Supporting Online Material for - sciencemag.org filePublished 22 September 2005 on Science Express...

www.sciencemag.org/cgi/content/full/1116789/DC1

Supporting Online Material for

Synthesis of a Stable Compound with Fivefold Bonding Between Two Chromium(I) Centers

Tailuan Nguyen, Andrew D. Sutton, Marcin Brynda, James C. Fettinger, Gary J. Long, Philip P. Power*

*To whom correspondence should be addressed. E-mail: [email protected]

Published 22 September 2005 on Science Express

DOI: 10.1126/science.1116789

This PDF file includes:

Materials and Methods

Figs. S1 to S3

Tables S1 to S16

References and Notes

Supporting Information S1

Synthesis of a Stable Compound with Quintuple Bonding between Chromiums Tailuan Nguyen, Andrew D. Sutton, Marcin Brynda, James C. Fettinger, Gary J. Long and Philip P. Power*

Department of Chemistry, University of California, Davis, One Shields Avenue, Davis, California 95616

Supporting Information

General Information: The quantum mechanical calculations were performed using DFT on the X-ray

diffraction structure of Ar'CrCrAr' as well as on different model molecules described below. The electronic

structures of the Ar'CrCrAr' molecule as well as of simpler model molecule (MeCrCrMe) were calculated

at a restricted level using basis sets of different sizes. The details of the calculations are described in the

following sections. All the DFT calculations were carried out using the Gaussian 03 package [Ref. RS1],

and the molecular orbitals were generated with the Molekel program [Ref. RS2]. The overlap populations

were generated from the Gaussian outputs with AOMIX program [Ref. RS3]. Additional CASSCF

calculations on a MeCrCrMe model molecule were performed with Gaussian 03. Bond orders were

calculated either with AOMIX or with the AIM program [Ref. RS4] implemented in Gaussian 03.

CS1 Electronic structure of ArCrCrAr

CS1.1 Analysis of the Kohn-Sham orbitals from the restricted DFT calculations

The electronic structure of the Ar'CrCrAr' molecule in the gaseous phase was calculated with the all

electrons, double zeta basis set augmented with one d polarization function (6-31g*) and the hybrid B3LYP

functional. The relevant MOs were generated from a single point (SP) calculations on the atomic

coordinates extracted from the X-ray diffraction studies. The pictures of the relevant orbitals with the


corresponding energies are presented in table S1. As an additional check, SP calculations for this molecule

were performed at an unrestricted level, and with a broken-symmetry DFT approach. In the latter case, the

wave function converged to an unrestricted solution with a very small spin contamination (S2 = 0.036),

yielding the orbital picture similar to that obtained from the restricted level DFT calculations. The singlet

diradical state is the ground state at this level of theory, but the calculated energy difference (0.44 kcal

mole-1) between the restricted and the broken-symmetry approach is insignificant.

Graphical representation of the KS orbital KS orbital, Energy (eV)

-0.5667

-1.6377

-1.6960


-3.7109

-4.1239

-5.2371

-5.4453


-5.5870

-6.2776

-6.4314

-7.3864


-7.4036

Table S1. Kohn-Sham orbitals for Ar'CrCrAr' obtained from SP closed shell spin restricted DFT

calculations (B3LYP/6-31g*).

Additional calculations were performed on the same molecular structure extracted from the X-ray

diffraction study using a smaller basis set 3-21g* combined with pure BP86 and BLYP functionals as well

as with hybrid B3LYP and B3BP86 functionals, in order to compare the influence of the functional on the

resulting electronic structure. The obtained KS orbitals are almost identical when obtained with either pure

or hybrid functionals, and are not reported here.

