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Imaging of the electron density distributions of hydrogen in LiH and LiOH by maximum entropy method
Journal of Physics and Chemistry of Solids 60 (1999) 1721–1724
Imaging of the electron density distributions of hydrogen in LiH and LiOH by maximum entropy method Shigefumi Yamamura a,*, Satoshi Kasahara b,1, Masaki Takata c, Yoko Sugawara a, Matoto Sakata b a Department of Physics, School of Science, Kitasato University, Sagamihara 228-8555, Japan Department of Applied Physics, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan c Department of Material Science, Interdisciplinary Faculty of Science and Engineering, Shimane University, Matsue 690-8504, Japan b
Received 13 January 1999; accepted 26 February 1999
Abstract In order to explore the electron distribution of hydrogen, an electron density study was carried out by maximum entropy method (MEM) using the single crystal X-ray diffraction data of LiH measured by Vidal-Valat et al. [Acta Crystallogr. A48 (1992) 46–60] and those of LiOH measured by Go¨ttlicher and Kieselbach [Acta Crystallogr. A32 (1976) 185–192]. It was found that the electron distribution of hydrogen in LiH is very spherical as a consequence of high symmetrical crystalline field. It was also recognized that there exists very weak covalent bond between lithium and hydrogen along the 具100典 direction. These features were consistent with the results of difference Fourier synthesis and multipole analysis by Vidal-Valat et al. Contrary to the LiH case, the position of hydrogen in LiOH was hardly assigned from the electron density map and only the contribution of hydrogen was recognized as a distortion of electron clouds of OH ellipse. The present study demonstrated that the electron distribution of hydrogen can be detected by MEM but it should be kept in mind that the distribution of electron from hydrogen was severely affected by the crystal field, which may result in the fact that the electron from hydrogen is far from a spherical distribution. 䉷 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. Inorganic compounds; C. X-ray diffraction
1. Introduction Maximum entropy method (MEM) is a statistical deduction which is based on information theory. If MEM is applied to crystallography, one can provide electron density distribution in crystalline materials, which is consistent with experimental observation. We have shown that MEM can yield high-resolution electron density distribution without using any structural models. For example, sp 3 hybridized orbital for silicon has been clearly detected in MEM charge density [1,2] and charge transfer from boron to nitrogen in hexagonal boron nitride has been observed by MEM [3]. Besides, the electron density studies of hydrogen bond in * Corresponding author. 1 Present address: Nagoya Regional Office, Nippon Steel Information and Communication Systems Inc., 503, Tokai-machi, Tokai 476-0015, Japan.
ice (Ih) [4] and tetragonal KDP (KH2PO4) [5], where the hydrogen atoms are said to be disordered, reveal that the hydrogen in these compounds exhibits no local maxima of electron density along the hydrogen bonds. The interesting feature of MEM is that no use of structural models to obtain electron density distribution is needed. This feature is seemed to be very effective when the structural model cannot be predicted. Hydrogen compounds are one of the examples of such cases. Even in non-hydrogen bond case, the electron distribution of hydrogen may change largely from that of a free atom with a spherical distribution. In this article the electron density distributions of lithium hydride (LiH) and lithium hydroxide (LiOH) were analyzed by MEM and the electron density distributions of hydrogen in these compounds were compared in terms of the bonding nature of hydrogen. The bonding nature of LiH is basically ionic and the hydrogen exists as H ⫺ ion. On the contrary, the hydrogen in LiOH forms covalent bond with oxygen.
0022-3697/99/$ - see front matter 䉷 1999 Elsevier Science Ltd. All rights reserved. PII: S0022-369 7(99)00026-8
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Shigefumi Yamamura et al. / Journal of Physics and Chemistry of Solids 60 (1999) 1721–1724
In the following sections, firstly the structure factor data used in the analysis are mentioned, secondly the electron density distributions of LiH and LiOH obtained by MEM are described and finally, the electron distributions of hydrogen in the two compounds are discussed.
