Chemical Applications of Charge Density Louis J Farrugia Jyväskylä Summer School on Charge Density August 2007.

Chemical Applications of Charge Density

Louis J Farrugia

Jyväskylä Summer School on Charge Density August 2007

http://www.westchem.ac.uk/

Chemical applications of charge densityJyväskylä Summer School on Charge Density August 2007

1. VSEPR rules and the Laplacian1. VSEPR rules and the Laplacian2. Hydrogen bonding2. Hydrogen bonding3. Metal-metal bonding3. Metal-metal bonding

VSEPR rules and the LaplacianJyväskylä Summer School on Charge Density August 2007

VSEPR (Valence Shell Electron Repulsion) rules are used to teach the VSEPR (Valence Shell Electron Repulsion) rules are used to teach the elements ofelements of

structure for main group compounds.structure for main group compounds.

Simple theory based on a few elementary concepts :Simple theory based on a few elementary concepts :1.1. Electrons in the valence shell around central atom are paired (Lewis Electrons in the valence shell around central atom are paired (Lewis

structures)structures)2.2. Electrostatic repulsion between pairs leads to structures with the Electrostatic repulsion between pairs leads to structures with the

maximal distance between themmaximal distance between them3.3. Repulsions for single bonds follows order Repulsions for single bonds follows order lone-pair lone pair > lone-pair bond pair > bond pair bond pairlone-pair lone pair > lone-pair bond pair > bond pair bond pair4.4. Multiple bonds have stronger repulsion than single bondsMultiple bonds have stronger repulsion than single bonds5.5. Bond pair repulsion decreases with increasing electronegativity of Bond pair repulsion decreases with increasing electronegativity of

ligandligand6. 6. Explains why HExplains why H22O is bent, NHO is bent, NH33 is pyramidal but BF is pyramidal but BF33 is planar , ClF is planar , ClF33 is is

T-shaped ..... T-shaped .....

R. J. Gillespie & P. L. A. Popelier Chemical Bonding and Molecular Geometry, OUP, 2001.





Laplacian “emphasises”local charge concentration



Laplacian recovers the shell structure of the atom (here a free S atom -Laplacian recovers the shell structure of the atom (here a free S atom -33P). This is P). This is completely invisible in the density completely invisible in the density . Shows alternate shells of charge . Shows alternate shells of charge concentrationsconcentrations and charge and charge depletionsdepletions. . Here we are concerned with the Valence Shell Charge Here we are concerned with the Valence Shell Charge Concentration (VSCC). UnitsConcentration (VSCC). Unitsof Laplacian in experimental CD studies usually given as e Åof Laplacian in experimental CD studies usually given as e Å -5-5..



Plots of L -2 for the SCl2 molecule(a) in molecular plane (b) close-up of VSCC of S atom(c) plot in the plane perpendicular to (a)

Critical points are marked by dots



Plots of L -2 for the T-shaped moleculeClF3 (a) in molecular plane (b) plot in the plane perpendicular to (a)

5 charge concentrations – 3 bond pairs and2 lone pairs

a

b


R. J. Gillespie, R. F. W. Bader et al (1998) J. Phys Chem. A. 102, 3407

““The Lennard-Jones Function: A Quantitative Description of the Spatial Correlation of The Lennard-Jones Function: A Quantitative Description of the Spatial Correlation of Electrons As Determined by the Exclusion Principle” - provides a Electrons As Determined by the Exclusion Principle” - provides a physical basisphysical basis for for electron pairing through the operation of the Pauli exclusion principle – the conditional electron pairing through the operation of the Pauli exclusion principle – the conditional probability function for same spin electron is called the LJ function in honour of Lennard-probability function for same spin electron is called the LJ function in honour of Lennard-Jones.Jones.

Is BF3 ionic ?Jyväskylä Summer School on Charge Density August 2007

R. J. Gillespie et al (1997) Inorg Chem. 36, 3022.

Arguments :Arguments :1.1. Bader atomic charges Bader atomic charges

indicate high ionic indicate high ionic character.character.

2.2. F-F “non-bonded” distances F-F “non-bonded” distances are remarkably constant, in are remarkably constant, in line with observed structure line with observed structure being dominated by ligand-being dominated by ligand-ligand repulsions.ligand repulsions.