The atomic orbitals (AO) contributions to molecular orbitals (MO's) and overlap populations, as

well as bond orders in Ar'CrCrAr', were calculated using the AOMix program. Similar calculations were

also performed on compounds Ar'CoCoAr' and Ar'FeFeAr', in order to compare the differences in bonding

interactions for these three compounds. The KS-MO's obtained from a single point calculation (B3LYP/6-

31g*) on Ar'CrCrAr' yielded a HOMO-LUMO energy difference of 2.02 eV. The Wiberg bond order index

calculated for the CrCr bond in Ar'CrCrAr' is 4.1. The same calculation in the Lödwin basis yielded a value

of 4.5. For the cobalt and iron congeners Ar'EEAr' (E = Co, Fe) these bond orders indices calculated at the

same level of theory are 1.0 and 0.9 for the CoCo and the FeFe bond respectively; In Lödwin basis they are

1.5 for the CoCo bond and 1.2 for the FeFe bond (Ref. RS5).

CS1.2 Analysis of the bonding interactions obtained from the restricted DFT calculations

Three types of interactions were considered: (A) Cr-Cr (B) Cr-Cipso of the ligand, (C) Cr-phenyl

carbons of the flanking aryls of the ligands.


(A) Cr-Cr

The participation of the fragments and the overlap population between two Cr atoms for the five d-d

interactions considering the atomic orbitals belonging to 4 fragments (2 chromium atoms and two

ligands, the 2 Cr fragments were split into (1) s,p contributions and (2) d,f contributions; f contributions

are insignificant) calculated with the AOMIX program from the restricted SP B3LYP/6-31g*

calculation on Ar'CrCrAr' are presented in tables S2 and S3.

CrCr

interaction

Cr1 s,p Cr1 d,f Ligand 1

Cr2 s,p Cr2 d,f Ligand 2

LUMO -1.70 9.4 25.7 17.8

5.9 26.0 15.1

HOMO -3.71 0.8 33.8 15.5

0.8 32.9 16.2

HOMO-1 -4.12 20.9 26.5

2.6 20.4 27.1

2.5

HOMO-2 -5.24 0.6 44.5

4.6 1.1 44.6

4.6

HOMO-3 -5.45 4.2 36.2

9.5 4.2 36.2

9.6

HOMO-4 -5.59 3.4 43.3

3.2 3.6 43.4

3.1

Table S2. Participation of the fragments for the five d-d interactions considering the atomic orbitals

belonging to four fragments: 2 chromium atoms and two ligands, the 2 Cr fragments were split into (1) s,p

contributions and (2) d,f contributions; f contributions are insignificant.

CrCr

interaction

Overlap for Cr1

d,f-Cr2d,f

LUMO -0.015

HOMO 0.016

HOMO-1 0.013

HOMO-2 0.111

HOMO-3 0.074

HOMO-4 0.096

Table S3. Overlap population between two Cr atoms for the five d-d interactions considering the atomic

orbitals belonging to four fragments; Fragments defined as in Table S2.


(B).Cr-Cipso of the ligand

The contribution of the different type orbitals from both Cr and C atom in a Cr-C bond, as

compared to the contribution from atomic Cr and C units was analyzed. These contributions were obtained

from an analysis in which the overall participation of the relevant M.O.'s is split into the specific partial

contributions of the s, p, and d orbitals. In order to determine the s, p, d orbitals contribution to Cr-Cipso

bond, 6 different orbitals combinations were considered for the possible non-zero overlaps:

OV1 sCr-sCipso; OV2 sCr-pCipso; OV3 pCr-sCipso; OV4 pCr-pCipso; OV5 dCr-sCipso; OV6 dCr-pCipso

The values of the participation of the different fragments are printed in table S4, S5 and the overlap

integrals in table S6. Simultaneous analysis of tables S4, S5 and table S6, shows that HOMO-13 and

HOMO-14 include

type orbitals between Cr and Cipso carbon; some

character with a smaller overlap is

found in HOMO-1, HOMO-3, HOMO-12. Also, a part the non-zero overlaps for sCr-pCipso, pCr-sCipso

combinations found in HOMO-2, HOMO-4, HOMO-13, HOMO-17 (and to some extent in HOMO-19),

which contribute to the

bonding, clearly a

type interactions are present in the five highest occupied

MO's (except HOMO-2), as well as in HOMO-13, HOMO-14, HOMO-17 and HOMO-19. Moreover, the

analysis of these same latter orbitals reveals a similar magnitude of the overlap for dCr-pCipso interactions,

with the highest dCr-pCipso value (0.025) present in HOMO-13. Small dCr-pCipso interactions are found in

HOMO-13, HOMO-14 and HOMO-17.

