Water binding in cryogenic liquids: The H2O…N2 hydrogen bond

Volume 141, number 6

CHEMICAL PHYSICS LETTERS

27 November 1987

WATER BINDING IN CRYOGENIC LIQUIDS: THE H20...Nz HYDROGEN BOND Douglas B. KITCHEN, Thomas P. RUANE and Leland C. ALLEN ’ Department @Chemistry, Princeton University,Princeton, NJ 08544, USA Received 23 August 1987; in final form 3 September 1987

Ab initio calculations for the Nz...HOH complex have been carried out to provide spectroscopic parameters to help determine if formation of the complex can plausibly account for the high solubility of water in liquid nitrogen. Basis sets for optimization and energy determination included 6-3 1lG**//6-3 1 I G** and 6-3 14 + G//6-3 lG* and correlation corrections up to MP4 (SDTQ) were employed. 0, was found to be 1.2 kcal/mol, in close agreement with the prediction of a simple hydrogen bond model. The dipole moment, IR intensity enhancement, harmonic frequencies, and zero-point energies were also obtained. Parallel calculations for the N,...HF complex enabled us to validate our procedure by comparison with previous high-accuracy calculations and experiments.

1. Introduction Recent spectroscopic evidence has shown that the solubility of water in cryogenic liquids such as liquid nitrogen is at least ten orders of magnitude higher than had been expected based on experimental thermodynamic estimates [ 11. This evidence confirms recent gravimetnc studies which gave approximately the same concentration [ 21, but neither result provides information on the type or degree of aggregation of the water. The purity of liquid nitrogen is a critical parameter for many uses and it is important to understand its mode of binding to water in order to develop strategies for removing it. The nature of the interaction between Hz0 and Nz has not yet been investigated either experimentally or theoretically. Hydrogen bonding is a principle candidate and this type of interaction has been observed to span a wide range of binding energies. Application of the simple hydrogen bonding model of Allen [ 31 to the N2...H20 hydrogen bond gives a dimerization energy of 1.4 kcal/mole, The high-accuracy calculations reported here show that there is indeed a hydrogen bond in this system and that its strength is approximately 1.2 kcal/mole, in surprisingly close agreement with the simple model (zero’ To whom correspondence should be addressed.

point corrections reduce this value by approximately 0.6 kcal/mole) , Thus we believe that hydrogen bonding is the origin of the observed solubility of water in liquid nitrogen. Proof of this hypothesis can be obtained by experimental measurement of the IR intensity of the OH stretching band. The intensity enhancement of this band is characteristically large for hydrogen bonds and we give a predicted value. The significant increase in the dipole moment of the complex over that of the monomer sum is also a manifestation of hydrogen bonding. High-accuracy calculations on another dimer of NZ, N*...HF have been carried out by Benzel and Dykstra [ 41. They obtained a dimerization energy, D,, of 2.27 kcall mole and using our methods we almost exactly reproduce this energy. An empirical extrapolation based on experimental values of the internuclear separation and force constants gives a De of 1.83 kcal/mole [ 51.

2. Computational methods Force methods were employed to obtain fully optimized solutions at the 4-3 1G, 6-3 1G* and 6-3 1lG** levels. Correlation effects were included using Mnrller-Plesset perturbation theory up to third order (MP3). The effect of higher-order perturbation the-

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Volume141,number6

CHEMICAL PHYSICSLETTERS

ory on the results was determined by a fourth-order calculation including singles, doubles, triples and quadruples (MP4(SDTQ)) with the 6-31G* basis set. The effect of diffuse functions was investigated using the 6-311 t t G** basis at the 6.31G’ geometry. Dimerization energies are given in table 1. The vibrational frequencies were calculated at the 4-3 1G and 6-3 1G* basis sets using analytical second derivatives. The intensities of the O-H stretch vibrational modes were determined from the normal modes or the 4-3 1G frequency analysis. Calculations were carried out on the N,...HF complex in order to compare with results that employed other highly accurate theoretical methods. Comparisons are made in table I between the results of Benzel and Dykstra [4] and the various methods used in this study. It can be seen that correlation up to the MP3 level is necessary but that MP4 is not expected to significantly alter the results at the 6-3 1 I + + G** level. The additional correlation corrections decrease in magnitude from second to third to fourth order. The fourth-to-thirdorder correction is only 751 of the third to second at 6-3 1G*.Also as the basis set is improved the relative decrease in the magnitude of the correlation correction decreases. Therefore at the 6-3 11 + + G** level the MP4 level is expected to introduce only a 0.06 kcaYmole increase in binding relative to MP3 for N2...HF. This extrapolation gives a result of 2.29 kcal/mole in close agreement with Benzel and

27 November1987

Dykstra. It is also noteworthy that even at MP31 6-3 1 1 + + G** the result is only 0.04 kcal/mole lower. Overall, correlation corrections account for approximately one third of the D, value, again, a result in close agreement with Benzel and Dykstra on N*...HF. This is a high percentage of D,for a system that separates into closed-shell monomers and is a consequence of the weak binding of these complexes.

