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Theoretical studies of potential gas-phase charge-transfer complexes: NH3 + HX (X = Cl, Br, I)
Volume 130, number 1,2
THEORETICAL STUDIES NH3 + HX (X=Cl, Br, I)
CHEMICAL PHYSICS LETTERS
OF POTENTIAL
GAS-PHASE
26 September 1986
CHARGE-TRANSFER
COMPLEXES:
Paul G. JASIEN ’ and Walter J. STEVENS Molecular Spectroscopy Divwon, National Bureau of Standards, Galthersburg. MD 20899, USA
Received 14 May 1986; in final form 10 July 1986
Theoretical calculations of the potential curves for the NH2+ HX systems (X=CI, Br, 1) predict only a single minimum for the HCI and HBr complexes, corresponding to the hydrogen-bonded structure. In the case of the HI complex, a double-well protontransfer potential curve with a small barrier is found. The presence of this second minimum corresponding to the NHf I - structure may result in an anomalous intensity and transition energy for excitation of the HI stretch in the NHj-HI complex.
1. Introduction Hydrogen bonding in the vapor phase is an area of immense interest in the chemical community. Many theoretical and experimental studies of hydrogenbound complexes are described in the literature. In most cases, the experimental data on hydrogenbonded systems have exceeded that from theoretical studies, due to the difficulties in obtaining accurate wavefunctions for systems with large numbers of electrons. In the case of hydrogen-bonded complexes between NH3 and the hydrogen halides there seems to be a lack of experimental gas-phase data, although some information is available from matrix isolation work [ l-41. On the other hand, these systems have yielded a fairly rich literature based upon theoretical study. Complexes of NH3 with HF, HCl, HBr, and HI have all been the subject of such studies [ 5-101. One of the reasons for the interest in complexes of this sort is the possibility for the formation of an ionic proton-transfer complex in addition to the neutral hydrogen-bonded structure. Such a possibility brings up the question as to whether these complexes exhibit a single-well potential, corresponding to either the neutral or ionic structures, or a double-well potential with a barrier to interconversion of the two forms. A number of factors influence the final character’ NRC-NBS Postdoctoral Fellow. 0 009-2614/86/$03.50 OElsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
istics of the potential energy surface, three of the more important are: (1) the relative proton affinity of the NH3 versus X-, (2) the electrostatic interaction of the NH3 and the HX, and (3) the polarization relaxation of the X- in the presence of an ion such as NH,+. All three of these factors become more favorable for the formation of an ionic complex in the heavier hydrogen halides. The halide anions show a decrease in proton affinity on going from F- to I(see table 1) as well as an increase in polarizability, which both favor an ionic complex. In addition, the heavier hydrogen halides have slightly reduced dipole moments, which provides a slightly less favorable dipole-dipole interaction. From table 1, it is clear that the proton affinities
Table 1 Proton affinities (kcal/mol) ”
CIBrINH,
SCF
ACCD
Experiment
331.8 321.3 309.6 217.0
336.0 327.2 316.2 215.6
336.6 b’ 326.4 b’ 316.6 b’ 213( f3) ”
a) I kcal/mol = 4. I84 kJ/mol. b, Data obtained via thermodynamic cycle utilizing dissociation energies and vibrational frequencies from ref. [ I I ] and electron af?inities and ionization potentials from refs. [ 12,131. a Ref. [ 141.
127
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PHYSICS
of X- are still more than 100 kcal/mol # greater than that of NHJ. Despite this large energy difference, the ionic structure has a comparable energy to the neutral, indicating that large Coulombic and polarization effects are present in these systems. It is also true that these forces are so well balanced that fairly small changes on going from Cl to I may totally change the character of the potential-energy surface. In this work we report theoretical calculations for NH3 complexes with HCI, HBr, and HI to determine the nature of the hydrogen-bonded complexes. In the cases of the HCI and HBr complexes, only a single minimum is found, which is in agreement with previous results [ 561. In the case of the HI complex, the potential surface is determined to have a rather intriguing double-well shape which may lead to interesting spectroscopic properties. This result is in disagreement with previous work on NH, + HI which indicated that only a single-proton transfer minimum exists [ IO].
