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Basis set influence in ab initio calculations: The case of 2-aminoethanol and N-formylproline amide
THEO CHEM ELSEVIER
Journal of Molecular Structure (Theochem) 310 (1994) 45-53
Basis set influence in ab initio calculations: the case of 2-aminoethanol and N-formylproline amide Anne-Marie Kelterer", Michael Ramek":", Regina F. Frey'', Ming Cao", Lothar Schafer" "Institut fur Physikalische und Theoretische Chemie, Technische Universitdt Graz, A·80lO Gras, Austria "Biosym Technologies. 207 Portland Terrace, St. Louis, AlD 63II9, USA "Department of Chemistry and Biochemistry. University of Arkansas, Fayetteville. AR 72701. USA
(Received 19 July 1993;accepted 13 August 1993)
Abstract
The number of local minima which can be located in the potential energy surfaces of 2-aminoethanol and Nformylproline amide depends on the basis set employed. This effect was explored using a number of standard basis sets and the stability of the questionable conformers is discussed in detail.
1. Introduction The increase in computational power which has become available for routine calculations in recent years is reflected in the increased attention that has been attributed to the topic of basis set dependence of ab initio results recently. While in most cases the term "basis set dependence" means the alteration of molecular geometry data such as bond lengths and angles, a significant number of cases have arisen in which basis set variation changes local minima to saddle points, or vice versa [I-A]. The case of glycine and the related systems ,B-alanine and glycine amide, which have been discussed recently [5], are even more striking. In these cases the addition of polarization functions to double zeta basis sets results in a significant overestimation of nonbonded interactions, especially if the range of polarization functions is limited to d functions "Corresponding author.
on non-hydrogen atoms. As a consequence, a new local minimum is formed on the (RHF) potential energy surface of each of these compounds, which is not present without polarization functions. This new minimum, in which the intramolecular N·· ·H-O hydrogen bond is replaced by a clustering of the hydrogen atoms of both functional groups, disappears again when the basis set is increased further. It is the purpose of this contribution to describe a similar basis set dependence that occurs in ab-initio calculations of the two title compounds. The interest in reliable descriptions of these compounds is obvious, because 2-aminoethanol and N-formylproline amide are both biologically important species. Proline is one of the essential amino acids; it is unique due to its ring structure with only one hydrogen atom bonded to the nitrogen atom. This hydrogen atom is eliminated when proline becomes part of a peptide chain, and as a consequence proline cannot take part in the N-H·· ·O=C hydrogen bonds that stabilize
0166-1280/94/S07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0166-1280(93)03520-H
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the helices and sheet structures in proteins. Hence proline is a delimiter of these structural units, which makes it important for the secondary protein structure [6]. N-Formylproline amide is the simplest possible approach to mimic a proline residue of a peptide chain. 2-Aminoethanol is a part of the most important phospholipids and plays an essential role in biological membranes [7]. Furthermore small polyfunctional molecules like 2-aminoethanol are used as model compounds in investigations of biological systems [8]. 2-Aminoethanol in particular has recently been used in a study of ligand-ji-adrenoceptor complexes [9]. The pair of compounds 2-aminoethanol and N-formylproline amide is also fascinating, because it represents two different extremes in the field of ab-initio structure investigations. 2-Aminoethanol on the one hand is a small molecule that has been the target of quantum chemical calculations several times in the past [10-14]. N-Formylproline amide on the other hand is a relatively large molecule, the investigation of which requires considerable computational power. To the best of our knowledge, N-formylproline amide has not so far been . investigated via ab-initio methods.
2. Computational details The RHF calculations reported here were carried out with the programs GAMESS [15] and TX90 [16]. The MP2 calculations were performed using the Turbomole program of Biosym Technologies, Inc., which was originally developed by Ahlrichs et al. [17,18]. The standard basis set definitions coded in GAMESS were used except for the 4-210 basis, which was used as defined in Ref. 19. The uniform quality basis set UQIO is defined in Ref. 20 and the Dunning and Hay basis set (abbreviated as "DH" in Table 1) is given in Ref. 21. Basis sets including d functions employed six d functions in the case of RHF calculations and five d functions in the case of MP2 calculations. Geometries were fully optimized with remaining root-mean-square gradients less than 0.0001 H Bohr-I. The nature
(Theochem} 3/0 (/994) 45-53
of all of local minima and all saddle points was confirmed by computing the eigenvalues of the Hessian matrix.
