- Email: [email protected]
Correlation effects in the proton transfer of the [FHF]− system
Journal of
MOLECULAR STRUCTURE ELSEVIER
Journal of Molecular Structure 404 (1997) 83-85
Correlation effects in the proton transfer of the [FHF]- system Henryk Chojnacki* Institute of Physical and Theoretical Chemistry, Wroctaw Technical University, Wyb. Wyspiahskiego 27, 50-370 Wroctaw, Poland
Received 15 January 1996; accepted 22 April 1996
Abstract
The role of correlation effects in the potential energy surface for the proton transfer in the hydrogen bond of the model [FHF]- system has been studied at the non-empirical level (MP2, MP3, MP4). The calculations were performed in 15 different bases including a complete basis set. The possible reasons of the incorrect results are considered. © 1997 Elsevier Science B.V. Keywords: Hydrogen bonding; Ab initio calculation; Correlation effect; Proton transfer; Hydrogen difluoride anion
1. Introduction
Due to its biological implications, the proton transfer reaction in hydrogen bonded systems has received increasing attention both from experimental and theoretical points of view. On the other hand, hydrogen bonds represent great challenge for quantum chemical methods when one would like to bring the calculated properties close to chemical accuracy. In fact, several studies, carried out on small model systems, have shown that the strength of hydrogen bridges is very sensitive to the level of approximation used in the calculation. The situation is even more involved as regards the analysis of the potential energy surfaces governing the transfer of a proton across a hydrogen bridge and the study of the dynamics of this process. The hydrogen difluoride anion [FHF]-, well characterized in the liquid and solid phases, has attracted great interest from the theoretical point of view as a
* Corresponding author. E-mail: [email protected]
model hydrogen bonded system. The experimental F-..F distance of 2.26 A [1] results in a single potential minimum for the proton motion within the hydrogen bond. However, the barrier and double minimum on the hypersurface may occur for longer interfluorine F-..F distances. From this point of view this anion was the object of quantum chemical studies for testing some theoretical approaches [2-4] as well as for interpretation of vibrational spectra [5,6].
2. Method
The electronic structure of the linear [FHF]system has been studied at the non-empiriocal level assuming the F.--F distance equal to 3.0 A. Correlation energies and potential hypersurfaces for the possible proton transfer process were studied by using the GAUSSIAN 94 package [7] for 15 different basis sets at the MP2, MP3 and MP4 perturbation approach. The configuration interaction calculations were performed for both singly and doubly excited configurations.
0022-2860/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved PII S0022-2860(96)09365-9
H. ChojnackiHournal of Molecular Structure 404 (1997) 83-85
84 4000
8000
3 5 O0 6 0 O0 u
3 0 O0
4 0 O0 I
25 O 0
m
20 O0
1500
I
20.00
---RH F
I
Mip2
I
MP2l - E
I
MP3
MP4
Fig. 1. Barrier height evaluated within the RHF and M011er-Plesset MP2, MP2-E (extrapolated), MP3 and MP4 approach for the CBSB5 [8] basis set.
3. Results and discussion It was shown in the MP2, MP3 and MP4 as well as within the configuration interaction calculations that the potential energy surface is strongly influenced by correlation energy (Fig. 1). In the CBCB5 basis set [8] the barrier height for the proton transfer of 36.03 kcal mol -] at the Hartree-Fock level lowers to 22.77 kcal mo1-1 in the MP2 approach. It grows to 23.32 kcal tool -~ when extrapolated to the complete basis set and to 27.95 kcal tool -1 at the MP3 level. Finally, it lowers to 22.43 kcal mol -t when the MP4 method is used. The role of the correlation effects can be clearly seen when improving the basis set (Fig. 2). The barrier is negative for the STO-3G basis set (the first point on the curve) and grows asymptotically to 22.5 kcal mol -~ for the complete basis set CBSB5 [8] (the lastpoint on
000 0 0000
~L
I
0 2000
0 3000
04000
0 5000
~E(CORR) ( A , U )
Fig. 3. Dependence of the barrier height on the correlation energy evaluated with the frozen core orbitals within the Moller-Plesset method for the 6s3pld and 3s2p2d contracted basis set [9] of fluorine and hydrogen, respectively.
