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Molecular dynamics and quantum chemical studies on diborane
Journal of Molecular Structure (Theochem) 629 (2003) 279–284 www.elsevier.com/locate/theochem
Molecular dynamics and quantum chemical studies on diborane Lemi Tu¨rker Department of Chemistry, Middle East Technical University, 06531 Ankara, Turkey Received 22 January 2003; accepted 27 February 2003
Abstract Within the limitations of AM1 (restricted Hartree –Fock) type semiempirical quantum chemical calculations, molecular dynamics of B2H6 system at constant temperature conditions was investigated. Adopting the molecular geometry at an elevated temperature certain molecular orbital characteristics of B2H6 were obtained. Also, the vibrational spectrum at the elevated temperature was compared with the corresponding one at T ¼ 0 K: q 2003 Elsevier B.V. All rights reserved. Keywords: Diborane; Boranes; Molecular dynamics; Austin model 1 calculations; Vibrational spectra
1. Introduction Diborane, B2H6 is a gaseous substance which is diamagnetic hence the molecule contains no unpaired electrons. It is electron deficient and has 12 valency electrons although its structural formula corresponds to that of ethane, C2H6 which has 14 electrons all of which are in shared pairs [1]. The generally accepted structure for diborane is bridged and contains two three-centered bonds (Fig. 1) [1,2]. Diborane shows no sign of thermal dissociation up to 100 8C. The value of enthalpy of the dissociation (B2H6 ! 2BH3) is about 150 kJ [2]. Diborane can be converted to higher boranes by moderate heat. Depending on the further reaction conditions, by heat treatment diborane can yield B5H11, B4H10, B5H9, B10H14 and some others via indirect routes [1,2]. When heated to 300 8C it yields boron and hydrogen [1]. As mentioned above, the thermal decomposition of diborane with or E-mail address: [email protected] (L. Tu¨rker).
without added hydrogen leads to complex mixtures of higher hydrides and hydrogen, but yields of a particular hydride can be optimized by suitable choice of temperature, pressure, hydrogen pressure and reaction time. Much effort has been devoted to sorting out the reactions that occur. These are many, and varied and somewhat akin to the thermal cracking of hydrocarbons. Still there is not yet general agreement about several aspects of the interconversion reactions suggested by different groups of workers [2]. Since the thermal decomposition of diborane involves such a complicated set of inter-related equilibria [3], the identity and proportions of the products which can ultimately be isolated depend critically on the initial partial pressures of hydrogen and diborane, the temperature and the reaction time. 2. Method In the present treatise, the geometry optimizations of diborane leading to energy minima were achieved
0166-1280/03/$ - see front matter q 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0166-1280(03)00202-1
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L. Tu¨rker / Journal of Molecular Structure (Theochem) 629 (2003) 279–284
Fig. 1. The kinetic and potential energy variations and their deviations from the mean vs. time.
by using AM1 (Austin model 1) self-consistent fields molecular orbital [4] method at the restricted Hartree –Fock (RHF) level [5]. The optimizations were obtained by the application of the steepestdescent method followed by conjugate gradient methods, Fletcher-Rieves and Polak-Ribiere, consecutively (convergence limit of 4.18 £ 1024 kJ/mol (0.0001 kcal/mol) and RMS gradient of 4.18 £ 107 kJ/(m mol) (0.001 kcal/(A mol)). For the constant temperature molecular dynamic (quantum dynamics) simulations a protocol consisting of 0.1 ps heating from 0 to 473 K, 10 ps run-time (equilibration) at 473 K (200 8C) and 1 ps cooling to 472 K (199 8C) was applied. Time step size of 0.0005 ps and temperature step of 20 8C were used. The molecular dynamics of the B2H6 was carried out at AM1 level and the data collection period was set to 1 time step. All these computations were performed by using the Hyperchem (release 5.1) and ChemPlus (2.0) package programs.
Fig. 2. The temperature variation and its deviation from the mean vs. time.
Fig. 3. Snapshots from the trajectory.
Table 1 Some results of the molecular dynamic study Considered variable
Average value
Deviation from the mean
Ekin Epot Etot Temp a123 a143 a214 a234 a635 a718 b12 b14 b23 b34 b17 b18 b35 b36 d13 d24
11.0949 2567.6041 2556.5091 465.2703 81.9328 81.9363 96.9790 96.9708 123.3089 123.3089 1.3419 1.3417 1.3419 1.3418 1.1967 1.1988 1.1974 1.1972 1.7581 2.0070
2.5397 2.5932 1.5461 106.5040 5.4412 5.3993 6.1236 6.1436 7.5589 7.5166 0.0625 0.0610 0.0624 0.0618 0.0413 0.0413 0.0449 0.0454 0.0878
Energies in kcal, temperatures in K, aijk stands for a bond angle at center j. bkl represents bond length between atoms k and l in 10210 m.
