covalency and bond strength in heavy element compounds from the quantum theory of atoms in molecules...

Covalency and bond strength in heavy element compounds

from the quantum theory of atoms in molecules

Nik KaltsoyannisDepartment of Chemistry, University College London

Plan of campaign

• Why is covalency in the actinides important?

• Unexpected covalency in actinide dioxides

• Actinide-cyclopentadienyl complexes; an introduction to the QTAIM

• Applications of the QTAIM to covalency in other actinide-element bonds

An(Se2PMe2)4 [U(OPh)3]2(µ-η2:η2-N2)

• Do QTAIM metrics correlate with the strength of heavy element bonds?

Metal-metal bonding in M2X6 (M = Mo, W, U; X = Cl, F, OH, NH2, CH3)

M(CO)5-imidazole isomers (M = Cr, Mo, W)

Uranyl phosphine oxide and phosphinimine compounds

[AnX3]2(µ-η2:η2-N2) (An = Th-Pu; X = F, Cl, Br, OPh, H, Me)

AnOn+ and AnO2n+ (An = Th-Cm; n = 1, 2)

AnL3+ and AnL33+ (An = Th-Cm; L = Py, Pz, Tz)

M(BTP)3+ (M = La, Ce, Eu, Th, Pa, U, Np, Pu, Am, Cm)

• Conclusions

Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr

“minor actinides”

N

N

N

N

N

N

N

R

RR

R

Typical R = CH3, C2H5, n-C3H7, i-C3H7, n-C4H9, i-C4H9, CyMe4 (one per triazin-3-yl ring)

N

N

N

N

N

N

N

N

R

R

R

R

BTBP

N

N

N

N

N

N

N

N

N

R

R

R

R

BTTP

“the level of understanding of BTPs’ selectivity on a molecular level is insufficient to target the design of new, more efficient and selective partitioning reagents or fine tune partitioning process conditions. Such advances are presently empirical, on a trial and error basis”. Girnt et al. Inorg. Chem. 49 (2010) 9627

BTP

“It is evident that the formal expectations are encountered for the lighter actinides. The situation changes at AmO2 and especially at CmO2….Cm borrows O spin density in order to approach the stability of the half-filled f7 subshell, and this leads to a calculated net spin of the metal in CmO2 between those corresponding to the formal Cm3+ f7 and Cm4+ f6 configurations…. These spin densities (and the covalency they imply)….”

I. D. Prodan, G. E. Scuseria and R. L. Martin Phys. Rev. B 76 (2007) 033101

Th Pa U Np Pu Am Cm

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Act

inid

e s

pin

de

nsi

ty

Covalency in AnO2?

Valence molecular orbital energy level diagrams for AnCp4 (Cp = h5-C5H5)

5f0 5f1 5f2 5f3 5f4 5f5 5f7 cf CmO2

M. J. Tassell and N. Kaltsoyannis Dalton Trans. 39 (2010) 6719

Th Pa U Np Pu Am Cm0

5

10

15

20

25

30

35

6d in e6d in t25f in t1

Mu

llike

n p

op

ula

tion

(%

)

Metal contributions to the Cp-based e, t2 and t1 molecular orbitals in AnCp4


Metal spin densities for AnCp3.Values shown are the differences from the formal value for An(III)

Behaviour of formally trivalent Am in AmCp3 very similar to that of formally tetravalent Cm in CmO2. Both formally 5f6 ions borrow spin density to approach the

stability of the half-filled shell.

I. Kirker and N. Kaltsoyannis Dalton Trans. 40 (2011) 124

What is the Quantum Theory of Atoms-in-Molecules?

• Topology of the electron density .

• Critical point (CP): a point in space where vanishes.

• Different types of CP: characterise by analysing 2 (curvature of ) at CP.

• 2 is a 3x3 matrix, diagonalise to give three values of curvature.

• Bond critical point (BCP): one positive and two negative curvatures, is a maximum in two directions and a minimum in the third.

• Bond path (BP): line of locally maximum between any two chemically bonded atoms.

• BCP is the point on the BP with lowest .

Richard Bader

z-z

-y

y

-x

x

-x x -y y -z z

A simple example: H2 BCP at midpoint of H-H axis

BCP BCP BCP

Rules of Thumb

Properties at the BCP can be used to characterise the nature of the bond.