the curve). The estimated Hartree-Fock limit for the equilibrium [FHF]- system (R(F...F) = 3.0 ,~) is -199.57009 a.u. whereas the correlation energy found from the random phase approximation [9] amounts to -0.77820 a.u. The relevant value resulting from the Sinanoglu method [10] is similar to this result. The freezing of some core orbitals may lead to different unreasonable results both in the case of the Moller-Plesset (MP2) level (Fig. 3) as well as in the configuration interactions (Fig. 4) (for different basis sets). Thus, many accidental results could be generated when no full configuration space is considered in the calculations. 7 0 O0
_
30.00
I O. iO00
60 O0
50 O0
20 OO 4000
,~
10 O 0 3 0 O0
0 O0 20 O0 m -I000
~0 O0 0 O0 ~ 00000 00500
- 2 0 O0
-300C 0 0000
~ 0 IO00
02000
~ 0.3000
0 4000
] 0 5000
[ 0.6000
0 7000
-E(CORR) (A U)
Fig. 2. Barrier height dependence on the correlation energy taken into account 15 different basis sets. The first point is for the STO3G, the last one for the CBSB5 [8] basis set.
I 1 0 I000 01500
[ I ] I 0 2000 0 2500 0 3000 0.300 - E (CORR)
I 0 4000 04500
Fig. 4. Dependence of the barrier height on the correlation energy evaluated with the frozen core orbitals for the case of single and double substitutions of the configuration interaction method for the 6s3pld and 3s2p2d contracted basis set [9] of fluorine and hydrogen, respectively.
H. Chojnacki/Journal of Molecular Structure 404 (1997) 83-85
85
4. Conclusions
References
It seems that the barrier height for the model [FHF]- system within the Hartree-Fock limit amounts to 22.5 kcal tool -1 (for R(F...F) = 3.0 ,~). It approaches asymptotically at the correlation level to 22.5 kcal mo1-1. In some cases, however, the results may be wrong when not all molecular orbitals are taken into account i.e. in the case of M011er-Plesset or configuration interaction calculations with the frozen core orbitals. In general, the results seem to be reliable when at least 60% of the correlation energy is taken into account in the calculations.
[1] K. Kawaguchi and E. Hirota, J. Chem. Phys., 84 (1986) 2953. [2] A. Stoegard, A. Strich, J. Almloef and B. Roos, Chem. Phys., 8 (1975) 405. [3] C.I. Janssen, W.D. Allen, H.F. Schaefer III and J.M. Bowman, Chem. Phys. Lett., 131 (1986) 352. [4] Z. Latajka, Y. Bouteiller and S. Scheiner, Chem. Phys. Lett., 234 (1995) 159. [5] V. Spirko, G.H.F. Diercksen, A.J. Sadlej and M. Urban, Chem. Phys. Lett., 161 (1989) 519. [6] V. Spirko, A. Cejchan and G.H.F. Diercksen, Chem. Phys., 151 (1991) 45. [7] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. AlLaham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P. Stewart, M. Head-Gordon, C. Gonzalez and J.A. Pople, GAUSS1AN 94, Revision B.3 (Gaussian, Inc., Pittsburgh, PA, 1995). [8] G.A. Petersson, A. Bennett, T.G. Tensfeldt, M.A. AI-Laham, W.A. Shirley and J. Manzaris, J. Chem. Phys., 89 (1988) 219. [9] H. Chojnacki, to be published. [10] O. Sinanoglu and H. Pamuk, Theor. Chim. Acta, 27 (1972) 289.
