- Email: [email protected]
The structure of supercritical ammonia as studied by molecular dynamics simulations
15 September 2000
Chemical Physics Letters 327 Ž2000. 425–428 www.elsevier.nlrlocatercplett
The structure of supercritical ammonia as studied by molecular dynamics simulations M. Kiselev a , T. Kerdcharoen b, S. Hannongbua c,) , K. Heinzinger d a
Institute of Solution Chemistry, Russian Academy of Sciences, 153045 IÕanoÕo, Russia Department of Physics, Faculty of Science, Mahidol UniÕersity, Bangkok 10300, Thailand Department of Chemistry, Faculty of Science, Chulalongkorn UniÕersity, Bangkok 10300, Thailand d Max-Planck-Institut fur Chemie (Otto-Hahn-Institut), 55020 Mainz, Germany b
c
Received 4 May 2000; in final form 11 July 2000
Abstract The results of molecular dynamics simulations of supercritical ammonia are reported for the first time. Good agreement is found with results of neutron diffraction studies, thus far the only experimental evidence on the structure of supercritical ammonia. The partial radial distribution functions and the running integration numbers indicate that hydrogen bonding exists under supercritical conditions and seems to increase with decreasing density. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction The structural changes found in hydrogen bonded pure liquids w1–3x and mixtures w4–6x with increasing temperature and pressure have been drawn a lot of attention from both theoreticians and experimentalists. This interest is connected with the special abilities of these solvents under supercritical conditions, e.g. as a medium for chemical reactions which do not occur under standard conditions. Within this context, ammonia has the special feature that below its boiling point the number of nearest neighbors round an ammonia molecule is about 12, the closest packing with almost no preferential orientation between ammonia molecules. The counter-balance between hydrogen bonding and dipole–dipole interac) Corresponding author. Fax: q66-2-252-1730; e-mail: [email protected]
tions is supposed to be responsible for such structural peculiarities. The only experimental study on this subject is a neutron diffraction experiment by Bausenwein et al. w7x. They measured pure ammonia at 449 K and four different densities. They analyzed the experimental data by the reverse Monte Carlo method ŽRMC. and compared the results for the three radial distribution functions ŽRDF. with those from calculations with the site–site Ornstein–Zernicke ŽSSOZ. by employing various potential models available in the literature. To the best of our knowledge, there is no computer simulation study of supercritical ammonia. After a short description of the simulation details in Section 2, the changes in the radial distribution functions ŽRDF. with increase in temperature and decrease in density are discussed. The results are compared with those from the neutron diffraction measurements.
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 8 3 6 - 8
M. KiseleÕ et al.r Chemical Physics Letters 327 (2000) 425–428
426
2. Molecular dynamics simulations The three simulations, the result of which are reported here, were performed for an NVT ensemble consisting of 215 flexible ammonia molecules. The ammonia model shown in Eq. Ž1. Ž V Ž R . in 10 y1 9 J ˚ . has been taken from Ref. w8x. and R in A VNN Ž R . s 14.85rR q 55719rR12 y 13.6rR 6 , VNH Ž R . s y4.95rR q 0.01042 exp y4.6 Ž R y 2.4 . y 2 exp y2.3 Ž R y 2.4 .
4,
VHH Ž R . s 1.65rR q 48.64exp Ž y3.7R . .
Ž 1.
The shifted force method has been used again with a cut-off length of half the box size. Periodic boundary conditions were employed as well. Some comments should be made concerning the use of shifted force-potential method and the system size dependence of the results. They have been observed that no significant different between the RDFs obtained from the simulations those employ shifted force-potential method and Ewald summation w9x as well as those consist of 32 and 256 ammonia molecules w10x. For the subcritical simulation, a temperature of 220 K was chosen. With a density of 0.71 grcm3 a pressure of 20 MPa results w11x. For both simulations at supercritical conditions the temperature was set to 430 K, with densities of 0.53 and 0.73 grcm3 pressures of 20 and 400 MPa resulted, respectively. Note that critical temperature, pressure and density are 405.4 K, 11.33 MPa and 0.225 grcm3 , respectively. ˚ The side length of the basic cube was about 20 A. The time step length was chosen to be 0.125 fs. The simulations extended over 10 ps each.
