Comparative First-Principles Study of Structural and Optical Properties

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9856

J. Phys. Chem. B 2006, 110, 9856-9862

Comparative First-Principles Study of Structural and Optical Properties of Alkali Metal Azides Weihua Zhu,* Jijun Xiao, and Heming Xiao† Institute for Computation in Molecular and Materials Science and Department of Chemistry, Nanjing UniVersity of Science and Technology, Nanjing 210094, China ReceiVed: February 27, 2006; In Final Form: April 1, 2006

A comparative first-principles study of the structural and optical properties of the alkali metal azides has been performed with density functional theory within the generalized gradient approximation. The crystal structures of the alkali azides compare well with experimental data. Their ionic character is manifested by the closeness of their internitrogen distances to the calculated N-N bond length for the free azide ion. An analysis of electronic structure, charge transfer, and bond order shows that the alkali azides are all wide-gap insulators and ionic compounds. The energy band and density of states for lithium azide and R-sodium azide are very similar, while these for potassium azide, R-rubidium azide, and R-cesium azide are alike, but some modifications are observed with the increment of alkali metals’ electropositivity. These changes are closely related to the differences of the crystal structures. The general shapes of the real and imaginary parts of the dielectric function, adsorption coefficient, and electron energy-loss spectra are quite similar. The peaks originate from the electron transitions from the alkali metal s and p states to the conduction band. Our calculated optical properties for the alkali azides are found to be in good agreement with available experimental data. The absorption spectra of the alkali azides show a number of absorption peaks, which are believed to be associated with different exciton states, in the fundamental absorption region. In general, the electron energyloss spectra have two plasma frequencies.

1. Introduction Inorganic azides exhibit a comparatively rare set of physical and chemical properties that have made them attract considerable attention.1-6 Apart from their industrial usefulness as explosives and gas generators, the inorganic azides are potentially model systems for theories of fast reactions in solids because they are chemically and structurally simple among solids that deflagrate or detonate. Additionally, the azides are of interest to solidstate chemists and physicists because, as crystalline substances, they represent a degree of sophistication beyond the metal halides challenging quantitative description. Metal azides exhibit behavior that ranges from stable to extremely unstable, so detailed study of this homologous series of compounds offers the possibility of determining microscopic properties, which are critical to macroscopic energetic behavior. The electronic structure of metal azides is intimately related to their fundamental physical and chemical properties including optical absorption and exothermicity (or endothermicity) on conversion to decomposition products; moreover, an understanding of electronic structure and properties is necessary for discussion of electronic processes as they relate to decomposition and initiation. Therefore there has been considerable interest in the optical and electrical properties of monovalent metal azides in order to understand the mechanisms of decomposition.4 These azides are also most suitable to investigate the main regularities of chemical reactions in solids.1 Thus the knowledge of their optical and electrical properties appears to be very important in understanding the reasons of their high reactivity and in developing models that adequately describe their behavior. * Address correspondence to this author. E-mail: [email protected]. † Fax: +86-25-84303919. E-mail: [email protected].

Alkali metal azides are known to be the typical series of the materials mentioned and potentially model systems for theories of fast reactions in solids. It is hence necessary to investigate their electronic structure and optical properties. Theoretical calculations are an effective way to model the physical and chemical properties of complex solids at the atomic level as a complement to experimental work. Previously, a condensed matter study in the ab initio Hartree-Fock (HF) approximation was performed to investigate band structure and electronic properties of lithium azide.7 Xiao and Li8 have used a cluster model to study the electronic structure of alkali metal azides at the semiempirical DV-XR level. Gordienko et al.9 presented a theoretical study on the electronic structure of alkali metal azides. Afterward, an ab initio HF investigation was presented to study the electronic structure of lithium azide, sodium azide, and lead azide.10 There are few studies including electron correlation at an ab initio level on the electronic structure of alkali metal azides. Recently, Gordienko and Poplavnoi11 presented density functional theory (DFT) calculations within a local density approximation (LDA) to study the electronic structure of lithium azide. Ju et al.12 used the periodic DFT-B3LYP technique to investigate the electronic structure of lithium azide, R-sodium azide, and potassium azide. These were done for the observed crystal structure and do not shed any light on the structure. Recently DFT with pseudopotentials and a plane wave basis set, often used within the generalized gradient approximation (GGA), has been well established and has been successfully applied to the study of structures and properties of solids. This method not only includes electron correlation but also relaxes crystal structure. As the structural and optical properties of the alkali azides are not systematically