Counter arguments :Counter arguments :1.1. While the B-F bond is While the B-F bond is

undoubtedly highly polar, undoubtedly highly polar, an ionic model can only an ionic model can only account for ~ 60% of bond account for ~ 60% of bond energyenergy

2.2. The F atom is strongly The F atom is strongly polarised, indicating polarised, indicating significant covalent significant covalent charactercharacter

3.3. It is a gas.It is a gas.

Bader charge onfluoride

Bader charge oncentral atom

A. Haaland et al (2000) J. Chem. Ed. 77, 1076

Hydrogen bonds Jyväskylä Summer School on Charge Density August 2007

Hydrogen bonds were first described (probably) by M. L. Hydrogen bonds were first described (probably) by M. L. Huggins Huggins in 1919, but Linus Pauling (1931) was the first to coin the in 1919, but Linus Pauling (1931) was the first to coin the term term hydrogen bondhydrogen bond to describe the bonding in the [F- to describe the bonding in the [F-H...F]H...F]-- anion. anion.

G. A. Jeffrey (1997) An Introduction to Hydrogen Bonding, OUP, New York.


G. Gilli, P. Gilli (2000) “Towards a Unified H-bond Theory” J. Mol. Struct 552, 1

Hydrogen bonds


R.F.W. Bader & C. Gatti (1998) Chem. Phys. Lett 287, 233 (source function)E. Espinosa et al (1999) Acta Cryst B55, 563. (topology of H-bonds)E. Espinosa & E. Molins (2000) J. Chem. Phys. 113, 5686 (interaction energies)

Hydrogen bonds

It is generally agreed that weak H-bonds are primarily It is generally agreed that weak H-bonds are primarily electrostaticelectrostatic in nature, while strong H-bonds have in nature, while strong H-bonds have considerable covalent character. considerable covalent character.

How can we use charge density methods to shed light on this How can we use charge density methods to shed light on this area?area?• use topological properties to characterise bondsuse topological properties to characterise bonds• use charge densities to extract use charge densities to extract interaction energiesinteraction energies

The values of The values of ((rr))bcpbcp and and 22((rr))bcpbcp provide provide some some information, information, but recently other tools, such as the Source Function, have but recently other tools, such as the Source Function, have proved to provide interesting additional information. proved to provide interesting additional information.

Approximate potential and kinetic energy densities may be Approximate potential and kinetic energy densities may be derived from derived from ((rr) and ) and 22((rr) using DFT type functionals – ) using DFT type functionals – exact electrostatic energies may be computedexact electrostatic energies may be computed


U. Koch & P.L. A. Popelier (1995) J. Phys Chem 99, 9747.

Topological Definition of Hydrogen Bonding

Koch & Popelier have examined the characterisation of C-H...O bonds on Koch & Popelier have examined the characterisation of C-H...O bonds on the basis of charge density. The derived criteria have been used to the basis of charge density. The derived criteria have been used to induce the presence or absence of weak to moderate H-bonds in induce the presence or absence of weak to moderate H-bonds in general.general.

1. A bond path and bcp between H and acceptor atom.2. The value of (r)bcp in the range 0.05 0.2 eÅ-3

3. The value of the Laplacian is positive and “reasonable” 0.5 3.3 eÅ-5

4. Mutual penetration of hydrogen and acceptor, r = r0 –rbcp is positive for both.

5. Loss of charge on H atom – basin charge in H-bonded complex minus “free” monomer.

6. Energetic destabilisation of H atom.7. Decrease of dipolar polarisation of H atom.8. Decrease in atomic basis volume.Criteria 5-8 difficult to apply in experimental studies, but first four criteria often used.


E. Espinosa et al (1999) Acta Cryst B55, 563.

Topology of Hydrogen bonds Espinosa Espinosa et alet al have examined the topological properties of a large have examined the topological properties of a large number of H-bonded compounds. number of H-bonded compounds.

Two clear cut cases emerged in terms of Two clear cut cases emerged in terms of ((rr))bcpbcp and and 22((rr))bcpbcpfor the D-H for the D-H and the H...A interactionsand the H...A interactions• strong H-bonds - strong H-bonds - ((rr))bcpbcp ~ 1-1.3 eÅ ~ 1-1.3 eÅ-3-3 22((rr))bcpbcp is negative ~ -5-15 eÅ is negative ~ -5-15 eÅ-5-5

• weak H-bonds - weak H-bonds - ((rr))bcpbcp ~ 0.5, 0.02 eÅ ~ 0.5, 0.02 eÅ-3-3 22((rr))bcpbcp is positive ~ 0.5 - 5 is positive ~ 0.5 - 5 eÅeÅ-5-5