3. Results and discussion The N–N and N–H RDFs from two simulations at supercritical conditions are compared in Fig. 1 with one of liquid ammonia at 220 K and a density of 0.71 grcm3. The subcritical simulation agrees favorably with a former simulation with the same ammonia model at 235 K and a density of 0.69 grcm3 w8x.
It can be seen from Fig. 1 that at the higher temperature the height of the first peak is lower and broadened for all RDFs. Also the other maxima and minima are less pronounced. The effect is more significant for the N–N when compared with the N–H RDFs as the latter ones are already very broad even at the low temperature. Furthermore, the positions of the first maxima remain unchanged with the increase in temperature at constant density. If the temperature is kept constant but the density decreased then the positions of the first maxima shift to larger distances while the positions of all other maxima and minima seem to be unchanged. All RDFs extend at the high temperature to shorter distances, more pronounced at the lower than at the higher density. This feature is reflected also in the running integration as shown in Fig. 1 additionally. Below about ˚ n NN Ž r . is larger for the higher temperature 3.3 A which is even true for the lower density. The number of nearest neighbors as defined by the integration of ˚ does the N–N RDF up to the first minimum at 5 A not depend on temperature. But it is reduced from 12.5 to 10.5 by a decrease in density of 30%. The N–H RDF at the high temperature and the low density extends to exceptionally short distances and reaches almost intramolecular separation. It can be seen from the insertion in Fig. 1 where n NH Ž r . is shown on an expanded scale that only a very small number of hydrogen atoms of neighboring ammonia molecules are involved in this approach. The opti˚ mized N–H distance in the ammonia dimer is 2.44 A w8,9,12–18x. Therefore, the integration over the first peak or in our case the shoulder in the N–H RDF can be considered a qualitative measure of hydrogen ˚ n NH Ž r . indicates a slightly bonding. Below 2.5 A stronger hydrogen bonding at the higher temperature ˚ the difference and the lower density. At about 2.6 A between all three simulations disappears. Obviously, an increase in temperature alone does not change hydrogen bonding significantly. A more detailed analysis of the configurations, including the hydrogen bond angle, is necessary to reach any quantitative conclusion. To the best of our knowledge, there is no other simulation and only one experimental investigation of supercritical ammonia for comparison. Bausenwein et al. w7x performed neutron diffraction mea-
M. KiseleÕ et al.r Chemical Physics Letters 327 (2000) 425–428
surements at 449 K and four different densities in the range 0.318–0.700 grcm3. The authors calculated from the intermolecular total RDF the partial ones by RMC simulations and compared them with results from SSOZ calculations by employing various ammonia models from the literature, one of which was the model also used in this work. In Fig. 2 the total neutron weighted RDF from the simulation at 430 K and 0.730 grcm3 is compared with that from the neutron diffraction study at 449 K and 0.700 grcm3. Obviously good agreement exists between simulation and experiment except for a shift
427
˚ to shorter distances of the simulation of about 0.1 A curve. It is not clear whether this shift has to be attributed solely to limitations of the ammonia model employed in the simulations. Part of the difference might result from the different temperatures and densities and part from the experimental data evaluation, especially the Fourier transformations. Unfortunately, the partial RDFs cannot be compared because of the strong noise in the experimental ones, especially in the range of the first peak. There are some differences in the positions and the heights of the first maxima in the RDFs between
Fig. 1. Nitrogen–nitrogen and nitrogen–hydrogen radial distribution functions and running integration numbers from simulations of supercritical ammonia. The insertion depicts the running integration over the N–H RDF at short distances on an expanded scale. The full, dashed, and dotted lines refer to temperatures of 220, 430, and 430 K and densities of 0.71, 0.73, and 0.53 grcm3 , respectively.