10.1021/jp0612275 CCC: $33.50 © 2006 American Chemical Society Published on Web 05/03/2006

Study of the Properties of Alkali Metal Azides

J. Phys. Chem. B, Vol. 110, No. 20, 2006 9857

Figure 1. Unit cells for (a) LiN3 and R-NaN3 and (b) KN3, R-RbN3, and R-CsN3. Big spheres are metal cations and small spheres are nitrogen anions.

investigated and compared, there is a clear need to gain an understanding of those at the atomic level. In this study we performed periodic DFT total energy calculations to study the structural and optical properties of alkali metal azides. The atomic positions and the unit-cell parameters were allowed to relax to the minimum energy configuration to investigate the crystal structure. Then we examined the differences in the structural and electronic properties among these azides. Finally we studied and compared their optical properties. The remainder of this paper is organized as follows. A brief description of our computational method is given in section 2. The results and discussion are presented in section 3, followed by a summary of our conclusions in section 4. 2. Computational Method The calculations performed in this study were done within the framework of DFT,13 using Vanderbilt-type ultrasoft pseudopotentials14 and a plane-wave expansion of the wave functions. The self-consistent ground state of the system was determined by using a band-by-band conjugate gradient technique to minimize the total energy of the system with respect to the plane-wave coefficients. The electronic wave functions were obtained by a density-mixing scheme15 and the structures were relaxed by using the Broyden, Fletcher, Goldfarb, and Shannon (BFGS) method.16 The GGA proposed by Perdew and Wang,17,18 named PW91, was employed. The cutoff energy of plane waves was set to 500.0 eV. Brillouin zone sampling was performed by using the Monkhost-Pack scheme with a k-point grid of 4 × 4 × 4. The values of the kinetic energy cutoff and the k-point grid were determined to ensure the convergence of total energies to within 0.01%. In the geometry relaxation, the total energy

of the system was converged less than 1.0 × 10-6 eV, the residual force less than 0.02 eV/Å, the displacement of atoms less than 0.001 Å, and the residual bulk stress less than 0.1 GPa. Bulk lithium azide (LiN3) and R-sodium azide (R-NaN3) are isomorphous and crystallize in a monoclinic C2/m space group with two molecules per unit cell. Each azide group is surrounded by six cations, and vice versa. Pringle and Noakes19 have determined both structures, shown in Figure 1a. Potassium azide (KN3), R-rubidium azide (R-RbN3), and R-cesium azide (RCsN3) crystals are isostructural at room temperature with a bodycentered tetragonal space group I4/mcm containing four molecules per unit cell (Figure 1b). Each azide ion in the KN3type structure is surrounded by eight cations, four at each end, and vice versa. Mu¨ller20 has reported the crystal structures of KN3, R-RbN3, and R-CsN3. Afterward Choi and Prince21 have reinvestigated KN3 and R-RbN3 structures. 3. Results and Discussion 3.1. Crystal Structure and Ionic Character. The full relaxation of the structure was performed to allow the ionic configurations, cell shape, and volume to change. In our previous study22 we applied two different functionals (LDA and GGA) to bulk lithium azide as a test and found that the GGA (PW91) may be expected to produce more reliable predictions of the structures. Therefore GGA was used in all calculations here. The calculated structural parameters, atomic fractional coordinates, and bond lengths of alkali metal azides are given in Table 1 together with their experimental results.19-21 The calculated results well reproduce the measured lattice constants of the alkali azides. To check the effect of the relaxation on the ion configuration, we compared relaxed atomic fractional coordinates for the azides with experimental values in Table 1. The results show that the effect of the relaxation on the ionic positions is very small. We also note that the internal structure parameters of the azides assigned by the bond lengths are very close to the experimental data. The ionic character of the alkali metal azides is manifested by their relatively simple crystal structure. According to our previously calculated N-N bond length of 1.177 Å for the isolated N3- ion,22 the closeness of their internitrogen distances to the calculated N-N bond length for the free azide ion, ∆(N-N), is calculated and shown in Table 2 along with bond angle N-N-N. Formal ionicities expressed as percent ionic

