A New Hydrogen Bond Angle Distance Potential Energy

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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.
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

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