2. Calculations
All calculations done at the SCF level were performed with the HONDO series of programs [ 151. Full gradient-optimized structures were obtained at the SCF level subject to a Csv symmetry constraint. Various tests probing the bent C, symmetry structures indicated that the complexes do indeed have Cav symmetry with a very low bending potential. Harmonic vibrational frequencies were obtained via finite differencing of the analytic first derivatives. Calculations which included electron correlation were performed with the approximate coupled cluster doubles ( ACCD) technique of Bachrach et al. [ 161. The ACCD wavefunction includes in addition to single and double excitations, all even-order higher excitations and has the important property of size consistency. In all calculations, the inner core electrons were replaced by compact effective potentials ##, which li 1kcal/mol=4.184 kJ/mol. R1lThe compact effective potentials for Br and I were obtained similarly to those in ref. [ 171, but were based uponj-averaged relativistic atomic potentials. The basis sets for these atoms were also generated as in ref. [ 171. 128
26 September
LETTERS
1986
reduced the treatment of the halogens and nitrogen to seven- and five-electron systems, respectively. The H basis set was the scaled Dunning [ 181 double-zeta (DZ) set with a p polarization function of exponent 1.OO.The N basis was the valence DZ set of Stevens et al. [ 171 augmented with two d functions with exponents 0.9 and 0.15. Halogen basis sets were va lence DZ sets [ 171, which were augmented with a set of shared exponent diffuse sp functions (a = 0.04, 0.043,0.02 for Cl, Br, I) and two sets of d polarization functions. The exponents of these functions are as follows: a,(Cl) =0.60, 0.09; (Yd(Br)=0.45, 0.058; and ad(I) =0.30,0.055. The diffuse d functions were chosen to optimize the polarizability of X-. These basis sets provide adequate flexibility in describing the basic electronic structures of both the protonated and deprotonated species as well as the permanent and induced electric moments. The accuracy of the calculations in terms of the relative proton affinities of NH3 and X- and the dipole moments of NH3 and HX, may be seen in tables 1 and 2. At the SCF level, the X- proton affinities are too low by 4-7 kcal/mol, while that of NH3 is slightly too high. Such an effect will bias the SCF potential surface slightly toward the ionic species. Correlation effects bring these quantities into excellent agreement with the experimental values for the halide anions. In the case of NH3, the agreement is slightly worse, but this small deviation from experiment should not lead to an appreciable error, since the induced electronic effects which are described well, also play a significant role in the determination of the potential energy.surface. In the case of the dipole moments, extremely good agreement between the calculated and experimental results is found. The position of transition states was determined at the SCF level assuming a one-dimensional reaction Table 2 Monomer
dipole moments
HCI HBr HI NH3
(D)
Theory a)
Experiment
1.16 0.89 0.59 1.50
1.11 0.83 0.45 1.47
a) ACCD calculations at SCF optimized “Ref. [II]. ” Ref. [ 191.
b’ b’ b’ c’
geometries.
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PHYSICS
in which the N-H(X) distance is the reaction coordinate. For various values of R(N-H), the remaining degrees of freedom were fully optimized and the position of the trangition state for the proton transfer was taken as the highest energy point. The influence of correlation on the transition state was studied via a single-point calculation done at the SCF determined geometry; under the assumption that the correlation energy is only weakly dependent on small changes in geometry. path
3. Results and discussion 3.1. Energetics 3. I. 1. NH,-HCl and NH,-HBr In agreement with the results of others [ 561, we conclude from our most accurate calculations that there is only a single minimum in the potential surface for NH3 bound to HCl or HBr. At the SCF level, however, energetics from fully optimized calculations do indicate the presence of a secondary minimum, corresponding to an ionic structure, and an extremely small barrier. With the addition of correlation however, the ionic minimum disappears and only a single-minimum potential is obtained. The calculated binding energies for the NHJ-HCl and NH3-HBr hydrogen-bonded systems are given in table 3. The effect of correlation is to increase the stability by 2.0 and 1.7 kcal/mol, respectively for the HCl and HBr complexes. Our calculated result of 9.2 kcal/mol for the stability of the HCl complex is in fair agreement with the correlated results of Brciz et al. [ 6 ] (8.6 kcaYmo1) and Raffenetti and Phillips [ 5 ] (9.0 kcal/mol). In the case of the HBr complex, the calculated stability of 7.5 kcal/mol is also in reasonTable 3 Calculated
H,N-HCI HIN-HBr H,N-HI H,NH+I[ H,N-H-I
stabilities
1’
of NH, + HX extrema
(kcal/mol)
a)
ESCF
E ACCD
EACCD+ZPE
1.2 5.8 4.0 8.8 I.2
9.2 7.5 5.1 6.6 4.3
4.1 I.0 2.9
a ’ I kcal/moI = 4.184 kJ/mol.
