MMH-2 as a new approach for the prediction of intermolecular interactions: the crystal packing of...

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MMH-2 as a new approach for the prediction of intermolecularinteractions: the crystal packing of acetamide†

Edelsys Codorniu-Hern�andez,‡*a A. Daniel Boese,b Carsten Schauerte,b Alberto Rolo-Naranjo,a

Ram�on Miranda-Quintana,a Luis A. Montero-Cabrerac and Roland Boeseb

Received 23rd March 2009, Accepted 8th June 2009

First published as an Advance Article on the web 23rd July 2009

DOI: 10.1039/b905779j

A new approach (MMH-2) was applied and tested for the prediction of intermolecular interactions in

the crystal packing of acetamide. In MMH-2, energies of random molecular interaction configurations

are computed. It uses molecular association quantities from statistical thermodynamics in order to

obtain intermolecular interaction motifs that follow a ranking process. The most important motifs are

optimized. Here, the AM1 semiempirical Hamiltonian was applied for the calculation and optimization

of each obtained configuration and a comparison to MP2 results is provided. Such a stepwise procedure

follows the assumed genesis of crystal growth without using experimental input. For evaluation

purposes, graph set analysis was used to classify the structural patterns of both acetamide polymorphs.

It was also necessary to introduce a new geometrical similarity index for the comparison of calculated

and experimental motifs. As a result, all experimental hydrogen bond patterns were found and

molecular synthons in both polymorphic acetamide structures were predicted as local minima. This

suggests a new strategy for crystal structure prediction of flexible molecules with a possible subsequent

progress in crystal engineering in silico.

1. Introduction

Most of the neat solids contain crystals or crystalline regions

which influence the respective solid state properties. All funda-

mental chemical and physical properties such as solubility,

melting temperature, hardness or hygroscopicity are therefore

determined not only by molecular structure but also by the

packing of the molecules in the crystals. This becomes particu-

larly evident with polymorphs which have the same molecules

arranged with different crystal packing. For active pharmaceu-

tical ingredients polymorphism has become an important issue

not only for the obvious reasons of modulated properties which

influence the bioavailability and other features but also for legal

issues in the context of intellectual property protection.1 This

caused a boom in research activities but the possibility to predict

a crystals structure starting from a molecular structure is still in

its infancy. Even though more than 450 000 crystal structures of

aDepartment of Molecular Design and Synthesis, Higher Institute ofTechnologies and Applied Sciences, Ave Salvador Allende y Luaces,Quinta de los Molinos, Plaza de la Revoluci�on, Ciudad Habana, CP10600 AP 6163, CubabDepartment of Chemistry, University of Duisburg-Essen,Universit€atsstrasse 5-7, 45117 Essen, GermanycLaboratory of Computational and Theoretical Chemistry, Faculty ofChemistry, University of Havana, Zapata e G y Maz�on, CP 10400Ciudad Habana, Cuba

† Electronic supplementary information (ESI) available: A brief outlineof MMH procedures; results of MMH-1/AM1 for acetamide dimers(Fig. S1–S4); additional results comparing MMH-2/AM1 with MP2and DFT calculations (Tables S1–S12, Fig. S5–S6). See DOI:10.1039/b905779j

‡ Current address: Department of Chemistry. University of Calgary.2500 University Drive N.W., Calgary, Alberta, Canada, T2N 1N4.E-mail: [email protected]; Tel.: +1(403)220-7561.

2358 | CrystEngComm, 2009, 11, 2358–2370

organic molecules are precisely described in literature

(Cambridge Structural Database (CSD)),2 the open problem of

‘crystal structure prediction’ (CSP) has not been conclusively

solved.3–7

The Cambridge Crystallographic Data Centre (CCDC) orga-

nized regularly blind tests in CSP since 2000 with the participa-

tion of different computational laboratories, but the problem

turned out to be much more subtle than originally anticipated.

There were severe restrictions for the candidates selected for the

tests in respect of the size of the molecules, the number of

molecules in the asymmetric unit, the kind of elements, flexibility,

space groups etc. which were thought to reduce the problem and

computational times. However the restrictions had a significant

influence on the approaches, in spite of major advances8 there

still seems to be no general solution in sight.9–11

The restriction of space groups and the number of independent

molecules in the asymmetric unit favoured approaches which

start with a symmetry relationship between two molecules and by

adding further molecules ending in a pattern that corresponds to

one of the most favourable space groups for organic molecules as

found in the CSD.

Amongst different strategies there is one which assembles

molecules according to the most frequent and robust patterns

found in the CSD, called supramolecular synthons.12 Such

preferred motifs went through different steps of crystal growth

and therefore they represent an experimental result which has all

the prerequisites of an existing crystal.

Other approaches follow much more the genesis of a crystal

and do not apply symmetry restrictions when assembling clus-

ters. Two molecules meeting each other do not have symmetry in

mind, their goal is to minimize their relative energy followed by

adding stepwise an increasing number of molecules.

This journal is ª The Royal Society of Chemistry 2009

A strategy which seems to be most promising, combines the

two approaches which consider the genesis of a crystal by ana-

lysing the energy for clusters of increasing size and then selecting

motifs which proved to be stable synthons for existing crystals.

The first step is therefore the formation of clusters without

employing any symmetry restrictions. The second step consists of

finding motifs which can be localised with the help of the less

specific graph-set analysis for hydrogen bonds and the third step

is allocating the supramolecular synthons. The final step should

be generally constituted as a selective aid used to rule out less

favourable patterns which are less likely to exist according to

statistical searches in the CSD.

