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WATER WATER 2 14 28 5 February 2010 14 A New Hydrogen Bond Angle Distance Potential Energy Surface of the Quantum Water Dimer Scott JN1 Vanderkooi JM1 1 Department of B Department of Biochemistry and Biophysics School of Medicine University of Pennsylvania 257 Anatomy Chem istry Bldg 3620 Hamilton Walk Philadelphia PA 19104 USA
WATER, Vanderkooi 2005 Scott et al 2008 Sharp et al ometries. but that we also purposefully restricted, 2001 Sharp and Vanderkooi 2009 Sorin et al the intermolecular orientation to examine very. 2006 Vanderkooi et al 2005 specific variables As such the vast majority of. our calculated PES is far away from any sort of, Though there is widespread agreement that H minimum structure or transition state Our rea . bonding is very important both in its theoreti soning for adopting this approach was twofold . cal context and for its effect on the elements of Since the dimer is used as a simplified mock up. life there is still no consensus as to the precise of liquid water and liquid water itself contains. nature of the H bond or exactly what consti , constantly fluctuating H bonds we reasoned. tutes an H bond Barbiellini and Shukla 2002 , that areas of the PES far away from equilibrium. Gallagher and Sharp 2003 Isaacs et al 1999 , might be of interest in their applicability to H . Isaacs et al 2000 Kumar et al 2007 Smith et, bond geometries in real water This simplified. al 2004 Weinhold et al 2005 Wernet et al , approach also gave us the opportunity to specif . 2004 Insofar as water is concerned the prin , ically address the relative independent effects. ciple problem lies in the fact that there exists no. of H bond angle and H bond length which in,experimental probe of water water orientation . this case were defined as the HOO angle and the,Therefore though radial distribution functions. O O distance ,can be obtained for bulk water s individual at . oms using scattering methods Brady et al ,2006 Hura et al 2000 Narten and Levy 1971 . Materials and Methods, Soper 2000 Soper and Phillips 1986 Strassle The internal molecular geometry for each water. et al 2006 Wernet et al 2004 it is difficult molecule constituting the water dimers stud . to determine with any degree of experimental ied was constructed such that its OH lengths. certainty the average intermolecular geometry were set to 0 0991 nm and its HOH angle was. of condensed phase water molecules set to 105 5 Silvestrelli and Parrinello 1999 . Fortunately where direct experimental evidence This internal geometry was held rigid for both. is lacking theoretical methods still allow us to water monomers throughout all of the calcu . probe chemically interesting systems or interac lations described here The dimers were then. tions The water dimer is one such system con formed to test two general hydrogen bonding. stituting the simplest example of a water water schemes In the first formulation the H bond. H bond This system is especially amenable to donor molecule s oxygen atom and the H bond. study using quantum mechanical methods due donor hydrogen were placed in the plane with. to its relatively small number of electrons The the H bond acceptor water molecule Figure. water dimer has even become a de facto test for 1A This geometry is henceforth referred to as. new quantum mechanical methods since there planar for the sake of brevity In the second H . is experimental gas phase binding data against bonding arrangement the H bond donor mol . which their results can be compared Curtiss et ecule is placed relative to the H bond acceptor. al 1979 Mas et al 2000 molecule such that it donates its H bond to lone. pair electrons of the H bond acceptor s oxygen, A great deal of the quantum mechanical work atom Figure 1B Odutola and Dyke 1980 . on the water dimer has aimed at describing lo This geometry will hereafter be referred to as. cal minima and stationary points in its multi tetrahedral . dimensional potential energy surface see Ref , Scheiner 1994 for an excellent review of early All calculations were carried out using Gauss . work in the field A recent study by Shank et al ian 03 Revision D 01 Frisch 2004 All data. 2009 for instance fits a coupled cluster cal manipulation and plotting was performed using. culated 30 000 point full dimensional global MATLAB 7 6 0 Calculations for each geometry. PES encompassing 10 stationary points for a were performed using both MP2 Head Gordon. water dimer The present study differs from this et al 1988 and B3LYP Becke 1993 Lee et al . and other previous studies of the water dimer 1988 Miehlich et al 