Clear correlations between these topological and geometrical parameters Clear correlations between these topological and geometrical parameters were found, the clearest being with were found, the clearest being with 33(curvature along bond path)(curvature along bond path)

The Source Function

R. F. W. Bader & C. Gatti, (1998) Chem. Phys. Lett. 287, 233J. Overgaard et al (2001) Chem. Eur. J. 7 3756C. Gatti et al (2003) J. Comput. Chem. 24, 422

),(S r Source function from atom to (r)

Green’s Function or influence function. It represents the effectiveness of how the cause 2(r’) gives rise to the effect (r)

),(S)d,(LSd)ρ(

)41()(ρ2

rr'r'rr'r'r

r'r

LS(r,r’) = (-1/4 )(|r-r’|)-1 2(r’) Local source

Potentially available from experimental densityPotentially available from experimental densityDoes not require the presence of a bond critical pointDoes not require the presence of a bond critical point



C. Gatti et al (2003) J. Comput. Chem. 24, 422

Topology of Hydrogen bonds

Gatti has examined the nature of H-bonds, within the scheme of Gilli & Gatti has examined the nature of H-bonds, within the scheme of Gilli & GilliGilliusing the Source Function. Posed the question – how do the balance of using the Source Function. Posed the question – how do the balance of contributions to H-bonding (covalent contributions to H-bonding (covalent vsvs electrostatic) change with the electrostatic) change with the nature of the H-bond ?nature of the H-bond ?

Calculations on water dimer at varying D-H...A

distances• atomic percentage contributions

change dramatically along reaction profile

• at long D-H...A distances, source for H is very negative (i.e a sink)

• at long D-H...A distances all atoms make significant contributions – indicative of the importance of the delocalised electrostatic component

• at short D-H...A distances, the 3-centre nature of the H-bond is emphasised


C. Gatti et al (2003) J. Comput. Chem. 24, 422

Topology of Hydrogen bonds

Gatti has examined the nature of H-bonds, within the scheme of Gilli & Gatti has examined the nature of H-bonds, within the scheme of Gilli & GilliGilliusing the Source Function. Posed the question – how do the balance of using the Source Function. Posed the question – how do the balance of contributions to H-bonding (covalent contributions to H-bonding (covalent vsvs electrostatic) change with the electrostatic) change with the nature of the H-bond ?nature of the H-bond ?

1. H5O2+ +CAHB

2. formic acid-formate complex –CAHB3/4. malonaldehyde (Cs equi and C2v t.s.)

RAHB5. water trimer PAHB6. water dimer IHB

Clear that these different H-bonds have very

different source contributions


E. Espinosa et al (1998) Chem. Phys. Lett. 285, 1790.

Energetics of Hydrogen bonds Espinosa Espinosa et alet al have also shown strong correlations between approximate have also shown strong correlations between approximate GG((rrbcpbcp) and ) and VV((rrbcpbcp) (derived from Abramov functionals) and D(H...O). ) (derived from Abramov functionals) and D(H...O). HOWEVER, Spackman has shown that the promolecule density gives very HOWEVER, Spackman has shown that the promolecule density gives very similar results !similar results !

M. A. Spackman (1999) Chem. Phys. Lett. 301, 425


Energetics of Hydrogen bonds The question then arises – “are the experimental data providing anything The question then arises – “are the experimental data providing anything more than noise about a trendline determined by the promolecule more than noise about a trendline determined by the promolecule electron distribution” ?electron distribution” ?

M. A. Spackman (1999) Chem. Phys. Lett. 301, 425

Conclusion : “experimental electron Conclusion : “experimental electron densities in weak interactions are densities in weak interactions are indeed systematically different from indeed systematically different from those of a promolecule”those of a promolecule”


Atomic Energies in QTAIM There are two forms of the kinetic energy expression :There are two forms of the kinetic energy expression :

Y. A. Abramov, (1997) Acta Cryst. A53, 264.

GG((rr) = (3/10)(3) = (3/10)(322))2/32/3((rr))5/35/3 + (1/6) + (1/6)22((rr) ) Abramov approximation for Abramov approximation for GG((rr) at bcp (ONLY valid for regions where ) at bcp (ONLY valid for regions where 22 < 0, < 0, i.e.i.e. closed-shell interactions). closed-shell interactions).