The importance of the first step is undisputed and consists of

the development and application of reliable methods for the

correct estimation of intermolecular interactions. Our aim is to

introduce and test a new approach (MMH-2) in order to provide

the packing motifs. MMH-2 is based on a previous methodology

‘‘Multiple minima hypersurface procedure’’ (MMH, now to be

called MMH-1) published ten years ago by one of the authors

(LMC)13 as an alternative method for the study of explicit solvent

effects. MMH-1 has been extensively applied in the last years for

the study of intermolecular associations.13–18 In recent papers,

MMH-1 was also recognized as a very reliable procedure for

searching minima in weakly interacting complexes.16–18 The new

approach keeps the conception of the original MMH-1

combining quantum mechanical methods and statistical ther-

modynamics in order to obtain thermodynamic magnitudes

related with molecular association processes.

The remainder of this article is organized as follows: In section

2 we describe the general steps of the proposed approach (MMH-

2) and the consecutive procedures for the application of MMH-2

and MMH-1 in the elucidation of acetamide hydrogen bond

motifs. In this section we also discuss our computational setup

with the application of different simulation packages. In section

3 we present the graph set results and supramolecular synthons

of acetamide polymorphs in order to have the experimental

patterns for comparison with the theoretical results. Finally, in

section 4 we summarize our findings and discuss the possible

application of MMH-2 for CSP.

2. Theory and procedures

The original MMH-1 approach has already been explained in

details13–15 and is also explained in the supplementary

information.‡ It was created with the original purpose of eval-

uating the thermodynamic association functions of various

molecular clusters (using the partition function) and to randomly

explore the multiple minima hypersurface of a supermolecular

system. The exploration is made by generating several sets of

initial random geometries. This is followed by a gradient

pathway search to the local minima that could be statistically

significant.

MMH-1 outlines as:

(1) Random generation of different molecular configurations

starting from the optimized fragment geometries.

(2) Geometry optimization of the selected configurations by

standard gradient path minimization.

(3) Selection of the most important configurations through

molecular association magnitudes obtained by statistical


thermodynamic formulas (association energies and entropies,

population of states, See Supplementary Information).

This scheme is modified in MMH-2 in the following way:

(1) Random generation of different molecular configurations

starting from the optimized fragment geometries.

(2) Single-point energy calculations of each different configu-

ration.

(3) Selection of the most important configurations through

molecular association magnitudes obtained by statistical ther-

modynamic formulas (association energies and entropies,

population of states, See Supplementary Information).

(4) Geometry optimization of the selected configurations by

standard gradient path minimization.

(5) Ranking order of the structural motifs by the configuration

energies (Scheme 1).

Thus, the MMH-1 method consists of steps 1, 4, and 3 from

the MMH-2 scheme.

If we have to compare with experimental patterns, one extra

point should be added:

(6) Selection of the best superimposed structures (comparing

theoretical and experimental patterns) through the similarity

index values. Graph set analysis was used to classify the struc-

tural patterns of acetamide.

After the last step in this scheme, the simulation is stopped

after a yet undefined halting criterion has been met. In our case,

the calculation finishes after the intermolecular associations of

the experimental structures for acetamide that favour the growth

of both polymorphs and the three-dimensional behaviour of the

crystal have been found. Association complexes with many

monomers are likely to show the building blocks when predicting

crystal structures. Here, another criterion to stop the simulation

can be found when a large increase in the dissociation energy is

observed.

For this scheme, two crucial choices have to be made in each

particular test applying MMH-2 for CSP:

—The appropriate selection of the underlying methodology

for the single point energy calculation (step 2) and the optimi-

zation (step 4) of each supermolecule.

—The way to compare calculated and experimental structural

motifs (step 6)

Concerning the first choice, our aim herein is to find those

crystal structures favoured by nature, which can become

a formidable task. In some cases, the experimentally obtained

structures are not related to the computed ‘‘global minimum’’ of

either the condensed structure or the fragments. Here, kinetic

effects might become important. Thus, previous attempts to

apply quantum chemical methods (ab initio or DFT) to find the

global minimum for CSP did not succeed in all cases.8–11

We believe that a statistical thermodynamic approach to find

the most important local minima will prove more successful.

Following a recent experience with MMH-1,13–15 the structural

analysis shows that various ‘‘local minima’’ may contribute

significantly to the stabilization of the system. However, in the

case of acetamide, MMH-1 was unable to reproduce the exper-

imental patterns found in the crystal structure.

MMH-2 is much faster and as we shall see later, much more

robust in the prediction of the experimental patterns. The AM1

semiempirical Hamiltonian is used to calculate the preliminary

energies of all the generated molecular arrangements.

CrystEngComm, 2009, 11, 2358–2370 | 2359

Scheme 1 Graphic representation of the novel MMH-2 approach

Since several hundred supermolecular geometries are gener-

ated during the first step, the use of ab initio methods for struc-

tures larger than dimers is computationally not feasible.

semiempirical methods have been confirmed as a good choice for

the discrimination of geometries.16–19 Here, the computational

process is fast enough to treat a huge number of different

structures that could also include large molecular systems (such

as proteins and nanoclusters). For acetamide, semiempirical

results can be tested and complemented with more sophisticated

and accurate calculations. This provides a useful test for the

reliability of this kind of Hamiltonian. In this work, we compare

the results of the AM1 Hamiltonian with the experimental

patterns as well as other methods (DFT and MP2).

