6708
J. Phys. Chem. 1996, 100, 6708-6714
Electronic Structure of Sodium Nitrate: Investigations of Laser Desorption Mechanisms Maureen I. McCarthy,* Kirk A. Peterson,† and Wayne P. Hess EnVironmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, Washington 99352 ReceiVed: October 20, 1995; In Final Form: January 29, 1996X
This theoretical study uses ab initio quantum mechanical methods to investigate the electronic properties of ground and excited state sodium nitrate. We calculated electronic properties of the crystalline material for bulk, clean, and defected surfaces. The results of these calculations are used to explain the photoexcitation/ desorption mechanism and support the conclusions of an earlier experimental investigation of the laser desorption of NO from single-crystal sodium nitrate. Ab initio periodic Hartree-Fock (PHF) theory was used to investigate the “molecular-ionic” character of crystalline sodium nitrate. The calculations indicate that the electronic structure of the bulk and cleavage surface are virtually identical (i.e., no shift in the resonant absorption profile is expected). This finding is consistent with the experimental results on the wavelength dependence of NO desorption yields for crystalline NaNO3. However, changes in the absorption manifold are found to accompany the removal of external nitrate oxygens (producing surface nitrite groups). The presence of these chemical defects causes states to appear in the band gap producing a red shift in the absorption band. Complete active space self-consistent field (CASSCF) calculations on NO3-, NO3, and NO2-, support the “local excitation model” of the π* r π2 transition. These calculations also indicate that the transition energies of the nitrate ion are unaffected by the presence of the surrounding ions. The photoexcitation/ dissociation mechanism of the nitrate ions in the crystal, however, differs from gas-phase processes in that the neutral photodetachment channel, observed in the gas phase, is energetically inaccessible in the solid due to the stabilization of ionic species (relative to neutrals) by the crystalline field.
I. Introduction Laser-ablation/laser-desorption techniques are important tools in many fields including chemistry, physics, materials science, microelectronics, and medicine.1 These techniques can be used to study the properties of a wide variety of materials. In particular, the combination of laser desorption and mass spectrometry has been applied to determine the composition of refractory materials including high molecular weight biomolecules.2,3 Laser desorption mass spectrometry (LDMS) can be used as an analytic tool for determining the atomic and molecular composition of mixed hazardous wastes.4 A LDMS technique is currently being developed and applied in the analysis of mixed wastes extracted from the underground storage tanks at the U.S. Department of Energy’s Hanford nuclear reservation. A major component of these tanks is sodium nitrate (NaNO3); hence, understanding the photodesorption mechanisms of this material is essential to analyzing these wastes. The experimental details and results of laser desorption studies on NaNO3 have been discussed recently by Bradley et al.5 Sodium nitrate is a wide-band-gap insulating material that forms a molecular-ionic crystal with a hexagonal unit cell (R3hc) of D3d symmetry.6 It is isostructural with calcite (CaCO3), and the nitrate and carbonate anions are isoelectronic.7 The cleavage plane of NaNO3 (and CaCO3) is along the 101h4 direction in the hexagonal unit cell, which intersects the c-axis at an angle of 43°49′.6 [N.B. This cleavage plane is sometimes described in the literature as the (101h1) plane of the “cleavage rhombohedral”.6 The cleavage rhombohedral should not be confused with the primitive rhombohedral of the R3hc space group.] Molecular-ionic materials are unique in that they display properties that are characteristic of both ionic and molecular † X
Department of Chemistry, Washington State University. Abstract published in AdVance ACS Abstracts, March 1, 1996.
0022-3654/96/20100-6708$12.00/0
crystals. They are mostly electrical insulators. The ionic character is evident from the segregation of charge in the crystals which produces large gaps between the valence bands (highest occupied crystalline orbitals, HOCO) and the conduction bands (lowest unoccupied crystalline orbitals, LUCO). However, unlike purely ionic crystals they also display “local” molecular properties. In particular, some of the electronic transitions in these crystals behave as if they were localized on the molecular subgroups and, hence, are well-described by the analogous gasphase transitions. Examples of this are the π* r π2 bands observed in the alkyl nitrate family. The absorption spectra of NaNO3 shows a strong band (S1) centered at ∼6 eV, which is assigned to the π* r π2 transition localized on the nitrate moiety.6 A much weaker transition (with 1000 times less oscillator strength), resulting from the n2 (or n1) to π*, transition occurs at ∼4 eV. The charge transfer bands, observed at higher energies (S2 at ∼10.5 eV and S3 at ∼12 eV), result from excitation out of the n and π2 levels, respectively, into the “cationic states” ascribed to sodium 3s orbitals.8 The laser desorption experiments reported earlier5 indicate a dramatic enhancement of NO desorption yield (of ∼1000) for resonant excitation of the π* r π2 over nonresonant (sub-bandgap) excitation. Resonant excitation of sodium nitrate leads preferentially to photochemical desorption of NO neutral and no sodium desorption is observed. The much weaker O2 yield is far below the stoichiometric ratio, and hence both Na+ and O2- appear to remain trapped on the surface. The goal of the theoretical studies described in this work is to probe the ground-state electronic properties of crystalline NaNO3 and to examine the photoexcitation/desorption mechanism. The molecular-ionic properties of bulk sodium nitrate were investigated using periodic Hartree-Fock (PHF) theory. The calculations, reported in section II, probe the ground-state electronic character of the crystal and examine changes in the © 1996 American Chemical Society
Electronic Structure of Sodium Nitrate
Figure 1. Crystal structure of sodium nitrate. The hexagonal unit cell is shown; notations to the a, b, and c axes are with respect to the hexagonal unit cell. The 101h4 cleavage surface is designated by the dark plane in the lower portion of the panel.
