Anharmonic Effects in Ammonium Nitrate and Hydroxylammonium

Jan 3, 2007 - The covalent and ionic clusters of ammonium nitrate and hydroxyl ammonium nitrate are characterized using density functional theory and ...
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J. Phys. Chem. B 2007, 111, 4653-4658

4653

Anharmonic Effects in Ammonium Nitrate and Hydroxylammonium Nitrate Clusters† Malika Kumarasiri, Chet Swalina, and Sharon Hammes-Schiffer* Department of Chemistry, 104 Chemistry Building, PennsylVania State UniVersity, UniVersity Park, PennsylVania 16802 ReceiVed: August 28, 2006; In Final Form: October 26, 2006

The covalent and ionic clusters of ammonium nitrate and hydroxyl ammonium nitrate are characterized using density functional theory and second-order vibrational perturbation theory. The most stable structures are covalent acid-base pairs for the monomers and ionic acid-base pairs for the dimers. The hydrogen-bonding distances are greater in the ionic dimers than in the covalent monomers, and the stretching frequencies are significantly different in the covalent and ionic clusters. The anharmonicity of the potential energy surfaces is found to influence the geometries, frequencies, and nuclear magnetic shielding constants for these systems. The inclusion of anharmonic effects significantly decreases many of the calculated vibrational frequencies in these clusters and improves the agreement of the calculated frequencies with the experimental data available for the isolated neutral species. The calculations of nuclear magnetic shielding constants for all nuclei in these clusters illustrate that quantitatively accurate predictions of nuclear magnetic shieldings for comparison to experimental data require the inclusion of anharmonic effects. These calculations of geometries, frequencies, and shielding constants provide insight into the significance of anharmonic effects in ionic materials and provide data that will be useful for the parametrization of molecular mechanical force fields for ionic liquids. Anharmonic effects will be particularly important for the study of proton transfer reactions in ionic materials.

I. Introduction The physical properties of hydrogen-bonded acid-base complexes impact a wide range of materials. One example is room temperature ionic liquids, which are typically defined to be organic salts that melt below 100 °C.1-3 Ionic liquids have many potential technological applications because of their low vapor pressure, versatility, and environmentally benign nature. Protic ionic liquids, which are formed by proton transfer between acids and bases, are potentially relevant to high temperature fuel cell applications.4 Although not room temperature ionic liquids, ammonium nitrate (AN) and hydroxylammonium nitrate (HAN) serve as useful model systems for the development of methods to study the properties of ionic liquids. AN has been used as a solid oxidizer in rocket propulsion fuels,5,6 and HAN has been used in liquid propellants.7,8 Understanding the fundamental properties of these ionic materials will provide the foundation for future studies of ionic liquids. A topic of particular interest is the role of proton transfer reactions in hydrogen-bonded acid-base complexes. Hydrogen tunneling and coupling between heavy atom motions and the transferring proton are expected to be important in these types of reactions. A variety of theoretical studies have investigated the role of proton transfer reactions in hydrogen-bonded acid-base complexes. Thompson and co-workers used density functional theory and ab initio MP2 theory to study proton transfer in gas phase clusters of ammonium nitrate,9 ammonium dinitramide,10 and hydroxylammonium nitrate.11 In addition, Morokuma and coworkers studied ammonium dinitramide clusters at both the RHF and the MP2 levels.12 The calculations on single acid-base pairs in the gas phase indicate that the hydrogen-bonded, neutral

acid-base pair is the only stable structure (i.e., the ionic pairs are not stable) at correlated levels of theory. The ionic dimers (i.e., two ionic acid-base pairs) are stable minima on the correlated potential energy surfaces. Thus, the properties of ionic dimers are expected to be more relevant to bulk ionic materials. In addition to these studies, Schmidt, Gordon, and Boatz performed calculations on proton transfer in triazoliumdinitramide ion pairs.13 Guillot and Guissani performed onephase and two-phase molecular dynamics simulations to study the impact of proton transfer on the phase behavior of ammonium chloride (NH4Cl).14 They determined that the existence of both ionic and covalent species in the liquid phase influences the melting process. The objective of this paper is to characterize covalent and ionic clusters of ammonium nitrate (NH4+NO3-) and hydroxyl ammonium nitrate (HONH3+NO3-). We perform density functional theory calculations of the isolated neutral and ionic components, the covalent monomers, and the ionic dimers. In each case, we use the second-order vibrational perturbation theory (VPT2) to calculate the frequencies and geometries. This approach leads to more accurate frequencies and geometries than previous calculations of frequencies directly from the Hessian because the anharmonic effects are included. We also calculate the anharmonic effects on the nuclear magnetic shielding constants for nitrogen, oxygen, and hydrogen nuclei in the covalent monomers and ionic dimers. All of these calculations provide insight into the significance of anharmonic effects in ionic materials and provide data that will be useful for the parametrization of molecular mechanical force fields for ionic liquids and other ionic materials. II. Methods