2. Data set and analysis 2.1. LiH
Fig. 1. MEM electron density maps of LiH at 293 K for: (a) the (002) plane; (b) the (110) plane. Contour lines are drawn from 0.2 to ˚ 3] intervals. Some atomic sites are indicated by letters. 2.0 at 0.2 [e/A
The set of observed structure factor data used in this study for LiH analysis was measured by Vidal-Valat et al. at 293 K [6]. They made a thermal and annealing treatment with subsequent quenching in order to minimize the effect of extinction. They stated that there was no indication of significant extinction effects in the data. The space group of LiH is Fm3¯m and LiH has the NaCl type structure with the ˚ . The set of observed struclattice parameter a 4.0752 A ture factors consists of 26 reflections and corresponds to ˚ resolution in real space. The observed structure 0.51 A factors were analyzed by a computer program, MEED, [7] to have an electron density distribution by MEM. In MEM analysis, the unit cell was divided into 64 × 64 × 64 pixels. The reliable factor of MEM electron density based on structure factors, RMEM, is expressed by Sk 兩F kobs ⫺ F kMEM 兩= Sk 兩F kobs 兩; where F(k)obs is the observed structure factor of the reflection k, and F(k)MEM the structure factor calculated from electron density distribution obtained by MEM. In the present case RMEM was 0.37%, which can be regarded to be a very low value.
2.2. LiOH
Fig. 2. MEM electron density map of LiH at 293 K for lower density region in Fig. 1(b). Contour lines are drawn from 0.06 to ˚ 3] intervals. 0.2 at 0.02 [e/A
The set of observed structure factor data used in this study for LiOH analysis was measured by Go¨ttlicher and Kieselbach at room temperature [8]. The space group of LiOH is ˚, c P4/nmm. The lattice parameters are a 3.549 A ˚ 4.334 A. The set of observed structure factors consists of ˚ resolution in real 152 reflections and corresponds to 0.50 A space. The observed structure factors were also analyzed by MEED. In MEM analysis, the unit cell was divided into 72 × 72 × 84 pixels and the second setting of the space group P4/ nmm was applied to have a center of symmetry at the origin of the unit cell. In Go¨ttlicher and Kieselbach’s paper [8] the error for each structure factor was not listed but error ranges were given with respect to 兩F兩, i.e. less than 1% for 兩F兩 ⬎ 2, 1–2% for 1 ⬍ 兩F兩 ⬍ 2, 2–5% for 兩F兩 ⬍ 1, where 兩F兩 is an amplitude of structure factor. In this study, averaged values of error ranges were employed as the experimental error, i.e. 1% for 兩F兩 ⬎ 2, 1.5% for 1 ⬍ 兩F兩 ⬍ 2, 3.5% for 兩F兩 ⬍ 1. The value of RMEM was 1.6%, which was not as low as the LiH case but still good enough to discuss the electron distribution of hydrogen.
Shigefumi Yamamura et al. / Journal of Physics and Chemistry of Solids 60 (1999) 1721–1724
Fig. 3. MEM electron density map of LiOH at room temperature for the section x 1/4, which includes Li, O and H. The dot and the cross indicate the positions of hydrogen and oxygen nuclei obtained by Go¨ttlicher and Kieselbach using neutron diffraction data [8], respectively. Contour lines are drawn in the same way as those in Fig. 1(b).