1989 chemistries with the. PES in that we chose to not only simplify the aug cc pVTZ Davidson 1996 Kendall et al . two water monomers by fixing their internal ge 1992 and 6 311 G d p Krishnan et al 1980 . WATER 2 14 28 5 February 2010 15, WATER,basis, sets respectively These chemistry basis also. implemented in an effort to place the H ,set combinations are not sufficient for high lev . bonded dimer in the context of a simple liquid,el calculations of H bond interactions Boese et. water reaction field The PCM solvation method,al 2007 Bukowski et al 2008 Inada and Orita . is rudimentary when compared with the effect, 2007 Lee 2007 Riley and Hobza 2007 San of explicit first solvation shell water molecules . tra et al 2007 Schutz et al 1997 the coupled, but the inclusion of first shell water molecules. cluster methods currently give the most accu would have made it difficult if not impossible . rate H bonding energies Huang et al 2008 to unambiguously attribute changes in the PES. Shank et al 2009 Tschumper et al 2002 butto intermolecular orientation of the H bond of. were deemed to be acceptable for the sort of interest The combinations of dimer geometry . comparative analysis performed in this study model chemistry and basis set and solvation. All vacuum energy calculations used the coun state yielded eight complete data sets All fig . terpoise method of basis set superposition error, ures shown in this paper are for the cases of the. correction Boys and Bernardi 1970 Simon et planar and tetrahedral water dimers in vacuum . al 1996 calculated using the MP2 aug cc pVTZ model. chemistry and basis set Data for the other six, In addition to standard gas phase vacuum cal combinations of dimer geometry model chem . culations the Polarizable Continuum Model istry and basis set and solvation state is dis . PCM solvation model Cossi et al 2003 was cussed in the text however figures for these. Figure 1 Intra and inter molecular geometries of the planar and tetrahedral water dimers . WATER 2 14 28 5 February 2010 16, WATER, combinations have not been included since the the Morse potential function . two cases for which figures have been shown, were felt to be representative and sufficient 1 V r De 1 e a r re 2. For both H bonding dimer geometries the O O Results. distance was scanned at a fixed H bond angle , Energies Energies are given in kcal mol . defined herein as the angle between the H bond, relative to the calculated minimum energy for. donor molecule s donor OH vector and the O O, a particular set of calculations The true calcu . vector The H bond angle was subsequently lated minimum energy and O O distance H . increased by one degree and the O O distance bond angle position of that energy for each of. was scanned again for the new angle Angles the eight sets of calculations is given in Table I . from 0 to 90 in 1 increments were used and In Figures 2A and 3A the 3 dimensional energy. O O distances from 0 25 nm to 0 40 nm were landscapes for the MP2 aug cc pVTZ planar. scanned at every 0 01 nm For each O O dis and tetrahedral vacuum cases are shown and. tance and HOO angle system energy was cal Figures 2B and 3B contain the same informa . culated Natural Population Analysis a part of tion in 2 dimensional color mapped projec . the Natural Bond Orbital formalism Rives and tions Each of the calculated energy surfaces. Weinhold 1980 was used to calculate atomic has the same essential characteristics indicat . charges The calculated energy surface for the ing that the trends we observe are not simply. dimers was also examined by taking slices along model or basis set dependent Each of the sur . the H bond angle dimension This subset of the faces has its global minimum at an H bond an . data was analyzed by fitting the energy vs O O gle of about 0 the angle is somewhat distorted. distance data for a particular H bond angle to for both of the tetrahedral vacuum cases and. Table I Calculated Energy Minimum and Position for Individual Calculations. H Bond O O Distance nm Energy Hartrees , Angle , B3LYP Planar Vacuum 0 0 30 152 921808332442. B3LYP Planar PCM 2 0 28 152 947883176000, B3LYP Tetrahedral Vacuum 6 0 29 152 922480853247. B3LYP Tetrahedral PCM 3 0 28 152 948069476000, MP2 Planar Vacuum 2 0 29 152 661892519226. MP2 Planar PCM 2 0 29 152 142119811000, MP2 Tetrahedral Vacuum 6 0 29 152 662601687797. MP2 Tetrahedral PCM 3 0 29 152 142102842000, WATER 2 14 28 5 February 2010 17. WATER, anO O distance of about 0 29 nm Increases in energy. of O O distance lengthening for a fixed, O O distance beyond the global minimum for H bond angle and H bond angle distortion for. a given PES result in energy increases of 2 5 to a fixed O O separation for each chemistry basis. 