ONIOM study on the equilibrium geometries

of some cyclopeptides

Francesco Ferrante, Gianfranco La Manna*

Dipartimento di Chimica Fisica ‘F. Accascina’, Universita di Palermo, Viale delle Scienze, 90128 Palermo, Italy

Received 5 February 2003; accepted 30 April 2003

Abstract

The geometries of two octacyclopeptides, cyclo[(D-AmP-L-AmP)4] (AmP ¼ a-aminopentanoic acid) and cyclo[(D-Ala-L-

Phe)4] were obtained by DFT and ONIOM methods. The resulting data show a substantial agreement with a computing time

about three times lower in the case of the ONIOM procedure. This can be exploited in the study of polymeric structures set up

by cyclopeptidic monomeric units.

q 2003 Elsevier B.V. All rights reserved.

Keywords: ONIOM method; Cyclopeptides; DFT calculation

1. Introduction

Theoretical ab initio calculations on systems of

large dimensions can be performed by a simplification

of the overall structure, with the consequence of

neglecting the effects coming from the parts of the

system that are not explicitly considered. Alterna-

tively, a calculation at lower level can be carried out

on the whole structure, giving rise to not always

reliable results.

The ONIOM (our own N-layered integrated

molecular orbital and molecular mechanics)

approach, developed in the second half of nineties

by Morokuma and co-workers [1], seems to be a valid

alternative for affording the problem of performing

accurate calculations on systems of large dimensions

without changing the structure of the system. In this

approach a molecule is divided into several parts, or

layers, each one described at a different level of

theory. The molecular portion that is presumably the

most important in determining the physico-chemical

properties of the system is treated at the highest level

of theory, while the effect due to the parts that can be

considered as substituents is estimated by using

progressively lower-level methods.

In the calculations on molecular systems defined by

the appropriate layers, dangling bonds are saturated

with link atoms, which are generally hydrogens and are

always aligned along the bond vectors.

ONIOM can be considered a hybrid computational

method, according to a general approach that is used

nowadays in different fields of the computational

chemistry.

The implementation of the ONIOM method into

the GAUSSIAN package [2] enabled to perform

0166-1280/03/$ - see front matter q 2003 Elsevier B.V. All rights reserved.

doi:10.1016/S0166-1280(03)00340-3

Journal of Molecular Structure (Theochem) 634 (2003) 181–186

www.elsevier.com/locate/theochem

* Corresponding author. Tel.: þ39-091-6459851; fax: þ39-091-

5900-15.

E-mail address: lamanna@unipa.it (G. La Manna).

a number of tests which showed the reliability of the

method for evaluating different molecular properties

like geometries [3], IR frequencies [4],

activation energies [5], NMR shielding tensors [6],

as well as for studying reactive processes like

dissociation [7], tautomeric equilibria [8], molecular

absorption on surface [9]. Recently, this

approach has been extended to the study of

systems in solution according to the method of

Tomasi [10].

Since our research group is interested in the

quantum-mechanical characterisation of polymeric

tubular structures set up by monomeric units contain-

ing peptidic bonds [11], we investigated the possi-

bility of utilizing the ONIOM procedure on

octacyclopeptidic systems containing neutral alter-

nating D-and L-a-aminoacids in order to perform

accurate calculations with an appreciable lowering of

the computing time.

In this paper we considered the following two

octacyclopeptides: cyclo[(D-AmP-L-AmP)4] (I),

where AmP is a-aminopentanoic acid, and

cyclo[(D-Ala-L-Phe)4] (II). Both of them are macro-

cyclic compounds showing a planar-like confor-

mation having C4 symmetry, where the amidic

groups are perpendicular to the molecular plane and

the aminoacidic residues point outward of the ring

(see Fig. 1). Such systems are able, in principle, to

give rise to open-ended hollow tubular structures

Fig. 1. Systems considered in this work: cyclo[(D-AmP-L-AmP)4] (a); cyclo[(D-Ala-L-Phe)4] (b); section of the backbone (c).

