Hydrogen Bonding between Water and Tetrahydrofuran Relevant to

Nov 13, 2014 - Briefly, because the guest molecule is normally insoluble in water, clathrate hydrate formation requires high pressure, namely, tens to...
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Hydrogen Bonding Between Water and THF Relevant to Clathrate Formation Mary Jane Shultz, and Tuan Hoang Vu J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp509343x • Publication Date (Web): 13 Nov 2014 Downloaded from http://pubs.acs.org on November 17, 2014

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Hydrogen Bonding Between Water and THF Relevant to Clathrate Formation

Authors, Mary Jane Shultz†,* and Tuan Hoang Vu§ Affiliation: †

Laboratory for Water and Surface Analysis, Department of Chemistry, Tufts University, Medford, MA 02155,

USA. Email: [email protected] §

Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA

Email [email protected]

Abstract Tetrahydrofuran, THF, is a well-known clathrate former and a promoter for gas hydrate

formation.

This

work

examines

interactions between

water

and

tetrahydrofuran via the effect of interaction on water’s vibrational frequency. Due to water’s large oscillator strength in the hydrogen bonded region, interactions are diagnosed by isolating small clusters in a transparent medium (carbon tetrachloride in this report). The weak THF-water hydrogen bond is reflected in the 3450 cm-1 donorOH vibration – blue of the water-water hydrogen bond – and the nonbonded 3685 cm-1

*

Corresponding author

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OH stretch that is 22 cm-1 blue of the decoupled OH stretch in this medium. Increasing THF concentration results in a further 20cm-1 blue shift of the donor-OH stretch. The additional THF does not complex free water, but rather joins with existing THF·water structures to form a cluster enriched in THF. These results complement previous work examining THF vibrations in clathrate hydrates. Together they generate a picture in which water mediates between THF pairs; a mediation that affects vibrational frequencies of both species. In addition to the frequency shift, the water hydrogen-bonded resonance gains oscillator strength due to the mediating configuration. Key Words: Water, clathrate, spectroscopy, H-bond interactions

Introduction Hydrogen-bond interactions with water are interesting from a chemical perspective as well as playing central roles in biological,1-4 geological,5 and environmental6-9 chemistry. Chemically, water is a responsive molecule10 adapting due to interaction both with nearest neighbors as well as the larger environment.11-13 Clathrate hydrates, consisting of hydrophobic guests in cages of water molecules,14 are firmly in the chemically interesting category, evidenced by more than one thousand publications on the subject in the last decade. Significant progress has been made in understanding both how the guest is incorporated and, since empty clathrate cages are inherently unstable,15,16 how guest incorporation stabilizes the water cages. An intriguing development in clathrate work, both from a fundamental and a practical point of view, is identification of socalled promoters. Briefly, since the guest molecule is normally insoluble in water, clathrate hydrate formation requires high pressure: tens to thousands of atmospheres (as in the case of H2).

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Addition of a promoter can significantly lower the pressure requirement.17,18 When considering clathrates as a condensed phase storage medium for gaseous molecules such as hydrogen,19,20 methane,13,21-23 or CO2,24-26 a lower pressure requirement has advantageous practical and energy implications. Of the helper compounds, tetrahydrofuran, THF17,27-29 is particularly interesting due to its ability to form hydrogen-bonds with water, leading to classification as a nonclassical promoter.30 Indeed, THF can catalyze subpicosecond clathrate formation from aerosols in the 140-220 K range.31 One effect of the helper-host hydrogen bond is generation of Bjerrum L-defects (two adjacent water molecules with no covalently bonded hydrogen atom between them) providing an opening for small guests to penetrate and load the smaller cages.17,32 In addition, the helper modulates the vibrational frequency of the guest; a modulation mediated by water despite lack of direct hydrogen bonding by the guest. Due to the large oscillator strength of hydrogen-bonded water, the resulting broad, intense vibrational spectrum challenges attempts to probe modulation of the water vibrational frequency due to this mediating role. One solution to this challenge is to carefully subtract spectra. However, subtraction is often complicated by sensitivity of the oscillator strength to the environment. Another solution consists of isolating a small cluster to separate the relevant resonances. If the isolating medium is a liquid at the temperature of interest and is transparent in the hydrogen-bonding region, then one can probe small clusters with relevant thermal energies. This approach is dubbed room-temperature matrix-isolation spectroscopy (RT-MIS) to distinguish it from classic matrix isolation that employs a lowtemperature solid matrix. RT-MIS has been used to generate clear spectral evidence of a blueshifting hydrogen bond,33 to isolate the stretch resonance in OH-,34 and to determine competitive binding between guests.35