2 9 kcal mol for the MP2 aug cc pVTZ calcula set solvation state and geometry combination. tions and 2 7 to 4 3 kcal mol for the B3LYP 6 used The difference in the effects of O O dis . 311 G d p calculations tance lengthening and H bond angle distortion. can also be seen in the 2 dimensional energy, maps in Figures 2B and 3B where the cold . or low energy portions of the energy surface, are restricted to H bond angles below approxi . mately 50 while the higher energy regions of, the surface are all found in the cases of more. substantially bent H bonds In all cases short , ening of the O O distance below 0 28 nm causes. an abrupt increase in system energy due to re , pulsion . O O Energy Fits, In Figures 4A and 5A 2 dimensional plots of. the dimer system energy versus O O distance, for the MP2 aug cc pVTZ planar and tetrahe . dral vacuum cases are shown for H bond angles, of 0 to 90 at 5 intervals Figures 4B and 5B. show R2 values obtained from fitting a standard, Morse potential to every calculated angle s en . ergy dependence on O O distance These slices , taken along the O O distance dimension of the. 3 dimensional energy surfaces reveal energy, profiles that fit extremely well to a Morse po . tential energy function for small H bond an , gles Though the exact point where Morseness . breaks down is difficult to quantify significant, deviations in the R2 value of the fits begin to. occur at approximately 50 65 for the vacuum, calculations Figures 4B and 5B and 30 40 for. the PCM calculations not shown These angles, are also where errors increase greatly for the in . dividual Morse fit parameters not shown and, where the energy curves cease to have a local. minimum For example the well depth param , Figure 2 3D a and 2D b views of the calculated eter in the Morse function De fits with a 95 . energy landscape for the MP2 aug cc pVTZ planar confidence interval of hundredths of a kcal . vacuum dimer Energies are relative to the calcu mol for all angles up to 60 for the MP2 aug . lated minimum for this particular PES cc pVTZ planar vacuum case at which point the. confidence intervals grow to several tenths of a, Increases in HOO angle beyond the calculated kcal mol By the time the H bond is distorted. minimum energy for a given PES result in en to 73 fits are exceptionally poor yielding con . ergy increases from 5 4 to 6 5 kcal mol for the fidence intervals of more than 1 kcal mol Simi . MP2 aug cc pVTZ calculations and 7 4 to 8 1 lar trends were obtained for the other combina . kcal mol for the B3LYP 6 311 G d p calcu tions of model chemistry basis set solvation. lations Table II catalogs the effect on dimer state and dimer geometry with only the par . WATER 2 14 28 5 February 2010 18, WATER, ticular, angle at which Morseness breaks down donor. atoms At the dimer s minimum energy, changing with the PES in question configuration the hydrogen atom has its largest. positive charge and the charge decreases slight , ly as the O O distance grows and more signifi . cantly as the H bond angle increases The same, trend is seen for the charge on the oxygen atom . with its being the most negative at the dimer s, minimum energy configuration and becoming. slightly less negative as the O O distance grows, and much less negative as the H bond angle in . creases Exact values are given in Table III for, the relative effects of O O distance lengthening. versus H bond angle bending In nearly every, case H bond angle distortion has at least twice. the effect on charge as O O lengthening does , though the PCM solvation method reverses the. effect on the H bond donor hydrogen atom , Discussion. There has been a tremendous amount of re , search and discussion on the nature of H bonds. over the years The H bond itself is still so poor . ly understood at the fundamental level that it, remains unclear exactly what geometry consti . tutes a real H bond with a variety of distance, and angle cutoffs used to specify H bonding. interactions This question is deeper than mere, nomenclature and instead points to the under . lying question that being what is the funda , mental nature of the H bond and how do we. know when one exists In this study we chose, to focus on one of the most commonly used the . oretical instances of H bonding in chemistry , the single H bond between two water molecules. Figure 3 3D a and 2D b views of the calculated, in which one water molecule s oxygen atom ac . energy landscape for the MP2 aug cc pVTZ tetra , hedral vacuum dimer Energies are relative to the