LETTERS
26 September
1986
able agreement with the value of 8.1 kcal/mol found by Brciz et al. from their correlated calculations. As in that work, we also find a distortion in the potential surface in the vicinity of what would be the ionic minimum, but as stated earlier, no minimum does exist. 3.1.2. NH,-HI As was discussed in section 1, the existence of a secondary ionic minimum is more favored for the heavier halides, and indeed in the case of the complex with HI a double minimum potential is found. From table 3, we see that at the SCF level, the stability of the ionic structure is 8.8 kcal/mol while that of the neutral is only 4.0 kcal/mol. On the addition of correlation there is a large change in the relative stability, bringing the neutral complex to within 1 kcal/mol of the ionic structure. Such a large differential correlation effect is consistent with the abovementioned results of the disappearance of the ionic minima for the correlated calculations on the Cl and Br complexes. The energy of the transition state for proton transfer is found to lie below the dissociation asymptote for NH3 + HI with a barrier height 1.4 kcaYmo1 above the minimum energy of the neutral complex. Although the position of the transition state was determined at the SCF level and the absolute position may differ somewhat for the case of the correlated surface, we feel that the value of 1.4 kcal/mol is a fairly good representation of the barrier height on the latter surface due to its flatness. It is worth mentioning that the magnitude of the barrier in the present work is similar to the 1.2 kcal/mol barrier found in ref. [ 61 for the H&NH* + HBr surface. Having determined the existence of the ionic minimum in the proton-transfer energy curve, harmonic force constant calculations were performed for the three extrema to estimate the effect of zero-point vibration on the relative energies. Such an analysis shows a dramatic effect. Comparing the zero-point energy (ZPE) sums for the two minima as well as the NH3 + HI asymptote reveals a large differential ZPE correction as is shown in table 3. This harmonic ZPE correction appears to make the ionic minimum almost disappear. Thus it appears unlikely that this complex exhibits proton transfer in the gas phase. Such a conclusion differs from that of Kollman et al. 129
Volume 130, number 1,2
CHEMICAL PHYSICS LETTERS
[ lo]. However, their work was performed with a smaller basis set and also did not include the effects of electron correlation or ZPE. Closer examination of the vibrational frequencies reveals that this difference of 4 kcal/mol in the ZPE is almost entirely due to only one vibrational mode. In the case of the neutral hydrogen-bonded structure, the hindered rotational motion of the HI molecule leads to a degenerate bending mode at approximately 400 cm- ‘. Upon transfer of the proton to form NH$I-, this previously low energy mode correlates with a doubly degenerate mode which is essentially an HNH bending motion in the NHf . The energy of this mode is on the order of 1640 cm- ‘, which leads to the large difference in zero-point corrections for the two complexes. The large difference in the energy of this mode on going from the neutral to the ionic form, raises some question concerning a simple one-dimensional treatment of the proton transfer process. In fact, a more appropriate treatment would require at least two dimensions: one along the direction of proton transfer and a perpendicular coordinate representing the N-H-I bending motion. Nevertheless, the simple treatment does lead to some interesting possibilities concerning the spectroscopic character of the H-I stretching mode in this complex. It seems unlikely that either minimum is capable of supporting an excited vibrational level for the H-I stretch. However, as in the case of other hydrogen-bonded complexes, the coupling of the H-I stretch to the dissociative stretching mode may be weak enough to lead to an observable transition. If indeed this is the case, then the presence of the ionic minima may alter dramatically the position and intensity of the H-I stretching fundamental. Since the V= 1 level of the H-I stretch in the neutral complex will lie above the small barrier to proton transfer, excitation of this mode will terminate in a vibrational state which encompasses a very wide potential region, yielding a large amplitude motion. Due to the charge transfer nature of this vibration, such a mode would possess an enhanced intensity due to the large dipole moment change. 3.2. Structures The calculated structural parameters and dipole moments for the NHJ-HX systems are reported in 130
26 September 1986
Table 4 Structural parameters and dipole moments R(H-X) H,N-HCl H,N-HBr H,N-HI H,N+II [ H,N-H-I 1’
1.297 a’ 1.426 a’ 1.614 a’ 2.221 1.769
(A)
WN-X)
(A)
3.263( 3.225) 3.468( 3.406) 3.822( 3.698) 3.294 3.268
p(D) 4.02 3.90 3.61 11.26
a’ Changes from the calculated monomer bond lengths are 0.027, 0.023 and 0.016 A for HCI, HBr and HI.