3. Results 3.1. 2-AminoetlzmlOl
Comparison of the results of complete RHF geometry optimizations with different basis sets for 2-aminoethanol shows that some of the local minima, which were found with minimal basis sets [11], are inaccessible with split valence basis sets [12,13], but are accessible with basis sets augmented by d functions [14]. All conformations of 2-aminoethanol, which show this basis set dependence, are related to the global minimum by an internal rotation of one of the two functional groups. In the context of the results for glycine and its analogues it is noteworthy that the global minimum is stabilized by an intramolecular N·· ·H-O interaction, the nature of which is on the borderline between hydrogen bond and electrostatic interaction. According to the frequently used criterion that requires the interatomic distance to be less than the sum of the van der Waals radii [22], and according to the energy gap between the global minimum and all other local minima of the potential energy surface, this interaction is a hydrogen bond; according to the electron density, which does not have a critical point along the N-H connection line, it does not have the characteristics of a chemical bond [23]. In accordance with earlier work [10] we denote all 2-aminoethanol conformations by a unique symbol xyz, in which x, y and z describe the approximate orientation of the amino group, the N-C-C-O chain, and the hydroxy group, respectively. In terms of dihedral angles, x = g, t and g' corresponds to HI-N-C-CfH2-N-CC = 180°/-60°, 60°/-60°, and 180°/60°, y = 0 and T corresponds to N-C-C-O = 60° and 180°, and z = g, t, and g' corresponds to H -O-C-C = 600, 180°, and -60°, respectively. In this notati n, the conformers, which are discussed here, are labelled gOg', tOg', g'Ot, g'Gg, and
A.-M. Ketterer et al.jl. Mol. Struct. (Theochem) 3/0 (1994) 45-53
47
Table I Relative energies (kJ mol-I) of the four 2-aminoethanol conformers tGg', gGg', g'Gg, and g'Gt obtained with various standard basis sets and ab-initio RHF calculations' Basis set
tGg'
gGg'
g'Gg
g'Gt
Ref.
STO·3G STO-6G 3-21G 4·21G 3·21+G 4-21+G UQIO 4-31G 4-31G' 4-3IG" 6-31G 6-31+G 6-31++G
13.00 12.58 19.09 17.45
8.68 8.66
12.83 13.23
17.30 18.50
11
14.06 13.32
7.72 7.80
23.56 22.82
13.96 13.11 11.77 11.76 14.23 12.38 11.23 11.26
7.32 7.37 6.26 6.25 7.45 7.47 6.42 6.48
22.95 22.25 20.53 20.25 22.60 21.43 19.23 19.15
12
13
DH 6-311G 6·311+G 6-311++G 6-3IG' 6-3IG" 6·31+G" 6-31++G" 6-31IG' 6-3I1G" 6-311+G" 6-311++G"
14
Zero energy corresponds to the conformer g'Gg', which is the global minimum with all basis sets. "-" indicates that no stationary point exists for the conformation with the respective basis set.
a
g'Gg'. The conformer g'Gg' is the global minimum of the potential energy surface that is stabilized by the weak intramolecular N·· ·H-O interaction. Table I lists the relative energies of the four other conformers gGg', tGg', g'Gt, and g'Gg obtained with various basis sets, with which these conformers are local minima of the potential energy surface. The data in Table 1 yield a simple pattern at the SCF level, which allows the distinction of four groups of basis sets. The first group contains the minimal basis sets STO-nG; with these basis sets all four conformations (tGg', gGg', g'Gg, and g'Gt) are local minima of the potential energy surface. The second group contains the basis sets 3-21G and 4-21G; with these basis sets tGg' is a local minimum, but gGg', g'Gg, and g'Gt are not local minima. The third group is made up of all other split valence, double and triple zeta basis sets; with these basis sets none of the four confor-
mations in question is a local minimum. The fourth group contains basis sets augmented with polarization functions; with these basis sets tGg', gGg', and g'Gt can be found as local minima. Inclusion of diffuse functions in the basis set changes this pattern in the case of 3-21G and 4-21G; tGg', which is a local minimum with these basis sets, is not a local minimum with 3-21+G or 4-21+G, as with all other split valence basis sets with or without diffuse functions. Full MP2 optimizations have been performed with one basis set out of each of these groups except the minimal basis sets. The results of these calculations can be summarized as follows: tGg' and g'Gt can be found with 3-21G and 6-311G", but not with 4-31G; gGg' cannot be found with any of these basis sets. A detailed investigation of the 6-31G" RHF potential energy surface reveals that each of
48
A.-M. Kelterer et
r
au, Mol. Struct.
(Theochem) 310 (1994) 45-53
-209.110
E [a.u.J -209.115
Wt
gGt
-209.120 +------r---...,...------r----.-.r---.....,...---.,---...,...-60 -90 0 -30 0 0
Hl-N-C-C
H-O-C-C
Fig. I. The 6·310" potential energy surface shows that tOg' is quite stable with respect to an amino group rotation. The internal rotation of the hydroxy group, however, has a barrier of only 0.82 kJ mol", which vanishes with most split valence or triple zeta basis sets. (e) Stationary points of the potential energy surface.
