Multistep conformational interconversion mechanism of cyclododecane. A simple and fast analysis...

Multistep Conformational Interconversion Mechanism ofCyclododecane. A Simple and Fast Analysis UsingPotential Energy Curves

Edgardo J. Saavedra,[a] Sebastian A. Andujar,[b,c] Fernando D. Suvire,[b,c]

Miguel A. Zamora,[b] Monica L. Freile,[a] and Ricardo D. Enriz*[b,c]

An ab initio and Density Functional Theory (DFT) study of the

conformational properties of cyclododecane was carried out. The

energetically preferred equilibrium structures, their relative

stability, and some of the transition state (TS) structures involved

in the conformational interconversion pathways were analyzed

from RHF/6-31G(d), B3LYP/6-31G(d,p) and B3LYP/6311þþG(d,p)

calculations. Aug-cc-pVDZ//B3LYP/6311þþG(d,p) single point

calculations predict that the multistep conformational

interconversion mechanism requires 11.07 kcal/mol, which is in

agreement with the available experimental data. These results

allow us to form a concise idea about the internal intricacies of

the preferred forms of cyclododecane, describing the

conformations as well as the conformational interconversion

processes in the conformational potential energy hypersurface.

Our results indicated that performing an exhaustive analysis

of the potential energy curves connecting the most

representative conformations is a valid alternate tool to

determine the principal conformational interconversion paths for

cyclododecane. This methodology represents a satisfactory first

approximation for the conformational analysis of medium- and

large-size flexible cyclic compounds.VC 2011 Wiley Periodicals, Inc.

DOI: 10.1002/qua.23239

Introduction

There are several algorithms[1–6] and techniques (systematic

and random) available to perform an exhaustive conforma-

tional study of flexible cyclic compounds. Many of them allow

us to obtain the different critical points [minima and transi-

tion states (TSs)] on the potential energy hypersurface (PEHS).

However, present versions of automatic search programs do

not deal with the relationships of the local energy minima on

the energy hypersurface; in particular, the (lowest) barriers

separating the various conformations are generally ignored,

possibly leading to a poor understanding of the conforma-

tional properties of a cyclic molecule. The above methods in

general give a manifold account of cartesian coordinates,

which must be optimized using accurate calculations and

then classified to determine which type of critical point are

they. Thus, despite the apparent capability of the present meth-

ods of calculations (ab initio and DFT) or simulations (the differ-

ent molecular dynamic techniques) to predict critical points on

a hypersurface, conformational analysis of flexible medium and

large-size cyclic compounds, including the conformational inter-

conversion paths, has not yet become routine limiting seriously

their practical applications to cyclic compounds of biological in-

terest. There are many reasons for such situation being probably

the following the principal ones.

i. Exploration of conformational space is a difficult problem,

which is especially acute for cyclic molecules due to the inter-

dependence of torsional angles.[7] Previously, we reported a

comprehensive conformational study of the hypersurface of

cyclononane using ab initio and DFT calculations.[8] Our results

showed that this hypersurface apparently simple in fact is very

complex. More recently, we reported a topological analysis of

the PEHS of cyclic triglycine[9] and cyclotrisarcosyl (unpub-

lished results) showing that these hypersurfaces are very intri-

cate too. From these results, it is evident that a systematic and

a topological conformational analysis of the hypersurface for

medium or large-size cyclic compounds is a very tedious task

and many times very difficult too.

ii. The relatively tedious and insecure process required to

obtain the different TS structures for a flexible cyclic com-

pound with respect to a lineal molecule.

iii. Multidimensional conformational analysis concepts[10,11]

are very useful to perform the conformational study of lineal

compounds; particularly in the case of compounds possessing

many torsional angles[12] or possessing symmetry.[13,14] How-

ever; such concepts and topological premises in general are

not valid for flexible cyclic compounds due to the interde-

pendence among the torsional angles. Nobody can make

[a] E. J. Saavedra, M. L. Freile

Facultad de Ciencias Exactas y Naturales, Universidad Nacional de La

Patagonia San Juan Bosco, Comodoro Rivadavia, Chubut, Argentina

[b] S. A. Andujar, F. D. Suvire, M. A. Zamora, R. D. Enriz

Departamento de Quımica, Facultad de Quımica, Bioquımica y Farmacia,

Universidad Nacional de San Luis, Chacabuco 915, 5700 San Luis, Argentina

E-mail: [email protected]

[c] S. A. Andujar, F. D. Suvire, R. D. Enriz

IMIBIO-CONICET, UNSL, Chacabuco 915, 5700 San Luis, Argentina

VC 2011 Wiley Periodicals, Inc.

