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Chemical Physics 322 (2006) 289–297

Characterization of conformers of non-ionized proline on the basisof topological and NBO analyses: Can nitrogen be a donor of

hydrogen bond?

Ali Ebrahimi *, Hosein Roohi, Mostafa Habibi, Marzie Mohammadi, Rahele Vaziri

Department of Chemistry, University of Sistan & Balouchestan, Zahedan 98135-674, Iran

Received 19 May 2005; accepted 17 August 2005Available online 4 October 2005

Abstract

A detailed population analysis of 10 most stable conformers of neutral proline was undertaken by the natural bond orbitals (NBO)and the atoms in molecules (AIM) methods. The optimized geometries (at MP2/6-311++G(d,p) level) were employed to perform theNBO analysis and also to obtain the suitable wave function files for the AIM analysis. With the exception of OH� � �NH and CH� � �OHhydrogen bond critical points, corresponding to four conformers, the BCPs can be observed just for those which located at the inter-atomic paths that are defined by the covalent bonds. The charge transfer energy of nðNÞ ! r�O–H interactions are 18.31 and15.63 kcal/mol which are related to conformers that exhibit the OH� � �NH hydrogen bonds. Similar interactions higher than 0.5 kcal/mol threshold limit do not observe for other conformers. Thus, the NBO and AIM analyses do not confirm the presence of N–H� � �O@Cand N–H� � �O–H hydrogen bonds in the conformers of proline. On the other hand, improper hydrogen bonds (C–H� � �O–H) reveal intwo conformers.� 2005 Elsevier B.V. All rights reserved.

Keywords: Amino acid; Proline; Hydrogen bond; NBO; AIM

1. Introduction

Amino acids are biochemical building blocks. Proline isa major amino acid which is found in cartilage and it is alsoimportant for maintaining youthful skin, repair of muscle,connective tissue and skin damage [1].

Experimental information about the proline demon-strated that the proline molecules exist in the neutral formin the gas phase (Fig. 1) [2]. The conformational structuresof proline have been studied by both experimental and the-oretical methods. For example, a theoretical study located12 conformers of proline at the B3LYP/6-311++G(d,p)level [3]. Also, the conformational structures of prolinehave been investigated using the matrix-isolation techniqueand ab initio calculations by Adamowicz and co-workers

0301-0104/$ - see front matter � 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.chemphys.2005.08.039

* Corresponding author. Fax.: +98 541 244 6565.E-mail address: ebrahimi@hamoon.usb.ac.ir (A. Ebrahimi).

[4]. Their calculations were carried out at B3LYP/aug-cc-PVDZ level, and 15 conformers of proline were found.Ten conformers are illustrated in Fig. 1 and the rest ofthem (five conformers) can be obtained from these in aninterchangeable approach by rotation about C–OH bondby approximately 180�. They presented evidence of exis-tence of two conformers of proline with different intramo-lecular hydrogen bonds in the matrix: the lowest energyconformer with an N� � �H–O intramolecular hydrogenbond and the second conformer with an N–H� � �O@Chydrogen bond. The intramolecular N� � �H–O hydrogenbond in the lowest energy conformer was much strongerthan the corresponding hydrogen bond in other aminoacids. Also, the experimental structures of neutral prolinehave been reported with the analysis of the rotational spec-trum in a collisionless environment of a supersonic jet [5].

At the present work, a detailed population analysis of 10most stable conformers (Fig. 1) of neutral proline was

Fig. 1. The most important geometrical parameters needed to characterize the 10 low energy conformers of proline.

290 A. Ebrahimi et al. / Chemical Physics 322 (2006) 289–297

undertaken by natural bond orbitals (NBO) [6] and atomsin molecules (AIM) [7] methods. The NBO and AIM anal-yses indicated no evidence for N–H� � �O@C hydrogenbonds in the conformers 2a and 2b, and also N–H� � �O–Hhydrogen bonds in the conformers 3a and 3b. On the otherhand, improper hydrogen bonds (C–H� � �O–H) revealed inthe conformers 4a and 4b.

2. Computational methods

The ab initio geometry optimizations and frequency cal-culations were performed with Gaussian 98 package [8]using 6-311++G(d,p) [9] basis set and the post-Hartree–Fock at the second order Møller–Plesset (MP2) level [10].The nature of the optimized structures as potential energyminima have been established at the MP2/6-311++G(d,p)levels in all cases by verifying that all the corresponding fre-quencies to be positive. Then, the optimized geometrieswere used to perform NBO analysis and also to obtainthe suitable wave function files for AIM analysis.