these local minima has one reaction path with an extremely low potential barrier (see Figs. 1-3). The comparison of the 6-31G', 6-31G", 6-311G**, and 6-311++G*' data, which are collected in Table 2, shows that the height of this barrier parallels the localizability with the small split valence basis sets 3-21G and 4-21G. tGg', which can be localized with these basis sets, has not only the largest, but also a fairly constant, value for this barrier; the values for gGg' and g'Gt, which cannot be localized with 3-21G and 4-21G, are lower and decrease with increasing basis set quality. 3.2. N-Formylprolille amide
Figure 4 displays the conformers I and II, which are discussed here. I is related to the global
r
minimum in the N-formylproline amide potential energy surface by a puckering motion of the fivemembered proline ring. It has a significant intramolecular hydrogen bond between the oxygen atom of the formyl group and one of the amide group hydrogen atoms, which closes a seven-membered ring. In the course of the internal rotation of the -CONH 2 group, which destroys this hydrogen bond, the amide group comes into the vicinity of the proline nitrogen atom. This results in an electrostatic interaction, which yields either a flat region in the potential energy surface or II as a local minimum that cannot be localized with some basis sets. Due to the large amount of computer time necessary for the investigation of Nformyl proline amide, only a subset of the basis sets employed for 2-aminoethanol was exploited
-209.110
E [a.u.J -209.115
tGt
gGg'
-209.120+-~~L---r---..------r---.---,----r---~---r
60 0
1200
1500
1800
-150 0
-120 0
-90 0
_60 0
H1-N-C-C
-30 0 ---+
Fig. 2. The 6-310" potential energy surface has a barrier of only 0.44 kl rnol" for the amino group rotation gOg' .=: g'Og'. gOg' is no local minimum with split valence and triple zeta basis sets. (e) Stationary points of the potential energy surface.
A.-M. Kelterer et al.jJ, Mol. Struct, [Theochem} 3/0 (/994) 45-53
49
-209.105
E [a.u.] -209.110
g'Gt
-209.115
-209.120 +----r----,-----.-------,-----r-----,.----,---r-45 0 180 0 H-O-G-C
--+
Fig. 3. The 6-3IG" potential energy surface has a barrier of only 0.62 kJ mol-I for the hydroxy group rotation g'Gt <=' g'Gg'. g'Gt is not a local mimimum with split valence and triple zeta basis sets. (e) Stationary points. The shoulder in the energy profile corresponds to the conformation g'Gg, which is a local minimum only with minimal basis sets.
here. II is a local rmrnmum with the basis sets 3-2IG, 4-3IG, 6-3IG, 6-3l+G, 6-3I1G, and 6-31G**, but not with the basis set 6-31G*. The relevant energy profile is shown in Fig. 5 for the basis sets 4-31G and 6-31G*. The potential barrier is also extremely low; with the 4-31G basis set it amounts to 0.21 kJ mol ",
4. Discussion A common feature in the RHF calculations for both of the study compounds are local minima, which are characterized by a very low potential barrier along one reaction path. For both comTable 2 RHF potential barriers (kJ mol") of the three 2-aminocthanol conformers IGg', gGg', and g'Gt as obtained with several polarized basis sets Basis set
tGg'
gGg'
g'GI
6-31G' 6·3IG" 6-31IG" 6-311++G"
0.85 0.82 0.96 0.84
0.47 0.44 0.35 0.37
0.72 0.62 0.54 0.15
pounds the existence of these minima is basis-set dependent, but the striking difference is that most of those basis sets, which allow the localization of these minima for 2-aminoethanol, are not able to localize them for N-formylproline amide, and vice versa. Moreover, the results for 2-aminoethanol follow the pattern that has been observed for glycine and its analogues: the new minima occur with polarized basis sets and exhibit structures in which the eclipsed orientation of hydrogen atoms is the predominant feature (Fig. 6). While the case of glycine seemed to be linked to the existence of a strong intramolecular hydrogen bond, the N·· ·H-O interaction in 2-aminoethanol has only marginal hydrogen-bond character. In contrast, N-formylproline amide has a significant c=o·· ·H-N hydrogen bond, but here the additional minimum is found with the split valence and triple zeta basis sets. This basis set dependence is a pronounced contrast to the fact that no significant basis set influence onto the RHF electron densities can be observed along the N·· ·H-O connection line in the global minimum g'Gg' of the 2-aminoethanol potential energy surface. As this interaction is
50
A.-M. Kelterer et al.fJ. Mol. Struct, [Theochem) 310 (1994) 45-53
1
-490.950
E[a.u.]
II -490.955
-490.9604---...,..----r-----,---~
r
-491.680
E[a.u.] -491.685
I -491.690+----r---~----,----.-
150·
180·
-150·
_120·
-90·
O=C-C-N
Fig. 5. The energy profile for the internal rotation of the -CONH 2 group in N-formylproline amide, obtained in RHF calculations with the 4-3lG basis set (top) and the 6-3IG' basis set (bottom). (.) Stationary points.
Fig. 4. Ball-and-stick models overlayed with fused spheres of the corresponding van der Waals radii of the N-formylproline amide conformers I (top) and II (bottom).