3. Results and analysis A significant interaction was found between N2 and H20. Zero-point energy corrections are 0.65 and 0.79 kcal/mole using the RHF/6-3 1G*//RHF/6-3 lG* vibrational frequencies and both should be decreased by 10% to compensate for the known overestimate of vibrational frequencies by Hartree-Fock wavefunctions. The dimerization energy is predicted to be about 0.64 kcal/mole. Basis set superposition error was approximately 0.29 kcal/mole at the 6311 t tG** level for N,...HF, but a very thorough study of BSSE by Schwenke and Truhlar [ 61 on the HF dimer has shown that counterpoise-corrected interaction energies are not more reliably accurate than the uncorrected values. Therefore, the best theoretical value for this hydrogen bond is then 0.64 kcall mole with the inclusion of zero-point energy. The value for the dimerization energy appears to

Table1 N2...HZ0 andN2...HFhydrogenbondenergies(kcallmole)a)

N*...H,O

N,...HF

RHF

MP2

MP3

MP4(SDTQ)b,

X14-3lGNRHF/4-3 I G X16-31G*//RHF/6-3 lG* X/6-3 1lG**I/RHF/6-31 lG** X16-3I+ +G**NRHF/6-3lG*

1.75 0.841 0.816 0.741

1.55 1.46 1.28

1.37 1.29 1.20

(1.51) (1.41) (1.24)

X/4-3 1G//RHF/4-3 1G X16-31G*//RHF/6-3 1G* X/6-3 11G*URHF/6-3 11G** X16-3It +G**//RHF/6-3 1G*

3.26 1.64 1.77 1.67

2.61[2.74] c’ 2.68 2.35

2.35[2.41]” 2.44 2.23

2.55 (2.59) (2.29)

Ref. [4]

2.3

” In the description of the calculations X is the method employed followed by the basis set used followed by the method and basis set used for the geometry optimization. Thus MP2/6-3 1G*//RHF/6-3 lG* implies and MP2 single-point calculation with the 6-3 1G* basis set for which the geometry is that optimized at the restricted Hartree-Fock (RHF) method with a 6.3lG* basis set. ‘) Numbers in parentheses are extrapolated correlation corrections based on the pattern shown by the X16-3lG*NRHF/6-3lG* results for N,...HF. ‘) Numbers in square brackets are with optimized N-H distance and fixed NN and HF distances at the RHF/6-31G*NRHF/6-31G* geometry of complex. E,( MP2) = - 209.434 13 kcal/mol, E,(MP3) = - 209.43256 kcallmol.

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PHYSICS LETTERS

be relatively independent of the basis set used but the basis set superposition error decreases dramatically with an improvement in the basis set. The effect of diffuse functions on the dimerization energy is significant due to the small value of the dimerization energy. The correlation effects are important but is only needed up to the MP3 level. Correlation increases the binding energy by 0.6 kcal/mole for the HF dimer and by 0.5 kcal/mole for the water dimer (see table 1). Results on acetylene hydrogen bonding by Pople and co-workers [ 71 show similar trends but larger magnitudes. Correlation increases the hydrogen-bond energy by 0.8 and 0.9 kcahmole for HzO-acetylene and HF-acetylene dimers, respectively. Basis set effects are also larger for the acetylene cases. Their results indicate 0.4-2.2 kcal/mole decreases as the basis set is improved beyond the 63 1G* level in comparison to less than 0.1 kcal/mole in N2...H,0. Some of the differences are likely to be due to the larger hydrogen-bond energies in the acetylene systems. It is also likely that the larger polar-

Table 2 Optimized

geometries

of monomers,

ON

Hz0

r(OH) LHOH

HP

r(HF)

NI...H20

r(N-N) r(N-H) r(O-H,) r(O-Hz) r(N-0) LNNH, LNH,O LH,OHz

Nl...HF

r(N-N) r(N-H) r(H-F) r(N-F)