charge density that result from cleaving the crystal and defecting the surface. These are used to characterize the electronic properties of the material prior to the laser desorption process. The “molecular” electronic properties of sodium nitrate were probed by computing the ground and excited-state energetics of gas-phase nitrate and nitrite ions. The quantum mechanical electronic structure calculations are based on complete active space self-consistent field (CASSCF) theory and are reported in section III. The conclusion section (section IV) integrates these complementary theoretical studies with the reported experimental data. II. Electronic Structure of Crystalline Sodium Nitrate Theoretical Method. The electronic structure of crystalline sodium nitrate was investigated using an ab initio quantum mechanical method based on periodic Hartree-Fock (PHF) theory9 as implemented in the program CRYSTAL92.10 The data reported here were computed using a standard Pople 6-31G* basis set on all atoms.11 The crystalline properties of NaNO3 were computed assuming a hexagonal unit cell (space group no. 167, R3hc) with the experimentally determined lattice constants a ) b ) 5.071 Å, c ) 16.825 Å.12 The rhombohedral setting of R3hc (used by CRYSTAL) contains two NaNO3 formula units and 1/6 of the hexagonal unit cell volume (shown in Figure 1). The electronic structure of the sodium nitrate surface was calculated using a finite thickness slab cleaved along the 101h4 direction at an angle of 43°49′ to the c-axis in the hexagonal unit cell (shown in Figure 2a).6 The calculations were performed on the two-dimensionally periodic object (replicated along the cleavage direction). The slab thickness used in most of these studies was three layers (corresponding to six NaNO3 formula units per two-dimensional unit cell). The slab thickness was chosen such that the properties of the middle layer(s) resembled those found in the bulk material. Calculations with thicker slabs (five and seven layers) confirmed that the surface formation energy and charge density of the center layer were converged using the three-layer model. The positions
J. Phys. Chem., Vol. 100, No. 16, 1996 6709
Figure 2. Slab models used to calculate surface electronic properties of crystalline sodium nitrate: (a) the clean surface constructed from a three layer infinite 2-D array with the atomic positions fixed at the corresponding bulk geometries; (b) oxygen-depleted defected surface.
of the atoms in the slab were fixed at the corresponding bulk geometries to maintain the in-plane symmetry operations thus reducing the computational requirements. This was justified because partial relaxation of the atomic coordinates produced only negligible changes in the computed properties. A variety of compositional and structural defects, including oxygen and NO depletions, F-center formations, and step edges and kinks, are expected to influence the electronic properties of NaNO3. In particular, it has been observed that NO emission increases with the formation of defects, at excitation energies insufficient for resonant excitation of the π* r π2 transition.5,13 A full experimental determination of the structure of the clean and laser-irradiated surfaces has not been possible, to date. The present study examines the changes in electronic structure that accompany the conversion of surface nitrate ions to nitrites. Because of the “molecular” character of the nitrate group in NaNO3, it is assumed (and our calculations support) that the surface can be defected by removing an oxygen atom without substantially perturbing the electronic character of the bulk material. This behavior is not observed when oxygen vacancies are created in purely ionic oxide materials, e.g. MgO or TiO2. A defected slab was constructed by removing the outer nitrate oxygen (shown in Figure 2b), to produce NO2- groups on the surface. The geometry of the defected slab was fixed at the clean slab coordinates. In this geometry, the internal structures of the surface NO2- groups are very close to those found in bulk sodium nitrite (NaNO2). The electronic structure of the defected material was interpreted by comparison to the properties of bulk NaNO2, which were computed assuming an orthorhombic unit cell (space group no. 44, Imm2) with the experimentally determined lattice parameters (a ) 3.55 Å, b ) 5.56 Å, c ) 5.38 Å).14 Such “surface nitrite” defects are likely formed during crystal cleaving and sample preparation (especially during polishing, annealing and baking). The NO3- to NO2- conversion energy is low (estimated to be ∼40 kcal/mol) and the NO3- and NO2- groups have similar orbital occupancies. In the gas phase, both groups have filled π, σ, and n valence molecular orbitals with lowest unoccupied molecular orbital being of π* character.
6710 J. Phys. Chem., Vol. 100, No. 16, 1996
Figure 3. Total density of states for bulk and clean (defect free) 101h4 slab of sodium nitrate. The energy of the highest occupied crystalline orbitals have been set to zero.