VV((rr) = (1/4) ) = (1/4) 22((rr) – 2) – 2GG((rr) - Virial relationship) - Virial relationship

These two forms are identical if the Laplacian vanishes, as it does when integrating over an atomic basin. Then E() = -G() = 1/2 V()

Exact expressions for G(r) are NOT available directly from experimental data


Weak interactions to covalent bonds Mallinson Mallinson et al et al have reported several experimental charge density have reported several experimental charge density studies on proton sponges which exhibit a range of H-bonded interactions studies on proton sponges which exhibit a range of H-bonded interactions - from very strong N-H..N to very weak C - from very strong N-H..N to very weak C..C..C interactions. They studies interactions. They studies reveal a reveal a continuous transitioncontinuous transition from weak H-bonding to covalent bonding. from weak H-bonding to covalent bonding.

P. R. Mallinson et al (1003) J. Am. Chem. Soc. 125, 4259


Limitations on Determining Interaction Energies de Vries de Vries et alet al have studied the intermolecular interaction energies in have studied the intermolecular interaction energies in urea crystals, using the multipole model refined against theoretical data. urea crystals, using the multipole model refined against theoretical data. They conclude that “it is not possible to extract the effect of They conclude that “it is not possible to extract the effect of intermolecular interactions from diffraction data with the current intermolecular interactions from diffraction data with the current multipolar refinement techniques”multipolar refinement techniques”

R. Y. de Vries, D. Feil & V. G. Tsirelson (2000) Acta Cryst. B56, 118.

same data but with different random noise added (contours at 0.002 au)


J. Dunitz & A. Gavezzotti (2005) “Molecular Recognition in Organic Crystals – Directed Intermolecular Bonds or Nonlocalized Bonding ?” Angew. Chem. Int. Ed., 44, 1766.

Review chapters on AIM concepts and H-bonding in books :"Hydrogen Bonding - New Insights" Ed A. J. Grabowski (2006) Springer, Dordrecht."The Quantum Theory of Atoms in Molecules" Ed. C.E. Matta & R. Boyd (2007), Wiley-VCH, Weinheim.

A Note of Caution

“… “… for H…O interactions, critical point densities for H…O interactions, critical point densities bcpbcp and their distance dependence are closely and their distance dependence are closely similar to those calculated for the overlap of the similar to those calculated for the overlap of the unperturbed atomic charge densities (the unperturbed atomic charge densities (the promolecule electron density) so that promolecule electron density) so that great great care in the interpretation of experimental care in the interpretation of experimental and theoretical intermolecular charge and theoretical intermolecular charge densities is called fordensities is called for.”.”

Topological studies on metal-metal bondsJyväskylä Summer School on Charge Density August 2007

Metal-metal bonding is an important aspect of organometallic chemistry. Metal-metal bonding is an important aspect of organometallic chemistry.

Undergraduate treatment – Undergraduate treatment – 18 electron rule18 electron rule. Very useful in explaining . Very useful in explaining short(ish) metal-metal distances, but ignores the effects of bridging short(ish) metal-metal distances, but ignores the effects of bridging ligands.ligands.

Numerous theoretical studies based on orbital interpretations conclude Numerous theoretical studies based on orbital interpretations conclude therethereis only (at best) a weak direct M-M interaction in bridged bonds.is only (at best) a weak direct M-M interaction in bridged bonds.

J. Reinhold, A. Barthel, C. Mealli (2003) Coord. Chem. Rev. 238-239, 333.

Fe2(CO)9 Fe-Fe = 2.523 Å

Short M-M distance Diamagnetic Required by 18-e rule

But what does CD say ?

Metal-metal bonding without bridging ligands

Mn2(CO)10

100 K, Nonius KappaCCD100 K, Nonius KappaCCD

I2/aI2/a

Spherical atom refinementSpherical atom refinement

RR(F) =0.021 wR(F(F) =0.021 wR(F22)=0.061)=0.061

GOF 1.11 GOF 1.11 0.62 0.62 -0.81 -0.81

7052 data 101 parameters7052 data 101 parameters

XD refinementXD refinement

RR(F) =0.014 wR(F(F) =0.014 wR(F22)=0.016)=0.016

GOF 2.16 GOF 2.16 0.27 0.27 -0.20 -0.20


Mn-Mn bondMn-Mn bond

Mn1-Mn1a 2.9031(2) ÅMn1-Mn1a 2.9031(2) Å

2.9042(8)2.9042(8)