For the geometrical comparison of the calculated and experi-

mental structural motifs, an overlap matrix was calculated

through TGSA2001 program,20 with the maximum overlap

among all the structures. Some quantum similarity indices were

tested in order to select the best overlap structures.21–24 Unfortu-

nately, none of them was useful for our approach. Here, the

geometric comparison was not explicitly considered. This possibly

caused some failures in the recognition of the best overlap between

calculated and experimental structures. We introduced a new

Positional similarity index (PSI). PSI ˛ [0, 1] while PSI ¼ 1

corresponds to an ideal structural overlap (eqn (1)). PSI is based

on the geometric coincidences among the atoms from two mole-

cules i and i0. Two atoms are considered coincident if the distance

between them is lower than a pre-defined thereshold (3).

PSIMOL ¼

PNATOM

i¼1

Ci;i0 ð3Þ

NATOM

(1)

The coincidence Ci,i0 is defined as:l

2360 | CrystEngComm, 2009, 11, 2358–2370

Ci;i0 ð3Þ ¼

8>><>>:

1 if dði; i0Þ# 3

5%ðdMAX � dði; i0ÞÞ if 3\dði; i0Þ# dMAX

0 if dði; i0Þ. dMAX

9>>=>>;(2)

dMAX is the maximum distance value considered in the specific

acetamide atomic comparison process. In the case of acetamide

dMAX has a the value of 3 �A. For d(i,i0 0) values higher than dMAX

the calculated molecules do not have geometrical proximity.

d (i,i0) represents the Euclidean norm between atoms i and i0. The

set of those superimposed structures having a higher overlap

between the experimental and predicted pairs of structures is an

automatic output of the methodology.

Computational details

Different calculations were carried out in order to compare the

results of MMH-2/AM1 and other ab initio and DFT methods.

The latter methods were used to reoptimize the local minima

found by the new approach.

semiempirical Hamiltonian. For obtaining minimal energy

structures AM1 was applied, using the MOPAC25 program. In all

calculations, the eigenvector following the routine was used and

all convergence thresholds have been tightened by a factor of

1000. The MMOK option for optimizing peptidic bonds was

used by means of a molecular mechanical field. This is better

suited to reproduce the planar geometry of the peptidic bond and

the experimental value of the Z/E interconversion barriers.

Ab initio methods. The lowest structures found by the AM1

Hamiltonian were optimized using different levels of calculation:


Fig. 1 A portion of the crystal structures of acetamide polymorphs

(ACEMID03 and ACEMID06).

The dimers were fully optimized with HF/6-311G(d,p)26 and

MP2/6-311G(d,p)27 using the Gaussian 0328 program. Further-

more, MP2/aug0-cc-pVTZ29,30 (denoting that we used diffuse

functions only on the nitrogen and oxygen atoms) values were

obtained using the Turbomole31 program. Here, MP2 was

calculated within the RI approximation. We used MP2 rather

than e.g. SCS-MP2 because of its good prediction of hydrogen

bonds, being still unsurpassed in accuracy by other methods of

this speed.32 Using these structures, single-point energies were

calculated using the MP2/aug0-cc-pVQZ29,30 and MP2/aug0-cc-

pV5Z29,30 basis sets. The trimers and tetramers from MMH-2/

AM1 were optimized by MP2/aug0-cc-pVTZ, the pentamers and

hexamers by MP2/aug0-cc-pVDZ.

Density functional theory. DFT calculations have been per-

formed using the CP2K33 simulation package for the optimiza-

tion of the acetamide trimers in isolated conditions. The density

functional theory implementation in CP2K (Quickstep)34 is

based on the hybrid Gaussian plane wave (GPW) scheme.35 In

this scheme, an efficient algorithm for the calculation of the

Kohn–Sham matrix is obtained through a dual representation of

the electron density. The Goedecker–Teter–Hutter (GTH)

pseudopotential36–38 has been employed for all DFT calculations

using the HCTH/120 functional.39 A 350 Ryd plane wave density

cut-off has been applied. Carbon, hydrogen and nitrogen of the

acetamide molecules were described by standard triple-z basis

with one set of polarization functions (TZVP).

In the paper we are presenting the results of MMH-2/AM1 and

MMH-1/AM1 in the prediction of structural motifs of acetamide

crystals, providing a clear comparison between both methodol-

ogies for the case of dimer configurations. The details in these

calculations are summarized as follows:

Details in the application of MMH-1/AM1 methodology.

Acetamide dimers and trimers calculations were performed

through the generation of 100 different random geometries,

starting from the optimized geometries. These 100 configurations

were optimized and final geometries and energies were processed

by statistical thermodynamic procedures in order to obtain

a reduced set of configurations that represent the most important

contributions to the whole system. The selected configurations

were used for the comparison with acetamide experimental

patterns. As a simultaneous step we also analyzed all the opti-

mized configurations created and optimized by MMH-1, in order

to look for the structural patterns in non-associated configura-

tions (higher energies).

Details in the application of MMH-2/AM1 methodology.

Acetamide dimer to hexamer calculations were performed

through the generation of 200 different random geometries of

acetamide clusters as the first step. Then, all consecutive steps

presented in Scheme 1 were followed. The most stable dimer

configurations were used as building blocks for the simulation of

trimers, those of trimers for tetramers, and so on. In addition,

different dimers–hexamers configurations were constructed

starting from the isolated acetamide molecules. In order to

compare all the structural patterns and theoretical results, the

best overlapped structures served as input file for calculating PSI

(eqn (1)).