The laser desorption process substantially alters the character of the surface structure. The π* r π2 resonant-enhanced laser desorption process has been shown to be very efficient at removing NO groups from the surface.5 This process presumably leaves O2- at or near the surface. The presence of this group following the desorption step has not been confirmed experimentally and its lifetime has not been estimated. In contrast with the formation of NO2- groups on the surface, the production of a significant number of O2- defect sites would be expected to perturb the electronic spectra, since O2- groups have an odd number of electrons and, hence, have partially filled crystalline orbitals. In a surface containing a high concentration of O2- groups, the existence of these half-filled crystalline orbitals could make the surface “metallic-like” due to increased mixing of the anion and cation bands. The present study is restricted to examining the properties of NO2- surface defects, however, because open-shell “metallic-like” surface structures are not well suited for study by PHF theory. Results and Discussion. The “molecular-ionic” character of NaNO3 is apparent from the computed band structure. The bands are essentially flat across the Brillouin zone, which is consistent with the ionic character of the material. The occupied (valence) bands and the unoccupied (conduction) bands occur in distinct groupings separated by several electronvolts and the anionic bands are distinct from the cationic bands. The molecular character is evident from the mixing of states within the nitrate group. The character of each of these bands can be determined by projecting the charge density onto one or more atom-centered orbitals. The resulting projected density of states (PDOS) spectra illustrate the orbital character of the bands, sampled across the entire Brillouin zone. Figure 3 shows the total density of states (DOS) spectra for the NaNO3 bulk and clean slab, obtained by projecting the fully converged ab initio charge density onto individual atomic orbitals that comprise the valence and lowest energy conduction bands.9 The energy corresponding to the top of the valence band or highest occupied crystalline orbital (HOCO), which is analogous to the highest occupied molecular orbital (HOMO) in finite systems, has been set to zero in all of the DOS and PDOS spectra displayed here. The orbital character of the bands calculated for the bulk material, (Figure 3) is displayed in Figure 4 as projections onto the oxygen 2s and 2p orbitals, nitrogen 2s and 2p, and sodium 2p, 3s, and 3p crystalline orbitals. It is apparent in these projections that the two HOCOs (0 to -3.9 eV) are predominantly oxygen 2p in character (Figure 4). Only
McCarthy et al.
Figure 4. Projected density of states spectra for bulk sodium nitrate. The oxygen 2p and 2s, nitrogen 2p and 2s, and sodium 3s and 2p projections are displayed from top to bottom, respectively. The two highest occupied orbitals are predominantly of oxygen 2p character while the lowest unoccupied orbital is composed of a mixture of oxygen 2p and nitrogen 2p bands.
small contributions from the nitrogen 2p orbitals are evident in the second band (-2.0 to -3.0 eV) and negligible contributions from sodium are observed in this energy region. Projections onto the nitrogen, oxygen, and sodium atomic orbitals illustrate the concentration of charge density about those nuclear centers. The observed charge partitioning is consistent with the anionic character of the NO3- group and the cationic character of the Na+. Mulliken population analyses indicate net charges of -0.95|e| on the nitrate group and +0.95|e| on the sodium, with the total atomic charges being oxygen 8.66 ( 0.02|e|, nitrogen 5.92|e|, and sodium 10.04|e|. The molecularionic character of sodium nitrate is evident from the character of the conduction bands shown in Figure 4. The lowest unoccupied crystalline orbital (LUCO) (+17.0 to 18.3 eV) is formed from a near equal mixture of O (2p) and N (2p) (with no cationic contributions). These bands are well-separated (∼4 eV) from the higher energy diffuse bands, which are more “ionic-like” with contributions from sodium 3s. A qualitative assignment of the upper valence and unoccupied bands in the PDOS spectra (Figures 3 and 4) is made by comparing to the experimental absorption spectra for bulk NaNO3 discussed above.15 It should be noted that the Hartree-Fock method is very limited in its ability to describe the unoccupied manifold; hence, the computed one-electron eigenvalues do not accurately describe the excitation spectra of a periodic (or finite) material. In particular, the band gaps of ionic and semiconducting materials computed using the PHF method are typically overestimated by factors of 2-3. Despite this inherent limitation of the method, it has been shown that the bandwidths of the occupied (valence) and lowest unoccupied (conduction) bands are usually described reasonably well using PHF theory.9 Therefore, the error in the computed band gap can be viewed as a constant offset in the excitation energies and the character (individual orbital contributions) of the valence and lowest conduction bands can still be deduced from the PDOS spectra. Given that the computed DOS spectra are based solely on the electronic ground-state character of the material and that the calculated band gap is in error, we can only make qualitative comparisons between the DOS bands and specific electronic transitions. Assuming that the ordering of the ground-state eigenvalues mirrors the electronic transitions, the uppermost valence bands would correspond to the n (0.0 to -2.2 eV) and
Electronic Structure of Sodium Nitrate
Figure 5. Total density of states for the clean (defect free) 101h4 slab vs the oxygen-depleted defected slab. The zero of energy was fixed at the top of the valence band for the clean slab.
