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Stretching vibrations of symmetrical hydrogen bonds
Spectrochimi~a Acta, Vol.
SOA, No. 819,pp. 1685-1686,1994 Copyright0 1994Elsevier ScienceLtd Printed in Great Britain. All rightsreserved 0584-8539/94$7.00+ 0.00
0584453!&)4)EO116-R
SHORT NOTE
Stretching vibrations of symmetrical (Received 24 November 1993; in final form
18 April
hydrogen bonds
1994; accepted
18 April
1994)
WE PROPOSED the ionic force field for analysis of the vibrational spectra of symmetrical hydrogen bonds, X-H-X [l]. Initially, the vibrational modes of X-H-X were treated on a symmetrical linear triatomic model (CO2 type). It is now proposed that the vibrational mode which was thought to be the symmetric stretching v, [X(+)-H-( +)X1 should be regarded as the hydrogen-bond stretching v, [X(-, )-H( -)-( +)X1. This note describes improved equations for v, [l] and discusses the cases of KHS and (C&I&NHBr2. In the ionic force field [l], the frequency of the out-of-plane bending yxux is given by
where k, is a force constant correlated with the Coulombic force, mH the mass of the central hydrogen, c the velocity of light, and the masses of X units are regarded as infinity. The frequency of the antisymmetric stretching v, is obtained from
where K is the stretching force constant of the H-X bond and k, is identical to that in eqn (1). In eqn (2), the masses of X units are treated as infinity in the same manner as eqn (1). Isotopical frequency ratios (yxuxlyxnx) calculated from eqn (1) and (vasxuxlvasxnx) from eqn (2) are V’2. Many of the observed ratios, especially for vasr are nearly d2 [2, 31. Equation (2) for v, is the same as that derived from the modified valence force field, if k, is assumed to be equal to k which is a bon&bond interaction force constant. Therefore, the vS vibration can be obtained from
where Mx denotes the mass of the X unit. However, the v, frequencies calculated with eqn (3) differ from those observed for the symmetrical HF; ions. We find that eqn (4) which was obtained by multiplying the right-hand side of eqn (3) by q2, is suitable for comparison of the observed and calculated values of v,. This means that the v, vibration is the hydrogen-bond stretching mode v, [l]
%=&J(F).
(4)
The hydrogen-bond stretching mode v, may be treated approximately on a diatomic model. We adopt the same model for v, of X-H-X. In this case, it is assumed that the central hydrogen is fixed to one X and vibrates with the same X in the manner [X(-, )-H(---, )-( +)X]. The reduced mass of v0 is given by 1
1
1
;=MX+H+MX where MX+H means Mx plus the mass of hydrogen. The factor 2lMx in eqn (4) coincides with 11~ if the mass of the above hydrogen is disregarded. Hereafter, l/p of eqn (5) is used to express v,. The definition of the reduced mass in eqn (5) may appear to be unsuitable for a symmetrical hydrogen bond. However, the mean position of the hydrogen may remain in the center when it is 1685
Short Note
1686
fixed alternatively to one of the two X units. This is identical to the description given by SPINNER[4].
of the HF; ion
If we use l/p of eqn (5) instead of 2/Mx of eqn (4), V, can be expressed as 1 %=g
K+k,
d(-_) p
.
(6)
Next, we apply the above considerations to the cases of KHF, and (CJ-I#JHBr,. The Y,, yxux and Y, wave numbers observed for KHFz are 1450,123O and 600 cm -’ [l , 51.By using eqns (1) and (2), K and k, are calculated to be 1.51 and 0.891 mdyn A-‘, respectively. The Y, wave number calculated by using eqn (6) is 647 cm-‘. This value corresponds rather well to the observed value (600 cm-‘). Similarly, K and k, for (CJ-I&NHBr2 are calculated to be 0.405 and 0.259 mdyn A-‘, respectively, from the observed Y,, and yXHXwave numbers (704 and 663 cm-i, respectively [l, 51). The calculated Y, wave number, 167cm-‘, agrees almost exactly with the observed value, 168 cm-‘. These results demonstrate that the ionic force field is useful for predicting the Y, wave number. Finally, it may be worth while to note that use of the repulsive force constant between nonbonded X-e .X (adopted in the Urey-Bradley force field) instead of k, in eqn (6) satisfactorily predicts the Y, wave number for KHFz as well as (CJ-I&,NHBrr. The repulsive force constant for Fe. .F (2.28 A) in KHFz and that for Br. * .Br (3.35 A) in (CJ-I&W-IBr2 are 0.6 and 0.3 mdyn A-‘, respectively [6]. By using these values instead of k, in eqn (6), the v, wave numbers are calculated to be 606 cm-’ for KHFz and 173 cm-’ for (CJ-I&NHBr2. These values are in good agreement with the observed values, 600 and 168 cm-‘, respectively. JASCO Corporation, Banzai-cho, Kita-ku, Japan
YOSHIKIMATSUI*
Osaka Service Center Osaka 530
Shionogi Research Laboratories, Fukushima-ku, Osaka 553 Japan
Shionogi
& Co., Ltd
REFERENCES
[l] Y. Matsui, K. Ezumi and K. Iwatani, J. C/rem. Phys. 84,4774 (1986). [2] A. Novak, Structure Bonding 18, 177 (1974). [3] E. Spinner, AUG. J. Chem. 33, 1167 (1977). [4] E. Spinner, Ausf. 1. Chem. 33, 933 (1980). [5] .I. C. Evans and G. Y.-S. Lo, J. Phys. Chem. 73, 448 (1969). [6] T. Shimanouchi, Pure Appl. Chem. 7, 131 (1963).
* Author to whom correspondence should be addressed.