TABLE 1: Relaxed and Experimental (in parentheses) Lattice Constants (Å), Atomic Fractional Coordinates, and Bond Lengths (Å) for the Alkali Azides atomic fractional coordinate compd LiN3

R-NaN3

KN3 R-RbN3 R-CsN3

lattice constant a ) 5.626 (5.627) b ) 3.317 (3.319) c ) 5.035 (4.979) β ) 106.7° (107.4°) a ) 6.218 (6.211) b ) 3.660 (3.658) c ) 5.413 (5.323) β ) 107.9° (108.4°) a ) 6.154 (6.113) b ) 6.154 (6.113) c ) 7.063 (7.094) a ) 6.379 (6.310) b ) 6.379 (6.310) c ) 7.508 (7.519) a ) 6.625 (6.541) b ) 6.625 (6.541) c ) 8.087 (8.091)

cation

end N

central N

N-N bond length

u ) 0.0 (0.0) V ) 0.0 (0.0) w ) 0.0 (0.0)

u ) 0.1040 (0.1048) V ) 0.5 (0.5) w ) 0.7376 (0.7397)

u ) 0.0(0.0) V ) 0.5 (0.5) w ) 0.5 (0.5)

1.171 (1.162)

u ) 0.0 (0.0) V ) 0.0 (0.0) w ) 0.0 (0.0)

u ) 0.0905 (0.1016) V ) 0.5 (0.5) w ) 0.7246 (0.7258)

u ) 0.0 (0.0) V ) 0.5 (0.5) w ) 0.5 (0.5)

1.172 (1.167)

u ) 0.0 (0.0) V ) 0.0 (0.0) w ) 0.25 (0.25) u ) 0.0 (0.0) V ) 0.0 (0.0) w ) 0.25 (0.25) u ) 0.0 (0.0) V ) 0.0 (0.0) w ) 0.25 (0.25)

u ) 0.1349 (0.1358) V ) 0.6348 (0.6358) w ) 0.0 (0.0) u ) 0.1300 (0.1315) V ) 0.6305 (0.6315) w ) 0.0 (0.0) u ) 0.1255 (0.1268) V ) 0.6255 (0.6268) w ) 0.0 (0.0)

u ) 0.0 (0.0) V ) 0.5 (0.5) w ) 0.0 (0.0) u ) 0.0 (0.0) V ) 0.5 (0.5) w ) 0.0 (0.0) u ) 0.0 (0.0) V ) 0.5 (0.5) w ) 0.0 (0.0)

1.174 (1.184) 1.175 (1.187) 1.176 (1.177)

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TABLE 2: The Closeness of the Internitrogen Distances of the Alkali Azides to the Calculated N-N Bond Length for the Free Azide Ion, ∆(N-N), Bond Angle N-N-N, and Formal Ionicities1 Expressed as Percent Ionic Character of Metal-to-Azide Bonds for the Alkali Azides compd

∆(N-N) (Å)

∠N-N-N (deg)

LiN3 R-NaN3 KN3 R-RbN3 R-CsN3

0.006 0.005 0.003 0.002 0.001

180 180 180 180 180

chemical bond Li-N3 Na-N3 K-N3 Rb-N3 Cs-N3

formal ionicity 67 70 74 74 76

character of metal-to-azide bonds for the alkali azides are from ref 1 and are also listed in Table 2 for comparison. We note that the ∆(N-N) values are very small. The entire calculated bond angle N-N-N of the alkali azides is 180°, equal to that for the free azide ion. It can be inferred that the structures of azide ions in the alkali azides are symmetric. This complies with previous experiment results.19-21 These give further evidence of the ionic character of the alkali azides. The order of ∆(N-N) for the alkali azides is as follows: LiN3 > R-NaN3 > KN3 > R-RbN3 > R-CsN3; so their ionic character intensifies in the following sequence: LiN3 < R-NaN3 < KN3 < R-RbN3 < R-CsN3. This is consistent with previous results based on formal ionicities in Table 1. The alkali azides are simple inorganic compounds in which all available valencies are bound to azide groups; thus their ionic character alone determines their chemical reactivity. Accordingly, the alkali metal azides are stable and their relative stable order is as follows: LiN3 < R-NaN3 < KN3 < R-RbN3 < R-CsN3. Some of them may be made in aqueous solution and the rest in nonaqueous media.