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In this contribution we describe results using RT-MIS to monitor interaction of water via vibrational spectroscopy. This work thus complements DFT calculations of 1:1 and 1:2 THF:water complexes36 and combined IR, NMR, DFT probes of THF hydrate.37 The consistent picture is that water and THF form a weak hydrogen-bonded complex. The hydrogen bond is weakened further by additional THF; the oscillator strength, however, is significantly increased. This work is laid out as follows. The spectra are presented after describing the experimental method. This is followed by a discussion including presentation of a DF-B3LYP 6-31G* conformation calculation generating a cartoon of the complex. The final section presents the conclusions.

Experimental Preparation of dry carbon tetrachloride has been described in previous publications.38,39 Briefly,

carbon

tetrachloride

(anhydrous

>99.5%) is obtained from Sigma Aldrich. Removal of adventitious water is done with Figure 1: Subsaturated neat water in dry carbon

silica

gel

and

confirmed

with

FTIR.

tetrachloride at -5 °C shows the symmetric stretch at

Subsaturation water is introduced by mass, the

3615 cm-1, the asymmetric stretch at 3705 cm-1 and the

vessel sonicated for 1-hr and cooled in a -10°

characteristic rotational wing due to water spinning on

C freezer overnight. THF (Sigma Aldrich,

the molecular axis, particularly evident to the blue side of the asymmetric stretch. At -5 °C, the solubility of

anhydrous, 99.9%) is introduced by mass and water is 4 mM. (Inset) Expanded view of the hydrogen-

spectra obtained at the specified temperature.

bonding region showing no evidence of H-bonded resonances indicating that water is monomeric.

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Infrared spectra are obtained with Nicolet Magma-IR 760 FTIR spectrometer (64 scans, 1 cm-1 resolution).

Results The spectrum of neat water in carbon tetrachloride has been thoroughly discussed in the literature.38 The spectrum at -5 °C (Figure 1) appears very similar to that at room temperature. The two prominent features are the symmetric stretch at 3615 cm-1 and the asymmetric stretch at 3705 cm-1. Figure 2: Water plus THF in carbon tetrachloride as a

Like room temperature, the symmetric function of THF concentration at -5 oC. Note the

stretch

is

relatively

enhanced

due

to

appearance of an H-donor feature around 3450 cm-1

interaction between oxygen of water the

and emergence of a dangling OH feature, just red of

positively charged carbon atom of carbon

the asymmetric stretch. (Features to the blue of the

tetrachloride. Steric hindrance due to this

asymmetric stretch are due to THF combination bands.)

interaction limits water rotational motion to that about the symmetry axis; the symmetry axis moment of inertia is nearly identical to that in the gas phase. Compared to room temperature, at -5 °C the rotational wings are drawn in by the expected temperature factor. The neat water spectrum indicates that carbon tetrachloride provides an excellent medium for monitoring H-donor interactions via collapse of the rotational wings.

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Addition of tetrahydrofuran alters the water spectrum significantly (Figure 2). Several features are of note: (1) the feature around 3450 cm-1 attributed to an H-donor resonance, (2) emergence of a sharp feature between the symmetric and the asymmetric stretch, attributed to a dangling-OH stretch, and (3) structure to the blue side of the asymmetric stretch. The latter is due to combination bands involving THF while the first two features are associated with H-bonded complexes with water (magnified in Figure 3). The donor-OH stretch for a water-water bond has previously been identified for several systems and appears at 3440 cm-1.40 The frequencies of the features in Figure 3A are blue of the water-water stretch by 10-30 cm-1 and increase with THF concentration. The ~ 3450 cm-1 feature has low intensity below 5 mM THF; beyond 5 mM it grows with increasing THF concentration, thus it is assigned to water associated with multiple THF molecules. The 3685 cm-1 feature in Figure 3B exhibits a similar trend. Below 5 mM, it has undetectable intensity; above 5 mM it grows with increasing concentration. The 3685 cm-1 feature is thus assigned to a dangling-OH resonance. Note that the fully decoupled OH resonance appears at the midpoint of the symmetric and asymmetric stretches at 3663 cm-1.34 The danglingOH resonance in THF-water is blue of the decoupled OH resonance by 22 cm-1 indicating weaker decoupling. The resonance is thus assigned to water weakly hydrogen bonded to THF, consistent with the H-bond donor peak and the known weak bond between THF and water.36 At -5 °C, the water monomer concentration is 3.5 mM. Addition of 2.5 mM THF reduces the free water absorbance by 22% indicating that 22% of the water is bound in a water·THF complex. Above 2.5 mM THF, the free water concentration remains constant, consistent with the remaining changes being due to addition of THF molecules to the THF·H2O complex. Implications for these spectroscopic results are delineated in the Discussion section.

