Topological Analysis and Charge Density Studies of an α-Diimine Macrocyclic Complex of Cobalt(II) - A Combined Experimental and Theoretical Study

Topological Analysis and Charge Density Studies of an

a-Diimine Macrocyclic

Complex of Cobalt(

ii)–A Combined Experimental and Theoretical Study

Jey-Jau Lee, Gene Hsiang Lee, and Yu Wang*

Abstract: A

combined

experimental

and theoretical study of the

paramag-netic

[Co

_(C

12

H

N

)(H

O)

] ¥ 2 ClO

complex was made on the basis of the

electron density distribution and

topo-logical analysis. Accurate single-crystal

diffraction data were measured on a

suitable crystal with Mo

radiation at

125 K. The Co

_{ion is coordinated in a}

square bipyramidal fashion with four

imino nitrogen atoms at the equatorial

plane and two water molecules at the

axial positions. The hydrogen-bonding

interaction at 125 K between the

coor-dinated water molecule and the ClO

ion makes the space group different

from that at 298K. Parallel MO

calcu-lations were made at UHF and DFT/

UB3LYP. The agreement between

ex-periment and theory is reasonably good.

The chemical bonding characterization

is presented in terms of the topological

properties associated with bond critical

points and the natural bond orbital

(NBO) analysis as well. The Co N

and Co O

bonds are dative bonds,

where the lone-pair electrons of N or O

serve as a

s-donor; however, a certain

covalent character is identified in the

Co N

bond. A delocalized C N,

N N

p-bond model is proposed. The

d-orbital energies of Co in this complex

are such that E(d

)

E(d

)

E(d

)

<

E(d

)

< E(d

); notice that d

and d

are d

orbitals in this case. The Co

ion

is in a low-spin d

_{state with the singly}

occupied d

orbital. The asphericity in

electron density at Co and Cl nuclei is

nicely demonstrated by the Laplacian of

electron density. The envelope plot of

the isovalue Laplacian surface around

the nucleus gives the exact shape of such

asphericity. The isovalue Laplacian

sur-faces of these two nuclei show

signifi-cantly different VSCC character in both

experimental and theoretical results.

Keywords: charge density ¥ cobalt ¥

hydrogen

bonds

¥

macrocyclic

ligands ¥ topological analysis

Introduction

The macrocyclic tetraimino ligand C

H

N

,

2,3,9,10-tetra-

methyl-1,4,5,7,8,11,12,14-octaazacyclotetradeca-1,3,8,10-tetra-ene is normally observed as a square planar tetradentate

ligand.

_{This macrocyclic ligand is often coordinated to a}

divalent 3d transition element like Fe

_{, Co}

_{, Ni}

_{, or Cu}

_.

However these complexes could also be square-pyramidal or

octahedral with additional axial ligands.

These complexes should play a key biological role since

they are similar to those found in natural biosystems, such as

metalloporphyrins, vitamin B

, or metal ± chlorophyll.

It

would be interesting to use this transition metal complex as a

model compound to mimic biological systems. There are

many stable divalent cobalt complexes of tetradentate Schiff

bases which are potential model systems for oxygen-binding

biomolecules, where molecular oxygen can be absorbed

reversibly under certain conditions.

_{The d-orbital energies}

and electronic structures of some Co

_{complexes have been}

characterized in detail on the basis of single-crystal ESR

measurement and simulation.

_{There is still controversy}

over the electronic configuration of the Co

_{ion in the}

square-planar case as to whether the unpaired electron is in the d

(

_A

1

) or the d

(

B

) orbital (state). When one axial ligand is

present, it is believed that the unpaired electron should be in

the d

(

A

) orbital.

Studies

_{of a series of [M(C}

10

H

N

)]

compounds

provide an interesting comparison of the ligand-field

charac-teristics of such tetraimino macrocyclic ligands. Four imino-N

centers in the equatorial plane usually exert a strong ligand

field toward the metal ion. The conjugated

p-orbital system of

the ligand (Scheme 1) incorporated with the suitable d-orbital

of the metal ion gives rise to a low-spin state in the central

metal ion.

The electron density distribution is useful for chemical

bond characterization. The asphericity in electron density

near the metal nucleus could give direct evidence on the effect

of chemical bonding owing to the crystal field splitting. We

have therefore carried out a combined experimental and

[a] Prof. Dr. Yu. Wang, Dr. J.-J. Lee, G. H. Lee

Department of Chemistry, National Taiwan University Taipei (Taiwan)

Fax: (‡886)2-23636359

E-mail: [email protected]

Supporting information for this article is available on the WWW under http://www.wiley-vch.de/home/chemistry/ or from the author.

Scheme 1. The partial double bond system of the macrocyclic tetraimino tetraene ligand.

theoretical study of the electron density distribution of the

cobalt(

ii) octaazabisdiimine macrocyclic complex

_{in order}

to better understand the chemical bonding of this complex.

Results and Discussion

Structure: The molecular structure with thermal ellipsoids of

the title complex cation at 125 K is depicted in Figure 1a. The

hydrogen atoms are omitted for clarity. The exact molecular

symmetry is C

. However, the geometry of the cation is

Figure 1. a) Molecular drawing of cobalt complex cation with 30 % probability in thermal ellipsoids and bond order at 125 K; the heavy arrows represent dative bonds; b) the choice of local Cartesian axes for each atom.

essentially the same as that at room temperature, which has

higher symmetry, C

. Atomic coordinates and equivalent

isotropic displacement parameters obtained by full-matrix

least-squares refinements based on spherical and multipole

models both at 298K and at 125 K are given in Tables 1 and 2,

respectively. Selected bond lengths and angles are listed in

Table 3. The coordination geometry around the Co ion is a

tetragonally distorted octahedron owing to the Z-out Jahn ±

Teller distortion.

_{Four imino nitrogen atoms are in the}

equatorial plane and two oxygen atoms of water molecules

Table 1. Atomic fractional coordinates and Beqvalues [ä2] of

non-hydro-gen atoms at 298K in space group Cmca.