Fig. 2. Pictorial representation of the layers adopted in the ONIOM

procedure for cyclo[(D-AmP-L-AmP)4].

F. Ferrante, G. La Manna / Journal of Molecular Structure (Theochem) 634 (2003) 181–186182

[12–17] by a stacking process through the hydrogen

bond formation between carbonyl oxygens

and amidic hydrogens belonging to two adjacent

molecules. The II system is a molecule whose

capability of forming a polymeric structure by such

self-assembling process was already investigated

both experimentally [13] and theoretically [18],

whereas tubular structures built by the structure I

were not synthesised so far. These systems have

been chosen because the side groups are quite large

so as to allow a substantial simplification through

the ONIOM procedure.

In this paper we test the ONIOM method to obtain

the ground-state geometry of the monomers, and

compare the result with the full optimisation data

obtained at DFT level. This is a necessary preliminary

step for further studies on aggregates of larger

dimension, where a substantial amount of computing

time can be saved by treating the side groups with a

semiempirical hamiltonian.

Table 1

Geometrical parameters of cyclo[(D-AmP-L-AmP)4] (distances in A, angles in degrees) obtained from full geometry optimisation at DFT level

(B3LYP parameterisation) and corresponding deviations as evaluated from ONIOM procedures

DFT/6-31G(d,p) ONIOM(PM3) ONIOM(AM1) ONIOM(UFF)

Ca–C 1.539 þ0.011 þ0.012 þ0.003

C–N 1.356 20.002 20.003 0.000

N–C0a 1.458 þ0.002 þ0.007 20.002

C–O 1.231 20.002 20.001 20.002

N–H 1.016 20.002 20.001 20.001

Ca–H 1.095 þ0.008 þ0.002 20.001

Ca–C–N 115.6 20.3 20.3 20.2

N–C0a–C0 106.2 þ0.2 20.2 þ0.8

C–N–C0a 122.4 þ0.4 0.0 20.5

C–Ca–Ha 110.8 þ0.6 þ0.3 þ0.4

N–C–O 123.8 þ0.6 þ0.4 þ0.3

C–N–H 119.8 þ0.7 þ0.7 þ0.2

H–N–C0a 113.3 þ0.9 þ0.3 þ0.4

N–C0a–H0a 107.3 20.2 20.2 þ0.9

Ca–C–O 120.6 20.2 20.1 20.1

Ca–C–N–H 216.5 þ3.4 þ3.4 21.1

Ca–C–N–C0a 2171.2 22.9 þ0.5 21.3

C–N–C0a–C0 130.9 20.4 þ1.3 22.1

N–C0a–C0 –N0 2155.6 þ2.9 þ0.7 þ0.1

O–C–N–C0a 10.8 24.1 21.0 21.4

Ha–Ca–C–O 2143.2 21.2 þ1.6 20.9

Ha–Ca–C–N 39.0 22.6 0.0 21.3

O–C–N–H 165.5 þ2.2 þ1.9 21.2

H–N–C0a–H0a 2143.8 26.5 21.6 23.7

H–N–C0a–C0 225.3 25.8 21.4 22.3

N–C0a–C0 –O0 27.1 þ1.2 21.5 20.9

RMSD

Bond distances (A) 0.006 0.006 0.002

Angles (8) 0.5 0.3 0.5

Torsional angles (8) 3.5 1.6 1.7

O–Oa 8.720 8.696 8.756 8.632

N–Na 9.360 9.345 9.375 9.372

Cavity surface (A2)b 64.2 63.9 64.5 63.6

a Distance between the atoms of two opposite peptidic groups.b Calculated as the surface of a circle having the diameter as the average value of the O–O and N–N distances above.

F. Ferrante, G. La Manna / Journal of Molecular Structure (Theochem) 634 (2003) 181–186 183

2. Computational details

The geometries of the considered systems have

been optimised at DFT level with B3LYP parameter-

isation [19] and the 6-31G(d,p) basis set, as well as

with the ONIOM 2-layer combinations B3LYP/6-

31G(d,p):PM3, B3LYP/6-31G(d,p):AM1 and

B3LYP/6-31G(d,p):UFF (UFF ¼ Universal Force

Field). In all cases the ONIOM results were compared

with the data obtained from full optimisations at DFT

level. All computations were performed using the

GAUSSIAN 98W package programme [20] on Pentium-

IV processors.

