A Combined Experimental and Theoretical Electron Density Study of Intra- and Intermolecular Interactions in Thiourea S,S-Dioxide

A Combined Experimental and Theoretical Electron Density Study of

Intra-and Intermolecular Interactions in Thiourea S,S-Dioxide

Chi-Rung Lee,*

[b]

_{Ting-Hua Tang,}

[a]

_{Likey Chen,}

[a]

_{and Yu Wang*}

[a]

Abstract: The

thiourea

S,S-dioxide

molecule is recognized as a zwitterion

with a high dipole moment and an

unusually long C S bond. The molecule

has a most interesting set of

intermolec-ular

interactions

in

the

crystalline

state–a relatively strong O ¥¥¥H N

hy-drogen bond and very weak

intermolec-ular C ¥¥¥S and N ¥¥¥O interactions. The

molecule has C

s

symmetry, and each

oxygen atom is hydrogen-bonded to two

hydrogen atoms with O ¥¥¥H N

distan-ces of 2.837 and 2.826 ä and angles of

176.61 and 158.38

8. The electron density

distribution is obtained both from X-ray

diffraction data at 110 K and from a

periodic

density

functional

theory

(DFT) calculation. Bond

characteriza-tion is made in terms of the analysis of

topological properties. The covalent

characters of the C N, N H, C S, and

S O bonds are apparent, and the

agree-ment on the topological properties

be-tween experiment and theory is

ade-quate. The features of the Laplacian

distributions, bond paths, and atomic

domains are comparable. In a systematic

approach, DFT calculations are

per-formed based on a monomer, a dimer,

a heptamer, and a crystal to see the

effect on the electron density

distribu-tion due to the intermolecular

interac-tions. The dipole moment of the

mole-cule is enhanced in the solid state. The

typical values of

1

b

and H

b

of the

hydrogen bonds and weak

intermolecu-lar C ¥¥¥S and N ¥¥¥O interactions are

given. All the interactions are verified

by the location of the bond critical point

and its associated topological properties.

The

isovalue

surface

of

Laplacian

charge density and the detailed atomic

graph around each atomic site reveal the

shape of the valence-shell charge

con-centration and provide a reasonable

interpretation of the bonding of each

atom.

Keywords: charge density ¥ density

functional calculations ¥ hydrogen

bonds ¥ topological analysis ¥ X-ray

diffraction

Introduction

Intermolecular interactions, particularly hydrogen bonds, play

a key role in molecular recognition in a wide range of

chemical and biological systems.

[1]

_{These interactions are}

almost ubiquitous in molecular crystals and biological

mole-cules. For the hydrogen-bond interaction, studies that use the

theory of atoms in molecules (AIM),

[2]

_{based on both}

theoretical

[3±14]

_{and experimental}

[15±25]

_{electron densities, have}

drawn considerable interest recently. Different types of

hydrogen bonding and weak interactions have been studied

to elucidate the nature of these interactions. The topological

properties of the electron density distribution of both a

molecule and a crystal are based on the gradient vector field

of the electron density

r1(r) and on the Laplacian

distribu-tion of the electron density

r

2

_{1(r). Several excellent reviews}

have been published

[2, 15, 26±28]

_{on this subject. In the light of the}

AIM approach, experimental and theoretical research into

the charge density distributions of many different types of

chemical bond in organic, sulfur-containing compounds and

metal complexes

[29±32]

_{has been studied in terms of local charge}

concentration and local charge depletion of a Lewis acid ±

base concept.

[2]

_{This general phenomenon has been well}

studied in many other kinds of interaction, such as the

formation of hydrogen bonds,

[3±25]

_{the directional}

intermolec-ular interaction of Cl

2[33]

and S

4

N

4[34, 35]

in the solid state, and

even the binding interaction in van der Waals dimers and a

trimer,

[36]

_{as well as the adsorption of molecules on a}

surface.

[37]

The charge density, chemical bonding, and intermolecular

interactions of urea and thiourea have all been extensively

investigated.

[8, 25, 38±41]

_{It was reported}

[38]

_{that the observed}

planar geometries of guanidine and urea in the crystal form

[a] Prof. Y. Wang, Prof. T.-H. Tang, Dr. L. Chen

Department of Chemistry National Taiwan University

Taipei 106, Taiwan (Republic of China) Fax: (‡886)-2-23636359

E-mail: yuwang@xtal.ch.ntu.edu.tw [b] Prof. C.-R. Lee

Department of Chemical Engineering Minghsin University of Science and Technology Hsin-chu 304, Taiwan (Republic of China) E-mail: crlee@mhit.edu.tw

Supporting information for this article is available on the WWW under http://www.chemeurj.org/ or from the author.

are probably due to hydrogen bonding. In a theoretical study,

hydrogen-bonded aggregates of urea and thiourea were

reported

[39]

_{to form chains and ribbons. The structure and}

charge density of the complex of thiourea with parabanic acid

were studied at room temperature,

[25]

_{and two N H ¥¥¥S and}

N H ¥¥¥O weak hydrogen-bonding interactions were located

in the cyclic parabanic acid ± thiourea dimer. A preliminary

study was carried out for crystalline urea a decade ago with

the ab initio approach.

[40]

_{In a further study using the periodic}

Hartree ± Fock (PHF) approach,

[8]

_{with the geometry taken}

from the accurate neutron diffraction,

[41]

_{two in-plane and two}

out-of-plane hydrogen bonds, as well as intramolecular

interactions, were described in terms of the AIM theory in

the crystal structure of urea. The topological properties

associated with the bond critical points (BCPs) were

inves-tigated in the gas phase and the solid state, for the purpose of

understanding changes in the properties due to changes in the

packing environment, in other words, the crystal packing

effect. It was found that, on going from molecule to crystal,

both the

j H

b

j and 1

b

values increase for the C N bond, while

these values decrease for all other bonds.

[8]

_{This means that}

only the C N bond is strengthened, where an increase of

p

character is induced by crystal packing. It is not often found

that a carbonyl oxygen atom is involved in four hydrogen

bonds, as in this case; the calculated sublimation energy was

91.21 kJ mol

1[8]

_{in comparison with the experimental value of}

88

 2 kJmol

1

_.

[42]

_{Recently, quantitative comparisons of the}

experimental and theoretical charge densities of urea were

made.

[43]

_{The intermolecular interaction energy in crystalline}

urea was calculated both from diffraction data and with the

PHF approach by using a modified atom ± atom

approxima-tion

scheme;

the

calculated

sublimation

energy

was

90 kJ mol

1

_{, which is very close to the value of 96 kJ mol}

1

obtained by experiment.