Atom x y z Beq[a] Co 1/2 0 0 2.28(4) O5 1/2 0.0432(2) 0.2037(4) 3.8(2) N1 0.6240(3) 0.0672(2) 0.0441(3) 2.5(1) N4 0.6034(3) 0.1376(2) 0.1057(3) 3.2(1) C7 0.7258(3) 0.0390(2) 0.0300(3) 2.7(1) C5 1/2 0.1765(3) 0.0619(6) 3.4(3) C80.8336(4) 0.0778(3) 0.0704(4) 4.1(2) Cl 3/4 0.31894(8) 1/4 3.71(7) O2 3/4 0.4009(3) 1/4 7.1(3) O3 0.7693(6) 0.2815(2) 0.1426(4) 11.4(4) O4[b] _{0.6221(7) 0.3154(5) 0.229(1) 8.5(5)} [a] Beqˆ (8p2/3)SiSjUija*ia*jaiaj. [b] Occupancy is 0.5.

Table 2. Atomic fractional coordinates and Beqvalues [ä2] of

non-hydro-gen atoms at 125 K in space group Pbca: first line from full data refinement; second line from multipole refinement.

Atom x y z Beq Co 0.5000 0.0000 0.0000 0.87(4) 0.5000 0.0000 0.0000 0.83(8) O5 0.4921(6) 0.0410(5) 0.2069(7) 1.52(2) 0.4921(4) 0.0411(7) 0.2071(1) 1.48(2) N1 0.6216(6) 0.0690(4) 0.0469(7) 1.04(2) 0.6215(6) 0.0692(4) 0.0469(8) 1.02(2) N2 0.3739(6) 0.0678(4) 0.0416(7) 1.04(2) 0.3739(6) 0.0680(4) 0.0416(8) 1.02(2) N3 0.3917(7) 0.1393(5) 0.1018(8) 1.27(2) 0.3915(7) 0.1393(5) 0.1016(9) 1.25(2) N4 0.5993(7) 0.1394(5) 0.1070(8) 1.28(2) 0.5996(7) 0.1394(5) 0.1069(8) 1.26(2) C5 0.4965(8) 0.1783(5) 0.0582(9) 1.30(2) 0.4966(6) 0.1784(5) 0.0584(9) 1.28(2) C6 0.2724(7) 0.0370(5) 0.0278(8) 1.15(2) 0.2723(6) 0.0370(5) 0.0276(8) 1.11(2) C7 0.7251(7) 0.0418(5) 0.0317(8) 1.13(2) 0.7251(6) 0.0418(5) 0.0319(8) 1.11(2) C8 0.8311(8) 0.0847(7) 0.0710(1) 1.76(3) 0.8313(8) 0.0846(6) 0.0706(1) 1.71(3) C9 0.1625(8) 0.0742(7) 0.0701(1) 1.63(3) 0.1624(7) 0.0743(6) 0.0697(1) 1.60(3) CL 0.7339(2) 0.1789(1) 0.2462(2) 1.25(6) 0.7339(1) 0.1788(1) 0.2461(2) 1.20(6) O1 0.7636(9) 0.2124(5) 0.1252(8) 2.55(3) 0.7634(1) 0.2124(8) 0.1246(1) 2.47(4) O2 0.7653(7) 0.0961(4) 0.2476(8) 1.98(3) 0.7651(1) 0.0958(5) 0.2476(1) 1.93(3) O3 0.7905(7) 0.2205(5) 0.3469(8) 2.38(3) 0.7904(1) 0.2206(8) 0.3476(1) 2.31(4) O4 0.6111(7) 0.1840(5) 0.2632(1) 2.62(3) 0.6106(9) 0.1838(7) 0.2634(1) 2.56(4)

are at the axial positions. The Co atom is located with 1≈ site

symmetry in the same plane of four imino nitrogen atoms.

Co N distances are 1.9026(7) ä (Co N1) and 1.9153(7) ä

(Co N2), which are in the same range as related compounds

(1.897 ± 1.915 ä).

_{The Co O5 bond length at 125 K is}

2.2854(8) ä, which is significantly shorter than the one

(2.302(4) ä) at 298K. Contrary to the case at room

temper-ature, the oxygen atom of the axial ligand is not exactly at the

vertical position but is displaced by about 48 from the normal

of the plane. This significant difference found between the

low-temperature and the room-temperature structures is

believed to be the cause for the space group change from

Cmca (298K) to Pbca (125 K). The tilt of the water molecule

is a consequence of the hydrogen bond between the water

molecule and the perchlorate anion. The close proximity of

O

¥¥¥ O

(2.842(1) and 2.854(1) ä) along the a axis at

125 K, are significantly shorter than those at 298K (2.890(9)

and 3.250(5) ä). The crystal structure at 125 K can be

described as a polymeric chain along the a axis through

hydrogen bonds between cations and anions, shown in

Figure 2, whereas at 298K, one of these hydrogen bonds is

missing because of the disorder of the ClO

ion. The N N

bond lengths are 1.374(1) and 1.383(1) ä for N1 N4 and

N2 N3, respectively, which are slightly shorter than those at

298K; this may be regarded as caused by slight improvement

of the delocalization of the macrocyclic ring at 125 K. The C5,

N1, N2, N3, N4, and Co atoms make a chairlike six-membered

ring.

Deformation density: The agreement indices of multipole

refinements based on two symmetries C

and C

are

compared in Table 4. The internal coordinates applied in the

multipole model are indicated in Figure 1b. Significant

improvements on the agreement indices based on the

addi-tional multipole terms are apparent. Since there is no

significant difference between the two models, the subsequent

analyses will be based on the C

model. The aspherical

electron distribution of an atom owing to bonding can be

illustrated by experimental static deformation density maps

(

D1

) and theoretical deformation maps (

D1

,

D1

).