only weak (e.g. it lowers the O-H vibrational frequency by 41 em"! [13]), it should be quite sensitive to basis-set quality. Figure 7 shows contour maps of the electron density in the relevant plane with several basis sets, which exemplify that the description of the intramolecular N·· ·Ho interaction is practically identical with all basis sets. The MP2 optimizations, which were performed for 2-aminoethanol, do not really help in solving
the puzzle. On the one hand the height of the low potential barrier that is listed in Table 2 compares well with the MP2 results; gGg', which cannot be found with any of the employed basis sets at MP2 level, is the conformer with the lowest RHF potential barrier among the questionable three structures. This matches with the observation that the main effect of correlation in the case of molecules, which are well described by a single determinantal wavefunction, is the reduction of potential barriers. On the other hand g'Gt, which is not a local minimum with the 3-21G basis set in RHF calculations, is a local minimum with this basis set at MP2 level. The situation is similar for tGg', which is controversial in every sense. It certainly is the most questionable of the conformations discussed here due to its clustering of hydrogen atoms. This consideration of "chemical common sense" is depreciated by the fact that tGg' has a rather constant value of the low potential barrier height. At the same time, however, tGg' also exhibits an
A.-M. Ketterer et al./f. Mol. Struct, (Theochem) 3/0 (1994) 45-53
51
Fig. 6. Ball-and-stick models overlayed with fused spheres of the corresponding van der Waals radii of g'Gt (top left), gGg' (top right), IGg' (bottom left), and g'Gg' (bottom right) as obtained from RHF geometry optimizations with the 6-3IG" basis set.
extreme scatter of the relative energy values: for the RHF energies the maximum difference within the polarized basis sets is 3.0 kJ mol -I, and this value extends to 7.8kJmol- 1 between the 3-21G and the 6-31+0" basis set. The same is true for the relative MP2 energies: here the difference between the 3-21G and the 6-311G" value is 8.1kJmol- l . Inspection of the vibrational frequencies, which were calculated with the usual harmonic oscillator approximation, shows that for each of the conformers tGg', gGg', g'Gt, and II the zero-point energy of the vibration mode in the direction of the low barrier reaction path is higher than the barrier. Of course the applicability of the harmonic oscillator approximation is questionable for minima with such a low barrier, and the zero-point energy will be lowered by including the strong anharmonicity. Nevertheless, the height of the potential barrier and the vibrational zero-point energy will remain in the same order of magnitude. Hence, these
shallow minima can be considered as physically meaningless.
5. Conclusion There are two major conclusions that can be drawn from the results obtained for the two title compounds. The first conclusion is that minima with extremely low potential barriers, that may even be lower than the vibrational zero-point energy, seem to occur rather often. The second conclusion is that a change of basis set quality does affect the localizability of these minima in a more or less unpredictable manner. This is of considerable importance for conformational studies, because the sophisticated algorithms for geometry optimization, which are incorporated into standard ab initio program packages, will locate most of these minima, despite the fact that they may be meaningless. These conclusions seem to be valid for both RHF and MP2 calculations.
52
A.-M. Kelterer et
a.u. Mol. Struct,
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Fig. 7. Maps of the electron density in g'Gg', obtained with the basis sets 4-31G (bottom), 6-3IG' (middle), and 6·3IG" (top). The plane of the drawing is defined by the hydroxy group, which is oriented horizontally, and-the nitrogen atom. Contour lines are plotted for the electron densities 0.01,0.02, ... , 0.1,0.15,0.20, ... ,0.50, 0.75, 1.00, ... The irregularities at high electron densities are an artefact of the plotting program [24]. which is based on values calculated on a finite sized grid.
A.-M. Ketterer et al.fl. Mol . Struct, (Th eochem} 3/0 (1994) 45-53
Acknowledgements The support of this work by the Austrian Fonds zur F6rderung der wissenschaftlichen Forschung (project No. P6856) is gratefully acknowledged. Several calculations were performed using the IBM 3090 VF operated by the Vienna University computer centre within IBM's European Academic Superconducting Initiative; A.-M.K. and M .R. appreciate the opportunity to join this program.
References (I] M. Ramek, V.K .W. Cheng, R.F. Frey, S.Q. Newton and L. Sch afer, J. Mol. Struct, (Theochem), 235 (1991) I. (2] M . Flock and M . Ramek, Int . J. Quantum Chern., Quantum Chern. Symp., 26 (1992) 505. (3] M.N. Glukhovtsev, P.v.R. Schleyer, N.J.R . van Eikema Hommes, J.W. de M . Carneiro and W. Koch, J. Comput Chern., 14 (1993) 285. (4] M . Rernko, P. Mach, P.v. R. Schleyer and O. Exner, J. Mol. Struct. (Theochem), 279 (1993) 139. (5) M. Rarnek a nd V.K.W. Cheng, Int. J. Quantum Chern., Quantum BioI. Symp., 19 (1992) 15. (6) K. Yutani, S. Hayashi, Y. Sugis aki and K. Ogasahara, Proteins, 9 (1991) 90. 17] B. Alberts, D. Bray, J. Lewis, M . Raff, K. Roberts and J .D. Watson, Molecular Biology of The Cell, Garl and, New York, 1989. (8) A.J. Mulholland, G.H. Grant and W.G. Richards, Protein Eng ., 6 (1993) 133.