((rrbcpbcp) 0.144(3)e Å) 0.144(3)e Å-3-3

0.190(4)0.190(4) 0.1920.192

22((rrbcpbcp) 0.720(3) e Å) 0.720(3) e Å-5-5

0.815(8)0.815(8) 0.1240.124

L. J. Farrugia, P. R. Mallinson, B. Stewart (2003) Acta Cryst. B59, 234R. Bianchi, G. Gervasio, D. Marabello (2000) Inorg. Chem. 39, 2360.Co2(CO)6(AsPh3)2 P. Macchi, D. E. Proserpio, A. Sironi (1998) J. Am. Chem. Soc. 120, 13429.


Mn2(CO)10


I2/aI2/a


RR(F) =0.021 wR(F(F) =0.021 wR(F22)=0.061)=0.061

GOF 1.11 GOF 1.11 0.62 0.62 -0.81 -0.81



RR(F) =0.014 wR(F(F) =0.014 wR(F22)=0.016)=0.016

GOF 2.16 GOF 2.16 0.27 0.27 -0.20 -0.20


Mn-Mn bondMn-Mn bond

Mn1-Mn1a 2.9031(2) ÅMn1-Mn1a 2.9031(2) Å

2.9042(8)2.9042(8)

((rrbcpbcp) 0.144(3)e Å) 0.144(3)e Å-3-3

0.190(4)0.190(4) 0.1920.192

22((rrbcpbcp) 0.720(3) e Å) 0.720(3) e Å-5-5

0.815(8)0.815(8) 0.1240.124

(Mn-Mn) 0.29(Mn-Mn) 0.29L. J. Farrugia, P. R. Mallinson, B. Stewart (2003) Acta Cryst. B59, 234R. Bianchi, G. Gervasio, D. Marabello (2000) Inorg. Chem. 39, 2360.Co2(CO)6(AsPh3)2 P. Macchi, D. E. Proserpio, A. Sironi (1998) J. Am. Chem. Soc. 120, 13429.


Metal-metal bonding without bridging ligands

Source function for Mn2(CO)10

C. Gatti, D. Lasi (2007) Faraday Discuss., 135, 55.

Contributions to the source function at Contributions to the source function at thetheMn-Mn bcp from (a) Mn atoms (b) COMn-Mn bcp from (a) Mn atoms (b) COeqeq and and (c) CO(c) COaxax Blue curve = real system, red Blue curve = real system, red curvecurveto two non-interacting Mn(CO)to two non-interacting Mn(CO)55 groups groups


Metal-metal bonding with carbonyl bridgesMetal-metal bonding with carbonyl bridges

P. Macchi, L. Garlaschelli, A. Sironi (2002) J. Am. Chem. Soc. 124, 14173.

P. Macchi, A. Sironi (2003), Coord Chem. Rev. 238-239, 383

Evolution of metal-metal bonding in [FeCo(CO)8]- anion

Conclusion – metal-metal bonding disappears early on in the profile, with initial formation of ring structure

Symmetrized correlation plotSymmetrized correlation plot of M(of M(-CO)M from CCD and -CO)M from CCD and experimental charge densities experimental charge densities in Coin Co44(CO(CO1111)(PPh)(PPh33) and ) and CoCo22(CO)(CO)66(AsPh(AsPh33))33


Source function for Co2(CO)8

C. Gatti, D. Lasi (2007) Faraday Discuss., 135, 55.

Source function shows that Source function shows that the basic picture is similar the basic picture is similar for the two isomers, the all-for the two isomers, the all-terminal terminal DD3d3d which has a which has a bcp, and the bcp, and the CC2v2v isomer isomer which does not.which does not.

In the unbridged case, the In the unbridged case, the Co atoms act as a sink at Co atoms act as a sink at the bcp.the bcp.

In the bridged case, they In the bridged case, they act (very marginally) as a act (very marginally) as a source.source.

Due to differing behaviour Due to differing behaviour of the Laplacian near the of the Laplacian near the reference point (an order of reference point (an order of magnitude more positive in magnitude more positive in the the CC2v2v isomer). isomer).


The “bent” Co-Co bond in CoThe “bent” Co-Co bond in Co22(CO)(CO)88

J.Reinhold & M. Finger (2003), Inorg. Chem. 42, 8128

J.Reinhold et al (2005), Inorg. Chem. 44, 6494


Reinhold Reinhold et alet al interpret the minimum in the total energy density interpret the minimum in the total energy density HH as indicative of a “bent” Co-Co bond.as indicative of a “bent” Co-Co bond.