Deformation density maps and a residual map,

D1

, of the

molecular plane (xy) containing the

a-diimine moiety and the

octaaza moiety are shown in Figure 3. It is apparent that large

positive deformation densities are found at the midpoint of

CˆN and C C bonds. A good agreement between experiment

and theory (both UHF and DFT) is depicted in Figure 3a, 3 c,

and 3 d. The residual density map,

D1

(Figure 3b), is

essentially featureless except near the Co ion. There is

positive deformation density at each N atom pointing toward

the Co center, an observation that strongly substantiates the

s-donor character of the imino-N ligand. The lone-pair

electron density of the oxygen atoms also indicates a

s-donor

character towards the electron depletion position of the Co

nucleus, though lower density depletion around the Co

nucleus is found in the z direction than in the xy direction

(Supporting Information). An asymmetric appearance was

often observed around the Co nucleus in experiments

_in

Table 3. Selected bond lengths [ä] and angles [8] with esds in parentheses: spherical model in normal typeface, multipole model in italics.

Bond (angle) 125 K 298K cation Co N1 1.9026(7) 1.902(3) 1.9041(2) Co N2 1.9153(7) 1.9169(2) Co O5 2.2854(9) 2.302(4) 2.2876(4) N1 N4 1.374(1) 1.390(4) 1.370(1) N2 N3 1.383(1) 1.378(1) N1 C7 1.301(1) 1.288(5) 1.303(1) N2 C6 1.301(1) 1.303(1) N4 C5 1.462(1) 1.453(5) 1.462(1) N3 C5 1.459(1) 1.464(1) C6 C7 1.475(1) 1.477(7) 1.476(1) ClO4 Cl O1 1.437(1) 1.438(1) Cl O2 1.447(1) 1.508(8) 1.453(1) Cl O3 1.438(1) 1.398(5) 1.438(1) Cl O4 1.445(1) 1.334(4) 1.452(1) hydrogen bond O4 H(O5a) 2.07(3) 2.166(1) 1.876(1) O2 H(O5b) 2.13(4) 2.149(8) 1.852(1) O2 ¥¥¥ O5 2.842(1) 2.890(9) 2.841(1) O4 ¥¥¥ O5 2.854(1) 3.250(5) 2.843(1) cation N1-Co-N2 98.29(3) 98.7(1) 98.12(1) N2-Co-O5 86.24(3) 90 86.25(1) N1-Co-N2A 81.73(3) 81.3(1) 81.88(1) N1-Co-O5 88.28(3) 90 88.40(1)

Table 4. Agreement indices of two multipole refinements, (1) Cisymmetry,

(2) C2hsymmetry. NP[b] _R 1[c] R1w[d] R2[e] R2w[f] S[g] conventional 191 0.0330 0.0369 0.0355 0.0416 2.40 monopole (1) 176 0.0330 0.0360 0.0473 0.0555 2.34 (2) 165 0.0437 0.0369 0.0495 0.0559 2.23 octapole (1) 442 0.0271 0.02580.0326 0.0346 1.72 (2) 307 0.0288 0.0284 0.0360 0.0403 1.86 hexadecapole[a] _{(1) 460 0.0264 0.02480.0320 0.0341 1.66} (2) 331 0.0284 0.0278 0.0357 0.0401 1.82 [a] Only Co and Cl atoms up to hexadecapole. [b] NPˆ no. of parameters. [c] R1ˆ SjFo Fcj/SjFoj. [d] R1wˆ (SwjFo Fcj2/SwjFoj2)1/2. [e] R2ˆ SjFo2

F2

cj/SjFoj2. [f] R2wˆ (SwjFo2 Fc2j2/SwjFoj4)1/2. [g] Sˆ [SwjFo2 Fc2j2/(NO

coordination spheres with a significant difference in the bite

angles, for example 98

8 versus 828 (aN-Co-N) in this case.

Laplacian of electron density: The local electron density

accumulation and depletion, or the valence-shell charge

concentration (VSCC), can be visualized by a Laplacian of

the electron density,

r

_{1. The Laplacian of the total electron}

density derived from experiment (multipole model) and from

UHF and DFT/UB3LYP calculations in the equatorial (xy)

plane are displayed in Figure 4.

The charge concentration (CC)

of the covalent bond character

of intraligand C C, C N, and

N N bonds and the lone-pair

regions of imino-N toward Co

are clearly shown. The local

electron density concentrations

of imino-N and of water-O

atoms are directed toward the

metal center, demonstrating the

s-donor character of the ligand.

Thus the metal ± ligand bond

can be recognized as that of a

Lewis acid ± base pair. There is

no significant difference

be-tween the UHF and DFT

cal-culation, so in the subsequent

results we will only show the

DFT calculation.

Figure 2. Packing diagram (aˆ 0 ± 3/2, b ˆ 0 ± 1/2, c ˆ 0 ± 1): for clarity, methyl groups and H atoms of the cation are neglected; the dashed line indicates the hydrogen bond between coordinated water molecules and perchlorate anions.

Figure 3. Deformation density distribution,D1, in the molecular plane (xy); solid line positive, dotted line negative, contour interval 0.1 e ä 3_{, up}

to 2 e ä3_{: a)D1}

M±Afrom experiment; b)D1residual; c)D1M±Afrom UHF;

d)D1M±Afrom DFT.

Figure 4. Laplacian in the xy plane derived from: a) experiment; b) UHF calculation; c) DFT calculation; solid line negative, dotted line positive, contours are ( 1)l₂m₁₀n_{(lˆ 1, 0; m ˆ 1  3; n ˆ 3  3) e ä}5_.

The asphericity in electron density distribution around the

Co nucleus is an important piece of evidence for the

under-standing of the properties of metal ± ligand bonding, which

can also be recognized by the Laplacian of the electron

density. The Laplacians for four unique planes around Co are

shown in Figure 5. The CCs of the valence shell at the metal

nucleus certainly appear at its third quantum shell. The local

CC in d

directions (d

, d

, d

) and the local charge

depletion in the d

direction (d

, d

) are clearly shown on the

map. For example, density depletion is visible in the d

direction (d

orbital) towards the nitrogen atoms, but density

accumulation is found in the d

(d

) direction (coordination

is defined as in Figure 1b) in the horizontal plane. The

agreement between experiment and theory is satisfactory.

However, the separation between positive and negative

Laplacian near the Co nucleus is much more pronounced in

the experimental maps than in the theoretical maps. The other

three planes also show large CCs in the d

direction (d

, d

)

and charge depletion in the d

direction (d

) both in

experimental and in theoretical maps.