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(9) M .R. Linschoten, G .W. Klein Kranenbarg, SJ . de Kirnpe, J. Wilting, L.H.M . Jans sen and J.H . van Lenthe, J. Mol. Struct. (Theochem), 237 (1990) 339. (10] L. Radom, W.A . Lathan, W.L. Hehre and J.A. Pople, J. Am. Chern . Soc. , 95 (1973) 693. (II] M . Rasanen, A. Aspiala, L. Homanen and J. Murto, J. Mol. Struct. (Theochem), 96 (1981) 81. [12J C. van Alsenoy, K. Siam, J.D. Ewbank and L. Schafer, J . Mol. Struct. (Theochem), 136 (1986) 77. [I3J A .-M. Kelterer and M . Ramek, J. Mol. Struct, (Theochem), 232 (1991) 189. [14] L.G. Vanquickenborne, B. Coussens, C. Verlinde and C. de Ranter, J. Mol. Struct. (Theochem), 201 (1989) I. [15) M .W. Schmidt, K .K. Baldridge, J.A . Boatz, J .H . Jen sen, S. Ko seki, M.S. Gordon, K.A. Nguyen, T.L. Windus and S. Elbert, QCPE Bull ., 10 (1990) 52. [16] P. Pulay and co-workers, TX90, Fayetteville, AR, 1990. [17] R. Ahlrichs, M. Bar, M. Haser, H. Horn and Ch . Kolmel, Chern . Phys . Let!., 162 (1989) 165. [18] M . Haser and R. Ahlrichs, J. COmpUI. Chern ., 10 (1989)
104. [19) P. Pulay, G. Fo garasi, F. Pang and J.E. Boggs, J. Am. Chern. Soc., 101 (1979) 2550. [20] P.G. Mezey and I.G. Csizmadia, Can. J. Chern., 55 (1977) 1181. [21] D .H . Dunning Jr. and P.J. Hay, in H .F. Schaefer III (Ed.), Methods of Electronic Structure Theory, Plenum, New York, 1977, p. Iff. [22) A.A. Hasenein and A. Hinchliffe, in R. Carbo and M. Klobukowski (Eds.), Self-Consistent Field, Theory and Applications, Elsevier, Amsterdam, 1990, p. 670. [23] R.W.F. Bader, Atoms in Molecules, Clarendon, Oxford, 1990, p. 19. [24] 1.1. Kurnig, Diplomarbeit, Technische Universitiit Graz, 1983.
Journal of Molecular Structure (Theochem) 310 (1994) 45-53
Basis set influence in ab initio calculations: the case of 2-aminoethanol and N-formylproline amide Anne-Marie Kelterer", Michael Ramek":", Regina F. Frey'', Ming Cao", Lothar Schafer" "Institut fur Physikalische und Theoretische Chemie, Technische Universitdt Graz, A·80lO Gras, Austria "Biosym Technologies. 207 Portland Terrace, St. Louis, AlD 63II9, USA "Department of Chemistry and Biochemistry. University of Arkansas, Fayetteville. AR 72701. USA
(Received 19 July 1993;accepted 13 August 1993)
Abstract
The number of local minima which can be located in the potential energy surfaces of 2-aminoethanol and Nformylproline amide depends on the basis set employed. This effect was explored using a number of standard basis sets and the stability of the questionable conformers is discussed in detail.
1. Introduction The increase in computational power which has become available for routine calculations in recent years is reflected in the increased attention that has been attributed to the topic of basis set dependence of ab initio results recently. While in most cases the term "basis set dependence" means the alteration of molecular geometry data such as bond lengths and angles, a significant number of cases have arisen in which basis set variation changes local minima to saddle points, or vice versa [I-A]. The case of glycine and the related systems ,B-alanine and glycine amide, which have been discussed recently [5], are even more striking. In these cases the addition of polarization functions to double zeta basis sets results in a significant overestimation of nonbonded interactions, especially if the range of polarization functions is limited to d functions "Corresponding author.
on non-hydrogen atoms. As a consequence, a new local minimum is formed on the (RHF) potential energy surface of each of these compounds, which is not present without polarization functions. This new minimum, in which the intramolecular N·· ·H-O hydrogen bond is replaced by a clustering of the hydrogen atoms of both functional groups, disappears again when the basis set is increased further. It is the purpose of this contribution to describe a similar basis set dependence that occurs in ab-initio calculations of the two title compounds. The interest in reliable descriptions of these compounds is obvious, because 2-aminoethanol and N-formylproline amide are both biologically important species. Proline is one of the essential amino acids; it is unique due to its ring structure with only one hydrogen atom bonded to the nitrogen atom. This hydrogen atom is eliminated when proline becomes part of a peptide chain, and as a consequence proline cannot take part in the N-H·· ·O=C hydrogen bonds that stabilize
0166-1280/94/S07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0166-1280(93)03520-H
46
A.-t.!. Kelterer et
sur. Mol. Struct.
the helices and sheet structures in proteins. Hence proline is a delimiter of these structural units, which makes it important for the secondary protein structure [6]. N-Formylproline amide is the simplest possible approach to mimic a proline residue of a peptide chain. 2-Aminoethanol is a part of the most important phospholipids and plays an essential role in biological membranes [7]. Furthermore small polyfunctional molecules like 2-aminoethanol are used as model compounds in investigations of biological systems [8]. 2-Aminoethanol in particular has recently been used in a study of ligand-ji-adrenoceptor complexes [9]. The pair of compounds 2-aminoethanol and N-formylproline amide is also fascinating, because it represents two different extremes in the field of ab-initio structure investigations. 2-Aminoethanol on the one hand is a small molecule that has been the target of quantum chemical calculations several times in the past [10-14]. N-Formylproline amide on the other hand is a relatively large molecule, the investigation of which requires considerable computational power. To the best of our knowledge, N-formylproline amide has not so far been . investigated via ab-initio methods.