428
M. KiseleÕ et al.r Chemical Physics Letters 327 (2000) 425–428
further simulations of supercritical ammonia for the time being. Acknowledgements Financial support by the Russian Fund for Basic Research through Grant Nos. RFBR-99-03-32064 and 98-03-33237, INTAS Project No. 96-1989, the Department of Physics of the Mahidol University and the Chulalongkorn University are gratefully acknowledged. It is a pleasure to thank the National Electronic and Computer Technology Center in Bangkok for a generous supply of computer. Fig. 2. Total radial distribution function for ammonia from a neutron diffraction study Ždots. and an MD simulation at 449 and 430 K and densities of 0.700 and 0.730 grcm3 , respectively.
the simulation data presented in Fig. 1 and the SSOZ calculations. This is not surprising as it is well known that the employment of the SSOZ method for hydrogen-bonded liquids is connected with some difficulties. In spite of the noise in the partial RDFs from the RMC calculations, some small differences in the positions and the heights of the first maxima of all RDFs between simulation results and neutron diffraction data can be recognized. But the tendencies of the changes in going from sub- to supercritical conditions are the same. At constant density the heights of the first peaks decrease and broaden with increasing temperature while the positions remain unchanged. At constant temperature and decreasing density the positions shift to larger distances and the heights decrease for the N–N RDFs but increase for the N–H RDFs. This means that even under supercritical conditions the hydrogen bonding seems to increase with decreasing density. The qualitative agreement between simulation and experiment indicates – at least at this stage – that the ammonia model employed in the simulations does not lead to serious discrepancies with the experiment. Therefore, it is justified to use this model for
References w1x A.G. Kalinichev, S.V. Churakov, Chem. Phys. Lett. 302 Ž1999. 411. w2x M. Chalaris, J. Samios, J. Phys. Chem. 103B Ž1999. 1161. w3x J. Marti, J. Chem. Phys. 110 Ž1999. 6876. w4x J. Gao, J. Am. Chem. Soc. 115 Ž1993. 6893. w5x T. Ebukuro, A. Takami, Y. Oshima, S. Koda, J. Super. Fluids 15 Ž1999. 73. w6x M. Kiselev, S. Noskov, Y. Puhovski, T. Kerdcharoen, S. Hannongbua, submitted for publication. w7x T. Bausenwein, H. Bertagnolli, A. David, K. Goller, H. Zweier, K. Toedheide, P. Chieux, J. Chem. Phys. 101 Ž1994. 672. w8x S. Hannongbua, T. Ishida, E. Spohr, K. Heinzinger, Z. Naturforsch. A, 1988, p. 572. w9x L. Perera, U. Essmann, M. Berkowitz, J. Chem. Phys. 102 Ž1995. 450. w10x M. Diraison, G.J. Martyna, M.E. Tuckerman, J. Chem. Phys. 111 Ž1999. 1096. w11x R. Tillner-Roth, F. Harms-Watzenberg, H.D. Baehr, DKV Tagungsbericht 20 Ž1999. 167. w12x D.D. Nelson, G.T. Fraser, W.K. Klemperer, J. Chem. Phys. 83 Ž1985. 6201. w13x D.D. Nelson, W.K. Klemperer, G.T. Fraser, F.J. Lovas, R.D. Suenram, J. Chem. Phys. 87 Ž1987. 6364. w14x Z. Latajka, S. Scheiner, J. Chem. Phys. 84 Ž1986. 341. w15x M.J. Frisch, J.E. Del Bene, J.S. Binkley, H.F. Schaefer, J. Chem. Phys. 84 Ž1986. 2279. w16x S.Y. Liu, C.E. Dykstra, K. Kolenbrander, J.M. Lisy, J. Chem. Phys. 85 Ž1986. 2077. w17x K.P. Sagarik, R. Ahlrichs, S. Brode, Mol. Phys. 57 Ž1986. 1247. w18x J.E. Del Bene, J. Chem. Phys. 86 Ž1987. 2110.