KOUJI IWATANI KIYOSHIEZUMI
SOA, No. 819,pp. 1685-1686,1994 Copyright0 1994Elsevier ScienceLtd Printed in Great Britain. All rightsreserved 0584-8539/94$7.00+ 0.00
0584453!&)4)EO116-R
SHORT NOTE
Stretching vibrations of symmetrical (Received 24 November 1993; in final form
18 April
hydrogen bonds
1994; accepted
18 April
1994)
WE PROPOSED the ionic force field for analysis of the vibrational spectra of symmetrical hydrogen bonds, X-H-X [l]. Initially, the vibrational modes of X-H-X were treated on a symmetrical linear triatomic model (CO2 type). It is now proposed that the vibrational mode which was thought to be the symmetric stretching v, [X(+)-H-( +)X1 should be regarded as the hydrogen-bond stretching v, [X(-, )-H( -)-( +)X1. This note describes improved equations for v, [l] and discusses the cases of KHS and (C&I&NHBr2. In the ionic force field [l], the frequency of the out-of-plane bending yxux is given by
where k, is a force constant correlated with the Coulombic force, mH the mass of the central hydrogen, c the velocity of light, and the masses of X units are regarded as infinity. The frequency of the antisymmetric stretching v, is obtained from
where K is the stretching force constant of the H-X bond and k, is identical to that in eqn (1). In eqn (2), the masses of X units are treated as infinity in the same manner as eqn (1). Isotopical frequency ratios (yxuxlyxnx) calculated from eqn (1) and (vasxuxlvasxnx) from eqn (2) are V’2. Many of the observed ratios, especially for vasr are nearly d2 [2, 31. Equation (2) for v, is the same as that derived from the modified valence force field, if k, is assumed to be equal to k which is a bon&bond interaction force constant. Therefore, the vS vibration can be obtained from
where Mx denotes the mass of the X unit. However, the v, frequencies calculated with eqn (3) differ from those observed for the symmetrical HF; ions. We find that eqn (4) which was obtained by multiplying the right-hand side of eqn (3) by q2, is suitable for comparison of the observed and calculated values of v,. This means that the v, vibration is the hydrogen-bond stretching mode v, [l]
%=&J(F).
(4)
The hydrogen-bond stretching mode v, may be treated approximately on a diatomic model. We adopt the same model for v, of X-H-X. In this case, it is assumed that the central hydrogen is fixed to one X and vibrates with the same X in the manner [X(-, )-H(---, )-( +)X]. The reduced mass of v0 is given by 1
1
1
;=MX+H+MX where MX+H means Mx plus the mass of hydrogen. The factor 2lMx in eqn (4) coincides with 11~ if the mass of the above hydrogen is disregarded. Hereafter, l/p of eqn (5) is used to express v,. The definition of the reduced mass in eqn (5) may appear to be unsuitable for a symmetrical hydrogen bond. However, the mean position of the hydrogen may remain in the center when it is 1685
Short Note
1686
fixed alternatively to one of the two X units. This is identical to the description given by SPINNER[4].
of the HF; ion
If we use l/p of eqn (5) instead of 2/Mx of eqn (4), V, can be expressed as 1 %=g
K+k,
d(-_) p
.
(6)
Next, we apply the above considerations to the cases of KHF, and (CJ-I#JHBr,. The Y,, yxux and Y, wave numbers observed for KHFz are 1450,123O and 600 cm -’ [l , 51.By using eqns (1) and (2), K and k, are calculated to be 1.51 and 0.891 mdyn A-‘, respectively. The Y, wave number calculated by using eqn (6) is 647 cm-‘. This value corresponds rather well to the observed value (600 cm-‘). Similarly, K and k, for (CJ-I&NHBr2 are calculated to be 0.405 and 0.259 mdyn A-‘, respectively, from the observed Y,, and yXHXwave numbers (704 and 663 cm-i, respectively [l, 51). The calculated Y, wave number, 167cm-‘, agrees almost exactly with the observed value, 168 cm-‘. These results demonstrate that the ionic force field is useful for predicting the Y, wave number. Finally, it may be worth while to note that use of the repulsive force constant between nonbonded X-e .X (adopted in the Urey-Bradley force field) instead of k, in eqn (6) satisfactorily predicts the Y, wave number for KHFz as well as (CJ-I&,NHBrr. The repulsive force constant for Fe. .F (2.28 A) in KHFz and that for Br. * .Br (3.35 A) in (CJ-I&W-IBr2 are 0.6 and 0.3 mdyn A-‘, respectively [6]. By using these values instead of k, in eqn (6), the v, wave numbers are calculated to be 606 cm-’ for KHFz and 173 cm-’ for (CJ-I&NHBr2. These values are in good agreement with the observed values, 600 and 168 cm-‘, respectively. JASCO Corporation, Banzai-cho, Kita-ku, Japan
YOSHIKIMATSUI*
Osaka Service Center Osaka 530
Shionogi Research Laboratories, Fukushima-ku, Osaka 553 Japan
Shionogi
& Co., Ltd
REFERENCES
[l] Y. Matsui, K. Ezumi and K. Iwatani, J. C/rem. Phys. 84,4774 (1986). [2] A. Novak, Structure Bonding 18, 177 (1974). [3] E. Spinner, AUG. J. Chem. 33, 1167 (1977). [4] E. Spinner, Ausf. 1. Chem. 33, 933 (1980). [5] .I. C. Evans and G. Y.-S. Lo, J. Phys. Chem. 73, 448 (1969). [6] T. Shimanouchi, Pure Appl. Chem. 7, 131 (1963).
* Author to whom correspondence should be addressed.
KOUJI IWATANI KIYOSHIEZUMI