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Calculations for the vibration frequencies of the OH⋯O bond in KH2PO4 by a semiempirical method
Spechchimin, A&z. Vol. 49A. No. 7. pp. 1015-1019. Printed in Great Britain
1993 0
0584-8539193 $6.00+0.00 1993 Pergamon Press Ltd
Calculations for the vibration frequencies of the 0-H. . -0 bond in KH,pO, by a semiempirical method Y. Q. JIA Changchun Institute of Applied Chemistry, Academia Sinica, Changchun, Jilin, China (Received 28 April 1992; in final from 4 September 1992; accepted 7 September 1992) Abstract-The frequencies of the stretching vibration and the bending vibration of the 0-H. . .O bond in potassium dihydrogen phosphate have been calculated by means of two semiempirical formulae with three parameters. The calculated results can give satisfactory explanation for the experimental spectra of the potassium dihydrogen phosphate crystal. The parameters used in the calculations may be related to the chemical bonding and the charge distribution about the two oxygen atoms of the 0-H. . +0 bond system.
THE RESEARCHon the IR spectra
of the O-H - - *0 bond in both the inorganic compounds and the organic compounds has been an interesting subject. The IR spectra of the potassium dihydrogen phosphate crystal containing the hydrogen bond system have been previously investigated [l-7]. To determine the IR absorption bands from the vibrations of the 0-H. . - 0 bond in a hydrogen bond system, like potassium dihydrogen phosphate, several potential models, such as the single symmetric minimum potential model, and the symmetric double minimum potential model, have been proposed [4-61. The possible proton-tunneling mechanism in the hydrogen bond system of the potassium dihydrogen phosphate crystal has also been assumed. However, how to predict or to determine the absorption frequencies from the vibrations of the 0-H. - - 0 bond in any hydrogen bond system by a simple method is still very interesting. The asymmetric double minimum potential model presented by Gou and ZHAO can give not only a better modification for the calculations of the energy levels of the stretching vibration of the O-H - - *0 bond, but also the corresponding vibration wave functions [7]. Besides, Gou and ZHAO have rejected the possible presence of the protontunneling mechanism in the hydrogen bond system of the potassium dihydrogen phosphate crystal. Recently, some experiments have given a negative evidence for a proton-tunneling mechanism in the phase transition of the potassium dihydrogen phosphate type crystals [S]. Therefore, we feel that the asymmetric double minimum potential model of Gou and ZHAO may be more reasonable for the explanation of the IR spectra of the hydrogen bond system. However, the bending vibration of the O-H - . - 0 bond is not considered in their calculations. In this case, some big deviations between the calculated results and the experimental results for some absorption bands like the absorption bands at 1580 and 1700 cm-‘, can be expected. The absorption bands at 1580 and 170Ocm-’ in the IR spectra of the potassium dihydrogen phosphate crystal may be attributable to the bending vibration of the O-H - . - 0 bond [4]. Therefore, a potential model to calculate the energy levels of the bending vibration of the 0-H. - . 0 bond will be necessary. In this paper, we shall propose an approximate method to calculate the frequencies of the stretching vibration and the bending vibration of the O-H - - - 0 bond. The calculated results can give a reasonable explanation for the experimental IR spectra in the potassium dihydrogen phosphate crystal. The parameters used in the calculations may be related to the electric field distribution around the two oxygen atoms in the O-H *- ~0 bond and the covalence of the O-H - *- 0 bond. 1015
1016
Y. 0.
JIA
Fig. 1. Two vibration modes of the 0-H. . . 0 bond system in the potassium dihydrogen phosphate crystal.
