Density Functional Studies onN-Methylacetamide-Water Complexes
Wen-Ge Han and Sa´ndor Suhai*Molecular Biophysics Department, German Cancer Research Center, Im Neuenheimer Feld 280,D-69120 Heidelberg, Germany
ReceiVed: August 4, 1995; In Final Form: NoVember 22, 1995X
Density functional theory (DFT) calculations were performed to study the conformations, hydrogen-bondingeffects, and the stabilities of different methyl group orientations of isolatedtrans- andcis-N-methylacetamide(NMA) and of 12 NMA-water complexes. The DFT functionals B3LYP, BLYP, and the basis set 6-311++G-(d,p) were used all through the calculations. The isolatedtrans-NMA structures obtained from these twoDFT methods are consistent with experimental data from gas-phase electron diffraction and comparable toMP2 calculations at a much lower cost. Cooperative effects of hydrogen bonding were found in thetrans-NMA ‚2H2O complexes, in which the two water molecules attach to the NsH and CdO groups oftrans-NMA, respectively. No substantial H-bonding cooperative effect was found forcis-NMA-water complexes.The trans-NMA structures with the methyl orientationsΦ ) Ψ ) 0° andΦ ) 180° andΨ ) 0° are the moststable conformations of isolatedtrans-NMA, and the structure withΦ ) 180° andΨ ) 0° corresponds tothe energy minimum state oftrans-NMA in hydrated situations. The methyl group orientation ofΦ ) Ψ )180° corresponds to the most stable structure both for gas-phasecis-NMA and thecis-NMA-water complexes.
1. Introduction
For the understanding of the structural properties and biologi-cal functions of proteins, it is important to know how theyinteract with an aqueous environment through hydrogen bond-ing. N-Methylacetamide (NMA), one of the simplest modelsfor the main chain of proteins, has been extensively studied inthis respect, and it is still of great interest from both thetheoretical and experimental points of view.1-17 To model thehydrogen-bonding interactions and their effect on the structureof NMA, Guo and Karplus1 recently studied several NMA-water complexes by using ab initio quantum mechanicalmethods, in whichtrans-NMA interacted with one, two, andthree water molecules, respectively. They found that watermolecules cooperatively bind to the peptide group and thehydrogen bond increases the methyl rotational barriers. Baudryand Smith2 applied molecular mechanics for the same complexesand obtained results similar to those of Guo and Karplus.Subsequently, Dixon et al.3 performed ab initio calculations upto the MP2 level to investigate the strength of the hydrogenbonds intrans- andcis- (t- andc-)NMA interacting with a singlewater molecule.So far, all theoretical investigations concerned with the
structural, energetic, and vibrational aspects of hydrogen bond-ing in NMA complexes either used ab initio molecular orbitaltheory or molecular mechanics procedures. Density functionaltheory (DFT) methods18-20 may provide, on the other hand, aninteresting and powerful methodological alternative in this field.In the past years, with the development of more accurateexchange-correlation potentials and of advanced numericalprocedures, DFT has been more and more frequently appliedto investigate the properties of both small and large systems.Many evidences21-30 show that the results of DFT calculationsare fairly consistent with experimental data for a number ofmolecular properties and are well comparable to post-Hartree-Fock calculations such as MP2 at a relatively lower cost. Inthis paper, we will use DFT to study the properties of severalt- and c-NMA-water complexes. Ourt-NMA-water com-plexes are the same as those of Guo and Karplus.1
To understand the dependence of the results on the size ofthe atomic basis sets and on the form of the exchange-correlationpotential (EXC), we used several basis sets, up to 6-311++G-(2d,2p), in combination with a number ofEXC expressionsincluding gradient corrections. To obtain reasonably reliableresults, we used the relatively large basis set 6-311++G(d,p)throughout our calculations. For comparison, ab initio calcula-tions up to the MP2 level have also been performed for isolatedt-NMA and for one of its water complexes. In section 2, wewill describe our models and methods. In section 3, we willpresent and discuss our results obtained for isolated and hydratedt- andc-NMA structures including the interaction energies inNMA-water complexes and the role of different methylorientations in the gas phase as well as in the hydratedenvironment.
2. Models and Methods
Seven t-NMA-water complexes and fivec-NMA-watercomplexes have been studied in this paper. The water positionsin t- andc-NMA-water complexes are illustrated in Figures 1and 2, respectively. Fort-NMA + 1H2O structures, a watermolecule can act as a donor and bind to the CdO group atposition I (we call this conformation TI hereafter) or at positionIII (complex TIII ), or it can be an acceptor and bind to the N-Hgroup at position II (complex TII). There are threet-NMA +2H2O complexes: TI,II , TII,III , and TI,III , with two water moleculesbinding to thet-NMA at two of the three positions. TI,II,III is acomplex in which thet-NMA interacts simultaneously with threewater molecules. For thec-NMA complexes, our models aresimilar to those of Dixon et al.3 and of Mirkin and Krimm.7
We studied three one-waterc-NMA complexes: CI, CII, andCIII , whose water positions are shown in Figure 2. Twoc-NMA+ 2H2O complexes are studied here. They are conformationsCI,III and CII,III . The unique feature in CI and CI,III is that onewater molecule can act as an acceptor and a donor simulta-neously and form two H bonds with the NsH and CdO groupsof c-NMA. All t-NMA structures here have the methyl grouporientations ofΦ ) 180° andΨ ) 0° (Figure 1). Φ ) 180°means that one of the hydrogens (H7, which is on the C1-N2-C3-C5 plane) in the (N)CH3 group is trans to the N2-X Abstract published inAdVance ACS Abstracts,February 1, 1996.