3. The system under study

We investigated the structure of acetamide, which was described

by Bernstein et al. in 199540 concerning its hydrogen bond

patterns and its respective graph sets. Solid acetamide exists in

two crystal forms under ambient conditions.41 The most stable

modification is rhombohedral42,43 which contains one molecule

in the asymmetric unit and the metastable is an orthorhombic

form with two molecules in the asymmetric unit.44,45 The

crystal structures of the two forms were taken from the crystal

structures database, which we refer to as ACEMID06 and

ACEMID03 henceforth. Fig. 1 shows a part of the crystal

structures of both polymorphs. The hydrogen bond patterns

presented in both acetamide polymorphs were obtained

through a graph set analysis. Therefore, each acetamide poly-

morph was analyzed and catalogued in a readily recognizable

notation (Fig. 2 and Fig. 3).40 All these structures were used as

experimental patterns for comparison with the theoretical

predictions.

4. Results and discussion

MMH-1/AM1 is unable to reproduce the experimental patterns

of acetamide polymorphs. This can be deduced from the

behaviour of the thermodynamic association magnitudes of

acetamide dimers which is shown in the supplementary materi-

al.‡ The MMH-1/AM1 method predicts the true global minimum

corresponding to the R22(8) pattern shown in Fig. 2. This

CrystEngComm, 2009, 11, 2358–2370 | 2361

Fig. 2 Hydrogen bond motifs from ACEMID03 polymorph.

Fig. 3 Hydrogen bond motifs from ACEMID06 polymorph.

2362 | CrystEngComm, 2009, 11, 2358–2370

structure coincides with the structural pattern present in the

asymmetric unit of one of the acetamide polymorphs (ACE-

MID06). However, none of the other structural motifs are found

with MMH-1/AM1. Only the C11(4) pattern is present if we

consider energies more than 3 kcal mol�1 above the global

minimum, which is one of the structural patterns presented in

ACEMID03. The other experimental patterns found are not

predicted as stable structures. Thus, the information provided by

MMH-1/AM1 is incomplete, especially if several patterns and

polymorphs are present. MMH-1/AM1 was designed to predict

clusters in the gas phase to condense without any other

interaction than those among the considered molecules. Those

interactions could be exaggerated because they are focused

exclusively on the gradient path optimization after the random

cell generation.

Hence, an extension of this approach is needed, where the most

important local minima are considered and calculated, arriving

at the new MMH-2/AM1 method. Here, Scheme 1 is used for the

prediction of crystal structures.

4.1 MMH-2/AM1 results

4.1.1 Acetamide dimer configurations. Fig. 4 shows the

behaviour of the association thermodynamic magnitudes

obtained by MMH-2/AM1 for the acetamide dimers. It is evident

that other possibilities of acetamide associations are now

provided by the new approach, rather than just finding one

minimum structure. MMH-2/AM1 yields many dimer molecular

associations within 3 kcal mol�1 of the global minimum. In the

graphical representation of the population of the states of

MMH-2/AM1 (Fig. 5) there are several structures with


Fig. 4 Thermodynamic association magnitudes of acetamide dimer configurations obtained by MMH-2/AM1.

Fig. 5 Population of states and energies of each acetamide dimer

configuration obtained by MMH-2/AM1. Note that the structures with

any significant population correspond to the four local minima also

found in the experimental patterns.

Fig. 6 Superimposed experimental and predicted acetamide dimer

structures obtained by MMH-2/AM1. d1, d2 and d4 correspond to

ACEMID06, whereas d3 and d4 can be found in ACEMID03.

important statistical contributions. All these structures lead to

the local minima reported in Fig. 6. These structures were

collected and superimposed with all the dimer acetamide patterns

in order to obtain the similarity indices.

The four predicted MMH-2/AM1 structures with the

lowest energies coincide with the four experimental patterns

found. Hence, all experimentally found dimer patterns were

predicted by MMH-2/AM1 as minima (Fig.6). MMH-2/AM1

is thus able to reproduce the most important hydrogen bond

motifs.

In order to provide a comparison among the structures

obtained by MMH-2/AM1 and more sophisticated ab initio

methods, the energies are presented in Table 1.

For MMH-2/AM1, all energies obtained by the calculated

dimer structures of acetamide are basically equivalent to MP2. d2

is the most important dimer, followed by d3, with d1 and d4

having the smallest interaction energies. Note that for MP2

without diffuse functions, d3, d1 and d4 are basically equivalent,

and it is imperative to include diffuse basis functions in such

a study.


The d2 structure has two strong hydrogen bonds (Fig. 6). This

corresponds to the experimental findings: d2 is the dimer present

in tACEMID06 form. From the geometry optimizations

obtained by MP2 (supplementary material‡), d2 and d3 do

not change much when the AM1 optimized structure is provided.

For the other two structures d1 and d4, which are the

starting blocks for the growing of linear chains in the crystal, the

deviations from the experiments and AM1 are larger. They

do not distort completely, however, so that the building

blocks are still visible. These results can be confirmed when using

AM1 to optimize the MP2 structures. The deviation between

MP2 and AM1 is thus likely to be caused by the AM1

parametrization.

Hydrogen bond distances from MP2 results are smaller than

those found in the crystal patterns (Table 2). This is because of

the lack of other acetamide molecules in the calculations in the

CrystEngComm, 2009, 11, 2358–2370 | 2363

Table 1 Energy differences (kcal mol�1) of fully optimized acetamide dimers by different methodologies

