7273
J. Phys. Chem. 1992,96,1213-1287
Ab Initio Studies of Hydrogen Bonding of N-Methyiacetamide: Structure, Cooperativlty, and Internal Rotational Barriers Hong Guo and Martin Karplus* Department of Chemistry, Harvard University, Cambridge, Massachusetts 02138 (Received: December 6, 1991)
Hydrogen bonding interactions and their effect on the structure and the energetics of the rotation about N-Cu and Cu-C’ bonds are studied for N-methylacetamide (NMA) by use of ab initio quantum mechanical calculations. The structureand methyl rotational barriers for isolated NMA have k e n determined at the Hartree-Fock (HF) level with 6-31G. 6-31G*, and 6-31 1G** basis sets and at the second-order Mdler-Plesset perturbation (MP2) level with a 6-31G* basis set including geometry optimization for the different methyl orientations. The optimized geometries, the hydrogen bonding interaction energies, and the methyl rotational barriers for 11 complexes in which NMA is hydrogen bonded to H20 and/or formamide (FM) [i.e., NMA + H20(3 complexes), NMA + 2H20 (2 complexes), NMA + 3H20 (1 complex), NMA + FM (2 complexes), NMA + (FM and H20) (1 complex), NMA + 2FM (1 complex), and NMA + (2FM and 1H2O) (1 complex)] have been calculated at the HF/6-31G level; HF/6-31G* calculations were performed for the 3 NMA + H20 complexes and 1 of the NMA + 2H20complexes. For isolated NMA, the torsional potentials for both methyl group are predicted to be very flat and the rotational bamers are only -0.1 kcal/mol. This contrasts with some of the earlier calculations in which larger barriers were obtained due to lack of geometry optimization of the rotated conformers. The bamers in the hydrogen bonded systems are calculated to be significantlylarger (0.2-0.9 kcaljmol). The increase of the C‘=O bond length from the gas-phase to crystallinestate NMA componds to that found in the ab initio calculations with hydrogen bonding ligand^, but the d8erence (0.1 A) in the experimental C’(0)-N bond distance is significantly larger than the calculated value. This suggests that the crystal structure may be in error. In agreement with the crystal structure, the lowest energy conformationin all the hydrogen bonded systems is predicted to have an ecliped (C’)CH3group and a staggered (N)CHpgroup with respect to the C’(0)-N bond; this contrasts with isolated NMA, where the conformationswith the different methyl orientations have similar energies with a difference of only -0.1 kcaljmol. In accord with the general trend observed in hydrogen bonding in a crystal data base, the ab initio calculations show that the hydrogen bond distance involving ‘multiple acceptors” (i.e., the C ‘ 4 group that accepts two hydrogen bonds) is 0.02-0.06 A longer than that involving a ‘single acceptor”. The calculated hydrogen bond energy is -0.5-1.5 kcal/mol smaller when two acceptors are present. By contrast, the formation of a hydrogen bond to the NH group reduces the hydrogen bond distance for the hydrogen bond to the C ’ 4 group by -0.02-0.045 A and increases the correspondinghydrogen bond energy by -0.3-0.9 kcal/mol. Correspondingly,the formation of each hydrogen bond to C ‘ 4 reduces the hydrogen bond distance for the hydrogen bond to the NH and increases the corresponding hydrogen bond energy by about the same amount. When one ligand is bound to the carbonyl group, the C - - H ( N ) angle is nearly linear ( -160°-165’), while, for two ligands (Le., with any additional H20ligand), the angle is reduced to 130°, in accord with an analysis of structural data. The changes in the geometrical parameters and the increase of the methyl rotational bamers as a result of hydrogen bonding are interpreted in terms of Mulliken populations, and their importance for empirical force fields is briefly discussed.
