O 10 ?O 19 O 4 ?O 19 ?O 10 O 11 ?O 4 ?O 19 Ca structure, Defect II possesses 12 H-bonds albeit 7 of which may be considered relatively weak because their lengths exceed 2 A. What is most impressing in the H-bonded pattern of Defect II is that water molecule H 14 H 15 O 11 is weakly bonded to its nearest neighbours.This is clearly seen in the fact that the inwarding H-bonds, such as O 11 ?H 8 and O 11 ?H 22 have the lengths 2.24 and 2.37 A, respectively.The outwarding H-bond O 4 ?H 14 is also strongly elongated to 2.21 A. The angles \O 5 ?H 8 ?O 11 = 136:03 o , \O 4 ?H 14 ?O 11 = 137:24 o , and \O 11 ?H 22 ?O 19 = 129:83 o keep, therefore, a very low pro le.The angle \O 11 ?O 4 ?O 19 O O 6O 28 = 4113.9cm?1 with IR intensity 453.6km/mol attributed chie y to the stretching of O 1 ?H 3 bond.The second one, H 2 O 20 = 3978 cm ?1 , with Raman activity 142.27A 4 /amu and IR intensity 429.7 km/mol, is assigned to the composed symmetric stretching vibration of O 1 ?H 2 and O 18 ?H 16 bonds.From table 8 one can easily recognize the grouping of bands in the region 4091-4168 cm ?1 corresponding to the stretching vibrations of three O-H bonds which establish the ve-fold coordination of the H 6 H 7 O 4 water molecule and of the other two directed to H 14 H 15 O 11 .

Table 8 .
Most intensive bands of defect water octamer.For notations see caption of table5.Values for fully deuterated Defect II are given in parenthesis.

Table 8 .
Continuation from previous page.