The presence of such an interaction is also indicated from an The presence of such an interaction is also indicated from an orbital study.orbital study.

Co2(CO)8

Metal-metal bonding with hydride bridges Metal-metal bonding with hydride bridges

P. Macchi, D. Donghi, A. Sironi (2005) J. Am. Chem. Soc. 127, 16494.

“we note that the M-H-M systems have undisputedly many subtler features associated with even smaller energy gradients that therefore hamper an easier rationalization of the bonding effects”

Experimental study on [CrExperimental study on [Cr22((-H)-H)(CO)(CO)1010]]--


Metal-metal bonding with alkylidyne bridges Metal-metal bonding with alkylidyne bridges

L. J. Farrugia, C. Evans (2005) Comptes Rendu Chimie. 8, 1566.

Co3(3-CX)(CO)9 (X=H,Cl)

GeometryGeometryDist Dist ÅÅCo1-Co2 Co1-Co2 2.4772.477Co1-Co3 Co1-Co3 2.4872.487Co2-Co3 Co2-Co3 2.4732.473Co1-C1 Co1-C1 1.8921.892Co2-C1 Co2-C1 1.8951.895Co3-C1 Co3-C1 1.8951.895C1-H1 C1-H1 1.0841.084


Metal-metal bonding with alkylidyne bridgesMetal-metal bonding with alkylidyne bridges

L. J. Farrugia, C. Evans (2005) Comptes Rendu Chimie. 8, 1566.

Co3(3-CX)(CO)9 (X=H,Cl)

GeometryGeometryDist Dist ÅÅCo1-Co2 Co1-Co2 2.4772.477Co1-Co3 Co1-Co3 2.4872.487Co2-Co3 Co2-Co3 2.4732.473Co1-C1 Co1-C1 1.8921.892Co2-C1 Co2-C1 1.8951.895Co3-C1 Co3-C1 1.8951.895C1-H1 C1-H1 1.0841.084

Delocalization indices (A,B)


Metal-metal bonding with alkylidyne bridges Metal-metal bonding with alkylidyne bridges

a b

a b

Atomic graph of Atomic graph of alkylidyne carbon. Critical alkylidyne carbon. Critical points inpoints inLaplacianLaplacian L L - -22 (3,-3) charge (3,-3) charge concentrationsconcentrations(3,-1) saddle points(3,-1) saddle points(3,+1) charge depletions(3,+1) charge depletions

Co3(3-CX)(CO)9 (a=H, b=Cl)

Isosurface of the Isosurface of the LaplacianLaplacian L L - -22 at +10 at +10 eÅeÅ-5-5


Structural variability in M3(-H)(-CX)(CO)10

AAX=COMe, M=RuX=COMe, M=Ru

= 94.9= 94.9oo

Ru….C = 2.921ÅRu….C = 2.921Å

BBX=Ph, M=OsX=Ph, M=Os

= 78.2= 78.2oo

Os….C = 2.585ÅOs….C = 2.585Å

CCX=H, M=OsX=H, M=Os= 69.7= 69.7oo

Os….C = 2.353ÅOs….C = 2.353Å

DDX=Ph, M=OsX=Ph, M=Os

= 66.6= 66.6oo

Os….C = 2.286ÅOs….C = 2.286Å

A - M. R. Churchill et al (1983) Organometallics . 2, 1179.

B, C, D – Shapley et al (1983) J. Am. Chem. Soc. 105, 140 ; Organometallics (1985) 4, 767,1898


Charge density in Fe3(-H)(-COMe)(CO)10

Experimental data Experimental data


P2P211/c/c


RR(F) =0.026 (F) =0.026 wR(FwR(F22)=0.059)=0.059

GOF 1.04 GOF 1.04 0.72 0.72 -0.90 -0.90

17177 data 243 17177 data 243 parametersparameters


RR(F) =0.018 (F) =0.018 wR(FwR(F22)=0.016)=0.016

GOF 1.53 GOF 1.53 0.30 0.30 -0.30 -0.30

13970 data 701 13970 data 701 parametersparameters

ÅÅ

Fe1-Fe2 2.64603(16)Fe1-Fe2 2.64603(16)

Fe1-Fe3 2.67669(17)Fe1-Fe3 2.67669(17)