L. Tu¨rker / Journal of Molecular Structure (Theochem) 629 (2003) 279–284
281
Fig. 6. Deviation from the mean values vs. time for certain distances.
3. Results and discussion
Fig. 4. Numbering of B2H6 structure for the data in Table 1.
Fig. 5. Deviation from the mean values vs. time for certain bond lengths.
The unimolecular dissociation of diborane into two borane fragments (B2H6 ! 2BH3) is characterized with enthalpy change of about 150 kJ [2] and the activation energy for the dissociation can be expected to be greater. Actually, the thermal decomposition of diborane involves many complicated set of interrelated equilibria. The unimolecular thermal decomposition reaction is just one of these reactions.
Fig. 7. Deviation from the mean value vs. time plots for certain angles in B2H6 structure.
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L. Tu¨rker / Journal of Molecular Structure (Theochem) 629 (2003) 279–284
Fig. 8. Molecular orbital energy spectrum and the HOMO and LUMO of B2H6 structure at two different temperatures.
The molecular dynamic studies may help one to envisage this decomposition reaction better at the molecular level. In the present study, a constant temperature (isothermal) molecular dynamics has been studied. The bath relaxation constant, t; is set to 0.1 ps (a moderately weak coupling to bath). Fig. 1 shows the kinetic and potential energy variations as well as their deviations from the mean versus time. Whereas Fig. 2 stands for the temperature variation and its deviation from the mean. As seen in the figures, the trajectory is quite stable. Note that in tight coupling,
the temperature during the molecular dynamics is close to the chosen temperature. Whereas a weaker coupling, allowing more fluctuations in temperature and possibly an unstable trajectory. However, weak coupling leads to a more natural trajectory [6 –8]. Fig. 3 contains snapshots for B2H6 at t ¼ 5 ps ðT ¼ 426 KÞ and 10 ps ðT ¼ 503 KÞ: Table 1 shows the average values and deviation from the average value of many variables of the molecular dynamics described above. Fig. 4 shows the numbering of centers in the structure of B2H6 for the data included in Table 1.
L. Tu¨rker / Journal of Molecular Structure (Theochem) 629 (2003) 279–284
283
Fig. 9. The vibrational spectra for B2H6 at two different temperatures.
Various experimental techniques yield the terminal hydrogen – boron bond length as 1.08 – 1.19 £ 10210 m and the bridging hydrogen – boron bond length as 1.25 – 1.33 £ 10210 m after heat treatment, the value for the later type of bonds on the average becomes 1.34 £ 10210 m. Whereas, the terminal hydrogen – boron bonds become 1.19 £ 10210 m [9 – 11]. During the molecular dynamics, deviation from the mean values for bond lengths are not much different from each other (see Fig. 5). The average distances, d 13 (boron –boron) and d24 (hydrogen – hydrogen) are 1.76 £ 10210 and 2.01 £ 10210 m, respectively. Their deviations from the mean are 0.08 £ 10210 and 0.09 £ 10210 m, respectively (Fig. 6).
On the other hand, a214 and a234 angles experimentally were found to be 90– 978 [9 –11]. The present value for them is approximately 978. The angles, a718 and a635, experimentally are 119 – 1228 [9 – 11]. Whereas, the present value is about 1238. In general, the angles of B2H6 deviate from the mean about 6%. However, this value reaches about 6.6% on the bridging hydrogens. Fig. 7 shows deviation from the mean values for some angles of B2H6 structure. Fig. 8 shows the molecular orbital energy spectrum and the HOMO and LUMO of B2H6 structure (AM1 (RHF) type calculations) at T ¼ 0 and 503 K (D2h and C1 type symmetry, respectively). At T ¼ 0 K the HOMO and LUMO have B1G and B2U symmetry,
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L. Tu¨rker / Journal of Molecular Structure (Theochem) 629 (2003) 279–284
respectively and the energies of them are 2 11.3860 eV and 1.4030 eV, respectively. Whereas, at T ¼ 503 K the HOMO has A type symmetry and its energy is 2 11.3720 eV. Also the LUMO possesses A type symmetry and energy of 1.1402 eV. The above data for the molecular orbital energies indicate that as temperature rises the HOMO level raises up slightly whereas the LOMO level decreases rather sharply. Fig. 9 shows the vibrational spectra of B2H6 structure at T ¼ 0 and 503 K. As seen there, increase in temperature causes increase in intensities of BH2 symmetric and asymmetric stretchings (above 2500 cm21). The bridge BH2B stretching at the elevated temperatures appears as lower intensity band but more lines emerge. In general, more lines exists in the spectrum of B2H6 at the elevated temperatures because the corresponding geometry have lower symmetry.