In the topological theory of AIM, [7] the chemical bondsand molecular reactivity is interpreted in terms of the totalmolecular electronic density, q(r), and its correspondingLaplacian, $2q(r). The values of q(r) and the $2q(r) atthe bond critical point (BCP) allow the characterizationof the chemical bonds of the atoms in the molecules.Another parameter used to describe a bond is the ellipticity(e) that shows if the electronic charge is preferentially accu-mulated in a given direction between two bonded atoms.The atomic basins in AIM theory are separated by surfacesdefined by the condition

rqðrÞT � nðrÞ ¼ 0

for all points r in the surface where $q(r) is the gradientvector of q(r), and n(r) is the vector normal to the surface.Atomic properties are then calculated by 3D volume inte-grations over the atomic basins.

Here, the topological properties of the electronic chargedensity have been characterized using the AIM methodol-ogy with the AIM2000 program package [11] on the wavefunctions obtained at MP2/6-311++G(d,p) level. Most ofthese calculations were not possible with the default set-tings; to meet the Poincare–Hopf criterion, additional crit-ical points were sought with the decrement of stepsize. Acorrect topology of the gradient vector field is the first nec-essary condition to confirm the presence of a hydrogenbond [12]. In addition, there are other criteria. Two criteriaare connected to the electron density (qBCP) and Laplacian($2qBCP) of the electron density which are evaluated atH-bond critical point. The typical ranges of qBCP and($2qBCP) for H-bonding are 0.002–0.035 e=a3

0 and 0.020–0.139 e=a5

0, respectively.The NBO analyses were carried out on the MP2/6-

311++G(d,p) wave functions obtained for this basis setgeometries using the NBO package included in the Gauss-ian 98 suite of programs [13]. The NBO package includes asuite of methods for describing the N-electron wave func-tion in terms of localized orbitals or configurations thatare closely tied to chemical bonding concepts. Underlyingthese methods are the sets of localized intrinsic naturalatomic orbitals (NAOs) and bond orbitals (NBOs) whichare in close correspondence with the Lewis structure

Table 1Relative stabilization energies (including the zero point energy), enthal-pies, and Gibbs free energies (in kJ mol�1) of the conformers of proline

DEtot DH DG

1a �7.36 (�7.1) �8.36 �5.351b �4.39 (�4.7) �5.07 �3.722b 0.00 (0.0) 0.00 0.002a 0.56 (0.4) 0.55 �0.193b 5.58 (6.0) 5.73 3.674a 6.89 6.93 7.014b 8.50 8.52 8.283a 8.53 8.73 7.435b 9.40 9.45 9.485a 9.91 9.99 10.05

The data in the parentheses were taken from [3].

A. Ebrahimi et al. / Chemical Physics 322 (2006) 289–297 291

representations used by chemists [6]. These orbital setsare natural in the sense that the NBO algorithm tends tomaximize the electron density in the formally filled coreand valence functions. The occupancy of an orbital, eitherNAO or NBO, is given by its diagonal density matrix ele-ment, and atomic populations are obtained as sums ofNAO occupancies. The strengths of the orbital interactionscan be estimated by perturbative analysis of the Fockmatrix in the NBO basis. These analyses were performedto understand some factors contributing to the stabilityof conformers.

3. Results and discussion

3.1. Geometric and energetic aspects

The preliminary study of the present work was to opti-mize the geometries of 10 lowest energy conformers of pro-line. The conformational structures were optimized usingthe standard optimization at the MP2/6-311++G(d,p)level. The most important geometrical parameters neededto characterize these structures are illustrated in Fig. 1.The optimized geometry parameters of four lowest energyconformers of proline were previously obtained in theMP2/Aug-cc-pVDZ level [4]. But, the geometries of 10lowest energy conformers have been optimized at the men-tioned level to identify the relevant wave functions in orderto determine the electronic properties.

With respect to the relative directionality of COOHgroup and ring, a hydrogen bond is predicted: (1) betweenthe nitrogen atom of ring and the hydrogen atom of hydro-xyl group (N� � �H–O, type 1), (2) between the hydrogenatom of imino group and the oxygen atom of carbonylgroup (N–H� � �O–C, type 2), (3) between the hydrogenatom of the imino group and the oxygen atom of hydroxylgroup (N–H� � �O–H, type 3), (4) between the oxygen atomof OH group and a hydrogen atom of the ring (H–O� � �H–C weak hydrogen bond, type 4), and finally (5) between theoxygen atom of CO group and a hydrogen atom of the ring(C–O� � �H–C weak hydrogen bond, type 5). Conformers a

and b differ in the ring pucker; a and b stand for endo-likeand exo-like conformations of pyrrolidine ring with respectto the carboxy moiety.

The relative stabilization energies, including the zero-point energy corrections (Etot), were evaluated at theMP2/6-311++G(d,p) level, and the obtained results arereported in Table 1. The relative enthalpies and Gibbs freeenergies are gathered in Table 1. As can be seen, the entro-pic effects change the relative stability of 2a and 3a with 2b

and 4b, respectively. The MP2 method is not able to predictthe relative energies of the conformers of proline with aquantitative accuracy [4], but it predicts the order of rela-tive stability of these conformers.