MODEL AND CALCULATIONS We can use an isolated triatomic system composed of a hydrogen atom and two oxygen atoms to simulate a hydrogen bond system. As Fig. 1 shows, in equilibrium state, the hydrogen atom is in the line connecting the two oxygen atoms, but the distance between the hydrogen atom and the oxygen atom (0,) is smaller than that between the hydrogen atom and the oxygen atom (03. Especially, the 0,-H bond is a covalent one and possesses much larger bond energy than the He . *0 bond. Therefore, for the proton, the binding force from the Oi is very different from that from the 02, when the proton moves along the line connecting the Or and the Oz. To describe such an asymmetric stretching motion of the proton along the line connecting the two oxygen atoms in an 0-H. . -0 bond system (Fig. l), the following asymmetric potential function may be more reasonable: U(x)= -A(2e-“-e-h),
(1)
where A and GIare the parameters and x is the displacement of the proton along the line connecting the two oxygen atoms, i.e. the x-direction (Fig. 1). It must be pointed out that the physical meaning of Eqn (1) is very different from that of the well-known Morse potential function. The Morse potential function describes the interaction between two atoms in a diatomic molecule. However, Eqn (1) describes an asymmetric potential field. There is a standard solution to such a one-dimensional oscillator problem in the above asymmetric potential field 191. The energy levels of the oscillator can be obtained from the following formula:
where p is the reduced mass, n is a positive integer and can take the value from zero to the maximum, which is smaller than a/ah-+, and A and a are the potential parameters. As Fig. 1 shows, the proton may also move along the y-direction perpendicular to the O-O axis, besides the stretching motion of the proton along the direction of the O-O axis. In this motion, the proton can both move up and down along the direction perpendicular to the O-O axis and the bond angle 0-H. +*0 will be changed with the motion of the proton along the y-direction. So, we can use this motion of the proton to approximate the bending vibration of the hydrogen bond. For this motion of the proton, the possible potential function we proposed is U(y) = - Blcosh2 by,
(3)
where B and @are the potential parameters and y is the displacement of the proton along the y-direction. There is also a standard solution to this one-dimensional oscillator
Vibration frequencies of the 0-H.
*.O bond in KHZP04
1017
problem in such a potential field [9]. The energy levels to the oscillator can be calculated by the following formula:
&-!$
2
2 ti.s-@n+l) 1 +p2h2 N
1 2
(4)
where ,Uis the reduced mass, n is a positive integer and can take a value from zero to the maximum, which is smaller than i( - 1 + ql + (8@j?2h2)), and B and /3 are the potential parameters. Therefore, the energy levels for the stretching vibration and the bending vibration of the O-H ***0 bond can be evaluated by Eqns (2) and (4), respectively, after determination of the parameters A, a and B, /I. We have noted that the parameter A in Eqn (1) must be equal to the parameter B in Eqn (3). This is because the potential at the proton from either Eqn (1) or Eqn (3) must be the same when the proton is at the origin of the coordinate, i.e. at the equilibrium position of the proton in this hydrogen bond system. In practice, the parameters A and B can be considered to be the dissociation energy of the hydrogen bond [6]. In addition, we consider that the parameters a and B may be related to the gradient of the electric field created by the two oxygen atoms along the x-direction and y-direction, respectively. We can also assume that the electric field gradient along the x-direction may not be very different from that along the y-direction. So, we can expect that the value of the parameter a and /3 may have a same order of magnitude. In this case, we may need only three parameters (U,= A, B; a and /?) and can carefully choose the appropriate parameters to fit to the experimental absorption bands of the hydrogen bond system. We have carried out a systematical calculation for the vibration frequencies of the 0-H. -. 0 bond in potassium dihydrogen phosphate and obtained the energy level diagrams for the stretching vibration and the bending vibration of the O-H - . -0 bond (Fig. 2). The experimental and the calculated results are listed in Table 1.