Fe2-Fe3 2.60037(15)Fe2-Fe3 2.60037(15)

Fe1...C1 Fe1...C1 2.6762(4)2.6762(4)

Fe2/Fe3-C1 1.86Fe2/Fe3-C1 1.86

= 90.1(1) = 90.1(1) oo


Main features :Main features :1.1. Ring cp for Fe(Ring cp for Fe(-H)(-H)(--

CR)FeCR)Fe2.2. Bond cp’s for other two Bond cp’s for other two

Fe-Fe interactionsFe-Fe interactions3.3. Ring cp between Fe…Ring cp between Fe…

C(alk)C(alk)


(r) (eÅ(r) (eÅ-3-3) ) 22 (eÅ (eÅ-5-5) ) Fe-Fe (bcp) 0.24 0.30 Fe-Fe (bcp) 0.24 0.30 0.400.40Fe-Fe (rcp) 0.35 2.09 -Fe-Fe (rcp) 0.35 2.09 -Fe...C (rcp) 0.22 1.31 -Fe...C (rcp) 0.22 1.31 -

optimised B3LYP 6-311G (C/H/O) Wachters+f Fe optimised B3LYP 6-311G (C/H/O) Wachters+f Fe

Geometry ÅGeometry Å

Fe1-Fe2 2.739Fe1-Fe2 2.739

Fe1-Fe3 2.744Fe1-Fe3 2.744

Fe2-Fe3 2.646Fe2-Fe3 2.646

Fe1...C1 Fe1...C1 2.6852.685

Fe2/Fe3-C1 1.86Fe2/Fe3-C1 1.86

= 87.5 = 87.5 oo


Main features :Main features :1.1. Ring cp for Fe(Ring cp for Fe(-H)(-H)(--

CR)FeCR)Fe2.2. Bond cp’s for other two Bond cp’s for other two

Fe-Fe interactionsFe-Fe interactions3.3. Bond cp between Fe-Bond cp between Fe-

C(alk)C(alk)


(r) (eÅ(r) (eÅ-3-3) ) 22 (eÅ (eÅ-5-5) ) Fe-Fe (bcp) 0.23 0.46 Fe-Fe (bcp) 0.23 0.46 0.850.85Fe-Fe (rcp) 0.34 2.28 -Fe-Fe (rcp) 0.34 2.28 -Fe-C (bcp) 0.23 1.48 Fe-C (bcp) 0.23 1.48 0.680.68

Geometry ÅGeometry Å

Fe1-Fe2 2.741Fe1-Fe2 2.741

Fe1-Fe3 2.752Fe1-Fe3 2.752

Fe2-Fe3 2.650Fe2-Fe3 2.650

Fe1...C1 Fe1...C1 2.6532.653

Fe2/Fe3-C1 1.86Fe2/Fe3-C1 1.86

= 85.9 = 85.9 oo

optimised B3LYP Ahlrichs TZV optimised B3LYP Ahlrichs TZV


Main features :Main features :1.1. Ring cp for Fe(Ring cp for Fe(-H)(-H)(-CR)Fe-CR)Fe2.2. NO bond cp’s for other two NO bond cp’s for other two

Fe-Fe interactionsFe-Fe interactions3.3. Bond cp between Fe…CBond cp between Fe…C


(r) (eÅ(r) (eÅ-3-3) ) 22 (eÅ (eÅ-5-5) ) Fe-Fe (rcp) 0.24 1.44 -Fe-Fe (rcp) 0.24 1.44 -Fe..C (bcp) 0.24 1.40 Fe..C (bcp) 0.24 1.40 2.372.37

Experimental multipole densityExperimental multipole density


Multipole refinements with synthetic data

Gas phase wavefunction B3LYP/6-Gas phase wavefunction B3LYP/6-331G331G

s.f. from 30 Å pseudo cubic unit cell s.f. from 30 Å pseudo cubic unit cell

refine elaborate XD multipole model refine elaborate XD multipole model refine XD multipole model refine XD multipole model

project DFT density into s.f. project DFT density into s.f.