Acetamide dimer configuration DEMMH-2/AM1 DEMP2/6-311G** DEMP2/aug0-cc-pVTZ DEMP2/aug0-cc-pVQZ (SP)

d1 3.89 5.86 7.03 5.74d2 0 0 0 0d3 2.35 5.05 5.49 4.01d4 4.04 5.78 6.93 5.89

Table 2 Geometrical parameters experimental and theoretical of acetamide dimers

Conf d(H-bond)/�A Exp. MMH-2/AM1 MP2/aug0-cc-pVTZ MP2/6-311G**

d1 CO–NH2 1.86 2.19 1.94 1.99NH2–CH3 3.08 3.11 4.05 3.89

d2 CO–NH2 2.02 2.05 1.82 1.882.05 2.07 1.82 1.88

d3 NH2–CO 1.89 2.09 1.88 1.94CO–CH3 2.72 2.23 2.29 2.30

d4 CO–NH2 2.01 2.21 1.88 1.99

Fig. 7 Superimposed experimental and predicted structures by MMH-2/

AM1 of acetamide trimers. t2, t3, t4, t5 and t6 correspond to ACEMID06,

whereas t1 and t6 can be found in ACEMID03.

gas phase, as normally occur in the crystal. Since the hydrogen

bond interaction energies are not additive, a hydrogen bond in

the crystal will be somewhat weaker. This phenomenon is also

present in AM1 optimizations. Here, the parameterization of

AM1 probably yields worse structures for the gas phase, but

better structures for the crystal, giving the right answer for the

wrong reason. As shown in Table 1 both d1 and d4, which are

found in the experimental patterns, have the largest energies for

all methods. d2 and d3 correspond to each polymorph, which

means that by MP2, both polymorph building blocks are pre-

dicted. However, d1 and d4 are needed for predicting the full

crystal of both polymorphs, since these interactions are impor-

tant for the interactions of the individual d2 and d3 building

blocks.

The structures of acetamide trimers, tetramers, pentamers

and hexamers were built using the dimer configurations as

building blocks for larger simulations. For comparison,

MMH-1/AM1 was applied as well, but the methodology

failed completely, giving none of the experimentally found

structures.

In MMH-2/AM1, two main pathways were followed to

construct the corresponding structures: (1) generation of acet-

amide trimers, tetramers, pentamers and hexamers starting from

isolated acetamide molecules and (2) generation of acetamide

trimers, tetramers, pentamers and hexamers starting from the

most important dimer (or n � 1 order) motifs as building blocks

(Scheme 1). The results are summarized as follows:

4.1.2 Acetamide trimer configurations. MMH-2/AM1

provided all the trimer acetamide patterns obtained from the

graph set analysis of the experimental patterns. Here, the six

lowest energy structures correspond to the experimental findings.

For trimers, the populations of states of MMH-2/AM1 and their

consequent optimizations only lead to these local minima. As we

can see in Fig. 7, the superimposed structures between calculated

and experimental patterns are not always exactly the same, but

the approach reproduces the structural motifs.

Table 3 shows the energetic ranking of the trimers by different

methodologies. In this case, MMH-2/AM1 finds a difference

2364 | CrystEngComm, 2009, 11, 2358–2370

between linear trimer patterns and the more associated ones. The

MP2 and DFT methods basically yield the same energetic

pattern but the optimized geometries of the MP2 calculations

again deviate from both the experimental patterns and MMH-2/

AM1, especially in the cases of t5 and t6 (ESI‡). Those corre-

spond to the two linear structures found in the experimental

patterns. Again, these two structures are highest in energy, as

predicted by all methods used. In contrast to d2 and d3, t5 and t6

do not exist in the gas phase and get completely distorted by MP2

(as shown in Fig. 8). DFT, lacking a good performance to van

der Waals interactions, interestingly yields the same results as

AM1. However, they correspond to experimentally important


Table 3 Energetic differences (kcal mol�1) of acetamide trimers among different methods

Acetamide trimer configuration DEMMH-2/AM1 DEMP2/aug0-cc-pVTZ DE CP2K HCTH120/TZVP

t1 3.35 3.44t2 0 1.57 0t3 2.67 0 0.23t4 2.66 0.11 0.85t5 5.29 4.24 5.08t6 5.44 4.64 3.76

Fig. 8 Geometrical orientations of t6 by different methods.

geometrical patterns. Since we are looking for the most impor-

tant interactions that favour the growth of the crystal, a majority

of them are linear structures. The success of the MMH-2/AM1

approach is the combinations of several steps (Scheme 1) that

includes a selection of representative clusters by statistical ther-

modynamics, a good strategy for the generation of the random

configurations and the use of a semiempirical Hamiltonian for

the final optimization. The potential energy surface of AM1 is in

some cases quite flat, providing geometries of several local

minima very close to the experimental patterns, without moving

the structures to the global minimum. In the case of trimers, the

found structures do not always correspond to the minimum in

the gas phase, but model the crystal structure with a surprising

Table 4 Geometrical parameters of acetamide trimers by different methodo

Configuration d(H-bond)/�A Exp. MMH-2/A

t1 CO–CH3 (1) 2.01 2.24CO–NH2 (1) 1.89 2.09CO–CH3 (2) 2.73 2.28CO–NH2 (2) 1.89 2.08

t2 CO–NH2 (1) 2.09 2.15CO–NH2 (2) 2.05 2.09CO–NH2 (3) 2.02 2.05

t3 CO–NH2 (1) 2.09 2.15CO–NH2 (2) 2.05 2.09CO–NH2 (3) 2.02 2.05

t4 CO–NH2 (1) 2.01 2.20CO–NH2 (2) 2.02 2.10CO–NH2 (3) 2.05 2.05

t5 CO–NH2 (1) 2.01 2.17CO–NH2 (2) 2.01 2.14

t6 CO–NH2 (1) 1.86 2.13CO–NH2 (2) 1.86 2.37


accuracy. A similar behaviour is presented in the results of

tetramers–hexamers.

The fact that MMH-2/AM1 is able to reproduce the associated

trimers (t2, t3 and t4) as the most stable ones, gives the possibility

to see the possible interactions among different layers in the

crystal.