DISCUSSION
The results indicate that the IR absorption bands at 1300 cm-’ and at about 2800 cm-’ may be attributable to the transition between the energy levels of the stretching vibration of the 0-H.. . 0 bond. From Fig. 2, we can expect that the relative intensity of this IR absorption band at about 2800 cm-’ will be weaker due to An = 3. This is in agreement with the experimental IR spectra [4]. The absorption band at 1580 cm-’ in the experimental IR spectra is from the transition between the energy levels of the bending vibration of the O-H - *- 0 [l]. The IR absorption band at about 2400 or 2445 cm-’ may be attributable to the transition between the energy levels of bending vibration with An =2, hence the relative intensity of this absorption band in the experimental IR spectra of the potassium dihydrogen phosphate is not very strong [l]. This is also in good agreement with the calculated result.
3810 cm-’ 3622
y
(4
0)
Fig. 2. Energy level diagrams of two vibration modes of the 0-H. . .O bond in the potassium dihydrogen phosphate crystal. (A) Thestretching vibration; (B) the bending vibration (the bondangle interaction). WA) 49:w
Y. Q. JIA
1018
Table 1. The absorption frequencies from the vibrations of the O-H..* 0 bond in potassium dihydrogen phosphate Y
v (exp.) (cm-‘) 2825 [3] 2800 PI 2750 [4]
(talc.) (cm-‘) A
B
2822
2445 [3] 2400 [I, 2741
2498
1700 [2] 1580 [l, 41 1300 [4]
1535 1317
A: the stretching vibration; B: the bending vibration. The parameters used in the calculations are: &(A, B) = 3810 cm-‘; Vjz&h = 4.5; /L?W/~ = 71 cm-‘.
However, we must point out that the method here is only an approximate one. This is not only because the interaction between the hydrogen atom and the oxygen atom in the O-H bond is not a pure electrostatic one and possesses a certain covalent property, but also because the model is too simple for a hydrogen bond system. For example, as Fig. 1 shows, when the proton moves along the y-direction perpendicular to the 0. . - 0 axis, both the bond-angle of the 0-H. *- 0 bond and the distances between the hydrogen atom and the two oxygen atoms will be changed at the same time. Therefore, practically, this vibration mode is not a real bending one, but a bond-angle interaction vibration one. Especially, a hydrogen bond system in any compound is not an isolated triatomic system and the various effects of the neighbor atoms on the vibration of the hydrogen bond cannot be neglected. However, why can such a simple method give some satisfactory results? Perhaps, this is because the model may be reasonable, although it is very simple, and can very well simulate the hydrogen bond system. Besides, the parameters used in the calculations must have contained some effects neglected in the model, such as the covalence in the O-H bond and the electric field distribution around the two oxygen atoms as well as the various effects of the different neighbour atoms. We have noted that the parameter a in Eqn (1) and the parameter /? in Eqn (3), obtained by fitting to the experimental absorption bands, is equal to 13.72-M and 16.85-/h, respectively. As mentioned above, the parameter a and /? may indicate the gradient of the electric field created by the two oxygen atoms along the x-direction and the y-direction, respectively. As we have pointed out, indeed, the values of the two parameters possess a same order of magnitude. But, the slightly large value of the parameter #?may imply that the electric field gradient along the y-direction is larger than that along the x-direction. This indicates that the charge distribution about the two oxygen atoms is not symmetric and that the chemical bonding of the hydrogen atom with the oxygen atoms along the line connecting the two oxygen atoms must be rather different from that along the line perpendicular to the O-O axis. Therefore, this will mean that some properties of a line-type hydrogen bond, in which the hydrogen atom is in the O-O axis, must be different from those of a bridge-type hydrogen bond, in which the hydrogen atom is not in the O-O axis. We want to emphasize that the potential parameters (U,,, a and /I) will have different values in different hydrogen bond systems due to different effects of the neighbor atoms
Vibration frequencies of the O-H **-0 bond in KHrPO,
1019
about the oxygen atoms on the properties of the hydrogen bond. Besides, these parameters are obtained by means of fitting to the experimental absorption bands, so these parameters will contain the effects of the various factors on the hydrogen bond system in the compounds. These parameters are only some empirical parameters and do not possess any strict physical meanings, although they may be related to the chemical bonding and the charge distribution about the oxygen atoms in the hydrogen bond system.