[44]

The purpose of the present study is to investigate the

intra-and intermolecular interactions, particularly the hydrogen

bonding, in a molecular crystal. Thiourea S,S-dioxide was

chosen due to its zwitterionic character and its C S bond,

which is the longest known (1.8592 ä), to best of our

knowledge. The extensive hydrogen-bond network

through-out the crystal may well be the result of the high dipole

moment of the molecule. The molecule is quite unique and,

together with the previous knowledge about urea and

thiourea,

[8, 25, 38±44]

_{it is bound to give much insight into the}

intermolecular interactions. A systematic study concerning

the intermolecular interactions of this molecule should be

very interesting. According to our previous studies, the crystal

structure

[45]

_{of this molecule is in space group Pnma. Each}

oxygen atom is involved in two hydrogen bonds similar to

those in urea. A preliminary electron density study

[46]

_was

made by single-crystal X-ray diffraction at 110 K and by a

molecular-orbital calculation based on an isolated molecule.

The agreement on the chemical bonding characterization

between the experimental and theoretical results was

ad-equate.

[46]

_{The main interests of this work are, however, the}

hydrogen bonds and other weak intermolecular interactions.

In order to understand the nature of such intermolecular

interactions in this molecule in the solid state, theoretical

charge densities are to be calculated systematically for the

monomer, dimer, heptamer, and crystal. The effect on the

chemical bonds due to molecular packing will be investigated

in terms of the AIM theory.

Results and Discussion

Structure and multipole model: The molecular structure of

thiourea S,S-dioxide with its atomic labeling and internal

coordinates is depicted in Figure 1. The molecular symmetry

is C

s

, and two types of hydrogen bond exist in the crystal. In

Figure 1. The molecular structure of thiourea S,S-dioxide with atomic labeling and internal coordinates.

the first, molecules are linked to each other through hydrogen

bonds in pairs between the N H1 group and an O atom to

form a ™head-to-tail∫ type bond with an O ¥¥¥H1 N distance

of 2.837 ä and an angle of 176.61

8 (Figure 2a, b). The other

type of bond is between the N H2 group and a neighboring O

atom with an O ¥¥¥H2 N distance of 2.826 ä and an angle of

158.38

8 (Figure 2a, b). Each H atom is involved in one type of

hydrogen bond, but each O atom is involved in two hydrogen

bonds. These two types of hydrogen bond form a zig-zag

network and give rise to an infinite network of molecules

throughout the crystal (Figure 2 a, b). In addition, there are

weak C ¥¥¥S and N ¥¥¥O interactions in the crystal as shown in

Figure 2 c. The structural parameters are the same (within

standard deviations) as those given in the previous work,

[46]

where the deformation density maps based on the multipole

model were also shown. In this work, multipole refinements

are performed with an additional quadrupole term for the H

atom and

k' for each atom. Parallel multipole refinements

based on the structural amplitudes (F values) derived from a

periodic density functional theory (PDFT) calculation are

also carried out. The residual maps after the multipole

refinements based on experimental structural amplitudes

and the theoretically derived ones are displayed in Figures 3 a

and b, respectively. The maps are essentially featureless. The

agreement indices and the multipole coefficients from various

refinements are qualitatively the same. Of course, the U

ij

values were set to zero for the model derived from the PDFT

calculation. The list of parameters is given in the Supporting

FULL PAPER

C.-R. Lee, Y. Wang et al.

Figure 2. The intramolecular bonds (sticks) and intermolecular hydrogen bonds and weak interactions (dashed lines) in the crystal packing. a) Projection on the a,b plane showing the hydrogen bonds, b) display of the in-plane and out-of-plane hydrogen bonds, c) depiction of the C S and N O weak intermolecular interactions.

Figure 3. Residual maps after the multipole refinement based on a) ex-perimental data and b) theoretically derived structural factors. Solid contours denote positive values, dashed contours denote negative values. The contour interval is 0.1 e ä 3_.

Information. The additional parameters in the present study

do improve the refinements. The refinement based on the

theoretically derived structure amplitudes is particularly

successful, with the lowest agreement indices shown in

Table 1. The refinements on the experimental data with

k'

constrained from, and free from, the values derived from the

PDFT refinement do not appear to show any difference. The

k'-restricted multipole model (KRMM)

[47]

_{is used for the}

subsequent density studies.

Intramolecular interactions: The comparison of the thiourea

S,S-dioxide molecule with the crystal geometry (CG) and the

optimized geometry (OG) in the gas phase was made, and the

Table 1. Agreement indices of various multipole refinements.

R(F) Rw(F) R(F2_{) Rw(F}2_{) GOF Variable}

octapole[a][46] _{0.0174 0.0217 0.0317 0.0468 1.47 97}

KRMM 0.0169 0.0150 0.0278 0.0299 4.28 111

UMM[b] _{0.0166 0.0149 0.0282 0.0297 4.25 115}

PDFT/XD program 0.0097 0.0092 0.0119 0.0205 4.79 85 [a] Octapole with hexadecapole of the S atom. [b] UMMˆ Unrestricted multipole model.

optimized geometry of the molecule was constrained to C

s

symmetry. Significant differences are found in these two

geometries: 1) Marked lengthening of the C S bond length is

found in the OG (1.9888 rather than 1.8592(6) ä); 2) a bigger

dihedral angle is found between the SO

2

and (NH

2

)

2

C groups

in the OG (78.9 compared with 69.18); and 3) two extra

intramolecular hydrogen bonds (O ¥¥¥H2 N) are present in

the OG that are absent in the CG (Figure 4). However, the

Figure 4. Laplacian charge density distributions of the molecule with a) crystal geometry, and b) optimized geometry. Dashed contours denote positive values and solid contours denote negative values. Solid circles denote the BCPs. Heavy solid lines denote the bond paths. The locations of nuclei are labeled in a). Contours are in steps of 2m_{ 10}n_{e ä}5_{(mˆ 1 ± 3,}

nˆ 3 ± 1).

energy difference between the two geometries is relatively

small (30.59 kJ mol

1

_{). Therefore the crystal geometry is used}

for the subsequent analyses. In the light of the topological

properties analysis of the charge density distribution, the

1

b

,

r

2

₁

b

, and H

b

values (Table 2) of all intramolecular bonds are

in good agreement between the two geometries. The only

discrepancy found is the values related to the S C bond, due

to the marked lengthening of the bond length in the OG. In

addition, the charge concentration of the S atom is different

between the CG and OG in the thiourea plane shown in

Figure 4; this is apparently owing to the extra hydrogen bond

in the OG. It is clearly shown that all the intramolecular bonds

are covalent in character. The C N and S O bonds have

relatively large

1

b

and

jH

b

j values, which indicates a possible

double bond. The

r

2

₁

b

value of the S O bond is positive, but

the H

b

value is negative and the BCP is significantly closer to

the S atom; this indicates a highly polarized covalent bond,

although similar findings would also occur in a very short

polarized bond.