The hydrogen bond distances obtained by different methods

are shown in Table 4, where we obtain the same behaviour as

with the dimers. The t5 and t6 MP2 results are not comparable

because of the above mentioned changed geometries.

Correlating the theoretical results of dimers and trimers with

the crystal structures of the different acetamide polymorphs we

obtain the following conclusions: from the MMH-2/AM1

method, we obtain four dimer structures (d1–d4), in which d1 and

d4 are more thermodynamically unstable (Table 1). For the

trimers (Fig. 6), the d2 building block is combined via d1 and d4,

however not with d3. We deduce that d2, d1 and d4 belong to the

same polymorph. These results are in agreement with

the experimental crystal structures found. t2, t3 and t4 (Fig. 6) are

the most stable structures and show interactions between two

different layers in the polymorph that contain the d2, d1 and d4

building blocks of ACEMID06. We can identify the trimer

structures t5 and t6 as linear chains of one of these layers of the

ACEMID06 polymorph and t1 as linear chain of the other

polymorph ACEMID03.

Commencing from these results, we build tetramers–hexamers

starting from different combinations of d3 and t1 building blocks

in order to model the growing of ACEMID03 and different

combinations of (d2, d1 and d4) and (t2, t3, t4, t5 and t6) in order to

logies

M1 CP2K (HCTH120/pVTZ) MP2/aug0-cc-pVTZ

2.63 1.891.95 2.282.69 1.871.97 2.281.98 2.162.00 1.861.89 1.801.98 1.932.00 1.861.89 1.771.89 1.811.93 1.871.91 1.921.89 N/A1.881.87 N/A1.88

CrystEngComm, 2009, 11, 2358–2370 | 2365

model the growing of ACEMID06. Additionally, all kinds of

possible tetramers–hexamers associations starting from the iso-

lated molecules were performed. For that reason, the theoretical

results are presented now correlated with the experimental result

of each crystal packing:

4.1.3 Modelling the main intermolecular associations that

support the growing of ACEMID06 crystal structure (tetramers,

pentamers and hexamers). MMH-2/AM1 finds again four tetra-

mers as the most stable configurations (q1–q4) in perfect agreement

with the experimental results. No other local minima were found.

The superimposed experimental and theoretical structures are

provided in the supplementary material.‡ The structures q3 and q4

are more associated configurations that show the interactions

among different layers (similar to t3 and t4 in Fig. 6). The struc-

tures q1 and q2 are linear chains corresponding to the trimers t5

and t6 in Fig.6, which were no minima on the MP2 surface.

This general behaviour was found for all the MP2 optimiza-

tions of the MMH-2/AM1 geometries, going from tetramers to

hexamers: here, the linear chains reproduced by AM1 changed to

more associated clusters using the MP2 method. However, AM1

is in good agreement with the experimental crystal structures and

yield valuable information for the associated state. The

geometrical orientations of the four tetramers obtained by MP2

and MMH-2/AM1 are provided in the supplementary material.‡

Tables 5 and 6 show the energetic and geometrical parameters

of the tetramer configurations, also calculated by MP2. q1 and q2

optimized by MP2 do not even closely resemble the AM1 or

experimental linear structures, completely distorting to more

Table 5 Energetic differences of acetamide tetramers among differentmethodologies

Acetamidetetramerconfiguration DEMMH-2/AM1 DEMP2/aug0-cc-pVTZ

q1 1.85 4.72q2 1.75 4.07q3 0 0q4 0.25 1.48

Table 6 Geometrical parameters experimental and theoretical of acet-amide tetramers

Config d(H-bond)/�A Exp. MMH-2/AM1 MP2/aug0-cc-pVTZ

q1 CO–CH3 (all) 3.02 2.36 N/ACO–NH2 (1) 2.01 2.17CO–NH2 (2) 2.01 2.14CO–NH2 (3) 2.01 2.14

q2 CO–NH2 (1) 1.87 2.17 N/ACO–NH2 (2) 1.87 2.14CO–NH2 (3) 1.87 2.14CO–CH3 2.92 2.36

q3 CO–NH2 (1) 2.01 2.16 1.81CO–NH2 (2) 2.01 2.16 1.87CO–NH2 (3) 2.02 2.05 1.92CO–NH2 (4) 2.05 2.09 1.87

q4 CO–NH2 (1) 2.01 2.16 1.81CO–NH2 (2) 2.01 2.16 1.87CO–NH2 (3) 2.02 2.05 1.92CO–NH2 (4) 2.05 2.09 1.87

2366 | CrystEngComm, 2009, 11, 2358–2370

associated structures. Still, the interaction energies remain much

lower compared to q3 and q4. In these last geometries the most

stable dimer (d2) is present, probably causing this effect. This

structure has two strong hydrogen bonds that favour the stability

of acetamide associations and is responsible for the lower energy

structure. A similar energetic behaviour can be seen in the MMH-

2/AM1 results, although q1 and q2 are recognized as stable

configurations which are in good agreement with experiment.

Considering the geometries in detail, we do not report the MP2

q1 and q2 results because of the above mentioned deviation. The

MMH-2/AM1 distances are close to experiment and the orien-

tation of the molecules (supplementary material‡) is quite good

even for these simulations. The hydrogen bonds obtained by

MP2 are again smaller than the values from the experiments, as

was the case for both dimers and trimers.

