Periodic Hartree-Fock study of nitric acid monohydrate crystal: bulk

Jul 1, 1993 - Frank E. Livingston and Steven M. George. The Journal of Physical Chemistry B 1999 103 (21), 4366-4376. Abstract | Full Text HTML | PDF ...
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J. Phys. Chem. 19!J3,97,7295-7303

7295

Periodic Hartree-Fock Study of Nitric Acid Monohydrate Crystal: Bulk and Clean Surface R. D. Poshusta and D. C. Tseng Chemistry Department and Materials Science Program, Washington State University, Pullman, Washington 99164-4630

Anthony C. Hess and Maureen 1. Maartby' Molecular Science Research Center (MS KI -9O),Pacific Northwest Laboratory, Richland, Washington 99352 Received: January 14, 1993; In Final Form: March 31, I993

This study reports the first quantum mechanical investigation of crystalline nitric acid monohydrate (NAM), HNO30H20. The goal of this work is to characterize the physical properties of NAM in order to better understand its role as a catalyst in the destruction of polar stratospheric ozone in the Antarctic. The computations probed energetic, electronic, and elastic properties of the crystalline material using the Periodic Hartree-Fock (PHF) method (as implemented in the program CRYSTAL92). All calculations were performed by using standard Pople basis sets. A description of the bulk material was obtained from calculations of the estimated cohesive binding energy, optimized lattice constants, band structure, total and projected density of states, Mulliken population analysis, electrostatic potentials, and elastic constants. The computed intracrystal interactions are consistent with the proposed hydronium/nitrate ionic crystal structure inferred from X-ray diffraction data. The calculated elastic constants, interlayer electrostatic potential maps, and characterization of the bonding in the crystal indicate that NAM is composed of weakly bound puckered layers aligned parallel to the (100) plane in the crystal. Accordingly, a surface that exposes such a puckered layer would be expected to have the minimum surface energy. The properties of this surface were studied by using a model system that consists of a two-layer slab of NAM formed by cleaving along the (100) direction in the crystal. This computational model represents a finite-thickness thin film that is periodic in two dimensions and finite along the remaining coordinate. A comparison is made between the computed properties of the bulk material and the model (100) N A M surface. Maps of the electrostatic potential above and within the slab are used to predict favorable sites for physisorption on the (100) surface of N A M crystals. These sites may be important regions for surface catalysis.

I. Introduction This is the first quantum mechanical investigationof crystalline nitric acid monohydrate (NAM), HNOrH20 (or H,O+.NO,-). It is motivated by the presumed role of hydrated nitric acid crystals in the depletion of Antarctic stratosphereozone-the "ozone hole". Several mechanisms have been proposed to account for reduced ozone concentrations observed in the lower stratosphere during the Antarctic spring.l-I1 It is widely believed that ozone is catalytically destroyed in reactions involving one or more of the active molecules, atomic chlorine C1, chlorine hydroxide HOCl, chlorine oxide C10, or its dimer and, to a lesser extent, with the analogous bromine compounds. These species are produced (at least in part) by the photolysis of chlorofluorocarbons in the stratosphere. A crucial step in the process occurs during the winter when C12, HOCl, and ClNO2 are regenerated from two principal inactive chlorinereservoir molecules, HC1and ClONO2. This regeneration occurs through reactions 1-3:

--

+ ClONO, ClONO, + H,O HCl

N,O,

+ HCl

N205

-.+

HNO,+ C1,

+ HNO, + HNO,

HOCl

ClNO,

+ H2O

+

2HNO3

(1)

(2) (3) (4)

These reactions are known to occur during the polar winter in the presence of polar stratospheric clouds (PSCs).1J2-14 Two types of PSCs have been observed. The most common PSC is type I, which is mainly composed of solid nitric acid hydrate compounds. The most prevalent of these species are nitric acid trihydrates (NAT), which have an H20:HNOa composition of around 3. Nitric acid hydrates-mostly the trihydrate (NAT) and to a 0022-3654/93/2097-7295S04.00/0

lesser extent the monohydrate (NAM) and amorphous solid forms-readily nucleate on H2SO4 aerosols to form the catalytically reactive surfaces of the Antarctic PSCs.lS-18 The type I1 PSCs are composed of ice (H20(s)) and exist at colder temperatures? Reactions 1-3 are heterogeneous reactions that are assumed to take place on the crystalline surfaces of the PSCs. They result in the production of the active chlorine species, Cl2, HOCl, and ClNO2. With the onset of the polar spring, these species are photolyzed to form C1 and C10, which react directly with ozone. In addition, the PSCs retain H N 0 3 in a condensed form, which reduces the NO, levels in the gas phase (see eq 4). This results in the suppression of the sink mechanisms for ozone destruction (e.g., reactions of active C10 with NO2 to produce inactive ClON02) and hence permit increased ozone depletion. Although the exact role that PSCs play in the ozone destruction is still being investigated with laboratory and field measurements, it is apparent that the crystal surfaces of the stratosphericclouds and the heterogeneous chemical mechanisms they facilitate are crucially important for ozone d e p l e t i ~ n . ~ , * J ~ J ~ J ~ ~ ~ ~ An accurate description of the structure of the hydrated nitric acid crystals is essential to understanding the mechanics of stratosphericchlorinechemistry. Both the mono- and trihydrated nitric acid crystals were isolated by Pickering21.22 and the crystal structureswere determined by Delaplane, Taesler, and Olovsson.u Recent experiments have studied the phase equilibria and vapor pressures16pl7 and the infrared spectraI2~24.25of NAM and NAT. However, the structures of the stable growth faces of NAT and NAM have not been fully characterized by experiments. In addition, the catalytic surface sites have not been identified and the sticking coefficients for HCl (or HOCl etc.) on NAM (or Q 1993 American Chemical Society

Poshusta et al.