3. Results and discussion

The partition utilised for performing the ONIOM

calculations is shown in Fig. 2. The model system is

the molecule cyclo[(Gly-Gly)4], which represents the

backbone of octacyclopeptides.

3.1. Cyclo[(D-AmP-L-AmP)4]

The geometrical parameters obtained from the

DFT calculation as well as from the three ONIOM

combinations here utilised are shown in the Table 1,

along with the values of root mean square deviations

(RMSD), computed by comparing the optimised

geometries of the backbone obtained from ONIOM

calculations with that obtained from the DFT method.

The adopted atoms numbering is shown in Fig. 3. The

small values of the deviations show that, as what

concerns the molecular geometry, the ONIOM

approach is able to reproduce the results obtainable

by the DFT treatment.

The combination B3LYP:UFF gives the lowest

value of RMSD as what concerns the bond distances,

whereas the other two procedures provide a better

result in the case of the evaluation of the value of the

cavity surface.

It is interesting to observe that a simple PM3

calculation gives much larger RMSD values,

namely 0.031 A for bond lengths, 3.28 for bond

angles and 13.38 for torsional angles.

A graphical comparison between DFT and

ONIOM(B3LYP/6-31G**:PM3) geometries is

shown in the Fig. 4: a very good overlap of the

backbones is observed.

3.2. Cyclo[(D-Ala-L-Phe)4]

The geometrical parameters obtained by using

the same ONIOM procedures previously utilized

for the system I are reported in the Table 2 along

with the DFT values obtained here, as well as with

other DFT data found in the literature [18]. The

geometrical data of Ref. [18], concerning the only

alaninic moiety, and obtained by using the

same DFT parameterisation with a basis set

Fig. 4. Geometries of cyclo[(D-AmP-L-AmP)4] obtained from the

DFT (black) and ONIOM(B3LYP:PM3) (light grey) calculations.

Fig. 3. Adopted symbols of the repeating unit in the considered

cyclopeptides. R1yR2yC2H5 in cyclo[(D-AmP-L-AmP)4]; R1 ¼ H,

R2 ¼ C6H5 in cyclo[(D-Ala-L-Phe)4].

F. Ferrante, G. La Manna / Journal of Molecular Structure (Theochem) 634 (2003) 181–186184

devoid of polarisation functions, show a substantial

agreement with our DFT results, with the exception

of the C – O bond length and N0– Ca– C – N

torsional angle.

The ONIOM:UFF method provides the best

agreement with the DFT bond distances, whereas

the other two procedures give a more satisfactory

evaluation of the bond and torsional angles. In all

cases, the deviations with respect to the DFT

geometry are larger for the parameters concerning

the phenylalaninic moiety. The error in the

evaluation of the cavity surface is approximately

1%.

As for cyclo[(D-AmP-L-AmP)4], a pictorial

comparison is reported between DFT and ONIOM

(B3LYP/6-31G**:PM3) geometries (see Fig. 5);

a good overlap of the backbones is observed, even if

of slightly lower quality than for system I.

Table 2

Geometrical parameters of cyclo[(D-Ala-L-Phe)4] (distances in A, angles in degrees) obtained from full geometry optimization at DFT level

(B3LYP parameterisation) and corresponding values as evaluated from ONIOM procedures