The characteristic geometrical parameters of these con-formers can be mentioned as follow: (1) The geometry offive-membered ring of atoms 1, 2, 6, 8, and 9 is approxi-mately planar in the conformers of type 1. Similar five-

membered rings are indicated in the conformers of types2, 3, and 5 with lesser planarity. Six and seven-memberedrings are illustrated in the conformers of type 4. (2) TheX–H� � �Y angle is equal to 130.6� (129.6�), 113.4� (103.2�),108.0� (100.3�), 107.6� (106.8�), and 97.1� (104.7�) in thetypes 1-5, respectively; the data in the parentheses are rele-vant to the type b. This angle is more suitable for hydrogenbond formation in the type 1. (3) Both C4–H14 and C5–H12 bond lengths of type 4 are slightly smaller than theothers. (4) With the exception of 4, the C5–H12 bond inthe conformers of type b is longer than the conformers oftype a.

With respect to the mentioned discussion, the questionthat would be made is that: do the five-membered ringrestriction and unsuitable relative orientation of H-donorsand H-acceptors permit hydrogen bond formation in thetypes 2, 3, and 5? Answer to this question is one of ourinterests in this work which would be followed in the nextsections.

3.2. Electronic properties

3.2.1. AIM analysis

In an attempt to characterize hydrogen bonds in a rigor-ous manner with the AIM theory, Popelier and co-workersstudied systems with well-known intermolecular H-bondsand proposed eight AIM-based criteria indicative of hydro-gen bonding [12,14,15]. Four of them are relevant to thetopological properties of the electron density. The othersare related to the integrated properties of the H atom. Theybelieved that the possible H-bonds which fail one or moreof these criteria can not be accounted as the real H-bonds.In this circumstance it is also assumed that they are equallyapplicable to the intermolecular and intramolecular hydro-gen bonds [14].

In order to have a deeper knowledge of the nature of thepossible hydrogen bonds in the conformers of proline, atopological analysis of the electronic charge density, q,and its Laplacian, $2q, were performed using the AIMtheory [16]. It is necessary to remember that $2q identifiesregions of space where the electronic charge is locally dep-leted ($2q > 0) or built up ($2q < 0). The former situation

292 A. Ebrahimi et al. / Chemical Physics 322 (2006) 289–297

is typically associated with the interactions between closedsystems (ionic bonds, hydrogen bonds, or van der Waalsinteractions), while the latter characterizes covalent bonds,where the electronic charge is concentrated between thenuclei. There are, however, significant exceptions to thisgeneral rule, mainly when highly electronegative atomsare involved in the bonding. Hence, we have also evaluatedthe energy density [17], H, which does not show theseexceptional features; in general, negative values of H areassociated with a stabilizing charge concentration withinthe bonding region.

In this work, with the exception of 1a, 1b, 4a, and 4b, theonly observed BCPs are those which located at the inter-atomic paths that are defined by the covalent bonds. Theyare illustrated by red spheres in the molecular graphs inFig. 2. Thus, the extra bond critical points (BCP) can beobserved only for these conformers in the paths joiningN1 and H9 (1a and 1b), O8 and H14 (4a), and O8 andH12 (4b) atoms. Moreover, the extra ring critical points(RCP) in the interior of the five and six-membered ringsformed by N1C2, C2C6, C6O8, O8H9, and H9� � �N1 (1a

and 1b), C4C3, C3C2, C2C6, C6O8, O8H14, and H14C4(4a), and N1C2, C2C6, C6O8, O8H12, H12C5, C5N1(4b) paths. The conformers 1a and 1b display similar fea-tures and roughly same lengths for the N1� � �H9 bonds(1.828 A in 1a and 1.858 A in 1b) and also approximatelyalike distances between the N1� � �H9 BCPs and the RCPs(1.845 A in 1a and 1.860 A in 1b). However, 4a and 4b

exhibit a different situation. In fact, the close proximitybetween BCP and RCP (0.110 A in 4a and 0.003 A in 4b)reveals a clear instability in the associated bond [14].

In addition, the map of q has been plotted for 1a in theplane containing the N1, O8, and H9 atoms and 2a in the

Fig. 2. Molecular graphs for conformers 1a, 1b, 4a, and 4b. Small red spher(BCP), ring critical points (RCP), and bond paths, respectively.

Fig. 3. Contour map of the MP2/6-311++G** electron density for conformer (containing the N1, H11, and O7 atoms.

plane containing the N1, H11, and O7 atoms (Fig. 3). Ascan be seen, the improper orientation of N–H with respectto the O atom can be accounted a remarkable factor for theabsent of a bond critical point between them. The countermaps of electron density for 4a and 4b show that the orien-tation of C–H with respect to the O atom is not proper andthis interaction may be very weak.