7296 The Journal of Physical Chemistry, Vol. 97, No. 28, 1993

NAT) have not been measured. However, a rough estimate of the sticking and uptake coefficients for these hydrated crystals may be made from the empirical data on ice.ZC2* This is the first paper in a series that will report results of investigations of the bulk, clean surface, and adsorbate/surface properties of NAM and NAT. This paper presents results of an ab initio quantum mechanical study of the energetics and physical properties of NAM. The calculations are based on periodic HartreeFock (PHF) theory and results are reported for the bulk and clean (100) surface of NAM. Initial studies were conducted on NAM because it contains fewer atoms in the unit cell than NAT (NAM, 32 atoms/unit cell, and NAT, 56 atoms/unit cell) and is, therefore, a computationally more tractable problem. Similar investigations have been done on NAT,*9 which is the more prevalent constituent of the PSCs. The NAM study does, however, provide a general understanding of the nature of nitric acid hydrates and it is anticipated that many of the results can be used to predict the behavior of NAT. The next paper in this series will examine the energetics of HC1 adsorption on the (100) surface of NAM and a future publication will include a comparison of the physical properties of NAM and NAT. 11. Theoretical Method

Periodic Hartree-Fock (PHF) theory, as implemented in the program CRYSTAL92?0-32 provides self-consistent field solutions to the Hartree-Fock-Roothaan equations subject to periodic boundary conditions. Details of the theory and method have been described earlier.32.33 This theory provides an accurate means to investigate the electronic structure of crystalline materials through the rigorous inclusion of full space group symmetry and periodic boundary conditions. Previous applications of the PHF method, using CRYSTAL, have treated ionic, covalent, and mixed ionic and covalent crystals.34-39 The method has also been used to study hydrogen-bonded molecular crystalsM and adsorbate/ surface interactions.41 A host of crystalline properties can be computed by using CRYSTAL.32J3 In this study, the elastic constants and optimization of the lattice parameters of NAM were obtained by monitoring changes in the total crystalline energy as a function ofgeometry. Physical properties, such as electrostatic potentials, Mulliken analyses, band structure, and total and projected density of states, were computed from the NAM ground-state wave function. Electrostatic potential maps probe the electronic charge distribution in a crystal and are used here to describe the bonding in NAM bulk and to predict chemically reactive sites on the surface. Insight into the nature and strength of the interatomic and intermolecular (or interionic) bonding in NAM is inferred from the calculated elastic constants of the bulk material. Comparisons are made between computed values and empirical data for the lattice constants and cohesive binding energy, but the reported theoretical elastic stiffness constants, band structure, and density of states have yet to be measured experimentally. In the absence of an experimental characterization of the growth surfaces of NAM (and NAT), it was decided that the surface calculations would be done on a slab with the lowest expected energy of formation (100). This prediction was based on calculations of the elastic constants and examination of the crystal structure. In this study, standard Pople values of orbital exponents and contraction coefficients are used for all basis functions (3-21, 6-21,6-21*, and 6-31**). Single-point calculations of the total energy, wave function, and selected physical properties were performed by using each basis and with the NAM crystal fixed at its experimentally determined geometry. Computations of the elastic constants required calculations at several geometries and were performed only by using the 6-21 basis. CPU timings for single-point calculations on a SGI 4D-35 were about 31 000 s in the 6-21 basis and 180 000 s in the 6-31G** basis. In the

TABLE I: Geometry Specifications. atom x, A Y,A z,A a. BulkNAMO 0.29642 0.0957 0.00000 0.22815 0.01844 0.17467 0.28346 0.04598 -0.2159 0.38406 0.22397 0.04424 0.44001 0.26163 -0.49246 0.383 0.352 -0.457 0.387 0.179 -0.4 16 0.415 0.255 -0.665 b. Two-Layer Slab NAMb 0.000 0.0957 1.8469 0.500 0.5957 1.2685 0.8253 0.0184 1.3823 0.2159 0.0460 1.7662 0.9558 0.2240 2.3930 0.4925 0.2616 2.7416 0.3253 0.5184 1.7331 0.7159 0.5460 1.3492 0.4558 0.7240 0.7224 0.9925 0.7616 0.3738 0.4570 0.3520 2.3864 OA160 0.1790 2.4113 0.6650 0.2550 2.5858 0.9570 0.8520 0.7290 0.9160 0.6790 0.7041 0.1650 0.7550 0.5296 Lattice constants and fractional atomic positions of nitric acid monohydrate at 85 K. Note that we adopt the standard setting Pna21 instead of the nonstandard P21cn setting used in ref 23. Z = 4; (a&) = (6.2308 AJ.6439 AJ.4647 A). b Symmetry grou P2111. x and in fractions of the slab lattice constants, u' = 5.4647 6' = 8.6439 z in angstroms. @

8,

Bulk

Pna21

Nitrogen e Oxygen 0 Hydrogen

1,

p2,11

Figure 1. Structure of nitric acid monohydratecrystal. The bulk crystal setting is shown on the left and the projections are parallel to (b,c) and (a,b) planes. The two-layer slab symmetry group and coordinates are shown on the right and the projections are parallel to (a,b) and (b,z) planes.

6-31** basis 2.1 Gbytes of diskstorage were required for integral storage. The tolerance parameter^'^ used for the evaluation of the infinite Coulomb and exchange series in all of the reported calculations were (sc = t , = 5 ) and (sex = pcx= 5 andpiex= 10).

III. Results and Discussion A. Bulk NAM. Crystalline Structure. The structure of nitric acid monohydrate, which crystallizes into an orthorhombic lattice (mp -36 "C), has been characterized by X-ray crystallography23 and the coordinates are shown in Table I. Interatomic distances are consistent with a structure composed of nitrate and hydronium ions as suggested by the empirical formula H3O+*NO3-. Figure 1 shows projections of the NAM crystal onto two planes: (b,c) in Figure l a and (a,b) in Figure Ib, where a, b, and c denote the

Hartree-Fock Study of Nitric Acid

The Journal of Physical Chemistry, Vol. 97, No. 28, 1993 7297

TABLE II: Contributions to the Cohesive Binding Energy of NAM Bulk Calculated by Using PHF (CRYSTAL) with Four Different Basis Sets' basis 3-21