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Discussion Hydrogen bond interactions involving water shape a significant portion of the world from determining the macromolecular structure of biologically active molecules such as proteins and DNA to determining the fate of anthropogenic molecules in the troposphere. Among hydrogenbond interactions, clathrate hydrates are particularly intriguing since these crystalline materials consists of ~ 10% hydrophobic molecules enclosed in cages of water molecules; furthermore these water cages are not stable in the absence of a guest.13,20,23 Probing the molecular-level water-guest interactions leading to either clathrate formation or stabilization presents a challenging experimental problem. Vibrational spectroscopy would seem an ideal technique for probing interactions with water since the O-H vibrational frequency is exquisitely sensitive to

(A)

(B)

Figure 3: (A) Magnification of the H-donor region shows the increasing blue shift and gain in oscillator strength with increasing THF concentration (Lorentzian fit to two peaks shown with solid lines.) (B) Magnification of the region red of the asymmetric stretch shows emergence of a dangling-OH feature at 15 mM THF that grows with concentration. The asymmetric stretch intensity, indicative of the free water concentration, does not change with increasing THF concentration.

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both the local and the longer range environment.11-13,41 Unfortunately, the oscillator strength of hydrogen bonded water results in opacity precisely in the hydrogen-bonded spectral region. One approach to overcome the opacity issue is to isolate a smaller cluster in an infrared transparent medium. If that medium is liquid at the temperature of interest, water and its bonding partners can interact with relevant thermal energies. This work adopts this strategy in what has been dubbed room temperature matrix isolation spectroscopy, RT-MIS. The isolation medium chosen is carbon tetrachloride since it is liquid at room temperature (and at -5 °C relevant to these experiments) and transparent in the H-bonding region. Clathrate formation involving hydrophobic guests generally requires high pressure – in the tens to thousands of atmospheres range – and/or low temperature. The primary observable effect of a promoter is lowering the required pressure. Lower pressure is advantageous when considering clathrates as storage media for gases such as hydrogen20 or methane.13,23 Thus, there is motivation for understanding helper function to devise more effective promoters enabling closer-to-ambient-pressure clathrate formation. Of the promoters, THF is particularly interesting since it is soluble in and forms H-bonds with water. In the clathrate structure, all water H-bonds are involved in either inter- or intra-cage binding; there are no dangling OH bonds. The helper appears to go into the larger cages disrupting the intra-cage bonds,17,32 generating Bjerrum Ldefects thus creating an opening for small guests such as H2, CH4, or CO2 to fill the smaller cages.17 In turn, the smaller guest modifies the vibrational frequencies of the helper17 despite not being involved in hydrogen bonding. Developing a complete picture of clathrate hydrate formation requires data not only for the guest or helper molecule but also for the water host. Recently, there has been considerable progress in developing a picture of the role of the promoter and its synergy with the