(C) Cr-phenyl carbons of the flanking aryls of the ligands

Due to the vicinity of the flanking aryls around the Cr-Cr fragment, there is a weak interaction,

coordinative in nature, between the p orbitals forming the bonds of the phenyl cycles and the chromium d

orbitals. These interactions are schematically represented in Fig. SF1(a-c). In order to quantify these

additional interactions their participation in the bonding and the values of the overlap integrals were also

analyzed. As it can be seen form the Tables S4, S5 and S6, in two of the five highest occupied molecular

orbitals (which are in fact almost pure dCr-dCr combinations), there is a non-negligible contribution from the

ligands. About 30% of the HOMO, is composed of the p orbitals of the phenylic carbons of terphenyls. Due

to the particular geometry of the complex, there is a weak overlap (0.016) of the dxy orbitals being involved

in the Cr-Cr

bond with the pz orbitals of the phenyl of the flanking aryl. This is schematized in Fig.


SF1(a). In similar manner in HOMO-1 (Fig. SF1(b)) there is a contribution of the Cipso pz orbital, which

also shows a weak overlap (0.031) with dx2

-y2 orbital of the neighboring chromium involved in another Cr-

Cr

bond. Another weaker interaction in the HOMO-4 involves Cr-Cr

orbital and pz orbitals of carbons

to Cipso of the flanking aryls.

a b

c

Figure SF1 a, b, c. Schematic representation of the interactions between the Cr atoms and the flanking

aryls.

In summary, the bonding in the Ar*CrCrAr* complex obtained from the analysis of the Kohn-Sham

orbitals involves principally five dCr-dCr interactions for the chromium-chromium bond, two sCr-sCipso

interactions, but minor contributions to from sCr-pCipso, pCr-sCipso as well as

type interactions composed

of pCr-pCipso are also present to a lesser extent. Additionally, weak interactions of the Cr d orbitals forming

the Cr-Cr

bond with the pz orbitals of the carbon atoms in the phenyl cycle of the flanking aryl are also

present.