Their ionic character will be further discussed below on the basis of electronic structure. 3.2. Electronic Structure. The energy band structures of the alkali azides are shown in Figure 2. The origin of the energy is taken to be the Fermi level. Clearly, the structures are similar and appear to vary only in the width of the energy band and the flatness of the top of the valence band. Several characteristic features should be emphasized. First, LiN3, R-NaN3, KN3, R-RbN3, and R-CsN3 exhibit large energy gaps of 4.684, 5.034, 4.334, 4.404, and 4.344 eV between valence and conduction bands, respectively, indicating that they are wide-gap insulators. In comparison with experiments, band gaps are generally underestimated in DFT calculations, but these errors are close to being shifts of band energies. Thus these band gaps are regarded as the lower limits. On general grounds, the larger band-gap azides are expected to be relatively less energetic compared to the end products of light decomposition, and the smaller band-gap azides relatively more energetic. The alkali azides have large energy gaps, thus one may envision that they are relatively less energetic. These suggestions agree with the conclusion that ionic azides are stable, heavy-metal azides explode on provocation, and covalent azides explode spontaneously.1,8 Second, the energy band structures of LiN3 and R-NaN3 are very alike, and yet these of KN3, R-RbN3, and R-CsN3 are quite similar. This is supported by the fact that LiN3 and R-NaN3 are isomorphous, while KN3, R-RbN3, and R-CsN3 are isostructural, as shown in Figure 1. Third, the width of the energy band narrows in the following sequence: LiN3 > R-NaN3 > KN3 > R-RbN3 > R-CsN3. The more narrow the width of the band becomes, the stronger the interactions between the bands

Figure 2. Energy band structures of (a) LiN3, (b) R-NaN3, (c) KN3, (d) R-RbN3, and (e) R-CsN3.

Study of the Properties of Alkali Metal Azides

Figure 3. Total density of states (DOS) of the alkali azides. The Fermi energy is shown as a dashed vertical line.

are, and the more intensive is the ionic character. Therefore their ionic character intensifies in the following sequence: LiN3 < R-NaN3 < KN3 < R-RbN3 < R-CsN3. This is consistent with the results presented in Table 2. Finally, the flatness of the top of the valence band varies in the following order: LiN3 < R-NaN3 < KN3 < R-RbN3 < R-CsN3. The more even the top of the valence band becomes, the stronger the interactions between metal and azide are. This implies that their ionic character intensifies in the same order as the increase in their flatness of the top of the valence band. To obtain further information about the bond nature of the alkali azides the electronic density of states (DOS) are calculated and displayed in Figure 3. We observe several general features. Although the Fermi energy levels occur at the peaks of DOS, the alkali azides have large band gaps, indicating that they are all insulators. This is supported by previous reports that the alkali azides have poor electrical conductivity.23,24 As with the energy band structures, there are some strong similarities in DOS between LiN3 and R-NaN3 along with some subtle differences. The same is true of KN3, R-RbN3, and R-CsN3. With the increment of alkali metals’ electropositivity of these azides, the peaks of DOS in the valence band region have a tendency to shift to the Fermi level. For R-CsN3, the shift of the peaks is more obvious. This indicates that the overlap of the energy bands is increased. In the conduction band region, the states become more and more localized from LiN3 to R-CsN3. These observations imply that the ionic character of the alkali azides intensifies with the increment of alkali metals’ electropositivity. The states can be classified as s and p states. The identification of these features is made straightforward by the examination of the partial DOS (PDOS) on the states. The atom-resolved PDOS of the alkali azides are shown in Figures 4, 5, and 6, respectively. The main features can be summarized as follows. (i) The peaks of DOS at the Fermi levels are dominated by the end N-p contributions. The alkali metal states have hardly any projection in the energy range from -4.0 eV up to the Fermi level, indicating that they play the role of electron donors in the systems. Therefore the valence bands are dominated largely by the strong attractive potential of the end N states. (ii) In the valence band region of DOS, the peaks originating from the alkali metal states hardly overlap those arising from the N states. This does suggest that the alkali azides have ionic character. (iii) In the conduction band region of DOS, the peaks are superimposed by the alkali metal and N states. (iv) In Figure 4, from Li to Cs states, the PDOS in the valence band region

J. Phys. Chem. B, Vol. 110, No. 20, 2006 9859

Figure 4. Partial density of states (PDOS) of alkali metal cations for the alkali azides.