2382 International Journal of Quantum Chemistry 2012, 112, 2382–2391 WWW.CHEMISTRYVIEWS.ORG

FULL PAPER WWW.Q-CHEM.ORG

even an ‘‘educated guess’’ of how many conformers might be

associated with a medium or large flexible cyclic molecule.

This is a striking difference between flexible and lineal

compounds.

Potential energy curves of flexible cyclic compounds

One-dimensional search has been termed ‘‘primitive’’ and need

the subjective judgment of the user.[2] However, this method,

with judicious driving of torsional angles and especially in

association with ab-initio optimizations, can provide much in-

formation about the energy surface, including the lowest bar-

riers between all pairs of conformations. Fortunately for many

purposes, it is sufficient to identify only selected critical points

on the hypersurface (for example, the low-energy conformers

and their conformational interconversion paths). One way to

obtain these critical points following a relatively systematic

way is to analyze the potential energy curves (PECs), which are

interconnecting the different conformers in the hipersurface. It

is clear that these curves are very useful to visualize and

understand the overall conformational behavior of these cyclic

compounds. On the other hand in these curves, visual distinc-

tion between local minima and saddle points on a PEC is

rather trivial; in contrast mathematical distinction is far more

difficult. Both local minima and saddle points are stationary

points on any dimensional hypersurface. The difference

between minima and saddle point can only be detected by

considering the Hessian matrix.

The conformational problem of cyclododecane

Cyclododecane is generally considered as the first member of

the large-ring cycloalkanes and it is the smallest cycloalkane

which is crystalline at room temperature. However, it has a dis-

ordered crystal structure and this has caused difficulties in the

determination of its conformation by X-ray diffraction meth-

ods.[15] The conformation of cyclododecane found in the crys-

talline state can be conveniently described by Dale’s nomen-

clature[16] as [3333] (the digits in the square brackets refer to

the number of CAC bonds between the ‘‘corner’’ atoms).

Dunitz has suggested that above the transition temperature

the molecules undergo rapid inversion, below the transition

temperature no molecular motion occurs and the structure is

frozen in some order-disorder arrangement.[17]

Several force-field calculations have been carried out on

cyclododecane,[4,5,16,18] and the lowest energy conformation

has always been found to be the [3333] conformation (confor-

mation 1 in Table 1). Dale[16] first, and Anet and Rawdah[18]

later, have presented schemes for site exchange in this confor-

mation and have shown that conformations of higher energies

are involved as intermediates. The reports of Saunders[4] and

Kolossvary and Guida[5] are probably the most exhaustive con-

formational searches performed for cyclododecane. Saunders

Table 1. Relative energies obtained at the different levels of theory for the different critical points (minima and TSs).

Conf./TS

RHF/6-31G(d) B3LYP/6-31G(d,p) B3LYP/6-311þþG(d,p) Aug-cc-pvdz//B3LYP/6-311þþG(d,p)