6-21

6-21,

6-31**

-816.1 25.6 691.1 -24.8

-823.4 26.7 751.8 -1 1.2

-703.0 7.5 672.6 -5.7

system NAM-4(NO,-+HoO+) -824.4 BSSE(NO3-+H30+) 27.4 4(NOa-+HsO+-HNO3-H20) 690.0 [ N A M - ~ ( H N O ~ + H Z O ) ] / ~ -26.7

a All species are at their respective experimental geometries. The energy difference NAM-4(NOn-+HNOa+) represents the stabilization when the isolated ions are arranged in the N A M lattice. BSSE is the approximate basis set superpositionerror in nitrate and hydronium ions due to the prcsencc of basis functionsonthe neighboring ions. The quantity O the energy to transfer a labeled by N O ~ - + H ~ O + - H N O ~ - H Zdenotes proton from HNO3 to H20 followed by geometry relaxation. The last row is the sum of preceding rows and represents our best estimate of the cohesive binding energy.

axes in an orthorhombic lattice. Each nitrate ion is hydrogen bonded to three neighboring hydroniums to form infinite planar tapes with the long axis parallel to the c axis. These tapes are inclined at approximately 60' and 30' to the a and b axes. Hydronium ionsjoin adjacent tapes into pleated sheets or puckered layers along the b axis. The pleats of neighboring sheets are nested along the a axis. In the present work, the structure is described and the computations are performed by using the standard setting Pnu21 of the space group (group No. 3342).The experimental results are reported in the nonstandard settingP2p1, related by the transformation (-c,b,u)std ( U , ~ , C ) ~ , , ~ ~hence ,J, the pleated sheets are nested along the c axis in the P2lcn setting. Hydronium oxygen atoms on any pleat fold are collinear and have hydrogen bonds linking two nitrates on one side and one nitrate on the other side of the fold. This triangular pattern (two nitrates-ne hydronium-one nitrate) is constant throughout any one sheet but is reversed (one nitrate-one hydronium-two nitrates) in adjacent sheets. When viewed together in the (a,b) projection, these two triangles in adjacent sheets form a hexagonal network with H 3 0 + in the center (see Figure la). From interatomic distances alone, it is suggested that NAM crystals exhibit covalent bonds within the nitrate and hydronium ions, electrostatic interactions between the ionic units, hydrogen bonding within the pleated sheets, and attractive dispersion type forces between layers (see a similar discussion in refs 23 and 43 and also below). The ab initio quantum mechanical calculations of the energetics and physical properties of NAM are a means of probing the character of thesevariousinteractionsin the crystal. SCF Energy and Cohesive Binding Energy. We have estimated the cohesive binding energy of NAM using the total PHF energy of the crystalline unit cell and the corresponding SCF energies of isolated HN03, H20, NO3-, and H 3 0 +in several basis sets. Computations were performed at experimental geometries of the NAM crystal,z3at geometries of NO3- and H 3 0 +as found in the NAM crystal, and at spectroscopic geometries of isolated H N 0 3 and H20.44.45 The results are summarized in Table 11. Binding energy is estimated by using, first, the energy differenceE(NAM - 4(NO3- H30+)), which represents the stabilization energy upon forming the crystal lattice. Next, the approximate basis set superposition energy (BSSE) is estimated by the counterpoise method to be the sum of the energy differences E(NO3-.3H@+) - E(NOp-.3ghostH3O+) - 36(H30+) and E(H@+.3NO3-) E(H30+.3ghostN03-) - E(H30+) - 3E(NO3-). The first difference gives the energy lowering of a NO3- ion due to orbitals borrowed from neighboring hydroniums, while the second is the energy lowing of H30+ from orbitals on neighboring nitrates. Finally, the difference E(N03-+H30+) - E(HN03+H20) is the energy of proton transfer between isolated H N 0 3 and H20 (including geometry relaxation). The sum of these quantities is

-

+

our best estimate for the cohesive binding energy AE = E(NAM bulk)/4 - E(HN03) - E(H20). The computed PHF binding energies show significant variation intheseriesofbasissets 3-21,6-21,6-21*,and6-31**. Evidently, still larger basis sets will be required to reach convergence of this property. The BSSE decreases as polarization functions are added, suggesting that further polarization functions should be added. The NAM crystal is bound in the four basis sets we have employed,near the limit of currently feasiblecomputations.Future computations using larger basis sets and fully optimizing the NAM geometry are necessary to achieve better quantitative agreement of the calculated and experimental enthalpy changes for the reaction HNO3(g) + H2O(g) HNOs.H2O(c); AHo(200 K) = -30.5 f 1 kcal/m01.'~$~ Optimization of Lattice Constants. The lattice constants in NAM were optimized by using the 6-21G basis. The PHF energy was minimized with respect to the three cell parameters (a, b, c), while the 24 fractional coordinates of the eight symmetry distinct atoms in the cell were held constant. The large number of independent parameters in this system (27) computationally precludes a full optimization of the NAM geometry, via a pointwise sampling of the energy surface, a computationally intractable problem. The computed optimized cell parameters are (a, b, c) = (5.898 A, 9.417 A, 5.585 A) and the corresponding experimental values are (6.2308 A, 8.6439 A, 5.4647 A). Calculated ratios of the lattice constants are a:bc = 1.056:1.686: 1.OOO,while the experimental ratios are 1.140:1.582: 1.OOO. Errors in the computed latticeconstants (-5.3%, +8.9%, +2.2%) in (a, b, c) result in similar errors in the internal bond lengths and angles of the hydronium and nitrate groups in the crystal. The mean N O and OH bond lengths in NAM, from the optimized lattice parameters, are 1.309 and 0.9514 A, respectively, while at the corresponding values from the experimental structure are 1.257and 0.909 A. A large portion of the error in lattice constants probably results from the fact that with the 6-21G basis the gasphase H 3 0 +geometry is predicted to be planar; HOH angle = 120'. This is in contrast to the experimental values for hydronium in the gas phase, 115.3°,47and an average value of 109.3' for hydrated protons in several different crystalline environments!* The optimization of the lattice parameters in NAM increases b and decreases a, which causes the HOH angle to change from 107.8' in theexperimentalstructureto 110.2' with theoptimized lattice constants. Because the 6-21G basis is biased to a planar hydronium it tends to enlarge the dihedral angle of hydronium ions in NAM and hence also enlarge b. The inclusion of polarization functions in the basis should reduce this error by decreasing the hydronium angle (e.g., LHOH = 110.6' with 6-21G*). Band Structure and Density of States. The electronic band structure has been computed, with a 6-21G* basis, along lines connecting the special points in the rectangular prism-shaped Brillouin zone(BZ). Points in the BZ were sampled along segments RI', I'Z, and in the notation of ref 49 and a plot of the valence bands is shown in Figure 2. The top of the highest occupied band (Fermi level) is set to zero on this energy scale. The distinct separation between groups of nondispersing bands in the occupied space in NAM is characteristic of an insulating ionic solid. Core orbitals lying at -551.4 eV (hydronium 0 Is), -549.0 eV (nitrate 0 Is), and -421.3 eV (N 1s) below the top of the highest occupied band are not shown in the figure. The valence bands (or highest occupied crystalline orbitals HOCOs) consist of three very narrow bands at -32.1, -30, and -25.6 eV, followed by several more diffuse bands between -13 and 0 eV. Interpretations and assignments of these bands are made from the projected densities of states. Plots of the DOS and PDOS for the valence bands in NAM are shown in Figure 3. The total DOS can be interpreted by