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guest;17,36,37,42,43 the picture for the water host is less well developed. It is challenging to obtain experimental data about the host: its concentration is greater so the difficulty lies in deconvoluting small changes due to interaction from the larger concentration features. For water, this problem is compounded due to changes in oscillator strength with environment. The carbon tetrachloride isolation system offers a solution. Because water is not very soluble in carbon tetrachloride, interaction between one or a few water molecules and a co-solute are isolated from bulk features of the larger system. Since carbon tetrachloride is transparent in the OH stretch region, it is compatible with infrared spectroscopy. Thus fragments of the clathrate structure can be probed with ambient energies in the -20 °C to above room temperature range. At room temperature, the solubility of water in carbon tetrachloride is 7.5 mM and its vibrational spectrum is well analyzed.38 The OH stretch region consists of a symmetric stretch at 3615 cm-1, an asymmetric stretch at 3705 cm-1, and rotational wings associated with the asymmetric stretch. The rotational wings, due to symmetry axis rotation, provide an excellent diagnostic tool for recognizing H-bond donor interactions. In addition, H-bond donor interaction decouples the two OH stretches. The peak of the rotational wings draw in toward the asymmetric stretch at -5 ° C (the target of this work) compared with room temperature; the solubility drops to 4.0 mM. Magnification of the H-bond region (Figure 1 inset) shows that water also exists as monomers at -5 °C. This work thus investigates the specific water-THF interaction. The target temperature is -5 °C since at high pressure, clathrates form at this temperature and are stable to above 0° C. The -5° C temperature provides comparable thermal energies to clathrate formation conditions. The targeted mixing ratios ensure saturation of water with THF: ratios are 1:1 to 1:10 water:THF. As shown in Figure 2, addition of 5 mM THF substantially alters the water spectrum. The free water

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intensity drops by 22% and an H-bond donor feature appears at ~3450 cm-1. With 5 mM THF, the water concentration is nearly the same as that of THF. Thus this broad feature is attributed to a THF·water complex. Since THF can only act as an H-bond acceptor, this feature is expected. Increasing the THF concentration to simulate a guest-water-guest interaction produces a nearly doubled oscillator strength H-bond donor feature. (Ten mixtures from 2.5 mM THF to 30 mM were generated; three representative mixtures are shown for clarity.) The increased H-bond donor resonance is not accompanied by a reduction in free water. Thus the additional THF does not complex free water, but rather joins with THF·water structures already present to form a cluster enriched in THF. Increasing THF from 15 mM to 25 mM shows an increase in the Hdonor resonance; the free water resonance remains undisturbed. The set of ~3450 cm-1 features at several concentrations are well-fitted with a convolution of two Lorentzian resonances: a low frequency component at 3450 ± 3 cm-1 and a higher frequency component at 3470 ± 2cm-1. Both are broad: FWHM = 80-90 cm-1. The solid lines in Figure 3A show the resulting fit. The lower frequency feature is relatively weak, so has large intensity error bars. The higher frequency feature has low intensity below 5 mM. In the 15 to 25 mM range, the intensity increases essentially quadratically: Rc = (Ra)γ where Rc is the THF concentration ratio, Ra is the integrated peak area and γ a constant. The best fit yields γ = 2 ±0.2 indicating quadratic dependence on the THF concentration. Quadratic dependence indicates that the complex consists of H2O·2THF. Qquadratic increase in integrated area supports the interpretation that the cluster formed consists of H2O·2THF. At ~ 3450 cm-1, the O-H stretch must be due to H-bond donor water. The increased integrated area of the higher frequency feature in the presence of a constant free water intensity indicates that the H2O·2THF cluster grows due to addition of THF to the water·THF

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cluster. The much larger oscillator strength of the higher frequency feature thus indicates greater polarization of the water O-H bond as a result of the second THF. The blue shift indicates that the multiple-THF complex hydrogen bond is weaker than the single-water-THF hydrogen bond. Complementing observation of a blue shift in the donor-OH resonance, a new feature is observed at 3685 cm-1 just to the red side of the asymmetric stretch. A stretch in the region between the symmetric and the asymmetric stretch is indicative of decoupled OH stretches. In free water, the symmetric and asymmetric stretches are separated due to coupling of the two OH stretches. One method to decouple these two stretches is to examine HDO. The isotope-shift completely decouples the two OH stretches so that the OH stretch is observed at 3663 cm-1.34 Thus, observing the d-OH feature at 3685 cm-1 indicates incomplete decoupling of the two OH resonances; a conclusion consistent with the weak hydrogen bond indicated by the blue shifted donor-OH stretch. All three observations: blue shift of the donor-OH stretch, emergence of a d-OH blue of the decoupled frequency, and constancy of the freewater

absorbance

indicate

that

multiple THF molecules complex the water

molecule.