DE IF DE IF DE IF DE

1 0.00 0.00 0.00 0.00

2 2.55 2.43 2.47 2.28

3 3.56 3.56 3.48 3.27

4 3.89 3.57 3.56 3.53

5 4.12 4.21 4.21 3.82

6 4.89 4.98 4.88 4.58

7 5.6 5.37 5.26 5.11

8 6.17 5.28 5.24 5.23

9 7.39 6.77 6.75 6.65

10 8.16 7.35 7.32 6.99

11 9.79 9.15 9.02 8.88

12 10.97 13.39 9.94 12.96

13 12.28 11.04 10.99 10.77

14 12.95 11.42 11.35 11.03

15 6.55 6.23 6.17 5.85

TS 5-6 6.08 �164.34 5.91 �75.19 5.73 �70.05 5.46

TS 3-6 8.22 �111.27 7.80 �99.19 7.54 �94.79 7.33

TS 1-2 9.38 �173.71 8.94 �163.58 8.81 �162.57 8.39

TS 1-5 10.63 �164.20 9.98 �156.1683 9.92 �157.10 9.42

TS 3-12 11.86 �129.26 10.89 �120.9564 10.72 �119.01 10.31

TS 11-9 12.23 �116.06 11.44 �108.7828 11.37 �110.52 10.86

TS 2-4 13.05 �192.87 11.66 �177.5295 11.38 �175.51 11.07

TS 8-2 13.23 �136.84 12.17 �147.8501 11.92 �146.61 11.47

TS 13-14 17.02 �155.30 15.74 �144.2258 15.49 �142.55 15.03

TS 5-15 12.45 �175.82 11.58 �164.3105 11.40 �162.59 10.98

TS 15-6 14.78 �209.59 13.58 �192.5292 13.42 �190.80 13.02

TS 6-10 10.8 �129�98 9.86 �124.65 9.72 �123.11 9.48

TS 2-10 14.26 �120.17 13.09 �118.28 12.85 �120.48 14.32

The frequences values for the TSs are also shown in this table.

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International Journal of Quantum Chemistry 2012, 112, 2382–2391 2383

found 111 conformers, whereas Kolossvary and Guida reported

117 different conformers and 462 TSs. More recently, Christen-

sen and |||Flemming[19] reported a conformational study of

cyclododecane using molecular dynamics simulations; they

found 116 conformations from their simulations. Thus, there

appears to be a large amount of impressive information about

the conformational intricacies of cyclododecane. However, the

reality is somewhat different; there is, in fact, only partial infor-

mation about this old and interesting problem. It should be

noted that all the studies previously reported have been per-

formed using very simple molecular mechanics calculations,

invariably MM2 and/or MM3 or even less accurate methods.

Other force fields included in the molecular dynamic simula-

tions have been used. However, to the best of our knowledge,

there are not conformational studies reported for cyclodode-

cane using high levels of theory or more accurate calculations.

The question arises as to whether one is justified in categoriz-

ing all the previously reported energetically preferred confor-

mations and their connecting TSs as minima on the hypersur-

face of cyclododecane. Are these previously reported critical

points ‘‘real minima’’ or some of them are only artifacts of less-

accurate theoretical calculations? Are the previously proposed

conformational interconversion paths the low-energy ways for

such interconversions? Are the energy gaps proposed for the

minima and the different interconversion paths the correct

ones?

It is well known that cyclododecane has a numerable num-

ber of conformers on its PEHS, but where does one form

change to the other and how far from an energy minimum

can the molecule stray away before ceasing to be in a confor-

mation referred to as the energy minimum? It is clear that in-

formation about local and global minima of a molecule such

as cyclododecane is not enough. We need to have at least a

good notion of the shape and also some indication about the

dynamic behaviour of the internal degrees of freedom of the

cyclododecane molecule. May be because it is more difficult

to locate saddle points than local minima, or may be because

the importance of saddle points has simply not been well

appreciated, conformational analysis of ciclododecane has

been synonymous with a search for low-energy minima on the

hypersurface. Although there has been a clear appreciation in

the literature for the need of locating the low-energy saddle

points, few examples have appeared in the literature. Confor-

mational interconversions in cyclononane have been studied

with some details by Dale,[20] Anet and Rawdah,[18] and later

by Saunders.[4] However, these studies have been performed

using molecular mechanics calculations and these results can

explain only a partial aspect of the overall problem.

Our study has two principal objectives; the first one is to

found a general, simple, and economical approach (at least a

preliminary one), which allows to determine and at the same

time to understand the different conformational interconver-

sion paths for flexible medium-size cyclic compounds. For that

purpose, we calculate the PECs interconnecting the different

low-energy conformers using PM6 calculations. A second

objective is to corroborate the previously reported energeti-

cally preferred forms of cyclododecane and their lowest energy

paths using more accurate computations. Thus, we performed

a conformational study for the preferred forms of cyclodode-

cane using ab-initio and DFT calculations. Aside from the pop-

ulations of the conformers, it is of great interest to know how

the interconversions between the conformers are and which

of them occur most readily. Thus, we sought to locate the pos-

sible equilibrium structures, their relative stability, and the TS

structures involved in the conformational interconversion path-

ways. Harmonic frequency calculations were performed for an

unambiguous characterization of the stationary points located

on the multidimensional hypersurface of cyclododecane.