The values of the electron density (q), its Laplacian($2q) and the energy density (H) at the hydrogen bondcritical points, as well as the bond ellipticities e are re-ported in Table 2 for conformers 1a, 1b, 4a and 4b. Itmust be noted that the two negative eigenvalues k1 andk2 of the Hessian of density in a (3,�1) BCP are usedto define e [=(k1/k2) � 1]. The ellipticity is taken as a mea-sure of the extent to which q is accumulated in the planedefined by the axes of curvature k1 and k2, both perpen-dicular to the bond path.

With respect to the interaction energy EI, which isdefined as the energy of hydrogen-bonded complex minusthe sum of energies of monomers for intermolecular hydro-gen bonds, the HBs can be classified as weak, medium andstrong. A hydrogen bond is weak when EI is less than12.0 kcal/mol, medium when EI is between 12.0 and24.0 kcal/mol, and strong when this interaction is greaterthan 24.0 kcal/mol [18]. By considering the classificationof HBs, Rozas and co-workers have found that the weakHBs show both $2qBCP and HBCP > 0, and the mediumHBs illustrate $2qBCP > 0 and HBCP < 0, while the strongHBs (and therefore low-barrier hydrogen bond interactionswhich are particularly short and strong interactions) exhibitboth $2qBCP and HBCP < 0 [19]. From the obtained resultsof the current work, the N� � �HO hydrogen bonds of theconformers 1a (q = 0.041849, $2qBCP = 0.12755, HBCP =

es, small yellow spheres, and lines correspond to the bond critical points

a) 1a in the plane containing the N1, O8, and H9 atoms, (b) 2a in the plane

Table 2Critical point properties (in a.u.) of electron density for conformers 1a, 1b,4a, and 4b of proline

q $2q H e

1a

N1� � �H9 0.042 0.128 �0.004 0.010O8–H9 0.338 �2.492 �0.681N1–H11 0.344 �1.679 �0.475

1b

N1� � �H9 0.039 0.124 �0.003 0.013O8–H9 0.341 �2.523 �0.688N1–H11 0.345 �1.675 �0.475

4a

O8� � �H14 0.007 0.030 0.001 2.92C4–H14 0.284 �1.021 �0.295O8–H9 0.361 �2.663 �0.725

4b

O8� � �H12 0.007 0.031 0.001 120.4C5–H12 0.287 �1.047 �0.298O8–H9 0.361 �2.661 �0.724

A. Ebrahimi et al. / Chemical Physics 322 (2006) 289–297 293

�0.00408) and 1b (q = 0.038623, $2qBCP = 0.124159,HBCP = �0.00257) are classified as medium HBs and theCH� � �OH hydrogen bonds of the conformers 4a (q =0.006597, $2qBCP = 0.030278, HBCP = 0.001244) and 4b

(q = 0.007063, $2qBCP = 0.030606, HBCP = 0.001248) areplaced in the weak HB category. The values of q and $2qat the N1� � �H9 bond critical point of 1a are greater thanthe corresponding values of 1b. On the other hand, theN1� � �H9 bond length of 1a is shorter than the correspond-ing value of 1b (see Fig. 1). Thus, the N1� � �H9 hydrogenbond in 1a is stronger than 1b.

The differences between q, $2qBCP, and HBCP values atthe O–H bond critical point of conformers 1a-5a fromthe corresponding values of 5b are given in Table 3. Thesedata are also in agreement with the previous result(N1� � �H9 bond in 1a is stronger than 1b).

The values of q and $2q at the CH� � �O bond criticalpoint of 4b are slightly greater than the correspondingvalues of 4a. The H� � �O bond length of 4b is approximately0.02 A greater than the corresponding value of 4a but C–H–O bond angle of 4a (107.6�) is bigger than the relatedvalue of 4b (106.8�). Furthermore, the C2–O8–H12–C5

Table 3The differences between q, $2qBCP, and HBCP values (in a.u.) at the O–H and N5b

1a 1b 2a 2b

O–Hq 0.023 0.020 0.001 0.001$2q 0.043 0.036 0.000 0.001H �0.044 �0.037 0.000 �0.001

N–Hq 0.000 0.000 0.000 0.001$2q �0.010 �0.009 �0.019 �0.013H 0.008 0.007 0.017 0.010

dihedral angle of 4b (�2.7�) is smaller than the C2–H8–H14–C4 dihedral angle of 4a (13.3�). Thus, the orientationof C–H group with respect to the O atom in 4b is more suit-able than 4a; this orientation is more important than theH� � �O bond length.