table 4. For some of these systems in addition to a full optimization at the SCF level, a second determination of the N-X distance at the correlated level, utilizing monomers frozen at the experimental geometries was made. These results are given in parentheses in table 4. The correlated results for the structures of the Cl and Br complexes are in fair agreement with the results of Brciz et al. who determined N-X distances of 3.270 and 3.380 8, compared to our values of 3.225 and 3.406 A. In the case of the calculated dipole moments our values are 0.4 and 0.7 D smaller than those from ref. [ 61. In the case of the HI complex, comparisons can be made between the ionic and neutral structural parameters. The ionic minimum possesses a significantly shorter (0.5 A) N-X distance than the neutral species and as would be expected a much larger dipole moment. The transition state structure has the curious characteristic that although it occurs very early in the proton transfer, corresponding to a relatively small displacement of the H-I bond distance, the N-X distance is already shorter than that found in the ionic minimum. Upon complete transfer of the proton, the N-X length relaxes somewhat, becoming slightly longer at equilibrium. As is the case with most hydrogen bonded complexes, the potential surface for the NHJ-HX complexes is extremely flat in certain regions. In particular, a very flat potential for the displacement of the two monomers is found. Therefore, the N-X R, distances reported here may differ substantially from the R.distances which would be observed from experiment.
Volume
130, number
1,2
CHEMICAL
PHYSICS
LETTERS
26 September
1986
3.3. Vibrational shifts
Acknowledgement
an accurate prediction of the H-I stretching frequency may require a more sophisticated treatment of the H motion, the shifts of the N-H frequencies of the ammonia-upon-hydrogen bond formation may still be qualitatively described by a harmonic force field analysis. We find extremely small shifts in the NH3 modes upon complexation. These shifts are less than 5 cm-’ in the case of the asymmetric and symmetric stretch as well as the asymmetric bending motion. Only for the symmetric bend is there an appreciable shift of approximately 30 cm-’ to higher energy upon complexation. Calculation of any other vibrational frequencies via a harmonic analysis is not justifiable.
We would like to thank Drs. J. Hougen and P. Julienne for helpful discussions and Dr. M. Krauss for suggesting the proton transfer problem.
Although
4. Conclusion Theoretical calculations on the NH,-HX systems (X = Cl, Br, I) show only a single minimum in the cases of Cl and Br. In the case of the I complex, a double-well proton-transfer potential curve with a small barrier is found. Large differential ZPE corrections favoring the neutral complex reverse the order of stability of the ionic and neutral systems. The presence of the ionic minimum may result in large amplitude hydrogen motion in the H-I V= 1 state, giving rise to an anomalous intensity and transition energy for this mode. Large coupling of the N-H-I bending to the proton transfer motion may necessitate a two-dimensional treatment of the potential surface in order to predict an accurate excitation energy for the H-I stretch.
References [ I] B.S. Ault and G.C. Pimentel, J. Phys. Chem. 77 (1973) 1649. [2] B.S. Ault, E. Steinback and G.C. Pimentel, J. Phys. Chem. 79 (1975) 615. [3] G.L. Johnson and L. Andrews, J. Am. Chem. Sot. 104 (1982) 3043. [4] A.J. Barnes, T.R. Beech and Z. Mielke, J. Chem. Sot. Faraday Trans. II 80 (1984) 455. [ 51 R.C. Raffenetti and D.H. Phillips, J. Chem. Phys. 71 (1979) 4534. [6] A. Brciz, A. Karpfen, H. Lischka and P. Schuster, Chem. Phys. 89 (1984) 337. [ 71 A. Hinchliffe, J. Mol. Struct. THEOCHEM 105 (1983) 335. [8] A. Hinchliffe, J. Mol. Struct. THEOCHEM 121 (1985) 201. [ 91 Z. Latajka and S. Scheiner, J. Chem. Phys. 8 1 (1984)4014. [ IO] P. Kollman, A. Dearing and E. Kochanski, J. Phys. Chem. 86 (1982) 1607. [ 111K.P. Huber and G. Herzberg, Molecular spectra and molecular structure, Vol. 4. Constants of diatomic molecules (Van Nostrand Reinhold, New York. 1979). [ 121 H. Hotop and W.C. Lineberger, J. Phys. Chem. Ref. Data 4 (1975) 539. [ 131 C.E. Moore, Atomic energy levels, NSRDS-NBS 35 (197I ). [ 141 S.G. Lias, J.F. Liebman and R.D. Levine, J. Phys. Chem. Ref. Data 13 (1984) 695. [ 151 M. Dupuis and H.F. King, Intern. J. Quantum Chem. 11 (1977) 613; J. Chem. Phys. 68 (1978) 3998. [ 161 S.M. Bachrach, R.A. Chiles and C.E. Dykstra, J. Chem. Phys. 75 (1981) 2270. [ 171 W.J. Stevens, H. Basch and M. Krauss, J. Chem. Phys. 81 (1984) 6026. [ 181 T.H. Dunning, J. Chem. Phys. 53 (1970) 2823. [ 191 W.H. Weber, J. Mol. Spectry. 105 (1984) 405.