Focus on (though there are many other QTAIM metrics….see later)

at BCP (rb) > 0.2 electron/bohr3 shared shell interactions (covalent bonding)

at BCP (rb) < 0.1 electron/bohr3 closed shell interactions (e.g. ionic, van der Waals, hydrogen bonding)

Th Pa U Np Pu Am Cm0

0.05

0.1

0.15

0.2

0.25

0.3

C-C AnCp4An-C AnCp4An-C AnCp3

Ele

ctro

n d

en

sity

at b

on

d c

ritic

al p

oin

t

C-C ethene 0.337

C-C ethane 0.239

Electron density at the bond critical points of the C-C and An-C bonds in AnCp4 and AnCp3

Electron density in the An–C bonding region is small, increasingly so in the compounds of the minor actinides


Electron density along an An-C bond in AnCp3

I. Kirker and N. Kaltsoyannis Dalton Trans. 40 (2011) 124

Three dimensional representations of one component of the “t1” molecular orbitals

UCp4 AmCp4


N. Kaltsoyannis Inorg. Chem. 52 (2013) 3407

An(Se2PMe2)4 (An = Th, Pa, U, Np, Pu)

M. B. Jones, A. J. Gaunt, J. C. Gordon, N. Kaltsoyannis, M. P. Neu and B. L. Scott Chem. Sci. 4 (2013) 1189

Th Pa U Np Pu

eV

-5.5

-6.0

-6.5

-7.0

-7.5

-8.0

-8.5

-5.0

Pa U Np Pu-0.1

0

0.1

0.2

0.3

0.4

0.5

De

via

tion

fro

m fo

rma

l sp

in

de

nsi

ty

Th Pa U Np Pu0.04

0.042

0.044

0.046

0.048

0.05

Ele

ctro

n d

en

sity

at M

-Se

bo

nd

cr

itica

l po

int

M. B. Jones, A. J. Gaunt, J. C. Gordon, N. Kaltsoyannis, M. P. Neu and B. L. Scott Chem. Sci. 4 (2013) 1189

[An(Se2PMe2)4] (An = Th, Pa, U, Np, Pu)

S. M. Mansell, N. Kaltsoyannis and P. L. Arnold J. Am. Chem. Soc. 133 (2011) 9036

Expt Calc Calc (free N2)

r(U-N)/Å 2.407 2.398

r(N-N)/Å 1.190,1.236 1.255 1.104

(N-N)/cm-1 1451 1486 2454

at N-N bond critical point/e bohr-3 0.461 0.661

at U-N bond critical point/e bohr-3 0.073

[U(OPh)3]2(µ-η2:η2-N2)

M = Mo, W, UX = Cl, F, OH, NH2, CH3

M

X

• Formally the metals are in the +3 oxidation state• d3d3 configurations for Mo and W, and f3f3 for U• Metal-metal triple bonds• Ziegler-Rauk energy decomposition scheme

G. Cavigliasso and N. Kaltsoyannis Inorg. Chem. 45 (2006) 6828

Do QTAIM metrics correlate with the strength of heavy element bonds?

The Ziegler-Rauk Energy Decomposition Scheme

Total Bonding Energy (EB) = Electrostatic (EE) + Pauli (EP) + Orbital (EO)

energy difference between

the molecular fragments at

their positions within the

molecule and at infinite

separation

nucleus/nucleus, nucleus/electron,

electron/electron Coulombic

interactions

relaxation of the fragment

orbitals to self-consistency,

i.e. interaction between the

orbitals of the fragments

Based on the idea that molecules may be broken down into fragments, which may be single atoms or groups of atoms

energy change associated with

ensuring compliance with the Pauli

principle

Choice of fragments: [X3M] (↑↑↑) + (↓↓↓) [MX3] ↔ M2X6

a11e2 configuration (C3v)

Principal conclusions from Ziegler-Rauk study of M2X6

• Total bonding energy EB significantly smaller in the uranium dimers

• Orbital interaction energy EO significantly larger for the uranium dimers

• Reduced contributions of the electrostatic interactions EE were determined to be the principal reason for the relative weakness of the U–U bonds

G. Cavigliasso and N. Kaltsoyannis Inorg. Chem. 45 (2006) 6828

0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2

-5

-4

-3

-2

-1

0

b (e/bohr3)

EB

(e

V)

Metal–metal b against EB for M2X6 (M = Mo, W, U; X = Cl, F, OH, NH2, CH3).

Mo diamonds: W squares: U circles. Cl blue: F red: OH green: NH2 purple: CH3 black.

The most covalent bonds are the

weakest….

A. R. E. Mountain and N. Kaltsoyannis Dalton Trans. 42 (2013) 13477

R2 = 0.860

0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2

-12

-11

-10

-9

-8

-7

-6

b (e/bohr3)E

O (

eV

)

Metal–metal b against EO for M2X6 (M = Mo, W, U; X = Cl, F, OH, NH2, CH3).