Chemical Physics Letters 327 Ž2000. 425–428 www.elsevier.nlrlocatercplett
The structure of supercritical ammonia as studied by molecular dynamics simulations M. Kiselev a , T. Kerdcharoen b, S. Hannongbua c,) , K. Heinzinger d a
Institute of Solution Chemistry, Russian Academy of Sciences, 153045 IÕanoÕo, Russia Department of Physics, Faculty of Science, Mahidol UniÕersity, Bangkok 10300, Thailand Department of Chemistry, Faculty of Science, Chulalongkorn UniÕersity, Bangkok 10300, Thailand d Max-Planck-Institut fur Chemie (Otto-Hahn-Institut), 55020 Mainz, Germany b
c
Received 4 May 2000; in final form 11 July 2000
Abstract The results of molecular dynamics simulations of supercritical ammonia are reported for the first time. Good agreement is found with results of neutron diffraction studies, thus far the only experimental evidence on the structure of supercritical ammonia. The partial radial distribution functions and the running integration numbers indicate that hydrogen bonding exists under supercritical conditions and seems to increase with decreasing density. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction The structural changes found in hydrogen bonded pure liquids w1–3x and mixtures w4–6x with increasing temperature and pressure have been drawn a lot of attention from both theoreticians and experimentalists. This interest is connected with the special abilities of these solvents under supercritical conditions, e.g. as a medium for chemical reactions which do not occur under standard conditions. Within this context, ammonia has the special feature that below its boiling point the number of nearest neighbors round an ammonia molecule is about 12, the closest packing with almost no preferential orientation between ammonia molecules. The counter-balance between hydrogen bonding and dipole–dipole interac) Corresponding author. Fax: q66-2-252-1730; e-mail: [email protected]
tions is supposed to be responsible for such structural peculiarities. The only experimental study on this subject is a neutron diffraction experiment by Bausenwein et al. w7x. They measured pure ammonia at 449 K and four different densities. They analyzed the experimental data by the reverse Monte Carlo method ŽRMC. and compared the results for the three radial distribution functions ŽRDF. with those from calculations with the site–site Ornstein–Zernicke ŽSSOZ. by employing various potential models available in the literature. To the best of our knowledge, there is no computer simulation study of supercritical ammonia. After a short description of the simulation details in Section 2, the changes in the radial distribution functions ŽRDF. with increase in temperature and decrease in density are discussed. The results are compared with those from the neutron diffraction measurements.
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 8 3 6 - 8
M. KiseleÕ et al.r Chemical Physics Letters 327 (2000) 425–428
426
2. Molecular dynamics simulations The three simulations, the result of which are reported here, were performed for an NVT ensemble consisting of 215 flexible ammonia molecules. The ammonia model shown in Eq. Ž1. Ž V Ž R . in 10 y1 9 J ˚ . has been taken from Ref. w8x. and R in A VNN Ž R . s 14.85rR q 55719rR12 y 13.6rR 6 , VNH Ž R . s y4.95rR q 0.01042 exp y4.6 Ž R y 2.4 . y 2 exp y2.3 Ž R y 2.4 .
4,
VHH Ž R . s 1.65rR q 48.64exp Ž y3.7R . .
Ž 1.
The shifted force method has been used again with a cut-off length of half the box size. Periodic boundary conditions were employed as well. Some comments should be made concerning the use of shifted force-potential method and the system size dependence of the results. They have been observed that no significant different between the RDFs obtained from the simulations those employ shifted force-potential method and Ewald summation w9x as well as those consist of 32 and 256 ammonia molecules w10x. For the subcritical simulation, a temperature of 220 K was chosen. With a density of 0.71 grcm3 a pressure of 20 MPa results w11x. For both simulations at supercritical conditions the temperature was set to 430 K, with densities of 0.53 and 0.73 grcm3 pressures of 20 and 400 MPa resulted, respectively. Note that critical temperature, pressure and density are 405.4 K, 11.33 MPa and 0.225 grcm3 , respectively. ˚ The side length of the basic cube was about 20 A. The time step length was chosen to be 0.125 fs. The simulations extended over 10 ps each.