131
THEORETICAL STUDIES NH3 + HX (X=Cl, Br, I)
CHEMICAL PHYSICS LETTERS
OF POTENTIAL
GAS-PHASE
26 September 1986
CHARGE-TRANSFER
COMPLEXES:
Paul G. JASIEN ’ and Walter J. STEVENS Molecular Spectroscopy Divwon, National Bureau of Standards, Galthersburg. MD 20899, USA
Received 14 May 1986; in final form 10 July 1986
Theoretical calculations of the potential curves for the NH2+ HX systems (X=CI, Br, 1) predict only a single minimum for the HCI and HBr complexes, corresponding to the hydrogen-bonded structure. In the case of the HI complex, a double-well protontransfer potential curve with a small barrier is found. The presence of this second minimum corresponding to the NHf I - structure may result in an anomalous intensity and transition energy for excitation of the HI stretch in the NHj-HI complex.
1. Introduction Hydrogen bonding in the vapor phase is an area of immense interest in the chemical community. Many theoretical and experimental studies of hydrogenbound complexes are described in the literature. In most cases, the experimental data on hydrogenbonded systems have exceeded that from theoretical studies, due to the difficulties in obtaining accurate wavefunctions for systems with large numbers of electrons. In the case of hydrogen-bonded complexes between NH3 and the hydrogen halides there seems to be a lack of experimental gas-phase data, although some information is available from matrix isolation work [ l-41. On the other hand, these systems have yielded a fairly rich literature based upon theoretical study. Complexes of NH3 with HF, HCl, HBr, and HI have all been the subject of such studies [ 5-101. One of the reasons for the interest in complexes of this sort is the possibility for the formation of an ionic proton-transfer complex in addition to the neutral hydrogen-bonded structure. Such a possibility brings up the question as to whether these complexes exhibit a single-well potential, corresponding to either the neutral or ionic structures, or a double-well potential with a barrier to interconversion of the two forms. A number of factors influence the final character’ NRC-NBS Postdoctoral Fellow. 0 009-2614/86/$03.50 OElsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
istics of the potential energy surface, three of the more important are: (1) the relative proton affinity of the NH3 versus X-, (2) the electrostatic interaction of the NH3 and the HX, and (3) the polarization relaxation of the X- in the presence of an ion such as NH,+. All three of these factors become more favorable for the formation of an ionic complex in the heavier hydrogen halides. The halide anions show a decrease in proton affinity on going from F- to I(see table 1) as well as an increase in polarizability, which both favor an ionic complex. In addition, the heavier hydrogen halides have slightly reduced dipole moments, which provides a slightly less favorable dipole-dipole interaction. From table 1, it is clear that the proton affinities
Table 1 Proton affinities (kcal/mol) ”
CIBrINH,
SCF
ACCD
Experiment
331.8 321.3 309.6 217.0
336.0 327.2 316.2 215.6
336.6 b’ 326.4 b’ 316.6 b’ 213( f3) ”
a) I kcal/mol = 4. I84 kJ/mol. b, Data obtained via thermodynamic cycle utilizing dissociation energies and vibrational frequencies from ref. [ I I ] and electron af?inities and ionization potentials from refs. [ 12,131. a Ref. [ 141.
127
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CHEMICAL
PHYSICS
of X- are still more than 100 kcal/mol # greater than that of NHJ. Despite this large energy difference, the ionic structure has a comparable energy to the neutral, indicating that large Coulombic and polarization effects are present in these systems. It is also true that these forces are so well balanced that fairly small changes on going from Cl to I may totally change the character of the potential-energy surface. In this work we report theoretical calculations for NH3 complexes with HCI, HBr, and HI to determine the nature of the hydrogen-bonded complexes. In the cases of the HCI and HBr complexes, only a single minimum is found, which is in agreement with previous results [ 561. In the case of the HI complex, the potential surface is determined to have a rather intriguing double-well shape which may lead to interesting spectroscopic properties. This result is in disagreement with previous work on NH, + HI which indicated that only a single-proton transfer minimum exists [ IO].