C3 bond, andΨ ) 0° means that one hydrogen (H10, also onthe C1-N2-C3-C5 plane) of the (C)CH3 group is cis to theN2-C3 bond. According to our DFT calculations, this structureof t-NMA is one of the lowest energy conformations in the gasphase, and it is the most stable configuration in hydratedsituations (see the discussion in section 3.5). Allc-NMAstructures in our complexes have the methyl group orientationsof Φ ) Ψ ) 180° (Figure 2). Later, we will see that thisstructure ofc-NMA is its most stable form both in the gas phaseand in hydrated states.Our DFT calculations for the isolated NMA and for the NMA
complexes mentioned above were performed using the Gaussian92/DFT package31with internally stored 6-31G(d), 6-31G(d,p),6-311G(d,p), 6-311++G(d,p), and 6-311++G(2d,2p) basis sets.To compare different DFTEXC functionals and to be able tochoose the appropriate ones to perform the bulk of these studies,we first studied the complex TIII using six DFT functionals:(1) HFB (Becke’s 1988 exchange functional only),32 (2) HFS(Slater local spin-density exchange functional only),33 (3) SLYP(Slater exchange and the Lee, Yang, and Parr, LYP,34 correlationfunctional), (4) SVWN (Slater exchange and the local spindensity correlation functional of Vosko et al.35), (5) B3LYP(Becke’s three-parameter exchange36 and the LYP correlationfunctional), and (6) BLYP (Becke’s 1988 exchange and the LYPcorrelation functional).To obtain more accurate interaction energies between the
NMA and water molecules, we performed counterpoise cor-rections (CPC)37,38 in all of our calculations on NMA-watercomplexes to at least partially correct the basis set superpositionerror (BSSE). IfE(NMA+W) denotes the total energy of theoptimized structure of an NMA+ H2O complex, for exampleTI, E(NMA) the energy of NMA with the relaxed structure inthe optimized TI complex, andE(W) the energy of H2O withits geometry in TI, then the interaction energy between NMAand the water molecule with BSSE is
If E(NMA+w) represents the energy of NMA calculatedusing the basis of NMA plus the ghost basis on the water
molecule according to the optimized geometry of TI, andE(nma+W) is the energy of water molecule which is obtainedusing the basis of H2O plus the ghost basis on NMA with itsgeometry in TI, then the interaction energy of TI with counter-poise correction will be
This will be our final expression for the corrected interactionenergy of the complexes.
3. Results and Discussion
3.1. Comparison of Different DFT Functionals. SeveralEXC functionals have been proposed in the past years, but theirapplicability for properly describing the fine details of hydrogen-bonding interactions is still a matter of discussion. Therefore,we decided to test first the six functionals defined above incomputing the optimized geometries and interaction energiesof the complex TIII using the basis set 6-311G(d,p), togetherwith the HF and MP2 methods. The H-bond lengths and theinteraction energies obtained from different methods are listedin Table 1. We also present the bond lengths of N2-C1 and
Figure 1. Atom labels fort-NMA with Φ ) 180° (H7-C1 trans toC3-N2) andΨ ) 0° (H10-C5 cis to C3-N2). Three water positionsfor forming t-NMA-water complexes are shown, and the annotationsof H-bond geometry parameters are defined.
∆E(BSSE)) E(NMA + W) - E(NMA) - E(W) (1)
Figure 2. c-NMA with Φ ) 180° (H7-C1 trans to C3-N2) andΨ) 180° (H10-C5 trans to C3-N2). Possible H-bonds formingpositions with water are shown and the annotations of H-bond geometryparameters are defined.
