- Email: [email protected]
Prediction of a stable free standing nitrogen oligomer
Computational and Theoretical Chemistry 966 (2011) 137–139
Contents lists available at ScienceDirect
Computational and Theoretical Chemistry journal homepage: www.elsevier.com/locate/comptc
Prediction of a stable free standing nitrogen oligomer Frank J. Owens Department of Physics, Hunter College and the Graduate Center, City University of New York, 695 Park Ave., NY 10065, NY, United States
a r t i c l e
i n f o
Article history: Received 28 December 2010 Received in revised form 2 February 2011 Accepted 22 February 2011 Available online 22 March 2011 Keywords: Density Functional Theory Nitrogen oligomer Frequencies of normal modes Energy output Band gap Bond dissociation energy
a b s t r a c t Density Functional Theory is used to predict the possibility of a double chain nitrogen oligomer. Calculation of the frequencies of the normal modes for various chain lengths show no negative frequencies indicating the structures are stationary states. The calculations indicate that this nitrogen oligomer can exist without the need to be stabilized inside carbon nanotubes or between graphene planes as has been predicted for other forms of nitrogen oligomers. It is also predicted that the oligomer is semiconducting. The calculations also show that the material is quite stable and on decomposition to n[N2] is more exothermic than any existing energetic material. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction A number of calculations have indicated that molecules or clusters containing only nitrogen atoms such as N8, N10, N12 and N20 would be very energetic explosive materials releasing much more energy on exothermic reaction compared to presently used materials [1,2]. For example the exothermic reaction of the cubic N8 molecule is predicted to release 4.13 kcal/gm which is 2.8 times that of HMX (C4H8N8O8) the most energetic material in use today. However, none of these structures have yet been synthesized and their synthesis remains a challenge. These would also be environmentally friendly because the products of their decomposition are nitrogen molecules. Further they could be quite stable because of the strength of the N–N bond. Recently attention has turned to polymeric nitrogen as a high energy material because of two reports of its possible existence [3,4]. Polymeric nitrogen would also be expected to be a very energetic material. In one report a polymeric form of nitrogen having an unusual cubic gauche structure (cg-N) was synthesized from molecular nitrogen by high pressure and temperature, (2000 K and 110 GPa). Another report suggested the existence of polymeric nitrogen in sodium azide, (NaN3) subjected to a pressure of 160 GPa at temperatures ranging from 120 K to 3300 K. The pressure induced an interaction between the linear N 3 azide ions as indicated by the emergence of new lines in the Raman spectra possibly forming some polymeric structure of nitrogen perhaps a linear chain. However the structure of this polymer in NaN3 has not been determined. More recently Density Functional Theory (DFT) has been used to show that a N8 single E-mail address: [email protected] 2210-271X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.comptc.2011.02.026
zigzag chain of nitrogens is stable inside carbon nanotubes and between sheets of graphene [5–7]. In this work DFT is used to obtain the structure of a larger nitrogen chain consisting bonded double chains of nitrogen. The possibility of the double nitrogen chain has not previously been considered. It is found that this nitrogen oligomer is stable without the need to be contained in carbon nanotubes or between sheets of graphene. Raman active vibrational frequencies, band gaps, bond dissociation energies and energy released in decomposition to N2 molecules are calculated as a function of the number of nitrogens in the chains to asses its potential as an energetic material. 2. Methods and results The optimized structure of the double chain oligomer at different lengths is obtained employing Density Functional Theory (DFT) at the B3LYP/6-31G level using Gaussian 03 software [8]. The frequencies at each length were calculated to verify that the structures were stationary states i.e. a minimum on the potential energy surface. The band gap at the center of the Brillouin zone was obtained by performing a single point calculation on the B3LYP/6-31G optimized structure using the local spin density approximation employing the Slater exchange functionals and the VWN correlation function. The band gap is obtained by taking the difference in energy between the highest occupied orbital and the lowest unoccupied orbital. Previous calculations of band gaps in materials indicate this approach is necessary to obtain reliable band gaps [9]. Fig. 1a shows the calculated minimum energy structure of the nitrogen oligomer [N2]12. The oligmer can be viewed as two single
138
F.J. Owens / Computational and Theoretical Chemistry 966 (2011) 137–139
13
1
16
(a) 11
3 2
6
14 20 18
15 12 4
7 5
9
19
22
23
17 24
10
21
8
(b) 7 10
1 5 8
9
2
12 6
3
11 4
Fig. 1. The Density Functional calculated minimum energy structure of an [N2]12 double chain nitrogen oligomer (a) and an [N2]6 oligomer (b).