2. Calculations
All calculations done at the SCF level were performed with the HONDO series of programs [ 151. Full gradient-optimized structures were obtained at the SCF level subject to a Csv symmetry constraint. Various tests probing the bent C, symmetry structures indicated that the complexes do indeed have Cav symmetry with a very low bending potential. Harmonic vibrational frequencies were obtained via finite differencing of the analytic first derivatives. Calculations which included electron correlation were performed with the approximate coupled cluster doubles ( ACCD) technique of Bachrach et al. [ 161. The ACCD wavefunction includes in addition to single and double excitations, all even-order higher excitations and has the important property of size consistency. In all calculations, the inner core electrons were replaced by compact effective potentials ##, which li 1kcal/mol=4.184 kJ/mol. R1lThe compact effective potentials for Br and I were obtained similarly to those in ref. [ 171, but were based uponj-averaged relativistic atomic potentials. The basis sets for these atoms were also generated as in ref. [ 171. 128
26 September
LETTERS
1986
reduced the treatment of the halogens and nitrogen to seven- and five-electron systems, respectively. The H basis set was the scaled Dunning [ 181 double-zeta (DZ) set with a p polarization function of exponent 1.OO.The N basis was the valence DZ set of Stevens et al. [ 171 augmented with two d functions with exponents 0.9 and 0.15. Halogen basis sets were va lence DZ sets [ 171, which were augmented with a set of shared exponent diffuse sp functions (a = 0.04, 0.043,0.02 for Cl, Br, I) and two sets of d polarization functions. The exponents of these functions are as follows: a,(Cl) =0.60, 0.09; (Yd(Br)=0.45, 0.058; and ad(I) =0.30,0.055. The diffuse d functions were chosen to optimize the polarizability of X-. These basis sets provide adequate flexibility in describing the basic electronic structures of both the protonated and deprotonated species as well as the permanent and induced electric moments. The accuracy of the calculations in terms of the relative proton affinities of NH3 and X- and the dipole moments of NH3 and HX, may be seen in tables 1 and 2. At the SCF level, the X- proton affinities are too low by 4-7 kcal/mol, while that of NH3 is slightly too high. Such an effect will bias the SCF potential surface slightly toward the ionic species. Correlation effects bring these quantities into excellent agreement with the experimental values for the halide anions. In the case of NH3, the agreement is slightly worse, but this small deviation from experiment should not lead to an appreciable error, since the induced electronic effects which are described well, also play a significant role in the determination of the potential energy.surface. In the case of the dipole moments, extremely good agreement between the calculated and experimental results is found. The position of transition states was determined at the SCF level assuming a one-dimensional reaction Table 2 Monomer
dipole moments
HCI HBr HI NH3
(D)
Theory a)
Experiment
1.16 0.89 0.59 1.50
1.11 0.83 0.45 1.47
a) ACCD calculations at SCF optimized “Ref. [II]. ” Ref. [ 191.
b’ b’ b’ c’
geometries.
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130, number
CHEMICAL
1,2
PHYSICS
in which the N-H(X) distance is the reaction coordinate. For various values of R(N-H), the remaining degrees of freedom were fully optimized and the position of the trangition state for the proton transfer was taken as the highest energy point. The influence of correlation on the transition state was studied via a single-point calculation done at the SCF determined geometry; under the assumption that the correlation energy is only weakly dependent on small changes in geometry. path
3. Results and discussion 3.1. Energetics 3. I. 1. NH,-HCl and NH,-HBr In agreement with the results of others [ 561, we conclude from our most accurate calculations that there is only a single minimum in the potential surface for NH3 bound to HCl or HBr. At the SCF level, however, energetics from fully optimized calculations do indicate the presence of a secondary minimum, corresponding to an ionic structure, and an extremely small barrier. With the addition of correlation however, the ionic minimum disappears and only a single-minimum potential is obtained. The calculated binding energies for the NHJ-HCl and NH3-HBr hydrogen-bonded systems are given in table 3. The effect of correlation is to increase the stability by 2.0 and 1.7 kcal/mol, respectively for the HCl and HBr complexes. Our calculated result of 9.2 kcal/mol for the stability of the HCl complex is in fair agreement with the correlated results of Brciz et al. [ 6 ] (8.6 kcaYmo1) and Raffenetti and Phillips [ 5 ] (9.0 kcal/mol). In the case of the HBr complex, the calculated stability of 7.5 kcal/mol is also in reasonTable 3 Calculated
H,N-HCI HIN-HBr H,N-HI H,NH+I[ H,N-H-I
stabilities
1’
of NH, + HX extrema
(kcal/mol)
a)
ESCF
E ACCD
EACCD+ZPE
1.2 5.8 4.0 8.8 I.2
9.2 7.5 5.1 6.6 4.3
4.1 I.0 2.9
a ’ I kcal/moI = 4.184 kJ/mol.