Atomic graph of Co and Cl atoms: In general, the bonded and

nonbonded charge concentrations in the valence shell of a

bonded atom, determined by the Laplacian of

1(r), are in

good agreement with the corresponding properties that are

ascribed to bonded and nonbonded pairs in Gillespie×s

VSEPR model of molecular geometry.

_{An atomic}

graph

_{is a polyhedron around the nucleus. Such a}

polyhedron is defined by the vertices, V(CCs), the edges, E,

and the faces, F, where the face critical point is a local

maximum Laplacian value and represents a local depletion of

the charge density. The polyhedron follows Euler×s formula

V

E

‡F ˆ 2.

A three-dimensional envelope plot of an isovalue Laplacian

surface, L(r), of the Co atom derived from experiment and

from the DFT calculation is presented in Figure 6. The atomic

Figure 6. Envelope map of isovalue surfaces of the Laplacian around Co: a) from experiment; b) from DFT; c) schematic drawing for the atomic graph of Co: vertices are marked as V; edges are linked between verticies ; face CPs are along the Co L bonds.

graph shows eight vertices (CCs) in the VSCC of the Co

nucleus, forming a cubelike polyhedron. This geometry can be

explained as the linear combination of d

, d

, and d

orbitals of the cobalt atom. The polyhedron consists of eight

vertices, six faces, and twelve edges, following Euler×s

formula. The vertices, edges centered at the bond critical

point (BCP), and the face critical point (CP) around the Co

center are plotted in Figure 6c. The detailed descriptions of

each polyhedron from experiment and from theoretical

calculation agree well with each other (Supporting

Informa-tion). Each CC of a coordinated ligand atom (N, O) caps one

of the six faces (F) of the approximately cubic polyhedron

Figure 5. Laplacian of the Co atom in four different planes, defined on the left of the drawing; DZ is the plane perpendicular to the molecular plane and passing through N1-Co-N1': column a) from experiment; b) from DFT; contours are as in Figure 4.

formed by the eight vertices, which are the CCs in the VSCC

of the Co atom. The detailed geometry of the polyhedron of

the atomic graph is comparable with those reported by

Bader.

_{Such an atomic graph was firstly described in the}

case of [Cr(CO)

],

where the vertices are at the corners of

a cube.

The perchlorate anion has a tetrahedral geometry.

Accord-ing to the VSEPR model, four bonded pairs should be formed

around the Cl center. The Laplacian in the plane of O1-Cl-O2

is shown in Figure 7. It is clearly demonstrated that the local

Figure 7. Laplacian in one of the O-Cl-O planes; contours are as in Figure 4;&denotes the local Laplacian minimum,F denotes the local Laplacian maximum, a) from experiment; b) from DFT calculation.

CCs of the chlorine atom (

) are directed toward the local

depletion (

F) of the oxygen atoms, and Cl-

-

F-O is almost

collinear. This indicates that the bond pair has donating

character, from the Cl to the O atom.

The three-dimensional envelope plots of isovalue Laplacian

surface, L(r), and the atomic graph of the chlorine atom are

shown in Figure 8. There are four vertices (V

ˆ 4), six edges

(E

ˆ 6), and four faces (F ˆ 4) in the atomic graph of Cl. Each

CC is directed toward an oxygen atom. Apparently the

bonding characteristics of ClO

are quite different from

those in the corresponding Co complex cation. In the case of

ClO

, the central Cl atom serves as an electron-pair donor,

while in the case of [Co

_(C

12

H

N

)(H

O)

], the central Co

atom serves as an electron-pair acceptor along the interatomic

axis. The latter is encountered in coordination complexes,

Figure 8. Envelope map isovalue surface of Laplacian around Cl: a) from experiment; b) from DFT; c) schematic drawing for the atomic graph of Cl. Vertices, edges, and face CP are marked in as V, E, and F respectively.

whereas the former is usually found in normal metal oxides or

chlorides.

Topological properties: The gradient vector fields of the

electron density of the cation in the molecular plane derived

from experiment and theoretical calculation are shown in

Figure 9. The CP of atomic sites (3,

3) and the ring CP (3,

‡1) in the five- and six-membered rings are quite observable

from the termination of the trajectories. The atom domain can

be recognized from this figure as well. The imino N atom and

the connected C atom in this projection adopt a triangular

shape indicating an sp

_{-type bonded atom. The Co atom in}

this plane shows a square planar shape. The BCP and bond

paths are located at each chemical bond; for example, those in

the xy plane from experiment and theory are shown in

Figure 10. Atom domains in this projection are also clearly

shown in this figure. The agreement between experiment and

theory is good. From the partition of the atom domain, the

AIM integrated charge

_{can be derived. Detailed}

topolog-ical properties associated with the BCP are listed in Table 5.

According to the Laplacian at the BCP, the Co N and Co O

bonds are in closed-shell interactions (ionic character);

however, the local energy density, H

, certainly indicates that

there is covalent character, at least, in the Co N bond.

Further investigation by Fermi hole function (shown below)

suggests there is certainly some covalent character in the

Co N bond but very little in Co O bonds.

The density at the BCP,

1(r

), of the Co O bond is

significantly lower than the densities of M O bonds (0.2 vs.

the Jahn ± Teller distortion of the d

_{system, which results in}

the lengthening of the axial M O bond. All C C, C N, and

N N bonds of the ligand, as well as the Cl O bond of the

anion, show clear covalent character with

r

_1(r

c

)

< 0 and a

value of 1.5 ± 2.8for

1(r

). More importantly, the large

negative H

values indicate the substantial stabilization of

the local potential energy due to the shared interaction

(covalent character). The N N and N C7 bonds appear to

have higher

1(r

) values of 2.0 ± 2.3 than the other bonds (1.5 ±

2.0). It may be fair to say that partial double-bond character is

delocalized in these N N and N C bonds (as indicated in

Scheme 1); this will be substantiated in the Fermi hole

function analysis discussed in the following.