chains linked together by inter-chain bonds such as N14–N12. The numbers are those on Fig. 1a. Table 1 gives the bond lengths for the bonds within the chains and the bond lengths connecting the two chains as well as bond angles. The inter-chain bonds at the end are considerably shorter than the other inter-chain bonds having a value of 1.206 A. The other inter-chain bonds show small variations down the length of the oligomer having an average value of 1.522 A. Fig. 1b shows the structure of a shorter oligomer [N2]6. The bond lengths of the shorter oligomer are not terribly different from the longer oligomer. For example the average inter-chain bond excluding the end bonds is 1.522 A in the longer oligomer compared to 1.511 A in the shorter oligomer. The vibrational frequencies of the normal modes as well as the Raman activity were calculated as a function of the number of nitrogens in the chain. At all lengths calculated there were no negative frequencies indicating that the structures are true stationary states. This means the structures are stable as free standing entities not requiring encapsulation in carbon nanotubes or between
sheets of graphene for stability as has previously been reported [5–7]. The most intense Raman lines have frequencies in the vicinity of 1547 cm1 and 950 cm1 for the [N2]13 chain. There is some dependency of the frequencies on the chain length as shown in Fig. 2 for the 950 cm1 vibration. The band gap at K = 0 was calculated as a function of chain length. As shown in Fig. 3 there is some oscillation in the band gap energy with chain length. However at all lengths the magnitude of the gap indicates the oligomers are semiconductors. A similar observation was previously reported for a single chain nitrogen structure [6]. The importance of nitrogen containing oligomers is their potential use as energetic materials. Thus it is of interest to determine the energy released and how the length of the chain affects it. It is assumed that the final products of the exothermic reaction of the polymer are nitrogen molecules, i.e. that the reaction is;
½N2 n ! n½N2
ð1Þ
Table 1 Bond lengths and bond angles of an N24 oligomer. Numbers of the nitrogen atoms refer to Fig. 1a. Inter-chain bonds
Length (A)
Intra chain bonds
Length (A)
Bond angles
Degrees
9–10 7–8 6–5 3–4 1–2 13–11 14–12 16–15 18–17 20–19 22–12 23–24
1.206 1.517 1.531 1.521 1.511 1.509 1.526 1.535 1.521 1.527 1.517 1.260
10–8 8–5 4–2 2–11 11–12 12–15 15–17 17–19 19–21 21–24
1.449 1.479 1.452 1.513 1.459 1.455 1.458 1.458 1.478 1.450
10–8-5 8–5-4 5–4-2 4–2-11 11–12-15 12–15-17 15–17-19 17–19-21 19–21-24 4–3-1 2–19-20 8–5-6 17–15-16 12–11-13
106.52 104.94 104.80 111.69 105.46 105.50 105.29 104.96 106.566 89.78 89.69 90.34
139
F.J. Owens / Computational and Theoretical Chemistry 966 (2011) 137–139
FREQUENCY (cm-1)
960
Table 2 Calculated bond dissociation energies to break the center and end bond of some nitrogen oligomers.
940 920 900
(N2)n ? [N2]n1 + N2 (kcal/mole)
34.38 58.93
91.36 92.54
2.60 2.55
BDE ¼ EðN2 Þ12 ½EðN2 Þ11 þ EðN2 Þ
2.50
where E is the electronic energy plus the zero point vibrational energy. Table 2 summarizes the BDEs calculated for removal of the end N2 for two different chain lengths. It is clear that the BDE is quite high averaging 91.3 kcals/mole meaning this bond is quit strong. Another possible initial reaction step could be the cleavage of the center bond in the polymer to form two shorter polymers of equal length, i.e.