LETTERS
26 September
1986
able agreement with the value of 8.1 kcal/mol found by Brciz et al. from their correlated calculations. As in that work, we also find a distortion in the potential surface in the vicinity of what would be the ionic minimum, but as stated earlier, no minimum does exist. 3.1.2. NH,-HI As was discussed in section 1, the existence of a secondary ionic minimum is more favored for the heavier halides, and indeed in the case of the complex with HI a double minimum potential is found. From table 3, we see that at the SCF level, the stability of the ionic structure is 8.8 kcal/mol while that of the neutral is only 4.0 kcal/mol. On the addition of correlation there is a large change in the relative stability, bringing the neutral complex to within 1 kcal/mol of the ionic structure. Such a large differential correlation effect is consistent with the abovementioned results of the disappearance of the ionic minima for the correlated calculations on the Cl and Br complexes. The energy of the transition state for proton transfer is found to lie below the dissociation asymptote for NH3 + HI with a barrier height 1.4 kcaYmo1 above the minimum energy of the neutral complex. Although the position of the transition state was determined at the SCF level and the absolute position may differ somewhat for the case of the correlated surface, we feel that the value of 1.4 kcal/mol is a fairly good representation of the barrier height on the latter surface due to its flatness. It is worth mentioning that the magnitude of the barrier in the present work is similar to the 1.2 kcal/mol barrier found in ref. [ 61 for the H&NH* + HBr surface. Having determined the existence of the ionic minimum in the proton-transfer energy curve, harmonic force constant calculations were performed for the three extrema to estimate the effect of zero-point vibration on the relative energies. Such an analysis shows a dramatic effect. Comparing the zero-point energy (ZPE) sums for the two minima as well as the NH3 + HI asymptote reveals a large differential ZPE correction as is shown in table 3. This harmonic ZPE correction appears to make the ionic minimum almost disappear. Thus it appears unlikely that this complex exhibits proton transfer in the gas phase. Such a conclusion differs from that of Kollman et al. 129
Volume 130, number 1,2
CHEMICAL PHYSICS LETTERS
[ lo]. However, their work was performed with a smaller basis set and also did not include the effects of electron correlation or ZPE. Closer examination of the vibrational frequencies reveals that this difference of 4 kcal/mol in the ZPE is almost entirely due to only one vibrational mode. In the case of the neutral hydrogen-bonded structure, the hindered rotational motion of the HI molecule leads to a degenerate bending mode at approximately 400 cm- ‘. Upon transfer of the proton to form NH$I-, this previously low energy mode correlates with a doubly degenerate mode which is essentially an HNH bending motion in the NHf . The energy of this mode is on the order of 1640 cm- ‘, which leads to the large difference in zero-point corrections for the two complexes. The large difference in the energy of this mode on going from the neutral to the ionic form, raises some question concerning a simple one-dimensional treatment of the proton transfer process. In fact, a more appropriate treatment would require at least two dimensions: one along the direction of proton transfer and a perpendicular coordinate representing the N-H-I bending motion. Nevertheless, the simple treatment does lead to some interesting possibilities concerning the spectroscopic character of the H-I stretching mode in this complex. It seems unlikely that either minimum is capable of supporting an excited vibrational level for the H-I stretch. However, as in the case of other hydrogen-bonded complexes, the coupling of the H-I stretch to the dissociative stretching mode may be weak enough to lead to an observable transition. If indeed this is the case, then the presence of the ionic minima may alter dramatically the position and intensity of the H-I stretching fundamental. Since the V= 1 level of the H-I stretch in the neutral complex will lie above the small barrier to proton transfer, excitation of this mode will terminate in a vibrational state which encompasses a very wide potential region, yielding a large amplitude motion. Due to the charge transfer nature of this vibration, such a mode would possess an enhanced intensity due to the large dipole moment change. 3.2. Structures The calculated structural parameters and dipole moments for the NHJ-HX systems are reported in 130
26 September 1986
Table 4 Structural parameters and dipole moments R(H-X) H,N-HCl H,N-HBr H,N-HI H,N+II [ H,N-H-I 1’
1.297 a’ 1.426 a’ 1.614 a’ 2.221 1.769
(A)
WN-X)
(A)
3.263( 3.225) 3.468( 3.406) 3.822( 3.698) 3.294 3.268
p(D) 4.02 3.90 3.61 11.26
a’ Changes from the calculated monomer bond lengths are 0.027, 0.023 and 0.016 A for HCI, HBr and HI.