[2, 48]

_{It was reported}

[49]

_{that the S O bond in}

compounds containing a hypervalent sulfur atom in

> SO and

>SO

2

fragments could involve possible participation of an

ionic

p bond, however more than 90% of the charge density is

located at the O atoms in such a

p bond. This is in agreement

with the results based on a different population analysis.

[50]

_In

one recent report,

[51]

_{the S O bond was also expressed as a}

typical polarized

s bond. Compared with the topological

analysis of the S O bond in Me

2

SO

2

and H

2

SO

2[51]

this bond is

longer in thiourea S,S-dioxide (1.500 compared with 1.456/

1.466 ä); the

1

b

and H

b

values of the S O bond in this

compound are also slightly smaller in magnitude. With a

1

b

value of 1.71 e ä

3

_{(versus 1.97 in Me}

2

SO

2

) and a negative H

b

( 2.04 Hartree ä

3

_{), there is definitely an indication of a}

partial double bond, and the polarity of the charge density is

toward the oxygen atom, a fact which is quite consistent with

earlier findings.

[49, 51]

_{The C S bond is the longest single bond}

found in the literature.

[46]

_{The BCP is slightly closer to the S}

atom, which indicates that the S atom is slightly more positive

than the C atom; this is indeed so, as observed from the

atomic charge (Table 4). The

1

b

and

jH

b

j values of the C S

bond are relatively low. This indicates that the C S bond here

is a rather weak single bond. An empirical linear correlation

between the bond length and the values of

1

b

was reported

recently for C S bonds of several sulfur-containing

com-pounds.

[30]

_The

1

b

value and bond length of this molecule fit

well with this linear relationship. The C N bond here is

shorter than that of urea.

[8]

_The

₁

b

values are comparable. The

large negative H

b

value of

4.01 Hartree ä

3

certainly

indicates that the C N bond is more than a single bond. It

was also reported that the

p character of the C N bond is

enhanced for urea from the isolated molecule to the solid

form.

[8]

In order to realize the effect of intermolecular interactions

exerted on the chemical bonds in the solid, the systematic

topological properties analysis is applied to the theoretically

calculated electron densities of a monomer, a heptamer, and a

Table 2. The topological properties of the theoretically calculated charge densities at the bond critical point for the crystal geometry (CG) and the optimized geometry (OG).[a]

Bond Bond length d1[b] ₁

b r21b Hb [ä] [ä] [e ä 3_{] [e ä} 5_{] [Hartree ä} 3_] S O 1.4997(6) 0.583 1.71 18.96 2.04 1.509 0.586 1.68 17.54 2.00 S C 1.8592(6) 0.884 1.12 6.69 0.87 1.988 0.975 0.88 2.76 0.50 C N 1.3096(7) 0.444 2.28 17.90 4.01 1.310 0.445 2.27 18.01 3.99 H1 N 1.030 0.259 2.12 41.18 3.22 1.013 0.250 2.20 43.36 3.39 H2 N 1.030 0.238 2.10 42.24 3.24 1.022 0.234 2.14 43.18 3.33 O ¥ ¥ ¥ H2 2.226 0.876 0.12 1.41 0.00

[a] First line for the CG, second line for the OG. [b] d1 is the distance from the BCP to the first atom.

FULL PAPER

C.-R. Lee, Y. Wang et al.

crystal; the results are tabulated in Table 3. The

correspond-ing values obtained by experiment and from the multipole

model imposed on theoretical structure factors are also listed

in the table for comparison. The trend of strengthening the

intramolecular bond in terms of

1

b

from the monomer and the

heptamer to the crystal is detectable in the theoretical results.

Some discrepancies of the topological properties are found

between the experimental and theoretical values, particularly

on the sign of the

r

2

₁

b

value of S O bonds. It is noticeable

that the BCP of the S O bond observed in the experiment is

not as close to the S atom as in the theoretical calculations,

therefore the

l

3

value is reasonable to make the

r

2

1

b

negative

as expected.

[48]

_{It was pointed out}

[52]

_{that topological}

discrep-ancies between experimental and theoretical crystal charge

densities are mainly attributed to the nature of the radial

function in the experimental multipole model, which would

result in the difference of the

l

3

value. It is worth mentioning

that the intramolecular bonds, except the N H bond, are all

enhanced by the intermolecular interactions according to the

topological analyses. The N H bonds are weakened in the

solid, which is expected when the corresponding

intermolec-ular hydrogen bond is strengthened. In general, the

agree-ment in

1

b

between the experiment and theory improves when

intermolecular interactions are taken into account from a

monomer to a heptamer and then to a crystal. However, the

H

b

values do not follow the same trend. This may result from

the approximate expression

[19, 53±55]

_{in the experimental values,}

which does not strictly fit for a covalent bond.

Atomic domains and atomic net charges: According to AIM

theory,

[2]

_{a set of zero-flux surfaces partitions the molecule}

into unique atom domains (

W). These zero-flux surfaces

projected onto a molecular plane, which contained the S, C,

and N atoms of a moiety, together with the total electron

density distribution, bond paths, and BCPs, are illustrated in

Figure 5 from a DFT calculation of a heptamer model and

from experimental results. The shape and the size of these

domains are nearly identical between the theory and

experi-ment.

The AIM net atomic charge (q

_W

) can be obtained by

numerical integration of the electron density distribution

within the atomic domain (W) and subtraction from the

atomic number (Z

n

): q

W

ˆ Z

n

„

W

1(r)dt. The net atomic

charges and the fragment charges are tabulated in Table 4.

The H, C, and S atoms are positively charged and the O and N

atoms are negatively charged. The agreement between

experiment and theory is reasonable. This charge distribution

gives a positive C(NH

2

)

2

moiety and a negative SO

2

fragment,

which fits the zwitterionic description; however the negative

charge is mainly on the O atoms of the SO

2

fragment. The

dipole moment of the molecule seems to be enhanced from

the monomer to the crystal (12.6 versus 14.6 Debye), which

was also found in the case of urea (2.02 versus 2.77 Debye)

[8]

and nitro aniline compounds (13.3 versus 16.1 Debye).

[56, 57]

The dipole moment derived from the Mulliken charges or the

monopole values obtained from the multipole refinement

gives roughly the same value. This confirms the earlier

finding.