Again, detailed information on the geometrical orientation

and geometrical parameters of pentamers and hexamers is

provided in the supplementary material.‡ As before, linear

chains are found by MMH-2/AM1 in good agreement with the

experimental structures. For each of the pentamers and hexam-

ers, the associated cluster is obtained as the global MP2

minimum. In these larger simulations, new information can be

gathered about the structural motifs of the interacting molecular

synthons of these polymorphs (Fig. 9). Even in MP2, a large

building block of the crystal is predicted as minimum. It is

evident that dimer d2 favours the associations between different

layers or molecular synthons in the crystal. The distances of the

calculated interactions have the same behaviour already pre-

sented for dimmers, trimers and tetramers, where MP2 obtains

smaller H-bond distances in comparison to experiment (supple-

mentary material). The energetic differences of pentamers and

hexamers will be presented at the end of the article together with

the results of the second polymorph.

Fig. 9 Representative structures obtained by MMH-2/AM1 for pen-

tamers and hexamers.


Fig. 10 3D view of h4 by MMH-2/AM1 (a) and the behaviour in the

crystal packing of ACEMID06 (b).

Fig. 10a shows a three-dimensional view of h4 obtained by

MMH-2/AM1 as an example of the behaviour of the interaction

among the three structural motifs (d1, d2 and d4), previously

selected by the theoretical results. The interactions among these

three linear chains represent an example of MMH2 to predict the

3D structural motif of the crystal packing.

From the theoretical predictions going from tetramers to

hexamers, there is enough information about the intermolecular

associations related with this acetamide polymorph. From our

experience, it is not necessary to include more than six molecules

in the calculations, as molecular synthons have already been

predicted. They give sufficient information about the way in

which they interact to create the three dimensional packing.

Concluding this section, we find that the dimer structures d1, d2

and d4 prevail as the most important associations of ACEMID06

polymorph, where the dimer structure d2 is responsible for the

interactions among different molecular synthons of this poly-

morph.

Fig. 11 (a) Superimposed experimental and predicted structures (MMH-2/AM

by MP2 calculations.


4.1.4 Modelling the main intermolecular associations that

support the growth of ACEMID03 crystal structure (tetramers,

pentamers and hexamers). With the theoretical information

obtained from the dimers and trimers, the second acetamide

polymorph has only interactions via the dimer d3 structure.

Fig. 11a shows the superimposed experimental and predicted

structures (MMH-2/AM1) of tetramers of ACEMID03. This

structure is in agreement with the experimental crystal structure

but is not reproduced by MP2 (Fig. 11b). Table 7 shows the

geometrical parameters of this structure by MMH-2/AM1.

Two pentamer structures were obtained as stable configura-

tions by MMH-2/AM1 (p4 and p5), in agreement with the

experimental patterns (see supplementary information‡). In this

case, a new interaction between the building block t1 and other

two acetamide molecules yields the pentamer p5. Fig. 12 shows

two different views of this structure where these interactions are

associated with the chain formed by dimer d4 (interactions via d1

and d4). This new pentamer coincides with C22(8), (Fig. 2). The

superimposed experimental and predicted structure of pentamer

(p5) is provided in the supplementary material.‡

The orientations and geometrical parameters of pentamers

and hexamers, calculated by MMH-2/AM1 and MP2 are given as

supplementary material.‡ The geometry of p4 coincides with the

extension of tetramer q5. The pentamer p5 mentioned earlier

reveals the interactions between d1 and d4 in this polymorph. As

for the other polymorph, MP2 does not find these structures as

local minima in the gas phase. In the case of hexamers of this

polymorph, there are two linear chains predicted by MMH-2/

AM1 that are in agreement with the experimental results. MMH-

2/AM1 is reproducing these structural patterns well. This

includes chains as well as the more associated structures. The

geometric parameters have the same behaviour as already seen

before, where MP2 provides smaller distances compared to

experiment. Fig. 13 shows the most important cluster for the

hexamers of this polymorph (h6). It was obtained using d1 and d4

as building blocks in the simulation. Analysing the structure

presented in h6, we obtain already a representative 3D structure

of this polymorph. It is formed by the interactions among the

structural patterns of the linear chains.

As we already stated in the case of the predictions of ACE-

MID06 molecular structures, a study going up to hexamers is

enough to reproduce the most important molecular synthons of

1) of tetramers for ACEMID03 and (b) geometrical orientation obtained

CrystEngComm, 2009, 11, 2358–2370 | 2367

Table 7 Geometrical parameters experimental and theoretical of acet-amide tetramer q5

Config d(H-bond)/�A Exp. MMH-2/AM1 MP2/aug0-cc-pVTZ

q5 CO–CH3 (all) 3.02 2.36 N/ACO–NH2 (1) 2.01 2.17CO–NH2 (2) 2.01 2.14CO–NH2 (3) 2.01 2.14

Fig. 13 A 3D view of h6 by MMH-2/AM1 (a) and the behaviour in the

crystal packing of ACEMID03 (b).

ACEMID03. This also gives some insight into the 3D crystal

packing.

4.1.5 Energetic prediction of polymorph stabilities by MMH-

2/AM1. The energetic behaviour of the predicted structures from

dimers, trimers and tetramer has been presented above when

comparing each structure. Tables 8 and 9, in contrast, show the

dissociation energy of each acetamide cluster compared to the

monomer provided by MMH-2/AM1 and MP2. For MP2, we

can compare those energies to the ones usually obtained for

hydrogen bonds.32 The range for a single hydrogen bond is

between 2 and 13 kcal mol�1. The acetamide dimer has an

interaction energy of 15 kcal mol�1 having two hydrogen bonds

in the most stable dimer. The strength of the hydrogen bond in

NH3–H2O is, in comparison, 6.5 kcal mol�1.