CONCLUSION
The vibration frequencies from the O-H *. a0 bond in potassium dihydrogen phosphate can be calculated by using a semiempirical method. The results show that the experimental absorption bands may be attributable not only to the stretching vibration of the O-H... 0 bond, but also to the bending vibration. The parameters used in the calculations may be related to the chemical bondings and the electric field distribution around the oxygen atoms. Perhaps this method may also be useful for determining and predicting the vibration frequencies from the hydrogen bond systems in other organic or inorganic compounds and in the metal hydrides. Acknowledgement-The author thanks Dr G. F. Zeng at the Changchun Institute of Applied Chemistry, Academia Sinica for his discussions.
REFERENCES G. M. Murphy, G. Weiner and J. J. Oberly, /. Chem. Phys. 22, 1322 (1954). M. A. Kovner and V. N. Kapshtd, Izuest. Akad. Nauk. SSSR. Ser. Fiz. 17,561 (1953). A. N. Lazarev and A. S. Zaitseva, Fiz. Tverdogo Tela. 2,3026 (1960). R. Bhnc and D. Hadzi, hiolec. Phys. 1,391 (1958). D. Hadzi and H. W. Thompson, Hydrogen Bonding. Pergamon Press, Oxford (1959). C. Reid, J. f&m. Phys. 38, 1982 (1959). 0. Q. Gou and J. Y. Zhao, 1. Moles. Sci. 3. 17 (1983). M. Ichikawa, K. Motida and N. Yamada, Phys. Reu. B. 36,874 (1987). L. D. Landau and E. M. Lifshitz, Quunfum A4echanic.r(Non-relatiubticTheory). Pergamon Press, Oxford (1976). [lo] K. Nakamoto, Infrared and Raman Spectra of Inorganic and Coordination Compounds, 3rd Edn. John Wiley and Sons (1978). [l] [2] [3] [4] [S] [6] [7] [S] [9]
1993 0
0584-8539193 $6.00+0.00 1993 Pergamon Press Ltd
Calculations for the vibration frequencies of the 0-H. . -0 bond in KH,pO, by a semiempirical method Y. Q. JIA Changchun Institute of Applied Chemistry, Academia Sinica, Changchun, Jilin, China (Received 28 April 1992; in final from 4 September 1992; accepted 7 September 1992) Abstract-The frequencies of the stretching vibration and the bending vibration of the 0-H. . .O bond in potassium dihydrogen phosphate have been calculated by means of two semiempirical formulae with three parameters. The calculated results can give satisfactory explanation for the experimental spectra of the potassium dihydrogen phosphate crystal. The parameters used in the calculations may be related to the chemical bonding and the charge distribution about the two oxygen atoms of the 0-H. . +0 bond system.