[47]

Intermolecular interactions

Intermolecular hydrogen bonding: The existence of two types

of hydrogen bonds is confirmed by the topological properties

analysis of electron density (Table 5). According to the

topological properties associated with the BCP of the

Table 3. Intramolecular interactions : the topological properties associated

with the BCPs.[a]

Bond/ d1 1b r21b Hb

Bond length [ä] [ä] [e ä 3_{] [e ä} 5_{] [Hartree ä}3_]

S O 0.583 1.709 18.964 2.038 /1.4997(4) 0.583 1.749 19.469 1.958 0.581 1.779 20.866 2.012 0.609 1.772 6.825 1.677 0.608 1.852 5.353 1.772 S C 0.884 1.117 6.686 0.873 /1.8592(6) 0.922 1.173 7.790 0.878 0.939 1.186 6.984 0.817 0.933 1.167 4.967 0.867 0.985 1.195 2.977 0.838 C N 0.444 2.279 17.900 4.007 /1.3096(5) 0.452 2.322 22.396 4.103 0.442 2.419 18.488 4.125 0.450 2.444 22.419 3.135 0.479 2.302 17.770 2.906 H1 N 0.259 2.124 41.180 3.224 /1.030 0.237 2.102 41.805 3.246 0.230 2.170 41.395 3.217 0.233 1.916 30.605 2.482 0.203 1.776 29.992 2.382 H2 N 0.238 2.102 42.242 3.238 /1.030 0.224 2.077 41.942 3.227 0.230 2.170 41.395 3.227 0.241 1.946 30.513 2.503 0.179 1.532 25.074 2.165 S O[51] _{1.97 22.94 2.38} /1.456 S O[51] _{1.94 20.55 2.36} /1.466 S O[51] _{0.878 1.357 0.502} /1.514 S C[30] _{0.79 1.36 3.75 1.03} /1.712 0.71 1.42 8.97 1.60 S [30] _{0.96 1.21 3.53 0.90} /1.824 0.96 1.22 6.78 0.83 S C[30] _{0.83 1.35 6.91 1.13} /1.721 0.78 1.40 9.78 1.37 S C[30] _{0.78 1.50 4.87 1.46} /1.657 0.64 1.45 0.18 1.71 C N[30] _{0.71 2.45 11.15 2.43} /1.326 0.45 2.30 18.05 3.83 C N[30] _{0.69 2.53 6.28 2.95} /1.318 0.45 2.32 18.43 3.83 C N[30] _{0.60 2.51 24.80 2.82} /1.338 0.46 2.27 21.35 3.73 C N[8] _{0.442 2.30 22.65} /1.345 0.451 2.36 27.71 ± C N[75] _{0.52 2.31 20.65} /1.322 0.52 2.39 21.39 ±

[a] For thiourea S,S-dioxide: first line from DFT calculations of monomer, second line from DFT calculations of heptamer, third line from DFT calculations of crystal, fourth line from PDFT/XD program, fifth line from KRMM. For other compounds (with references): first line from calcula-tions, second line from experiment.

Figure 5. Total electron density, 1(r), bond paths, and atom domains partitioning by zero-flux surfaces in the molecular plane derived from a) the DFT calculation of a heptamer and b) experimental diffraction data. The nuclei at the plane are labeled in (a). The charge density contours are in steps of 2m_{ 10}n_{e ä} 3_{(mˆ 1 ± 3, n ˆ 3 ± 3).}

H1 ¥¥¥O and H2 ¥¥¥O hydrogen bonds, these are relatively

strong hydrogen bonds with a

1

b

value of

0.2 eä

3

, which is

in accordance with values obtained elsewhere,

[19, 21, 55]

_for

example,

1

b

ˆ 0.199 eä

3

for the F ¥¥¥H hydrogen bond.

[55]

There is no obvious difference in the

1

b

or H

b

values from a

dimer, a heptamer, and a crystal; nevertheless the

exper-imental values are significantly lower. However the kinetic

energy density, G

b

(Table 5) fits well with the exponential

expression given in the literature.

[19]

_{It also fits in the linear}

relationship

[53]

_{between G}

b

and

l

3

.The

1

b

value of the O ¥¥¥H1

bond is slightly larger than the O ¥¥¥H2 interaction. The BSSE

(basis set superposition error) corrected binding interaction

energies are calculated based on the specifically chosen

dimers shown in Figures 6 and 7. This correction results in

energies of

40.83 and

54.53 kJ mol

1

_{for N H1 ¥¥¥O and}

N H2 ¥¥¥O, respectively. In general the nonbonded charge

concentrations are the preferred sites of protonation. There

are two Laplacian charge concentrations (vertex critical point

in the atomic graph) in the valence-shell charge concentration

(VSCC) of the O atom (see Supporting Information) and a

Laplacian local minimum (face critical point) of hydrogen

toward this charge concentration of the O atom. In principle,

the locations of the N H bond with its Laplacian local

minimum and the charge concentration of O should be in

alignment as far as possible. This is true in cases of both

N H2 ¥¥¥O and N H1 ¥¥¥O hydrogen bonds. A similar feature

was reported in crystalline urea.

[8]

_{Furthermore the}

BSSE-corrected binding energies of N H1 ¥¥¥O and N H2 ¥¥¥O

were calculated for a trimer including both N H1 ¥¥¥O and

N H2 ¥¥¥O type interactions. The values were

45.66 and

54.15 kJ mol

1

_{, respectively. The binding energies increase a}

bit for the N H1 ¥¥¥O bond from a dimer to a trimer.

Weak intermolecular binding interactions C ¥¥¥ S

' and O ¥¥¥ N':

In addition to the intermolecular hydrogen bonds, the

thiourea S,S-dioxide molecules in the crystal are linked to

one another through weak C ¥¥¥S

' and O ¥¥¥N' binding

interactions between neighboring moieties (Figure 2 c). These

binding interactions are again confirmed by the location of the

BCPs and the trace of the associated bond path to the relevant

nuclei, as displayed in Figure 8. The related topological

properties are listed in Table 5. It is obvious that the

1

b

values

(approximately 0.02 ± 0.06 e ä

3

_{) are much less than those of}

hydrogen bonds (

0.2 eä

3

_{). The bond paths of C ¥¥¥S}

_{' and}

O ¥ ¥ ¥ N

' are slightly longer than the respective geometrical

distances (bond lengths), so they are slightly bent as shown in

Figure 8. The nature of these weak intermolecular binding

interactions can be understood correctly by the VSCC

Laplacian critical points. The 3D isovalue surfaces of

Lap-lacian distributions derived by experiment and theory are

depicted in Figure 9, where a nonbonded charge

concentra-tion is located at the VSCC of the S atom and two charge

depletions are located above and below the C atom. While in

the crystal, the nonbonded charge concentration of the S atom

is directly inserted toward the charge depletion of the C atom

from the molecule below to form the C ¥¥¥S

' binding

interactions (Figure 9 a, b). In other words, the nonbonded

Laplacian charge concentration of the S atom serves as a

Lewis base or an electrophile and the Laplacian charge

Table 4. The atomic AIM charges (qW) and the molecular dipole moments (Debye).