Acknowledgements This work has been partly sponsored by the D3 COST program and Wroctaw Technical University.
MOLECULAR STRUCTURE ELSEVIER
Journal of Molecular Structure 404 (1997) 83-85
Correlation effects in the proton transfer of the [FHF]- system Henryk Chojnacki* Institute of Physical and Theoretical Chemistry, Wroctaw Technical University, Wyb. Wyspiahskiego 27, 50-370 Wroctaw, Poland
Received 15 January 1996; accepted 22 April 1996
Abstract
The role of correlation effects in the potential energy surface for the proton transfer in the hydrogen bond of the model [FHF]- system has been studied at the non-empirical level (MP2, MP3, MP4). The calculations were performed in 15 different bases including a complete basis set. The possible reasons of the incorrect results are considered. © 1997 Elsevier Science B.V. Keywords: Hydrogen bonding; Ab initio calculation; Correlation effect; Proton transfer; Hydrogen difluoride anion
1. Introduction
Due to its biological implications, the proton transfer reaction in hydrogen bonded systems has received increasing attention both from experimental and theoretical points of view. On the other hand, hydrogen bonds represent great challenge for quantum chemical methods when one would like to bring the calculated properties close to chemical accuracy. In fact, several studies, carried out on small model systems, have shown that the strength of hydrogen bridges is very sensitive to the level of approximation used in the calculation. The situation is even more involved as regards the analysis of the potential energy surfaces governing the transfer of a proton across a hydrogen bridge and the study of the dynamics of this process. The hydrogen difluoride anion [FHF]-, well characterized in the liquid and solid phases, has attracted great interest from the theoretical point of view as a
* Corresponding author. E-mail: [email protected]
model hydrogen bonded system. The experimental F-..F distance of 2.26 A [1] results in a single potential minimum for the proton motion within the hydrogen bond. However, the barrier and double minimum on the hypersurface may occur for longer interfluorine F-..F distances. From this point of view this anion was the object of quantum chemical studies for testing some theoretical approaches [2-4] as well as for interpretation of vibrational spectra [5,6].
2. Method
The electronic structure of the linear [FHF]system has been studied at the non-empiriocal level assuming the F.--F distance equal to 3.0 A. Correlation energies and potential hypersurfaces for the possible proton transfer process were studied by using the GAUSSIAN 94 package [7] for 15 different basis sets at the MP2, MP3 and MP4 perturbation approach. The configuration interaction calculations were performed for both singly and doubly excited configurations.
0022-2860/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved PII S0022-2860(96)09365-9
H. ChojnackiHournal of Molecular Structure 404 (1997) 83-85
84 4000
8000
3 5 O0 6 0 O0 u
3 0 O0
4 0 O0 I
25 O 0
m
20 O0
1500
I
20.00
---RH F
I
Mip2
I
MP2l - E
I
MP3
MP4
Fig. 1. Barrier height evaluated within the RHF and M011er-Plesset MP2, MP2-E (extrapolated), MP3 and MP4 approach for the CBSB5 [8] basis set.
3. Results and discussion It was shown in the MP2, MP3 and MP4 as well as within the configuration interaction calculations that the potential energy surface is strongly influenced by correlation energy (Fig. 1). In the CBCB5 basis set [8] the barrier height for the proton transfer of 36.03 kcal mol -] at the Hartree-Fock level lowers to 22.77 kcal mo1-1 in the MP2 approach. It grows to 23.32 kcal tool -~ when extrapolated to the complete basis set and to 27.95 kcal tool -1 at the MP3 level. Finally, it lowers to 22.43 kcal mol -t when the MP4 method is used. The role of the correlation effects can be clearly seen when improving the basis set (Fig. 2). The barrier is negative for the STO-3G basis set (the first point on the curve) and grows asymptotically to 22.5 kcal mol -~ for the complete basis set CBSB5 [8] (the lastpoint on
000 0 0000
~L
I
0 2000
0 3000
04000
0 5000
~E(CORR) ( A , U )
Fig. 3. Dependence of the barrier height on the correlation energy evaluated with the frozen core orbitals within the Moller-Plesset method for the 6s3pld and 3s2p2d contracted basis set [9] of fluorine and hydrogen, respectively.