cepts a single H bond from an H bond donor. calculated minimum for this particular PES water molecule By standardizing the internal. molecular geometries we were able to examine, Charges in detail the effect that intermolecular orien . tation specifically the O O separation and the, Figures 6A and 7A for the MP2 aug cc pVTZ H bond angle had on a number of quantum. planar and tetrahedral vacuum cases are 2 di mechanically calculable quantities Though in . mensional color maps depicting the magnitude ternal fluctuations in OH bond length and HOH. of the charge on the oxygen atom of the H bond angle are certainly important in the energetics. acceptor water molecule and Figures 6B and 7B of real water H bonds it is only through the use. show similar maps for the charge on the H bond of the rigid monomer approximation that we. donor hydrogen atom The overall similarity of were able to elucidate the relative and indepen . the potential energy surfaces calculated for the dent effects of H bond angle and O O distance. different model chemistries and geometries on the single intermolecular H bond . extends to the charges on the H bond accep , tor water molecule s oxygen and the hydrogen The first calculated quantity of interest in any. WATER 2 14 28 5 February 2010 19, WATER, quantum mechanical system is the energy and 311 G d p calculations the PCM solvation. the 3 dimensional and 2 dimensional energy method serves to flatten the PES at large H . landscapes shown in Figures 2 and 3 clearly bond angles due to interaction between the. show that H bond angle has a far more pro H bond donor hydrogen atom and the reaction. nounced effect on system energy than does the field In liquid water O O separation of first. linear separation of the individual water mol shell water molecules is tightly confined as can. ecules At the known O O distance for liquid be seen in the narrow and well defined peak at. water approximately 0 28 nm Strassle et al 0 28 nm in the oxygen radial distribution The. 2006 the MP2 aug cc pVTZ dimers show en computational results presented here seem to. ergy increases of between 5 4 and 6 4 kcal mol indicate that the small fluctuations in O O sepa . when distorting the H bond angle from 0 to ration and therefore H bond length which are. 90 while lengthening the O O distance to 0 40 possible in condensed phase water are likely to. nm with a fixed H bond angle of 0 increases have only very small effects on H bond energy. the energy by between 2 5 and 2 8 kcal mol or and that the principal factor in determining H . about half the effect seen upon increasing the bond strength is in fact H bond angle . H bond angle The B3LYP 6 311 G d p di ,mers though presenting a slightly more curved. energy landscape show the same behavior ,with energy increases of 7 0 to 7 9 kcal mol. due to angular distortion for a dimer with the,O O distance fixed at 0 28 nm and only 2 7 to. 4 2 kcal mol for increase in O O separation to,0 28 nm with a fixed H bond angle of 0 For. both the MP2 aug cc pVTZ and the B3LYP 6 , Table II Change in System Energy Relative to the Minimum Energy Geometry. for a Given PES with Increase in H Bond Angle or O O Distance. Anglea kcal mol Distanceb kcal , mol ,B3LYP Planar Vacuum 7 6 2 7. B3LYP Planar PCM 7 9 4 3,B3LYP Tetrahedral Vacuum 7 4 3 0. B3LYP Tetrahedral PCM 8 1 4 3,MP2 Planar Vacuum 6 4 2 6. MP2 Planar PCM 5 4 2 5,MP2 Tetrahedral Vacuum 6 5 2 9. MP2 Tetrahedral PCM 5 6 2 5, a Angle energies were determined by subtracting the energy of the minimum energy geom . etry for a particular PES from the energy of the geometry with the same O O distance but HOO. 90 , b Distance energies were determined by subtracting the energy of the minimum energy ge . ometry for a particular PES from the energy of the geometry with the same H bond angle but. O O 0 40 nm , WATER 2 14 28 5 February 2010 20, WATER. PCM, calculations The well depth of the energy, profiles is at its deepest for small H bond angles. and gradually grows shallower as the H bond, angle distorts At the point where there ceases to. be a local minimum the interaction is entirely, repulsive and a Morse fit becomes nonsensical . Though a water dimer with fixed bond lengths, and angles is a simplification of real water H . bonding it is not difficult to envision a similar . though likely more complex H bonding cutoff, scheme for H bonds in liquid water . MP2 aug cc pVTZ and B3LYP 6 311 G d p , calculations both for the vacuum and PCM. cases similarly point to H bond angle having a, much larger effect on the H bond acceptor wa . ter molecule s oxygen and H bond donor hydro , gen charges than does the H bond distance For. the MP2 aug cc pVTZ vacuum calculations for, instance the donor hydrogen charge decreases. by 0 033 e to 0 038 e when the angle of the H , bond is increased from 0 to 90 with the O O. distance fixed at 0 28 nm whereas the increase, of H bond distance from 0 28 nm to 0 40 nm at. a 0 H bond angle causes a decrease in charge, of only 0 023 to 0 024 e data read from Figures. 