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Electrically caused vibrational frequency shifts and dipole moments in rare gas hydrogen bonded complexes
Volume 136, number 1
CHEMICAL PHYSICS LETTERS
24 April 1987
ELECTRICALLY CAUSED VIBRATIONAL FREQUENCY SHIFTS AND DIPOLE MOMENTS IN RARE GAS HYDROGEN BONDED COMPLEXES Shi-yi LIU and Clifford E. DYKSTRA
Received 24 November 1986; in final form 20 February 1987
The Liu-Dykstra theory of electrical influence on vibrational potentials in hydrogen bonded complexes is shown to account very well for vibrational frequency shifts and induced dipoles in a series of rare gas complexes with hydrogen fluoride. The behavior of the electrical interaction energy and dipole moment are shown in detail for Ar-HF.
1. Introduction In a recent paper [ 11, we developed the idea that simple, mutual electrical influence including polarization effects produced the bulk of the changes upon hydrogen bond formation in intramolecular stretching potentials and so led to the vibrational frequency shifts that are characteristic of these complexes. In a subsequent study of the Hz-HF complex ]2], we predicted a small red-shift of 19 cm-’ for the HF stretch. Hunt and Andrews have measured this shift in a neon matrix and found it to be 15 cm-’ [ 31. Lovejoy and Nesbitt [ 41 have assigned the gas phase spectrum and obtained a frequency shift of almost 12 cm- ‘, and a like value has been measured by Jucks and Miller f4]. Since our theory implies that primary electronic structure changes upon hydrogen bond formation are charge polarization, it follows that electrical properties of complexes should be reasonably accounted for in the same way. We have demonstrated this in the case of (HF) z where even something as exotic as the axial dipole hyperpolarizability can be explained from mutual polarization of the monomers [ 61. Another result that follows is that the electrical influence identifies enhancement in vibrational transition moments [7] that usually accompanies complexation. In our picture of weakly bonded complexes, the vibrational potential of a constituent monomer is perturbed by the interaction between its permanent
22
and induced electrical moments with those of its bonding partner. Knowledge of the uncomplexed monomer’s vibrational potential and its electrical properties as a function of the vibrational coordinates make it possible to construct the monomer’s vibrational potential as experienced when embedded in the complex. From that, vibrational frequencies and so forth may be calculated, a process which may often be done with low-order pe~urbation theory ill* Complexes containing rare gas atoms may seem to be outside electrical pictures of interaction since dispersion effects are potentially important. For instance, applying the classical electrical analysis to the interaction of two neon atoms trivially give a flat, zero potential. Quantum effects such as dispersion are unavoi~bly impo~ant there. In this paper we show that electrical ideas can be satisfactorily used certain features of rarein understanding gas-molecule complexes. The physical basis for this success is that a monomer such as HF seems to induce sizeable moments in an attached rare gas atom and that plus back-perturbation becomes a significant effect. Quantum effects between the rare gas and HF do not seem to have as sizable a role in the vibrational frequency shifts. 2. Calculations The vibrational
potential
and anharmonicity
0 009-26 14/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume136,number1
24 April1981
CHEMICALPHYSICSLETTERS
parameters of HF and the electrical properties of HF were the same as those used in our first study of HF-base complexes [ 11. The electrical properties of the rare gas atoms, He, Ne, Ar and Kr, are those of Mahan [ 81 which were obtained from a modified Stemheimer analysis [ 91. For Ar, these properties are in line with the recent extensive calculations of Cemusak et al. [ lo]. Only the dipole and quadrupole polarizabilities, designated (Ydand or, for atoms, were available for the entire series of rare gas atoms. Relative to the molecules, this meant the dipoledipole-quadrupole hyperpolarizability was left out for the rare gases. Test calculations using a limited basis ab initio value for this hyperpolarizability for Ne yielded little difference. However, the size of this property should increase with atomic number in the rare gas series, and so beyond Ne it may have a slightly more noticeable effect. In the electrical evaluations, center of mass properties were used for HF. In the initial electrical interaction calculations, the distances between the rare gas atoms and the HF were fixed at their vibrationally center of mass, R,,., averaged separations for Ar-HF [ 111 and Kr-HF [ 121 as obtained from rotational spectra. The same parameter was estimated for the He-HF and Ne-HF complexes based on the separations in the other systems and their van der Waals radii. For the evaluation of the total dipole moments of the various complexes, equilibrium molecular electrical properties were used. Dipole moments were calculated for both equilibrium structures and vibrationally averaged structures, as known.