880
12.0
16.0
20.0
24.0
28.0
NUMBER OF NITROGENS Fig. 2. Dependence of the frequency of the 950 cm1 vibration on the number of nitrogens in the chain.
BAND GAP (eV)
(N2)n ? 2[N2]n/2 (kcal/mole)
N24 N20
Another important property bearing on the potential application of the material as an energetic material is stability. It is important that new developed materials be insensitive, i.e. not be easily initiated to exothermic reaction. In order to asses the stability, the bond dissociation energy (BDE) has been calculated for some possible decomposition routes of the nitrogen polymer. Previous work has shown that BDEs of the weakest bond of the molecules of energetic materials correlate to various measures of sensitivity [10]. The first reaction step considered is the removal of an end N2 from the polymer. The bond dissociation energy for this step is defined for the [N2]12 oligomer as
860 8.0
2.45 2.40 2.35 2.30 2.25 10.0
ðN2 Þn ! 2½N2 n=2 15.0
20.0
25.0
30.0
35.0
NUMBER of NITROGENS Fig. 3. Calculated band gap at center of zone versus the number of nitrogens in the chain.
The energy released is calculated by taking the difference between then total electronic energy including the zero point vibrational energy of the parent and the products,
DQ ¼ ½Ee ð½N2 n Þ þ Ezpe ð½N2 n Þ n½Ee ðN2 Þ þ Ezpe ðN2 Þ
ð2Þ
Fig. 4 shows the calculated energy output versus number of nitrogens in the oligomer showing a systematic increase in the energy with length. At the largest nitrogen number there is some evidence of saturation. This oligomer is predicted to releases more than 2 times energy released by HMX the most energetic material in use today. 3.20
ENERGY OUT [KCal/Gm]
Polymer
3.16
3. Conclusion Density Functional Theory of the minimum energy structure and the vibrational frequencies of the normal modes indicate a double chain nitrogen oligomer is stable at all lengths calculated up to (N2)16. Unlike previous predictions of nitrogen oligomers, this double chain structure is stable without the need to be incorporated in carbon nanotubes or between the planes of graphene. Calculation of the energy released in the dissociation to N2 molecules show that the structure would be very energetic having more than twice the energy released than HMX. Calculation of the bond dissociation energy for some possible decomposition routes, show the structure to be quite stable. The calculations indicate the oligomers have small band gap in the range of typical semiconductors. An energetic material which is semiconducting opens the possibility of initiation of reaction by excitation of electrons to the conduction band such as by photo excitation. References
3.04 12.0
16.0
20.0
24.0
28.0
NUMBER OF NITROGENS Fig. 4. Calculated energy released versus number of nitrogens in the chain on decomposition from [N2]n to n[N2].
ð4Þ
The calculated BDEs for this reaction shown in Table 2 are somewhat smaller than for removal of the end nitrogen molecule but are still large enough to suggest the oligomers are stable. The bond dissociation energy to open a single end bond such as N22– N23 bond in Fig. 1a has also been calculated and is 95.52 kcal/mole.
3.12
3.08
ð3Þ
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
R. Engelke, J. Am. Chem. Soc. 115 (1993) 2961. F.J. Owens, J. Mol. Struct. 623 (2003) 197. M.I. Ermets et al., Nature Mater. 3 (2004) 558. M.I. Ermets et al., J. Chem. Phys. 120 (2004) 10618. H. Abou-Rachid et al., Phys. Rev. Lett. 100 (2008) 196401. V. Timoshevshii et al., Phys. Rev. B80 (2009) 115409. W. Ji et al., Appl. Phys. Lett. 95 (2009) 021904. M.J. Frisch et al., Gaussian 03, Revision B.04. M.S. Hybertsen, S.G. Louie, Phys. Rev. Lett. 55 (1985) 1418. B.M. Rice, S. Sahu, F.J. Owens, J. Mol. Struct. 583 (2002) 69.