table 4. For some of these systems in addition to a full optimization at the SCF level, a second determination of the N-X distance at the correlated level, utilizing monomers frozen at the experimental geometries was made. These results are given in parentheses in table 4. The correlated results for the structures of the Cl and Br complexes are in fair agreement with the results of Brciz et al. who determined N-X distances of 3.270 and 3.380 8, compared to our values of 3.225 and 3.406 A. In the case of the calculated dipole moments our values are 0.4 and 0.7 D smaller than those from ref. [ 61. In the case of the HI complex, comparisons can be made between the ionic and neutral structural parameters. The ionic minimum possesses a significantly shorter (0.5 A) N-X distance than the neutral species and as would be expected a much larger dipole moment. The transition state structure has the curious characteristic that although it occurs very early in the proton transfer, corresponding to a relatively small displacement of the H-I bond distance, the N-X distance is already shorter than that found in the ionic minimum. Upon complete transfer of the proton, the N-X length relaxes somewhat, becoming slightly longer at equilibrium. As is the case with most hydrogen bonded complexes, the potential surface for the NHJ-HX complexes is extremely flat in certain regions. In particular, a very flat potential for the displacement of the two monomers is found. Therefore, the N-X R, distances reported here may differ substantially from the R.distances which would be observed from experiment.
Volume
130, number
1,2
CHEMICAL
PHYSICS
LETTERS
26 September
1986
3.3. Vibrational shifts
Acknowledgement
an accurate prediction of the H-I stretching frequency may require a more sophisticated treatment of the H motion, the shifts of the N-H frequencies of the ammonia-upon-hydrogen bond formation may still be qualitatively described by a harmonic force field analysis. We find extremely small shifts in the NH3 modes upon complexation. These shifts are less than 5 cm-’ in the case of the asymmetric and symmetric stretch as well as the asymmetric bending motion. Only for the symmetric bend is there an appreciable shift of approximately 30 cm-’ to higher energy upon complexation. Calculation of any other vibrational frequencies via a harmonic analysis is not justifiable.
We would like to thank Drs. J. Hougen and P. Julienne for helpful discussions and Dr. M. Krauss for suggesting the proton transfer problem.
Although
4. Conclusion Theoretical calculations on the NH,-HX systems (X = Cl, Br, I) show only a single minimum in the cases of Cl and Br. In the case of the I complex, a double-well proton-transfer potential curve with a small barrier is found. Large differential ZPE corrections favoring the neutral complex reverse the order of stability of the ionic and neutral systems. The presence of the ionic minimum may result in large amplitude hydrogen motion in the H-I V= 1 state, giving rise to an anomalous intensity and transition energy for this mode. Large coupling of the N-H-I bending to the proton transfer motion may necessitate a two-dimensional treatment of the potential surface in order to predict an accurate excitation energy for the H-I stretch.
References [ I] B.S. Ault and G.C. Pimentel, J. Phys. Chem. 77 (1973) 1649. [2] B.S. Ault, E. Steinback and G.C. Pimentel, J. Phys. Chem. 79 (1975) 615. [3] G.L. Johnson and L. Andrews, J. Am. Chem. Sot. 104 (1982) 3043. [4] A.J. Barnes, T.R. Beech and Z. Mielke, J. Chem. Sot. Faraday Trans. II 80 (1984) 455. [ 51 R.C. Raffenetti and D.H. Phillips, J. Chem. Phys. 71 (1979) 4534. [6] A. Brciz, A. Karpfen, H. Lischka and P. Schuster, Chem. Phys. 89 (1984) 337. [ 71 A. Hinchliffe, J. Mol. Struct. THEOCHEM 105 (1983) 335. [8] A. Hinchliffe, J. Mol. Struct. THEOCHEM 121 (1985) 201. [ 91 Z. Latajka and S. Scheiner, J. Chem. Phys. 8 1 (1984)4014. [ IO] P. Kollman, A. Dearing and E. Kochanski, J. Phys. Chem. 86 (1982) 1607. [ 111K.P. Huber and G. Herzberg, Molecular spectra and molecular structure, Vol. 4. Constants of diatomic molecules (Van Nostrand Reinhold, New York. 1979). [ 121 H. Hotop and W.C. Lineberger, J. Phys. Chem. Ref. Data 4 (1975) 539. [ 131 C.E. Moore, Atomic energy levels, NSRDS-NBS 35 (197I ). [ 141 S.G. Lias, J.F. Liebman and R.D. Levine, J. Phys. Chem. Ref. Data 13 (1984) 695. [ 151 M. Dupuis and H.F. King, Intern. J. Quantum Chem. 11 (1977) 613; J. Chem. Phys. 68 (1978) 3998. [ 161 S.M. Bachrach, R.A. Chiles and C.E. Dykstra, J. Chem. Phys. 75 (1981) 2270. [ 171 W.J. Stevens, H. Basch and M. Krauss, J. Chem. Phys. 81 (1984) 6026. [ 181 T.H. Dunning, J. Chem. Phys. 53 (1970) 2823. [ 191 W.H. Weber, J. Mol. Spectry. 105 (1984) 405.
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