Atom Monomer Heptamer PDFT PDFT/XD program Experiment/KRMM

S 2.164 2.141 2.145 1.955 1.759 O 1.313 1.347 1.362 1.339 1.255 N 1.287 1.386 1.407 1.246 1.452 C 1.214 1.221 1.277 0.790 0.893 H1 0.410 0.502 0.522 0.611 0.671 H2 0.500 0.550 0.538 0.602 0.707 SO2 0.46 0.55 0.58 0.72 0.75 C(NH2)2 0.46 0.55 0.58 0.72 0.75 dipole moment 12.6 14.2 14.6 15.5 16.3

FULL PAPER

C.-R. Lee, Y. Wang et al.

depletion of the C atom is the Lewis acid or a nucleophile.

Similarly the N atom possesses two nonbonded charge

concentrations, one on each side of the plane. One of these

charge concentrations of the N atom can align itself toward

the Laplacian charge depletion of the O atom of a

neighbour-ing molecule to form the O ¥¥¥N

' binding interaction. These

weak C ¥¥¥S and N ¥¥¥O interactions together with hydrogen

bonds demonstrate the 3D directional ™key ± lock∫

architec-ture in the crystal. Based on the chosen dimer model, the

BSSE-corrected binding interaction energies,

DE, are 9.48

and

5.80 kJ mol

1

_{for C ¥¥¥S}

_{' and O ¥¥¥N', respectively.}

Conclusion

An exact comparison has been accomplished between the

experiment and theory of electron density based on the

multipole model. The covalent bonding characters of the C S,

S O, and C N bonds in thiourea S,S-dioxide have been

illustrated by topological analysis. The partial double bond

character of the S O and C N bonds is recognized, with ionic

p character of the S O bond. A highly polar single C S bond

between two oppositely charged fragments has been

estab-lished. The large dipole moment results from a positive

C(NH

2

)

2

moiety and a negative SO

2

fragment, a firm

illustration of the zwitterionic character. Two categories of

intermolecular interactions are identified: the relatively

strong hydrogen bonds, with

1

b

 0.2 eä

3

and binding

energies (

DE) of 50 kJmol

1

_{, and the relatively weak C ¥¥¥S}

'

and O ¥¥¥N

' interactions, with 1

b

 0.02 ± 0.05 eä

3

and

DE  6 ± 9 kJmol

1

_{. The natures of these intermolecular}

interactions have been demonstrated as 3D directional

interactions. The effect of such intermolecular interactions

on the chemical bond is detected through the systematic

studies. The chemical reactivity of this molecule can be

understood according to the fragment charges of the SO

2

and

C(NH

2

)

2

groups as well as the knowledge of VSCC

distribu-tion.

Computational Methods

Multipole refinement: Thiourea S,S-dioxide was prepared by oxidation of thiourea with hydrogen peroxide at 08C and crystallized in an aqueous solution.[45]_{The intensity data were collected on a CAD4 diffractometer at}

110 K. Details were described in our previous work.[46]_{A multipole model}

refinement was reinvestigated by using the XD program.[58]_{The multipolar}

model is expressed as a series expansion of spherical harmonic terms (ylmp)

multiplied by a Slater-type radial function Rl(r).[17, 59]Spherical harmonic

expansion terms up to hexadecapoles were included for S atoms, up to octapoles for O, N, and C atoms, and up to quadruples for H atoms. The core and valence electron scattering factors for each atom are taken from International Tables for X-rayCrystallography(1974, Vol. IV). The core electron configurations are assumed to have Ne core for S and He core for O, N, and C atoms. During the refinement, H atoms are moving along N H vectors to make an N H distance of 1.03 ä.[60]_{The n}

lvalues (lˆ 1 ± 4) of S

are 4, 4, 4, 4, those of N, O, and C are 2, 2, 3, and those of H are 1, 2. The k'-restricted multipole model (KRMM)[47]_{was carried out at the final stage.}

The radial k' coefficients were fixed at values derived from multipole refinement of theoretical structure factors obtained from PDFT calcula-tions (k' coefficient for S: 0.890; O: 2.315; N: 0.939; C: 0.725; and H: 1.2). Table 5. Intermolecular interactions: the topological properties associated with the BCPs.[a]

Bond/bond length [ä]/ d1 1b r21b Gb Hb DE[b]

bond path [ä] [ä] [e ä3_{] [e ä}5_{] [Hartree ä} 3_{] [Hartree ä}3_{] [kJ mol} 1_]

O ¥¥¥H1 1.176 0.222 2.486 0.176 0.002 40.83 /1.810(2) 1.179 0.225 2.479 0.176 0.003 /1.811 1.179 0.235 2.376 0.171 0.005 1.192 0.216 2.232 0.167 0.010 1.202 0.178 2.883 0.180 0.022 O ¥¥¥H2 1.199 0.199 2.171 0.152 0.000 54.53 /1.843(2) 1.197 0.196 2.210 0.155 0.001 /1.849 1.189 0.204 2.267 0.157 0.002 1.221 0.166 2.649 0.164 0.022 1.237 0.146 2.323 0.141 0.022 S ¥ ¥ ¥ C' 1.820 0.054 0.649 0.031 0.010 9.48 /3.3128(6) 1.813 0.055 0.666 0.036 0.010 /3.323 1.805 0.058 0.659 0.036 0.010 1.776 0.064 0.718 0.042 0.009 1.769 0.062 0.766 0.044 0.010 O ¥ ¥ ¥ N' 1.794 0.018 0.270 0.015 0.004 5.80 /3.619(2) 1.787 0.019 0.278 0.016 0.004 /3.630 1.791 0.019 0.279 0.016 0.004 1.851 0.017 0.247 0.012 0.005 1.836 0.019 0.261 0.013 0.005 O ¥ ¥ ¥ H[21] _{0.273 3.40 0.216 0.013} /1.72 0.295 3.10 0.242 0.020 O ¥ ¥ ¥ H[21] _{0.230 2.88 0.202 0.000} /1.81 0.248 2.66 0.202 0.000 O ¥ ¥ ¥ H[21] _{0.174 2.49 0.155 0.013} /1.93 0.188 2.30 0.149 0.007

[a] First line from DFT calculations of chosen dimers, second line from DFT calculation of heptamer, third line from PDFT calculations of crystal, fourth line from PDFT/XD program, fifth line from KRMM. The intermolecular binding interaction energies are calculated based on the corresponding dimer models in the BSSE correction.