Hydrogen bond: There is a hydrogen-bond interaction

between the oxygen atom of perchlorate and the coordinated

water molecule. It can be substantiated by the topological

analysis results. The density at the BCP,

1(r

), is about

0.1 e ä

_{, and the near-zero value of H}

b

(Table 5) is

compa-rable to a medium hydrogen-bond interaction.

_{The 3D}

topological envelope in the environment of the hydrogen

bond between the O4 atom of ClO

and the H5 ± O5 of water

molecule is depicted in Figure 11. A Laplacian vertex of O4 is

directed toward the secondary Laplacian charge depletion of

H5, which is a Lewis acid ± base pair binding interaction.

Fermi hole function: It has been demonstrated

_{that all}

physical measures of electron localization or delocalization

can be determined by the corresponding localization or

delocalization of the Fermi hole density. The Fermi hole

density is depicted in Figure 12a ± d with the reference

electron located at 0.35 ä above the molecular plane at

various atomic sites. The density spread in space indicates the

existence of delocalization. However, the density spread in

the space of the p

direction is not a very extensive one, being

limited to the atoms in the molecular plane, namely

N4-N1-C7, where the

1(r

) values are significantly higher than those

of other bonds (Table 5).

In order to probe the Co N and Co O

s-bond character,

we have plotted a Fermi hole density in Figure 12e ± f, with the

reference electron located at the CCs of O and N atoms

toward the Co atom. The Fermi hole density clearly indicates

the covalent character along the Co N

s-bond (Figure 12f).

The Co O bond has nearly ionic character, with very little

Fermi density distribution found near the Co center atom

(Figure 12e); this fact is consistent with the difference in

1(r

)

and H

values of the Co N and Co O bond. The covalent

character between Co and the four imino-N atoms can be

easily recognized as the interaction between the sp

_hybrid

Figure 9. Gradient vector field in the xy plane: a) from experiment; b) from DFT calculation.

Figure 10. Total electron density, bond path, and atom domain in the molecular plane: a) from experiment; b) from DFT calculation.

orbital of N and the d orbital of Co as found in NBO analysis,

even though it is characterized as a nonbonding orbital both of

imino-N and Co d-orbitals (Table 6). It is clear that the Fermi

hole density does help to clarify the bond character of an M L

bond.

Natural bond orbital analysis: The bond hybridization and the

bond order of various chemical bonds can also be derived

from NBO analysis based on DFT/UB3LYP calculations. The

natural bond hybrid orbital, bond occupancies, and bond

order are listed in Table 6. Selected bond orders are shown in

Figure 1a. Here, the N1 C7 bond has double-bond character

with a bond order of 1.83. This bond is stronger than that in

the free ligand, which is proved by the C N stretching

frequency,

nÄ

, being blue-shifted from that of the free ligand

(1575

! 1597 cm

_).

_{N N and C C bonds are all single}

bonds; nevertheless, this represents only one of the possible

resonance forms. Co N and Co O bonds are essentially

dative, illustrated in Figure 1a by heavy arrows. The

non-bonding electron density around Co is evidently in a low-spin

d

_{configuration with the unpaired electron in the d}

z2

orbital,

though no CC is found in the Laplacian in this direction.

Net atomic charges and d orbital populations: Net atomic

charges derived from multipole model and MO calculations

are given in Table 7. Although the values differed somewhat

between various analyses, the general trend is roughly the

same. The coordinated atoms (N and O) of the octaaza ligand

are all negatively charged, with the oxygen atom more

negative than nitrogen atoms. This may indicate more

polarized bond character in the Co O bond than in the

Co N bond. The net atomic charge normally correlates

strongly with the bonded atomic charge; the fragment charge

is therefore compared. It is clearly indicated that the positive

charge of the cation is dissipated among the atoms of the

macrocyclic ligand. The water molecule is negatively charged

on the basis of AIM charge; however it results as neutral from

both monopole refinement and MO calculations. Since the

MO calculations do not include the perchlorate anion, that is,

the cation charge is fixed at 2

‡ , the comparison in values

between experiment and theory is not exactly relevant.

The electron populations in the d orbitals can be derived

from the multipole coefficients, P

, of the Co atom, which

are listed in Table 8. The d-orbital populations are presented

in Table 9. The electronic configuration of cobalt is regarded

as a low-spin d

_{configuration both from the experimental and}

MO calculations, that is d

xz

, d

, d

, d

. It is evident that

the d

orbitals (d

and d

) are the most destabilized and the

Table 5. Properties of bond critical point: a) experimental; b) UHF; c) DFT. Bond/bond length [ä] d1[ä] l3[e ä5] r21(rc) [e ä5] 1(rc) [e ä3] Hb[H ä3] cation Co N1 a 0.926 19.85 11.98 0.783 0.255 1.9026(7) b 0.883 22.04 18.17 0.588 0.052 c 0.874 22.10 17.49 0.507 0.078 Co O5 a 1.144 6.00 4.13 0.279 0.001 2.2854(9) b 1.088 5.79 4.70 0.202 0.007 c 1.082 5.05 4.14 0.132 0.019 N1 N4 a 0.705 32.91 7.182.446 3.731 1.374(1) b 0.713 17.58 19.56 2.140 3.308 c 0.719 22.08 18.01 2.174 3.348 N1 C7 a 0.837 11.84 29.04 2.503 4.381 1.301(1) b 0.876 32.85 0.61 2.030 2.626 c 0.868 24.95 10.93 2.178 3.192 N4 C5 a 0.875 12.90 10.81 1.720 2.234 1.462(1) b 0.951 9.31 11.12 1.518 1.869 c 0.935 9.74 12.50 1.565 1.985 C6 C7A a 0.737 13.16 17.85 2.042 3.054 1.475(1) b 0.737 5.01 17.50 1.551 2.076 c 0.735 7.39 19.33 1.638 2.277 C7 C8a 0.87811.09 7.65 1.589 1.915 1.492(1) b 0.853 5.54 13.281.433 1.772 c 0.870 8.07 12.84 1.491 1.861 anion Cl O1 a 0.731 29.66 10.282.809 4.728 1.437(1) b 0.54830.353 4.382.624 4.548 c 0.564 21.04 7.93 2.529 4.338 Cl O2 a 0.701 24.21 12.182.536 4.052 1.447(1) b 0.556 23.80 10.06 2.590 4.525 c 0.576 14.93 13.47 2.491 4.246 hydrogen bond O4 HO5A a 1.3282.95 1.41 0.115 0.015 2.07(3) b 1.253 3.85 2.14 0.179 0.004 c 1.232 3.82 1.92 0.196 0.005 O2 HO5B a 1.2583.82 2.02 0.102 0.025 2.13(4)

Figure 11. Three-dimensional Laplacian envelope of the O4 ¥¥¥ H5 hydro-gen bond from: a) experiment; b) DFT calculation.

least populated. The d

orbital (directed toward the nitrogen)

is more so than the d

orbital owing to Jahn ± Teller distortion.