Consequently,

a

Figure 4: Cartoon rendition of a DF-B3LYP 6-31G* calculation of the 2THF·H2O configuration. Note the water mediated

calculation (DF-B3LYP 6-31G*) was interaction including a H-bond donor interaction between the

run to generate a qualitative picture of

water OH and the ether oxygen atom of the THF and an acceptor

the 2THF·H2O complex (Figure 4).

interaction between the water oxygen atom and a hydrogen atom

Interaction between the ether oxygen

of the α methylene carbon of THF.

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atom of THF and water is expected due to the slightly basic nature of THF. Water does not form a bridging donor-donor structure with two THF molecules.

Instead, an H-bond acceptor

interaction occurs between the water oxygen atom and the α-methylene group of the other. A similar water-methylene interaction was previously observed for propane-water. The use of CD3CH2CD3-propane results in an easily identified, blue-shifting C-H2…O hydrogen bond.33,44 A blue-shifting H-bond was also noted in THF clathrate.37 Together these results support the interpretation that the spectral observations for water are due to a H2O·2THF· complex. The complex is stabilized by 40.6 kJ/mol compared with the separated THF dimer plus water, driving complex formation.

Conclusions Interactions between water and tetrahydrofuran, THF, are examined with vibrational spectroscopy. Normally, it is challenging to monitor the H-bonding region of water via infrared spectroscopy due to the large oscillator strength of water rendering the H-bonding region opaque. This work uses an adaptation of classical matrix isolation spectroscopy by isolating small water complexes in a medium that is transparent in the H-bonding region, yet with relevant thermal energies. Carbon tetrachloride is used as the matrix isolation medium in this work. The results of this work suggest that water mediates interaction between two THF molecules, stabilizing the THF·THF interaction45 via a water H-bond donor to the ether oxygen atom of one THF molecule and a blue-shifting acceptor interaction involving the α-methylene group of the other THF. This water-mediated interaction results in a blue-shift of the water H-bond donor resonance relative to the single THF·water donor interaction and a weakly decoupled danglingOH resonance for the other OH bond. It is concluded that a single THF binds water more

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strongly than a pair binds the mediating water; the pair oscillator strength is greater due to polarization of the intervening water molecule. These results complement previously reported work examining vibrations of the promoter.17,37 The implication for clathrate formation is that the promoter modifies hydrogen bonding in the water host and that the modification is mitigated upon guest incorporation. Further experimental and theoretical work is needed to identify the ideal helper-water-guest interaction for low-pressure clathrate formation.

Acknowledgements The authors gratefully acknowledge US National Science Foundation grant #CHE1306933 for partial financial support of this work.