∆E(CPC)) E(NMA+W) - E(NMA+w) - E(nma+W)(2)
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C5-C3 together with the corresponding experimental results.Here, we do not compare the length of the C3-N2 bond, sinceits value as determined in a crystal by X-ray diffraction15 isshorter by∼0.1 Å than as obtained from gas-phase electrondiffraction.16 We will return to this problem later.From Table 1, one can see that the bond lengths of N2-C1,
C5-C3, and the H-bond obtained by the HFB method are allmuch longer than the corresponding experimental and MP2results. On the contrary, the bond lengths obtained by themethods containing Slater exchange (SLYP and SVWN) aremuch shorter. The H-bond length of 1.7563 Å obtained by theHFS method is also very short, as compared with the MP2 valueof 1.9081 Å. The two main bond lengths in the HF results areall shorter than the corresponding experimental values and theMP2, B3LYP, and BLYP results. On the other hand, theH-bond length in HF calculation is significantly longer thanthat obtained from the MP2, B3LYP, and BLYP methods,respectively. The interaction energies,∆E, obtained from HFS,SLYP, and SVWN are, even after the counterpoise correction,still too large. The quality of the Slater exchange resultsobserved here (resulting in short bond lengths and largeinteraction energies) is in agreement with earlier calculations.27,30
Upon comparing the results of B3LYP and BLYP with theMP2 calculations, we see that the bond lengths of N2-C1 andC5-C3 obtained from B3LYP are in very good agreement withthe corresponding MP2 results. Using the BLYP method, thesetwo bonds turn out to be slightly longer than those obtainedfrom MP2, but are consistent with the experimental data. Thecorresponding H-bond lengths and interaction energies ofB3LYP, BLYP, and MP2 are all close to each other. On thebasis of these results, it seems that it is reasonable to choosethe functionals B3LYP and BLYP, respectively, to further studythe properties of isolatedt- and c-NMA and their watercomplexes.3.2. Properties oft- and c-NMA. The properties of isolated
NMA, including the geometry, vibrational spectra, dipolemoment, energy differences betweent- andc-NMA, etc., havebeen extensively studied using ab initio and molecular mechan-ics methods. It is, however, of great interest to see if the DFTmethods lead to results comparable to or better than thoseobtained from former theoretical work. Very recently, Mirkinand Krimm8 optimized the isolatedt-NMA structure startingfrom different geometries with HF and post-HF methods andwith different basis sets. They concluded that, within theexpected torsion angle variations in the calculations, theequilibrium structure of isolatedt-NMA has planar symmetry.To see if the equilibrium structures oft- andc-NMA still haveCs symmetry within DFT calculations, we optimized thet- andc-NMA starting from nonplanar geometries. It turned out thatboth optimized structures went back to the planar symmetry.Using the potentials B3LYP and BLYP, we optimized the
isolated planart- and c-NMA structures with the basis sets6-31G(d), 6-31G(d,p), 6-311G(d,p), 6-311++G(d,p), and
6-311++G(2d,2p). The initial geometries were ofCs symmetry(t-NMA with Φ ) 180°, Ψ ) 0°, andc-NMA with Φ ) Ψ )180°) and the optimizations did not change them. As areference, we also obtained thet-NMA optimized structures atthe HF and MP2/6-311++G(d,p) levels, respectively. TheB3LYP and BLYP geometries of NMA obtained using the basisset 6-311++G(d,p) are compared with those obtained from MP2and HF calculations and with the experimental results in Table2.Looking at the first four “main-chain” bond lengths, our
B3LYP results are very close to the corresponding MP2 ones.Furthermore, compared with the electron diffraction data forthe gas phase oft-NMA,16 our B3LYP results for the bondlengths of N2-C1, C3-N2, and C5-C3 are even better thanthose obtained from MP2. The bond lengths in BLYP resultsare somewhat longer (about 0.01 Å) than the correspondingvalues obtained from B3LYP. It is difficult, however, todetermine which is better than the other. Comparing with theelectron diffraction data,16 the bond lengths of N2-C1 and C3-N2 obtained from BLYP are more accurate. On the other hand,the B3LYP results for the bond lengths O4dC3 (1.2216 Å) andC5-C3 (1.5191 Å) are almost the same as the experimentaldata (1.225 and 1.520 Å, respectively). As to the HF calcula-tion, the four main bond lengths are all shorter (about 0.01-0.03 Å) than the corresponding electron diffraction data andworse than the B3LYP, BLYP, and MP2 results.Comparing the geometries oft-NMA and c-NMA, we see
from Table 2 that the largest bond length difference is 0.005 Åat the bond C3-N2 both for B3LYP and BLYP calculations.Other bond lengths are all quite similar. The bond angle C3-N2-C1 is by about 5.7-5.9° larger inc-NMA, and angle H6-N2-C3 is by about 5.3-5.5° smaller in c-NMA than thecorresponding ones int-NMA. Other bond angles show nosubstantial differences between these two structures.Under a certain method (B3LYP or BLYP), the NMA
structures obtained from the basis sets 6-31G(d) to 6-311++G-(2d,2p) have no much differences. The biggest bond lengthchange is 0.006 Å (on O4dC3 bond) occurring from basis set6-31G(d,p) to 6-311G(d,P) for both B3LYP and BLYP methods.From smaller to bigger basis sets, the NMA structures have noregular changing tendencies. As discussed by Guo and Kar-plus,1 the bond length of C3-N2 (1.290 Å) obtained in a crystalby X-ray diffraction15 seems too short. Our shortest value forthis bond in the isolatedt-NMA is 1.3612 Å obtained fromB3LYP/6-311++G(2d,2p). We will see later that when NMAis hydrated, this bond will become shorter.Within a certain basis set, the bond lengths obtained from
BLYP are always larger than the corresponding ones fromB3LYP. Furthermore, the difference between the bond lengthsdevelops in parallel. For example, using the basis set 6-311++G-(d,p), the bond lengths from BLYP are all larger by about 0.013Å than the corresponding ones obtained from B3LYP.