Fragment 1 2 3 4 5 6

HOMO -3.71 0.8 33.8

15.5 0.8 32.9 16.2

HOMO-1 -4.12 20.9

26.5 2.6 20.4 27.1

2.5

HOMO-2 -5.24 0.6 44.5 4.6

1.1 44.6

4.6

HOMO-3 -5.45 4.2 36.2 9.5

4.2 36.2

9.6

HOMO-4 -5.59 3.4 43.3 3.2

3.6 43.4

3.1

HOMO-5 -5.99 0.1

0.8 76.8 0.1 0.5 21.7

HOMO-6 -6.04 -0.1 0.1 22.1 0.4 0.3 77.3

HOMO-7 -6.10 0.8

1.0 56.2 0.9 0.8 40.2

HOMO-8 -6.12 0.4

1.5 34.1 0.5 1.4 61.9

HOMO-9 -6.14 0.6

1.2 90.3 0.0 0.5 7.4

HOMO-10 -6.17 0.1

0.3

5.1

0.1 0.4 94.1

HOMO-11 -6.19 0.2

0.6 34.5 0.2 1.0 63.5

HOMO-12 -6.22 0.2

0.3 72.1 0.3 0.6 26.5

HOMO-13 -6.28 3.5 10.0

38.4 3.3 9.5 35.3

HOMO-14 -6.43 5.3

4.5 39.5 4.6 5.0 41.0

HOMO-15 -7.23 1.5

6.6

3.5 0.1 1.0 87.5

HOMO-16 -7.27 0.1

0.7 87.8 1.5 6.1 3.8

HOMO-17 -7.39 0.7

4.7 38.6 0.7 3.1 52.2

HOMO-18 -7.40 1.0

4.9 50.1 1.2 6.6 36.2

Table S4. Participation of different fragments in the molecular orbitals (B3LYP/6-31g*). Fragments defined as: Fragment 1 is (Chrom 1 Others) Basis functions: 1 - 17 Fragment 2 is (Chrom 1 D-orb) Basis functions: 18 - 36 Fragment 3 is (left fragment) Basis functions: 37 - 408 Fragment 4 is (Chrom 2 Others) Basis functions: 409 - 425 Fragment 5 is (Chrom 2 D-orb) Basis functions: 426 - 444 Fragment 6 is (right fragment) Basis functions: 445 - 816


Fragment 1 2 3 4 5 6 7

HOMO -3.71 0.0 0.8 33.8 0.0

0.2

15.2 50.0

HOMO-1 -4.12 18.9 2.0 26.5 0.1 1.0 3.6

50.0

HOMO-2 -5.24 0.5 0.2 44.5

0.1

0.6 4.0

50.3

HOMO-3 -5.45 -0.3 4.6 36.2 0.3

3.8 5.5

50.0

HOMO-4 -5.59 0.1 3.3 43.3 0.0

0.0 3.2

50.1

HOMO-5 -5.99 -0.1 0.2

0.8

0.0

1.7

75.2 22.3

HOMO-6 -6.04 -0.2 0.1

0.1 0.0 0.2

21.8 78.0

HOMO-7 -6.10 0.0 0.8

1.0

0.1 13.4 42.7 41.9

HOMO-8 -6.12 0.0 0.5

1.5

0.0 12.1 22.0 63.9

HOMO-9 -6.14 0.1 0.5

1.2

0.0

4.5 85.8 7.9

HOMO-10 -6.17 0.0 0.0

0.3

0.0

1.3 3.8

94.6

HOMO-11 -6.19 0.0 0.2

0.6

0.0

1.6

32.9 64.7

HOMO-12 -6.22 0.2 0.0

0.3

0.2

1.1

70.8 27.4

HOMO-13 -6.28 1.7 1.8 10.0 4.0 18.5 15.9 48.1

HOMO-14 -6.43 3.0 2.3

4.5

3.9 17.7 17.9 50.7

HOMO-15 -7.23 0.0 1.5

6.6

0.0

0.0 3.5

88.4

HOMO-16 -7.27 0.0 0.1

0.7

0.0

0.0

87.7 11.4

HOMO-17 -7.39 0.4 0.3

4.7

1.0 1.5 36.0 56.0

HOMO-18 -7.40 0.5 0.4

4.9

0.1

3.3

46.7 44.0

Table S5. Participation of different fragments in the molecular orbitals (B3LYP/6-31g*). Fragments defined as: Fragment 1 is (Chrom 1 S-orb) Basis functions: 1 - 2 6 10 14 Fragment 2 is (Chrom 1 P-orb) Basis functions: 3 - 5 7 - 9 11 - 13 15 - 17 Fragment 3 is (Chrom 1 D-orb) Basis functions: 18 - 36 Fragment 4 is (Carbon 1 S-orb) Basis functions: 37 - 38 42 Fragment 5 is (Carbon 1 P-orb) Basis functions: 39 - 41 43 - 51 Fragment 6 is (left aryl fragment) Basis functions: 52 - 408 Fragment 7 is (right aryl fragment) Basis functions: 409 - 816