3. Results and discussion The N–N and N–H RDFs from two simulations at supercritical conditions are compared in Fig. 1 with one of liquid ammonia at 220 K and a density of 0.71 grcm3. The subcritical simulation agrees favorably with a former simulation with the same ammonia model at 235 K and a density of 0.69 grcm3 w8x.
It can be seen from Fig. 1 that at the higher temperature the height of the first peak is lower and broadened for all RDFs. Also the other maxima and minima are less pronounced. The effect is more significant for the N–N when compared with the N–H RDFs as the latter ones are already very broad even at the low temperature. Furthermore, the positions of the first maxima remain unchanged with the increase in temperature at constant density. If the temperature is kept constant but the density decreased then the positions of the first maxima shift to larger distances while the positions of all other maxima and minima seem to be unchanged. All RDFs extend at the high temperature to shorter distances, more pronounced at the lower than at the higher density. This feature is reflected also in the running integration as shown in Fig. 1 additionally. Below about ˚ n NN Ž r . is larger for the higher temperature 3.3 A which is even true for the lower density. The number of nearest neighbors as defined by the integration of ˚ does the N–N RDF up to the first minimum at 5 A not depend on temperature. But it is reduced from 12.5 to 10.5 by a decrease in density of 30%. The N–H RDF at the high temperature and the low density extends to exceptionally short distances and reaches almost intramolecular separation. It can be seen from the insertion in Fig. 1 where n NH Ž r . is shown on an expanded scale that only a very small number of hydrogen atoms of neighboring ammonia molecules are involved in this approach. The opti˚ mized N–H distance in the ammonia dimer is 2.44 A w8,9,12–18x. Therefore, the integration over the first peak or in our case the shoulder in the N–H RDF can be considered a qualitative measure of hydrogen ˚ n NH Ž r . indicates a slightly bonding. Below 2.5 A stronger hydrogen bonding at the higher temperature ˚ the difference and the lower density. At about 2.6 A between all three simulations disappears. Obviously, an increase in temperature alone does not change hydrogen bonding significantly. A more detailed analysis of the configurations, including the hydrogen bond angle, is necessary to reach any quantitative conclusion. To the best of our knowledge, there is no other simulation and only one experimental investigation of supercritical ammonia for comparison. Bausenwein et al. w7x performed neutron diffraction mea-
M. KiseleÕ et al.r Chemical Physics Letters 327 (2000) 425–428
surements at 449 K and four different densities in the range 0.318–0.700 grcm3. The authors calculated from the intermolecular total RDF the partial ones by RMC simulations and compared them with results from SSOZ calculations by employing various ammonia models from the literature, one of which was the model also used in this work. In Fig. 2 the total neutron weighted RDF from the simulation at 430 K and 0.730 grcm3 is compared with that from the neutron diffraction study at 449 K and 0.700 grcm3. Obviously good agreement exists between simulation and experiment except for a shift
427
˚ to shorter distances of the simulation of about 0.1 A curve. It is not clear whether this shift has to be attributed solely to limitations of the ammonia model employed in the simulations. Part of the difference might result from the different temperatures and densities and part from the experimental data evaluation, especially the Fourier transformations. Unfortunately, the partial RDFs cannot be compared because of the strong noise in the experimental ones, especially in the range of the first peak. There are some differences in the positions and the heights of the first maxima in the RDFs between
Fig. 1. Nitrogen–nitrogen and nitrogen–hydrogen radial distribution functions and running integration numbers from simulations of supercritical ammonia. The insertion depicts the running integration over the N–H RDF at short distances on an expanded scale. The full, dashed, and dotted lines refer to temperatures of 220, 430, and 430 K and densities of 0.71, 0.73, and 0.53 grcm3 , respectively.