Calculations

All the calculations reported here were performed using the

GAUSSIAN 03 program.[21] Critical points (low-energy confor-

mations and TS structures) were optimized at RHF/6-31G(d),

RB3LYP/6-31G(d,p) and RB3LYP/6-311þþG(d,p) levels of theory.

Vibrational frequencies for the optimized structures were com-

puted to evaluate the zero-point energies as well as to confirm

the nature of the singular points along the potential energy

surface. The stationary points have been identifies as a mini-

mum with no imaginary frequencies, or as a first-order TS

characterized by the existence of only one imaginary fre-

quency in the normal mode coordinate analysis. TS structures

were located until the Hessian matrix had only one imaginary

eigenvalue, and the TSs were also confirmed by animating the

negative eigenvectors coordinate with a visualization program

and internal reaction coordinate (IRC) calculations.[22,23] HF/6-

31G(d) IRC calculations were performed on the TS structures

to check that the TSs structures lead to the initial conformer

and to the final conformation (forward and reverse directions

of the conformational interconversion path). IRC calculations

steps six points in cartesians coordinates in the forward direc-

tion and six points in the reverse direction, in step of 03 amu1/

2 bohr along the path were carried out. After obtaining the

optimized structures from RHF/6-31G(d) calculations, single

point calculations using the most reliable and flexible basis set

(aug-cc-pVDZ) were carried out to evaluate the energies of the

preferred conformers.

The search for the different conformational interconversion

paths was carried out in four discrete steps. In the first step, a

geometrical optimization and frequency analysis using RHF/6-

31G (d,p), B3LYP/6-31G(d,p), and B3LYP/6-311þþG(d,p) calcula-

tions was carried out for the low-energy conformers previously

reported for cyclododecane. A careful analysis of each tor-

sional angle and their respective frequencies was carried out.

From such analysis we chose the torsional angles to be eval-

uated by using PECs. In the second step, we evaluate the dif-

ferent PECs using semiempirical PM6 calculations. The torsional

angles selected for such analysis were chosen in function of

the values of the torsional angles as well as from the fre-

quency analysis performed in the previous step. To check the

validity of this procedure we evaluate all the torsional angles

obtained for many conformers (no matter the value of the

dihedral neither the frequency). In the third step, we analyze

the different curves obtained from PM6 calculations,



optimizing all the possible critical points observed in each

curve using ab initio and DFT calculations. A frequency analysis

for each structure was also carried out in this step to confirm

each critical point. Next the most relevant conformers and TSs

were selected to perform more accurate calculations. Thus, sin-

gle point calculations using the most reliable and flexible basis

set (aug-cc-pVDZ) were carried out to evaluate the energies of

the preferred conformers. Finally, the TSs were also confirmed

by animating the negative eigenvectors coordinate with a vis-

ualization program and IRC calculations.

Results and Discussion

Low-energy conformers of cyclododecane

The lowest energy conformation of cyclododecane is con-

former 1 (Table 1), which agrees with all the previously

reported works.[5b,7,8] Dale[20] and Anet[18] reported that the

next two conformations in order of increasing total strain

energies are conformers 2 and 4. However, we found con-

formation 3 possessing 3.27 Kcal/mol above 1 as the third

energetically preferred form. A very similar conformation to

3 was previously reported by Saunders.[4] It should be

noted however, that conformer 3 is not directly related with

the global minimum (the conformational interconversions

for these conformers are discussed in the next section).

Only 15 different conformations of cyclododecane were

included in our conformational analysis (Table 1), but all of

them were included in our study about the conformational

interconversion paths, which is useful to better understand the

conformational intricacies of this cycloalkane. In fact, there are

at least 100 other possible conformations for cyclododecane,

but all the previous conformational analysis[5b,7,8,24,26,29]

have already reported that these conformations have very

high strain energies, and therefore we did not consider it

worthwhile to carry out ab initio and DFT optimizations on

them.

The reliability of both RHF/6-31G(d) and RB3LYP/6-31G(d)

geometries can be investigated here since we have results

from RB3LYP/6311þþG(d,p) optimization. It is worthwhile, at

this point, to make a comparison. The preliminary semiempiri-

cal PM6 calculations were also included in this comparative

analysis. Interestingly RB3LYP/6311þþG(d,p) optimizations pro-

duce only moderate changes in the RHF/6-31G(d) and B3LYP/6-

31G(d) geometries (Fig. 1). More significant differences were

found comparing the PM6 results. The accuracy of the key tor-

sion angles (in the present case the CAC) is of great impor-

tance. The correlation of the above torsion angles computed at

three levels of theory for cyclododecane is shown in Figure 1.