4. Conclusion Diborane, B2H6, undergoes various products by heat treatment depending on the reaction conditions. Therefore, the molecular dynamic studies and the trajectory for B2H6 enlighten some previously
unknown or obscure points. Depending on the reaction, the protocol for the molecular dynamic study can be modified, e.g. constant energy, etc. In the present study only the constant temperature molecular dynamics coupled to bath rather weakly has been studied.
References [1] P.J. Durant, B. Durant, Introduction to Advanced Inorganic Chemistry, Longman, London, 1970. [2] K. Wade, Electron Deficient Compounds, Nelson, London, 1971. [3] L.H. Long, J. Inorg. Nucl. Chem. 32 (1970) 1097. [4] M.J.S. Dewar, E.G. Zoebish, E.F. Healey, J.J.P. Stewart, J. Am. Chem. Soc. 107 (1985) 3902. [5] A.R. Leach, Molecular Modelling, Addison-Wesley/Longman, London, 1996. [6] Hypercube Inc., Hyperchem-Computational Chemistry, Hyperchem, Hypercube Inc., Gainesville, FL, 1996. [7] K.B. Lipkowitz, D.B. Boyd, Reviews in Computational Chemistry, VCH, New York, 1990. [8] H.J.C. Berendser, J.P.M. Postma, W.F. van Gunsteren, A. di Nola, A. di Nola, J.R. Haak, J. Chem. Phys. 81 (1984) 3684. [9] L.S. Bartell, B.L. Carroll, J. Chem. Phys. 42 (1965) 1135. [10] W.J. Lafferty, A.G. Maki, T.D. Coyle, J. Mol. Spectrosc. 33 (1970) 345. [11] H.W. Smith, W.N. Lipscomb, J. Chem. Phys. 43 (1965) 1060.
Molecular dynamics and quantum chemical studies on diborane Lemi Tu¨rker Department of Chemistry, Middle East Technical University, 06531 Ankara, Turkey Received 22 January 2003; accepted 27 February 2003
Abstract Within the limitations of AM1 (restricted Hartree –Fock) type semiempirical quantum chemical calculations, molecular dynamics of B2H6 system at constant temperature conditions was investigated. Adopting the molecular geometry at an elevated temperature certain molecular orbital characteristics of B2H6 were obtained. Also, the vibrational spectrum at the elevated temperature was compared with the corresponding one at T ¼ 0 K: q 2003 Elsevier B.V. All rights reserved. Keywords: Diborane; Boranes; Molecular dynamics; Austin model 1 calculations; Vibrational spectra
1. Introduction Diborane, B2H6 is a gaseous substance which is diamagnetic hence the molecule contains no unpaired electrons. It is electron deficient and has 12 valency electrons although its structural formula corresponds to that of ethane, C2H6 which has 14 electrons all of which are in shared pairs [1]. The generally accepted structure for diborane is bridged and contains two three-centered bonds (Fig. 1) [1,2]. Diborane shows no sign of thermal dissociation up to 100 8C. The value of enthalpy of the dissociation (B2H6 ! 2BH3) is about 150 kJ [2]. Diborane can be converted to higher boranes by moderate heat. Depending on the further reaction conditions, by heat treatment diborane can yield B5H11, B4H10, B5H9, B10H14 and some others via indirect routes [1,2]. When heated to 300 8C it yields boron and hydrogen [1]. As mentioned above, the thermal decomposition of diborane with or E-mail address: [email protected] (L. Tu¨rker).