THE RESEARCHon the IR spectra
of the O-H - - *0 bond in both the inorganic compounds and the organic compounds has been an interesting subject. The IR spectra of the potassium dihydrogen phosphate crystal containing the hydrogen bond system have been previously investigated [l-7]. To determine the IR absorption bands from the vibrations of the 0-H. . - 0 bond in a hydrogen bond system, like potassium dihydrogen phosphate, several potential models, such as the single symmetric minimum potential model, and the symmetric double minimum potential model, have been proposed [4-61. The possible proton-tunneling mechanism in the hydrogen bond system of the potassium dihydrogen phosphate crystal has also been assumed. However, how to predict or to determine the absorption frequencies from the vibrations of the 0-H. - - 0 bond in any hydrogen bond system by a simple method is still very interesting. The asymmetric double minimum potential model presented by Gou and ZHAO can give not only a better modification for the calculations of the energy levels of the stretching vibration of the O-H - - *0 bond, but also the corresponding vibration wave functions [7]. Besides, Gou and ZHAO have rejected the possible presence of the protontunneling mechanism in the hydrogen bond system of the potassium dihydrogen phosphate crystal. Recently, some experiments have given a negative evidence for a proton-tunneling mechanism in the phase transition of the potassium dihydrogen phosphate type crystals [S]. Therefore, we feel that the asymmetric double minimum potential model of Gou and ZHAO may be more reasonable for the explanation of the IR spectra of the hydrogen bond system. However, the bending vibration of the O-H - . - 0 bond is not considered in their calculations. In this case, some big deviations between the calculated results and the experimental results for some absorption bands like the absorption bands at 1580 and 1700 cm-‘, can be expected. The absorption bands at 1580 and 170Ocm-’ in the IR spectra of the potassium dihydrogen phosphate crystal may be attributable to the bending vibration of the O-H - . - 0 bond [4]. Therefore, a potential model to calculate the energy levels of the bending vibration of the 0-H. - . 0 bond will be necessary. In this paper, we shall propose an approximate method to calculate the frequencies of the stretching vibration and the bending vibration of the O-H - - - 0 bond. The calculated results can give a reasonable explanation for the experimental IR spectra in the potassium dihydrogen phosphate crystal. The parameters used in the calculations may be related to the electric field distribution around the two oxygen atoms in the O-H *- ~0 bond and the covalence of the O-H - *- 0 bond. 1015
1016
Y. 0.
JIA
Fig. 1. Two vibration modes of the 0-H. . . 0 bond system in the potassium dihydrogen phosphate crystal.
MODEL AND CALCULATIONS We can use an isolated triatomic system composed of a hydrogen atom and two oxygen atoms to simulate a hydrogen bond system. As Fig. 1 shows, in equilibrium state, the hydrogen atom is in the line connecting the two oxygen atoms, but the distance between the hydrogen atom and the oxygen atom (0,) is smaller than that between the hydrogen atom and the oxygen atom (03. Especially, the 0,-H bond is a covalent one and possesses much larger bond energy than the He . *0 bond. Therefore, for the proton, the binding force from the Oi is very different from that from the 02, when the proton moves along the line connecting the Or and the Oz. To describe such an asymmetric stretching motion of the proton along the line connecting the two oxygen atoms in an 0-H. . -0 bond system (Fig. l), the following asymmetric potential function may be more reasonable: U(x)= -A(2e-“-e-h),
(1)
where A and GIare the parameters and x is the displacement of the proton along the line connecting the two oxygen atoms, i.e. the x-direction (Fig. 1). It must be pointed out that the physical meaning of Eqn (1) is very different from that of the well-known Morse potential function. The Morse potential function describes the interaction between two atoms in a diatomic molecule. However, Eqn (1) describes an asymmetric potential field. There is a standard solution to such a one-dimensional oscillator problem in the above asymmetric potential field 191. The energy levels of the oscillator can be obtained from the following formula:
where p is the reduced mass, n is a positive integer and can take the value from zero to the maximum, which is smaller than a/ah-+, and A and a are the potential parameters. As Fig. 1 shows, the proton may also move along the y-direction perpendicular to the O-O axis, besides the stretching motion of the proton along the direction of the O-O axis. In this motion, the proton can both move up and down along the direction perpendicular to the O-O axis and the bond angle 0-H. +*0 will be changed with the motion of the proton along the y-direction. So, we can use this motion of the proton to approximate the bending vibration of the hydrogen bond. For this motion of the proton, the possible potential function we proposed is U(y) = - Blcosh2 by,
(3)
where B and @are the potential parameters and y is the displacement of the proton along the y-direction. There is also a standard solution to this one-dimensional oscillator
Vibration frequencies of the 0-H.