Thez values of H, N, O, and S are 3.1762, 3.8407, 4.4724 and 3.9496, respectively. The experimental Laplacian distributions are depicted with the XD program,[58]_{and the}

contour maps of the charge density distri-butions, zero-flux surfaces, and bond paths are drawn with the PROP program.[61]

The total energy density at the bond critical point Hb values evaluated from

the experimental electron density by the multipole model was derived according to the approximate expression,[54]_{where the}

kinetic energy density, Gb, is directly

related to the electron density, introduced by the semiclassical Thomas ± Fermi equa-tion, whereD1(r) ˆ 1(r) 1ci(r); in

prac-tice,1ci(r) is the deformation density, that

is,1ci(rc)ˆ 1mul(rc) 1iam(rc). The Hbvalue

is the sum of Gb and Vb, which can be

estimated roughly by this generalized ap-proach.

Theoretical calculations: All DFT[62]

cal-culations, including those for the single molecule and oligomers of thiourea S,S-dioxide, were carried out with the GAUS-SIAN 98 program.[63]_{The correlation}

cor-rection by Lee, Yang, and Parr (LYP)[64]

Figure 6. a) Model of the chosen dimer with O ¥¥¥H1 N hydrogen bonds. Laplacian charge density distributions in the plane containing O ¥¥¥H1 N hydrogen bonds are shown as calculated from b) the DFT calculation of the chosen dimer, c) the PDFT calculation, d) the multipole model of theoretically derived structure factors and e) the multipole model of experimental data. Contours are stepped as in Figure 4.

Figure 7. a) Model of the O ¥¥¥H2 N hydrogen bond. Laplacian charge density distributions of the O ¥¥¥H2 N hydrogen bond are shown in b) ± e) as defined as in Figure 6. Contours are stepped as in Figure 4.

Figure 8. Weak intermolecular interactions indicated by bond paths (black lines), critical points (black dots), and charge density distribution (con-tours) in a heptamer model: a) C ¥¥¥S' interaction, b) O ¥¥¥N' interaction. Contours in1(r) are stepped as in Figure 5.

FULL PAPER

C.-R. Lee, Y. Wang et al.

together with Becke×s nonlocal, gradient approach to the exchange functional in its three-parameter hybrid density form (B3LYP)[65] _was

used. The standard split-valence 6-31G(d,p) basis set[62, 66]_{was employed for}

all the calculations. Fully PDFT calculation of the crystal was incorporated in the CRYSTAL algorithm by Saunders et al.[67]_{by using the CRYSTAL 98}

program.[67]_{According to the Bloch function for an insulator, the K-point}

sampling of 6, 6, and 6 was chosen isotropically along the reciprocal axis a*, b*, and c* respectively. The structural amplitudes (Ftheo) were thus derived

from this calculation. The multipole refinement[59]_{was then applied to these}

theoretically calculated structural amplitudes, and thek' thus obtained was adapted in the experimental multipole model.

Topological properties analysis: The total electron density obtained from the experiment was calculated according to the multipole refinement model.[59] _{The total electron density for the theoretical model was}

calculated on the basis of the aforementioned DFT and PDFT calculations. The topological properties, maps of the charge density distributions, and Laplacian distributions were performed with the programs AIMPAC[68]_and

AIM98PC[69]_{for the single molecule and oligomers, with the program}

TOPOND[70]_{used for the crystal.}

The magnitude of the electron density at the BCP,1b, correlates with the

bond distance and the bond order and, therefore, with the bond strength.[71, 72] _{The sign of the Laplacian distribution of1 at the BCP,}

r2₁

b, could be used to distinguish bonding features between a shared

interaction (covalent bond) and a closed-shell interaction (ionic bond). It was suggested[27, 73]_{that the negative total energy density value, H}

b, at the

BCP can be interpreted as the sufficient condition of a covalent bond and could be used as a qualitative measure for covalence. Correlation between the bonding and strain energies of hydrocarbon molecules was reported with1band Hbvalues.[74]The network of bond paths defines the shape of

the molecule. A gradient path for which the electron density decreases most rapidly is developed in all directions normal to the bond. The set of such gradient paths starting at each BCP defines a zero-flux surface separating two bonded atoms. The network of these surfaces (one per

bond) will partition the molecule into unique atomic domains (basins) for which the hypervirial theorem is satisfied. Numerical integration of the electron density within such a region yields the net charge of the given atom[75]_{called the AIM charge. The Laplacian distribution,r}2_{1(r), is also a}

very useful tool for understanding the chemical reactivity and revealing a simple 3D directional interaction in the molecular crystal. Similarly to the aforementioned1(r) distribution, the topological properties of r2_{1(r) can}

be summarized by its critical points. The atomic graph thus defined denotes the connectivity of the local valence shell charge concentration (VSCC). Such a polyhedron obeys Eular×s formula: V E‡F ˆ 2, where V, E, F stand for the number of vertices, edges, and faces, respectively. A correlation between these critical points ofr2_{1(r) in the valence shell}

and the location of the active site has been established.[2, 14, 76]

Acknowledgement

The authors thank the National Science Council of the Republic of China for the financial support and are grateful to the National Center of High-Performance Computing for access to their computing facilities and software packages.

[1] a) C. F. Mellot, A. M. Davidson, J. Eckert, A. K. Cheethan, J. Phys. Chem. B 1998, 102, 2530 ± 2535; b) S. E. Barber, K. E. S. Dean, A. J. Kirby, Can. J. Chem. 1999, 77, 792 ± 801; c) C. Cox, T. Lectka, J. Am. Chem. Soc. 1998, 120, 10 660 ± 11 668; d) K.-J. Lin, Y. Wang, J. Phys. Chem. 1994, 98, 11 685 ± 11 693; e) A. Ivancich, T. A. Mattioli, Photo-synth. Res. 1998, 55, 207 ± 215; f) A. Aurora, G. D. Rose, Protein Sci., 1998, 7, 21 ± 38; g) G. R. Desiraju, Crystal Engineering ± The Design of Organic Solids, Elsevier, New York, 1989.

[2] R. F. W. Bader, Atoms in Molecules : a Quantum Theory, Clarendon Press, Oxford, 1990.