The d

orbitals (d

, d

, d

) are all fully occupied. The singly

occupied d

orbital is clearly indicated in the MO calculation

with

a-spin only (Table 9). Thus the Co

_{ion is in a low-spin d}

state and tetragonal bipyramidal coordination with the

d-orbital energy levels of the order of E(d

)

> E(d

)

>

E(d

)

 E(d

, d

). This order of d-orbital energies is the

same as found previously.

Conclusion

The present study provides a detailed description of chemical

bonding

in

[Co

_(C

12

H

N

)(H

O)

] ¥ 2 ClO

paramagnetic

complex in terms of deformation density, Laplacian and

topological analyses by X-ray diffraction and quantum

mechanical MO calculation. The Co

_{ion in tetragonal}

bipyramidal N

O

coordination is in a d

low-spin state with

the singly occupied orbital being d

. The bonding between Co

and N or O in the coordination sphere is essentially a dative

bond but with some covalent bond character in Co N bond.

The atomic graph of Co is a hexahedron with eight vertices of

charge concentration and six faces of charge depletion. The

eight-cornered shape of the CC can be viewed as the linear

combination of three fully occupied d

(d

, d

, d

) orbitals.

Each of the ligands caps one of the six faces of this

Figure 12. Fermi hole (FH) distribution from DFT calculation: a) ± d) in the plane 0.35 ä above the molecular plane; the reference electron is indicated by X at a) N1; b) N4; c) C7; d) C5; e) and f) are the FH distribution in the molecular plane with the reference electron situated at the lone pair density maximum of e) O5; f) N1 toward the Co center.

Table 6. Natural bond hybrid orbital (NHO), bond order, and bond occupancies of various bonds from DFT calculations.

Bond/bond type[a] _{Spin Center NHO Occ. Bond order}

N1 N4 0.98 s a ‡ b N1 spx(54 %) 1.98 N4 spx(46 %) N1 C7 1.89 s a ‡ b N1 spxpy(61 %) 1.98 C7 spxpy(39 %) p a ‡ b N1 pz(63 %) 1.96 C7 pz(37 %) N4 C5 0.98 s a ‡ b N1 spypzpx(61 %) 1.98 N4 spypzpx(38%) C7 C80.98 s a ‡ b N1 spypx(55 %) 1.98 N4 spypx(45 %) C6 C7A 0.98 s a ‡ b C6 spx(50 %) 1.98 C7A spx(50 %) n a Co dz2 0.99 n a ‡ b Co dxz 1.98 n a ‡ b Co dyz 1.98 n a ‡ b Co dx2y2 1.98 n a ‡ b N3, N4 spypx 1.98 n a ‡ b N1, N2 spypx 1.98 n a ‡ b O5 spz 1.98 n a ‡ b O5 spzpx 1.98 [a] nˆ non-bonding.

Table 7. Net atomic and fragment charges.

Atom Experimental Theoretical MO calculations

AIM Z Pval UHF DFT/UB3-LYP

Charge NPA NPA

Co 0.80 0.41 1.31 1.48 N1, N2 0.96, 0.95 0.17 0.35, 0.36 0.50, 0.51 N3, N4 0.62, 0.79 0.26 0.41, 0.41 0.46, 0.45 O5 1.38 0.72 0.76 0.90 C5 0.25 0.20 0.07 0.04 C6, C7 0.45, 0.44 0.05 0.25, 0.25 0.34, 0.34 C8, C9 0.44, 0.40 0.67 0.55, 0.55 0.55, 0.58 H(N3), H(N4) 0.38, 0.37 0.25 0.32, 0.32 0.36, 0.36 H(O5a), H(O5b) 0.37, 0.34 0.380.43, 0.43 0.46, 0.46 H(C5a) 0.11 0.20 0.25 0.28 H(C5b) 0.11 0.280.14 0.16 3H(Me C8) 0.56 1.00 0.64 0.68 3H(Me C9) 0.52 1.00 0.67 0.72 Cl 2.31 1.37 ± ± O1, O3 0.68, 0.66 0.50 ± ± O2, O4 0.72, 0.69 0.54 ± ± fragment charges Co 0.80 0.41 1.31 1.48 C10H20N8 1.36 0.97 0.57 0.47 H2O 0.67 0.01 0.06 0.02 ClO4 0.43 0.702 1.0 1.0

hexahedron. In contrast, the atomic graph of the Cl of the

perchlorate ion is a tetrahedron with four CCs at the vertices,

each pointing toward a charge depletion of an oxygen atom.

The bonding of a coordinated dative bond and a normal

covalent bond is thus clearly demonstrated.