A significant correlation was found between the torsion angles

optimized at one level of theory and those optimized at other

levels. Thus, only minute deviation was found between the tor-

sion angle values found at RHF/6-31G(d) and RB3LYP/6-31G(d)

when compared to those found at the RB3LYP/6-311þþG(d,p)

level. For example, when correlating the torsion angles opti-

mized at RHF/6-31G(d) against those optimized at the RB3LYP/

6-311þþG(d,p) level, a strong correlation that has a least

square value of R2 ¼ 0.9936 was found (Fig. 1a). When correlat-

ing the torsion angles optimized at RB3LYP/6-31G(d), another

strong correlation with a least square value of R2 ¼ 0.9985 was

found (Fig. 1b). Although the trend observed at PM6 versus

RB3LYP/6-311þþG(d,p) was clearly less strong, the obtained

correlation was still significant (R2 ¼ 0.9915) (Fig. 1c).

Figure 1. A graph showing the correlation between the dihedral angles

(D1-D12) optimized for cyclododecane: a) HF/6-31G(d) vs. B3LYP/

6311þþG(d,p); b) B3LYP/6-31G(d,p) vs. B3LYP/6311þþG(d,p), and c) PM6 vs

B3LYP/6311þþG(d,p). [Color figure can be viewed in the online issue,

which is available at wileyonlinelibrary.com.]



The energy gaps (DE values in kcal/mol) for the different

conformers studied here were correlated between each level

of theory (Fig. 2). Thus, regarding the results shown in Figure

2, it is clear that PM6 and RHF/6-31 G(d) calculations displayed

different results for the energy gaps among the conformers

with respect to those obtained from DFT results. This is partic-

ularly apparent for the semiempirical results. On the basis of

the above results, it appears that the PM6 calculations are

only useful in a preliminary and exploratory conformational

analysis. It is clear that higher levels of theory are necessary

to confirm critical points and to assign the conformational

preferences of cyclododecane. Figure 2 illustrates this point

very well.

Analyzing the PECs of cyclodecane

The calculations and efforts performed in this work have been

directed toward finding non-expensive theoretical calculations

to achieve maximum practicality. Our results indicate that

semiempirical PM6 calculations are a reliable and non expen-

sive approach (in terms of time of calculation) to obtain these

PECs. However, our ab initio and DFT results indicate that

more accurate calculations are necessary to confirm the struc-

tures obtained with the semiempirical approach (see Fig. 2).

The question which arises is: is it necessary to evaluate the

PEC for all the torsional angles of a flexible cyclic compound?

This is not a trivial question; after all if we need to evaluate

the curve of each torsional angle in a molecule, this procedure

will be almost impracticable for molecules possessing many

torsional angles. In fact, the problem it is not related at all

with the computational requirements because PM6 calcula-

tions demand a very few computational capability. The prob-

lem is related with the time required for the modeller them-

selves, not only to prepare the input files but also for the

analysis of all the different curves obtained which can convert

this task in a very tedious work. Fortunately, our results indi-

cate that it is not necessary to evaluate all the torsional angles

in a flexible cyclic compound like cyclododecane. The question

now is which are the torsional angles which deserve to be an-

alyzed from curves? Which is the characteristic or parameters

defining such situation?

There are two different aspects to consider to determine,

which are the torsional angles (best candidates) to be analyzed

using PECs. The first one is related with the value of the tor-

sional angle. Angles possessing values near to cero (or near to

gaucheþ or gauche – extending the security margin) are good

candidates to be evaluated. The second aspect is related with

the values of imaginary frequencies obtained for the torsional

angles. From a frequency analysis, it is possible to differentiate

the metylene groups possessing low values of vibration fre-

quencies which are associated with conformational changes.