OV1 OV2 OV3 OV4 OV5 OV6

HOMO

HOMO-1 0.005 0.023 0.002 0.009 1E-3 0.014

HOMO-2 1E-3 1E-3 1E-3 1E-3 0 0.002

HOMO-3 0.005 0.011 0.005 0.009 0 0.008

HOMO-4 0 0 0 0.003 0 0.002

HOMO-5 1E-3 1E-3 0 0 0 1E-3

HOMO-6 1E-3 1E-3 0 0 0 0

HOMO-7 1E-3 0 0 0.006 0 0.003

HOMO-8 0 0 0 0.009 0 0.004

HOMO-9 0 0 0 0.003 0 0.003

HOMO-10 0 0 0 1E-3 0 1E-3

HOMO-11 0 0 0 0.002 0 1E-3

HOMO-12 0.005 0 0 1E-3 0 0

HOMO-13 0.037 0.02 0.013 0.009 0.011 0.025

HOMO-14 0.017 0.015 0.023 0.018 0.009 0.02

HOMO-15 0 0 0 1E-3 0 0

HOMO-16 0 0 0 1E-3 0 0

HOMO-17 0.011 1E-3 0.004 0.002 0.007 0.004

HOMO-18 1E-3 1E-3 1E-3 1E-3 1E-3 0.002

HOMO-19 0.008 0.003 0 0.005 0 0

Table S6. Values of the relevant overlap integrals for fragments 1-7 (Fragments defined as in Table S5). Fragment 1 is (Chrom 1 S-orb) Basis functions: 1 - 2 6 10 14 Fragment 2 is (Chrom 1 P-orb) Basis functions: 3 - 5 7 - 9 11 - 13 15 - 17 Fragment 3 is (Chrom 1 D-orb) Basis functions: 18 - 36 Fragment 4 is (Carbon 1 S-orb) Basis functions: 37 - 38 42 Fragment 5 is (Carbon 1 P-orb) Basis functions: 39 - 41 43 - 51 Fragment 6 is (left fragment) Basis functions: 52 - 408 Fragment 7 is (right fragment) Basis functions: 409 - 816 Relevant overlap values: OV1 sCr-sCipso

OV2 sCr-pCipso

OV3 pCr-sCipso

OV4 pCr-pCipso

OV5 dCr-sCipso

OV6 dCr-pCipso


CS1.2 NBO Analysis from the restricted DFT calculations

NBO analysis was also performed on the Ar'CrCrAr' compound. Normal orbitals (NOs) were

calculated from a SP calculation (see table S9). The Cr-Cr bond is composed of five bonds between two Cr

centers with an additional weak bonding between flanking aryl fragments and chromium atoms. The

calculated NBO coefficients show that the electronic structure for the Cr centers can be described as

Cr[core] 4s0.47 3d4.69 4p0.03 5p0.01 with a positive normal charge of 0.81 on each chromium atom. The

relevant coefficients for the different contributions into NBO bonds are presented in table S7, and the

composition of the Cr-Cr bonds in terms of participating orbitals is presented in table S8:

CrCr

interaction

Bond Occupation

% Electronic conf. % Electronic conf.

1 1.984 0.500 4s0.01 3d0.99 4p0.00

0.500 4s0.01 3d0.99 4p0.00

2 1.941 0.498 4s0.00 3d0.98 4p0.02

0.502 4s0.00 3d0.98 4p0.02

3 1.914 0.498 4s0.00 3d1.00 4p0.00

0.502 4s0.00 3d1.00 4p0.00

4 1.850 0.496 4s0.28 3d0.72 4p0.00

0.504 4s0.28 3d0.72 4p0.00

5 1.572 0.509 4s0.00 3d0.99 4p0.01

0.491 4s0.00 3d0.99 4p0.01

Table S7. Occupation coefficients for the different types of orbitals contributing into the NBO bonds

CrCr

interaction

Bond Energy a.u.