2. Computational details The RHF calculations reported here were carried out with the programs GAMESS [15] and TX90 [16]. The MP2 calculations were performed using the Turbomole program of Biosym Technologies, Inc., which was originally developed by Ahlrichs et al. [17,18]. The standard basis set definitions coded in GAMESS were used except for the 4-210 basis, which was used as defined in Ref. 19. The uniform quality basis set UQIO is defined in Ref. 20 and the Dunning and Hay basis set (abbreviated as "DH" in Table 1) is given in Ref. 21. Basis sets including d functions employed six d functions in the case of RHF calculations and five d functions in the case of MP2 calculations. Geometries were fully optimized with remaining root-mean-square gradients less than 0.0001 H Bohr-I. The nature
(Theochem} 3/0 (/994) 45-53
of all of local minima and all saddle points was confirmed by computing the eigenvalues of the Hessian matrix.
3. Results 3.1. 2-AminoetlzmlOl
Comparison of the results of complete RHF geometry optimizations with different basis sets for 2-aminoethanol shows that some of the local minima, which were found with minimal basis sets [11], are inaccessible with split valence basis sets [12,13], but are accessible with basis sets augmented by d functions [14]. All conformations of 2-aminoethanol, which show this basis set dependence, are related to the global minimum by an internal rotation of one of the two functional groups. In the context of the results for glycine and its analogues it is noteworthy that the global minimum is stabilized by an intramolecular N·· ·H-O interaction, the nature of which is on the borderline between hydrogen bond and electrostatic interaction. According to the frequently used criterion that requires the interatomic distance to be less than the sum of the van der Waals radii [22], and according to the energy gap between the global minimum and all other local minima of the potential energy surface, this interaction is a hydrogen bond; according to the electron density, which does not have a critical point along the N-H connection line, it does not have the characteristics of a chemical bond [23]. In accordance with earlier work [10] we denote all 2-aminoethanol conformations by a unique symbol xyz, in which x, y and z describe the approximate orientation of the amino group, the N-C-C-O chain, and the hydroxy group, respectively. In terms of dihedral angles, x = g, t and g' corresponds to HI-N-C-CfH2-N-CC = 180°/-60°, 60°/-60°, and 180°/60°, y = 0 and T corresponds to N-C-C-O = 60° and 180°, and z = g, t, and g' corresponds to H -O-C-C = 600, 180°, and -60°, respectively. In this notati n, the conformers, which are discussed here, are labelled gOg', tOg', g'Ot, g'Gg, and
A.-M. Ketterer et al.jl. Mol. Struct. (Theochem) 3/0 (1994) 45-53
47
Table I Relative energies (kJ mol-I) of the four 2-aminoethanol conformers tGg', gGg', g'Gg, and g'Gt obtained with various standard basis sets and ab-initio RHF calculations' Basis set
tGg'
gGg'
g'Gg
g'Gt
Ref.
STO·3G STO-6G 3-21G 4·21G 3·21+G 4-21+G UQIO 4-31G 4-31G' 4-3IG" 6-31G 6-31+G 6-31++G
13.00 12.58 19.09 17.45
8.68 8.66
12.83 13.23
17.30 18.50
11
14.06 13.32
7.72 7.80
23.56 22.82
13.96 13.11 11.77 11.76 14.23 12.38 11.23 11.26
7.32 7.37 6.26 6.25 7.45 7.47 6.42 6.48
22.95 22.25 20.53 20.25 22.60 21.43 19.23 19.15
12
13
DH 6-311G 6·311+G 6-311++G 6-3IG' 6-3IG" 6·31+G" 6-31++G" 6-31IG' 6-3I1G" 6-311+G" 6-311++G"
14
Zero energy corresponds to the conformer g'Gg', which is the global minimum with all basis sets. "-" indicates that no stationary point exists for the conformation with the respective basis set.
a
g'Gg'. The conformer g'Gg' is the global minimum of the potential energy surface that is stabilized by the weak intramolecular N·· ·H-O interaction. Table I lists the relative energies of the four other conformers gGg', tGg', g'Gt, and g'Gg obtained with various basis sets, with which these conformers are local minima of the potential energy surface. The data in Table 1 yield a simple pattern at the SCF level, which allows the distinction of four groups of basis sets. The first group contains the minimal basis sets STO-nG; with these basis sets all four conformations (tGg', gGg', g'Gg, and g'Gt) are local minima of the potential energy surface. The second group contains the basis sets 3-21G and 4-21G; with these basis sets tGg' is a local minimum, but gGg', g'Gg, and g'Gt are not local minima. The third group is made up of all other split valence, double and triple zeta basis sets; with these basis sets none of the four confor-
mations in question is a local minimum. The fourth group contains basis sets augmented with polarization functions; with these basis sets tGg', gGg', and g'Gt can be found as local minima. Inclusion of diffuse functions in the basis set changes this pattern in the case of 3-21G and 4-21G; tGg', which is a local minimum with these basis sets, is not a local minimum with 3-21+G or 4-21+G, as with all other split valence basis sets with or without diffuse functions. Full MP2 optimizations have been performed with one basis set out of each of these groups except the minimal basis sets. The results of these calculations can be summarized as follows: tGg' and g'Gt can be found with 3-21G and 6-311G", but not with 4-31G; gGg' cannot be found with any of these basis sets. A detailed investigation of the 6-31G" RHF potential energy surface reveals that each of
48
A.-M. Kelterer et
r
au, Mol. Struct.