In the earlier works, the N–H� � �O–C hydrogen bondhas been considered for the conformer 2b [4]. By our calcu-lations, a bond critical point has not been indicatedbetween H11 and O7 in the conformers 2a and 2b andbetween H11 and O8 in the conformers 3a and 3b (see Figs.3 and 4). The distance between H11 and O in theseconformers (2.22–2.43 A, see Fig. 1) is greater than theconformers 1a and 1b (1.83 and 1.86 A, respectively). Also,the orientation of N1–H11 towards the O atom is not suit-able for an appropriate hydrogen bond interaction in theconformers 2a–3b.

The differences between q, $2qBCP, and HBCP values atthe N–H bond critical point of all conformers and thecorresponding values of 5b are given in Table 3. The differ-ences are small and very similar for the entire conformers.Hence, the obtained data are compatible with the previousargument that has been predicted the lack of the N1–H11� � �O hydrogen bond in the conformers 2a–3b.

Using the AIM methodology, the properties of theatoms involved in the HBs have been applied to character-ize these interactions [12]. However, several employedproperties in the original study have shown exceptions[20], nevertheless they can present useful information onan initial analysis of these interactions. In other words,four criteria of proposed AIM-based criteria indicative ofhydrogen bonding refer to the integrated properties ofthe H atom. Upon formation of an H-bond (1) an increaseof the net positive atomic charge (loss of charge), (2) anatomic energy destabilization in the hydrogen involved inHBs, (3) a decrease in the dipolar polarization, and (4) areduction of the hydrogen atom�s volume in HBs has beengenerally observed.

With respect to these criteria, the AIM integrated prop-erties of the H9 and H11 atoms of all conformers arereported in Tables 4 and 5. A 0.001 e/a.u.3 electron densityhas been used to define the atomic volume. A check on theaccuracy of the numerical integrations is provided by L(X),the integral of $2q over the basin X of the atom: due to theboundary condition of zero flux to define X, it must be

–H bond critical points of each conformer and the corresponding values of

3a 3b 4b 4a 5a

0.001 0.001 0.000 0.000 0.0000.001 0.001 0.001 0.001 0.001�0.001 �0.001 �0.001 0.000 0.000

0.000 0.000 0.000 0.000 0.000�0.008 �0.010 �0.001 �0.008 �0.008

0.006 0.007 0.001 0.006 0.006

0

0.4

0.8

1.2

1.6

2

-10.00 -5.00 0.00 5.00 10.00 15.00θ/degrees

Δ/

Ekc

al/m

ola

0

0.4

0.8

1.2

1.6

2

-15 -10 -5 0 5 10

θ/degrees

ΔEkcal/mol

b

0

0.5

1

1.5

2

2.5

-30 -25 -20 -15 -10 -5θ/degrees

ΔE/

ackl/m

ol

c

0

0.5

1

1.5

2

2.5

-20 -15 -10 -5 0 5

θ/degrees

ΔE/

ackl/ m

old

Fig. 4. The changes of DE versus h for: (a) the most important interactions of 1a, (b) the most important interactions of 1b, (c) the most importantinteractions of 2a, and (d) the most important interactions of 2b. Here, DE ¼ Eð2Þ � Eð2Þmin and h = N1C2C6O7. Energies are in kcal/mol and angles are indegrees.

Table 4Integrated atomic properties (in a.u.) of H9 and H11 atoms of conformers 1a–5b

H9 H11

q E V L q E V L

1a 0.668 �0.3069 �0.6153 �0.0009 0.373 �0.4762 �0.9547 �0.00031b 0.670 �0.3057 �0.6127 �0.0010 0.368 �0.4794 �0.9613 �0.00022a 0.630 �0.3350 �0.6713 �0.0001 0.389 �0.4715 �0.9455 �0.00112b 0.610 �0.3499 �0.7012 0.0002 0.387 �0.4682 �0.9389 �0.00083a 0.638 �0.3302 �0.6617 0.0004 0.369 �0.4806 �0.9639 �0.00113b 0.635 �0.3315 �0.6642 0.0003 0.370 �0.4769 �0.9562 �0.00134a 0.632 �0.3343 �0.6698 0.0005 0.364 �0.4803 �0.9631 �0.00044b 0.630 �0.3351 �0.6716 0.0005 0.351 �0.4881 �0.9788 �0.00035a 0.633 �0.3326 �0.6665 0.0003 0.365 �0.4795 �0.9614 �0.00035b 0.630 �0.3344 �0.6701 �0.0004 0.350 �0.4882 �0.9789 �0.0003

q, E, V, and L correspond to the atomic charge, energy of atom, atomic volume, and the integral of $2q over the basin of H9 or H11 atom, respectively.

294 A. Ebrahimi et al. / Chemical Physics 322 (2006) 289–297

zero. The values of L (see Tables 4 and 5) are in the rangeof 1 · 10�4 to 11 · 10�4 which is known to represent errorsin the estimates of energies of �10�4 hartrees [16].