1987

izability of acetylene requires a better basis to describe charge redistribution. The geometries of the complexes (table 2) are not greatly affected by additions of diffuse functions but polarization functions do have a large effect on the N-O and N-F distances. Benzel and Dykstra [ 41 also found similar results in their study of N2...HF. The dipole moments (table 3 ) were consistent among the polarized basis sets and very good agreement was found with the results of Benzel and Dykstra for the HF dimer. Even though the bond energy is small there is definite evidence for hydrogen bonding. Thus in both the Nz-water and N2-HF complexes the dipole moments of the complexes are seen to be greater than the sum of the monomers (see table 3). Secondly, there is significant vibrational transition intensity enhancement: at the 4-3 1G level an intensity enhancement of the O-H stretch of 2.9 was calculated. The electrostatic attraction, induced polarization nature of these hydrogen bonds is manifest in the

N2...H20 and N,...HF a)

4.3lG

N2

27 November

1.0847

6-3lG’ 1.07839

6-3 11 G**

0.9473 105.495

0.9410 105.427

0.9222

0.9109

0.8959

1.0840

1.0780 2.5984 0.9473 0.9472

1.0835 2.1212 0.9225 3.0437

3.5360 174.013 170.428 105.474 1.0776 2.2907 0.9114 3.202 1

b,

MP3/6-3 1G* b,

1.0703

0.9504 111.233

2.3802 0.9501 0.9501 3.3264 171.425 174.786 111.319

MP2/6-31G*

Ref. [4] Cl 1.0734 (1.0997)

Exp. 1.0977

0.959 103.9 0.9027 (0.9210)

0.9168

3.069

3.082

1.0699 2.6112 0.9411 0.9409 3.5492 171.542 174.570 105.426 1.069 2.2691 0.8972 3.1663

2.141

2.191

3.052

3.103

a) Geometries optimized using RHF unless otherwise indicated. w r( N-N) and r( H-F) fixed at the 6-3 1G’ value for the complex. c1 Numbers in parentheses are from correlated solution (SCEP).

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Volume 141, number 6

27 November 1987

Table 3 Total energies (hartree) and dipole moments (D) aJ

N2 X14-3IGllRHFl4-3 1G RHF X16-3IG*//RHF/&3 1G’ RHF MP2 MP3 MP4( SDTQ) X16-3I 1G**//RHF/6-3 I 1G** RHF MP2 MP3 X16-311-h RHF

W

N,...HF

NZ...H20

108.75422

99.88729

75.90864

208.64670

184.66564

108.94395

100.00291 [ 1.9801 100.18158 100.18338 100.18780

76.01075 [2.199] 76.19596 76.20197 76.20632

208.94947 [2.354] 209.43393 209.43246 209.45836

184.95604 [ 2.3461 185.44662 185.44950

100.04690 [ 1.9721 100.26687 100.26710

76.04701 [2.138] 76.26328 76.26796

209.02 167 [2.373] 209.56185 209.55632

185.02026 [ 2.2741 185.55631 185.55534

100.05307 [ 2.0541 100.27886 100.27696

76.05334 [2.214] 76.27457 76.27742

209.0296 1 [2.431] 209.57916 209.57075

185.02839 [ 2.3401 185.57378 185.56955

109.24819 109.24534 109.26649 108.97195 109.29071 109.28533

+

HF

G**NRHFI6-3 1G*

MP2 MP3 Benzel, Dystra b, Hartree-Fock

108.97388 109.29716 109.29023

[2.06 ‘), 1.97 d)]

ACCD b’

209.03783 [2.51 ‘), 2.44 d’] 209.56865

‘) Dipole moments are calculated using RHF and are listed in square brackets. ‘) Ref. [4]. ” Triple-zeta plus polarization basis set at the SCF level. d, Triple-zeta plus polarization basis set with the SCEP method (ref. [ 41).

N2...HF charge density difference plot &-monomer placed at the equilibrium geometry of the complex) shown by Benzel and Dykstra [ 41. This plot closely resembles those obtained by Desmeules and Allen [ 81 for a collection of stronger hydrogen bonds. An alternating sequence of charge density gains and losses occurs as one proceeds from electron donor to proton donor along the hydrogen bond line, a feature characteristic of an electrostatically driven charge redistribution between closed-shell monomers. In N2...HF and N,...H,O the low-magnitude gain region between the Nz lone pair and the H atom losses is diagnostic for a weak complex with low charge transfer. These charge transfers (determined from Mulliken population analysis) are very small indeed: 0.005 and 0.0065 electrons for Nz...H20 and N,...HF, respectively (again in agreement with the finding of Benzel and Dykstra). This ultimately derives from the fact that the electron donor is a homonuclear diatomic. On the other hand, the charge shifts from hy528

drogen to the proton donor atom are an order of magnitude larger and more typical of stronger hydrogen bonds. The computed normal mode frequencies, table 4, show several interesting features. First, as shown by the comparison with monomer experimental numbers (and generally known from many other examples) the frequencies computed with the 4-3 1G and 6-3 lG* basis sets are almost uniformly 1OWhigher than experimental values. Second, as a consequence of the weak binding of our two complexes, frequency shifts from monomers to dimers are to higher frequencies. Third, the shift in the N2 stretch to higher frequency upon complexation can be understood as a charge transfer from its antibonding so* to the proton donor (the Nz lone pairs arise from the cancellation of the so and so* orbitals). Fourth, the up frequency shift upon complexation for the proton donors HF and HO is the opposite direction to that traditionally identified with hydrogen bonding and