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24. Herslung, Peter Jergensen; Thomsen, Kaj; Abildskov, Jens; Solms, Nicolas von, "Phase equilibrium modeling of gas hydrate systems for CO2 capture" J. Chem. Therm. 2012, 48, 13-27. 25. Lee, Yun-Je; Han, Kyu Won; Jang, Jin Seok; Jeon, Tae-In; Park, Jeasung; Kawamura, Taro; Yamamoto, Yoshitaka; Sugahara, Takeshi; Vogt, Thomas; Lee, Jong-Won; et. al. "Selective CO2 Trapping in Guest-Free Hydroquinone Clathrate Prepared by Gas-Phase Synthesis " ChemPhysChem. 2011, 12, 1056–1059. 26. Falenty, Andrzej; Kuhs, Werner F., "“Self-Preservation” of CO2 Gas Hydrates—Surface Microstructure and Ice Perfection" J. Phys. Chem. B. 2009, 113, 15975-15988. 27. Vallejos, Margarita M.; Peruchena, Nelinda M., "Preferential Formation of the Different Hydrogen Bonds and Their Effects in Tetrahydrofuran and Tetrahydropyran Microhydrated Complexes" J. Phys. Chem. A 2012, 116, 4199-4210. 28. Muro, Maiko; Harada, Makoto; Hasegawa, Takeshi; Okada, Tetsuo, "Formation and Growth of Tetrahydrofuran Hydrate at the Ice/Hexane Interface" J. Phys. Chem C 2012, 116, 1329613301. 29. Senadheera, Lasitha; Conradi, Mark S., "Hydrogen NMR of H2-TDF-D2O Clathrate" J. Phys. Chem. B. 2008, 112, 13695-13700. 30. Monreal, I. Abrrey; Cwiklik, Lukasz; Jagoda-Cwiklik, Barbara; Devlin, J. Paul, "Classical to Nonclassical Transition of Ether−HCN Clathrate Hydrates at Low Temperature" J. Phys. Chem. Lett. 2010, 1, 290-294. 31. Devlin, J. Paul, "Catalytic activity of methanol in all-vapor subsecond clathrate-hydrate formation" J. Chem. Phys. 2014, 140, 164505:1-7. 32. Monreal, I. Abrrey; Devlin, J. Paul; Maslakci, Zafer; Cicek, M. Bora; Uras-Aytemiz, Nevin, "Controlling nonclassical content of clathrate hydrates through the choice of molecular guests and temperature" J. Phys. Chem. A 2011, 115, 5822-5832. 33. Vu, Tuan Hoang; Kälin, Sarah; Shultz, Mary Jane, "Spectroscopic Identification of WaterPropane Interaction: Implications for Clathrate Nucleation" J. Phys. Chem. A 2010, 114, 63566360. 34. Vu, Tuan Hoang; Shultz, Mary Jane, "Vibrating Hydroxide in Hydrophobic Solution: The Ion to Keep an Eye On" Chem. Phys. Lett. 2013, 572, 13-15. 35. Vu, Tuan Hoang; Shultz, Mary Jane, "Competitive Binding of Methanol and Propane for Water Via Matrix Isolation Spectroscopy: Implications for Inhibition of Clathrate Nucleation" J. Phys. Chem. A 2011, 115, 998-1002. 36. Devlin, J. Paul; Monreal, I. Abrrey, "Instant Conversion of Air to a Clathrate Hydrate: CO2 Hydrates Directly from Moist Air and Moist CO2(g)" J. Phys. Chem. A 2010, 114, 13129-13133. 37. Mizuno, Kazuko; Masuda, Yohko; Yamamura, Takuya; Kitamura, Junya; Ogata, Hiroshi; Bako, Imre; Tamai, Yoshinori; Yagasaki, Takuma, "Roles of the Ether Oxygen in Hydration of Tetrahydrofuran Studied by IR, NMR, and DFT Calculation Methods" J. Phys. Chem. A 2009, 113, 906-915. 38. Kuo, Margaret; Kamelamela, Noelani; Shultz, Mary Jane, "Rotational Structure of Water in a Hydrophobic Environment: Carbon Tetrachloride" J. Phys. Chem. A 2008, 112, 1214-1218. -15ACS Paragon Plus Environment

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39. Kuo, Margaret Hsinjui; David, Alexander; Kamelamela, Noelani; White, Mike; Shultz, Mary Jane, "Nitric Acid-Water Interaction Probed via Isolation in Carbon Tetrachloride" J. Phys. Chem. C 2007, 111, 8827-8831. 40. Bisson, Patrick; Xiao, Han; Kuo, Margaret; Kamelamela, Noelani; Shultz, Mary Jane, "Ions and Hydrogen Bonding in a Hydrophobic Environment: CCl4" J. Phys. Chem. A 2010, 114, 4051-4057. 41. Shultz, Mary Jane; Bisson, Patrick; Vu, Tuan Hoang, "Molecular Dance: Water’s Collective Modes" Chem. Phys. Lett. 2013, 588, 1-10. 42. Alavi, Saman; Susilo, Robin; Ripmeester, John A., "Linking microscopic guest properties to macroscopic observables in clathrate hydrates: Guest-host hydrogen bonding " J. Chem. Phys. 2009, 130, 174501:1-9. 43. Park, Youngjune; Cha, Minjun; Shin, Woongchul; Lee, Huen; Ripmeester, John A., "Spectroscopic observation of critical guest concentration appearing in tert-butyl alcohol clathrate hydrate" J. Phys. Chem. B 2008, 112, 8443-8446. 44. Note: A blue-shifting, C-H2…O hydrogen bond results from charge transfer from oxygen to carbon changing the sp3 hybridization toward sp2, shortening and strengthening the bond, hence blue shifting it. 45. Silva, Larissa Tunes da; Politi, José Roberto dos Santos; Gargano, Ricardo, "Theoretical study of tetrahydrofuran: Comparative investigation of spectroscopic and structural properties between gas and liquid phases " Int. J. Quantum Chem. 2011, 111, 2914-2921.

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