In the study of intramolecular hydrogen bonds, thechanges of the above noted atomic properties can not beevaluated with respect to the isolated monomers, but to aconformer with a similar H bond not possible in it. InTable 4, the increase of atomic charge, energetic destabili-zation, decrease of dipolar polarization, and decrease ofatomic volume are observed for the H9 atom of the con-formers 1a and 1b in comparison with other conformers.However, the H11 atom of both 2a and 2b approximately

fails to meet these criteria. Therefore, they can not forma true intramolecular H-bond. In light of these criteria,the properties of the H-bond in 1a and 1b are nearly indis-tinguishable. Note how the hydroxyl bond length increasesin these conformers, as should be expected upon formationof the N1� � �H9O8 hydrogen bond according to the tradi-tional chemical criteria (1.828 and 1.858 A in 1a and 1b,respectively).

In the bibliography, it is traditional to treat the interac-tion between H11 and O7 (or O8) atoms as a true H-bondin the conformers 2a–3b. No hydrogen bond is shown bet-ween H11 and O7 (or O8) atoms on the basis of Popelier�s

Table 5A selection of NBO results (in kcal/mol) for the 10 conformers of prolineand the pyrrolidine ring

a b

1

n(N)! r*(OH) 18.31 15.63n(N) 1.92213 1.92889r*(OH) 0.03491 0.02965

2

n(2,O7)! r*(NH) 1.00 –n(2,O7) 1.88773 1.88213r*(NH) 0.01218 0.01077

3

n(1,O8)! r*(NH) 0.51 �n(1,O8) 1.98182 1.97940r*(NH) 0.01291 0.01055

4

n(O8)! r*(CH) – –n(1,O8) 1.98137 1.98143r*(CH) 0.01236 0.01881

5

n(N) 1.94168 1.94817n(O7) 1.97945 1.97949n(O8) 1.98186 1.98213r*(OH) 0.00752 0.00768r*(NH) 0.00928 0.01085r*(CH) 0.00811 0.00969

A. Ebrahimi et al. / Chemical Physics 322 (2006) 289–297 295

criteria but the integrated atomic properties of these con-formers (see Table 4) reveal valuable information accord-ing to the interactions involving the H11 atom. The q

value is slightly larger in the conformers 2a and 2b, whereasatomic volumes and energy values show no clear separa-tion. However, according to Popelier�s criteria no realintramolecular H-bond may be identified in conformers2a and 2b, but an interaction somewhat suggestive ofhydrogen bonding seems to exist between O7 and H11atoms of them. This could be understood in conventionalterms by thinking that the oxygen of hydroxyl group is aworse hydrogen acceptor than the oxygen of carbonylgroup.

3.2.2. NBO analysis

The formation of a hydrogen-bonded complex impliesthat a certain amount of electronic charge is transferredfrom the proton acceptor to the proton donor. In addition,there is a rearrangement of electron density within eachpart. Also, the NBO analysis of several typical hydrogen-bonded systems has demonstrated a charge transfer fromthe lone pairs of the proton acceptor to the antibondingorbital(s) of the proton donor [21].

In the current work, the NBO analysis was performedand a selection of the results was reported in Table 5 forthe 10 conformers of proline and also the pyrrolidine ring.This Table summarizes the second order perturbative esti-mates of ‘‘donor–acceptor’’ (bond–antibond) interactionsfor the couple [lone pair/OH (or NH) antibond] on thebasis of NBO with the limit of 0.5 kcal/mol threshold.

On passing from the isolated pyrrolidine ring (or a non-H-bonded conformer) towards an H-bonded conformer ofproline, it is expected that the characters of the lone pairsignificantly change: its population and stabilization energyincrease. Both of these aspects indicate a strong H-bondinginteraction.

As can be seen from the recorded results of Table 5, inthe conformers 1a and 1b, the electronic charge is trans-ferred from a lone pair orbital (n) of the N atom in thedonor fragment to a r�O–H antibonding orbital of theacceptor fragment; the lengthening of the O–H bond is aresult of such r�O–H character. The charge transfer energiesof n! r�O–H, listed in Table 5, are 18.31 and 15.63 kcal/mol for 1a and 1b, respectively. In the conformer 1a, thecharge transfer energy is greater than the conformer 1b.(see Table 5).

Moreover, the charge transfer from a lone pair orbital ofthe O atom in the donor fragment to a r�N–H antibondingorbital of the acceptor fragment is little in the conformers2a and 2b; the lengthening of the N–H bond is notobserved in these cases. The charge transfer energy ofnð2;OÞ ! r�O–H is 1.00 kcal/mol for the conformer 2a andlower than the threshold limit of 0.5 kcal/mol for the con-former 2b. There are not any similar interactions higherthan the mentioned threshold limit for the other confor-mers.