-

E

Poshusta et al.

7298 The Journal of Physical Chemistry, Vol. 97,No. 28, 1993

0

I

I

I

!

-30 -30

R r Z R Figure 2. Valence energy bands for nitric acid monohydrate (with a 6-21G* basis). Energy, in electronvoltsrelative to the top of the valence band (Fermi level), is plotted along three segments through the first

Brillouin zone: R

-r - Z

R.

Total DOS

1.

- r , l , , , , l , , , , l , r , r (

1

n1

1

1

,

1

IIA ,

1

1

1

1

-

Nitrate ion, NOS-

0-3d x 10

-

J

0-2p

1 ,

I

,

I

I

0-2s

*

,

I

,

/

,

~

,

I

I

I

~

I

I

I

I

~

I

I

I

N-3dxlO N-Zp I

/

I

N-ZS , I ~

I

Oxonium ion, H30’ L-+ A H - l s x 10 ~

0-3d x 10

1.

, ,,,

,, , , , , , ,

I

v

I

,

,, , ,

, , ,,

0-2p I

0-2s

examining the projections of the ground-state density onto the atomic orbitals (AOs) in the crystal. The PDOS spectra are used to determine the character of the electronic bands and the overlap of these states provides information about the intracrystal bonding in NAM. The HOCOs, between 0 and -1.1 eV (relative to the top of the occupied bands), consist predominantly of 0 2p orbitals (0 = nitrate oxygen, W = hydronium oxygen). The band between -1.9 and -3.0 eV also has a large component of 0 2p, with small contributions from N 3d and H Is, and the band between -5.8 and -7.2 eV is W 2p, with a very small admixture of H 1s. Several closely spaced bands between -10.4 and -13.5 eV are dominated by W 2p and H Is, with some 0 2s and 0 2p character. The sharp peak near -26 eV is largely 0 29, with only minor contributions from N 2p and 0 2p. The narrow band between -30.3 and -30.5 eV is almost entirely composed of W 2s plus a small amount from H 1s. Lastly, the peak near -32.5 eV is due to 0 2s and N 2s, with a slight admixture of 0 2p and 0 3d. The valence bands contain very little character from the d-typeorbitals (N.B. intensitiesof thed orbitalsare XlOin Figure 3). Some intensity from the N 3d orbitals appears in the HOCOs, the 0 3d orbitals contribute (to a small extent) to the character of all bands from -33 to -7.5 eV, and the W 3d orbitals have only very small projections in the range -13.5 to -10.3 eV.

The overlap between 0 2p, 0 2s, N 2p, and N 2s is indicative of the atomic orbital mixing that is expected to accompany intramolecular covalent bonding within the nitrate ion. A similar mixing is observed between the W 2p, W 2s, and H 1s in the hydronium ion. The most delocalized orbitals in the valence shell are the hydrogen 1s orbitals, which overlap to varying degrees with all of the other AOs in the region between -13.5 and 0 eV. The most delocalized heavy atom orbitals are the 0 2p and W 2p orbitals, which mix with H 1s and reflect the formation of H-bonds between neighboring nitrates and hydroniums. Mulliken Population Analysis. Mulliken population analyses were used in this study to qualitatively describe the partitioning of charge among (and between) atoms in NAM (see Tables I11 and IV). A comparison of the atomic charges in NAM to those found in the molecular reactants ( H N 0 3and H20) gives a rough estimate of the charge redistribution that occurs when NAM (bulk or surface) is formed (Table 111). The effect of the crystalline environment on the ionic units (NO3- and H30+)in NAM was also probed by comparing atomic charges in the crystal to those in the corresponding isolated ions. The geometry of the free NO3- and H30+ groups were fixed at their respective structures from NAM (with experimental lattice constants). The molecular species were computed at their experimentalgeometries {HzO(Cb) R(OH) = 0.9580 A, LHOH = 104.5°)45 and HNO3 (Cs)@ R(OH) = 0.961 A, R(NO(H)) = 1.40 A, R(NO(cis)) = 1.21 A, R(NO(trans)) = 1.20 A, LHON = 102.2’, LO(H)NO(cis) = 115.9’, LO(H)NO(trans) = 114.0°, LO(cis)NO(trans) = 130.3’1. All calculations were done with a 6-21G’ basis set. Some general trends can be deduced by comparing atomic charges on like atoms in the neutral molecules, isolated ions, and NAM (see Table 3). The overall charge on the nitrate group in NAM decreases’ (-0.3314, while the charge on the hydronium unit increases (~0.331eJ),with respect to the isolated ions, indicating a significant redistribution of charge among the ionic subunits in the crystal. The charges on the nitrate oxygens and the hydronium atoms increase over those on the isolated ions in response to the crystal field. When the crystal is formed from the neutral reactants ( H N 0 3 and H20) most of the charge redistribution is due to 0.114 being depleted from each hydrogen and accumulated on each of the nitrate oxygens. The overlap populations (reported in Table IIIB) do reveal some information about the bonding character in these species. According to these data, the NO bond exhibits less bonding character in NAM than in either NO3- or HN03. A decrease is also observed in the average magnitude of the WH bond order in the “water” series: 0.271 in H20, 0.261 in H30+,and 0.191 in NAM. This trend is accompanied by the nonbonded H,H interactions becoming more positive across this series. In addition, a positive overlap in NAM between the nitrate oxygens and the hydronium hydrogens (0,H = 0.080) is indicative of the formation of hydrogen bonds in the crystal. These bond order changes may be interpreted according to the charge redistribution and bonding characters of the corresponding HOMOand LUMO ofthenitrates and hydroniums. The transfer of charge from NAM(NO3-) to NAM(H3O+) probably occurs by removing electron density from the nitrate HOMO, which is N-0 nonbonding. The W-H bond in hydronium is weakened in the solid since electron density is added to its antibonding LUMO. In addition, a significant bond order arises between the nitrate oxygen and the neighboring hydronium hydrogen, consistent with the formation of hydrogen bonds. This qualitative interpretationof the bonding character in the NAM crystalinvokes a molecular orbital model of the charge distribution. This is almost certainly an oversimplificationof the electronicproperties of the solid, but it does account for the observed trends in the calculated Mulliken population analyses. Redistribution in the surface is discussed in the following sectiondealing with the NAM slab.