TABLE 1: Comparison of the Optimized Geometries (Å) and Interaction Energies∆E (kcal/mol) for T III (t-NMA with theH-Bonded Water Molecule at Position III in Figure 1), Using Different Methods and the Basis Set 6-311G(d,p)
N2-C1 1.4968 1.4561 1.4320 1.4340 1.4563 1.4690 1.4490 1.4506 1.465 (13) 1.469 (6)C5-C3 1.5610 1.5141 1.4843 1.4883 1.5146 1.5269 1.5105 1.5117 1.536 (16) 1.520 (5)r(H19‚‚‚O4) 2.1127 1.7563 1.6341 1.6884 1.8852 1.9054 1.9938 1.9081∆E(BSSE)c -5.44 -15.12 -22.28 -17.06 -9.20 -8.89 -7.20 -9.17∆E(CPC)d -2.82 -10.68 -17.64 -13.43 -6.38 -5.61 -5.71 -5.67a t-NMA geometries determined in a crystal by X-ray diffraction. Standard deviations are in parentheses (unit is 0.001 Å).b Isolatedt-NMA
geometries obtained from gas-phase electron diffraction. Standard deviations are also in parentheses.c Interaction energy containing basis setsuperposition error (BSSE).d Interaction energy obtained after counterpoise correction (CPC) according to eq 2.
3944 J. Phys. Chem., Vol. 100, No. 10, 1996 Han and Suhai
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From basis set 6-31G(d) to 6-311++G(d,p), the energydifference∆E between isolatedt- andc-NMA is increased from2.23(2.15) to 2.52(2.42) kcal/mol for B3LYP(BLYP) method;the dipole moment (µ) of t-NMA is changing from 3.729(3.618)to 3.971(3.911) D, and the dipole moment ofc-NMA is from3.917(3.798) to 4.315(4.260) D obtained from B3LYP(BLYP)calculations. Using the same method and basis set, our dipolemoment ofc-NMA is always larger than that oft-NMA, whichis in agreement with previous studies.12,13 The scattering ofthe experimental data for the dipole moment of NMA is quitelarge, lying in the region 3.53-4.39 D.39-43 The relativelyrecent experimental results range from 3.85 D in benzene to4.22 D in 1,4-dioxane as reported by Pralat et al.43 Our resultsof the dipole moment for botht- and c-NMA with differentbasis sets are all within the range of the experimental results.Comparing the results of∆E andµ obtained from different
basis sets, we found that, for both the B3LYP and BLYPcalculations, the values of∆E andµ slowly increase in goingfrom basis set 6-31G(d,p) to 6-311++G(d,p). The addition ofthe second set of polarization functions in 6-311++G(2d,2p)only insignificantly influences the results and slightly decreasessome of the∆E andµ values. We think that if we go to someother higher basis sets, the results will just oscillate around thoseobtained using the 6-311++G(d,p) basis set. Therefore, the6-311++G(d,p) basis set seems to be adequate to predict theproperties of NMA complexes. This is why we will use thisbasis set to perform the further calculations throughout our work.3.3. Geometries of Hydrogen-Bonded NMA Complexes.
Using the B3LYP and BLYP functionals and starting from theCs symmetry, we optimized all NMA-water complexes inFigures 1 and 2 with the basis set 6-311++G(d,p). We alsoperformed full optimizations using HF and MP2 on the TIII
complex with the same basis set. To compare our DFT resultswith the ab initio calculations, we list in Table 3 the main bondlengths and bond angles of TIII obtained by the B3LYP, BLYP,HF, and MP2 methods. We see that both the bond lengths andangles obtained from B3LYP are very close to those from MP2.As to the H-bond length, the B3LYP, BLYP, and MP2 resultsagree with each other very well. Especially the H-bond lengthsobtained from BLYP and MP2 are very close to each other.The covalent bond lengths of the HF calculation are all shorterthan the corresponding ones obtained from the other threemethods and the H-bond length of the HF method is too long(by 0.1 Å longer than the MP2 result).