†

Part of the special issue “Physical Chemistry of Ionic Liquids”. * To whom correspondence should be addressed. E-mail: shs@ chem.psu.edu.

All of the calculations were performed with density functional theory (DFT) using the B3LYP functional15-17 and the

10.1021/jp065569m CCC: $37.00 © 2007 American Chemical Society Published on Web 01/03/2007

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Figure 1. Optimized geometry for the covalent monomer AN with Cs symmetry. Hydrogen bonds are indicated by dashed lines. The hydrogen-bonding distances are given in Angstroms for the vibrationally averaged and equilibrium geometries, where the equilibrium distances are given in parentheses.

Figure 3. Optimized geometry for the ionic dimer (AN)2 with C2h symmetry. Hydrogen bonds are indicated by dashed lines. The hydrogen-bonding distances are given in Angstroms for the vibrationally averaged and equilibrium geometries, where the equilibrium distances are given in parentheses.

Figure 2. Optimized geometry for the covalent monomer HAN with Cs symmetry. Hydrogen bonds are indicated by dashed lines. The hydrogen-bonding distances are given in Angstroms for the vibrationally averaged and equilibrium geometries, where the equilibrium distances are given in parentheses.

6-311++G(d,p) basis set18,19 with the Gaussian 03 package.20 We used a pruned (99 770) grid for the numerical integrations. We calculated the frequencies on the basis of the harmonic approximation directly from the Hessian and the frequencies including anharmonic effects with the VPT2 method. In the VPT2 method, the zeroth-order vibrational wave functions are generated from the harmonic approximation, and the secondorder perturbation theory corrections are calculated from the cubic force constants and semidiagonal quartic force constants. The required cubic and quartic force constants are obtained by numerical differentiation of the analytical Hessians. The VPT2 method has been implemented by Barone21,22 in the Gaussian 03 package.20 We calculated the anharmonic contribution to the vibrationally averaged isotropic nuclear magnetic shielding constants for all nuclei by comparing shielding constants evaluated at the equilibrium and vibrationally averaged geometries. The gauge independent atomic orbital (GIAO) approach23 was used to calculate the nuclear magnetic shielding constants. This approach accounts specifically for the contribution to the shielding constants arising from the anharmonicity of the potential energy surface. Additional zero-point vibrational effects could be calculated from the curvature of the surface corresponding to the shielding constant and the harmonic frequencies,24-26 but such calculations are beyond the scope of this work. III. Results As observed previously for AN and HAN,9,11 the only stable structures for the monomers are hydrogen-bonded, neutral acid-

Figure 4. Optimized geometry for the ionic dimer (HAN)2 with C2 symmetry. Hydrogen bonds are indicated by dashed lines. The hydrogen-bonding distances are given in Angstroms for the vibrationally averaged and equilibrium geometries, where the equilibrium distances are given in parentheses.

base pairs, whereas the structures corresponding to two ionic acid-base pairs are the global minima for the dimers. The optimized geometries for the monomers and dimers of AN and HAN are shown in Figures 1-4. The AN and HAN monomers have Cs symmetry, the (AN)2 dimer has C2h symmetry, and the (HAN)2 dimer has C2 symmetry. The hydrogen-bonding distances are given for both the vibrationally averaged and the equilibrium structures. The vibrationally averaged structure is obtained by averaging the coordinates over the nuclear vibrational wave function calculated with the VPT2 method. Thus, the vibrationally averaged structures include anharmonic effects. As expected, the bond lengths for the bonds between the donor atoms and the hydrogen atoms increase when the anharmonic effects are included. For the structures given in Figures 1-3, the distance between the hydrogen atom and the donor atom increases and the distance between the hydrogen atom and the acceptor atom decreases in each hydrogen bond when anharmonic effects are included. The hydrogen bonding in the (HAN)2