-

Hartree-Fock Study of Nitric Acid

The Journal of Physical Chemistry, Vol. 97, No. 28, 1993 7299

TABLE IIk Mulliken Overlap Populations for HP,HNO%Isolated Hydronium and Nitrate Ions, and NAM Bulk and Slab. H20

atom N nitrate 0 nitrate 0 nitrate 0 water (W) H

HNO3

NO3-

NAM bulk

NAM slabb N0f up/dn or H30+ ridge/trough

8.82 0.59

5.75 8.58 [O(H)] 8.59 [O(cis)] 8.55 [O(trans)] 0.53

H

H net HNOs/NOsnet H20/H30+

HpO+ A. Atomic Charge

32.00 10.00

8.72 0.43 0.42 0.43 10.00

5.80 8.73 8.74 8.73

32.00

5.73 8.64 [0(l)] 8.65 [0(2)] 8.65 [0(3)] 8.88 0.49 [H(l)] 0.48 [H(2)] 0.48 [H(3)] 31.67 10.33

5.3015.30 8.7918.79 8.9218.92 0.4710.47 31.66/31.66 10.34/10.34

B. Bond Overlap Populations

A. E __,

0.225 [O(H)] 0.382 IO(cis)l 0.413 iO(trark)] -0.061 (av) 0.249

0.327 0.306/0.305 (av) 0.329 0.323 N, 0 nitrate 0,O -0.061 (av) -0.049/-0.050 (av) water (0),H 0.271 0.255,0.262,0.265 0.181,0.196,0.197 0.186/0.182(av) water (H), H -0.035 -0.010 (av) -0.009 (av) -0.007/-0.007 (av) nitrate (N), water (H) -0.008 -0.005/-0.005 nitrate (0),water (H) 0.080 0.090/0.089 nitrate (0),water (0) -0.017 -0.019/-0.018 a All calculations were done by using a 6-21G' basis. (A) Gross atomic charges and atomic overlap populations are shown for atoms. (B) Bond overlap populations are shown for neighboring and selcctive pairs of nonbonding atoms. 0 refers to oxygen atoms on the nitrate ions, while W refers to oxygen atoms on the hydronium ions. The geometries of the isolated hydronium and nitrate ions at their corresponding structure in NAM bulk and the neutral molecules are fixed in their experimentally determinedstructures.u*4s The two-layer slab has two kinds of Nos- and H20+ as defined in Table Ib: "up" refers to a nitrate that is hydrogen bonded to two trough and one ridge hydronium and "down" is the opposite configuration. The corresponding hydroniums are "ridge" and "trough". N, 0

N, 0

TABLE IV Calculated Normal Component Elastic Stiffness Constants in GPa and Compliance Constants, in GPa-l a components, i j stiffness, c compliance, s 191 9.14 i 0.09 0.175 2,2 80* 3 0.022 393 95.5 & 0.9 0.0 12 192 16.3 & 0.5 -0.037 1,3 2.0 0.9 0.006 2,3 24 f 3 -0.005 a External contributionsonly. Error bars indicate the uncertainty in the fit between Hooke's law and the 24 data points. 24 points in the neighborhood of the equilibriumcell parameters were computed: Ek = E(a + u l k ,b + uzk, c + u,~),k = 1,2, ...,24. A quadratic model function was then fit to these computed points: U([1,(2$(3) = UO+ (1/2)& aJb&-q), where (1 = a + UI, €2 = b + u2, €3 = c + u3. Then the improved equilibriumlattice constants are given by a = 01, b = 02, and c = a3. The fit was achievedby minimizingthe squareddeviation between the population of computed points, (k),and the model function. For several reasons, the fitted model parameters are uncertain: (1) the true energy functionE is only approximatelyquadratic, (2) computedEvalues contain some residual errors due to numerical approximations,and (3) the population of computed values is only a sample from the collection of possible computed values. Fitted parameter values contain an uncertainty from these causes, which we have estimated as follows: five randomly selected subsamples of 21 points from the population were separately fit to the model. The resulting five sets of fitted parameters were averaged and standard deviations computed. The results are shown in the table. Thefittedlatticeconstantsarea = 5.898 0.009, b = 9.417 h 0.008, c = 5.585 0.006 A.