Thus, a torsional angle possessing a very low energy frequency

vibration related with a torsion movement is an indication that

the energy surface requires careful examination. We finally

arrive to this conclusion after analysing a great number of

curves for many torsional angles of different conformations of

cyclododecane. The curves obtained for conformer 8 illustrate

this situation very well. Taken advantage of its symmetry, com-

pound 8 displays only four different torsional angles and

therefore a complete analysis for this conformer might be

reduced to only four curves (D1–D4, Fig. 3). Analysing the four

curves obtained for 8, it is interesting to note that only the

torsional angle D3 possessing 57.43� and a frequency value of

277.476 was the only which allows the conformational inter-

conversion for this conformer. These results account for the

general characteristic being representative of the overall phe-

nomenon. However, the same analysis was carried out for the

Figure 2. Energy diagram for the relative energies (DE rel) in kcal/ mol

obtained for the conformations of cyclododecane using different levels of

theory: a) PM6, b) HF/6-31G(d), c) B3LYP/6-31G(d,p), d) B3LYP/6-

311þþG(d,p), and e) Aug-cc-pVDZ//B3LYP/6311þþG(d,p). The different

conformers are denoted in different colors. [Color figure can be viewed in

the online issue, which is available at wileyonlinelibrary.com.]

Figure 3. Spatial view of the conformer 8. The torsional angles as well as

the virtual exes of symmetry showing the four equivalent quadrants are

denoted in this figure.



rest of the conformations analyzed here. Thus, we have per-

formed sufficient calculations to feel confident that the two

requirements considered here are adequate to determine the

torsional angles which deserve further analysis using PECs (at

least for cyclododecane).

An interesting question is: what kind of curves is possible

to obtain for cyclododecane and which information is possi-

ble to obtain from them? We obtained very different curves,

however, the following general characteristic behaviours

observed in the following curves might be remarked. We

obtained two different types of curves for cyclododecane.

PECs in which after a complete 360� of rotation it is possible

to return exactly to the same starting structure (or con-

former). This type of curve was generally observed for con-

formers of relatively high energy. In contrast, in a second

type of curves it is not possible to come back to the starting

conformation (making a complete 360� of rotation for a

dihedral angle). This curve was obtained for the low-energy

conformers of cyclododecane. Making a more detailed analy-

sis of these PECs it is possible to observe three different pro-

files in the general behaviour obtained for the different triads

(minumm-TS-minimum):

1. The curve connects in a continuum way both conformers

throughout a TS structure. This is the characteristic behaviour

of a conformational interconversion for a lineal compound

(Fig. 4).

2. The curve connects the first minimum with a TS struc-

ture, however continuing the rotation procedure a structural

reordering take place as consequence of the interdependence

among the dihedrals (Fig. 5). In this case the curve gives a sta-

ble minimum; however considering the discontinuity in the

curve it is necessary to confirm all these critical points using

an IRC analysis. This type of curve allow us to obtain confor-

mational interconversions which are not possible to predict

from the chemical intuition, simply considering symmetry ele-

ments or from the classical interconversion behaviours

observed for cyclic compounds.

3. A third type of behaviour was observed for the triads.

Once obtained the minimum and continuing with the

curve, a progressive increment of the potential energy take

place showing next an abrupt structural reordering giving

a new minimum which is not connected with the first con-

former (Fig. 6). Also it is interesting to note that the maxi-

mum obtained in these triads it is not a TS structure. It is

evident that this type of conformational exploration allows

obtaining new conformers which are not related at all

with the first conformer throughout the rotating torsional

angle.

From the different PECs obtained for the most representa-

tive conformers of cyclododecane, in the next step we ana-

lyzed and compared the different conformational interconver-

sion mechanisms for this compound.

Figure 4. PEC obtained rotating the dihedral angle 9 of conformer 1 (rota-

tion was performed each 2� clockwise). This curve connects in a contin-

uum way conformers 1 and 5 throughout TS1-5 and conformers 5 and 7

throughout TS5-7.

Figure 5. PEC obtained rotating the dihedral angle 9 of conformer 1

(rotation was performed each 2� anticlockwise). This curve connects the

low-energy minimum (conformer 1) with a TS structure (TS1-2), however

continuing the rotation a structural reordering take place as consequence

of the interdependence among the dihedrals.

Figure 6. PEC obtained rotating the dihedral angle 11 of conformer 2.

Once obtained the minimum (conformer 2) and continuing with the rota-

tion, a progressive increment of the potential energy take place finally giv-

ing an abrupt structural reordering which gives a new minimum

(conformer 13) which is not connected with the first conformer.



Figure 7. Optimized structures obtained for the conformational interconversion path involving the following minina: 1-2-4-20-10. The dot lines are denot-

ing the torsional angles involved in the conformational interconversion.