without added hydrogen leads to complex mixtures of higher hydrides and hydrogen, but yields of a particular hydride can be optimized by suitable choice of temperature, pressure, hydrogen pressure and reaction time. Much effort has been devoted to sorting out the reactions that occur. These are many, and varied and somewhat akin to the thermal cracking of hydrocarbons. Still there is not yet general agreement about several aspects of the interconversion reactions suggested by different groups of workers [2]. Since the thermal decomposition of diborane involves such a complicated set of inter-related equilibria [3], the identity and proportions of the products which can ultimately be isolated depend critically on the initial partial pressures of hydrogen and diborane, the temperature and the reaction time. 2. Method In the present treatise, the geometry optimizations of diborane leading to energy minima were achieved
0166-1280/03/$ - see front matter q 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0166-1280(03)00202-1
280
L. Tu¨rker / Journal of Molecular Structure (Theochem) 629 (2003) 279–284
Fig. 1. The kinetic and potential energy variations and their deviations from the mean vs. time.
by using AM1 (Austin model 1) self-consistent fields molecular orbital [4] method at the restricted Hartree –Fock (RHF) level [5]. The optimizations were obtained by the application of the steepestdescent method followed by conjugate gradient methods, Fletcher-Rieves and Polak-Ribiere, consecutively (convergence limit of 4.18 £ 1024 kJ/mol (0.0001 kcal/mol) and RMS gradient of 4.18 £ 107 kJ/(m mol) (0.001 kcal/(A mol)). For the constant temperature molecular dynamic (quantum dynamics) simulations a protocol consisting of 0.1 ps heating from 0 to 473 K, 10 ps run-time (equilibration) at 473 K (200 8C) and 1 ps cooling to 472 K (199 8C) was applied. Time step size of 0.0005 ps and temperature step of 20 8C were used. The molecular dynamics of the B2H6 was carried out at AM1 level and the data collection period was set to 1 time step. All these computations were performed by using the Hyperchem (release 5.1) and ChemPlus (2.0) package programs.
Fig. 2. The temperature variation and its deviation from the mean vs. time.
Fig. 3. Snapshots from the trajectory.
Table 1 Some results of the molecular dynamic study Considered variable
Average value
Deviation from the mean
Ekin Epot Etot Temp a123 a143 a214 a234 a635 a718 b12 b14 b23 b34 b17 b18 b35 b36 d13 d24
11.0949 2567.6041 2556.5091 465.2703 81.9328 81.9363 96.9790 96.9708 123.3089 123.3089 1.3419 1.3417 1.3419 1.3418 1.1967 1.1988 1.1974 1.1972 1.7581 2.0070
2.5397 2.5932 1.5461 106.5040 5.4412 5.3993 6.1236 6.1436 7.5589 7.5166 0.0625 0.0610 0.0624 0.0618 0.0413 0.0413 0.0449 0.0454 0.0878
Energies in kcal, temperatures in K, aijk stands for a bond angle at center j. bkl represents bond length between atoms k and l in 10210 m.
L. Tu¨rker / Journal of Molecular Structure (Theochem) 629 (2003) 279–284
281
Fig. 6. Deviation from the mean values vs. time for certain distances.
3. Results and discussion
Fig. 4. Numbering of B2H6 structure for the data in Table 1.
Fig. 5. Deviation from the mean values vs. time for certain bond lengths.
The unimolecular dissociation of diborane into two borane fragments (B2H6 ! 2BH3) is characterized with enthalpy change of about 150 kJ [2] and the activation energy for the dissociation can be expected to be greater. Actually, the thermal decomposition of diborane involves many complicated set of interrelated equilibria. The unimolecular thermal decomposition reaction is just one of these reactions.
Fig. 7. Deviation from the mean value vs. time plots for certain angles in B2H6 structure.
282
L. Tu¨rker / Journal of Molecular Structure (Theochem) 629 (2003) 279–284
Fig. 8. Molecular orbital energy spectrum and the HOMO and LUMO of B2H6 structure at two different temperatures.
The molecular dynamic studies may help one to envisage this decomposition reaction better at the molecular level. In the present study, a constant temperature (isothermal) molecular dynamics has been studied. The bath relaxation constant, t; is set to 0.1 ps (a moderately weak coupling to bath). Fig. 1 shows the kinetic and potential energy variations as well as their deviations from the mean versus time. Whereas Fig. 2 stands for the temperature variation and its deviation from the mean. As seen in the figures, the trajectory is quite stable. Note that in tight coupling,
the temperature during the molecular dynamics is close to the chosen temperature. Whereas a weaker coupling, allowing more fluctuations in temperature and possibly an unstable trajectory. However, weak coupling leads to a more natural trajectory [6 –8]. Fig. 3 contains snapshots for B2H6 at t ¼ 5 ps ðT ¼ 426 KÞ and 10 ps ðT ¼ 503 KÞ: Table 1 shows the average values and deviation from the average value of many variables of the molecular dynamics described above. Fig. 4 shows the numbering of centers in the structure of B2H6 for the data included in Table 1.