3. Results and discussion 3.1. MEM map of LiH The electron density contour maps of LiH obtained by MEM (MEM maps) are shown in Fig. 1. Fig. 1(a) is the
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(002) plane and Fig. 1(b) is the (110) plane. The peaks of electron densities can be assigned to Li and H without any problem, though the electron density for H is very low and diffuse compared with that for Li. Such distribution of hydrogen is in contrast to those of ice (Ih) [4] and tetragonal KDP [5] where hydrogen exists in hydrogen bond. In the MEM maps of ice (Ih) and tetragonal KDP, the electron of hydrogen is recognized only as a link of contour lines between two oxygen atoms and no local maxima of the electron distribution of hydrogen can be seen. It seems very unique in crystalline state that the electron of hydrogen exists as spherical distribution. For further examination of the interatomic region, the MEM map of lower density region for Fig. 1(b) is shown in Fig. 2. The electron density distribution of H slightly elongates toward neighboring Li atoms. This kind of elongation of H can be also seen in the difference maps obtained by Vidal-Valat et al. [6]. It is found that the electron density between Li and H is not zero and the contour lines link Li and H along the [001] direction, although contour levels are quite low in Fig. 2. Such a bonding nature between Li and H is clearly visible in MEM maps. Besides, this covalent bond like nature indicates that LiH is not completely ionic, that is consistent with X-ray diffraction studies [6,9] and selfconsistent-field molecular orbital calculation [10]. In order to confirm this, number of electrons in each atom was estimated. The atomic site is defined as the maximum region enclosing contour lines. In the present case, the atomic site was the spherical region which is greater than or equal to an ˚ 3. They were ⫹ 0.96 for Li site, electron density of 0.13 e/A ⫺ 0.15 for H site and 0.81 electrons for another region. It is found that almost one electron from Li site does not concentrate at H site but scatters in the unit cell. However it should be noted that there are ambiguities in the estimation of atomic site, especially for hydrogen whose electron distribution is quite diffuse. 3.2. MEM map of LiOH
Fig. 4. Asymmetric component of the electron density for OH in LiOH with respect to O atom. The area showed corresponds to the small square in Fig. 3. The dot and the cross represent the same as in ¨ 3] interFig. 3. Contour lines are drawn from 0.1 to 1.5 at 0.1 [e/A vals. Only positive contours are shown.
The MEM map of a section of x 1/4 in LiOH which includes both Li ⫹ and OH ⫺ is shown in Fig. 3 with the positions of hydrogen and oxygen nuclei obtained by Go¨ttlicher and Kieselbach using neutron diffraction data [8]. In this map the peaks of electron density corresponding to Li and O are clearly seen. In contrast to LiH, the peak of electron density for hydrogen is not found as a spherical distribution. Instead, a slight distortion of electron density distribution from OH ellipse can be recognized. This means that an electron, which comes from a hydrogen atom is completely mixed with oxygen electrons. The distortion of OH ellipse is the only trace of the existence of proton. In order to examine the distortion of OH ellipse, the electron density distribution of OH shown in the rectangle in Fig. 3 is divided into two components. One is a symmetric component and the other is an asymmetric component. The symmetric component r sym(r) and the
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Shigefumi Yamamura et al. / Journal of Physics and Chemistry of Solids 60 (1999) 1721–1724
asymmetric component r asym(r) are calculated as
rsym r r r ⫹ r ⫺r=2;
1
rasym r r r ⫺ r ⫺r=2;
2
where r (r) is the MEM electron density at the position r. The origin of r is chosen at the position of the peak top of oxygen. Then, r (r) becomes a simple sum of r sym(r) and r asym(r) as
r r rsym r ⫹ rasym r:
3
The asymmetric component of electron density for OH in Fig. 3 is shown in Fig. 4. It is found that the distribution of oxygen near the core region is not symmetric. It is rather difficult to specify the cause of such an asymmetry of oxygen. However this may be due to the chemical bonding of oxygen to form OH ⫺ ion. In addition to the asymmetric component of oxygen atom, the local maximum of electron density distribution, which must be the contribution of hydrogen can be recognized, though the peak height is quite low. It is noticeable that the peak position is considerably different from the nucleus position determined by neutron diffraction shown by the dot in Fig. 4. This implies that the electron of hydrogen in OH ⫺ ion strongly interacts with oxygen atom. 4. Concluding remarks In MEM maps, each of the electron density distribution of hydrogen in LiH and LiOH shows a striking contrast. In LiH the peak of hydrogen atom can be recognized clearly. However, the electron from hydrogen atom in LiOH cannot be found as a peak maximum of electron density but the contribution of hydrogen can be recognized as a distortion of OH ellipse. Such a difference must come from the difference of bonding nature of hydrogen in Li–H and O–H, i.e. basically ionic for Li–H and covalent for O–H, respectively
and these bonding nature of hydrogen is observable reasonably by MEM without using structural models. Such a direct observation of hydrogen in other bonding states is desirable to find out a new insight into the bonding nature of hydrogen. Acknowledgements The author (SY) thanks Prof. T. Ito of Kanagawa Institute of Technology for helpful advice. A part of the computations was carried out at Nagoya University Computation Center and University of Tokyo Computer Center. This study was partly supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture in Japan.