Contents lists available at ScienceDirect
Computational and Theoretical Chemistry journal homepage: www.elsevier.com/locate/comptc
Prediction of a stable free standing nitrogen oligomer Frank J. Owens Department of Physics, Hunter College and the Graduate Center, City University of New York, 695 Park Ave., NY 10065, NY, United States
a r t i c l e
i n f o
Article history: Received 28 December 2010 Received in revised form 2 February 2011 Accepted 22 February 2011 Available online 22 March 2011 Keywords: Density Functional Theory Nitrogen oligomer Frequencies of normal modes Energy output Band gap Bond dissociation energy
a b s t r a c t Density Functional Theory is used to predict the possibility of a double chain nitrogen oligomer. Calculation of the frequencies of the normal modes for various chain lengths show no negative frequencies indicating the structures are stationary states. The calculations indicate that this nitrogen oligomer can exist without the need to be stabilized inside carbon nanotubes or between graphene planes as has been predicted for other forms of nitrogen oligomers. It is also predicted that the oligomer is semiconducting. The calculations also show that the material is quite stable and on decomposition to n[N2] is more exothermic than any existing energetic material. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction A number of calculations have indicated that molecules or clusters containing only nitrogen atoms such as N8, N10, N12 and N20 would be very energetic explosive materials releasing much more energy on exothermic reaction compared to presently used materials [1,2]. For example the exothermic reaction of the cubic N8 molecule is predicted to release 4.13 kcal/gm which is 2.8 times that of HMX (C4H8N8O8) the most energetic material in use today. However, none of these structures have yet been synthesized and their synthesis remains a challenge. These would also be environmentally friendly because the products of their decomposition are nitrogen molecules. Further they could be quite stable because of the strength of the N–N bond. Recently attention has turned to polymeric nitrogen as a high energy material because of two reports of its possible existence [3,4]. Polymeric nitrogen would also be expected to be a very energetic material. In one report a polymeric form of nitrogen having an unusual cubic gauche structure (cg-N) was synthesized from molecular nitrogen by high pressure and temperature, (2000 K and 110 GPa). Another report suggested the existence of polymeric nitrogen in sodium azide, (NaN3) subjected to a pressure of 160 GPa at temperatures ranging from 120 K to 3300 K. The pressure induced an interaction between the linear N 3 azide ions as indicated by the emergence of new lines in the Raman spectra possibly forming some polymeric structure of nitrogen perhaps a linear chain. However the structure of this polymer in NaN3 has not been determined. More recently Density Functional Theory (DFT) has been used to show that a N8 single E-mail address: [email protected] 2210-271X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.comptc.2011.02.026
zigzag chain of nitrogens is stable inside carbon nanotubes and between sheets of graphene [5–7]. In this work DFT is used to obtain the structure of a larger nitrogen chain consisting bonded double chains of nitrogen. The possibility of the double nitrogen chain has not previously been considered. It is found that this nitrogen oligomer is stable without the need to be contained in carbon nanotubes or between sheets of graphene. Raman active vibrational frequencies, band gaps, bond dissociation energies and energy released in decomposition to N2 molecules are calculated as a function of the number of nitrogens in the chains to asses its potential as an energetic material. 2. Methods and results The optimized structure of the double chain oligomer at different lengths is obtained employing Density Functional Theory (DFT) at the B3LYP/6-31G level using Gaussian 03 software [8]. The frequencies at each length were calculated to verify that the structures were stationary states i.e. a minimum on the potential energy surface. The band gap at the center of the Brillouin zone was obtained by performing a single point calculation on the B3LYP/6-31G optimized structure using the local spin density approximation employing the Slater exchange functionals and the VWN correlation function. The band gap is obtained by taking the difference in energy between the highest occupied orbital and the lowest unoccupied orbital. Previous calculations of band gaps in materials indicate this approach is necessary to obtain reliable band gaps [9]. Fig. 1a shows the calculated minimum energy structure of the nitrogen oligomer [N2]12. The oligmer can be viewed as two single
138
F.J. Owens / Computational and Theoretical Chemistry 966 (2011) 137–139
13
1
16
(a) 11
3 2
6
14 20 18
15 12 4
7 5
9
19
22
23
17 24
10
21
8
(b) 7 10
1 5 8
9
2
12 6
3
11 4
Fig. 1. The Density Functional calculated minimum energy structure of an [N2]12 double chain nitrogen oligomer (a) and an [N2]6 oligomer (b).