π2 (-2.2 to -3.9 eV) levels, respectively, and the lowest unoccupied band would form the π* state. Likewise, the sodium (3s) bands would correspond to the final state for the charge transfer transitions (see Figure 3). It is important to note that very little change in the band positions is observed between the bulk and clean surface DOS spectra (see Figure 3) and the PDOS spectra for the finite thickness slab is virtually identical to those shown for the bulk material (Figure 4). This implies that the absorption spectra of the bulk and surface states in sodium nitrate will be nearly identical. Hence, for laser desorption, from an undefected sample, the absorption cross section is the same for surface and bulk nitrate ions; i.e., they are electronically indistinguishable. This is consistent with the experimental observation that the desorption yield of NO (ejected from the surface layer) mimics the bulk absorption profile; i.e., no shifts in the absorption profile or “surface states” were detected.5 However, changes are evident in the DOS spectra when the crystal is defected by the removal of the outer oxygen atoms from the surface nitrate groups. When compared to the clean slab data (Figure 5), the defected slab reveals a much more complex total DOS spectra with noticeable shifts in the density distribution in the upper valence (HOCO) region. The shifts in the band positions are indicative of a change in chemical identity of the surface groups and not representative of the formation of oxygen vacancies in an ionic material. The overall character of the valence and conduction bands is essentially unchanged. If a high concentration of the resulting NO2- groups are present on the surface of this material (either during initial sample preparation or as a result of exposure to the laser radiation), then a 1-2 eV red shift in the π2 f π* transition would be expected. This results from the increased electron density on the nitrogen centers which causes a mixed oxygen 2p, nitrogen 2s, nitrogen 2p band to appear in the band gap region. The introduction of defects by laser irradiation or electron bombardment13 dramatically increases the photodesorption yield of NO induced by irradiation at sub-bandgap energies. This result is consistent with the theoretical prediction that surface defects lead to the formation of states in the bandgap region. A deconvolution of the DOS spectra reveals significant differences between the top and middle layers of the defected slab (Figure 6). It is important to note that changes in the electronic structure of the slab are localized on the top nitrite-
J. Phys. Chem., Vol. 100, No. 16, 1996 6711
Figure 6. Projected density of states for the top (dashed lines) and middle (solid lines) layers of the oxygen-depleted defected slab. Projections onto the oxygen 2p and 2s, and nitrogen 2p and 2s are displayed from top to bottom, respectively.
containing layer. The PDOS spectra of the adjacent undefected nitrate-containing layer (middle) are virtually identical to those of the clean slab. Mulliken population analyses indicate that the resultant surface nitrite groups maintain an overall charge of -0.95|e| and that the atomic charges on sodium and oxygen change less than 0.02|e| from the clean slab values. The most significant change in the charge distribution occurs on the nitrogen centers, which have an overall charge of 6.59|e| in the nitrite group (top layer) and 5.92|e| in the nitrate group (middle layer). The middle layer (solid lines in Figure 6) is qualitatively similar to the bulk (and clean slab), with the HOCOs (0.0 to -4.0 eV) dominant electron density in the O (2p) orbitals (although the upper most band between 0.0 and -2.0 eV is split). In contrast, the top layer (dashed lines) PDOS reveals substantial contributions from the nitrogen (2s) and (2p) orbitals and a rearrangement of the O (2p) bands. These changes result from the increased charge density in the vicinity of the nitrogen centers and cause bands to shift into the gap region. Shifts in the valence band positions of the top layer suggest that lower energy transitions into the π* state may become accessible with the formation of surface nitrites. [Note that the character and position of the lowest unoccupied bands (π*) are virtually identical in the top and middle layers of the defected slab.] A red shift in the absorption spectra when surface nitrite groups are present is consistent with the gas-phase spectroscopy of NO2- vs NO3- (described below). The π* r σ transition in nitrite is centered at 3.8 eV and occurs with over a 15-fold increase in the transition moment over similar processes in NO3-. For comparison, the spectra of bulk sodium nitrite is shown in Figure 7. The top layer of the defected slab (Figure 6 dashed lines) strongly resembles the density distribution of bulk NaNO2. Therefore, we predict that oxygen-depleted sites in NaNO3 will allow the lower energy “nitrite-like transitions” (π* r σ) to become accessible at photon energies below the π* r π resonance, thus enhancing the low-energy (red) region of the absorption profile. III. Excited-State Properties of Nitrate and Nitrite Theoretical Method. A significant theoretical challenge, and area of active research, is the development of ab initio methods (analogous to those used to study finite systems) that are capable of directly computing the excitation properties of solid materials. Transition energies and absorption profiles cannot be computed,
6712 J. Phys. Chem., Vol. 100, No. 16, 1996
McCarthy et al. TABLE 1: Optimized Geometries and Total Energies Obtained in the Present Work species -
NO2
NO3NO3b
method
Ve (au)
re (Å)
θe (∠ONO)
CCSD(T) CASSCFa CCSD(T) CASSCF CCSD(T) CASSCF
-204.889 420 -204.314 746 -280.003 811 -279.224 721 -279.852 717 -279.134 172
1.2638 1.2691 1.2606 1.2606 1.2354 1.2426
116.41 116.32 120.0 120.0 120.0 120.0
a The CAS-CMRCI optimized geometry and total energy was r ) e 1.259 Å, θe ) 116.40°, and Ve ) -204.676 078 au. See the text. b Constrained to D3h symmetry for this species.