Figure 8. Optimized structures obtained for the conformational interconversion path involving the following minina: 1-2-8-20-10. The dot lines are denot-

ing the torsional angles involved in the conformational interconversion.



Conformational interconversion paths

All the critical points (minima and TSs) obtained from the PECs

were further analyzed and optimized by RHF/6-31G(d), B3LYP/

6-31G(d), and B3LYP/6-311þþG(d,p) calculations (Table 1).

Vibrational frequencies for the optimized structures were com-

puted to confirm the nature of the singular points along the

hypersurface. From these results, we analyzed and compared

the different multistep conformational interconversion mecha-

nism of cyclododecane.

Taking into account the importance of the global minimum,

we evaluated possible different conformational interconversion

paths for such conformer. This conformation is connected only

with two conformers 2 (Fig. 7–9) and 5 (Fig. 9), and the reason

is because the global minimum possesses only two types of

dihedral angles (four anti and eight gauche torsional angles,

Fig. 9). In turn, conformers 2 and 5 are respectively connected

with other two conformers (conformers 2 is connected with 4

and 8 (see Figs. 7 and 8); and 5 with 7 and 15) (Fig. 9).

It is particularly interesting to study the conformational

interconversion paths involving the specular structure (10) of

the global minimum. To avoid misleading terminology, from

now on the prime sing will be used only for specular images

(for example, 10 is the specular image of conformation 1).

Dale[16] first and Anet and Rawdah[15] later reported that the

energetically preferred mechanism for pseudorotation, or site

exchange, in the conformation 1 is that shown in Figure 9. In

this figure, it is possible to appreciate that the dihedral angle

involved in the conformational interconversion change from

gauche þ to gauche – throughout a TS near to cero (see for

example, 2-TS2-11-11 in Fig. 9). In this figure are indicated for

each triad the corresponding torsional angle involved. This

inversion proceeds with a symmetrical conformer (conformer

4) allowing to observe the complete process from specular

structures (compare the forms located up and down in Fig. 7).

A second symmetrical interconversion process for conformer

1 is shown in Figure 8. This interconversion path is exactly the

same until reach the conformer 2 or 20. The difference

between this path and the previous one might be appreciated

in the conformational behaviour of the triad 2-TS2-8-8. It

should be noted that 8 is a very symmetric form possessing

two planes of symmetry. This form behaves like a pivotal struc-

ture allowing the specular interconversion. Dale[20] and and

Rawdah[18] reported that this path involving 1--2--8--2--1

Figure 9. Optimized structures obtained for two different conformational interconversion paths involving 1-2-11-6-18-50-10 and 1-5-6-18-50-10 . The dot

lines are denoting the torsional angles involved in the conformational interconversion.



conformers could be excluded since the TS2-8 linking conforma-

tions 2 and 8 possessed a high strain energy. Our results are

only in partial agreement with those previously reported.

Although this process displayed higher energy with respect to

that shown in Figure 7, caution is needed here because the

energy gap between both mechanisms appears to be very close.

Once again, it is possible to obtain and follow this mechanism of

pseudorotation analysing the symmetry of the different critical

points involved in the interconversions. Our calculations are in

general agree with the previously reported results; however, DFT

calculations predicts that the strain energies in both mechanisms

differs only by 0.4 Kcal/mol and therefore they are not as differ-

ent as were reported by Anet and Rawdah.[18]

A further interesting result obtained from our conformational

analysis is that we found a new pseudorotation path for con-

former 1 to 10, which has not be previously analyzed in detail

(see Fig. 9). In general the conformational interconversions

migth be obtained from a symmetric structure. However, there

are some interconversion paths without symetric structures,

which are more difficult to rationalize; they are the so-called

no-intuitive paths. To perform the analysis of such processes, it

is necessary to carry out a systematic search. The interconver-

sion processes 1--2--10--6--15—50—10 and 1--5--6—15--50--10

(Fig. 9) displayed the above characteristics and require two

additional steps (involving two minima). It is important to

remark that it is very difficult to observe these multistep confor-

mational interconversion mechanisms from only the chemical

intuition or just observing the symmetry of the critical points.