Anharmonic Effects in AN and HAN Clusters

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TABLE 1: Frequencies (in cm-1) of Vibrational Modes in the Isolated Neutral Species species

label

description

NH3

V1(a1) V2(a1) V3(e) V4(e) V1(a′) V2(a′) V3(a′) V4(a′) V5(a′) V6(a′) V7(a′′) V8(a′′)

sym. stretch sym. bend asym. stretch asym. bend OH stretch NO asym. stretch NO sym. stretch NOH bend NO(OH) stretch ONO bend ONO(OH) bend N out-ofplane bend OH torsion OH stretch NH stretch HNH bend NOH bend NH2 wag NO stretch NH stretch NH2 twist OH torsion

HNO3

V9(a′′) HONH2 V1(a′) V2(a′) V3(a′) V4(a′) V5(a′) V6(a′) V7(a′′) V8(a′′) V9(a′′)

experimental frequencya,b,c harmonic VPT2 3337 950 3444 1627 3550 1709 1326 1304 878 647 580 763

3480 1006 3607 1669 3727 1756 1349 1320 897 649 587 773

3339 902 3440 1619 3548 1711 1319 1294 875 633 575 762

458 3650 3294 1604 1353 1115 895 3359 1294 386

461 3824 3448 1673 1390 1135 927 3528 1328 442

446 3631 3286 1609 1337 1096 900 3342 1286 419

a The experimental frequencies for NH3 are from ref 30. b The experimental frequencies for HNO3 are from refs 31-34. c The experimental frequencies for HONH2 are from ref 35.

TABLE 2: Frequencies (in cm-1) of Vibrational Modes in the Isolated Ionic Species species ΝΗ4+ a

ΝΟ3-

HONH3+

label

description

harmonic

VPT2

V1(a1) V2(e) V3(t) V4(t) V1(a′) V2(a′′) V3(e′) V4(e′′) V1(a′) V2(a′) V3(a′) V4(a′) V5(a′) V6(a′) V7(a′) V8(a′) V9(a′′) V10(a′′) V11(a′′) V12(a′′)

sym. stretch twist asym. stretch asym. bend sym. stretch N out-of-plane bend asym. stretch ONO asym. bend OH stretch NH stretch NH stretch HNH bend NH3 umbrella mode NOH bend NH3 wag NO stretch NH stretch HNH bend NH3 twist HONH torsion

3372 1727 3475 1489 1066 835 1378 709 3698 3426 3328 1640 1592 1476 1152 1016 3400 1639 1193 315

1044 825 1344 699 3523 3254 3202 1586 1542 1404 1126 981 3229 1591 1157 258

a The VPT2 method is not applicable to ΝΗ4+ because it behaves as a spherical top.

dimer shown in Figure 4 is more complex because one of the oxygen atoms on each ΝΟ3- moiety serves as the acceptor for two hydrogen bonds. The calculated frequencies for the isolated neutral and ionic species are given in Tables 1 and 2, respectively. The experimental frequencies for the isolated neutral species are also provided in Table 1. A comparison of the frequencies calculated with the VPT2 method to the experimental data enables us to benchmark the VPT2 method for these types of systems. As shown in Table 1, the frequencies obtained with the VPT2 method are in better agreement with the gas phase experimental data than those obtained with the conventional harmonic approach. These results illustrate the importance of anharmonic

TABLE 3: Frequencies (in cm-1) of Vibrational Modes in the Covalent Monomer AN label

description

harmonic

VPT2

V1(a′) V2(a′) V3(a′) V4(a′) V5(a′) V6(a′) V7(a′) V8(a′) V9(a′) V10(a′) V11(a′) V12(a′) V13(a′) V14(a′) V15(a′′) V16(a′′) V17(a′′) V18(a′′) V19(a′′) V20(a′′) V21(a′′)

NH3 asym. stretch NH3 sym. stretch OH stretch NO asym. stretch NH3 asym. bend NOH bend NO sym. stretch NH3 sym. bend NO(OH) stretch ONO bend ONO(OH) bend NH3 in-plane rotation NHO stretch NHO in-plane bend NH3 asym. stretch NH3 asym. bend NH3 out-of-plane torsion N out-of-plane bend OH torsion