DFT/6-31G(d,p)a (this work) DFT/6-31G [18]b ONIOM(PM3)a ONIOM(AM1)a ONIOM(UFF)a

Ca–C 1.539, 1.538 1.53 þ0.011, þ0.012 þ0.011, þ0.013 0, þ0.003

C–N 1.357, 1.352 1.35 20.001, þ0.002 20.001, þ0.001 20.003, þ0.004

N0 –Ca 1.456, 1.456 1.46 þ0.003, þ0.003 þ0.008, þ0.009 þ0.001, 0

C–O 1.230, 1.232 1.26 20.002, 20.003 20.002, 20.003 0, 20.003

N0 –H0 1.015, 1.014 1.01 20.001, 0 0, 0 0, 0

Ca–Ha 1.096, 1.096 – þ0.007, þ0.007 þ0.002, 0 20.002, 20.003

Ca–C–N 115.4, 116.1 116 20.3, 20.7 20.5, 20.6 þ0.1, 20.6

Ca–C–O 120.7, 120.0 121 20.1, þ0.3 0, þ0.2 20.3, þ0.5

N–C–O 123.9, 123.9 123 þ0.5, þ0.4 þ0.5, þ0.4 þ0.2, 23.4

C0 –N0 –Ca 122.3, 122.3 123 þ0.1, þ0.4 20.1, þ0.1 20.6, 20.2

C–N–H 119.9, 121.4 122 þ0.2, 20.6 20.1, 20.6 þ0.8, 21.5

Ca–N0 –H0 114.0, 114.2 115 þ0.2, þ0.3 20.4, 20.2 20.4, þ0.1

N0 –Ca–C 106.3, 106.6 – þ0.3, 0 0, 20.2 þ1.1, þ0.4

Ha–Ca–C 110.3, 111.8 – þ0.7, þ0.1 þ0.2, þ0.2 þ1.7, 20.8

N0 –Ca–Ha 107.6, 106.9 – 20.4, 20.1 20.3, 0 þ0.4, þ1.2

C0 –N0 –Ca–C 143.3, 2125.0 149 27.4, 20.2 26.4, þ0.6 215.0, 27.4

N0 –Ca–C–N 2159.8, 141.4 2149 þ1.8, þ6.1 22.3, þ7.2 þ5.0, þ11.6

Ca–C–N–C0a 172.7, 2174.7 176 þ0.5, þ0.6 21.8, þ2.0 þ3.1, þ4.8

Ca–C–N–H 15.1, 213.1 – 22.0, 20.6 21.0, 22.1 þ1.1, 23.1

O0 –C0 –N0 –Ca 7.0, 28.9 – 20.3, þ1.2 þ1.5, 20.9 þ4.0, þ2.9

Ha–Ca–C–N 243.4, 24.9 – þ0.8, þ6.2 22.6, þ7.3 þ6.9, þ10.4

O–C–N–H 2166.4, 168.6 – 21.4, 21.6 20.2, 22.6 þ0.7, 23.8

Ha–Ca–C–O 138.1, 2156.7 – þ0.3, 27.1 23.5, þ7.7 þ7.1, 211.1

H0 –N0 –Ca–Ha 2137.7, 153.4 – 26.8, þ2.4 22.7, þ1.0 210.2, 25.3

H0 –N0 –Ca–C 219.5, 33.8 – 26.1, þ2.2 22.6, þ0.8 27.4, 25.3

N0 –Ca–C–O 21.8, 240.2 – 0, þ7.0 23.4, þ7.6 þ5.2, þ12.3

RMSD

Bond distances (A) 0.005, 0.006 0.006, 0.007 0.002, 0.003

Angles (8) 0.4, 0.4 0.3, 0.3 0.8, 1.4

Torsional angles (8) 3.7, 4.3 3.0, 4.7 7.1, 7.9

Cavity surface (A2)c 64.5 63.8 63.9 64.0

a The two values correspond to the atomic centres close to alanine and L-phenylalanine, respectively. In the case of the phenylalanine, primed

atomic symbols become unprimed, and viceversa (see Fig. 3).b Data concerning the alaninic moiety.c Calculated as the surface of a circle having the diameter as the average value of the O–O and N–N distances.

F. Ferrante, G. La Manna / Journal of Molecular Structure (Theochem) 634 (2003) 181–186 185

4. Conclusions

The use of the ONIOM procedure allowed

obtaining very satisfactory geometries of the cyclo-

peptides here considered. The reduction factor of the

computing time with respect to a DFT calculation has

been evaluated about 3 in the case of system II and

could be still increased in presence of larger side

groups. These results confirm that ONIOM method is

a powerful tool for obtaining accurate geometries of

systems of medium and large dimensions and can be

utilized, with noticeable decreasing of the computing

time, in the case of the theoretical study of polymeric

structures.