*.O bond in KHZP04
1017
problem in such a potential field [9]. The energy levels to the oscillator can be calculated by the following formula:
&-!$
2
2 ti.s-@n+l) 1 +p2h2 N
1 2
(4)
where ,Uis the reduced mass, n is a positive integer and can take a value from zero to the maximum, which is smaller than i( - 1 + ql + (8@j?2h2)), and B and /3 are the potential parameters. Therefore, the energy levels for the stretching vibration and the bending vibration of the O-H ***0 bond can be evaluated by Eqns (2) and (4), respectively, after determination of the parameters A, a and B, /I. We have noted that the parameter A in Eqn (1) must be equal to the parameter B in Eqn (3). This is because the potential at the proton from either Eqn (1) or Eqn (3) must be the same when the proton is at the origin of the coordinate, i.e. at the equilibrium position of the proton in this hydrogen bond system. In practice, the parameters A and B can be considered to be the dissociation energy of the hydrogen bond [6]. In addition, we consider that the parameters a and B may be related to the gradient of the electric field created by the two oxygen atoms along the x-direction and y-direction, respectively. We can also assume that the electric field gradient along the x-direction may not be very different from that along the y-direction. So, we can expect that the value of the parameter a and /3 may have a same order of magnitude. In this case, we may need only three parameters (U,= A, B; a and /?) and can carefully choose the appropriate parameters to fit to the experimental absorption bands of the hydrogen bond system. We have carried out a systematical calculation for the vibration frequencies of the 0-H. -. 0 bond in potassium dihydrogen phosphate and obtained the energy level diagrams for the stretching vibration and the bending vibration of the O-H - . -0 bond (Fig. 2). The experimental and the calculated results are listed in Table 1.
DISCUSSION
The results indicate that the IR absorption bands at 1300 cm-’ and at about 2800 cm-’ may be attributable to the transition between the energy levels of the stretching vibration of the 0-H.. . 0 bond. From Fig. 2, we can expect that the relative intensity of this IR absorption band at about 2800 cm-’ will be weaker due to An = 3. This is in agreement with the experimental IR spectra [4]. The absorption band at 1580 cm-’ in the experimental IR spectra is from the transition between the energy levels of the bending vibration of the O-H - *- 0 [l]. The IR absorption band at about 2400 or 2445 cm-’ may be attributable to the transition between the energy levels of bending vibration with An =2, hence the relative intensity of this absorption band in the experimental IR spectra of the potassium dihydrogen phosphate is not very strong [l]. This is also in good agreement with the calculated result.
3810 cm-’ 3622
y
(4
0)
Fig. 2. Energy level diagrams of two vibration modes of the 0-H. . .O bond in the potassium dihydrogen phosphate crystal. (A) Thestretching vibration; (B) the bending vibration (the bondangle interaction). WA) 49:w
Y. Q. JIA
1018
Table 1. The absorption frequencies from the vibrations of the O-H..* 0 bond in potassium dihydrogen phosphate Y
v (exp.) (cm-‘) 2825 [3] 2800 PI 2750 [4]
(talc.) (cm-‘) A
B
2822
2445 [3] 2400 [I, 2741
2498
1700 [2] 1580 [l, 41 1300 [4]
1535 1317
A: the stretching vibration; B: the bending vibration. The parameters used in the calculations are: &(A, B) = 3810 cm-‘; Vjz&h = 4.5; /L?W/~ = 71 cm-‘.