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1. Introduction N-Methylacetamide (NMA) continues to attract attention as a model system for the main chain of proteins. Although it has been extensively studied both e~perimentallyl-~ and theoretically,&13uncertainties still exist concerning the effect of hydrogen bonding on its structure and conformation. For instance, the C(0)-N bond length determined in a crystal by X-ray diffraction2 is -0.1 A shorter than that from gas-phase electron diffracti0n.l It has been suggested that this is due to the hydrogen bond formation in the crystalline state.’ Gallaher and BaueP have studied the correlation between the internuclear distance and bond stretching frequencies for the gas and solid phases using Badger’s ruleI5and suggested that the C’(0)-N distance derived for NMA from the crystal data may be -0.04 A too short. Thus, it is not clear whether the large difference is due to experimental error or arises from hydrogen bonding in the crystal. Ottersed studied the effect of hydrogen bonding on the structure of fonnamide by ab initio calculations and found that the different values of the C’(0)-N bond lengths in the gas-phase and crystalline-state formamide are reflected in the theoretical calculations; i.e., the formation of two hydrogen bonds between two formamide molecules or formamide and two waters reduces the C’(0)-N bond distance by -0.025 A, which is close to the observed decrease (0.03-0.05 A) in going from the gas phase to the crystalline Since the difference for NMA is significantlylarger (-0.1 A) and NMA is a better model for the protein backbone than formamide, corresponding calculations for this molecule are of interest. The orientationof the (C’)CH,($) and (N)CH3(4) groups in NMA and the energetics of the corresponding rotations are also 0022-3654/92/2096-7213$03.00/0
of importance,because these torsions are related to the main chain angles t$(N-Cu) and tj(C%”) in peptides and proteins. In spite of the wealth of published research on this subject,6J9-26the properties of these rotations are not well understood. Hagler et a1.19 analyzed X-ray crystal structures for a number of simple amides and peptides. They found that 6 out of 12 molecules have (N)CH3 angles (4) close to 180’ [i.e., with two hydrogens staggered with respect to the C’(0)-N bond and one in the CN-C’ plane] with a deviation of less than 15’, and two of them exhibit a torsional angle of -0’ [i.e., with one hydrogen eclipsing the C’(0)-N bond]. For the four other molecules, the (N)CH3 angle (4) is -150’. For the (C’)CH, group, it was found that eight of ten molecules studied have (C’)CH3(tj) angles close to Oo [i.e., with one hydrogen eclipsing the C’(0)-N bond] with a deviation of leas than 15’; the only exceptions are rhombohedral acetamide (tj 30’) and N-acetylglycine with essentially free (C’)CH3 rotation (Le., the CH3group is disordered). This led to the suggestion that 4 = 180’ and $ = 0’ are the inherently preferred conformations for the methyl groups and that variations from these rotational minima are induced by crystal forces. The NMA structural study by the gas electron diffraction’ seems to support the suggestion that 4 = 180’ is most stable; a staggered N-methyl group with respect to the C’(0)-N bond (Le., 4 = 180O) led to a significantly better fit to the diffraction data than an eclipsed N-methyl group (Le., 4 = 0’). However, the gas-phase experimental data for N-methylf~rmamide’~ were insensitive to the orientation of the N-methyl group, as is the case for the C’-methyl group in NMA’ and acetamide.27 Hydrogen bonds generally exist in the crystalline state, so the orientations of the N- and C’-methyl groups found in most of the crystals by Hagler
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0 1992 American Chemical Society
1274 The Journal of Physical Chemistry, Vol. 96, No. 18, 1992
Guo and Karplus
(N)CH3]; the restriction of C,symmetry was used for the rest of the molecule (Le., the atoms not involved in the rotation). The MP2/6-31G* calculations were not performed on the (N)CH3 rotation because they are very time consuming and the effect of the correlation treatment was found to be unimportant on the (C')CH3 rotation. For the Hartree-Fock and MP2 calculations, I \ geometry optimizations were performed by use of the geometry i! HI JI: optimization facility based on the analytic gradient technique in the program. Additional calculations in the presence of ligands were performed to study the hydrogen bonding interactions of NMA and to obtain an estimate of the effect of hydrogen bonding on the molecular structure and on the energetics of the methyl rotations. x; NMA with fi = 0" and # = 180" is shown in Figure 1 with