The optimized geometries of TIII , CI, CII, CIII , and CI,III stillremain in theCs symmetry. In other complexes, the NMAstructures still maintain the planar geometries. Concerning thewater molecules, the torsional angles of the waters which attachto the C3dO4 group (∠O14-H13-O4-C3 and∠O20-H19-O4-C3) deviate from the NMA plane by 0-5°, and the waterwhich attaches to the N2-H6 group (i.e., water O16-H17H18)is very flexible. The dihedral angle of O16-H6-N2-C1 canreach 34.02° in TI,II for the B3LYP calculation.To see how hydrogen bonding influences the structure of
NMA, we compared the main bond lengths and bond anglesbetween the isolated and hydratedt-NMA structures which areobtained from B3LYP/6-311++G(d,p) calculations. The sig-nificant changes of bond length occur on C3-N2 and O4dC3.The length of C3-N2 decreases with the increasing number ofhydrogen bonds formed between NMA and water molecules.From isolatedt-NMA to TI,II,III , it decreases by 0.02 Å (from1.3642 to 1.3436 Å). When three waters bind tot-NMA, theO4dO3 bond increases by about 0.02 Å. The bond lengths ofN2-C1 and C5-C3 do not change much. When a watermolecule attaches to the N2-H6 group (in TII, TI,II , TII,III , andTI,II,III ), the bond N2-H6 will increase by 0.005-0.007 Å. Thebond angles have no much changes from gas-phaset-NMA to
TABLE 2: Comparison of the Geometries of Isolated NMAa
a All full geometry optimizations were performed using the 6-311++G(d,p) basis set.b t-NMA geometries are ofCs symmetry withΦ ) ∠H7-C1-N2-C3) 180° andΨ ) ∠H10-C5-C3-N2 ) 0°. c c-NMA geometries are ofCs symmetry withΦ ) ∠H7-C1-N2-C3) 180° andΨ) ∠H10-C5-C3-N2 ) 180°. d See notationsa andb of Table 1.eAveraged value of all H-C1 and H-C5 bond lengths.f Averaged value ofall H-C-H angles in two methyl groups.
TABLE 3: Optimized Geometries of the Complex TIII(t-NMA H-Bonding with the Water at Position III in Figure1) Obtained from B3LYP, BLYP, HF, and MP2Calculations, Respectively, Using the Basis Set6-311++G(d,p)
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hydrated cases. Waters attaching to the C3dO4 group (in TI,TIII , TI,III , and TI,II,III complexes) tend to increase the angle C3-N2-C1 by 0.30-1.47°. When three waters attach to thet-NMAmolecule,∠O4dO3sN2 and∠C5-C3-N2 will increase by0.20° and 0.94°, respectively. Accordingly,∠C5sC3dO4decreases by 1.17°.The changes in bond lengths observed from isolatedc-NMA
to c-NMA complexes are very similar to those int-NMAcomplexes. After hydration, the C3-N2 bond also decreasesby∼0.02 Å, and the O4dC3 bond increases by∼0.02 Å (bothin the CI,III complex).All the bond lengths obtained from the BLYP method are a
little longer than the corresponding values predicted by B3LYPcalculations. But this does not mean that the BLYP results areworse than those of B3LYP. Considering that the hydrogen-bonded situation in TII,III is closer to that found in the NMAcrystal, we compared in Table 4 the four main bond lengths ofTII,III obtained from B3LYP and BLYP with the correspondingvalues in the crystal.15 We see that the bond lengths of N2-C1 and C5-C3 in the BLYP calculation are much closer to theexperimental results. The bond length of C3-N2 is in dispute.So only the O4dO3 bond length gotten from B3LYP (1.2338Å) is closer to the experimental value (1.236 Å) than thatobtained from the BLYP calculation (1.2470 Å). In summary,we find that the tendencies of changes in bond lengths and bondangles between different complex structures obtained fromBLYP results are the same as those obtained from B3LYPcalculations.All the H-bond lengths and H-bond angles got from B3LYP/
6-311++G(d,p) calculations are shown in Table 5. For almostall geometries, the H-bond length obtained from the BLYPcalculation is about 0.02 Å longer than the corresponding resultof B3LYP. The length of H6‚‚‚O16 is always longer than thelength of O4‚‚‚H13 and O4‚‚‚H19 bond. For both thet- andc-NMA complexes, when a water molecule attaches to the N-Hgroup, the H-bond lengths of O4‚‚‚H13 and O4‚‚‚H19 will bereduced by about 0.02 Å fort-NMA complexe and by about0.01 Å for c-NMA cases (from CIII to CII,III ). Similarly, theformation of a H-bond to the CdO group (in both directions)reduces the H6‚‚‚O16 bond length by about 0.02-0.03 Å forthe trans and by 0.02-0.05 Å for the cis complexes, respec-tively. These phenomena are in agreement with the corre-sponding results of Guo and Karplus.1
Although the direction of the H-bond N2-H6‚‚‚O16 whichattaches to the N-H group of t-NMA is flexible, the H-bondangle of∠N2-H6‚‚‚O16 (R3) is almost linear (from 178.12°to 179.73°) for all t-NMA complexes and for both B3LYP andBLYP calculations. The H bonds C3dO4‚‚‚H13 andC3dO4‚‚‚H19 are less linear than N2-H6‚‚‚O16. On the otherhand, the formation of the H bond to the N-H group makesthe two H bonds to the CdO group linear. For example,∠O20-H19‚‚‚O4 (R4) increases by about 5° from TIII to TII,III ;and∠O14-H13‚‚‚O4 (R1) increases by about 3° from TI toTI,II .3.4. H-Bond Interaction Energies. According to eqs 1 and