CHEMICAL PHYSICS LETTERS

Volume 141, number 6 Table 4 4-3 I G and 6-3 lG* harmonic frequencies (cm- ’) RHF/4-3 1G/l RHF/4-31G

RHF/6-3 1G’// RHF/6-3 1G*

Nl...HlO

55.96 58.93 96.34 179.11 274.40 1753.32 2681.48 3973.49 4123.23

36.45 43.71 64.73 117.17 169.56 1830.29 2761.60 4077.78 4194.55

N>...HF

74.40 131.62 313.57 3 17.42 2686.54 4125.65

92.76 189.02(E) 2765.41 4356.49

Nz

2675.30

2757.76

2359

H20

1743.0 3958.4 4110.0

1826.93 4069.38 4187.48

1614.5 3693.8 3801.7

HF

4117.9

4358.63

4138.5

Exp.

37.50(E)

27 November 1987

estimated to be 0.55 kcal/mole) was calculated for the N2-water hydrogen bond in agreement with the simple model of Desmeules and Allen and indicating that the unexpectedly higher solubility of water in liquid nitrogen may be due to a hydrogen-bonding interaction. A few years ago, Flygare and co-workers [ 91, developed a pulsed nozzle expansion technique synchronized with a Fabry-Perot microwave cavity that makes it possible to get highly resolved rotational spectra for weak complexes of the sort discussed here. It is to be hoped that investigators will employ this method to measure properties of the Nz...H20 bond.

=I00

Acknowledgement

is clearly an important phenomenon that demands an explanation. It is a direct result of the unusually small charge transfer. It is charge transfer that is responsible for lowering the proton potential well and elongating the bond between H and the proton donor atom. However, as noted above, a large charge shift is present which increases the strength of this bond and the magnitude of its bond dipole (as seen from table 2 the change in the length of the HF and HO bonds upon complexation is negligible and thus the covalent contribution to these bonds is not being lowered as the ionic contribution is being raised). The increase in the strengths of the HF and HO bonds accounts for the majority of the binding energy of the complexes. Fifth, the IR intensity enhancement is a measure of the change in dipole moment with the normal mode stretching coordinate and the sign of the changes in the bond dipole are compatible with an enhancement. Its magnitude of 2.9 is several times smaller than many stronger hydrogen bonds because appreciable charge transfer is lacking. In conclusion, a Devalue of 1.2 kcal/mole (Dois

The authors wish to acknowledge the financial support of the US Army, ARDEC, Dover, New Jersey, grant DAAA2 l-86C-0101 and the ONR, grant NOO14-86-K-0557.

References [ 11 R. Rebiai, A.J. Rest and R.G. Scurlock, Nature 305 (1983) 412. [ 2) C. Beduz, R. Rebiai and R.G. Scurlock, Proc. ICEC, Japan 9 (1982) 802. [3] L.C.Allen, J.Am. Chem.Soc. 97 (1975) 6921. [4] M.A. Benzel and C.E. Dykstra, J. Chem. Phys. 78 (1983) 4052. [5] P.D. Soper, AC. Legon, W.G. Read and W.H. Flygare, J. Chem. Phys. 76 (1982) 292. [6] D.W. Schwenke and D.G. Truhlar, J. Chem. Phys. 82 ( 1985) 2418. [ 71 M.J. Frisch, J.A. Pople and J.E. de1 Bene, J. Chem. Phys. 78 (1983) 4063. [8] PI. Desmeules and L.C. Allen, J. Chem. Phys. 72 (1980) 4731. [9] T.J. Balle, E.J. Campbell, M.R. Keenan and W.H. Rygare, J. Chem. Phys. 71 (1979) 2723; 72 (1980) 922; AC Legon, P.D. Soper, M.R. Keenan, T.K. Minton, T.J. Balle and W.H. Flygare, J. Chem. Phys. 73 (1980) 583; A.C. Legon, P.D. Soper and W.H. Flygare, J. Chem. Phys. 74 (1981) 4944; T.J. Balle and W.H. Flygare, Rev. Sci. Instr. 52 (1981) 33; M.R. Keenan, T.K. Minton, A.C. Lcgon, T.J. Balle and W.H. Flygare, Proc. Natl. Acad. Sci. 77 (1980) 5583.

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