However, we must point out that the method here is only an approximate one. This is not only because the interaction between the hydrogen atom and the oxygen atom in the O-H bond is not a pure electrostatic one and possesses a certain covalent property, but also because the model is too simple for a hydrogen bond system. For example, as Fig. 1 shows, when the proton moves along the y-direction perpendicular to the 0. . - 0 axis, both the bond-angle of the 0-H. *- 0 bond and the distances between the hydrogen atom and the two oxygen atoms will be changed at the same time. Therefore, practically, this vibration mode is not a real bending one, but a bond-angle interaction vibration one. Especially, a hydrogen bond system in any compound is not an isolated triatomic system and the various effects of the neighbor atoms on the vibration of the hydrogen bond cannot be neglected. However, why can such a simple method give some satisfactory results? Perhaps, this is because the model may be reasonable, although it is very simple, and can very well simulate the hydrogen bond system. Besides, the parameters used in the calculations must have contained some effects neglected in the model, such as the covalence in the O-H bond and the electric field distribution around the two oxygen atoms as well as the various effects of the different neighbour atoms. We have noted that the parameter a in Eqn (1) and the parameter /? in Eqn (3), obtained by fitting to the experimental absorption bands, is equal to 13.72-M and 16.85-/h, respectively. As mentioned above, the parameter a and /? may indicate the gradient of the electric field created by the two oxygen atoms along the x-direction and the y-direction, respectively. As we have pointed out, indeed, the values of the two parameters possess a same order of magnitude. But, the slightly large value of the parameter #?may imply that the electric field gradient along the y-direction is larger than that along the x-direction. This indicates that the charge distribution about the two oxygen atoms is not symmetric and that the chemical bonding of the hydrogen atom with the oxygen atoms along the line connecting the two oxygen atoms must be rather different from that along the line perpendicular to the O-O axis. Therefore, this will mean that some properties of a line-type hydrogen bond, in which the hydrogen atom is in the O-O axis, must be different from those of a bridge-type hydrogen bond, in which the hydrogen atom is not in the O-O axis. We want to emphasize that the potential parameters (U,,, a and /I) will have different values in different hydrogen bond systems due to different effects of the neighbor atoms
Vibration frequencies of the O-H **-0 bond in KHrPO,
1019
about the oxygen atoms on the properties of the hydrogen bond. Besides, these parameters are obtained by means of fitting to the experimental absorption bands, so these parameters will contain the effects of the various factors on the hydrogen bond system in the compounds. These parameters are only some empirical parameters and do not possess any strict physical meanings, although they may be related to the chemical bonding and the charge distribution about the oxygen atoms in the hydrogen bond system.
CONCLUSION
The vibration frequencies from the O-H *. a0 bond in potassium dihydrogen phosphate can be calculated by using a semiempirical method. The results show that the experimental absorption bands may be attributable not only to the stretching vibration of the O-H... 0 bond, but also to the bending vibration. The parameters used in the calculations may be related to the chemical bondings and the electric field distribution around the oxygen atoms. Perhaps this method may also be useful for determining and predicting the vibration frequencies from the hydrogen bond systems in other organic or inorganic compounds and in the metal hydrides. Acknowledgement-The author thanks Dr G. F. Zeng at the Changchun Institute of Applied Chemistry, Academia Sinica for his discussions.
REFERENCES G. M. Murphy, G. Weiner and J. J. Oberly, /. Chem. Phys. 22, 1322 (1954). M. A. Kovner and V. N. Kapshtd, Izuest. Akad. Nauk. SSSR. Ser. Fiz. 17,561 (1953). A. N. Lazarev and A. S. Zaitseva, Fiz. Tverdogo Tela. 2,3026 (1960). R. Bhnc and D. Hadzi, hiolec. Phys. 1,391 (1958). D. Hadzi and H. W. Thompson, Hydrogen Bonding. Pergamon Press, Oxford (1959). C. Reid, J. f&m. Phys. 38, 1982 (1959). 0. Q. Gou and J. Y. Zhao, 1. Moles. Sci. 3. 17 (1983). M. Ichikawa, K. Motida and N. Yamada, Phys. Reu. B. 36,874 (1987). L. D. Landau and E. M. Lifshitz, Quunfum A4echanic.r(Non-relatiubticTheory). Pergamon Press, Oxford (1976). [lo] K. Nakamoto, Infrared and Raman Spectra of Inorganic and Coordination Compounds, 3rd Edn. John Wiley and Sons (1978). [l] [2] [3] [4] [S] [6] [7] [S] [9]