3. Results and discussion
At fixed separation distances, the electrical interaction energy was followed as a function of 0, the angle of the rare gas to molecule center of mass measured relative to the molecule’s axis. For HeHF, NeHF, ArHF, and KrHF, small changes in 8 away from a completely linear complex were found to be destabilizing in the electrical interaction analysis. This means that electrical effects predict a linear equilibrium or at least a local minimum at linear structures, and that appears consistent with analysis of rotational spectroscopic data which are available for a few of these systems [ 11,121. That electrical effects account for the orientational features of weak complexes has already been established by a number of different groups [ 13-20 ] employing slightly different schemes for evaluating electrical interaction. Table 1 lists the dipole moments of the complexes computed at equilibrium. There is a sharply increasing induced moment with increasing complexity of the rare gas atom. This follows because the bigger rare gas atoms are naturally more polarizable. Comparison with experiment is not direct because dipoles are computed for static structures with no accounting for vibrational averaging. One rough way of incorporating the vibrational averaging effects is to evaluate moments at the operational, on-average orientational angles. Doing this for Ar-HF gives an a-inertial axis dipole moment that differs from the experimental value by only 0.07 D. A representative dipole moment surface is depicted with contours for the Ar-HF complex in fig. 1. This can suggest how vibrational motion enters into the rotational spec-
Table1 Dipolemomentsa)of rare-gas-HFcomplexes Complex
Electrically obtained values at equilibrium (e=oO) P
He-HF Ne-HF Ar-HF Kr-HF
lndund
0.036 0.077 0.241 0.329
‘) Dipole values are in D.
P
tota,
1.851 1.892 2.056 2.144
Operational zero-point bending angle, 0’ (deg)
Measured u-inertial dipole component &I
41.27 b, 39.22 =’
1.3353
Electrically obtained values at angles 0’ total
PL,
P
1.404 1.478
1.875 1.920
‘) From ref. [ 111. ‘) From ref. [ 121.
23
CHEMICAL PHYSICS LETTERS
Volume 136, number 1
24 April 1987
7-r /
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6G.0 Fig. 1. Contours showing the total dipole moment (in D) of Ar-HF for placement of Ar around HF. The horizontal axis labels the Ar to HF cm. angles relative to the HF axis. The vertical axis is the Ar to HF c.m. distance.
Fig. 2. Contours showing the sensitivity of the HF red-shift (in cm - ’ ) computed with the Liu-Dykstra model [ 1] to placement of Ar around HF in Ar-HF. Axes are labelled the same as in fig. 1.
troscopy determination of the dipole. Notice that when the Ar is more than about 20” off-axis, the total dipole moment is insensitive to changes of -0.2 A in the separation distance. The computed frequency shifts for HF and DF stretching are given in table 2. The agreement with experimental values is good for Ar-HF and for Kr-HF. For the latter species, the electrical model undershoots, Some part of this is a consequence of
neglecting the rare gas dipole-dipole-quadrupole hyperpolarizability, an unmeasured electrical property which should be expected to be bigger and more noticeable for the heavier rare gas atoms. The computed shifts are naturally sensitive to relative positions of the bonding partners. For instance, with the Ar-HF complex, as the Ar swings away from collinearity with HF, it is polarized less, it back-polarizes less, and the net shift is lessened. However, this is not
Table 2 Intramolecular vibrational frequency shifts due to hydrogen bond formation Complex
R,,
(A)
Red-shift (cm- ’ ) calculated
He-HF Ne-HF Ar-HF ICr-HF Xe-HF He-DF ”
Ne-DF ” Ar-DF’) Kr-DF”
3.424 a’ 3.253 a’ 3.5095 b’ 3.6005 ‘) -
-1.2 -3.7 -9.4 - 12.2
exp.