3586 3472 2732 1733 1656 1511 1326 1151 953 691 660 430 248 106 3592 1668 1097 791 339 73 61

3416 3326 2266 1675 1629 1459 1290 1099 940 680 645 424 235 90 3420 1632 1051 782 349 68

TABLE 4: Frequencies (in cm-1) of Vibrational Modes in the Covalent Monomer HAN label

description

harmonic

VPT2

V1(a′) V2(a′) V3(a′) V4(a′) V5(a′) V6(a′) V7(a′) V8(a′) V9(a′) V10(a′) V11(a′) V12(a′) V13(a′) V14(a′) V15(a′) V16(a′) V17(a′′) V18(a′′) V19(a′′) V20(a′′) V21(a′′) V22(a′′) V23(a′′) V24(a′′)

OH(HONH2) stretch NH sym. stretch OH(HNO3) stretch ONO stretch HNH bend NOH(HNO3) bend NOH(HONH2) bend ONO stretch NH2 wag NO(HONH2) stretch NO(HNO3) stretch ONO bend ONO bend HONH2 in-plane wag NHO stretch

3682 3448 2660 1740 1665 1533 1487 1313 1191 984 963 698 655 271 200 163 3519 1320 1089 786 558 370 81 42

3480 3286 2106 1683 1605 1487 1442 1273 1164 953 937 687 643 26 190 147 3335 1274 1060 779 544 372 79 46

NH asym. stretch NH2 twist OH(HNO3) torsion N out-of-plane bend OH(HONH2) torsion NH2 twist

effects. In some cases, the anharmonic effects decrease the frequency by ∼200 cm-1, significantly improving the agreement with experiment. A more standard approach to account for vibrational anharmonicity in electronic structure calculations is to scale the calculated harmonic frequencies by an empirical scaling factor. The empirical scaling factor for the B3LYP DFT method with similar basis sets has been determined to be ∼0.96-0.97.27,28 While this empirical scaling procedure leads to qualitatively reasonable frequencies, Tables 1 and 2 indicate that the VPT2 method is more quantitatively accurate. The calculated frequencies for the covalent monomers and the ionic dimers of AN and HAN are given in Tables 3-6. The inclusion of anharmonic effects significantly decreases the frequencies of the vibrational modes in all of these clusters, particularly for the NH and OH stretching modes. The largest effects were observed for the NH and OH stretching modes involved in hydrogen-bonding interactions. The NH and OH stretching frequencies (i.e., ν2-4, 29-32) are decreased by up to

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TABLE 5: Frequencies (in cm-1) of Vibrational Modes in the Ionic Dimer (AN)2 label

description

harmonic

VPT2

label

description

harmonic

VPT2

V1(ag) V2(ag) V3(ag) V4(ag) V5(ag) V6(ag) V7(ag) V8(ag) V9(ag) V10(ag) V11(ag) V12(ag) V13(ag) V14(au) V15(au) V16(au) V17(au) V18(au) V19(au) V20(au) V21(au) V22(au) V23(au) V24(au)

NH asym. stretch NH(H-bonded) sym. stretch NH4+ twist NH4+ twist NH4+ asym. bend NO(H-bonded) asym. stretch NO3- sym. stretch N out-of-plane bend ONO asym. bend NH4+ wag breathing

3504 2943 1752 1726 1510 1309 1028 828 715 416 304 131 41 3503 2899 1751 1706 1518 1498 733 404 283 76 65

3332 1839 1680 1567 1443 1272 1001 814 701 364 291 126 30 3338 2554 1682 1617 1483 1436 721 374 270 73 65

V25(bg) V26(bg) V27(bg) V28(bg) V29(bg) V30(bg) V31(bg) V32(bg) V33(bg) V34(bg) V35(bg) V36(bu) V37(bu) V38(bu) V39(bu) V40(bu) V41(bu) V42(bu) V43(bu) V44(bu) V45(bu) V46(bu) V47(bu) V48(bu)

NH asym. stretch NH(H-bonded) asym. stretch NH4+ asym. bend NO3- asym. stretch NH4+ asym. bend ONO asym. bend NH4+ wag NH4+ wag

3577 2782 1623 1496 1361 723 436 311 178 105 72 3577 2913 1621 1404 1281 1025 828 714 463 332 254 100 33