Mo diamonds: W squares: U circles. Cl blue: F red: OH green: NH2 purple: CH3 black.


R2 = 0.859

N

N

M(CO)5

N

N

M(CO)5

N

N M(CO)5

IMIDnNHC aNHC

O

U

O

O=PCy3Cy3P=O

Cl

Cl

O

U

O

O=PCy3Cy3P=N

Cl

Cl

H

O

U

O

N=PCy3Cy3P=N

Cl

Cl

H

H

Systems in which EO determines EB (i.e. where EE and EP cancel)

R. Tonner, G. Heydenrych and G. Frenking Chem. As. J. 2 (2007) 1555

J. Haller, N. Kaltsoyannis, M. J. Sarsfield, I. May, S. Cornet, M. Redmond and M. Helliwell Inorg. Chem. 46 (2007) 4868

0.05 0.07 0.09

-3

-2

-1

b (e/bohr3)

EB

(e

V)

Metal–ligand b against EB for the nine Frenking systems, and uranyl phosphine oxide and phosphinimine compounds.

Cr triangles: Mo diamonds: W squares: U circles. nNHC red: aNHC blue: IMID black: U–N green: U–O purple.

Strong, positive correlation between b and bond energy (when the latter is dominated by the orbital interaction)

R2 = 0.953


[An(OPh)3]2(µ-η2:η2-N2) (An = Th-Pu)

Q.-R. Huang, J. R. Kingham and N. Kaltsoyannis Dalton Trans. 43 (2014) DOI: 10.1039/C4DT02323D

Th Pa U Np Pu1000

1100

1200

1300

1400

1500

1600

1700

- (

-1)

sNN

cm

Th Pa U Np Pu1.2

1.24

1.28

1.32

1.36

rN-N

(Å

)

[Pa(OPh)3]2(µ-η2:η2-N2) a HOMO-8 [Pa(OPh)3]2(µ-η2:η2-N2) a HOMO-1

Th Pa U Np Pu

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4Q

TA

IM c

ha

rge

on

ni-

tro

ge

n


Some more QTAIM metrics

At the bond critical point:

2 - sum of the three curvatures. Generally significantly less than zero for covalent bonds, reflecting the concentration of electron density along the bond path linking the bonded atoms.

H - energy density. Negative for interactions with significant sharing of electrons, its magnitude reflecting the covalence of the interaction.

Between two atoms:

d(A,B) - delocalisation index. Magnitude of the exchange of the electrons in the basin of atom A with those in the basin of atom B, i.e. the number of electrons shared between two atoms. QTAIM measure of bond order.

N2 Th Pa U Np Pu

0.661 0.455 0.352 0.459 0.479 0.500

2 -

2.021

-

0.937

-

0.543

-

0.945

-

1.033

-

1.129

H -

1.057

-

0.542

-

0.364

-

0.550

-

0.589

-

0.632

d(N,N) 3 2.166 1.661 2.085 2.149 2.223

QTAIM metrics for the N-N bond in N2 and [An(OPh)3]2(µ-η2:η2-N2) (An = Th-Pu)


Correlation of the QTAIM metrics with N-N distance

1.2 1.221.241.261.28 1.3 1.321.341.361.380.3

0.35

0.4

0.45

0.5

0.55

R² = 0.997289803074666

N-N distance (Å)

N-N

BC

P

1.2 1.221.241.261.28 1.3 1.321.341.361.38

-1.2

-1.1

-1

-0.9

-0.8

-0.7

-0.6

-0.5R² = 0.991915559375827

N-N distance (Å)

N-N

BC

P

2

1.2 1.22

1.24

1.26

1.28

1.3 1.32

1.34

1.36

1.38

-0.65

-0.6

-0.55

-0.5

-0.45

-0.4

-0.35R² = 0.991870466533654

N-N distance (Å)

N-N

BC

P H

1.2 1.221.241.261.28 1.3 1.321.341.361.381.6

1.7

1.8

1.9

2

2.1

2.2

2.3

R² = 0.96748173317481

N-N distance (Å)

(N

,N)

Correlation of the QTAIM metrics with N-N stretching wavenumber

1000 1100 1200 1300 1400 1500 1600 17000.3

0.35

0.4

0.45

0.5

0.55

R² = 0.990454163077279

N-N stretching vibration (cm-1)

N-N

BC

P

1000 1100 1200 1300 1400 1500 1600 1700

-1.2

-1.1

-1

-0.9

-0.8

-0.7

-0.6

-0.5R² = 0.98572195298559


N-N

BC

P

2

1000 1100 1200 1300 1400 1500 1600 1700

-0.65

-0.6

-0.55

-0.5

-0.45

-0.4

-0.35R² = 0.983648388460062


N-N

BC

P H

1000 1100 1200 1300 1400 1500 1600 17001.6

1.7

1.8

1.9

2

2.1

2.2

2.3

R² = 0.985899181283431


(N

,N)