1 0.63 3dxy + 0.57 3dx2

-y2 - 0.52 3dz

2 -0.22111

2 0.89 3dxz + 0.43 3dyz -0.20047

3 0.67 3dxy -0.74 3dx2

-y2 -0.19347

4 0.53 4s +0.29 3dxy + 0.28 3dx2

-y2 + 0.74 3dz

2 -0.17707

5 -0.45 3dxz + 0.88 3dyz -0.11086

Table S8. Composition of the Cr-Cr bonds in terms of participating orbitals.


NBO_01 (LUMO)

NBO_02 (HOMO)

NBO_03

NBO_04

NBO_05


NBO_06

Table S9. Orbital pictures for Ar'CrCrAr' from Natural Bonding Analysis (NBA).

The overall picture that emerges from the KS-MO's and NBO analysis is that Cr-Cr bond is formed

by 5 bonding interactions between 3d orbitals of chromium, in which two

and two

type bonds are

composed of chromium 3dxz/3dyz .and 3dxy/3dx2

-y2 orbitals respectively. In the

orbital an additional

contribution from the chromium 4s orbitals is present. The

bond, which corresponds to the HOMO

orbital, can be considered as a weakened

interaction between dxy orbitals, which shows however a non-

negligible overlap and can therefore be considered as a real "fifth" bond.

CS2 Electronic structure of MeCrCrMe models

Further calculations were performed on the model MeCrCrMe rather than on the Ar'CrCrAr'

species, because of the time/computational resources limitations. These include electronic structure

calculations on MeCrCrMe with the CrCr bond and CCrCr angle identical to those found in Ar'CrCrAr'

(denoted thereafter MeCrCrMe_F1), geometry optimizations of model compounds MeCrCrMe with

different functionals and several basis sets. As in the case of the ArCrCrAr the bond orders were calculated

with AIM and AOMIX approaches.

CS2.1 Electronic structure, AIM and bond order calculations in MeCrCrMe_F1.

The KS orbitals for the MeCrCrMe_F1 were generated form SP calculation at B3LYP/6-31g* level.

Rleveant KS orbitals are listed in table S10.


CrCr

interaction

KS orbital representation Energy (eV)

LUMO+2

LUMO+1

LUMO

HOMO

HOMO-1


HOMO-2

HOMO-3

HOMO-4

Table S10. Kohn-Sham orbitals for MeCrCrMe obtained from SP closed shell spin restricted DFT

calculations (B3LYP/6-31g*).

CS2.2 Electronic structure of a singlet diradical MeCrCrMe_F1.

The KS orbitals for the MeCrCrMe_F1 at the unrestricted level were generated form SP calculation

(B3LYP/6-31g*) combined with guess=mix option for the guess wavefunction (initial S2 = 1.00). Relevant

KS orbitals are listed in table S11. The energy difference between closed shell and singlet diradical

MeCrCrMe_F1 was calculated to be 13.2 kcal/mole in favor of the singlet diradical ground state.


CrCr

interaction

LUMO+2

LUMO+1

LUMO

HOMO

HOMO-1

HOMO-2


HOMO-3

HOMO-4

Table S11. Kohn-Sham

orbitals for MeCrCrMe obtained from SP spin unrestricted broken-symmetry

DFT calculations (B3LYP/6-31g*).

CS2.3 Geometry optimizations of MeCrCrMe.

The geometry of the MeCrCrMe were optimized first at B3LYP level with basis sets of increasing

size (LanL2DZ, 3-21g*, 6-31g*), ans subsequently with BLYP, BP86 and B3P86 functionals. Additionally,

the geometry of the MeCrCRMe model was optimized with the spin unrestricted broken-symmetry DFT

approach (B3LYP/6-31g*). Subsequent optimizations were carried out including the relativistic effects

with the use of the small core CRENBL basis set. This basis set was augmented with one polarization

function on C artoms and one polarization function on Cr atoms (Ref. RS6 and RS7). For all the

optimizations, tight SCF convergence criterion and fine grid were used. The geometries of the optimized

MeCrCrMe models are presented in table S12.