- 9.654 ” -17.518 ‘) -29.185 =)
-0.9 -2.7 -6.9 -9.0
a) Assumed separation distance. b)Fromref. [ll]. “Fromref. [21]. d’Fromref. [12]. e, For DF complexes, the same R,., as for HF complexes was assumed. 24
Fig. 3. Contours of the total electrical interaction energy (in cm- ’ ) for placement of Ar around HF in Ar-HF. Axes are labelled the same as in fig. 1.
Volume 136, number 1
CHEMICAL PHYSICS LETTERS
a sharp sensitivity since a change of only 1 cm- ’ in the HF stretching frequency results from about a 20” bend at fixed R,,.. Fig. 2 shows contours corresponding to the HF stretching red-shift obtained by our model as a function of the Ar position. For comparison fig. 3 gives contours of the total electrical interaction energy. These contours are similar in shape to thos in fig. 2 demonstrating in this case a simple correspondence between interaction strength and frequency shift. The electrical interaction energy of Ar-HF at the linear structure of R,.,. m 3.5 1 A is 114 cm-‘. It is interesting that this is similar to values inferred from the most recent spectroscopic study of Ar-HF, &=102 cm-’ [21] and 0,=117 cm-’ t221. From these results, it seems clear that intermolecular electrical effects satisfactorily account for orientation, frequency shifts and induced moments in complexes of small molecules and rare gas atoms.
Acknowledgement This work was supported, in part, by the Physical Chemistry Program of the National Science Foundation through a grant to CED (CHE 84-19496).
24 April1987
[21D.E. Bemholdt, S.-Y. Liu and C.E. Dykstra, J. Chem. Phys. 85 (1986) 5120.
[ 31 R.D. Hunt and L. Andrews, submitted for publication. [4] C.M. Lovejoy and D.J. Nesbitt, to be published. [ 5] K.W. Jucks and R. Miller, to be published. [6] C.E. Dykstra, S.-Y. Liu and D.J. Malik, J. Mol. Struct. THEOCHEM 135 (1986) 357. [7] S.-Y. Liu, C.E. Dykstra and D.J. Malik, Chem. Phys. Letters 130 (1986) 403. [ 81 G.D. Mahan, Phys. Rev. A22 (1980) 1780. [9] R.M. Stemheimer, Phys. Rev. 96 (1954) 951. [ lo] I. Cemusak, G.H.F. Diercksen and A.J. Sadlej, Chem. Phys. Letters 128 (1986) 18. [ 111T.A. Dixon, C.H. Joyner, EA. Baiocchi and W. Klemperer, J. Chem. Phys. 74 (1981) 6539. [ 121 L.W. Buxton, E.J. Campbell, M.R. Keenan, T.J. Balle and W.H. Flygare, Chem. Phys. 54 (198 1) 173. [ 131 A.D. Buckingham and P.W. Fowler, Can. J. Chem. 63 (1985) 2018. [ 141 S.-Y. Liuand C.E. Dykstra, Chem. Phys. 107 (1986) 343. [ 151 S.-Y. Liu, D.W. Michael, C.E. Dykstra and J.M. Lisy, J. Chem. Phys. 84 (1986) 5032. [ 161 A.P.L. Rendell, G.B. Bacskay and N.S. Hush, Chem. Phys. Letters 117 (1985) 400. [ 171 P.L. Cummins, A.P.L. Rendell, D.J. Swanton, G.B. Bacskay and N.S. Hush, Intern. Rev. Phys. Chem. 5 (1986) 139. [ 181 A.DIBuckingham, P.W. Fowler and A.J. Stone, Intern. Rev. Phys. Chem. 5 (1986) 107. [ 191 G.J.B. Hurst, P.W. Fowler, A.J. Stone and A.D. Buckingham, Intern. J. Quantum Chem. 29 (1980) 1223. [20] A.C. Legon and D.J. Millen, Proc. Roy. Sot. A404 (1986)
[ 211 b?F.Fraser and A.S. Pine, J. Chem. Phys. 85 (1986) 2502. [ 221 C.M. Lovejoy, M.D. Schuder and D.J. Nesbitt, Chem. Phys.
References
Letters 127 (1986) 374; J. Chem. Phys. 85 (1986) 4890.
[ 1 ] S.-Y. Liu and C.E. Dykstra, J. Phys. Chem. 90 ( 1986) 3097.