Figure 5. Partial density of states (PDOS) of end nitrogen anions for the alkali azides.

Figure 6. Partial density of states (PDOS) of central nitrogen anions for the alkali azides.

gradually shifts toward the Fermi level, and so the interactions between the alkali metal and N states become stronger. This shows that the ionic character of the alkali azides intensifies from LiN3 to R-CsN3. (v) In Figures 5 and 6, four strong peaks occur at the same energy in the PDOS of a particular central N atom and a particular end N atom. It can be inferred that the two atoms are strongly bonded. (vi) There are some differences

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TABLE 3: Calculated Charge Transfers and Bond Order for the Alkali Azides and Isolated Azide Ion

alkali metal end N central N

LiN3

R-NaN3

-0.87 0.48 -0.09

charge transfer(e) -0.93 -0.97 -0.93 0.50 0.50 0.49 -0.07 -0.03 -0.04

alkali metal-end N 0.14 end N-central N 1.26 end N-end N -0.23

KN3

bond order 0.12 0.02 1.24 1.22 -0.23 -0.22

R-RbN3 R-CsN3

0 1.19 -0.22

isolated N3-

-1.06 0.54 -0.01

0.56 -0.11

0 1.20 -0.22

1.08 -0.25

in the PDOS of central and end N atoms. This is due to the differences in their local bonding configurations. (vii) We also note that there is a quite small alkali metal contribution in DOS of these azides from -7.5 eV to 0 eV. In this sense, the alkali azides are not purely ionic compounds. In our previous study,22 we compared the calculated DOS of LiN3 with the observed X-ray photoelectron spectrum (XPS) of the azide ion’s valence molecular orbital levels without interference from cationic levels and found that our calculated results reproduce the ordering of valence bands from XPS data. Only one peak cannot be explained, probably due to contaminations or other extrinsic states. The same is true of R-NaN3 since the DOS of LiN3 is very similar to that of R-NaN3 as shown in Figure 3. This is because the two crystals are isomorphous. In comparison with the XPS of the azide ion’s valence molecular orbital levels, the DOS of KN3, R-RbN3, and R-CsN3 reproduce the sequence of several peaks from XPS, but in the adsorption region of the XPS, there are three peaks originating from the alkali metal states. It can be inferred that the interactions between K, Rb, or Cs and N states are stronger than these between Li or Na and N states. This further demonstrates the results discussed above. The electronic structure can be further analyzed by examining the charge transfer and bond order in the alkali azides. The Mulliken charge and overlap population are useful in evaluating the nature of bonds in a compound. Although the absolute magnitudes of Mulliken populations have little physical meaning, the relative values can still offer some useful information. Table 3 shows the charge transfer and bond order values for the alkali metal azides and isolated azide ion. The effective valences for Li, Na, K, and Rb in the alkali azides are in the range of 0.87-0.93, unequal to 1; moreover their end nitrogens have 0.48-0.50 e charge, smaller than the charge of 0.56 e on the end N of isolated azide ion. These values show that these alkali azides are mainly ionic compounds. The charge transfer from Cs to N is 1.06, close to 1. We also note that the charge of 0.54 e on the end nitrogen atoms of R-CsN3 is very close to 0.56 e for the end N atom in isolated azide ion. These features indicate that R-CsN3 has the highest ionicity among the alkali azides. This is supported by the calculated results displayed in Figure 3. Bond order is a measure of the overall bond strength between two atoms. A high value of the bond order indicates a covalent bond, while a low value shows an ionic nature. It is seen from Table 3 that the bond orders for the alkali metalend N bonds decrease in the following order: LiN3 > R-NaN3 > KN3 > R-RbN3 ∼ R-CsN3; so their ionic character intensifies in the following sequence: LiN3 < R-NaN3 < KN3 < R-RbN3 ∼ R-CsN3. This further confirms the above results. Since the Li-, Na-, and K-end N bonds have bond order of 0.14, 0.12, and 0.02, respectively, their bonds have visible polarizations. Obviously, this suggests that LiN3, R-NaN3, and KN3 are not purely ionic compounds. The entire end N-central N bonds for the alkali azides have considerable bond order values (1.19-

Figure 7. Imaginary parts 2(ω) of dielectric functions for the alkali azides.