CrCr bond CCrCr angle CrC bond CCrCrC angle

B3LYP/6-31g* 1.572 84.7 2.066 180

B3P86/6-31g* 1.559 83.0 2.056 180

BLYP/6-31g* 1.609 85.4 2.068 180

BP86/6-31g* 1.595 83.4 2.057 180

LSDA/6-31g* 1.570 80.3 2.023 180

B3LYP/6-31g* (BS)

1.572 91.5 2.068 180

B3LYP/CRENBL 1.620 97.6 2.070 180

Table S12. Relevant geometrical parameters of the optimized MeCrCrMe models. BS = Unrestricted KS

Broken Symmetry approach.

The scan of the singlet PES of the MeCrCrMe in planar C2h geometry, relative to the CrCrC angle is

presented in Fig. SF2.

60 80 100 120 140 160 180

-60

-50

-40

-30

-20

-10

0

E [K

cal/m

ole]

CrCrC angle

Figure SF2. Scan of the singlet PES of the MeCrCrMe in planar C2h geometry, relative to the CrCrC angle

(B3LYP/CRENBL).


CS2.4 CASSCF calculation on MeCrCrMe

Because of the computational limitations, a multiconfigurational approach was used for the

calculations on the small model MeCrCrMe compound. The two lowest d-d interactions were assigned to

the inactive space and they were kept doubly occupied through the CAS routine. CASSCF calculations

were carried out with small active space:(a) (4,4) corresponding to 4 electrons and 4 orbitals with 2 doubly

occupied

Ag orbitals, HOMO and HOMO-1, and the two unoccupied antibonding LUMO and LUMO+1

orbitals selected into the active space and (b) (6,6) corresponding to 6 electrons and 6 orbitals with 2

doubly occupied

Ag orbitals, one doubly occupied

orbital and the three unoccupied LUMO, LUMO+1

and LUMO+2 orbitals selected into the active space. At CASSCF (4,4) level, the predicted main

configuration of MeCrCrMe whose weight is 0.66, is indeed the one in which the 4 electrons occupy the

two

type orbitals with the occupancy numbers 1.83, 1.37, 0.17, and 0.64 (CAS_44_05 through

CAS_44_02) (see Table S13). Similar results are obtained with CASSCF (6,6) when the main

configuration of MeCrCrMe whose weight is 0.67, include again the 4 electrons occupy the two

type

orbitals and the s orbital. The corresponding occupancy numbers are 1.81, 1.59, 1.73, 0.46, 0.13, and

0.27(CAS_66_06 through CAS_66_01).

CrCr

interaction

KS orbital representation CASSCF

Orbital No.

CASSCF orbitals

LUMO+2 CAS_44_01

LUMO+1 CAS_44_02


LUMO CAS_44_03

HOMO CAS_44_04

HOMO-1 CAS_44_05

HOMO-2 CAS_44_06

HOMO-3 CAS_44_07


HOMO-4 CAS_44_08

Table S13. Kohn-Sham orbitals for MeCrCrMe obtained from SP closed shell spin restricted DFT

calculations B3LYP/6-31g* (left) compared to the orbitals obtained from CASSCF(4,4) calculations on

MeCrCrMe.

CS3 Geometry optimizations of the protonated Me(H)CrCr(H)Me

Two model structures Me(H)CrCr(H)Me (with protons connected to the Cr atom in trans (a) and

bridged (b) configurations) were optimized at B3LYP/6-31g* level and the vibrational frequencies were

calculated on the optimized geometries (Fig. SF3 a, b). Frequency calculations yield a value of 1790 [cm-1],

for (a) and 1630 [cm-1] for (b) and show that these structures are not minima on PES. The optimized CrCr

bond lengths and angle are reported in Table S14.

(a) (b)

Figure SF3. Optimized structure of the planar Me(H)CrCr(H)Me species. (a) trans (b) "bridged"

configuration.