The dissociation energy values presented in Tables 8 and 9 are

sensitive in the prediction of the crystal growing. Here, we

observe quite a different behaviour for the AM1 and MP2

methods. For AM1, trimers are very stable, while the predicted

tetramers are increasing the dissociation energy of the cluster by

only 2 kcal mol�1. When going from pentamers to hexamers, we

observe a large jump in the dissociation energy by 13 kcal mol�1

using AM1 and almost 30 kcal mol�1 using MP2. This is indic-

ative of the fact that one very important building block has been

obtained (Fig. 14). Here, we have obviously arrived at a very

stable structure. Overall, this shows the success of MMH-2 to

achieve the most stable isomers for larger structures, such as

hexamers. These can later be identified by ab initio methods, and

be preserved as a building block when predicting the crystal

structures.

Fig. 12 Different views of pentamer p5 which shows the inte

2368 | CrystEngComm, 2009, 11, 2358–2370

From Tables 8 and 9, we can also compare the stability of

the clusters between each other and predict the thermo-

dynamically most stable polymorph. The more stable acetamide

clusters (d2, t2, t3 and t4, q3 and q4, p3 and p4 and h3 and h4)

belong to ACEMID06. Therefore, from our predictions

ACEMID06 should be the thermodynamically more stable

polymorph.

ractions among two dimer structural motifs (d1 and d4).


Table 8 Formation energy (kcal mol�1) of acetamide clusters by MMH-2/AM1

Efdimer Eftrimer Eftetramer Efpentamer Efhexamers

d1 4.42 t1 11.92 q1 15.30 p1 20.95 h1 26.67d2 8.48 t2 15.28 q2 15.40 p2 21.12 h2 26.26d3 6.14 t3 12.55 q3 17.89 p3 27.00 h3 39.44d4 4.59 t4 12.62 q4 17.63 p4 23.30 h4 38.61

t5 9.98 q5 17.55 p5 20.37 h5 26.85t6 9.83 h6 27.58

Table 9 Formation energy (kcal mol�1) of acetamide clusters by MP2/aug0-cc-pVTZ

Efdimer Eftrimer Eftetramer Efpentamer Efhexamer

d1 8.31 t1 19.44 q1 N/A p1 N/A h1 N/Ad2 15.34 t2 21.47 q2 N/A p2 N/A h2 N/Ad3 9.85 t3 22.88 q3 31.53 p3 38.25 h3 66.77d4 8.40 t4 22.83 q4 31.28 p4 N/A h4 62.37

t5 N/A q5 N/A p5 N/A h5 N/At6 N/A h6 43.39

4.1.6 Possible contributions of MMH-2 to CSP. With the

results from MMH-2/AM1 we are presenting a way of predicting

the growth of crystal structures. For organic molecules, mainly

weak interactions favour the existence of stable and metastable

polymorphs in which active pharmaceutical ingredients (API)

have a crucial importance. Most computational methods of CSP

are based on searching the global minimum in the lattice energy.

This process is challenging because of the wide range of space

Fig. 14 Structure of the most stable pattern found by MMH-2/A


groups and cell dimensions which need to be considered. MMH-

2/AM1 provides the possibility to predict the most stable

intermolecular associations that favour the growing of crystal

structures without requiring any experimental input or symmetry

restrictions. Correlating to the theoretical results, we can also

recognize the structures that belong to different polymorphs with

their respective energetic stabilities. MMH-2 proved to be a very

promising approach and might be also combined with some

developed genetic algorithms methods46,47 in order to improve

the structural assembly. In our opinion, MMH-2 has a wide

range of applications due to the eminent importance of inter-

molecular interactions for the structure, function, and dynamics

of a vast number of chemical and biological systems. For CSP, it

could be an alternative, fast and useful tool.

Conclusions

We have introduced a novel approach (MMH-2) for the predic-

tion of intermolecular interactions with a broad range of appli-

cations and a contribution to crystal structure prediction. Our

results indicate that it is an important tool for the elucidation of

structural motifs of all possible molecular synthons. The interac-

tions among different layers in the crystal in one-dimensional and

three-dimensional structures are also observed. Moreover, it is an

efficient way to predict the existence of various polymorphic

structures and their respective thermodynamic stabilities.

MMH-2 was tested for the case of acetamide polymorphs,

giving the correct results compared to experimental findings.

Using AM1 as an underlying theoretical model, we were able to

predict all structures found in the graph set analysis of the

experimental patterns. As a more sophisticated method, we used

M1 and MP2 in good agreement with the crystal structure.

CrystEngComm, 2009, 11, 2358–2370 | 2369

MP2 for validation. MP2 does not always yield the linear asso-

ciated motifs found by AM1 as local minima in the gas phase.

Despite this drawback, the AM1 motifs proved very useful for

the construction of further associated structures in comparison

to experiment. For the very stable hexamer forms, MP2 finally

agrees with the AM1 results, showing how small building blocks

are formed and the crystal structure might evolve.

Thus, MMH-2 may be an important tool for the development

of crystal engineering.

Acknowledgements

E.C.H. acknowledges financial support by the Deutsche For-

schungsgemeinschaft, Forschergruppe 618 for research grant in

Essen, Germany, in 2007 and 2008. Most of the calculations were

performed using the computing facilities of the group of Prof.

Georg Jansen, Essen, whom we thank for useful discussions.

Additionally E.C.H. thanks Prof. Dr Michelle Parrinello for the

financial support of a scientific research grant in 2008, Dr Clo-

tilde S. Cucinotta for useful discussions and help for the DFT

calculations, and Sean Christopher Wood (Calgary, Canada) for

his kind review of the English version of this manuscript. We

want also acknowledge Prof. Ram�on Carb�o-Dorca for giving us

the access to TGSA program.

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