References [1] M. Sakata, M. Sato, Acta Crystallogr. A46 (1990) 263–270. [2] M. Takata, M. Sakata, Acta Crystallogr. A52 (1996) 287–290. [3] S. Yamamura, M. Takata, M. Sakata, J. Phys. Chem. Solids 58 (1997) 177–183. [4] M. Sakata, M. Takata, H. Oshizumi, A. Goto, T. Hondoh, Physics and Chemistry of Ice, Hokkaido University Press, Sapporo, 1992 pp. 62–68. [5] S. Yamamura, M. Takata, M. Sakata, Y. Sugawara, J. Phys. Soc. Jpn. 67 (1998) 4124–4127. [6] G. Vidal-Valat, J.-P. Vidal, K. Kurki-Suonio, R. KurkiSuonio, Acta Crystallogr. A48 (1992) 46–60. [7] S. Kumazawa, Y. Kubota, M. Takata, M. Sakata, Y. Ishibashi, J. Appl. Crystallogr. 26 (1993) 453–457. [8] S. Go¨ttlicher, B. Kieselbach, Acta Crystallogr. A32 (1976) 185–192. [9] R.S. Calder, W. Cochran, D. Griffiths, R.D. Lowde, J. Phys. Chem. Solids 23 (1962) 621–632. [10] B.K. Rao, P. Jena, J. Phys. C: Solid State Phys. 19 (1986) 5167–5172.
Imaging of the electron density distributions of hydrogen in LiH and LiOH by maximum entropy method Shigefumi Yamamura a,*, Satoshi Kasahara b,1, Masaki Takata c, Yoko Sugawara a, Matoto Sakata b a Department of Physics, School of Science, Kitasato University, Sagamihara 228-8555, Japan Department of Applied Physics, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan c Department of Material Science, Interdisciplinary Faculty of Science and Engineering, Shimane University, Matsue 690-8504, Japan b
Received 13 January 1999; accepted 26 February 1999
Abstract In order to explore the electron distribution of hydrogen, an electron density study was carried out by maximum entropy method (MEM) using the single crystal X-ray diffraction data of LiH measured by Vidal-Valat et al. [Acta Crystallogr. A48 (1992) 46–60] and those of LiOH measured by Go¨ttlicher and Kieselbach [Acta Crystallogr. A32 (1976) 185–192]. It was found that the electron distribution of hydrogen in LiH is very spherical as a consequence of high symmetrical crystalline field. It was also recognized that there exists very weak covalent bond between lithium and hydrogen along the 具100典 direction. These features were consistent with the results of difference Fourier synthesis and multipole analysis by Vidal-Valat et al. Contrary to the LiH case, the position of hydrogen in LiOH was hardly assigned from the electron density map and only the contribution of hydrogen was recognized as a distortion of electron clouds of OH ellipse. The present study demonstrated that the electron distribution of hydrogen can be detected by MEM but it should be kept in mind that the distribution of electron from hydrogen was severely affected by the crystal field, which may result in the fact that the electron from hydrogen is far from a spherical distribution. 䉷 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. Inorganic compounds; C. X-ray diffraction
1. Introduction Maximum entropy method (MEM) is a statistical deduction which is based on information theory. If MEM is applied to crystallography, one can provide electron density distribution in crystalline materials, which is consistent with experimental observation. We have shown that MEM can yield high-resolution electron density distribution without using any structural models. For example, sp 3 hybridized orbital for silicon has been clearly detected in MEM charge density [1,2] and charge transfer from boron to nitrogen in hexagonal boron nitride has been observed by MEM [3]. Besides, the electron density studies of hydrogen bond in * Corresponding author. 1 Present address: Nagoya Regional Office, Nippon Steel Information and Communication Systems Inc., 503, Tokai-machi, Tokai 476-0015, Japan.