[3] M. T. Caroll, C. Chang, R. F. W. Bader, Mol. Phys. 1988, 63, 387 ± 405. [4] M. T. Caroll, R. F. W. Bader, Mol. Phys. 1988, 65, 695 ± 722. [5] P. L. A. Popelier, R. F. W. Bader, Chem. Phys. Lett. 1992, 189, 542 ±

548.

[6] T.-H. Tang, D. M. Whitefield, S. P. Douglas, J. J. Krepinsky, I. G. Csizmadia, Can. J. Chem. 1992, 70, 2434 ± 2448.

[7] D. M. Whitefield, T.-H. Tang, J. Am. Chem. Soc. 1993, 115, 9648 ± 9654.

[8] C. Gatti, V. R. Saunders, C. Roetti, J. Chem. Phys. 1994, 101, 10 686 ± 10 696.

[9] U. Koch, P. L. A. Popelier, J. Phys. Chem. 1995, 99, 9747 ± 9754. [10] T.-H. Tang, Y.-P. Cui, Can. J. Chem. 1996, 74, 1162 ± 1170. [11] J. A. Platts, S. T. Howard, J. Chem. Phys. 1996, 105, 4668 ± 4674. [12] J. A. Platts, S. T. Howard, B. R. F. Bracke, J. Am. Chem. Soc. 1996, 118,

2726 ± 2733.

[13] P. L. A. Popelier, J. Phys. Chem. 1998, A102, 1873 ± 1878.

[14] C. Gatti, R. Bianchi, R. Destro, F. Merati, J. Mol. Struct.(THEO-CHEM) 1992, 255, 409 ± 433.

[15] T. S. Koritsanszky, P. Coppens, Chem. Rev. 2001, 101, 1583 ± 1627. [16] P. Coppens, X-rayCharge Densities and Chemical Bonding, Oxford

University Press, Oxford, 1997.

[17] P. Coppens, Acta Crystallogr. Sect. A 1998, 54, 779 ± 788.

[18] R. Flaig, T. Koritsa¬nszky, D. Zobel, P. Luger, J. Am. Chem. Soc. 1998, 120, 2227 ± 2238.

[19] E. Espinosa, E. Molins, C. Lecomte, Chem. Phys. Lett. 1998, 285, 170 ± 173.

[20] J. Overgaad, B. Schi˘tt, F. K. Larsen, A. J. Schultz, J. C. MacDonald, B. B. Iversen, Angew. Chem. 1999, 111, 1321 ± 1324; Angew. Chem. Int. Ed. 1999, 38, 1239 ± 1242.

[21] P. Coppens, Y. A. Abramov, M. Carducci, B. Korjov, I. Novozhilova, C. Alhambra, M. R. Pressprich, J. Am. Chem. Soc. 1999, 121, 2585 ± 2593.

[22] R. Flaig, T. Koritsa¬nszky, J. Janczak, H.-G. Krane, W. Morgenroth, P. Luger, Angew. Chem. 1999, 111, 1494 ± 1497; Angew. Chem. Int. Ed. 1999, 38, 1397 ± 1400.

[23] F. Benabicha, V. Pichon-Pesme, C. Jelsch, C. Lecomte, A. Khmou, Acta Crystallogr. Sect. B 2000, 56, 155 ± 165.

Figure 9. The isovalue surfaces (r2_{1(r) ˆ 11.0 eä} 5_{) of Laplacian}

dis-tributions concerning the C ¥¥¥S' interaction between two moieties from a) theory based on a heptamer model and b) experiment.

[24] W. D. Arnold, L. K. Sanders, M. T. McMahon, A. V. Volkov, G. Wu, P. Coppens, S. R. Wilson, N. Godbout, R. Oldfield, J. Am. Chem. Soc. 2000, 122, 4708 ± 4717.

[25] H.-P. Weber, B. M. Craven, Acta Crystallogr. Sect. B 1987, 43, 202 ± 209.

[26] R. F. W. Bader, Chem. Rev. 1991, 91, 893 ± 928.

[27] E. Kraka, D. Cremer in The Concept of the Chemical Bond, Theoretical Models of Chemical Bonding, Part 2 (Ed.: Z. B. Makic), Springer-Verlag, New York, 1990.

[28] R. F. W. Bader, J. Phys. Chem. 1998, A102, 7314 ± 7323.

[29] C.-R. Lee, T.-H. Tang, C.-C. Wang, L. Chen, Y. Wang, unpublished results.

[30] C.-R. Lee, L. Y. Tan, Y. Wang, J. Phys. Chem. of Solids, 2001, 62, 1613 ± 1628.

[31] C.-C. Wang, T.-H. Tang, Y. Wang, J. Phys. Chem. 2000, A104, 9566 ± 9572.

[32] C.-R. Lee, C.-C. Wang, K.-C. Chen, G.-H. Lee, Y. Wang, J. Phys. Chem. 1999, A103, 156 ± 165.

[33] V. G. Tsirelson, P.-F. Zou, T.-H. Tang, R. F. W. Bader, Acta Crystallogr. Sect. A 1995, 51, 143 ± 153.

[34] T.-H. Tang, R. F. W. Bader, P. J. MacDougall, Inorg. Chem. 1985, 24, 2047 ± 2053.

[35] W. Scherer, M. Spiegler, B. Pedersen, M. Tafiposky, W. Hieringer, B. Reinhard, A. J. Downs, G. S. McGrady, Chem. Commun. 2000, 635. [36] R. G. A. Bone, R. F. W. Bader, J. Phys. Chem. 1996, 100, 10 892 ±

10 911.

[37] a) Y. Aray, R. F. W. Bader, Surf. Sci. 1996, 351, 233 ± 249; b) Y. Aray, J. Rodriguez, D. Vega, J. Phys. Chem. 2000, B104, 5225 ± 5231. [38] A. Gobbi, G. Frenking, J. Am. Chem. Soc. 1993, 115, 2362 ± 2372. [39] A. Masunov, J. J. Dannenberg, J. Phys. Chem. 1999, A103, 178 ± 184;

A. Masunov, J. J. Dannenberg, J. Phys. Chem. 2000, B104, 806 ± 810. [40] R. Dovesi, M. Causa¬, R. Orlando, C. Roetti, V. R. Saunders, J. Chem.

Phys. 1990, 92, 7402 ± 7411.

[41] S. Swaminathan, B. M. Craven, R. K. McMullan, Acta. Crystallogr. Sect. B 1984, 40, 300 ± 306.

[42] K. Suzuki, S. Onishi, T. Koide, S. Seki, Bull. Chem. Soc. Jpn. 1956, 29, 127 ± 131.