0.368 0.370 0.368 -0.070 (av)

*

Electrostatic Potentials. The SCF wave function for NAM has been used to compute electrostatic potential mapssoin planes through crystalline NAM. These are shown in Figure 4. The calculated electrostaticpotential maps are not only an alternative to depicting charge distributions, they also reflect (in the spirit of molecular mechanics) bonding interactions in a crystal. Thus we view Figure 4 as further support and visualization of our interpretation of the interactions in NAM. The contour map in Figure 4a is taken along the solid line in the structure shown in Figure 4b. This view bisects a set of nearly planar nitrate groups surrounded by three adjacent hydronium units (with one out-

Figure 4. Electrostatic potential maps (a and c) for NAM,, computed with a 6-21G' basis. A ball and stick projection-ofthe NAM cryital in the ab plane is shown for reference (b). Potential contours shown start at -0.05 V (the dashed contour) and continuein steps of 0.05 up to +0.20 V; higher contours, within the excluded volume around the nuclei, were

culled out. The first plane (a) is the potential at points in a plane defined by collinear hydronium oxygen nuclei on opposite sides of an infinite ribbon of hydrogen-bondednitrate and hydroniumions comprisingNAM crystals. This plane is shown edgewise as a solid line in the ball and stick representation. A normal vector to this plane makes angles 28.7O and 61.3O with the lattice a and b vectors. The width of the ribbon, between the defininghydronium lines on opposite sides, is 4.928 A, and the width of the view shown extends an additional 4 A on both sides of the ribbon. The second plane (c) is the potential at points in a plane perpendicular to the first plane and bisecting the ribbon and extending from one ribbon to its nearest neighbor 2.69 A above and is shown as a dashed line in the ball and stick representation. of-plane hydrogen on each H3O+) and corresponds to the tape of nitrate and hydronium ions described earlier. Contours are also plotted (Figure 4c) along a plane normal to this view (see

7300 The Journal of Physical Chemistry, Vol. 97,No. 28, IC’93

dashed line in Figure 4b). This plane makes an angle of approximately 30° with the a axis in the crystal. This perpendicular plane intersects a line of collinear nitrate oxygen atoms. In both of these plots the large values of the electrostatic potential surrounding the atomic nuclei have been culled out in order to emphasizethe more chemicallyaccessible regions of the material. The nitrate and hydronium ions appear as distinct (but interacting) units in these plots. Closely spaced contour lines (corresponding toa large electric fields) are evident in the regions where hydrogen bonding between the nitrate and the adjacent (coplanar) hydroniums is anticipated. Conversely, regions of widely spaced contours that represent small electric fields are evident between the pleated layers. This is indicative of the weaker interlayer bonding in NAM. Elastic Constants. Elastic constants describe the response of a crystal to external (and internal) directional forces. These can then be used, in part, to predict energetically favorable cleavage planes in a solid. Elastic anisotropyreveals important differences in the nature of the intracrystal bonding along various directions in the lattice (e.g., ref 5 1). The elastic constants obtained in this work are fully consistent with the interpretation of bonding structure given by the Mulliken population analysis and the electrostatic potentialmaps. In this study the normal components of the elastic constants were computed from the ab initio crystal wave function for NAM by using a 6-21 basis. No experimental data are currently available to compare to the theoretical predictions. The present calculations refer to a crystal at zero temperature and, hence, ignore the temperature-dependent contribution of lattice vibrations to the elastic constants (e.g., see ref 52). For orthorhombic lattices, there are nine independent nonvanishing elastic constants making up the stiffness tensor, c: three diagonal normal components cll, CZZ, and ~33,three offdiagonal normal components c12, ~ 1 3 and , ~ 2 3 ,and three diagonal shear ComponentscM,~ 5 5 and , c66 (all other componentsvanish).53 The compliance tensor, s = c-l, has nine corresponding nonvanishing elements. The crystal energy per unit volume at selected values of the cell parameters a, 6, and c was computed. These energies were then fit to a quadratic form in the normal components of strain. This is equivalent to assuming Hooke’s law for small distortions. The elastic constants are calculated from the second derivatives of the energy per unit cell with respect to strain components. Predicted values for c11,c22, ~33,c12,~ 1 3 and , ~ 2 are 3 shown in Table IV. Shear components were not computed because these distortions reduce the crystal symmetry and greatly increase computationalcost. Since the fractional coordinatesof the atoms in the cell were not optimized, the reported results include only the “external” contributions to elastic constants and neglect the “inner”contributions. In a study of the elastic constants of MgF2 (also using periodic Hartree-Fock theory) the internal contributions were found to be 2 orders of magnitude smaller than the external contribution^.^^ It should be noted that the diagonal constant c11 is about 1 order of magnitude smaller than c22 and c33. The stiffness and compliance tensors relate the stress, u, and strain, e, tensors: u = ce and e = su. The positive and negative values for s11 and slz, respectively, indicate that for a normal uniaxial compression applied parallel to a, the NAM crystal responds by contracting along the interlayer direction, a, but simultaneously expanding along the folding direction, b. Similarly, the linear compressibility parallel to an arbitrary direction, @(ti), is the negative fractional change in length parallel to u under hydrostatic pressure. The following values for @ parallel to the crystal axes were computed from the complianceconstants in Table IV: @(i) = 0.143, @(i) = -0.020, and @(k) = 0.013/GPa. This implies that NAM crystals under hydrostatic pressure are most compressed in the direction of nested layers and that this compression is accompaniedby expansion parallel to j and slight