chains linked together by inter-chain bonds such as N14–N12. The numbers are those on Fig. 1a. Table 1 gives the bond lengths for the bonds within the chains and the bond lengths connecting the two chains as well as bond angles. The inter-chain bonds at the end are considerably shorter than the other inter-chain bonds having a value of 1.206 A. The other inter-chain bonds show small variations down the length of the oligomer having an average value of 1.522 A. Fig. 1b shows the structure of a shorter oligomer [N2]6. The bond lengths of the shorter oligomer are not terribly different from the longer oligomer. For example the average inter-chain bond excluding the end bonds is 1.522 A in the longer oligomer compared to 1.511 A in the shorter oligomer. The vibrational frequencies of the normal modes as well as the Raman activity were calculated as a function of the number of nitrogens in the chain. At all lengths calculated there were no negative frequencies indicating that the structures are true stationary states. This means the structures are stable as free standing entities not requiring encapsulation in carbon nanotubes or between
sheets of graphene for stability as has previously been reported [5–7]. The most intense Raman lines have frequencies in the vicinity of 1547 cm1 and 950 cm1 for the [N2]13 chain. There is some dependency of the frequencies on the chain length as shown in Fig. 2 for the 950 cm1 vibration. The band gap at K = 0 was calculated as a function of chain length. As shown in Fig. 3 there is some oscillation in the band gap energy with chain length. However at all lengths the magnitude of the gap indicates the oligomers are semiconductors. A similar observation was previously reported for a single chain nitrogen structure [6]. The importance of nitrogen containing oligomers is their potential use as energetic materials. Thus it is of interest to determine the energy released and how the length of the chain affects it. It is assumed that the final products of the exothermic reaction of the polymer are nitrogen molecules, i.e. that the reaction is;
½N2 n ! n½N2
ð1Þ
Table 1 Bond lengths and bond angles of an N24 oligomer. Numbers of the nitrogen atoms refer to Fig. 1a. Inter-chain bonds
Length (A)
Intra chain bonds
Length (A)
Bond angles
Degrees
9–10 7–8 6–5 3–4 1–2 13–11 14–12 16–15 18–17 20–19 22–12 23–24
1.206 1.517 1.531 1.521 1.511 1.509 1.526 1.535 1.521 1.527 1.517 1.260
10–8 8–5 4–2 2–11 11–12 12–15 15–17 17–19 19–21 21–24
1.449 1.479 1.452 1.513 1.459 1.455 1.458 1.458 1.478 1.450
10–8-5 8–5-4 5–4-2 4–2-11 11–12-15 12–15-17 15–17-19 17–19-21 19–21-24 4–3-1 2–19-20 8–5-6 17–15-16 12–11-13
106.52 104.94 104.80 111.69 105.46 105.50 105.29 104.96 106.566 89.78 89.69 90.34
139
F.J. Owens / Computational and Theoretical Chemistry 966 (2011) 137–139
FREQUENCY (cm-1)
960
Table 2 Calculated bond dissociation energies to break the center and end bond of some nitrogen oligomers.
940 920 900
(N2)n ? [N2]n1 + N2 (kcal/mole)
34.38 58.93
91.36 92.54
2.60 2.55
BDE ¼ EðN2 Þ12 ½EðN2 Þ11 þ EðN2 Þ
2.50
where E is the electronic energy plus the zero point vibrational energy. Table 2 summarizes the BDEs calculated for removal of the end N2 for two different chain lengths. It is clear that the BDE is quite high averaging 91.3 kcals/mole meaning this bond is quit strong. Another possible initial reaction step could be the cleavage of the center bond in the polymer to form two shorter polymers of equal length, i.e.