ice (Ih) [4] and tetragonal KDP (KH2PO4) [5], where the hydrogen atoms are said to be disordered, reveal that the hydrogen in these compounds exhibits no local maxima of electron density along the hydrogen bonds. The interesting feature of MEM is that no use of structural models to obtain electron density distribution is needed. This feature is seemed to be very effective when the structural model cannot be predicted. Hydrogen compounds are one of the examples of such cases. Even in non-hydrogen bond case, the electron distribution of hydrogen may change largely from that of a free atom with a spherical distribution. In this article the electron density distributions of lithium hydride (LiH) and lithium hydroxide (LiOH) were analyzed by MEM and the electron density distributions of hydrogen in these compounds were compared in terms of the bonding nature of hydrogen. The bonding nature of LiH is basically ionic and the hydrogen exists as H ⫺ ion. On the contrary, the hydrogen in LiOH forms covalent bond with oxygen.
0022-3697/99/$ - see front matter 䉷 1999 Elsevier Science Ltd. All rights reserved. PII: S0022-369 7(99)00026-8
1722
Shigefumi Yamamura et al. / Journal of Physics and Chemistry of Solids 60 (1999) 1721–1724
In the following sections, firstly the structure factor data used in the analysis are mentioned, secondly the electron density distributions of LiH and LiOH obtained by MEM are described and finally, the electron distributions of hydrogen in the two compounds are discussed.
2. Data set and analysis 2.1. LiH
Fig. 1. MEM electron density maps of LiH at 293 K for: (a) the (002) plane; (b) the (110) plane. Contour lines are drawn from 0.2 to ˚ 3] intervals. Some atomic sites are indicated by letters. 2.0 at 0.2 [e/A
The set of observed structure factor data used in this study for LiH analysis was measured by Vidal-Valat et al. at 293 K [6]. They made a thermal and annealing treatment with subsequent quenching in order to minimize the effect of extinction. They stated that there was no indication of significant extinction effects in the data. The space group of LiH is Fm3¯m and LiH has the NaCl type structure with the ˚ . The set of observed struclattice parameter a 4.0752 A ture factors consists of 26 reflections and corresponds to ˚ resolution in real space. The observed structure 0.51 A factors were analyzed by a computer program, MEED, [7] to have an electron density distribution by MEM. In MEM analysis, the unit cell was divided into 64 × 64 × 64 pixels. The reliable factor of MEM electron density based on structure factors, RMEM, is expressed by Sk 兩F kobs ⫺ F kMEM 兩= Sk 兩F kobs 兩; where F(k)obs is the observed structure factor of the reflection k, and F(k)MEM the structure factor calculated from electron density distribution obtained by MEM. In the present case RMEM was 0.37%, which can be regarded to be a very low value.