6B and 7B The same trend in the data is seen, for all of the vacuum calculations independent. of dimer geometry or model chemistry basis, set For the PCM calculations however this. finding is reversed with O O separation having, the greater effect on the charge of the H bond. Figure 4 a The change in system energy with donor hydrogen atom due to strong interaction. O O distance at fixed H bond angle for the MP2 between it and the solvation reaction field . aug cc pVTZ planar vacuum case Energy curves, are shown for H bond angles from 0 to 90 at 5 The MP2 aug cc pVTZ vacuum dimer H bond. intervals with the 0 curve being lowest in energy acceptor oxygen atoms show a change in charge. and 90 being highest in the figure b R2 values ob similar to that seen for the H bond donor hy . tained from fitting a standard Morse potential to drogen atom for both dimer geometries with an. every calculated angle s energy dependence on O O, increase of 0 021 to 0 033 e upon angular de . distance , viation at a fixed O O distance of 0 28 nm and. Examination of the slices along the H bond dis only 0 007 to 0 013 e when the O O separation. tance dimension of the energy landscape also is lengthened to its maximum value while the. points to the critical role that H bond angle H bond angle is held at 0 data read from Fig . plays in the H bonding interaction of the wa ures 6A and 7A In fact for all of the calcula . ter dimer in addition to defining a range over tions independent of model chemistry solva . which we may differentiate a strong H bond tion state or dimer geometry deviation of the. from a bent or broken H bond The H bond H bond angle to 90 with the O O distance fixed. distance versus energy plots show Morse like at 0 28 nm has over twice the effect on oxygen. distance dependence which is typically indica charge that keeping the H bond angle at 0 and. tive of covalent interactions up to about 50 65 separating the oxygen atoms to 0 40 nm does . for the vacuum calculations and 30 40 for the Though the exact charge magnitudes change. WATER 2 14 28 5 February 2010 21, WATER, somewhat based on the geometry model chem The. energy surfaces calculated show that there, istry and basis set and solvation state used the is a clear point beyond which the H bond is no. trend is consistent throughout the calculations longer attractive and though the exact angle. indicating that H bond angle has a much great at which this threshold is reached changes de . er effect on the charge of the two H bonding at pending on the particular model chemistry . oms than does their radial separation The only, basis set intermolecular geometry or solvation. exception to this finding is for the aforemen , state used the finding is consistent for each of. tioned H bond donor hydrogen atom involved, the eight calculations The surfaces also show. in PCM calculations , that O O separation has a very small effect on. the dimer energy as compared to distortion of, the H bond angle The effect of the strong bro . ken H bond dichotomy can also be observed in, its effect on atomic charges . We note that though we were mindful of liquid, water in carrying out the calculations discussed. here even going so far as to use water mono , mer internal geometries calculated by Silves . trelli and Parrinello 1999 as averages in liquid, water and discuss our results as they might be. applied to liquid water the approach we have, chosen is simplified Therefore though we can. speak with confidence about the trends in the, calculated PES an idealized OH O H bond and. a gas phase water dimer the exact numbers we, have calculated would not hold up to experi . mental scrutiny for real liquid water Neverthe , less the strong consistency of the results we. have presented here shows what we suggest are, general trends in H bond energetics . Conclusions, This paper presents a novel result on the in . fluence of H bond angle on the energetics and, charges of a singly H bonded water dimer We. Figure 5 a The change in system energy with have described what we believe to be new evi . O O distance at fixed H bond angle for the MP2 dence and insight into what may well be a gen . aug cc pVTZ tetrahedral vacuum case Energy eral feature of H