880
12.0
16.0
20.0
24.0
28.0
NUMBER OF NITROGENS Fig. 2. Dependence of the frequency of the 950 cm1 vibration on the number of nitrogens in the chain.
BAND GAP (eV)
(N2)n ? 2[N2]n/2 (kcal/mole)
N24 N20
Another important property bearing on the potential application of the material as an energetic material is stability. It is important that new developed materials be insensitive, i.e. not be easily initiated to exothermic reaction. In order to asses the stability, the bond dissociation energy (BDE) has been calculated for some possible decomposition routes of the nitrogen polymer. Previous work has shown that BDEs of the weakest bond of the molecules of energetic materials correlate to various measures of sensitivity [10]. The first reaction step considered is the removal of an end N2 from the polymer. The bond dissociation energy for this step is defined for the [N2]12 oligomer as
860 8.0
2.45 2.40 2.35 2.30 2.25 10.0
ðN2 Þn ! 2½N2 n=2 15.0
20.0
25.0
30.0
35.0
NUMBER of NITROGENS Fig. 3. Calculated band gap at center of zone versus the number of nitrogens in the chain.
The energy released is calculated by taking the difference between then total electronic energy including the zero point vibrational energy of the parent and the products,
DQ ¼ ½Ee ð½N2 n Þ þ Ezpe ð½N2 n Þ n½Ee ðN2 Þ þ Ezpe ðN2 Þ
ð2Þ
Fig. 4 shows the calculated energy output versus number of nitrogens in the oligomer showing a systematic increase in the energy with length. At the largest nitrogen number there is some evidence of saturation. This oligomer is predicted to releases more than 2 times energy released by HMX the most energetic material in use today. 3.20
ENERGY OUT [KCal/Gm]
Polymer
3.16
3. Conclusion Density Functional Theory of the minimum energy structure and the vibrational frequencies of the normal modes indicate a double chain nitrogen oligomer is stable at all lengths calculated up to (N2)16. Unlike previous predictions of nitrogen oligomers, this double chain structure is stable without the need to be incorporated in carbon nanotubes or between the planes of graphene. Calculation of the energy released in the dissociation to N2 molecules show that the structure would be very energetic having more than twice the energy released than HMX. Calculation of the bond dissociation energy for some possible decomposition routes, show the structure to be quite stable. The calculations indicate the oligomers have small band gap in the range of typical semiconductors. An energetic material which is semiconducting opens the possibility of initiation of reaction by excitation of electrons to the conduction band such as by photo excitation. References
3.04 12.0
16.0
20.0
24.0
28.0
NUMBER OF NITROGENS Fig. 4. Calculated energy released versus number of nitrogens in the chain on decomposition from [N2]n to n[N2].
ð4Þ
The calculated BDEs for this reaction shown in Table 2 are somewhat smaller than for removal of the end nitrogen molecule but are still large enough to suggest the oligomers are stable. The bond dissociation energy to open a single end bond such as N22– N23 bond in Fig. 1a has also been calculated and is 95.52 kcal/mole.
3.12
3.08
ð3Þ
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
R. Engelke, J. Am. Chem. Soc. 115 (1993) 2961. F.J. Owens, J. Mol. Struct. 623 (2003) 197. M.I. Ermets et al., Nature Mater. 3 (2004) 558. M.I. Ermets et al., J. Chem. Phys. 120 (2004) 10618. H. Abou-Rachid et al., Phys. Rev. Lett. 100 (2008) 196401. V. Timoshevshii et al., Phys. Rev. B80 (2009) 115409. W. Ji et al., Appl. Phys. Lett. 95 (2009) 021904. M.J. Frisch et al., Gaussian 03, Revision B.04. M.S. Hybertsen, S.G. Louie, Phys. Rev. Lett. 55 (1985) 1418. B.M. Rice, S. Sahu, F.J. Owens, J. Mol. Struct. 583 (2002) 69.