Experimental Section and Computational Details

Crystal structure and refinement: The title compound was prepared by template condensation according to the literature;[1, 2]_{the mother liquor}

was slowly evaporated under nitrogen and large dark brown prismatic crystals were formed. The chosen crystals were then sealed in a capillary and reflection intensities were measured on a CAD4 diffractometer both at 298K and at 125 K. The space group at 298K is Cmca, a total of 4107 reflections was measured within 2qmaxˆ 508, yielding 2163 unique

reflections, the structural analyses were processed using NRCVAX[19]

program based on 993 observed [I> 2s(I)] reflections. The C-centered systematic absences were checked thoroughly and only six out of 2051 such reflections are larger than 5s(I). However, at 125 K, the space group is Pbca and the C-centered absences no longer exist. Three reference reflections were measured every hour; the variations in intensity are within 2 %. Intensity data were first measured up to 2q ˆ 858 for a unique set of reflections ( h, k, l) to ensure the symmetry. Four additional equivalent reflections (h, k, ‡l), (‡ h, ‡k, l) were measured afterwards. These yielded a total of 40 050 reflections, which gave 8517 unique reflections after averaging of the equivalents. An absorption correction was applied before the averaging according to ten measured faces. The correctness of the absorption correction was checked against the

experimental psi curves for three reflections, the agreement between the measured relative intensities and the calculated transmission was reason-able. The interset agreement between the intensities of equivalent reflections is 0.029 after applying the absorption correction. Data were corrected for Lorentz and polarization effects. The structure factor, Fo, is

derived from the averaging intensity; the standard deviation, s(Fo), is

calculated from a geometric mean of all the s values of equivalents. Conventional full-matrix least-squares refinements were performed with all the positional and anisotropic thermal parameters. The H atoms were relocated along the C ± H vectors to give the C H bond length of 1.08ä[20, 21]_{for the purpose of the deformation density studies. The crystal}

data and other details of the experimental conditions and refinements are given in Table 10. CCDC-171337 and 171338contain the supplementary

crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/conts/retrieving.html (or from the Cam-bridge Crystallographic Data Centre, 12 Union Road, CamCam-bridge CB2 1EZ, UK; fax: (‡44)1223-336033; or [email protected]). Additional multipole refinements were performed with the XD program,[22]

in which the atomic density is described as the sum of a spherical and a nonspherical part. The spherical part consists of a core density (1core), a

valence density (1val) with adjustable population Pval and a radial

contraction ± expansion parameter (k). The nonspherical part of the atomic electron density can be expressed[23]_{as a series of spherical harmonic terms}

Ylmpwith variable population coefficients, Plmp. Pval, Plmp,k', and k are

refined parameters in addition to the atomic positional and thermal parameters. The multipole refinement was made with a multipole expansion of the valence shell up to hexadecapoles for the Co and Cl atom, up to octapoles for the C, N, and O atoms, and up to quadrupoles for the H atom. Thek'-unrestricted multipole model (UMM)[24]_{was created.}

Atomic scattering factors of both core and valence electrons were taken from the International Tables for X-Ray Crystallography.[21]_{A [He] core}

Table 8. Multipole population coefficients of the Co atom in Ciand C2h

molecular symmetry. Plmp Ci C2h[a] Functions P00 3.640 3.729 1 P20 0.142 0.123 2z2 x2 y2 P21 0.030 0.011 xz P2±1 0.006 0.030 yz P22 0.132 0.151 x2 y2 P2±2 0.013 0.008 xy P40 0.162 0.160 8z4 24x2z2 24y2z2‡ 6x2y2‡ 3x4‡ 3y4 P41 0.031 0.001 4xz3 3zx3 3zy2x

P4±1 0.006 0.032 4yz3 3zyx2 3zy3

P42 0.034 0.010 (x2 y2)(6z2 x2 y2) P4±2 0.0280.034 2xy(6z2 x2 y2) P43 0.052 0.000 z(x3 3xy2) P4±3 0.004 0.032 z(y3 3yx2) P44 0.133 0.0984x3y 4xy3 P4±4 0.014 0.010 x4 6x2y2‡ y4

[a] The Co site has Cisymmetry.

Table 9. Experimental and theoretical results for d-orbital populations of the Co atom. (NPAˆ natural orbital population analysis.)

d Exptl Theoretical MO calculations

UHF/(6 ± 31G*) DFT/6-31G*)

NPA NPA

total total a b total a b

dxy 0.85(7) 0.48 0.25 0.23 0.34 0.19 0.15 dz2 1.30(7) 1.07 0.99 0.081.05 0.99 0.06 dyz 2.2(1) 1.980.99 0.99 2.00 1.00 1.00 dx2y2 1.47(7) 1.980.99 0.99 2.01 1.01 1.00 dxz 1.6(1) 1.84 0.92 0.92 1.99 1.00 0.99 total 7.45 7.35 7.39

Table 10. Crystal structure data at 298K and 125 K. formula Co[C10N8H20](H2O)2

¥ 2 ClO4

Co[C10N8H20](H2O)2

¥ 2 ClO4

Mr 546.19 546.19

system orthorhombic orthorhombic

space group Cmca Pbca

a [ä] 11.646(4) 11.655(2) b [ä] 17.049(4) 16.930(4) c [ä] 10.706(3) 10.508(2) V [ä3_{] 2125.7(1) 2073.4(6)} Z 4 4 1calcd[g cm 3] 1.707 1.749 l(MoKa) [ä] 0.7107 0.7107 F(000) 1124 1124 2q range [8][a] _{30.2 ± 44.8 78.7 ± 84.1} scan type q/2q q/2q

scan width [8] 2 (0.65‡ 0.35tanq) 2 (0.70‡0.35 tanq)

2qmax[8] 50.0 85.0 m(MoKa) [cm1] 11.21 11.49 crystal size [mm] 0.35 0.40  0.50 0.35 0.40  0.50 T [K] 298125 reflections measured 1879 40 050 unique reflections 1864 8517 reflections observed [I> 2s(I)] 993 5547 R1/R1W 0.045/0.047 0.033/0.037 Rint[b] ± 0.029 S 1.35 2.40 g (ext. coeff.) 104 _{0.9(3) 0.27(3)} (D/s) max 0.0080.0009 (D1) min/max [e ä3_{] 0.4/0.64 0.56/0.68} minimization function S(w j Fo Fcj2) S(w j Fo Fcj2) weight 1/[s2_(F o)] 1/[s2(Fo)‡ 6  105Fo2]

was used for C, N, O, a [Ne] core for Cl, and a [Ca] core for Co. The valence electron configurations for Co, Cl, C, N, and O are d7_{, s}2_p5_{, s}2_p2_{, s}2_p3_{, and}

s2_p4_{, respectively. Two choices of molecular symmetry, C}

iand C2h, were

tried on the cation in the least-squares procedure for the multipole coefficients, Plmp. There are more variables in the Cimodel than in the C2h

model; however, insignificant improvement was found in the agreement indices of the Cimodel. Therefore the C2hmodel was chosen to be the basis

for discussion of the cation, but the Co coefficient is still in Cisymmetry in

order to be properly compared with the MO calculations. The coefficients of all the multipole terms together with positional and anisotropic thermal parameters were obtained by a full-matrix least-squares refinement based on F2

o.