2.2. LiOH
Fig. 2. MEM electron density map of LiH at 293 K for lower density region in Fig. 1(b). Contour lines are drawn from 0.06 to ˚ 3] intervals. 0.2 at 0.02 [e/A
The set of observed structure factor data used in this study for LiOH analysis was measured by Go¨ttlicher and Kieselbach at room temperature [8]. The space group of LiOH is ˚, c P4/nmm. The lattice parameters are a 3.549 A ˚ 4.334 A. The set of observed structure factors consists of ˚ resolution in real 152 reflections and corresponds to 0.50 A space. The observed structure factors were also analyzed by MEED. In MEM analysis, the unit cell was divided into 72 × 72 × 84 pixels and the second setting of the space group P4/ nmm was applied to have a center of symmetry at the origin of the unit cell. In Go¨ttlicher and Kieselbach’s paper [8] the error for each structure factor was not listed but error ranges were given with respect to 兩F兩, i.e. less than 1% for 兩F兩 ⬎ 2, 1–2% for 1 ⬍ 兩F兩 ⬍ 2, 2–5% for 兩F兩 ⬍ 1, where 兩F兩 is an amplitude of structure factor. In this study, averaged values of error ranges were employed as the experimental error, i.e. 1% for 兩F兩 ⬎ 2, 1.5% for 1 ⬍ 兩F兩 ⬍ 2, 3.5% for 兩F兩 ⬍ 1. The value of RMEM was 1.6%, which was not as low as the LiH case but still good enough to discuss the electron distribution of hydrogen.
Shigefumi Yamamura et al. / Journal of Physics and Chemistry of Solids 60 (1999) 1721–1724
Fig. 3. MEM electron density map of LiOH at room temperature for the section x 1/4, which includes Li, O and H. The dot and the cross indicate the positions of hydrogen and oxygen nuclei obtained by Go¨ttlicher and Kieselbach using neutron diffraction data [8], respectively. Contour lines are drawn in the same way as those in Fig. 1(b).
3. Results and discussion 3.1. MEM map of LiH The electron density contour maps of LiH obtained by MEM (MEM maps) are shown in Fig. 1. Fig. 1(a) is the
1723
(002) plane and Fig. 1(b) is the (110) plane. The peaks of electron densities can be assigned to Li and H without any problem, though the electron density for H is very low and diffuse compared with that for Li. Such distribution of hydrogen is in contrast to those of ice (Ih) [4] and tetragonal KDP [5] where hydrogen exists in hydrogen bond. In the MEM maps of ice (Ih) and tetragonal KDP, the electron of hydrogen is recognized only as a link of contour lines between two oxygen atoms and no local maxima of the electron distribution of hydrogen can be seen. It seems very unique in crystalline state that the electron of hydrogen exists as spherical distribution. For further examination of the interatomic region, the MEM map of lower density region for Fig. 1(b) is shown in Fig. 2. The electron density distribution of H slightly elongates toward neighboring Li atoms. This kind of elongation of H can be also seen in the difference maps obtained by Vidal-Valat et al. [6]. It is found that the electron density between Li and H is not zero and the contour lines link Li and H along the [001] direction, although contour levels are quite low in Fig. 2. Such a bonding nature between Li and H is clearly visible in MEM maps. Besides, this covalent bond like nature indicates that LiH is not completely ionic, that is consistent with X-ray diffraction studies [6,9] and selfconsistent-field molecular orbital calculation [10]. In order to confirm this, number of electrons in each atom was estimated. The atomic site is defined as the maximum region enclosing contour lines. In the present case, the atomic site was the spherical region which is greater than or equal to an ˚ 3. They were ⫹ 0.96 for Li site, electron density of 0.13 e/A ⫺ 0.15 for H site and 0.81 electrons for another region. It is found that almost one electron from Li site does not concentrate at H site but scatters in the unit cell. However it should be noted that there are ambiguities in the estimation of atomic site, especially for hydrogen whose electron distribution is quite diffuse. 3.2. MEM map of LiOH
Fig. 4. Asymmetric component of the electron density for OH in LiOH with respect to O atom. The area showed corresponds to the small square in Fig. 3. The dot and the cross represent the same as in ¨ 3] interFig. 3. Contour lines are drawn from 0.1 to 1.5 at 0.1 [e/A vals. Only positive contours are shown.