three Figwe 1. Atom labels for NMA,possible positions for forming H bonds, possible positions (1-111) for forming a hydrogen bond (or simply and definitions of H bond gcometrical parameters. H bond). The optimized geometries and total energies were determined at both the HF/6-31G and HF/6-31GS levels for the et aLI9w i d result from intermolecular hydrogen bonding rather following hydrogen bonded NMA systems with Merent N-methyl than the amformationalpreference of the isolated molecules. This and C'methyl orientations: (1) one water interacting with the suggestion is supported by the fact that the rotational barrier C ' 4 group of NMA at position I, i.e., the (C')O-.H H bond (-0.5 kcal/mol) of the C'methyl group in rhombohedral aceteclipsed to the C'(0)-N bond [NMA + H 2 0(I)]; (2) one water amide determined from inelastic neutron scattering28is signifiinteracting with the NH group at position I1 [NMA + H 2 0(II)]; cantly larger than that (-0.07 kcal/mol) found for acetamide (3) one water interacting with the C ' 4 group of NMA at in the gas phase by microwave spectroscopy.26 Although it is position 111, Le., the (C')O-H H bond trans to the C'(0)-N bond known that the formation of hydrogen bonds leads to changes in [NMA H 2 0 (III)]; (4)one water interacting with the C ' 4 the structural parameters of the peptide linkage,*the effect of group at position I and one water with the NH group at position hydrogen bonding on the orientation of the N-methyl and C'I1 [NMA 2H20(I and II)]. Additional HF/6-31G calculations methyl groups and on the energetics of the correspondingrotations were performed for the following systems: ( 5 ) two waters inhas not been examined. teracting with the C ' 4 at position I and I11 [NMA 2H20 In this paper, we use ab initio method to study hydrogen (I and III)]; (6) two waters interacting with C ' 4 at positions bonding interactions and their effect on the structure of NMA I and I11 and one water with NH [NMA 3H20 (I and I1 and and on the energetics of the rotations about N-Ca(#) and CaIII)]; (7) one formamide interacting with the NH of NMA at C'($) bonds. We also consider the energy of the hydrogen bonds position I1 [NMA + FM (II)]; (8) one formamide interacting and their nonadditivity. Section 2 briefly outlines the calculational with the C ' 4 of NMA at position I11 [NMA FM (III)]; (9) method. Results and Discussion are given in section 3. The one water and one formamide interacting with C ' 4 at positions conclusions are presented in section 4. Subsequent papers will I and 111, respectively [NMA + (FM and H20) (I11 and I)]; (10) be c " e d with the effect of hydrogen bonding on the structures one formamide interacting with the C ' 4 of NMA at position and on the energetics of the rotations about N-Ca(#) and CaI11 and one formamide with NH [NMA 2FM (I1 and III)]; C'($) bonds in N-formylglycylamide (a glycine dipeptide ana(1 1) one water and one formamide interacting with the C ' 4 logue)29*30 and (S)-a-(formy1amino)propanamide(an alanine at positions I and 111, respectively, and one formamide with the dipeptide a n a l ~ g u e ) . ~ ~ NH group [NMA (2FM and 1H20) (I1 and I11 and I)], 2. Method The relative positions and orientations of H20, FM, and NMA with the different methyl orientationsin the complexes 1-1 1 are Ab initio calculations have been performed at the Hartree-Fock given in Figures 2-7. All the internal structural parameters in (HF) and the second-order Moiler-Plesset perturbation (MP2) levels with the GAUSSIAN 82 program32with internal stored 6-31 ~ , 3 ~ H20, FM, and NMA in complexes 1-1 1 were optimized with the restriction of C,symmetry for FM and NMA. For the H bond 6-31G*,34and 6-31 lG**,35basis sets. The optimized geometry geometries, the following constraints were used in the geometry and energy for isolated NMA with different N-methyl and C'optimization: methyl orientations (i.e., eclipsed or staggered position with respect (1) For H 2 0hydrogen bonding to NH (II), the N-H-0 angle to the C(0)-N bond) have been determined at the Hartree-Fock is fmd at 180" and the plane of H 2 0is taken to be perpendicular levelwith6-31G,6-31G*,and6-311G** badissetsandat theMP2 to the NMA plane which corresponds to the lowest energy conlevel with the 6-31G* badis set with the restriction of C,symmetry formation of the hydrogen bor~ding.~ for the molecule. It has been shown that the relaxation of the (2) For H 2 0hydrogen bonding to C ' 4 (I or 111), H 2 0and constraint generally leads to a slightly nonplanar lowest energy NMA are in the same plane. conformation for NMA?6 but the energy difference between the (3) FM and NMA are in the same plane. lowest energy conformation of the planar and nonplanar structm We note that the arrangement and the constraintsfor some of is generally very small; it is only -0.01-0.03 kcal/mol from the the hydrogen bonded complexes may not lead to the optimized HF/6-31G*, HF/6-311G**, and MP2/6-31G* calculation^.'