[43] a) V. Zavodnik, A. Stash, V. Tsirelson, R. de Vries, D. Feil, Acta Crystallogr. Sect. B 1999, 55, 45 ± 54; b) K. Y. Suponitsky, V. G. Tsirelson, D. Feil, Acta Crystallogr. Sect. A 1999, 55, 821 ± 827; c) R. Y. de Vries, D. Feil, V. G. Tsirelson, Acta Crystallogr. Sect. B 2000, 56, 118 ± 123.

[44] H. G. M. De Wit, J. C. Van Miltenburg, C. G. De Kruif, J. Thermodyn. 1983, 15, 651 ± 654.

[45] I.-C. Chen, Y. Wang, Acta Crystallogr. Sect. C 1984, 40, 1937 ± 1938. [46] Y. Wang, N.-L. Chang, C.-T. Pai, Inorg. Chem. 1990, 29, 3256 ± 3259. [47] A. Volkov, C. Gatti, Y. Abramov, P. Coppens, Acta Crystallogr. Sect. A

2000, 56, 252 ± 258.

[48] T.-S. Hwang, Y. Wang, J. Phys. Chem. 1998, A102, 3726 ± 3731. [49] J. Cioslowski, P. R. Surja¬n, J. Mol. Struct.(THEOCHEM) 1992, 255,

9 ± 33.

[50] A. E. Reed, P. v. R. Schleyer, J. Am. Chem. Soc. 1990, 112, 1434 ± 1445. [51] J. A. Dobado, H. Martinez-Garcia, J. M. Molina, M. R. Sundberg, J. Am. Chem. Soc. 1998, 120, 8461 ± 8471; J. A. Dobado, H. Martinez-Garcia, J. M. Molina, M. R. Sundberg, J. Am. Chem. Soc. 1999, 121, 3156 ± 3164.

[52] A. Volkov, Y. Abramov, P. Coppens, C. Gatti, Acta Crystallogr. Sect. A 2000, 56, 332 ± 339.

[53] E. Espinosa, C. Lecomte, E. Molins, Chem. Phys. Lett. 1999, 300, 745 ± 748.

[54] Y. A. Abramov, Acta Crystallogr. Sect. A 1997, 53, 264 ± 272.

[55] E. Espinosa, I. Alkorta, I. Rozas, J. Elguero, E. Molins, Chem. Phys. Lett. 2001, 336, 457 ± 461.

[56] S. T. Howard, M. B. Hursthouse, C. W. Lehmann, P. R. Mallinson, C. S. Frampton, J. Chem. Phys. 1992, 97, 5616 ± 5630.

[57] Y. A. Abramov, A. V. Volkov, P. Coppens, Chem. Phys. Lett. 1999, 311, 81 ± 86.

[58] T. Koritsa¬nszky, S. Howard, T. Richter, Z. Su, P. R. Mallinson, N. K. Hansen, XD (Computer Program Package for Multipole Refinement and Analysis of Electron Densities from X-ray Diffraction Data), Free University of Berlin, Germany, 1996.

[59] N. H. Hansen, P. Coppens, Acta Crystallogr. Sect. A 1978, 34, 909 ± 921. [60] N H bond length 1.03 ä; see: F. H. Allen, Acta Crystallogr. Sect. B

1986, 42, 515 ± 522.

[61] M, Souhassou, R. H. Blessing, J. Appl. Crystallogr. 1999, 32, 210 ± 217. [62] a) P. Hohenberg, W. Kohn, Phys. Rev. 1964, 136(B), B864 ± 871; b) W. Kohn, S. J. Sham, Phys. Rev. 1965, 140(A), A1133 ± 1138; c) R. G. Parr, W. Yang, Density-Functional Theory of Atoms and Molecules, Oxford University Press, Oxford, 1989.

[63] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery, R. E. Strat-mann, 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, A. 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. G. Johnson, W. Chen, M. W. Wong, J. L. Andres, M. Head-Gordon, E. S. Replogle, J. A. Pople, Gaussian 98 (Revision A.7), Gaussian Inc., Pittsburgh, PA, 1998.

[64] C. Lee, W. Yang, R. G. Parr, Phys. Rev. B. 1988, 37(2), 785 ± 789. [65] A. D. Becke, J. Chem. Phys. 1993, 98, 5648 ± 5652.

[66] M. M. Francl, W. J. Pietro, W. J. Hehre, J. S. Binkley, M. S. Gordon, D. J. DeFrees, J. A. Pople, J. Chem. Phys. 1982, 77, 3654 ± 3665. [67] V. R. Saunders, R. Dovesi, C. Roetti, M. Causa¬, N. M. Harrison, R.

Orlando, C. M. Zicovich-Wilson, CRYSTAL 98 User×s Manual, Uni-versity of Torino, Italy, 1998.

[68] R. F. W. Bader, F. W. Biegler-Kˆnig, J. R. Cheeseman, J. A. Duke, T. A. Keith, P. Krug, K. E. Laidig, B. Langdon, AIMPAC (a set of programs for the theory of atoms in molecules), McMaster University, Hamilton, ON, Canada, 1994.

[69] D.-C. Fang, T.-H. Tang, AIM98PC (modified PC version of AIMPAC), 1998.

[70] C. Gatti, TOPOND98 User×s Manual 1998, CNR-CSRSRC, Milano, Italy.

[71] R. F. W. Bader, T.-H. Tang, Y. Tal, F. W. Biegler-Kˆnig, J. Am. Chem. Soc. 1982, 104, 946 ± 952.

[72] a) R. F. W. Bader, T. Slee, D. Cremer, E. Kraka, J. Am. Chem. Soc. 1983, 105, 5061 ± 5068; b) S. M. Bachrach, J. Comput. Chem. 1989, 10, 392 ± 406; c) S. M. Bachrach, J. Mol. Struct.(THEOCHEM) 1992, 255, 207 ± 219; d) S. M. Bachrach, J. Mol. Struct.(THEOCHEM) 1995, 337, 201 ± 207.

[73] D. Cremer, E. Kraka, Croatica Chem. Acta 1984, 57, 1259 ± 1281. [74] S. Grimme, J. Am. Chem. Soc. 1996, 118, 1529 ± 1534.

[75] F. W. Biegler-Kˆnig, R. F. W. Bader, T.-H. Tang, J. Comp. Chem. 1982, 3, 317 ± 328.

[76] R. F. W. Bader, P. L. A. Popelier, C. Chang, J. Mol. Struct.(THEO-CHEM) 1992, 255, 145 ± 17.

Received: October 21, 2002 Revised version: March 6, 2003 [F 4519]