Figure 10 gives a comparison between the two preferred

energy profiles obtained. Our results indicate that there is no

direct connection between conformers 1 and 3. In fact, the

global minimum has only two connections; one with con-

former 2 and other with conformer 5. The interconversion of

conformers 1 and 2 proceed via the TS TS1-2, whereas the 1-5

interconversion requires the TS1-5 transition sate. Figures 11

and 12 illustrate both situations very well.

We are reporting here a very simple and a relatively system-

atic way to obtain any multistep conformational interconver-

sion mechanism for cyclododecane or any other flexible cyclic

compound. Further interesting this technique allows that any-

body, even without experience in the intricacies of flexible

cyclic compounds, might analyze and understand these con-

formational interconversions, which in general are very difficult

to visualize without an adequate tool.

Conclusions

The PEHS of cyclododecane was investigated using theoretical

calculations. By combining the analysis of PECs with ab initio

and DFT calculations, a very simple and a generally applicable

procedure for conformational analysis of flexible cyclic com-

pounds has been reported here providing a clear picture for

the conformational hypersurface of this molecule from both

structural and energetic points of view.

Extensive searches of the conformational energy hypersurface

for local energy minima would, if at all possible, include the bar-

riers separating pairs of conformations. Progress in searching for

TSs and their significance is likely to be much more demanding in

computer power than simply a search for local energy minima

because it is not sufficient just to locate these saddle points on

the hypersurface. It is necessary to find out how the local energy

minima and the TSs are linked together, and this requires an ex-

ploration of a larger part of the hypersurface. Our results indicate

that to perform a careful analysis of the curves connecting the

most representative conformations is a valid alternate way toFigure 11. Schematic view of the potential energy profile obtained for the

conformational interconversion path involving the 1-2-11-6-18-50-10 conformers.

Figure 10. Schematic view of the potential energy profiles obtained for

the two preferred-energy pathways. The B3LYP/6311þþG(d,p) relative

potential energies of conformations and TSs have been drafted with

respect to the global minimum. [Color figure can be viewed in the online

issue, which is available at wileyonlinelibrary.com.]

Figure 12. Schematic view of potential energy profile obtained for the

conformational interconversion path involving the 1-5-6-18-50-10conformers.



determine the principal conformational interconversion paths in

a flexible cyclic compound. Fortunately computing power has

been continually increasing so that such a search may become

practical. However, it should be remarked that this methodology

must be considered as an exploratory and preliminary approach.

More accurate ab initio and DFT calculations are necessary to

confirm these preliminary data. In other words, the methodology

used in this article to obtain the different conformational inter-

conversion mechanisms represents a satisfactory first approxima-

tion for the conformational analysis of flexible cyclic compounds.

As was previously mentioned an exhaustive conformational

analysis for large-size cyclic molecules is a difficult task. The

major problem is to find all the preferred low-energy forms

and their corresponding conformational interconversion paths

with a high degree of certainty, irrespective of the different

types and degrees of conformational flexibility. Thus very im-

portant features of a conformational analysis method are that

it should be reliable, general, and simple. The predictions also

need to be achieved at modest computational cost.

Our results satisfy the above premises. The different confor-

mational interconversion mechanisms for the preferred confor-

mations of cyclododecane were obtained from the PECs inter-

connecting the low-energy conformers. Such calculations were

carried out using inexpensive semiempirical PM6 calculations,

which demand a very low computational requirement. Our

approach has worked very well for cyclododecane. By analyzing

a number of curves of the low-energy conformers, we have

shown that this procedure is a reliable, simple, and general tool

for conformational searching. Thus, it appears that this relatively

simple procedure represents a very useful alternate to other

methods for the conformational analysis of medium and large

flexible cyclic compounds. However, it should be noted that for

large-size cyclic compounds the number of relevant minima

might be located in the hypersurface far away among them,

possessing a significant number of intermediate conformations.

Thus, the appropriateness of this protocol should be tested

carefully for large-size cyclic compounds.

Acknowledgments

This work was supported by grants from Universidad Nacional de

San Luis (UNSL). R. D. Enriz is member of the Consejo Nacional de

Investigaciones Cientıficas y Tecnicas (CONICET-Argentina) staff.

Keywords: cyclododecane � conformational study � potentialenergy curves � ab initio and DFT calculations � transition states

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Received: 13 May 2011Revised: 7 June 2011Accepted: 5 July 2011Published online on 27 October 2011



Multistep conformational interconversion mechanism of cyclododecane. A simple and fast analysis...

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