(Theochem) 310 (1994) 45-53
-209.110
E [a.u.J -209.115
Wt
gGt
-209.120 +------r---...,...------r----.-.r---.....,...---.,---...,...-60 -90 0 -30 0 0
Hl-N-C-C
H-O-C-C
Fig. I. The 6·310" potential energy surface shows that tOg' is quite stable with respect to an amino group rotation. The internal rotation of the hydroxy group, however, has a barrier of only 0.82 kJ mol", which vanishes with most split valence or triple zeta basis sets. (e) Stationary points of the potential energy surface.
these local minima has one reaction path with an extremely low potential barrier (see Figs. 1-3). The comparison of the 6-31G', 6-31G", 6-311G**, and 6-311++G*' data, which are collected in Table 2, shows that the height of this barrier parallels the localizability with the small split valence basis sets 3-21G and 4-21G. tGg', which can be localized with these basis sets, has not only the largest, but also a fairly constant, value for this barrier; the values for gGg' and g'Gt, which cannot be localized with 3-21G and 4-21G, are lower and decrease with increasing basis set quality. 3.2. N-Formylprolille amide
Figure 4 displays the conformers I and II, which are discussed here. I is related to the global
r
minimum in the N-formylproline amide potential energy surface by a puckering motion of the fivemembered proline ring. It has a significant intramolecular hydrogen bond between the oxygen atom of the formyl group and one of the amide group hydrogen atoms, which closes a seven-membered ring. In the course of the internal rotation of the -CONH 2 group, which destroys this hydrogen bond, the amide group comes into the vicinity of the proline nitrogen atom. This results in an electrostatic interaction, which yields either a flat region in the potential energy surface or II as a local minimum that cannot be localized with some basis sets. Due to the large amount of computer time necessary for the investigation of Nformyl proline amide, only a subset of the basis sets employed for 2-aminoethanol was exploited
-209.110
E [a.u.J -209.115
tGt
gGg'
-209.120+-~~L---r---..------r---.---,----r---~---r
60 0
1200
1500
1800
-150 0
-120 0
-90 0
_60 0
H1-N-C-C
-30 0 ---+
Fig. 2. The 6-310" potential energy surface has a barrier of only 0.44 kl rnol" for the amino group rotation gOg' .=: g'Og'. gOg' is no local minimum with split valence and triple zeta basis sets. (e) Stationary points of the potential energy surface.
A.-M. Kelterer et al.jJ, Mol. Struct, [Theochem} 3/0 (/994) 45-53
49
-209.105
E [a.u.] -209.110
g'Gt
-209.115
-209.120 +----r----,-----.-------,-----r-----,.----,---r-45 0 180 0 H-O-G-C
--+
Fig. 3. The 6-3IG" potential energy surface has a barrier of only 0.62 kJ mol-I for the hydroxy group rotation g'Gt <=' g'Gg'. g'Gt is not a local mimimum with split valence and triple zeta basis sets. (e) Stationary points. The shoulder in the energy profile corresponds to the conformation g'Gg, which is a local minimum only with minimal basis sets.
here. II is a local rmrnmum with the basis sets 3-2IG, 4-3IG, 6-3IG, 6-3l+G, 6-3I1G, and 6-31G**, but not with the basis set 6-31G*. The relevant energy profile is shown in Fig. 5 for the basis sets 4-31G and 6-31G*. The potential barrier is also extremely low; with the 4-31G basis set it amounts to 0.21 kJ mol ",
4. Discussion A common feature in the RHF calculations for both of the study compounds are local minima, which are characterized by a very low potential barrier along one reaction path. For both comTable 2 RHF potential barriers (kJ mol") of the three 2-aminocthanol conformers IGg', gGg', and g'Gt as obtained with several polarized basis sets Basis set
tGg'
gGg'
g'GI
6-31G' 6·3IG" 6-31IG" 6-311++G"
0.85 0.82 0.96 0.84
0.47 0.44 0.35 0.37
0.72 0.62 0.54 0.15
pounds the existence of these minima is basis-set dependent, but the striking difference is that most of those basis sets, which allow the localization of these minima for 2-aminoethanol, are not able to localize them for N-formylproline amide, and vice versa. Moreover, the results for 2-aminoethanol follow the pattern that has been observed for glycine and its analogues: the new minima occur with polarized basis sets and exhibit structures in which the eclipsed orientation of hydrogen atoms is the predominant feature (Fig. 6). While the case of glycine seemed to be linked to the existence of a strong intramolecular hydrogen bond, the N·· ·H-O interaction in 2-aminoethanol has only marginal hydrogen-bond character. In contrast, N-formylproline amide has a significant c=o·· ·H-N hydrogen bond, but here the additional minimum is found with the split valence and triple zeta basis sets. This basis set dependence is a pronounced contrast to the fact that no significant basis set influence onto the RHF electron densities can be observed along the N·· ·H-O connection line in the global minimum g'Gg' of the 2-aminoethanol potential energy surface. As this interaction is
50
A.-M. Kelterer et al.fJ. Mol. Struct, [Theochem) 310 (1994) 45-53
1
-490.950
E[a.u.]