Figure 7. Total and projected density of states for bulk sodium nitrite (NaNO2). The zero of energy was fixed at the top of the valence band. The total DOS and the PDOS for the oxygen 2p and 2s, and the nitrogen 2p and 2s, are displayed from top to bottom, respectively. The top layer of the defected slab (dashed lines in Figure 6) resembles the bulk NaNO2 spectra.
at present, for many solids because we lack rigorous descriptions of the bulk excited electronic states. The “localized” transitions in molecular-ionic crystals, like NaNO3, are notable exceptions to this quandary because they are well described by studying the gas-phase anion spectroscopy. In the present work the “molecular-like” π* r π2 transition in sodium nitrate was probed by studying the energetics of isolated NO2-, NO3-, and NO3. The original assignments of the spectral features in NaNO3 between 4 and 11 eV6,8 were based on early molecular orbital calculations on NO3-.16,17 The present work examines the spectroscopy of NO2-, NO3-, and NO3 in more detail using correlated ab initio methods to investigate the effect of the crystalline environment on the excitation spectra. The study of gas-phase NO2-, NO3-, and NO3 photochemistry was carried out primarily at the complete active space selfconsistent field (CASSCF) level of theory.18-22 The active space consisted of all the valence molecular orbitals formed from the atomic 2p orbitals of oxygen and the 2s and 2p orbitals of nitrogen. All of the 1s-like core orbitals and the orbitals with primarily oxygen 2s character in NO3- and NO3 were fully optimized but otherwise remained doubly occupied. For the electronic ground states, this resulted in a total number of configuration state functions (CSFs) in C2V symmetry of 4067 for NO2- (18 electrons in 12 orbitals), 36 146 for NO3- (18 electrons in 13 orbitals), and 107 500 for NO3 (17 electrons in 13 orbitals). In addition, for NO2-, multireference configuration interaction (MRCI) calculations were also carried out with the CASSCF reference functions described above. In these MRCI calculations, the internally contracted MRCI method (CMRCI) of Werner and Knowles23,24 was used to make the CI expansion more computationally tractable and the 1s-like and oxygen 2slike electrons were not correlated. In all cases, the Gaussian basis set used in the present work consisted of the standard augmented correlation consistent polarized valence triple zeta (aug-cc-pVTZ) set25,26 with the omission of the diffuse f-type functions. Thus, the contracted basis can be denoted as [5s4p3d1f], which resulted in 117 and 156 contracted functions for NO2- and NO3-/NO3, respectively. Unless otherwise noted, C2V symmetry was used throughout. For the electronic ground states (X1A1 for NO2-, X1A1′ for NO3-, and X2A2′ for NO3), equilibrium geometries were calculated using the CASSCF method outlined above, as well as with the coupled cluster singles and doubles (CCSD)
method27,28 augmented by a perturbative estimate of triple excitations, CCSD(T).29,30 For the open-shell species NO3, the spin-restricted method of Knowles et al. [RCCSD(T)] was employed.31 In these coupled cluster calculations (in contrast to the MRCI work), the oxygen 2s-like electrons were correlated. Furthermore, in each case the NO3 radical was constrained to have D3h symmetry, even though it is known that CASSCF wave functions like the one used in this work yield global minima of only C2V symmetry for NO3.32 In contrast, both experimental results and previous CCSD(T) calculations suggest that the true equilibrium geometry is very close to D3h. Vertical electronic excitation energies (relative to the CASSCF ground state equilibrium geometry) were calculated via a two-state CASSCF state-averaged procedure with equal weights. Specifically, each excited electronic state was stateaveraged with the ground electronic state with weights of 0.5 each. Both singlet and triplet excited states were investigated for the two negative ions, while only the lowest two doublets were computed for NO3. For NO2- vertical excitation energies were computed for states with symmetries A1, B2, B1, and A2. The low-lying excited electronic states of NO3- in D3h symmetry are 1,3A1′′, 1,3E′′, and 1,3E′. The E′′ and E′ states are doubly degenerate and correspond to spatial symmetries of B1 + A2 and A1 + B2 in C2V. Likewise, the A1′′ state reduces to A2 symmetry in C2V. For the NO3 radical, the low-lying electronic states are X2A2′′ (2B2 in C2V), 2E′′, and 2E′. In general, for the degenerate E′′ and E′ states, only the B1 and B2 components, respectively, were explicitly computed. All calculations on the isolated NO2-, NO3-, and NO3 species were carried out with the MOLPRO suite of ab initio programs.33 Results and Discussion. Calculated CCSD(T) and CASSCF equilibrium