2, we calculated the interaction energies∆E for the 12
complexes using the functionals B3LYP and BLYP with thebasis set 6-311++G(d,p). To investigate the cooperative effect,we also calculated the∆∆E for the multiple-water complexes.∆∆E is defined as the difference between the∆E of a multiple-water complex and the sum of the∆E values for each of thecorresponding complexes involving a single water molecule.Recently, Dixon et al.3 studied the association energies of
five NMA ‚H2O complexes (corresponding to our TI, TII, TIII ,CI, and CIII structures) up to the MP2 level with the augmentedcorrelation consistent polarized valence double-ú basis set (aug-cc-pVDZ). They performed, however, only MP2 single-pointenergy calculations at the optimum Hartree-Fock structureswith only the valence electrons correlated. Our results of∆Efor the six single-water complexes are shown in the front partof Table 6. We also present the interaction energy of TIII
obtained by our MP2/6-311++G(d,p) calculation.The ∆E(CPC) values of HF/aug-cc-pVDZ calculations3
(-5.7,-3.5,-5.7,-6.8, and-5.6 kcal/mol for TI, TII, TIII ,CI, and CIII , respectively) are all much smaller than thecorresponding∆E(CPC) values obtained from MP2/aug-cc-pVDZ3 (-7.0, -4.8, -7.0, -8.9, and-7.0 kcal/mol for TI,TII, TIII , CI, and CIII , respectively) and from our B3LYP andBLYP calculations. On the other hand, the∆E(CPC) resultsfrom the B3LYP and BLYP calculations are comparable toDixon et al.’s corresponding MP2 results.The H-bonding effect further stabilizes thec-NMA structure.
The total energy difference between CI and TIII (the most stablesingle-watert-NMA complex) is only 0.37(0.38) kcal/mol forB3LYP(BLYP) result, while the∆E value between the isolatedc- and t-NMA is 2.52(2.42) kcal/mol obtained from B3LYP-(BLYP)/6-311++G(d,p) calculation.The total energies (E) and the interaction energies (∆E and
∆∆E) of the multiple-water NMA complexes are also given inTable 6. ∆E and ∆∆E are calculated with BSSE and withcounterpoise correction. The interaction energies (∆E) got byB3LYP calculations are larger than the corresponding valuesobtained by BLYP, but the∆∆E values of a certain complexobtained from the two methods are very similar.For all of thet- andc-NMA + 2H2O cases, we may observe
a cooperative effect in H bonding for the TI,II and TII,IIIcomplexes, i.e., the H-bond energies (∆E) of these two double-water complexes are larger than the sum of the∆E values ofthe corresponding single-water complexes (∆∆E’s are negativefor TI,II and TII,III ). This indicates that, as a result of thecooperative effect, the hydrogen bonds in the TI,II and TII,IIIcomplexes are more stable than those in TI, TII, and TIII .Looking at the∆∆E(CPC) values of TI,II and TII,III , we see thatthe cooperative effect stabilizes the two H bonds by an averagevalue of about 0.63 kcal/mol. On the contrary, the∆∆E’s ofthe TI,III , CI,III , and CII,III complexes are all positive. Thisindicates that the H bonds in TI,III , CI,III , and CII,III are less stablethan those in their corresponding single-water complexes.Because of the cooperative effect, at-NMA complex with
one H-bond (TI, TII, and TIII ) on either N-H or CdO groupfavors a second H bond formed at the other group. As discussedby Guo and Karplus,1 this cooperative effect may enhance thehydrogen bonding between peptide bonds and make the forma-tion of secondary structures more favorable. Although thestructure of TI,III is unstable, an extra H bond on the N-H groupmakes it stable. The∆∆E values ofTI,II,III are negative, meaningthat hydrogen bonding in TI,II,III is cooperative. Qualitatively,our ∆∆E results for TI,II , TI,III , and TI,II,III complexes are inagreement with Guo and Karplus’s ab initio calculations1 andBaudry and Smith’s molecular mechanics studies.2 The valuesof ∆E obtained by Guo and Karplus are usually larger than our
TABLE 4: Comparison of Four Main Bond Lengths inTII,III (t-NMA with Two H-bonded Waters at the Positions IIand III in Figure 1), Obtained from B3LYP and BLYP/6-311++G(d,p) Calculations, Shown Together with theObserved Values in the NMA Crystal15
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corresponding results, partly due to the BSSE contributions intheir numbers.For the c-NMA complexes, H-bonding effects make the
structures stable. From Table 6, we see that the total energy ofCI,III is the lowest one among our double-water complexes. Thisdoes not meanc-NMA is more stable thant-NMA in water.But it can explain the experimental observation thatc-NMAcan exist in aqueous solution.45-47 On the other hand, fromour interaction energy calculations, no cooperative effect isobserved for CI,III and CII,III complexes. This suggests thatc-NMA in an aqueous solution will be still unstable and this iswhy the concentration ofc-NMA in water is only a few percent.9