25
CHEMICAL PHYSICS LETTERS
24 April 1987
ELECTRICALLY CAUSED VIBRATIONAL FREQUENCY SHIFTS AND DIPOLE MOMENTS IN RARE GAS HYDROGEN BONDED COMPLEXES Shi-yi LIU and Clifford E. DYKSTRA
Received 24 November 1986; in final form 20 February 1987
The Liu-Dykstra theory of electrical influence on vibrational potentials in hydrogen bonded complexes is shown to account very well for vibrational frequency shifts and induced dipoles in a series of rare gas complexes with hydrogen fluoride. The behavior of the electrical interaction energy and dipole moment are shown in detail for Ar-HF.
1. Introduction In a recent paper [ 11, we developed the idea that simple, mutual electrical influence including polarization effects produced the bulk of the changes upon hydrogen bond formation in intramolecular stretching potentials and so led to the vibrational frequency shifts that are characteristic of these complexes. In a subsequent study of the Hz-HF complex ]2], we predicted a small red-shift of 19 cm-’ for the HF stretch. Hunt and Andrews have measured this shift in a neon matrix and found it to be 15 cm-’ [ 31. Lovejoy and Nesbitt [ 41 have assigned the gas phase spectrum and obtained a frequency shift of almost 12 cm- ‘, and a like value has been measured by Jucks and Miller f4]. Since our theory implies that primary electronic structure changes upon hydrogen bond formation are charge polarization, it follows that electrical properties of complexes should be reasonably accounted for in the same way. We have demonstrated this in the case of (HF) z where even something as exotic as the axial dipole hyperpolarizability can be explained from mutual polarization of the monomers [ 61. Another result that follows is that the electrical influence identifies enhancement in vibrational transition moments [7] that usually accompanies complexation. In our picture of weakly bonded complexes, the vibrational potential of a constituent monomer is perturbed by the interaction between its permanent
22
and induced electrical moments with those of its bonding partner. Knowledge of the uncomplexed monomer’s vibrational potential and its electrical properties as a function of the vibrational coordinates make it possible to construct the monomer’s vibrational potential as experienced when embedded in the complex. From that, vibrational frequencies and so forth may be calculated, a process which may often be done with low-order pe~urbation theory ill* Complexes containing rare gas atoms may seem to be outside electrical pictures of interaction since dispersion effects are potentially important. For instance, applying the classical electrical analysis to the interaction of two neon atoms trivially give a flat, zero potential. Quantum effects such as dispersion are unavoi~bly impo~ant there. In this paper we show that electrical ideas can be satisfactorily used certain features of rarein understanding gas-molecule complexes. The physical basis for this success is that a monomer such as HF seems to induce sizeable moments in an attached rare gas atom and that plus back-perturbation becomes a significant effect. Quantum effects between the rare gas and HF do not seem to have as sizable a role in the vibrational frequency shifts. 2. Calculations The vibrational
potential
and anharmonicity
0 009-26 14/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume136,number1
24 April1981
CHEMICALPHYSICSLETTERS
parameters of HF and the electrical properties of HF were the same as those used in our first study of HF-base complexes [ 11. The electrical properties of the rare gas atoms, He, Ne, Ar and Kr, are those of Mahan [ 81 which were obtained from a modified Stemheimer analysis [ 91. For Ar, these properties are in line with the recent extensive calculations of Cemusak et al. [ lo]. Only the dipole and quadrupole polarizabilities, designated (Ydand or, for atoms, were available for the entire series of rare gas atoms. Relative to the molecules, this meant the dipoledipole-quadrupole hyperpolarizability was left out for the rare gases. Test calculations using a limited basis ab initio value for this hyperpolarizability for Ne yielded little difference. However, the size of this property should increase with atomic number in the rare gas series, and so beyond Ne it may have a slightly more noticeable effect. In the electrical evaluations, center of mass properties were used for HF. In the initial electrical interaction calculations, the distances between the rare gas atoms and the HF were fixed at their vibrationally center of mass, R,,., averaged separations for Ar-HF [ 111 and Kr-HF [ 121 as obtained from rotational spectra. The same parameter was estimated for the He-HF and Ne-HF complexes based on the separations in the other systems and their van der Waals radii. For the evaluation of the total dipole moments of the various complexes, equilibrium molecular electrical properties were used. Dipole moments were calculated for both equilibrium structures and vibrationally averaged structures, as known.