geometries, together with their corresponding total energies, are shown in Table 1 for the electronic ground states of NO2-, NO3-, and NO3. For NO2- the CASSCF equilibrium bond length is longer by about 0.005 Å than that calculated by CCSD(T). Both values, however, are consistent with the CASSCF work of Peterson et al.,34 where a somewhat smaller basis set was used. The CCSD(T) and CASSCF values for re are calculated to be nearly identical for NO3-. In addition, the equilibrium NO bond lengths for both NO2- and NO3- are very similar to each other. For the NO3 radical, which is characterized by somewhat shorter equilibrium bond distances, the difference between CCSD(T) and CASSCF is somewhat larger and can perhaps be attributed to its larger multireference character. The difficulties associated with using single reference methods on NO3 are well documented.28 They arise from the strong interaction of the ground state with the first excited 1E′′ state, one component of which has 1B2 symmetry in C2V (the ground state has 1B2 symmetry in C2V). The equilibrium electron affinity of NO3 is calculated to be 2.46 and 4.11 eV at the CASSCF and CCSD(T) levels of theory, respectively, which can be compared to the experimental value of 3.937 eV.15 The relatively small value resulting from the CASSCF calculation
Electronic Structure of Sodium Nitrate
J. Phys. Chem., Vol. 100, No. 16, 1996 6713
Figure 8. Calculated energies for the electronic transitions in NO2-, NO3-, and NO3. Transition assignments and state symmetries are designated to the left and right of the calculated vertical energy levels (horizontal lines), respectively. Triplet state levels have been omitted for figure clarity. The corresponding transition moments are reported in Table 2.
TABLE 2: Calculated CASSCF Vertical Excitation Energies and Electronic Transition Moments for NO2-, NO3-, and NO3 species character
state
NO2-a π* r σ π* r n π* r π2 π* r π1 NO3-b π* r n π* r σ π* r π NO3c π r n nrσ
1B 1 1A 2 1B 2 1A 1 1A ′ (1 A2) 1 1E′′ (1B ) 1 1 E′ (1B2) 2 E′′ (2B1) 2E′ (2B ) 2
∆E (eV) µ (au) 3.830 4.445 6.583 7.492 4.585 6.441 6.944 0.959 1.934
-0.158 0.0 -1.048 0.067 0.0 0.009 -1.081 0.0 -0.545
state
∆E (eV)
3B 1 3A 2 3B 2 3A 1 3A ′′ (3 A2) 1 3E′′ (3B ) 1 3 E′ (3B2)
2.944 4.311 4.315 8.596 4.489 6.404 5.288
a Computed relative to r ) 2.398 a and θ ) 116.32°. Vertical 0 excitation energies at the CAS-CMRCI level (relative to r ) 2.379 a0 1 and θ ) 116.40°) are (in eV): 3.64 ( B1), 4.41 (1A2), 6.52 (1B2), 7.45 (1A1), 2.79 (3B1), 4.25 (3A2), 4.35 (3B2), 8.57 (3A1). b Computed relative to r ) 2.390 a0 and θ ) 120°. c Computed relative to r ) 2.350 a0 and θ ) 120°.
is primarily due to the lack of dynamical correlation, while the overestimation of the CCSD(T) calculation is presumably due to the poorer description provided by this method for the openshell NO3 radical compared to NO3-. Calculated CASSCF vertical electronic excitation energies are shown in Table 2 and Figure 8 for each species. Each transition is to a molecular orbital of π* character. Not surprisingly, the electronic spectra of the nitrite and nitrate ions are fairly similar. In each case, as shown in Table 2, the π* r π transition, 1B2 r X1A1 for NO2- and 1E′ r X1A1′ for NO3-, has the largest oscillator strength. As noted in previous studies, the excitation energies are also very similar in energy. The next strongest feature is the π* r σ transition, 1B1 r X1A1 for NO2- and 1E′′ r X1A1′ for NO3-. This transition occurs at much higher energy in NO3- than in NO2- (6.44 vs 3.83 eV, respectively) but is predicted to be much more intense in NO2than in NO3-. The CASSCF calculations for NO3 indicate that the 2E′ r 2 X A1′′ transition should be of moderately strong intensity. Our calculated excitation energy of 1.93 eV for the transition to the 2E′ state is in good agreement with the experimentally determined band origin near 1.87 eV. Although the 2E′′ state is not accessible from the ground state of NO3, it has been characterized indirectly from the photoelectron work of Weaver et al.15 on NO3-. Their study yielded a 2E′′ r X2A1′′ band origin of 0.87 eV. Our calculated Vertical excitation energy of 0.96 eV is somewhat larger than the experimental value but is consistent