3405 2292 1550 1460 1294 710 411 288 140 98 64 3402 2482 1541 1349 1235 996 812 700 463 311 201 99 22

NH asym. stretch NH(H-bonded) sym. stretch NH4+ twist NH4+ twist NO3- asym. stretch NH4+ asym. bend ONO asym. bend NH4+ wag

NH asym. stretch NH(H-bonded) asym. stretch NH4+ asym. bend NH4+ asym. bend NO(H-bonded) asym. stretch NO3- sym. stretch N out-of-plane bend ONO asym. bend NH4+ wag NH4+ wag

TABLE 6: Frequencies (in cm-1) of Vibrational Modes in the Ionic Dimer (HAN)2 label

description

harmonic

VPT2

label

description

harmonic

VPT2

V1(a) V2(a) V3(a) V4(a) V5(a) V6(a) V7(a) V8(a) V9(a) V10(a) V11(a) V12(a) V13(a) V14(a) V15(a) V16(a) V17(a) V18(a) V19(a) V20(a) V21(a) V22(a) V23(a) V24(a) V25(a) V26(a) V27(a) V28(a)

NH stretch OH stretch NH(H-bonded) stretch NH(H-bonded) stretch HNH bend NH3 umbrella mode HNH bend NOH bend NO(NO3) asym. stretch NH3 wag NH3 twist NH3 wag NO(NO3) sym. stretch NO(HONH3) stretch N out-of-plane bend OH(HONH3) twist ONO bend ONO bend NH3 twist breathing

3520 3307 3013 2836 1715 1633 1604 1583 1499 1310 1293 1219 1043 1031 828 802 728 707 458 286 233 177 145 124 111 71 52 30

3350 3096 2576 2355 1609 1587 1543 1525 1465 1269 1244 1188 1019 996 806 733 715 689 442 274 205 154 140 126 102 62 39 12

V29(b) V30(b) V31(b) V32(b) V33(b) V34(b) V35(b) V36(b) V37(b) V38(b) V39(b) V40(b) V41(b) V42(b) V43(b) V44(b) V45(b) V46(b) V47(b) V48(b) V49(b) V50(b) V51(b) V52(b) V53(b) V54(b)

NH stretch OH stretch NH(H-bonded) stretch NH(H-bonded) stretch HNH bend HNH bend NOH bend NH3 umbrella mode NO(NO3) asym. stretch NH3 wag NH3 twist NH3 wag NO(NO3) sym. stretch NO(HONH3) stretch N out-of-plane bend OH(HONH3) twist ONO bend ONO bend NH3 twist

3519 3318 3017 2881 1709 1626 1607 1577 1520 1311 1280 1220 1037 1029 826 782 726 701 460 289 256 190 151 133 115 48

3350 3039 2640 2460 1623 1566 1591 1527 1481 1273 1239 1186 1012 995 811 724 712 675 446 280 240 169 148 130 107 53

∼500 cm-1 in (HAN)2. Moreover, the ΝΗ4+ symmetric stretch frequency, ν2, is decreased by ∼1000 cm-1 in (AN)2. In these cases, the application of the empirical scaling factor leads to substantial errors in the predicted frequencies. In addition to providing the frequencies for all modes in the clusters, Tables 3-6 provide descriptions of the modes that are relatively localized with definitive character. The remaining modes are not straightforward to characterize. For the ionic dimers, we identified a mode corresponding to an intermolecular breathing mode, which corresponds to ν11 in (AN)2 and ν20 in (HAN)2. These breathing modes are associated with relatively low frequencies of ∼300 cm-1.

The nuclear magnetic shielding constants for all nuclei in the covalent monomers and the ionic dimers of AN and HAN are given in Tables 7-10. For both monomers, the shieldings for the oxygen nuclei involved in hydrogen-bonding interactions are influenced more by anharmonic effects than the other oxygen nuclei. For both dimers and the AN monomer, the shieldings for the nitrogen nuclei involved in hydrogen-bonding interactions are influenced more by anharmonic effects than the other nitrogen nuclei. For both monomers and (AN)2, the magnitude of the shift of the shieldings due to anharmonic effects is similar for all of the hydrogen nuclei, but the direction of this shift is different for the hydrogen nuclei involved in hydrogen bonds.