bond response to changes in. curves are shown for H bond angles from 0 to 90 basic donor acceptor intermolecular geometry . at 5 intervals proceeding from bottom to top in the. By simplifying the internal geometries of two,order 5 10 0 15 20 etc up to 90 b R2 values. obtained from fitting a standard Morse potential to water molecules we were able to examine in de . every calculated angle s energy dependence on O O tail the dependency of energy and charge on H . distance bond angle and O O separation We found that. WATER 2 14 28 5 February 2010 22, WATER, , Figure 6 2D charge landscapes for the H bond accepting oxygen atom a and H bond donating hydro . gen atom b for the MP2 aug cc pVTZ planar vacuum water dimer case . Table III Change in Charge with Increase in O O Distance and H Bond Angle. O Anglea e O Distanceb H Anglea e H Distanceb, e e . MP2 Planar 0 032 0 013 0 038 0 024, Vacuum, MP2 Planar 0 030 0 012 0 017 0 027. PCM, MP2 Tetrahe 0 022 0 008 0 033 0 023, dral Vacuum. MP2 Tetrahe 0 021 0 006 0 016 0 026, dral PCM, B3LYP Planar 0 033 0 013 0 030 0 015. Vacuum, B3LYP Planar 0 028 0 009 0 009 0 017, PCM. B3LYP Tetrahe 0 020 0 006 0 022 0 013, dral Vacuum. B3LYP Tetrahe 0 014 0 003 0 003 0 012, dral PCM, a Angle energies and charges were determined by subtracting the energy or charges of the. minimum energy geometry for a particular PES from the energy or charges of the geometry. with the same O O distance but HOO 90 , b Distance energies and charges were determined by subtracting the energy or charges of. the minimum energy geometry for a particular PES from the energy or charges of the geom . etry with the same H bond angle but O O 0 40 nm , WATER 2 14 28 5 February 2010 23. 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WATER,Discussion with Reviewers, lap hereafter referred to simply as overlap 1 . was bonding in nature i e positive as was, Ralph Dougherty1 Drs Scott and Vanderkooi the orbital overlap between the H bond donor. in view of the collection of evidence that shows O and H bond acceptor O hereafter referred. hydrogen bonds to be covalent see e g J to as overlap 2 As O O distance is increased . Li Inelastic neutron scattering studies of hy both overlap 1 and 2 decrease dramatically At. drogen bonding in ices J Chem Phys 105 an O O separation of 0 28 nm as the H bond. 1996 6733 6755 E D Isaacs A Shukla P M angle is increased from 0 to 30 overlap 1. Platzman D R Hamann B Barbiellini C A starts out about twice as large as overlap 2 and. Tulk Covalency of the Hydrogen Bond in Ice decreases quickly while overlap 2 decreases. A Direct X Ray Measurement Phys Rev Let very slowly At 50 overlap 1 and overlap 2 are. ters 82 1999 600 603 did the orbital over nearly equal and as the H bond angle is further. lap between the two water molecules correlate increased overlap 1 finally falls below overlap. strongly with the changes in potential 2 At the final angle of 90 both overlaps have. shrunk nearly to zero ,Nathan Scott and Jane Vanderkooi To attempt. to answer this question we re ran a subset of our The orbital overlap data for molecular orbital 8. original calculations such that orbital overlap shows that overlaps 1 and 2 shrink quickly with. information and the MP2 based electron densi increase in O O distance falling off to nearly. ty were output by Gaussian We also generated zero overlap at 0 37 nm At 0 H bond angle. potential energy grid data in the form of a cube and 0 28 nm O O distance overlap 1 is bond . file based on the MP2 based electron density ing in nature while overlap 2 is antibonding As. Given the strong support for Dyke and Odutu H bond angle is increased overlap 1 becomes. la s dimer geometry outlined in the response to less bonding becoming antibonding at 20 . question 2 below we chose to examine the MP2 and overlap 2 becomes less antibonding be . vacuum tetrahedral calculations at every 10 coming bonding in character at 30 At all H . 0 10 20 etc and at O O distances of 0 28 bond angles except 0 the combination of the 2. nm 0 31 nm 0 34 nm 0 37 nm and 0 40 nm overlaps is more antibonding in nature than it. is bonding indicating that molecular orbital 6, To determine which molecular orbitals we is the principle H bonding orbital in these cal . should concentrate on C2 population analysis culations . was performed for all of the valence orbitals in, order to analyze their individual atomic contri The correlation between the orbital overlaps. butions to orbital mixing Orbitals 6 and 8 at and electrostatic potential is far from certain. approximately 18 6 eV and 15 1 eV respec in these results but it does appear at least pos . tively for the case where the HOO angle is 0 sible Even for the linear H bond negative elec . and the O O separation is 0 28 nm were found trostatic potential begins to intercede between. to have significant contribution to their overall the H bond donor H and H bond acceptor O. electron occupation from the H bond donor hy at an O O separation of about 0 34 nm At this. drogen atom and the H bond acceptor oxygen distance orbital overlaps 1 and 2 have nearly. atom These are also the two oribitals that when vanished to zero At a fixed O O distance of. simply visualized using molecular orbital grid 0 28 nm negative potential begins to appear. data appear to have the most H bonding char between the water molecules at about 50 This. acter is the same angle at which orbital overlaps 1 and. 2 of molecular orbital 6 have shrunk to become, Plots of the atomic orbital overlap data were equal and very small relative to their values at. visualized using the freely available GaussSum the H bond angle of 0 . software package N M O Boyle A L Ten , derholt and K M Langner cclib A library for This is an intriguing question and probably. package independent computational chem warrants a more thorough study but it would. istry algorithms J Comp Chem 29 2008 not be surprising to find that the two quantities . 839 845 For molecular orbital 6 the H bond H bonding orbital overlap and electrostatic po . donor H and H bond acceptor O orbital over tential are in fact closely correlated . WATER 2 14 28 5 February 2010 27, WATER, Dougherty Would you specifically compare the temperature . results of this work with the microwave struc , ture of the water dimer obtained by Dyke and Scott and Vanderkooi One would certainly ex . his co workers pect there to be changes in water dimer struc . ture with temperature In particular rotational, Scott and Vanderkooi Our results appear to levels which are sure to be populated at all but. support the experimental data and analysis of the lowest temperatures would distort both the. Dyke and Odutola As noted in our article for intermolecular H bond as well as the geom . our tetrahedrally coordinated dimer calcula etries of the individual water monomers One of. tions we used a a angle Dyke s notation for the more impressive and ground breaking parts. the Euler angle between the OH donor vector of Dyke and Odutola s work was that they were. and the plane of the acceptor water molecule able to produce dimers with rotational tem . of 57 and this value was chosen specifically peratures under 20 K which allowed for very. based on Dyke s work However our OH bond high signal to noise data At increased temper . lengths and HOH angles were chosen to be fixed atures it seems unlikely that variations in dimer. at 0 0991 nm and 105 5 respectively quite dif structure would be observable due to the large. ferent from the 0 09572 nm and 104 52 degree degree of structural heterogeneity However . rigid rotor model applied by Dyke and Odutola though the variations might not be observable . to analyze their microwave spectra and based we can reasonably infer that they must still ex . on much earlier work by Plyler et al W S ist , Benedict N Gailar and E K Plyler Rotation 1 Professor Emeritus Department of Chemistry. Vibration Spectra of Deuterated Water Vapor and Biochemistry Florida State University . J Chem Phys 24 1956 1139 As noted in the Tallahassee FL USA. text our internal molecular geometry was cho ,sen to more accurately reflect what is believed. to be the average values for condensed phase,water molecules rather than those of a gaseous. water dimer Despite the substantial differences,between the two rigid models as can be seen. in Table 1 for both tetrahedral vacuum calcula ,tions we found the global energy minimum at a. position where the dimer oxygen oxygen sepa ,ration is 0 29 nm compare to Dyke s 0 2976 nm. 0 000 0 0030 nm and a xa angle Dyke s,notation for the HOO angle of 6 compare to. Dyke and Odutola s finding of 6 20 ,With only our a angle fixed at the value speci . fied by Dyke and Odutola the two dependent,variables in our study are extremely close to the. experimentally determined values ,Dougherty Since the structure of liquid water. is now known to undergo changes with tem ,perature see e g C Huang K T Wikfeldt T . Tokushima D Nordlunda Y Harada U Berg ,mann M Niebuhr T M Weiss Y Horikawa . M Leetmaa M P Ljungberg O Takahashi A ,Lenz L Ojam e A P Lyubartsev S Shin L . G M Pettersson A Nilsson Proc Natl Acad ,Sci 106 2009 15214 15218 would you ex . pect there to be observable variations in water,dimer structure or structure distribution with.