3. Results and discussion
At fixed separation distances, the electrical interaction energy was followed as a function of 0, the angle of the rare gas to molecule center of mass measured relative to the molecule’s axis. For HeHF, NeHF, ArHF, and KrHF, small changes in 8 away from a completely linear complex were found to be destabilizing in the electrical interaction analysis. This means that electrical effects predict a linear equilibrium or at least a local minimum at linear structures, and that appears consistent with analysis of rotational spectroscopic data which are available for a few of these systems [ 11,121. That electrical effects account for the orientational features of weak complexes has already been established by a number of different groups [ 13-20 ] employing slightly different schemes for evaluating electrical interaction. Table 1 lists the dipole moments of the complexes computed at equilibrium. There is a sharply increasing induced moment with increasing complexity of the rare gas atom. This follows because the bigger rare gas atoms are naturally more polarizable. Comparison with experiment is not direct because dipoles are computed for static structures with no accounting for vibrational averaging. One rough way of incorporating the vibrational averaging effects is to evaluate moments at the operational, on-average orientational angles. Doing this for Ar-HF gives an a-inertial axis dipole moment that differs from the experimental value by only 0.07 D. A representative dipole moment surface is depicted with contours for the Ar-HF complex in fig. 1. This can suggest how vibrational motion enters into the rotational spec-
Table1 Dipolemomentsa)of rare-gas-HFcomplexes Complex
Electrically obtained values at equilibrium (e=oO) P
He-HF Ne-HF Ar-HF Kr-HF
lndund
0.036 0.077 0.241 0.329
‘) Dipole values are in D.
P
tota,
1.851 1.892 2.056 2.144
Operational zero-point bending angle, 0’ (deg)
Measured u-inertial dipole component &I
41.27 b, 39.22 =’
1.3353
Electrically obtained values at angles 0’ total
PL,
P
1.404 1.478
1.875 1.920
‘) From ref. [ 111. ‘) From ref. [ 121.
23
CHEMICAL PHYSICS LETTERS
Volume 136, number 1
24 April 1987
7-r /
!
I
!
I ] I ;
I / I
I I i
/
i /
! i I i i j / I
I / i i I /
/
!
i
I j j / i Ii
J
6G.0 Fig. 1. Contours showing the total dipole moment (in D) of Ar-HF for placement of Ar around HF. The horizontal axis labels the Ar to HF cm. angles relative to the HF axis. The vertical axis is the Ar to HF c.m. distance.
Fig. 2. Contours showing the sensitivity of the HF red-shift (in cm - ’ ) computed with the Liu-Dykstra model [ 1] to placement of Ar around HF in Ar-HF. Axes are labelled the same as in fig. 1.
troscopy determination of the dipole. Notice that when the Ar is more than about 20” off-axis, the total dipole moment is insensitive to changes of -0.2 A in the separation distance. The computed frequency shifts for HF and DF stretching are given in table 2. The agreement with experimental values is good for Ar-HF and for Kr-HF. For the latter species, the electrical model undershoots, Some part of this is a consequence of
neglecting the rare gas dipole-dipole-quadrupole hyperpolarizability, an unmeasured electrical property which should be expected to be bigger and more noticeable for the heavier rare gas atoms. The computed shifts are naturally sensitive to relative positions of the bonding partners. For instance, with the Ar-HF complex, as the Ar swings away from collinearity with HF, it is polarized less, it back-polarizes less, and the net shift is lessened. However, this is not
Table 2 Intramolecular vibrational frequency shifts due to hydrogen bond formation Complex
R,,
(A)
Red-shift (cm- ’ ) calculated
He-HF Ne-HF Ar-HF ICr-HF Xe-HF He-DF ”
Ne-DF ” Ar-DF’) Kr-DF”
3.424 a’ 3.253 a’ 3.5095 b’ 3.6005 ‘) -
-1.2 -3.7 -9.4 - 12.2
exp.