Anharmonic Effects in AN and HAN Clusters

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TABLE 7: Nuclear Magnetic Shielding Constants for ANa,b atom

σeq

σeq - σvib

1N 2O 3O 4O 5N 6H 7,8H 9H

-116.6324 -73.7641 -189.1048 -211.7382 242.2423 14.1399 30.9618 30.4328

2.7692 10.0719 7.7809 4.6787 -15.1759 0.4162 -1.9366 -1.9017

a All shielding constants are given in ppm. σeq and σvib are the shieldings at the equilibrium and the vibrationally averaged geometries, respectively. b For reference, the nuclear magnetic shielding constant for H in TMS calculated at this level of theory is 31.9702.

TABLE 8: Nuclear Magnetic Shielding Constants for HANa,b atom

σeq

σeq - σvib

1N 2O 3O 4O 5O 6N 7H 8H 9H 10H

-114.9366 -78.2194 -172.1313 -216.7373 236.5382 141.3442 14.3767 26.0492 27.2008 27.2006

2.4143 9.0993 4.9056 2.7291 -1.9766 -2.1825 0.6096 -0.2386 -0.2030 -0.2032

a All shielding constants are given in ppm. σeq and σvib are the shieldings at the equilibrium and the vibrationally averaged geometries, respectively. b For reference, the nuclear magnetic shielding constant for H in TMS calculated at this level of theory is 31.9702.

TABLE 9: Nuclear Magnetic Shielding Constants for (AN)2a,b atom

σeq

σeq - σvib

6,11N 1,15N 8,9,10,13O 7,12O 3,4,14,16H 2,5,17,18H

-143.9728 224.5532 -187.3903 -129.3589 20.4853 28.5415

-0.5831 -1.8135 2.0320 2.1699 0.5080 -0.5431

a All shielding constants are given in ppm. σeq and σvib are the shieldings at the equilibrium and the vibrationally averaged geometries, respectively. b For reference, the nuclear magnetic shielding constant for H in TMS calculated at this level of theory is 31.9702.

For (HAN)2, the anharmonic effects on the shieldings for the hydrogen nuclei do not exhibit a clear trend because of the more complex hydrogen-bonding pattern. For reference, we also calculated the nuclear magnetic shielding constant for hydrogen in tetramethylsilane (TMS) at the same level of theory.29 This reference enables the calculation of chemical shifts that are experimentally observable. The nuclear magnetic shielding constants for other reference materials are also straightforward to calculate. These results indicate that the inclusion of anharmonic effects significantly alters the nuclear magnetic shielding constants. Thus, a quantitatively accurate prediction of chemical shifts for comparison to experimental data requires the inclusion of anharmonic effects. These calculations provide insight into several general features of covalent and ionic hydrogen-bonded clusters. As observed previously, the most stable structures for the monomers are covalent acid-base pairs, whereas the most stable structures for the dimers are ionic acid-base pairs. The hydrogen-bonding

TABLE 10: Nuclear Magnetic Shielding Constants for (HAN)2a,b atom

σeq

σeq - σvib

1,12N 6,16N 4,11O 2,14O 3,13O 5,19O 10,15H 7,17H 8,20H 9,18H

-142.7165 156.4747 -214.6025 -155.4694 -118.9725 208.0308 19.3276 20.7594 22.2187 26.7813

0.3727 2.0139 2.5519 1.3114 2.8498 3.4048 0.4135 0.3260 -0.0484 -0.0224

a All shielding constants are given in ppm. σeq and σvib are the shieldings at the equilibrium and the vibrationally averaged geometries, respectively. b For reference, the nuclear magnetic shielding constant for H in TMS calculated at this level of theory is 31.9702.