CRYSTAL03 periodic DFT CRYSTAL03 periodic DFT wavefunctionwavefunction

Fe...C(alkylidyne) bcp Fe...C(alkylidyne) bcp

highly curved Fe-Fe bcp


Isosurfaces of density Isosurfaces of density in Fe in Fe33((-H)(-H)(-COMe)(CO)-COMe)(CO)1010 viewed normal to the Feviewed normal to the Fe33 plane plane

0.25 e Å-3 0.15 e Å-3



Fe3(-H)(-COMe)(CO)10

Delocalisation Delocalisation indicesindices

Dist Dist (A-(A-B)B)Fe1-Fe2Fe1-Fe2

0.400.40Fe1-Fe3 Fe1-Fe3 0.380.38Fe2-Fe3 Fe2-Fe3 0.210.21Fe1-C15 Fe1-C15 0.190.19Fe2-C15 Fe2-C15 0.910.91Fe3-C15 Fe3-C15 0.930.93Fe2-H27 Fe2-H27 0.450.45Fe3-H27 Fe3-H27 0.440.44

Fe-C(O) Fe-C(O) ~1.0~1.0Fe2-C18 Fe2-C18 0.130.13Fe-O Fe-O ~0.17~0.17Optimised structure B3LYP – 6-311G* (C/H/O) Wachters+f Fe

C18


Source % contributions at Fe-Fe bcp (theoretical) and Fe-Fe midpoint (expt)Source % contributions at Fe-Fe bcp (theoretical) and Fe-Fe midpoint (expt)

Source Function in Fe3(-H)(-COMe)(CO)10


Source % contributions at Fe…CSource % contributions at Fe…Calkylidynealkylidyne rcp (theoretical) and bcp (expt) rcp (theoretical) and bcp (expt)

Source Function in Fe3(-H)(-COMe)(CO)10


Structural variability in M3(-H)(-CX)(CO)10

AAX=COMe, M=RuX=COMe, M=Ru

= 94.9= 94.9oo

Ru….C = 2.921ÅRu….C = 2.921Å

BBX=Ph, M=OsX=Ph, M=Os

= 78.2= 78.2oo

Os….C = 2.585ÅOs….C = 2.585Å

CCX=H, M=OsX=H, M=Os= 69.7= 69.7oo

Os….C = 2.353ÅOs….C = 2.353Å

DDX=Ph, M=OsX=Ph, M=Os

= 66.6= 66.6oo

Os….C = 2.286ÅOs….C = 2.286Å

A - M. R. Churchill et al (1983) Organometallics . 2, 1179.

B, C, D – Shapley et al (1983) J. Am. Chem. Soc. 105, 140 ; Organometallics (1985) 4, 767,1898


Fe3(-H)(-CH)(CO)10

Optimised structure B3LYP – 6-311G* (C/H/O) Wachters+f Fe

J. W. Kolis, E. M. Holt, D. W Shriver (1983) J. Am. Chem. Soc. 105, 7307. (spectroscopic data)

GeometryGeometryDist Dist ÅÅFe1-Fe2 Fe1-Fe2 2.6742.674Fe1-Fe3 Fe1-Fe3 2.6742.674Fe2-Fe3 Fe2-Fe3 2.6692.669Fe1-C1 Fe1-C1 2.1462.146Fe2-C1 Fe2-C1 1.8771.877Fe3-C1 Fe3-C1 1.8771.877Fe2-H2 Fe2-H2 1.6861.686Fe3-H2 Fe3-H2 1.6861.686C1-H1 C1-H1 1.0901.090

Fe1-C2-O2 Fe1-C2-O2 166.5166.5oo

Fe1-Fe2-Fe3-C1 Fe1-Fe2-Fe3-C1 65.865.8oo


Fe3(-H)(-CH)(CO)10

GeometryGeometryDist Dist ÅÅFe1-Fe2 Fe1-Fe2 2.6742.674Fe1-Fe3 Fe1-Fe3 2.6742.674Fe2-Fe3 Fe2-Fe3 2.6692.669Fe1-C1 Fe1-C1 2.1462.146Fe2-C1 Fe2-C1 1.8771.877Fe3-C1 Fe3-C1 1.8771.877Fe2-H2 Fe2-H2 1.6861.686Fe3-H2 Fe3-H2 1.6861.686C1-H1 C1-H1 1.0901.090

Fe1-C2-O2 Fe1-C2-O2 166.5166.5oo

Fe1-Fe2-Fe3-C1 Fe1-Fe2-Fe3-C1 65.865.8oo

Optimised structure B3LYP – 6-311G* (C/H/O) Wachters+f Fe

Molecular graph and critical points (bps’s in red, ring cp in yellow)


Chemical Applications of Charge Density Louis J Farrugia Jyväskylä Summer School on Charge Density August 2007.

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