Poshusta et al. compression parallel to k. When combined, the compliance constants determine the volume compressibility,K = s11 + s22 + sj3 2(sl2 ~ 1 3 s ~ ~which ) , has the value of 0.135/GPa for NAM. For an isotropic crystal, which NAM is certainly not, it is customary to define the reciprocal of the volume compressibility as the bulk modulus. The calculated values c22 = 80 GPa and c33 = 96 GPa for the normal stiffness constants in the b and c directions are typical of ionic crystals; e.g., the cubic crystals NaCl and NaF, for which cI1= c22 = c33, have cll = 48.7 GPa and 97.1 GPa, respecti~ely.~~ In contrast, the calculated cll = 9.1 GPa, the normal stiffness constant in the a direction, is an order of magnitude smaller, indicating a smaller resistanceto compression (and hence weaker interaction) interaction between layers. Many other layered materials exhibit similar anisotropy: e.g., layered Ti&, which intercalates Li, exhibits c11 + c12 = 285 GPa parallel to layers and c33 = 67 GPa perpendicular to the layers,55and the layered crystals Gas, GaSe, and InSe have cll = 123,103,73GPa parallel to their layers and c33 = 39, 34, 36 GPa perpendicular to their layers.51 B. NAM Surface. Since the structure of the catalytically active crystal face(s) in PSCs has not been characterized experimentally and the mechanism for catalytic action by such crystals (reactions 1-3) is unknown, we have constructed a plausible theoretical model for the NAM surface. Although it is possible that naturally occurring high-energy surfaces or localizied crystal defects may control the surface reactivity, it is also possible that catalysisoccurs on nearly perfect crystal surfaces or between layers of NAM crystals. On the basis of the computed elastic constants in bulk NAM, we selected the (100) surface as an energetically likely site for surface reactions. Because the bonding between puckered layers in NAM bulk is weak, little energy is required to expand the space between two such layers for intercalation or to cleave along this direction to expose a low-energy NAM surface. This study chose a 2-D slab (periodic in a’ and b’, where the primes denote the slab axes), containing two adjacent layers, as a model of a clean NAM surface and/or one side of an interlamellar intercalation layer. Figure 1 shows a top view of this slab along the (a’,b’) plane and an edge on view of the two layers (b’,z) plane. Each corrugatedsurface has alternating ridges and troughs running parallel to the a’ axis and with the b’ axis directed from ridge to ridge. One kind of hydronium oxygen atom lies at the peaks of the ridges, while another lies at the bottom of the troughs. Two kinds of nitrate ions are also present: the first kind is hydrogen bonded to two ridge hydroniums and one trough hydronium (“down pointing nitrate”), while thesecond is hydrogen bonded to two trough hydroniums and one ridge hydronium (“up pointing nitrate”). The two types of nitrate ions exist on opposite sides of the ridge. Ridge lines are coplanar in planes parallel to (100) in the standard Pna21 setting of bulk NAM, hence, this is described as the (100) surface [in the nonstandard setting, P 2 m they are (001) planes]. The slab unit cell is orthorhombic with lattice vectors a’ and b’, with a’ parallel to bulk c and b’ parallel to bulk b, and the surface normal (z axis) parallel to the bulk a. These calculations assume no relaxation of the surface layers so that a’ = 5.4647 A and b’ = 8.6439 A. Spacing between layers is also the same as in the bulk (3.1 154 A). Full specification of the atomic positions is shown in Table I. SurfaceTension. Energy differences,6E = E(s1ab) -E(bulk), can be used to estimate the (100) surface tension of NAM. This assumes that no surface relaxation occurs (i.e., the surface layer has the same geometry as all bulk layers) and that the interaction energy between a given surface layer and the remaining bulk is limited to nearest-neighbor interactions (i.e., next nearest layers and beyond are negligible). Therefore, the calculated value of 6E, subject to these assumptions, is simply twice the interaction

+

+ +

HartreeFock Study of Nitric Acid

The Journal of Physical Chemistry, Vol. 97, No. 28, 1993 7301

r

I

v

SLAB total DOS

1

SLAB PDOS: W2pz

i I

I

1

I BULK PDOS: W2p,

A

b

1

I I

! !

9

f

a

a

d

d

A

I

I

I

I

A !

!

Trough Ridge -7 .O -6.5 -6.0 -5.5 Figure 5. DOS and PDOS computed in the 6-21G* basis and expanded

I

! !

I I

in the region of energy near -6 eV. Total density of states is seen to be almost entirely composed of hydronium W 2px orbitals in the bulk and W 2pz in the slab.

energybetween nearest neighbor layers. At the 6-21G and 6-21G* levels, the energy differences are 6E = 0.01 5 1 and 0.01 13 hartree per unit cell, respectively. Since each layer has two surfaces, the surface tension (energy per unit area) becomes y = 6E/(4a'b9 = 23086Eergcm-2/hartree. The resultingestimatesof theNAM against vacuum surface tensions, with the respective basis sets, are 34.6 and 26.1 erg/cm2. Electronic Band Structure and Density of States. The electronic band structure, in the 6-21G* basis, for the two-layer slab has been computed along segments in the rectangular shaped BZ of the slab. The bands of the slab are very flat throughout the BZ and the band diagram of the slab is virtually indistinguishable from that of the bulk. The most notable difference between the bulk and slab electronic structure is in the region -5.9 to -6.4 eV (relative to the top of the valence bands). This energy region in the bulk spectra contains two closely spaced, slightly dispersed bands. The corresponding bands in the slab are essentially nondispersed (flat) with a larger energy gap. The character of these bands is assigned from the total and pertinent projected density of states spectra (shown in Figure 5). It is evident that they are predominantlycomposed of hydroniumoxygen 2p orbitals directed between the layers in the bulk (W 2px)or perpendicular to the surface of the slab (W 2p,). The greater dispersion in the bulk bands (with respect to the slab) indicates that these orbitals are involved in the interlayer bonding in the crystal. These bands are interpreted as nonbonding W 2p orbitals in the slab and the bonding W 2p crystal orbitals in the bulk. The latter are responsible for the interlayer forces that bind the layers of NAM. Mulliken Population Analysis. A Mulliken population analysis of the slab is reported in Table 111. Slight alterations of the charge distribution occur when this slab is formed. Virtually no change is seen in the net electron densities on nitrate and hydronium ions of the slab versus the bulk. However, about 0.43e move from N to 0 within the slab nitrate ions, while only 0.04e is transferred to H from W in hydronium ions. The overlap populations indicate that the NO bonds are weakened in the slab (vs the bulk) while the WH bonds remain essentially the same. The hydrogen bond order is also increased substantially in this model surface. The strengthening of the hydrogen bonds may result from contributions from the W 2p, orbitals that are nonbonding in the slab but are involved in the interlayer bonding in the bulk material. Electrostatic Potentials. Electrostaticpotential maps have also beencomputed within andabove theslab (with the6-21G* basis).

b

1

d

o

e

A I

I

I

o

6

A !

!