The MEM map of a section of x 1/4 in LiOH which includes both Li ⫹ and OH ⫺ is shown in Fig. 3 with the positions of hydrogen and oxygen nuclei obtained by Go¨ttlicher and Kieselbach using neutron diffraction data [8]. In this map the peaks of electron density corresponding to Li and O are clearly seen. In contrast to LiH, the peak of electron density for hydrogen is not found as a spherical distribution. Instead, a slight distortion of electron density distribution from OH ellipse can be recognized. This means that an electron, which comes from a hydrogen atom is completely mixed with oxygen electrons. The distortion of OH ellipse is the only trace of the existence of proton. In order to examine the distortion of OH ellipse, the electron density distribution of OH shown in the rectangle in Fig. 3 is divided into two components. One is a symmetric component and the other is an asymmetric component. The symmetric component r sym(r) and the
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Shigefumi Yamamura et al. / Journal of Physics and Chemistry of Solids 60 (1999) 1721–1724
asymmetric component r asym(r) are calculated as
rsym r r r ⫹ r ⫺r=2;
1
rasym r r r ⫺ r ⫺r=2;
2
where r (r) is the MEM electron density at the position r. The origin of r is chosen at the position of the peak top of oxygen. Then, r (r) becomes a simple sum of r sym(r) and r asym(r) as
r r rsym r ⫹ rasym r:
3
The asymmetric component of electron density for OH in Fig. 3 is shown in Fig. 4. It is found that the distribution of oxygen near the core region is not symmetric. It is rather difficult to specify the cause of such an asymmetry of oxygen. However this may be due to the chemical bonding of oxygen to form OH ⫺ ion. In addition to the asymmetric component of oxygen atom, the local maximum of electron density distribution, which must be the contribution of hydrogen can be recognized, though the peak height is quite low. It is noticeable that the peak position is considerably different from the nucleus position determined by neutron diffraction shown by the dot in Fig. 4. This implies that the electron of hydrogen in OH ⫺ ion strongly interacts with oxygen atom. 4. Concluding remarks In MEM maps, each of the electron density distribution of hydrogen in LiH and LiOH shows a striking contrast. In LiH the peak of hydrogen atom can be recognized clearly. However, the electron from hydrogen atom in LiOH cannot be found as a peak maximum of electron density but the contribution of hydrogen can be recognized as a distortion of OH ellipse. Such a difference must come from the difference of bonding nature of hydrogen in Li–H and O–H, i.e. basically ionic for Li–H and covalent for O–H, respectively
and these bonding nature of hydrogen is observable reasonably by MEM without using structural models. Such a direct observation of hydrogen in other bonding states is desirable to find out a new insight into the bonding nature of hydrogen. Acknowledgements The author (SY) thanks Prof. T. Ito of Kanagawa Institute of Technology for helpful advice. A part of the computations was carried out at Nagoya University Computation Center and University of Tokyo Computer Center. This study was partly supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture in Japan.
References [1] M. Sakata, M. Sato, Acta Crystallogr. A46 (1990) 263–270. [2] M. Takata, M. Sakata, Acta Crystallogr. A52 (1996) 287–290. [3] S. Yamamura, M. Takata, M. Sakata, J. Phys. Chem. Solids 58 (1997) 177–183. [4] M. Sakata, M. Takata, H. Oshizumi, A. Goto, T. Hondoh, Physics and Chemistry of Ice, Hokkaido University Press, Sapporo, 1992 pp. 62–68. [5] S. Yamamura, M. Takata, M. Sakata, Y. Sugawara, J. Phys. Soc. Jpn. 67 (1998) 4124–4127. [6] G. Vidal-Valat, J.-P. Vidal, K. Kurki-Suonio, R. KurkiSuonio, Acta Crystallogr. A48 (1992) 46–60. [7] S. Kumazawa, Y. Kubota, M. Takata, M. Sakata, Y. Ishibashi, J. Appl. Crystallogr. 26 (1993) 453–457. [8] S. Go¨ttlicher, B. Kieselbach, Acta Crystallogr. A32 (1976) 185–192. [9] R.S. Calder, W. Cochran, D. Griffiths, R.D. Lowde, J. Phys. Chem. Solids 23 (1962) 621–632. [10] B.K. Rao, P. Jena, J. Phys. C: Solid State Phys. 19 (1986) 5167–5172.