with the expected difference between the vertical and adiabatic excitation energies (as is also true for the 2E′ transition). Figure 1 summarizes the calculated electronic spectra for NO2-, NO3-, and NO3. A qualitative estimate of the effect of the crystalline environment on the transition energies was obtained by embedding the NO2-, NO3-, and NO3 groups in a finite array of charges designed to mimic the first two nearest-neighbor shells surrounding a nitrate ion. The positions of the charges corresponded to the bulk distances, and the magnitudes were obtained from the Mulliken atomic populations computed in the PHF calculations of the bulk crystal (reported above). This mock crystal environment stabilized all of the energy levels of the ionic species but had little or no effect on the neutral NO3 levels. The stabilization of the NO3- and NO2- energy levels shifted all of the levels (ground and excited states) equally and, hence, it did not alter the relative positions and transition energies. This result reaffirms that the photoabsorption step in the laser desorption processes is similar for gas-phase and crystalline nitrate ions. However, the subsequent dissociation step will be quantitatively different because the energy levels of the neutral NO3 fragment are only very slightly stabilized by the crystal field. The stabilization of the ionic species by the Coulomb field of the crystal causes the neutral photodetachment channel in the crystal to be energetically inaccessible. This effect was discussed in our earlier paper.5 At the crystal surface, the direct dissociation of excited state NO3- will produce (in the lowest energy channel) NO and O2-. The Coulomb field of the crystal will preferentially trap the ionic O2- species and, hence, the dominant dissociation product should be neutral NO. This is observed in the LDMS experiment and has been discussed in detail.5 IV. Conclusions This study is the theoretical component of a joint theoretical/ experimental investigation of laser desorption processes in sodium nitrate. The results of the experimental investigation of the laser desorption of NO from single-crystal sodium nitrate following the π* r π2 absorption were presented earlier.5 The electronic structure of NaNO3 is unique when compared to structurally similar materials such as CaCO3 because the lowest energy transitions are “localized” on the nitrate ion. The unique “molecular-ionic” nature of this material allowed us to investigate the ground state structure and the excitation spectra using complimentary theoretical methods. Ab initio PHF theory was used to investigate the electronic structure of bulk and cleaved sodium nitrate. The band structure and PDOS spectra reveal the combined molecular and ionic character of this material. The cationic (sodium) and anionic (nitrate) valence bands are well separated and flat across the Brillouin zone, with a large gap between the top of the valence and the bottom of the conduction bands. Nitrogen and oxygen orbitals combine to form the “molecular-like” nitrate bands. The uppermost valence bands in the bulk and clean surface consist predominantly of oxygen 2p orbitals. Photoexcitation of the π* r π2 transition is from the valence bands to the lowest unoccupied states. The latter formed from an equal mixture of oxygen and nitrogen 2p orbitals. The projected density of state spectra of bulk NaNO3 and the clean cleaved crystal (along the 101h4 direction) are nearly identical, indicating that the absorption profile of the bulk and surface nitrate anions will be the same. Hence, for laser desorption on an undefected sample the absorption cross section is the same for surface and bulk chromophores; i.e., they are electronically indistinguishable. This is consistent with the
6714 J. Phys. Chem., Vol. 100, No. 16, 1996 experimental observation that the NO photodesorption yield from the clean surface mimics the bulk absorption profile (i.e., minimal sub-bandgap desorption is observed). However, changes in the excitation spectra are, however, expected to occur when the surface is chemically or structurally defected. Converting NO3- to NO2- groups on the surface is energetically facile and could take place during experimental sample preparation or irradiation. The presence of surface nitrite is predicted to cause a shift in electron density into the gap region, producing a +1 to +2 eV red shift in the absorption profile. Such a red shift is inferred in the LDMS experiments from the high NO yield induced by sub-bandgap irradiation energies for heavily defected surfaces. The “localization” of the 6 eV band on the nitrate ion is due to the “molecular-like” character of crystalline NaNO3. The assignment of this band to the π* r π2 transition is based on the spectroscopy of other nitrate compounds in solids and in solution. The “molecular-like” spectroscopic properties of this material have been probed by quantum mechanical CASSCF calculations of the ground- and excited-state energies of the gasphase species (NO2-, NO3-, and NO3). These high-level ab initio calculations on the isolated gas-phase species reaffirm the spectroscopic assignment based on earlier molecular orbital calculations.16,17 The effect of the crystalline environment on the transition energies was investigated by embedding NO3-, NO2-, and NO3 in a finite array of point charges that mimic the first two nearest-neighbor