^ geometry corresponding to a global energy minimum. For inFurthermore, hydrogen bonding of NMA to other molecules (e.g., stance, for the NMA + 3H20 [see 6 above] the global energy water or formamide) moves the nonplanar minimum toward the minimum may correspond to a conformation in which the two planar conformation. For instance, in the HF/6-31G* nonplanar water molecules interacting with the C ' 4 group are also hystructure of isolated NMA?6 the C-C'-N-CT, 042'-N-CT, drogen bonded to each other to form a nonplanar threamcmbcred C-C'-N-HI $, and Q dihedral angles (see Figure 1) are about ring structure with relatively weak C ' 4 - H hydrogen bonds, 175". 4 O , 5", 22", and 169O, respectively, and they change to as suggested by AM^^^ calculation^.^^ However, the hydrogen 179O, -lo, 2", O", and 174", respectively, when two waters are bonding situation in Figures 2f, 4f. and 6f (e.g., H bonds in the hydrogen bonded to NMA at positions I and I1 (see same plane) is closer to that found in the NMA crystaL2 For Given the above analysis, the assumption of C, symmetry for NMA + 2FM [see 10 above] and NMA + (2FM and 1H20) [see NMA is satisfactory for studying the hydrogen bonding of NMA. 11 above], NMA and the two formamides are arranged in the The torsional potential was derived at the HF/6-31G, HF/6same way as in the NMA crystal2 (e&, see Figure 3d,e). 31G*, and MP2/6-31G* levels for the (C')CH3 group and at For the system of NMA + 3H20,the torsional potentials for HF/6-31G and HF/6-31G* levels for the (N)CH3 group with the (C')CH, and (N)CH3groups were derived at the HF/6-31G geometry optimizations at each torsional angle [i.e., O.Oo, 2O0, level with geometry optimization for the complex at each value 40°, and 6 0 O for (C')CH3 and 120", 140", 16O0, and 180° for
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Hydrogen Bonding of N-Methylacetamides
The Journal of Physical Chemistry, Vol. 96, No. 18, 1992 7275
1.8800
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176.84 (176.9 1)
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178.45 (18 1.06)
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Figure 2. H bond geometries from HF/6-31G calculations and arrangements of molecules in the complexes of NMA + H20(s) with $ = Oo and 4 = 180’: (a)NMA + H 2 0 (I);(b)NMA + H 2 0 (II);(c) NMA + H 2 0 (111); (d) NMA + 2H20 (I and 11); (e)NMA + 2H20 (I and III);(f) NMA + 3H20 (I aBd I1 and 111). The numbers in parentheses are from HF/6-31G* calculations.
of the torsional angles (see above); the restriction of C, sypnetry was used for the rest of the complex (i.e., the atoms not involved in the rotation).
3. Results and Discussion We first present the equilibrium geometries for isolated NMA and for NMA as part of a hydrogen bonded system. We then discuss the H bond geometries and interaction energies for the hydrogen bonded complexes. Finally, we describe the results for the relative energies of different methyl orientations and interpret them by means of population analyses. An important element of the present work is full geometry optimization of each methyl rotamer, which corresponds to an adiabatic torsional potential. 3.1. Equilibrium Geometries. The equilibrium geometries for NMA in the isolated case and in the hydrogen bonded complexes with $ = Oo and 4 = 180’ from various Hartree-Fock calculations are listed in Tables I and 11, along with the results given earlier.39 The optimized geometries for the systems with other methyl orientations (i.e., $ = Oo and 4 = Oo, $ = 180° and 4 = Oo, or $ = 180° and 4 = 180’) are not given, since they do not correspond to the lowest energy conformation. However, the optimized H bond geometries for different methyl orientations will be given (see below), because they are useful for understanding certain intra- and intermolecular interactions. As is evident from Tables
I and 11, the addition of d functions on the heavy atoms (6-31G to 6-31G*) has a significant effect on the C-C’(O), C ’ 4 , and N-CT bond distances for the systems with or without water ligand(s); i.e., the C-C’(O) bond length increases by -0.009 A, and the C ’ 4 and N-CT bond lengths decrease by -0.03 and -0.007 A, respectively, when the basis set changes from 6-31G to 6-31G*. The effect of d functions on other geometrical parameters is generally rather small (10.003 A for bond lengths and 10S0for angles). For isolated NMA, the expansion of the basis set from 6-31G* to 6-31 1G** causes only a small change in most of the geometrical parameters (