3.5. Stabilities of NMA in Different Methyl GroupOrientations. There are four kinds of methyl group orientationsin both planart- andc-NMA structures: (A)Φ ) Ψ ) 0° (H7-C1 and H10-C5 are cis to C3-N2); (B) Φ ) 180°, Ψ ) 0°(H7-C1 trans to C3-N2 and H10-C5 cis to C3-N2); (C)Φ) 0° andΨ ) 180° (H7-C1 cis to C3-N2 and H10-C5 transto C3-N2) and (D)Φ ) Ψ ) 180° (both H7-C1 and H10-C5 are trans to C3-N2). The isolated and hydrated NMAsthat we studied above are ofΦ ) 180°, Ψ ) 0° (B) for t-NMAandΦ ) Ψ ) 180° (D) for c-NMA. Hagler et al.47 analyzed
X-ray crystal structures for a number of simple amides andpeptides. They found that 6 of 12 molecules haveΦ close to180° and 8 of 10 molecules haveΨ close to 0°. Guo andKarplus’s HF/6-31G* calculations reveal that the orientationsof Φ ) 180° andΨ ) 0° are the minimal energy state for bothisolated and hydratedt-NMA. But the isolatedt-NMA struc-tures with different methyl orientations have similar energieswith a difference of only∼0.1 kcal/mol. Mirkin and Krimm’s6,7Hartree-Fock calculations indicate that in the gas-phase state,the lowest energy structure oft-NMA differs for different basissets. But for the hydrated state, the most stable structure is ofΦ ) 180°, Ψ ) 0° (B) for t-NMA, andΦ ) Ψ ) 180° (D) forc-NMA. Very recently, they8 studied the planarity of isolatedt-NMA starting from different initial geometries with HF andpost-HF methods. It seems that, the equilibrium structure oft-NMA has planar symmetry of (B).We wonder what kind of methyl group orientations cor-
respond to the minimal energy state of NMA in DFT calcula-tions. Using the potentials B3LYP and BLYP with diffrerentbasis sets, we optimized the isolatedt-NMA structures with themethyl orientations (A)-(D). The relative energies of thesefour structures according to different basis sets are shown in
TABLE 5: H-Bond Geometries of trans- and cis-NMA-Water Complexes, Containing Water Molecules at Different PositionsAs Defined in Figures 1 and 2, Respectively, Obtained from B3LYP/6-311++G(d,p) Calculations
BLYP -401.411 634 -13.42 -12.06 +0.06 +0.19a Total energy.b Interaction energy containing basis set superposition error (BSSE), calculated according to eq 1.c Interaction energy obtained
after counterpoise correction (CPC) according to eq 2.dDefined as the difference between the∆E(BSSE) of a multiple-water complex and the sumof the∆E(BSSE) values for each of the corresponding complexes involving a single-water molecule.eSubstitute∆E(BSSE) with∆E(CPC) in thedefinition of ∆∆E(BSSE).
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Table 7, with the BLYP results given in parentheses. Confor-mation (A) turns out to be the most stable form oft-NMA inall calculations. Using the basis sets 6-31G(d) and 6-311G-(d,p), the second and the third most stable conformationscorrespond to structures (C) and (B), respectively. But theenergy difference between (B) and (C) is very small (from 0.01to 0.12 kcal/mol). Then turning to the larger basis sets6-311++G(d,p) and 6-311++G(2d,2p), the second most stablestructure changes to conformation (B) and the energy differencebetween (B) and (C) becomes larger (more than 0.3 kcal/mol).On the other hand, the energy difference between (B) and (A)is very small (from 0.02 to 0.11 kcal/mol). The highest energystructure is conformation (D) in all calculations. To see ifconformation (A) is really the stationary structure and other onesare the transitional states, we performed frequency calculationsfor the optimized structures (A)-(D) using the B3LYP andBLYP potentials with the 6-31++G(d,p) basis set. We obtainedvery similar results from these two methods. There are 0, 1, 1,and 2 imaginary frequencies for structures (A)-(D), respec-tively. This means that conformation (A) is really the stationarystate fort-NMA, structures (B) and (C) are first order transitionalstates and structure (D) is a second-order transitional state. Ifwe add the zero-point vibrational energies to the molecular totalenergies, the energy of structure (B) turns out to be lower thanthat of structure (A) and the energy of structure (C) higher thanthat of structure (D). The relative energies for structures (A)-(D) are 0.06, 0, 0.28, and 0.22 kcal/mol in B3LYP calculations,and 0.14, 0, 0.36, and 0.18 kcal/mol in BLYP calculations.Furthermore, comparing the structure differences between (A)and (B) and between (C) and (D), we see that only the valuesof Φ are different from each other. Therefore, the tortionalpotential ofΦ seems to be so flat that it can essentially freelyrotate. Because the energy difference between (A) and (B) istoo small to be exactly predicted within the limits of accuracyof our calculation and it will be very sensitive to any kind ofexternal perturbations, one could imagine that the two structuresare basically equivalent minimum-energy states for isolatedt-NMA.To learn which methyl orientations correspond to the most
stable hydratedt-NMA structure, we optimized the complexesTI,II and TI,II,III with fixed Φ ) Ψ ) 0° (A) using the B3LYPmethod with the 6-311++G(d,p) basis set. We found that theenergies of these two complexes are higher than the corre-sponding ones withΦ ) 180°,Ψ ) 0° (B) which were obtainedin section 3.4. The energy difference between the two TI,II