Figure 8. Real parts 1(ω) of dielectric functions for the alkali azides.

1.26). It is obvious that the end N-central N bond is the strongest bond and has strong covalence in the systems. The bond orders for end N-central N bonds in the alkali azides are higher than these in isolated azide ion. This implies that the azide ions in the alkali azides are more stable than the isolated azide ion. 3.3. Optical Properties. In this section, we turn to investigate the optical properties of the alkali azides because they are unstable and decompose into metal and nitrogen under the action of light and heat. The interaction of a photon with the electrons in the system can result in transitions between occupied and unoccupied states. The spectra resulting from these excitations can be described as a joint density of states between the valence and conduction bands. The imaginary part 2(ω) of the dielectric function can be obtained from the momentum matrix elements between the occupied and unoccupied wave functions within the selection rules, and the real part 1(ω) of the dielectric function can be calculated from the imaginary part 2(ω) by the Kramer-Kronig relationship. The absorption coefficient R(ω) and the electron energy-loss function L(ω) can be evaluated from 1(ω) and 2(ω).25

R(ω) ) x2ω(x12(ω) + 22(ω) - 1(ω))1/2

(1)

L(ω) ) 2(ω)/[12(ω) + 22(ω)]

(2)

Study of the Properties of Alkali Metal Azides

J. Phys. Chem. B, Vol. 110, No. 20, 2006 9861

TABLE 4: Calculated and Experimental (in parentheses) Band Gap, Dielectric Constant E1(0), Refractive Index n, Main Peak in E2(ω), First Peak in r(ω), r(ω) at the First Peak, and Plasma Frequency ωp for the Alkali Azides band gap (eV) dielectric constant 1(0)4 refractive index n26 main peak in 2(ω) (eV) first peak in R(ω) (eV) R(ω) at the first peak (107 m-1) plasma frequency ωp (eV)

LiN3

R-NaN3

KN3

R-RbN3

R-CsN3

4.684 3.019 1.738 5.715 6.251 1.885 7.60, 19.9

4.614 2.493 (2.19) 1.579 (1.52) 5.714 6.072 1.529 7.18, 12.7, 15.3, 18.3

4.334 3.203 (2.25) 1.790 (1.66) 5.455 6.705 (6.5) 2.246 8.614, 12.3

4.404 2.854 1.689 5.455 5.947 2.268 8.44, 12.1

4.344 2.691 1.640 5.368 5.822 1.966 7.94, 13.3

As we know, the imaginary part 2(ω) of the dielectric function is the pandect of the optical properties for any materials, so we plot the imaginary parts 2(ω) of dielectric functions for the alkali azides in Figure 7. It can be seen that 2(ω) curves have thresholds of transition close to the band gap values of the corresponding compounds, then rise swiftly and peak around 5.3-5.8 eV. For insulators the peaks of 2(ω) originate from interband transition from valence-band into conduction-band states. Thus these peaks come from the electron transitions between alkali metal s and N 2p states. Beyond 7.5 eV, the 2(ω) spectra gradually increase again and peak at about 10.511 eV. The second peaks originate from the electron transitions between alkali metal p (1s for Li) and N 2p states. These also explain the origin of the peak structure in the adsorption coefficient and electron energy-loss spectra. The real parts 1(ω) of dielectric functions for the alkali azides are shown in Figure 8. Their general shapes are very similar since the 2(ω) spectra are quite alike. The refractive index n of an insulating crystal is the square root of the electric part of the dielectric constant at zero frequency, i.e., n ) x0, where 0 ) 1 (hω ) 0). The dielectric constants 1(0) and refractive indices n of the alkali azides are evaluated from Figure 8 and listed in Table 4. It is found that our calculated refractive indices are in good agreement with the corresponding experiments.26 The dielectric constant of R-NaN3 is close to the measured value, while that of KN3 is much larger than the experimental one.4 Since the calculated refractive index n of KN3 is consistent with the experiment, we conclude that its calculated 0 should agree with the measured value according to the relation n ) x0. Consequently, the discrepancy may be due to the use of different samples as well as different types of measurements in the experiments. The absorption coefficients R(ω) of the alkali azides are plotted in Figure 9. The first adsorption peaks in R(ω) and adsorption coefficients at the first peaks are presented in Table 4. The first absorption peaks in R(ω) spectra are found in the range of 5.822-6.705 eV, very close to an optical absorption