the curve). The estimated Hartree-Fock limit for the equilibrium [FHF]- system (R(F...F) = 3.0 ,~) is -199.57009 a.u. whereas the correlation energy found from the random phase approximation [9] amounts to -0.77820 a.u. The relevant value resulting from the Sinanoglu method [10] is similar to this result. The freezing of some core orbitals may lead to different unreasonable results both in the case of the Moller-Plesset (MP2) level (Fig. 3) as well as in the configuration interactions (Fig. 4) (for different basis sets). Thus, many accidental results could be generated when no full configuration space is considered in the calculations. 7 0 O0
_
30.00
I O. iO00
60 O0
50 O0
20 OO 4000
,~
10 O 0 3 0 O0
0 O0 20 O0 m -I000
~0 O0 0 O0 ~ 00000 00500
- 2 0 O0
-300C 0 0000
~ 0 IO00
02000
~ 0.3000
0 4000
] 0 5000
[ 0.6000
0 7000
-E(CORR) (A U)
Fig. 2. Barrier height dependence on the correlation energy taken into account 15 different basis sets. The first point is for the STO3G, the last one for the CBSB5 [8] basis set.
I 1 0 I000 01500
[ I ] I 0 2000 0 2500 0 3000 0.300 - E (CORR)
I 0 4000 04500
Fig. 4. Dependence of the barrier height on the correlation energy evaluated with the frozen core orbitals for the case of single and double substitutions of the configuration interaction method for the 6s3pld and 3s2p2d contracted basis set [9] of fluorine and hydrogen, respectively.
H. Chojnacki/Journal of Molecular Structure 404 (1997) 83-85
85
4. Conclusions
References
It seems that the barrier height for the model [FHF]- system within the Hartree-Fock limit amounts to 22.5 kcal tool -1 (for R(F...F) = 3.0 ,~). It approaches asymptotically at the correlation level to 22.5 kcal mo1-1. In some cases, however, the results may be wrong when not all molecular orbitals are taken into account i.e. in the case of M011er-Plesset or configuration interaction calculations with the frozen core orbitals. In general, the results seem to be reliable when at least 60% of the correlation energy is taken into account in the calculations.
[1] K. Kawaguchi and E. Hirota, J. Chem. Phys., 84 (1986) 2953. [2] A. Stoegard, A. Strich, J. Almloef and B. Roos, Chem. Phys., 8 (1975) 405. [3] C.I. Janssen, W.D. Allen, H.F. Schaefer III and J.M. Bowman, Chem. Phys. Lett., 131 (1986) 352. [4] Z. Latajka, Y. Bouteiller and S. Scheiner, Chem. Phys. Lett., 234 (1995) 159. [5] V. Spirko, G.H.F. Diercksen, A.J. Sadlej and M. Urban, Chem. Phys. Lett., 161 (1989) 519. [6] V. Spirko, A. Cejchan and G.H.F. Diercksen, Chem. Phys., 151 (1991) 45. [7] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. AlLaham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P. Stewart, M. Head-Gordon, C. Gonzalez and J.A. Pople, GAUSS1AN 94, Revision B.3 (Gaussian, Inc., Pittsburgh, PA, 1995). [8] G.A. Petersson, A. Bennett, T.G. Tensfeldt, M.A. AI-Laham, W.A. Shirley and J. Manzaris, J. Chem. Phys., 89 (1988) 219. [9] H. Chojnacki, to be published. [10] O. Sinanoglu and H. Pamuk, Theor. Chim. Acta, 27 (1972) 289.
Acknowledgements This work has been partly sponsored by the D3 COST program and Wroctaw Technical University.