Trough Ridge Figure 6. Electrostatic potential isosurfaces for the corrugated (100) surface of NAM computed at the 6-21G* level. Views are normal to a slab and consist of two layers parallel to the (100) plane of bulk NAM and with the parallel ridge and trough lines running vertically (only one layer of atoms are shown). The isosurfaces are constructed from calculating the electrostaticpotential in a series of planes extending into the center of the slab. Three hydronium oxygen atoms lie on a ridge line near the center of the view (marked on figure). Neighboring troughs to the left (marked) and right of the central ridge are bounded by two hydronium oxygens. The extreme left and right boundariesof the figure are delimited by hydronium ridges. Nitrate ions are inclined in strips connecting the troughs and ridges. Three hydrogen bonds link each ion to three neighboring ions. Two "uppointing" nitrates are shown to the left of the central ridge and three "down-pointing" nitrates are shown to the right. The view shows four unit cells of a 2-Dinfinite slab, which is periodic vertically and horizontally in the plane of the figure. The potential isosurfaces are at energies (a) V = +0.01 au (+0.27 eV) and (b) V = -0.01 au (-0.27 eV).

These are used to predict the chemically active adsorption sites on the undefected clean NAM (100) surface. A grid of the electrostatic potential was computed in 11 equally spaced planes parallel to (100) and separated by 0.5 A. (For reference, the plane defined by the ridge hydronium oxygen atoms is taken to have z = 0. Four parallel planes below and six above this reference were chosen: z = -1.0 8,-1.5 A, ...,+3.0 8.) Isosurfaces were then generated by interpolating between these planes. Figure 6 shows two potential isosurfaces at the (100) crystal surface. Figure 6a is the surface of constant potential, V = +0.01 au (+0.27 eV), defining a region that attracts a negativecharge. Figure 6b shows an isosurface of negative potential ( V = -0.01 au) that encompasses a region of space that is attractive to a positive test charge.

Poshusta et al.

7302 The Journal of Physical Chemistry, Vol. 97, No. 28, 1993

According to these views, a cation approaching the surface would seek the region on the ridge between two hydronium ions and near the up-pointing nitrate in the folded layer. Similarly, an anion would be attracted to the region directly above hydronium ions on the ridge. These locations are proposed as likely physisorption sites on the (100) NAM surface. A real atom or molecule will approach these sites until Pauli exclusion and nuclear repulsion forces overwhelm the electrostatic forces. According to this argument, nucleophiles and negative ends of molecular dipoles would prefer the hydronium sites, while electrophiles and positive ends of molecular dipoles will tend to orient over the nitrate sites. A similar result was observed in a recent study of the adsorption of diatomics on MgO (lOO).41 A periodic HF study of the interaction of HCl with NAM (100) is currently in progress and will be reported in a future work.

IV. Conclusions Hydrated nitric acid crystals are known to play a significant role in the destruction of polar stratospheric ozone. The goal of the present work was to gain insight into the chemistry of these materials from an ab initio theoretical investigation of a wellcharacterized clean material. To this end, this study probed the bulk and surface properties of NAM using the periodic H a r t r e e Fock method. Results of these calculations quantify the ionic model inferred from the X-ray crystal structure of the material. Nitrate and hydronium ions are bound in the crystal by Coulomb forces and hydrogen bonds between nearest neighbors. These strong forces are directed along pleated sheets or folded layers nominally parallel to the (b,c) plane (using the standard PnaZl setting). Adjacent sheets or layers are attracted by weaker electrostatic and van der Waals forces. The low-energy (100) surface can be formed by cleaving the crystal between these layers. The calculations of the surface properties of NAM used a finite thickness 2-D slab of NAM as a model for the (100) surface. Projected densities of states demonstrate that energy bands of NAM show distinct separation into nitrate bands and hydronium bands with the strongest overlap in the region 6-13 eV below the top of the valence band. Comparisons between projections onto the hydronium W 2px orbitals in the bulk and the corresponding W 2#, in the slab indicated that these orbitals are responsible (at least in part) for the interlayer bonding in the crystal. The computed elastic constants of the NAM crystal reflect the nature of the intracrystal interactionsand were used to predict the lowest energy cleavage surface and the optimized lattice constants. The diagonal compliance value s11 is an order of magnitude larger than s22 and s33, which indicates the relative ease with which the spacing between pleated sheets may be changed and the relative difficulty for changing atomic distances within the sheets. The negative off-diagonal value, S ~ Z reveals , that the easiest way for the sheets to relax when compressed is for the HOH dihedral angles at the folds to increase. Calculated mapsoftheelectrostatic potential in the bulk revealed the extensive network of hydrogen bonds between the nitrate groups and adjacent hydronium ions. Substantially weaker fields are evident in the interlayer region in NAM. Isosurfaces of the electrostatic potentials of the model (1 00) surface define the chemically accessible and potentially catalytically active regions of the surface. Nucleophiles approaching the surface are predicted to be attracted to the hydronium sites on the surface while electrophiles will tend to migrate to the region around the nitrate oxygens. Further theoretical studies of interfacial properties of NAM and the bulk and surfaceproperties of nitric acid trihydrate (NAT) are currently in progress. A quantitative assessment of the accuracy of these theoretical results will be made when additional empirical data are available. Acknowledgment. We appreciate helpful comments and discussions with Profs. S. M. George, R. Ravishankara, and M.

A. Tolbert of the University of Colorado. V. R. Saunders, C. Roetti, and R. Dovesi are also gratefully acknowledged for providing us with prereleased versions of CRYSTAL92. This work was performed under the auspices of the Divisionof Chemical Sciences, Office of Basic Energy Sciences, U S . Department of Energy, under Contract DE-AC06-76RLO 1830 with Battelle Memorial Institute, which operates the Pacific Northwest Laboratory. A.C.H. was supported in part by the Advanced Industrial Concepts Division of the Office of Conservation and Renewable Energies (Contract 16697). In addition, R.D.P. is very grateful to the Molecular Science Research Center, Pacific Northwest Laboratory, and Northwest College and University Association for Science for hospitality and support provided during sabbatical from Washington State University. We also thank the Scientific Computing Staff, Office of Energy Research, US. Department of Energy, for a grant of computing time at the National Energy Research Supercomputer Center.

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