CrCr bond CrH bond CCrCr angle CrC bond CrCrH angle

Me(H)CrCr(H)Me (a)

trans

1.804 1.651 119.5 2.003 97.6

Me(H)CrCr(H)Me (b)

bridged

1.843 1.671 139.8 2.011 61.8

Table S14. Geometrical parameters of the optimized Me(H)CrCr(H)Me models (B3LYP/6-31g*).


CS4 Electronic structure calculations on tetrakis(2-methoxy-5-methylphenyl)dichromium-Cr2[C6H3Me(OMe)]4

For comparison purposes, calculations of the electronic structure were also performed on the

tetrakis (2-methoxy-5-methylphenyl)dichromium Cr2[C6H3Me(OMe)]4 (Ref. RS8). The coordinates were

extracted from the X-ray diffraction study and the hydrogen atoms were added. The atomic orbitals (AO)

contributions to molecular orbitals (MO's) and overlap populations, as well as bond orders in

Cr2[C6H3Me(OMe)]4, were calculated using the AOMix program. NBO analysis was also performed on this

compound (Table S15). Normal orbitals (NOs) were calculated from a SP calculation (see Table S16).

CrCr

interaction

Bond Occupation

% Electronic conf. % Electronic conf.

1 1.866 0.499 4s0.20d0.79p0.00 0.501 4s0.20d0.794p0.00

2 1.914 0.500 4s0.013d0.994p0.00 0.500 4s0.013d0.994p0.00

3 1.908 0.501 4s0.003d1.00 4p0.00 0.499 4s0.003d1.00 4p0.00

4 1.741 0.488 4s0.00d1.004p0.00 0.512 4s0.003d1.00 4p0.00

Table S15. Occupation coefficients for the different types of orbitals contributing into the NBO bonds for

Cr2[C6H3Me(OMe)]4

NBO_01 (LUMO)


NBO_02 (HOMO)

NBO_03

NBO_04

NBO_05

Table S16. Orbital pictures for Cr2[C6H3Me(OMe)]4 from Natural Bonding Analysis (NBA).


CS 5 The temperature dependence of the diamagnetic susceptibility.

0.000

0.004

0.008

0.012

0.016

0.020

0 50 100 150 200 250 300Temperature, K

-0.012

-0.008

-0.004

0.000

0.004

0.008

0 50 100 150 200 250 300Temperature, K

Figure SF3. The temperature dependence of the diamagnetic susceptibility corrected molar magnetic susceptibility of 1, upper plot. The open points are the observed susceptibility, the solid curved line corresponds to the sum of the temperature independent paramagnetic susceptibility of 0.00112(5) emu/mol Cr, the solid straight line, and the paramagnetic susceptibility of a chromium(III) complex that is assumed to have an effective paramagnetic moment of 3.97 B, the broken curve. The difference between the observed susceptibility and the sum of the two components is shown in the lower plot. The peak below ca. 25 K indicates the possible presence of traces of antiferromagnetic Cr(II) or Cr(III) polymeric impurities. As a consequence, the value of 0.00112(5) emu/mol Cr should be considered as an upper limit to the temperature independent paramagnetic susceptibility of 1.


CS6 References:

RS1. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.;

Montgomery, J. A., Jr.; Vreven, T.; Kudin, K.N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.;

Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.;

Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai,

H.; Klene, M.; Li,X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.;Gomperts, R.;

Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.;

Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A.

D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.;

Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.;

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Gaussian 03, Revision A.1; Gaussian, Inc.: Pittsburgh, PA, 2003.

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Scientific Computing: Manno, Switzerland, 2000-2002.

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Molecules," Journal of the American Chemical Society, 1991, 113, 4142-4145.

RS5. Nguyen, P.; Sutton, A.D.; Brynda, M.; Fettinger, J.C.; Power, P.P., unpublished work

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R., Veldkamp A., Frenking, G., Chemical Physics Letters 1993, 208, 111-114.

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