428
M. KiseleÕ et al.r Chemical Physics Letters 327 (2000) 425–428
further simulations of supercritical ammonia for the time being. Acknowledgements Financial support by the Russian Fund for Basic Research through Grant Nos. RFBR-99-03-32064 and 98-03-33237, INTAS Project No. 96-1989, the Department of Physics of the Mahidol University and the Chulalongkorn University are gratefully acknowledged. It is a pleasure to thank the National Electronic and Computer Technology Center in Bangkok for a generous supply of computer. Fig. 2. Total radial distribution function for ammonia from a neutron diffraction study Ždots. and an MD simulation at 449 and 430 K and densities of 0.700 and 0.730 grcm3 , respectively.
the simulation data presented in Fig. 1 and the SSOZ calculations. This is not surprising as it is well known that the employment of the SSOZ method for hydrogen-bonded liquids is connected with some difficulties. In spite of the noise in the partial RDFs from the RMC calculations, some small differences in the positions and the heights of the first maxima of all RDFs between simulation results and neutron diffraction data can be recognized. But the tendencies of the changes in going from sub- to supercritical conditions are the same. At constant density the heights of the first peaks decrease and broaden with increasing temperature while the positions remain unchanged. At constant temperature and decreasing density the positions shift to larger distances and the heights decrease for the N–N RDFs but increase for the N–H RDFs. This means that even under supercritical conditions the hydrogen bonding seems to increase with decreasing density. The qualitative agreement between simulation and experiment indicates – at least at this stage – that the ammonia model employed in the simulations does not lead to serious discrepancies with the experiment. Therefore, it is justified to use this model for
References w1x A.G. Kalinichev, S.V. Churakov, Chem. Phys. Lett. 302 Ž1999. 411. w2x M. Chalaris, J. Samios, J. Phys. Chem. 103B Ž1999. 1161. w3x J. Marti, J. Chem. Phys. 110 Ž1999. 6876. w4x J. Gao, J. Am. Chem. Soc. 115 Ž1993. 6893. w5x T. Ebukuro, A. Takami, Y. Oshima, S. Koda, J. Super. Fluids 15 Ž1999. 73. w6x M. Kiselev, S. Noskov, Y. Puhovski, T. Kerdcharoen, S. Hannongbua, submitted for publication. w7x T. Bausenwein, H. Bertagnolli, A. David, K. Goller, H. Zweier, K. Toedheide, P. Chieux, J. Chem. Phys. 101 Ž1994. 672. w8x S. Hannongbua, T. Ishida, E. Spohr, K. Heinzinger, Z. Naturforsch. A, 1988, p. 572. w9x L. Perera, U. Essmann, M. Berkowitz, J. Chem. Phys. 102 Ž1995. 450. w10x M. Diraison, G.J. Martyna, M.E. Tuckerman, J. Chem. Phys. 111 Ž1999. 1096. w11x R. Tillner-Roth, F. Harms-Watzenberg, H.D. Baehr, DKV Tagungsbericht 20 Ž1999. 167. w12x D.D. Nelson, G.T. Fraser, W.K. Klemperer, J. Chem. Phys. 83 Ž1985. 6201. w13x D.D. Nelson, W.K. Klemperer, G.T. Fraser, F.J. Lovas, R.D. Suenram, J. Chem. Phys. 87 Ž1987. 6364. w14x Z. Latajka, S. Scheiner, J. Chem. Phys. 84 Ž1986. 341. w15x M.J. Frisch, J.E. Del Bene, J.S. Binkley, H.F. Schaefer, J. Chem. Phys. 84 Ž1986. 2279. w16x S.Y. Liu, C.E. Dykstra, K. Kolenbrander, J.M. Lisy, J. Chem. Phys. 85 Ž1986. 2077. w17x K.P. Sagarik, R. Ahlrichs, S. Brode, Mol. Phys. 57 Ž1986. 1247. w18x J.E. Del Bene, J. Chem. Phys. 86 Ž1987. 2110.