peak in the region of 6.5 eV reported in azide ion solution spectra.27 The nearest-neighbor charge-transfer exciton is also consistent with absorption peaks in the alkali azides at about 6.5 eV and is relatively constant from alkali azide to another. Thus the first absorption bands in the alkali azides may be the intra- and inter-azide ion transitions. The magnitudes of the absorption coefficients (107 m-1) in the neighborhood of the first absorption peaks indicate an allowed optical transition, probably to an exciton level. The absorption coefficient of the band of potassium azide at 6.705 eV is estimated by our calculations to be 2.246 × 107 m-1, near the absorption coefficient of ∼107 m-1 for the band at 6.5 eV estimated by Deb.28 We also note that the alkali azides have stronger optical absorptions from 4.0 to 20.0 eV. The magnitude of the absorption coefficients of these peaks allows an optical transition due to excitons. LiN3 and R-NaN3 have similar shapes of R(ω) spectra, and yet KN3, R-RbN3, and R-CsN3 have similar adsorption curves. This is because the former are isomorphous, while the latter are isostructural. Since the absorption coefficient in the fundamental region is very high (107 m-1), the alkali azides are unstable and decompose into metals and nitrogens under the action of light and heat. In conclusion, it is found that the absorption spectra of the alkali azides display a number of absorption peaks, which are believed to be associated with different exciton states, in the fundamental absorption region. The electron energy-loss function L(ω) is an important factor describing the energy loss of a fast electron traversing a material. The peaks in L(ω) spectra represent plasma resonance and the corresponding frequency is the so-called plasma frequency. Below the energy at which L(ω) peaks the material displays a metal-like dielectric function (1(ω) < 0) while above it it displays a dielectric type behavior (1(ω) > 0). That is to say, the positions of peaks in L(ω) spectra indicate the point of transition from the metallic property to the dielectric property for a material. In addition, the peaks of L(ω) correspond to the trailing edges in the reflection spectra. The electron energy-

Figure 9. Absorption coefficients R(ω) for the alkali azides.

Figure 10. Electron energy-loss functions L(ω) for the alkali azides.

9862 J. Phys. Chem. B, Vol. 110, No. 20, 2006 loss functions L(ω) of the alkali azides are plotted in Figure 10. In general, there are two plasma frequencies within the 5-22 eV region. These plasma peaks are shown in Table 4. The L(ω) structures of LiN3 and R-NaN3 are very alike, while those of KN3, R-RbN3, and R-CsN3 are quite similar. The features of the crystal structures shown in Figure 1 can explain this. 4. Conclusions In this study, we have performed a comparative firstprinciples study of the structural and optical properties of the alkali metal azides within density functional theory in the generalized gradient approximation. We examine the differences in the structural and electronic properties among these azides. The optical properties such as the real and imaginary parts of the dielectric function, adsorption coefficient, and electron energy-loss spectra are calculated. The crystal structures of the alkali azides compare well with experimental data. Their ionic character is manifested by the closeness of their internitrogen distances to the calculated N-N bond length for the free azide ion. An analysis of electronic structure, charge transfer, and bond order shows that the alkali azides are all wide-gap insulators and ionic compounds. The energy band and DOS for LiN3 and R-NaN3 are very similar, while those for KN3, R-RbN3, and R-CsN3 are alike, but some modifications are observed with the increment of alkali metals’ electropositivity. These changes are closely related to the differences of the crystal structures. The general shapes of the real and imaginary parts of the dielectric function, adsorption coefficient, and electron energyloss spectra are quite similar. The peaks originate from the electron transitions from the alkali metal s and p states to the conduction band. Our calculated optical properties for the alkali azides are found to be in good agreement with available experimental data. The absorption spectra of the alkali azides show a number of absorption peaks, which are believed to be associated with different exciton states, in the fundamental absorption region. In general, the electron energy-loss spectra have two plasma frequencies.

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