Acknowledgements

This work was performed with the contribution of

the 60% funds of the Italian Ministry of Scientific

Research.

References

[1] M. Svensson, S. Humbel, R.D.J. Froese, T. Matsubara, S.

Sieber, K. Morokuma, J. Phys. Chem. 100 (1996) 19357.

[2] S. Dapprich, I. Komaromi, K.S. Byun, K. Morokuma, M.J.

Frish, J. Mol. Struct. (Theochem) 461–462 (1999) 1.

[3] S. Humbel, S. Sieber, K. Morokuma, J. Chem. Phys. 105

(1996) 1959.

[4] T. Vreven, K. Morokuma, J. Comp. Chem. 21 (2000) 1419.

[5] S. Feldgus, G.C. Shields, Chem. Phys. Lett. 347 (2001) 505.

[6] P.B. Karadakov, K. Morokuma, Chem. Phys. Lett. 317 (2000)

589.

[7] T. Vreven, K. Morokuma, J. Phys. Chem. A 106 (2002) 6167.

[8] M. Remko, O.A. Walsh, W.G. Richards, J. Phys. Chem. A 105

(2001) 6926.

[9] T. Hai-Rong, F. Kang-Nian, Chem. Phys. Lett. 330 (2000)

509.

[10] T. Vreven, B. Mennucci, O.C. da Silva, K. Morokuma, J.

Tomasi, J. Chem. Phys. 115 (2001) 62.

[11] F. Ferrante, G. La Manna, J. Phys. Chem. A 107 (2003) 91.

[12] M.R. Ghadiri, J.R. Granja, R.A. Milligan, D.E. McRee, N.

Khazanovich, Nature 366 (1993) 324.

[13] M.R. Ghadiri, K. Kobayashi, J.R. Granja, R.K. Chadha, D.E.

McRee, Angew. Chem. Int. Ed. 34 (1995) 93.

[14] M.R. Ghadiri, K. Kobayashi, J.R. Granja, Angew. Chem. Int.

Ed. 34 (1995) 95.

[15] J.D. Hartgerink, J.R. Granja, R.A. Milligan, M.R. Ghadiri,

J. Am. Chem. Soc. 118 (1996) 43.

[16] H. Rapaport, H.S. Kim, K. Kjaer, P.B. Howes, S. Cohen, J.

Als-Nielsen, M.R. Ghadiri, L. Leiserowitz, M. Lahav, J. Am.

Chem. Soc. 121 (1999) 1186.

[17] D.T. Bong, T.D. Clark, J.R. Granja, M.R. Ghadiri, Angew.

Chem. Int. Ed. 40 (2001) 988.

[18] G. Chen, S. Su, R. Liu, J. Phys. Chem. B 106 (2002) 1570.

[19] A.D. Becke, J. Chem. Phys. 98 (1993) 5648.

[20] GAUSSIAN 98W, Revision A.6, M.J. Frisch, G.W. Trucks, H.B.

Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G.

Zakrzewski, J.A. Montgomery Jr., R.E. Stratmann, J.C.

Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N.

Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M.

Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo,

S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui,

K. Morokuma, D.K. Malick, D. Rabuck, K. Raghavachari, J.B.

Foresman, J. Cioslowski, J.V. Ortiz, B.B. Stefanov, G. Liu, A.

Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L.

Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng,

A. Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W. Gill,

B. Johnson, W. Chen, M. W. Wong, J.L. Andres, C. Gonzalez,

M. Head-Gordon, E.S. Replogle, J.A. Pople, Gaussian Inc.,

Pittsburgh, PA, 1998.

Fig. 5. Geometries of cyclo[(D-Ala-L-Phe)4] obtained from the DFT

(black) and ONIOM(B3LYP:PM3) (light grey) calculations.

F. Ferrante, G. La Manna / Journal of Molecular Structure (Theochem) 634 (2003) 181–186186