A further analysis was undertaken on the real nature ofthe specific and non-specific interactions acting betweenring and COOH group in the conformers of proline. In thisanalysis, the N1C2C6O7 = h dihedral angle was scannedaround the optimized value where other geometricalparameters were fixed and the NBO analysis performedfor each point. In order to have a reasonably limited num-ber of data (interaction energies) which are essential tointerpret, the interactions between the owned orbitals ofthe COOH group and the orbitals which belong to thefive-membered ring have been considered.

In the conformers 1a and 1b, from 160 donor–acceptorinteractions higher than the threshold limit, approximately60 interactions are between the owned orbitals of theCOOH group and the orbitals that belong to the five-mem-bered ring. Firstly, the differences between E(2) and Eð2Þmin

(Eð2Þmin is the minimum value in the scanned range) versus hhave been plotted for the entire of these interactions. Then,the most important curves (with the greatest changes of DE

versus h) have been selected and collected in separatedgraphs in Figs. 4(a) and (b). As can be observed, the mostimportant common interactions are n(N)! r*(O8H9),ðC2C3Þ ! r�2ðC6O7Þ, and rðC2H10Þ ! r�2ðC6O7Þ forconformers 1a and 1b. Also, ðC2H10Þ ! r�1ðC6O7Þ and(C2H10)! r*(C6O8) interactions have considerablechanges in the scanned ranges of 1a and 1b, respectively.Among these interactions, n(N)! r*(O8H9) has a maxi-mum around the stationary point for both conformers.Other interactions change linearly in the scanned region.

It is expected that the less important interactions arealso important (less than the previous interactions) on the

0

0.002

0.004

0.006

-10 -5 0 5 10 15

θ/degrees

Δn/e

σ(C2C3)σ(C2H10)σ(2 ,C6O7)n(N1)σ*(1,C6O7)σ*(2,C6O7)σ*(O8H9)

0

0.001

0.002

0.003

-15 -10 -5 0 5 10

θ/degrees

Δn/e

s(C2C3)s(C2H10)n(N)s*(2,C6O7)s*(O8H9)

a b

Fig. 5. The changes of Dn versus h for the most important orbitals of: (a) 1a, (b) 1b. Here, Dn = n � nmin and h = N1C2C6O7.

0.4

0.6

0.8

θ/degrees

0

0.0004

0.0008

-30 -20

b

a

0 0 10 20

Fig. 6. The changes of (a) DE (in kcal/mol) versus h for then(2,O7)! r*(NH) interaction of 2a and (b) Dn against h for r*(NH) in2a. The dihedral angle of the stationary point (h = �16.240�) is shown bya dashed line.

296 A. Ebrahimi et al. / Chemical Physics 322 (2006) 289–297

stability of these conformers. The most important inte-ractions of this group are r2(C6O7)! r*(C2C3) andr�ðC6O7Þ ! r�1ðC2H10Þ for 1a and r1ðC6O7Þ ! RY�1-ðC2Þ and r�ðC6O7Þ ! r�1ðC2H10Þ for 1b.

On the other hand, the differences of occupation num-bers of orbitals from the minimum value (Dn = n � nmin)against h have been also plotted in the scanned range andthen the most important curves have been selected for 1a

and 1b (see Figs. 5(a) and (b)). As can be seen, the changesof Dn for r�2ðC6O7Þ, r*(O8H9), n(N), and (C2H10) aregreater than the others. In this range, the curve of Dn

versus h has a minimum for n(N) and also a maximumfor r*(O8H9). All these orbitals participate in the mostimportant donor–acceptor interactions. Furthermore, thecurve of Dn against h indicates a maximum at the station-ary point for r*(O8H9); therefore, the O–H� � �N hydrogenbond may be formed in the conformers 1a and 1b.

The changes of the most important interactions and thechanges of occupation numbers of the related orbitals arenot generally in the same direction due to the other involvedinteractions that have been deleted from these figures. Thisobservation is also recognizable for other conformers.

A similar investigation was undertaken on the conform-ers 2a and 2b and the most important interactions werereported in Figs. 4(c) and (d). The most considerable inter-actions are rðC2C3Þ ! r�1ðC6O7Þ, rðC2C3Þ ! r�2ðC6O7Þ,rðC2H10Þ ! r�1ðC6O7Þ, and rðC2H10Þ ! r�2ðC6O7Þ inthese conformers. These interactions are very significanton the stability of these conformers. The changes of then(2,O7)! r*(NH) interaction of the conformer 2a versush is separately illustrated with an expanded range inFig. 6(a) and the dihedral angle that correspond to the sta-tionary point (h = �16.240�) is shown by a dashed line.The corresponding dihedral angle for the maximum of thisfigure is nearly equal to �4�. Thus, the orientation of N–Hbond towards the O atom is not proper for the maximuminteraction. The result of all interactions is the existenceof a stationary point in a dihedral angle that is not properfor the maximum interaction between nO2