II -490.955
-490.9604---...,..----r-----,---~
r
-491.680
E[a.u.] -491.685
I -491.690+----r---~----,----.-
150·
180·
-150·
_120·
-90·
O=C-C-N
Fig. 5. The energy profile for the internal rotation of the -CONH 2 group in N-formylproline amide, obtained in RHF calculations with the 4-3lG basis set (top) and the 6-3IG' basis set (bottom). (.) Stationary points.
Fig. 4. Ball-and-stick models overlayed with fused spheres of the corresponding van der Waals radii of the N-formylproline amide conformers I (top) and II (bottom).
only weak (e.g. it lowers the O-H vibrational frequency by 41 em"! [13]), it should be quite sensitive to basis-set quality. Figure 7 shows contour maps of the electron density in the relevant plane with several basis sets, which exemplify that the description of the intramolecular N·· ·Ho interaction is practically identical with all basis sets. The MP2 optimizations, which were performed for 2-aminoethanol, do not really help in solving
the puzzle. On the one hand the height of the low potential barrier that is listed in Table 2 compares well with the MP2 results; gGg', which cannot be found with any of the employed basis sets at MP2 level, is the conformer with the lowest RHF potential barrier among the questionable three structures. This matches with the observation that the main effect of correlation in the case of molecules, which are well described by a single determinantal wavefunction, is the reduction of potential barriers. On the other hand g'Gt, which is not a local minimum with the 3-21G basis set in RHF calculations, is a local minimum with this basis set at MP2 level. The situation is similar for tGg', which is controversial in every sense. It certainly is the most questionable of the conformations discussed here due to its clustering of hydrogen atoms. This consideration of "chemical common sense" is depreciated by the fact that tGg' has a rather constant value of the low potential barrier height. At the same time, however, tGg' also exhibits an
A.-M. Ketterer et al./f. Mol. Struct, (Theochem) 3/0 (1994) 45-53
51
Fig. 6. Ball-and-stick models overlayed with fused spheres of the corresponding van der Waals radii of g'Gt (top left), gGg' (top right), IGg' (bottom left), and g'Gg' (bottom right) as obtained from RHF geometry optimizations with the 6-3IG" basis set.
extreme scatter of the relative energy values: for the RHF energies the maximum difference within the polarized basis sets is 3.0 kJ mol -I, and this value extends to 7.8kJmol- 1 between the 3-21G and the 6-31+0" basis set. The same is true for the relative MP2 energies: here the difference between the 3-21G and the 6-311G" value is 8.1kJmol- l . Inspection of the vibrational frequencies, which were calculated with the usual harmonic oscillator approximation, shows that for each of the conformers tGg', gGg', g'Gt, and II the zero-point energy of the vibration mode in the direction of the low barrier reaction path is higher than the barrier. Of course the applicability of the harmonic oscillator approximation is questionable for minima with such a low barrier, and the zero-point energy will be lowered by including the strong anharmonicity. Nevertheless, the height of the potential barrier and the vibrational zero-point energy will remain in the same order of magnitude. Hence, these
shallow minima can be considered as physically meaningless.
5. Conclusion There are two major conclusions that can be drawn from the results obtained for the two title compounds. The first conclusion is that minima with extremely low potential barriers, that may even be lower than the vibrational zero-point energy, seem to occur rather often. The second conclusion is that a change of basis set quality does affect the localizability of these minima in a more or less unpredictable manner. This is of considerable importance for conformational studies, because the sophisticated algorithms for geometry optimization, which are incorporated into standard ab initio program packages, will locate most of these minima, despite the fact that they may be meaningless. These conclusions seem to be valid for both RHF and MP2 calculations.
52
A.-M. Kelterer et
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Fig. 7. Maps of the electron density in g'Gg', obtained with the basis sets 4-31G (bottom), 6-3IG' (middle), and 6·3IG" (top). The plane of the drawing is defined by the hydroxy group, which is oriented horizontally, and-the nitrogen atom. Contour lines are plotted for the electron densities 0.01,0.02, ... , 0.1,0.15,0.20, ... ,0.50, 0.75, 1.00, ... The irregularities at high electron densities are an artefact of the plotting program [24]. which is based on values calculated on a finite sized grid.
A.-M. Ketterer et al.fl. Mol . Struct, (Th eochem} 3/0 (1994) 45-53
Acknowledgements The support of this work by the Austrian Fonds zur F6rderung der wissenschaftlichen Forschung (project No. P6856) is gratefully acknowledged. Several calculations were performed using the IBM 3090 VF operated by the Vienna University computer centre within IBM's European Academic Superconducting Initiative; A.-M.K. and M .R. appreciate the opportunity to join this program.
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