Basis functions and geometry: For the ab initio MO calculation, the basis set used for the Co atom was (14,9,6)/[8,4,3] contractions : (62111111/5112/ 411),[25, 26]_{where the (14s,9p) primitive Gaussian functions are taken from}

Wachters[26]_{and (6d) functions are from Goddard.}[25]_{The basis sets used for}

N, O, C and H were 6-31G*. All computations are made only on the cation (2‡ ). Because of the odd number of electrons, the calculation was made at the UHF level. The density functional calculations (DFT) used were nonlocal spin density corrections to the local spin density approximation (LSDA)[27]_{functional with the LSD exchange and the Vosko, Wilk, and}

Nusair correction function (VWN). The exchange functional was the Becke×s three-parameter hybrid method[28] _{which used the correction}

functional of Lee, Yang, and Parr (B3LYP).[29, 30]_{The molecular geometry}

was taken from the diffraction study at 125 K. The internal coordinates of the Co atom were defined so that the y axis was at the bisection ofaN1-Co-N2A and the x axis was at the bisection ofaN1-Co-N2 (Figure 1b). Deformation electron density: The deformation density distribution based on the multipole model[23]_{was obtained by subtracting the spherical part of}

the atomic electron density with Pvalset as a neutral atom and thek values

reset to 1.0 from the total electron density. All computations were carried out with NRCVAX[19]_{and XD}[22]_programs.

The theoretical deformation density (D1theo) is defined as the difference

between the total molecular electron density and the promolecular electron density. The total molecular electron density was calculated either from UHF or from DFT calculated molecular wave functions. The promolecular electron density is the sum of the superposition of the spherical atomic density with atoms located at the same nuclear positions as in the molecular geometry. The spherical atomic density was calculated at the ROHF/GVB level. All computations were performed with the Gaussian 98[28]_program.

The AIMPAC[31] _{routine was used for the deformation density and}

topological analysis.

Natural bond orbital analysis: The natural bond orbital (NBO) analy-sis[32±35]_{comprises a sequence of transformations from the given basis sets to}

various localized MO sets. These procedures derive their names and inspirations from the natural orbitals of Lˆwdin,[36]_{which are obtained}

from the diagonalization of the one-particle density matrix. The given basis functions were taken from DFT/UB3LYP calculation. The results after NBO analysis were generally in good agreement with Lewis structure concept and the Pauling ± Slater ± Coulson[37]_{concept of bond hybridization}

and polarization. Net atomic charges, orbital populations, and bond orders were thus generated by means of NBO analysis. The charges and orbital populations obtained this way were designated as natural orbital popula-tion analysis (NPA), and were compared with the Mulliken populapopula-tion analysis (MPA).

Topological analysis: Topological analysis based on the theory of atoms in molecules (AIM)[14]_{was applied both to the experimental electron density}

(multipole model[23]_{) and to the theoretically calculated electron density}

(UHF and DFT). The BCPs and bond paths (BPs) of electron density can be used to construct a molecular graph representing the interactive network connecting bonded atoms.[38]

The Laplacian topology of electron density depicts the local charge concentration when r2_{1(r) < 0 and the local charge depletion when}

r2_{1(r) > 0. This Laplacian topology provides the physical basis for the}

Lewis structure and VSEPR models.[13]_{The electron density at the BCP,}

1(rc), is related to the bond strength or the bond order.[39]

It was suggested[39c]_{that the total energy density value, H}

b(which is the sum

of the kinetic energy density Gband the potential energy density Vb), at the

BCP could be interpreted as a sufficient condition for a covalent bond when the sign of Hbis negative. Such a value may be used as a qualitative

measure for covalency of a bond. The experimental Hbvalue is estimated

by a generalized approach of Abramov×s expression.[40]

Furthermore, the topological properties ofr2_{1(r) can be used to}

under-stand the active chemical reactive site and to reveal simple 3D directional interaction in the molecular crystal. A correlation between these CPs of r2_{1(r) in the valence shell and the location of the active site in the molecule}

has been established.[14, 15, 41] _{In principle, a Lewis acid ± base reaction}

occurs owing to the fact that a local maximum of the VSCC on the Lewis base aligns itself as far as possible with a local minimum of the VSCC on the Lewis acid.

On the basis of AIM theory,[14]_{the gradient vector field of the charge}

density is represented through a display of the trajectories traced out by the vectorr1. Every trajectory must originate or terminate at a point where r1(r) vanishes, that is, at a critical point of 1(r); starting at a BCP, paths for which the electron density decreases most rapidly are developed in all directions normal to the bond. The set of such paths defines a zero-flux surface separating a pair of bonded atoms. A set of those surfaces (one per bond) will partition a molecule into unique atom domains (W atomic basins) for which the hypervirial theorem is satisfied. Numerical integra-tion of the electron density within such a basin, W, yields the charge assigned to that given atom: qWˆ SW1(r)dt. This is called the AIM atomic

charge. The AIM atomic charges are calculated by the TOPXD[42]_program

from the experimental charge density.

The Fermi hole function[18]_{is an effective tool with which to study the}

electron localization and delocalization of the system. Therefore it can be utilized to understand the covalency of the bond. Detailed definitions of all these topological properties are given elsewhere.[13±15, 38±41]_{In this study,}

maps of the Laplacian were made by the XDPROP[22] _{program; the}

gradient vector field and bond path were obtained by means of PROP[43]

and AIMPAC[31]_programs.

Acknowledgements

Thanks are due to Dr. Y.S. You for the supply of single crystals. Thanks are also due to Prof. Coppens for making the TOPXD program available. The valuable discussion with Prof. T.-H. Tang is appreciated. The authors would like to thank the National Science Council of the Republic of China for financial support and to the National High-Performance Supercomputer Center for access to hardware and software.

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