distances are greater in the ionic dimers than in the covalent monomers. Although the hydrogen-bonding distances might be expected to be shorter for the charged species, the observed trend arises in part because the nitrogen and oxygen atoms are involved in multiple competing hydrogen-bonding interactions in the dimers. In addition, the frequencies undergo substantial qualitative shifts from the covalent monomers to the ionic dimers. Although the direct correspondence between specific modes in the covalent and ionic complexes is not rigorous due to mixing among the many modes, some general trends are observed. As expected, the NH stretching frequencies in NH3 and NH4+ for AN and (AN)2, respectively, differ significantly. The NO symmetric and asymmetric stretching frequencies in NO3 also differ substantially between the covalent and ionic AN clusters. Furthermore, the intermolecular hydrogen-bonding stretching motion shifts from ν13 ) 235 cm-1 in AN to a breathing mode of ν11 ) 291 cm-1 in (AN)2. Similar trends in the frequencies are observed for HAN and (HAN)2, although the characterization of the modes is not as straightforward. In this case, the intermolecular hydrogen-bonding stretching motion shifts from ν15 ) 190 cm-1 in HAN to a breathing mode of ν20 ) 274 cm-1 in (AN)2. The quantitative study of these changes in the structures and vibrational frequencies requires the inclusion of anharmonic effects. IV. Conclusions In this paper, we characterized the covalent and ionic clusters of ammonium nitrate and hydroxyl ammonium nitrate using density functional theory and second-order vibrational perturbation theory. These clusters exhibit strong hydrogen-bonding interactions. Our calculations confirmed that the most stable structures are covalent acid-base pairs for the monomers and ionic acid-base pairs for the dimers. The hydrogen-bonding distances were found to be greater in the ionic dimers than in the covalent monomers in part because the nitrogen and oxygen atoms are involved in multiple competing hydrogen-bonding interactions in the dimers. We also observed significant shifts in the stretching frequencies from the covalent monomers to the ionic dimers. Moreover, we identified an intermolecular hydrogen-bonding stretching motion of ∼200 cm-1 in the monomers that shifts to an intermolecular breathing motion of slightly higher frequency of ∼300 cm-1 in the dimers. Our calculations illustrate that the anharmonicities of the potential energy surfaces influence the geometries, frequencies, and nuclear magnetic shieldings for these systems. The inclusion of anharmonic effects was found to significantly decrease many of the calculated frequencies in these clusters and to improve

4658 J. Phys. Chem. B, Vol. 111, No. 18, 2007 the agreement of the calculated frequencies with the experimental data available for the isolated neutral species. Our results also indicate that the anharmonic effects should be included in calculations of nuclear magnetic shielding constants for these types of systems to ensure quantitatively accurate predictions for comparison to experimental data. Furthermore, the consideration of anharmonic effects in the development of molecular mechanical force fields will be important for simulations of proton transfer reactions in ionic liquids and other ionic materials. Acknowledgment. We gratefully acknowledge the support of AFOSR Grant No. FA9550-04-1-0062. We also thank Mike Pak and Ari Chakraborty for helpful discussions. References and Notes (1) Welton, T. Chem. ReV. 1999, 99, 2071. (2) Holbrey, J. D.; Seddon, K. R. J. Chem. Soc., Dalton Trans. 1999, 2133. (3) Brennecke, J. F.; Maginn, E. J. AIChE J. 2001, 47, 2384. (4) Yoshizawa, M.; Xu, W.; Angell, A. J. Am. Chem. Soc. 2003, 125, 15411. (5) Kondirkov, B. N.; Annikov, V. E.; Egorshev, V. Y.; DeLuca, L.; Bronzi, C. J. Propul. Power 1999, 15, 763. (6) Sinditskii, V. P.; Egorshev, V. Y.; Levshenkov, A. I.; Serushkin, V. V. Propellants, Explos., Pyrotech. 2005, 30, 269. (7) Lee, H.; Litzinger, T. A. Combust. Flame 2001, 127, 2205. (8) Lee, H.; Litzinger, T. A. Combust. Flame 2003, 135, 151. (9) Alavi, S.; Thompson, D. L. J. Chem. Phys. 2002, 117, 2599. (10) Alavi, S.; Thompson, D. L. J. Chem. Phys. 2003, 118, 2599. (11) Alavi, S.; Thompson, D. L. J. Chem. Phys. 2003, 119, 4274. (12) Mebel, A. M.; Lin, M. C.; Morokuma, K.; Melius, C. F. J. Phys. Chem. 1995, 99, 6842. (13) Schmidt, M. W.; Gordon, M. S.; Boatz, J. A. J. Phys. Chem. A 2005, 109, 7285. (14) Guillot, B.; Guissani, Y. J. Chem. Phys. 2002, 116, 2047. (15) Lee, C.; Yang, W.; Parr, P. G. Phys. ReV. B 1988, 37, 785. (16) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (17) Stephens, P. J.; Devlin, F. J.; Chablowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623. (18) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980, 72, 650.

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