and r�NH of theconformer 2a. This interaction is lower than the thresholdlimit of 0.5 kcal/mol for the conformer 2b. Furthermore,the difference of occupation number of each orbital fromthe minimum value has been investigated in the scanned

range of these conformers. For (C2C3), (C2H10), n2(O8),and r�2ðC6O7Þ orbitals of conformer 2a, the slope of thecurves of Dn versus h are greater than the others. Noneof these curves has a maximum or minimum in this span.For (N1H11), the corresponding curve is illustrated onan expanded span in Fig. 6(b). The occupation numberdoes not belong to a maximum at the stationary pointbut it is related to a specific dihedral angle which is attrib-uted to a maximum at the n(2,O7)! r*(NH) interaction.

In the conformer 2b, for R�1ðC2Þ, r�1ðC6O7Þ, (C2N1),and r�1ðC6O8Þ orbitals, the slope of the curves of Dn

versus h are greater than the others. All these orbitals par-ticipate in the most important donor–acceptor interactions.Thus, these data are not in agreement with the existenceof N–H� � �O@C hydrogen bond in the conformers 2a and2b.

The most important interactions of the conformers 3a–5b have also been investigated. The changes of these inter-actions versus h are not also compatible with the existenceof N–H� � �O@C or O–H� � �N hydrogen bonds in theseconformers.

4. Conclusions

The results of a detailed population analysis of 10 moststable conformers of neutral proline that was undertaken

A. Ebrahimi et al. / Chemical Physics 322 (2006) 289–297 297

by the natural bond orbitals (NBO) and the atoms in mol-ecules (AIM) methods are summarized as the followingpoints:

(1) With the exception of 1a, 1b, 4a, and 4b, the onlyobserved BCPs are those which located at the inter-atomic paths that are defined by the covalent bonds.

(2) The extra bond critical points (BCP) can be observedonly for the conformers 1a and 1b in the paths joiningN1 and H9, 4a in the path joining O8 and H14, andfinally 4b in the path joining O8 and H12 atoms.

(3) The extra ring critical points (RCP) in the interior ofthe five and six-membered rings are formed by N1C2,C2C6, C6O8, O8H9, and H9� � �N1 paths in 1a and1b, C4C3, C3C2, C2C6, C6O8, O8H14, and H14C4paths in 4a, and N1C2, C2C6, C6O8, O8H12,H12C5, and C5N1 paths in 4b.

(4) A bond critical point has not been predicted by thesecalculations between the H11 and O7 atoms of theconformers 2a and 2b, H11 and O8 atoms of the con-formers 3a and 3b, and also the H16 and O7 atoms ofthe conformers 5a and 5b.

(5) From the obtained results of the current work,the N� � �HO hydrogen bonds of conformers 1a

(q = 0.041849, $2qBCP = 0.12755, HBCP = �0.00408)and 1b (q = 0.038623, $2qBCP = 0.124159, HBCP =�0.00257) are classified as medium HBs and theCH� � �OH hydrogen bonds of the conformers 4a

(q = 0.006597, $2qBCP = 0.030278, HBCP = 0.001244)and 4b (q = 0.007063, $2qBCP = 0.030606, HBCP =0.001248) are placed in weak HBs category.

(6) The values of q and $2q at the N1� � �H9 bond criticalpoint of 1a are greater than the corresponding valuesof 1b. On the other hand, the N1� � �H9 bond length of1a is shorter than the corresponding value of 1b.Thus, the N1� � �H9 hydrogen bond of 1a is strongerthan 1b. Moreover, 1a is more stable than the con-former 1b.

(7) The increase of atomic charge, energetic destabiliza-tion, decrease of dipolar polarization, and decreaseof atomic volume are observed for the H9 atom inthe conformers 1a and 1b. However, the H11 atomof the conformers 2a and 2b approximately fails tomeet these criteria. Therefore, a true intramolecularH-bond can not exist in the conformers 2a and 2b.

(8) The charge transfer energies of nðNÞ ! r�O–H are18.31 and 15.63 kcal/mol for 1a and 1b, respectively.The charge transfer energy of nð2;OÞ ! r�N–H is 1.00kcal/mol for conformer 2a and lower than the thresh-old limit of 0.5 kcal/mol for conformer 2b. However,there are not any similar interactions higher than thementioned threshold limit for other conformers.

(9) A further analysis was undertaken on the real natureof the specific and non-specific interactions acting

between the ring and COOH group in the conformersof proline. In this analysis, the N1C2C6O7 = h dihe-dral angle was scanned around the optimized valuewhere other geometrical parameters were fixed andthe NBO analysis performed for each point. Despitethe previous reports which have predicted theexistence of the N–H� � �O@C hydrogen bond in theconformers 2a and 2b, the obtained data of NBOanalysis did not confirm this prediction.

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