shells in the bulk. All of the states (ground and excited) of the negative ions (NO3- and NO2-) were equally stabilized by the electrostatic field; thus the transition energies did not change when the ion was placed in the mock crystal field. In contrast to the negative ions, no stabilization of neutral NO3 occurred when it was embedded in the point charge array. This lack of stabilization causes the neutral photodetachment channel to be inaccessible in the 6 eV photoexcitation of the crystal, permitting the direct dissociation of excited state nitrate (NO3-)* to form NO + O2- to be the energetically allowed pathway. The NO is then ejected from the crystal leaving O2- trapped (for some time) on the surface. Since the yield of O2 to NO yield is far less than stoichiometric, the resonant desorption experiments are consistent with the O2trapping mechanism. Acknowledgment. The authors were supported by the Divisions of Chemical Sciences and Geosciences of the Office of Basic Energy Sciences, U.S. Department of Energy and the Strategic Environmental Research Development Program. K.A.P. also acknowledges the support of the National Science Foundation under a CAREER award No. CHE-9501262. We also thank the Scientific Computing Staff, Office of Energy Research, U.S. Department of Energy, for a grant of computing time at the National Energy Supercomputing Center. Pacific Northwest National Laboratory is operated for the U.S. Department of
McCarthy et al. Energy by Battelle under contract No. DE-AC06-76RLO 1830. We thank Kristine German, Tom Orlando, and Karen Knutsen for many valuable discussions. References and Notes (1) Laser Ablation: Mechanisms and Applications; Miller, J. C., Haglund, R. F., Jr., Eds.; Springer Lecture Notes in Physics; SpringerVerlag: New York, 1991; Vol. 389. (2) Karas, M.; Hillenkamp, F. Anal. Chem. 1988, 60, 2299. (3) Grotemeyer, J.; Schlag, E. W. Acc. Chem. Res. 1989, 22, 399. (4) Laser Ablation: Mechanisms and Applications-II; Miller, J. C., Geohegan, D. B., Eds.; AIP Conference Proceedings; AIP Press: New York, 1994; Vol. 288. (5) Bradley, R. A., Jr.; Lanzendorf, E.; McCarthy, M. I.; Orlando, T. M.; Hess, W. P. J. Phys. Chem. 1995, 99, 11715. (6) Yamashita, H. J. Phys. Soc. Jpn. 1972, 33, 1407. (7) Carbonates: Mineralogy and Chemistry; Reeder, R. J., Ed.; Mineralogical Society of America: Washington, DC, 1983; Vol. 11. (8) Yamashita, H.; Kato, R. J. Phys. Soc. Jpn. 1970, 29, 1557. (9) Pisani, C.; Dovesi, R.; Roetti, C. Hartree-Fock Ab Initio Treatment of Crystalline Systems; Lecture Notes in Chemistry; Springer Verlag: New York, 1988; Vol. 48. (10) CRYSTAL92 User Manual; Dovesi, R.; Saunders, V. R.; Roetti, C. “CRYSTAL92,” University of Torino, 1992. (11) Hehr, W. J.; Random, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. (12) Wells, A. F. Structural Inorganic Chemistry; Clarendon Press: Oxford, U.K., 1984. (13) Webb, R.; Dickinson, J. T.; Langford, S. C. Nucl. Instrum. Meth. Phys. ReV. B, submitted for publication. (14) Frazer, B. C. Acta Crystallogr. 1961, 14, 56. (15) Weaver, A.; Arnold, D. W.; Bradforth, S. E.; Neumark, D. M. J. Chem. Phys. 1991, 94, 1740. (16) McEwen, L. J. Chem. Phys. 1961, 34, 547. (17) Harris, L. E. J. Chem. Phys. 1973, 58, 5615. (18) Cheung, L. M.; Sundberg, K. R.; Reudenberg, K. Int. J. Quantum Chem. 1979, 16, 1103. (19) Roos, B.; Taylor, P.; Siegbahn, P. E. M. Chem. Phys. 1980, 48, 157. (20) Siegbahn, P. E. M.; Almlof, L.; Heiberg, A.; Roos, B. O. J. Chem. Phys. 1981, 74, 2384. (21) Werner, H.-J.; Knowles, P. J. J. Chem. Phys. 1985, 82, 5053. (22) Knowles, P. J.; Werner, H.-J. Chem. Phys. Lett. 1985, 115, 259. (23) Werner, H.-J.; Knowles, P. J. J. Chem. Phys. 1988, 89, 5803. (24) Knowles, P. J.; Werner, H.-J. Chem. Phys. Lett. 1988, 145, 514. (25) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007. (26) Kendall, R. A.; Dunning, T. H., Jr.; Harrison, R. J. J. Chem. Phys. 1992, 96, 6796. (27) Purvis, G. D.; Bartlett, R. J. J. Chem. Phys. 1982, 76, 1910. (28) Hampel, C.; Peterson, K. A.; Werner, H.-J. Chem. Phys. Lett. 1992, 190, 1. (29) Ragavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. Chem. Phys. Lett. 1989, 157, 479. (30) Deegan, M. J. O.; Knowles, P. J. Chem. Phys. Lett. 1994, 227, 321. (31) Knowles, P. J.; Hampel, C.; Werner, H.-J. J. Chem. Phys. 1994, 99, 5219. (32) Davy, R. D.; Schaefer, H. F. I. J. Chem. Phys. 1989, 91, 4410. (33) MOLPRO is a suite of ab initio programs written by Werner, H.J.; Knowles, P. J.; with contributions from Almlo¨f, J.; Amos, R. D.; Deegan, M. J. O.; Elbert, S. T.; Hampel, C.; Meyer, W.; Peterson, K. A.; Pitzer, R. M.; Reinsch, E.-A.; Stone, A. J.; Taylor, P. R.; “MOLPRO,” 1993. (34) Peterson, K. A.; Mayrhofer, R. C.; Sibert, E. L., III; Woods, R. C. J. Chem. Phys. 1991, 94, 414.
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