structures is 0.45 kcal/mol and between the two TI,II,III structures0.33 kcal/mol. Therefore,t-NMA with methyl orientationsΦ) 180° andΨ ) 0° seems to be the most stable structure in ahydrated environment.We also performed full optimization calculations on isolated
c-NMA structures with methyl group orientations (A)-(D) usingthe B3LYP and BLYP functionals with the 6-311++G(d,p)basis set. The relative energies of the fourc-NMA structuresare shown in Table 7. For both methods, the most stablec-NMA conformation is structure (D) (Φ ) Ψ ) 180°).Conformations (C) and (B) are first-order transitional states,
and (A) is second-order transitional state. Unlike the case oft-NMA, the first two most stablec-NMA conformations (D andC) have a relatively large energy difference (0.30 and 0.26 kcal/mol for the B3LYP and BLYP, respectively). Further frequencycalculations show that, structure (D) is the stationary state ofc-NMA and (C) is a transitional state. After adding the zero-point vibrational energy, the total energy difference between(C) and (D) is still 0.30 kcal/mol in the B3LYP/6-311++G-(d,p) calculations. To see if the hydratedc-NMA with Φ ) Ψ) 180° (D) is still the most stable structure, we optimized thecomplex CI,III with methyl orientationsΦ ) 0° andΨ ) 180°(C). We found that the energy of CI,III with structure (C) isstill higher than that with methyl orientations (D). The energydifference between the two CI,III structures is 0.35 kcal/mol.Therefore, it seems that the most stable hydratedc-NMA hasstill the Φ ) Ψ ) 180° methyl orientations.
4. Conclusions
From the comparison of the qualities of six DFTEXCfunctionals, we chose the B3LYP and BLYP functionals toperform full geometry optimizations for isolatedt- andc-NMAand 12 NMA-water complexes with the relatively large basisset 6-311++G(d,p). Considering the electron correlation effectis very important in studying the conformations and thehydrogen-bonding properties of amide and peptide systems.However, conventional many-body perturbation theory calcula-tions (such as MP2) are very time consuming for systems ofthis size. Density functional theory (DFT), as a cost-effectivecomputational procedure, will provide a powerful alternativein this field.Within a certain basis set, the bond lengths of NMA obtained
from B3LYP are in very good agreement with and some areeven better than the corresponding ones of MP2 results. Thebond lengths in BLYP calculations are always a little longerthan the B3LYP results. But the conformations of isolatedt-NMA obtained from these two methods are all consistent withthe experimental data of gas-phase electron diffraction.16 Thebond angles obtained from the B3LYP, BLYP, and MP2calculations do not show much difference. Comparing thegeometries of TIII in Table 3, we found that including electroncorrelation (in the B3LYP, BLYP and MP2 methods) willincrease the covalent bond lengths by up to 0.02 Å and decreasethe H-bond length by about 0.1 Å.Hydrogen-bonding effects will substantially influence the
conformational properties of NMA. After hydration, the C3-N2 bond will decrease and the O4dC3 bond will increase byabout 0.02 Å both fort- andc-NMA. The most stable structureof a hydratedt-NMA is that with the methyl orientationsΦ )180° andΨ ) 0°. While, in the gas-phase state, angleΦ oft-NMA can be considered rotating freely.Cooperative effects in hydrogen bonding were found for the
TI,II and TII,III complexes. The H-bond lengths H6‚‚‚O16,O4‚‚‚H19, and O4‚‚‚H13 are shortened by about 0.02 Å ascompared with the corresponding ones in TI, TII, and TIIIcomplexes. No H-bonding cooperativity was found in our
TABLE 7: Energy Differences (kcal/mol) between Isolated NMA Structures with Different Methyl Group Orientations,Obtained from B3LYP and BLYP Full Optimization Calculations, with the BLYP Results in Parentheses
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c-NMA-multiwater complexes. This can be a significantreason thatc-NMA is still unstable in water.In summary, as an improvement of the conventional ab initio
Hartree-Fock procedure, the DFT/B3LYP and BLYP methodscan give reliable results for the studying the properties of theNMA-water systems. We feel confident that the DFT proce-dures can also be further applied to study the amide-amideinteractions and the properties of oligopeptide systems.
Acknowledgment. The authors are grateful to Karl Jalkanenfor helpful discussions, to Gerd Ra¨ther for his help in performingthe counterpoise correlations, and to Martin Reczko for hisassistance in the computations. The generous support withcomputer time on the CONVEX and IBM/SP2 of DKFZ aregratefully acknowledged. This research has been supported bythe Commission of European Union (Grant No. CT-93-006).
References and Notes
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