- 9.654 ” -17.518 ‘) -29.185 =)
-0.9 -2.7 -6.9 -9.0
a) Assumed separation distance. b)Fromref. [ll]. “Fromref. [21]. d’Fromref. [12]. e, For DF complexes, the same R,., as for HF complexes was assumed. 24
Fig. 3. Contours of the total electrical interaction energy (in cm- ’ ) for placement of Ar around HF in Ar-HF. Axes are labelled the same as in fig. 1.
Volume 136, number 1
CHEMICAL PHYSICS LETTERS
a sharp sensitivity since a change of only 1 cm- ’ in the HF stretching frequency results from about a 20” bend at fixed R,,.. Fig. 2 shows contours corresponding to the HF stretching red-shift obtained by our model as a function of the Ar position. For comparison fig. 3 gives contours of the total electrical interaction energy. These contours are similar in shape to thos in fig. 2 demonstrating in this case a simple correspondence between interaction strength and frequency shift. The electrical interaction energy of Ar-HF at the linear structure of R,.,. m 3.5 1 A is 114 cm-‘. It is interesting that this is similar to values inferred from the most recent spectroscopic study of Ar-HF, &=102 cm-’ [21] and 0,=117 cm-’ t221. From these results, it seems clear that intermolecular electrical effects satisfactorily account for orientation, frequency shifts and induced moments in complexes of small molecules and rare gas atoms.
Acknowledgement This work was supported, in part, by the Physical Chemistry Program of the National Science Foundation through a grant to CED (CHE 84-19496).
24 April1987
[21D.E. Bemholdt, S.-Y. Liu and C.E. Dykstra, J. Chem. Phys. 85 (1986) 5120.
[ 31 R.D. Hunt and L. Andrews, submitted for publication. [4] C.M. Lovejoy and D.J. Nesbitt, to be published. [ 5] K.W. Jucks and R. Miller, to be published. [6] C.E. Dykstra, S.-Y. Liu and D.J. Malik, J. Mol. Struct. THEOCHEM 135 (1986) 357. [7] S.-Y. Liu, C.E. Dykstra and D.J. Malik, Chem. Phys. Letters 130 (1986) 403. [ 81 G.D. Mahan, Phys. Rev. A22 (1980) 1780. [9] R.M. Stemheimer, Phys. Rev. 96 (1954) 951. [ lo] I. Cemusak, G.H.F. Diercksen and A.J. Sadlej, Chem. Phys. Letters 128 (1986) 18. [ 111T.A. Dixon, C.H. Joyner, EA. Baiocchi and W. Klemperer, J. Chem. Phys. 74 (1981) 6539. [ 121 L.W. Buxton, E.J. Campbell, M.R. Keenan, T.J. Balle and W.H. Flygare, Chem. Phys. 54 (198 1) 173. [ 131 A.D. Buckingham and P.W. Fowler, Can. J. Chem. 63 (1985) 2018. [ 141 S.-Y. Liuand C.E. Dykstra, Chem. Phys. 107 (1986) 343. [ 151 S.-Y. Liu, D.W. Michael, C.E. Dykstra and J.M. Lisy, J. Chem. Phys. 84 (1986) 5032. [ 161 A.P.L. Rendell, G.B. Bacskay and N.S. Hush, Chem. Phys. Letters 117 (1985) 400. [ 171 P.L. Cummins, A.P.L. Rendell, D.J. Swanton, G.B. Bacskay and N.S. Hush, Intern. Rev. Phys. Chem. 5 (1986) 139. [ 181 A.DIBuckingham, P.W. Fowler and A.J. Stone, Intern. Rev. Phys. Chem. 5 (1986) 107. [ 191 G.J.B. Hurst, P.W. Fowler, A.J. Stone and A.D. Buckingham, Intern. J. Quantum Chem. 29 (1980) 1223. [20] A.C. Legon and D.J. Millen, Proc. Roy. Sot. A404 (1986)
[ 211 b?F.Fraser and A.S. Pine, J. Chem. Phys. 85 (1986) 2502. [ 221 C.M. Lovejoy, M.D. Schuder and D.J. Nesbitt, Chem. Phys.
References
Letters 127 (1986) 374; J. Chem. Phys. 85 (1986) 4890.
[ 1 ] S.-Y. Liu and C.E. Dykstra, J. Phys. Chem. 90 ( 1986) 3097.
25