Correlation of the QTAIM metrics with An-N distance

2.25 2.3 2.35 2.4 2.45 2.50.05

0.06

0.07

0.08

0.09

0.1

R² = 0.939688126158986

An-N distance (Å)

An

-N B

CP

2.25 2.3 2.35 2.4 2.45 2.5

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

6.93889390390723E-18

0.005

R² = 0.873912114590953

An-N distance (Å)

An

-N B

CP

H

2.25 2.3 2.35 2.4 2.45 2.50.16

0.18

0.2

0.22

0.24

0.26R² = 0.896328392286785

An-N distance (Å)

An

-N B

CP

2

2.25 2.3 2.35 2.4 2.45 2.50.4

0.45

0.5

0.55

0.6

0.65

0.7

R² = 0.983071372946954

An-N distance (Å)

(A

n,N

)

An-N interaction energies (kJ/mol) in [AnX3]2(µ-η2:η2-N2) (An = Th-Pu; X = F, Cl, Br, OPh, H, Me)

Th Pa U Np Pu

F -110.9 -139.0 -61.8 -39.6 -5.4

Cl -117.2 -134.9 -37.7 -21.5 9.0

Br -118.6 -135.2 -36.6 -19.0 9.8

OPh -110.7 -147.7 -77.0 -21.9

H -120.7 -155.7 -75.7 -12.9 -16.7

Me -114.0 -150.4 -77.5 -71.9 -33.0

R2 for correlation of An-N QTAIM metrics with An-N interaction energies:

ρ 2ρ H δ(An,N)

0.297 0.001 0.369 0.204

3 2 2 3 2An-N [AnX ] N AnX N

1( (2 ))4

E E E E


Define a new QTAIM metric

QTAIMAnQ

X = F X = Cl X = Br X = H X = Me X = OPh All X

0.994 0.969 0.960 0.942 0.832 0.996 0.882

R2 for correlation of QTAIMAnQ with An-N interaction energies:


General applicability?

R2 for correlation of QTAIMAnQ with other An-N interaction energies and An-O bond energies (An = Th-Cm):

AnO+ AnO2+ AnO2+ AnO2

2+ AnPy3+ AnPz3+ AnTz3+ AnPy33+ AnPz3

3+ AnTz33+

0.986 0.964 0.931 0.901 0.934 0.856 0.858 0.579 0.922 0.958

N N

NN

N

N

Pyridine (Py) Pyrazine (Pz) Triazine (Tz)


[M-BTP]3+ (M = La, Ce, Eu, Th, Pa, U, Np, Pu, Am, Cm)

N

N

N

N

N

N

N

-1800 -1700 -1600 -1500 -14000.6

0.7

0.8

0.9

1

1.1

1.2

R² = 0.954286219189169

M-BTP interaction energy (kJ/mol)

D׀Q

MQ

TA

IM׀

Conclusions - covalency

Calculations on AnCp4 and AnCp3 (An = Th-Cm) indicate that the metal–carbon bond becomes both more covalent (on the basis of orbital mixing and spin densities) and more ionic (as evidenced by QTAIM data) as the actinide series is crossed.

The metal-selenium bond in [An(Se2PMe2)4] (An = Th-Pu) behaves similarly.

We must be very clear as to what we mean when discussing covalency in the 5f series, especially when using this concept as a basis for interpreting experimental data such as the enhanced minor actinide separation factors achieved by BTP and related ligands.

Conclusions – bond strength

Excellent correlation of standard QTAIM metrics with N-N bond length and stretching frequency, and with An-N bond length.

Strong, positive correlation between b and bond energy (when the latter is dominated by the orbital interaction).

More generally, poor correlation of standard QTAIM metrics with bond/interaction energies.

Define a new QTAIM metric: QTAIMAnQ

Strong correlation of QTAIMAnQ with An-N interaction and An-O bond

energies.

The without whom department

National Service for Computational Chemistry Software

National Nuclear Laboratory

Nuclear Decommissioning Authority

UCL Research Computing Services

ElsewhereAndy GauntPolly Arnold

UCLMatthew TassellIan KirkerAbi MountainQian-Rui HuangJenny Kingham

covalency and bond strength in heavy element compounds from the quantum theory of atoms in molecules...

Documents

metal spin densities

bond critical point

metalmetal bonding

unexpected covalency

critical point cp

molecular level

metal contributions

h2 bcp