L. Tu¨rker / Journal of Molecular Structure (Theochem) 629 (2003) 279–284
283
Fig. 9. The vibrational spectra for B2H6 at two different temperatures.
Various experimental techniques yield the terminal hydrogen – boron bond length as 1.08 – 1.19 £ 10210 m and the bridging hydrogen – boron bond length as 1.25 – 1.33 £ 10210 m after heat treatment, the value for the later type of bonds on the average becomes 1.34 £ 10210 m. Whereas, the terminal hydrogen – boron bonds become 1.19 £ 10210 m [9 – 11]. During the molecular dynamics, deviation from the mean values for bond lengths are not much different from each other (see Fig. 5). The average distances, d 13 (boron –boron) and d24 (hydrogen – hydrogen) are 1.76 £ 10210 and 2.01 £ 10210 m, respectively. Their deviations from the mean are 0.08 £ 10210 and 0.09 £ 10210 m, respectively (Fig. 6).
On the other hand, a214 and a234 angles experimentally were found to be 90– 978 [9 –11]. The present value for them is approximately 978. The angles, a718 and a635, experimentally are 119 – 1228 [9 – 11]. Whereas, the present value is about 1238. In general, the angles of B2H6 deviate from the mean about 6%. However, this value reaches about 6.6% on the bridging hydrogens. Fig. 7 shows deviation from the mean values for some angles of B2H6 structure. Fig. 8 shows the molecular orbital energy spectrum and the HOMO and LUMO of B2H6 structure (AM1 (RHF) type calculations) at T ¼ 0 and 503 K (D2h and C1 type symmetry, respectively). At T ¼ 0 K the HOMO and LUMO have B1G and B2U symmetry,
284
L. Tu¨rker / Journal of Molecular Structure (Theochem) 629 (2003) 279–284
respectively and the energies of them are 2 11.3860 eV and 1.4030 eV, respectively. Whereas, at T ¼ 503 K the HOMO has A type symmetry and its energy is 2 11.3720 eV. Also the LUMO possesses A type symmetry and energy of 1.1402 eV. The above data for the molecular orbital energies indicate that as temperature rises the HOMO level raises up slightly whereas the LOMO level decreases rather sharply. Fig. 9 shows the vibrational spectra of B2H6 structure at T ¼ 0 and 503 K. As seen there, increase in temperature causes increase in intensities of BH2 symmetric and asymmetric stretchings (above 2500 cm21). The bridge BH2B stretching at the elevated temperatures appears as lower intensity band but more lines emerge. In general, more lines exists in the spectrum of B2H6 at the elevated temperatures because the corresponding geometry have lower symmetry.
4. Conclusion Diborane, B2H6, undergoes various products by heat treatment depending on the reaction conditions. Therefore, the molecular dynamic studies and the trajectory for B2H6 enlighten some previously
unknown or obscure points. Depending on the reaction, the protocol for the molecular dynamic study can be modified, e.g. constant energy, etc. In the present study only the constant temperature molecular dynamics coupled to bath rather weakly has been studied.
References [1] P.J. Durant, B. Durant, Introduction to Advanced Inorganic Chemistry, Longman, London, 1970. [2] K. Wade, Electron Deficient Compounds, Nelson, London, 1971. [3] L.H. Long, J. Inorg. Nucl. Chem. 32 (1970) 1097. [4] M.J.S. Dewar, E.G. Zoebish, E.F. Healey, J.J.P. Stewart, J. Am. Chem. Soc. 107 (1985) 3902. [5] A.R. Leach, Molecular Modelling, Addison-Wesley/Longman, London, 1996. [6] Hypercube Inc., Hyperchem-Computational Chemistry, Hyperchem, Hypercube Inc., Gainesville, FL, 1996. [7] K.B. Lipkowitz, D.B. Boyd, Reviews in Computational Chemistry, VCH, New York, 1990. [8] H.J.C. Berendser, J.P.M. Postma, W.F. van Gunsteren, A. di Nola, A. di Nola, J.R. Haak, J. Chem. Phys. 81 (1984) 3684. [9] L.S. Bartell, B.L. Carroll, J. Chem. Phys. 42 (1965) 1135. [10] W.J. Lafferty, A.G. Maki, T.D. Coyle, J. Mol. Spectrosc. 33 (1970) 345. [11] H.W. Smith, W.N. Lipscomb, J. Chem. Phys. 43 (1965) 1060.