Electronic Supplementary Information

Exploring the Nature of Excitation Energies

in [Re6(µ3-Q8)X6]4− Clusters: A Relativistic Approach

Walter A. Rabanal-León,† Juliana A. Murillo-López,‡ Dayán Páez-Hernández,† and Ramiro

Arratia-Pérez∗,†

‡Universidad Andrés Bello, Facultad de Ciencias Exactas,

Ph.D. Program in Molecular Physical Chemistry,

Relativistic Molecular Physics (ReMoPh) Group, Santiago, Chile, and

¶Universidad de Talca, Facultad de Ingeniería,

Centro de Bioinformática y Simulación Molecular (CBSM),

2 Norte 685, Casilla 721,Talca, Chile

E-mail: rarratia@unab.cl

Phone: +56-2-2770-3352. Fax: +56-2-2770-3352

∗To whom correspondence should be addressed†Universidad Andrés Bello, Relativistic Molecular Physics (ReMoPh) Group‡Universidad de Talca, Centro de Bioinformática y Simulación Molecular (CBSM)

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Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics.This journal is © the Owner Societies 2015

Figure S1: Excitation energies for the [Re6(µ3-Se8)X6]4− (X = F−, Cl−, Br− and I−)

clusters at spin-orbit relativistic level with the SAOP functional in acetonitrile solvent.

Osc

illat

or S

tren

gth

/ f

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

λ / nm

350 400 450 500 550 600 650

-F -Cl -Br -I

Figure S2: Excitation energies for the [Re6(µ3-Te8)X6]4− (X = F−, Cl−, Br− and I−)

clusters at spin-orbit relativistic level with the SAOP functional in acetonitrile solvent.

Osc

illat

or S

tren

gth

/ f

0.00

0.01

0.02

0.03

0.04

0.05

0.06

λ / nm

400 450 500 550 600 650 700 750

2222

-F -Cl -Br -I

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Figure S3: Excitation energies for the [Re6(µ3-Se8)X6]4− (X = CN−, NC−, SCN−,

NCS−, OCN−, NCO−) clusters at spin-orbit relativistic level with the SAOP functional

in acetonitrile solvent.

Osc

illat

or S

tren

gth

/ f

0.00

0.02

0.04

0.06

0.08

0.10

0.12

λ / nm

400 500 600 700 800 900 1000

-CN -NC -SCN -NCS -OCN -NCO

Figure S4: Excitation energies for the [Re6(µ3-Te8)X6]4− (X = CN−, NC−, SCN−,

NCS−, OCN−, NCO−) clusters at spin-orbit relativistic level with the SAOP functional

in acetonitrile solvent.

Osc

illat

or S

tren

gth

/ f

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

λ / nm

400 600 800 1000 1200

222222

-CN -NC -SCN -NCS -OCN -NCO

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Figure S5: Molecular spinor plots and density difference maps for all the [Re6(µ3-

Te8)X6]4− (X = CN−, NC−, SCN−, NCS−, OCN−, NCO−) clusters at spin-orbit rela-

tivistic level of theory.

Molecular SpinorsDensity

Di↵erence Maps

[Re6(µ3-S8)F6]4�

52 u3/2g ! 53 u3/2u

52 u3/2g ! 54 u3/2u

52 u3/2g ! 24 e5/2u

[Re6(µ3-S8)Cl6]4�

56 u3/2g ! 57 u3/2u

Molecular SpinorsDensity

Di↵erence Maps

56 u3/2g ! 25 e5/2u

56 u3/2u ! 25 e5/2g

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Molecular SpinorsDensity

Di↵erence Maps

[Re6(µ3-S8)Br6]4�

65 u3/2g ! 66 u3/2u

65 u3/2g ! 41 e1/2u

Molecular SpinorsDensity

Di↵erence Maps

[Re6(µ3-S8)I6]4�

32 e5/2u ! 75 u3/2g

74 u3/2u ! 33 e5/2g

74 u3/2g ! 46 e1/2u

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Molecular SpinorsDensity

Di↵erence Maps

[Re6(µ3-S8)CN6]4�

54 u3/2u ! 55 u3/2g

34 e1/2u ! 35 e1/2g

54 u3/2g ! 24 e5/2u

54 u3/2g ! 55 u3/2u

Molecular SpinorsDensity

Di↵erence Maps

[Re6(µ3-S8)NC6]4�

54 u3/2u ! 24 e5/2g

23 e5/2u ! 24 e5/2g

54 u3/2g ! 55 u3/2u

54 u3/2g ! 24 e5/2u

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Molecular SpinorsDensity

Di↵erence Maps

[Re6(µ3-S8)OCN6]4�

58 u3/2g ! 59 u3/2u

24 e5/2u ! 25 e5/2g

58 u3/2g ! 38 e1/2u

Molecular SpinorsDensity

Di↵erence Maps

[Re6(µ3-S8)NCO6]4�

24 e5/2u ! 59 u3/2g

57 u3/2u ! 25 e5/2g

24 e5/2u ! 25 e5/2g

58 u3/2g ! 59 u3/2u

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Molecular SpinorsDensity

Di↵erence Maps

[Re6(µ3-S8)SCN6]4�

60 u3/2g ! 41 e1/2u

25 e5/2u ! 63 u3/2g

40 e1/2g ! 41 e1/2u

62 u3/2u ! 63 u3/2g

Molecular SpinorsDensity

Di↵erence Maps

[Re6(µ3-S8)NCS6]4�

40 e1/2u ! 41 e1/2g

61 u3/2u ! 26 e5/2g

61 u3/2u ! 41 e1/2g

25 e5/2u ! 63 u3/2g

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Table S1 : Excitation energies (eV), wavelengths (nm), oscillator strengths (f ) and

orbital assignation for the [Re6(µ3-Se)8X6]4− complexes (X = F−, Cl−, Br−, I−).

Band Energy λ f(x100) Active MOs % Assignation

[Re6(µ3-Se)8F6]4−

a 3.04 406 1.281264 u3/2g → 65 u3/2u 57 CoreRe - CoreSe

64 u3/2g → 66 u3/2u 19 CoreRe - CoreRe

64 u3/2u → 30 e5/2g 16 CoreRe - CoreRe

b 2.91 425 0.8608 64 u3/2g → 39 e1/2u 86 CoreRe - CoreRe

c 2.83 438 0.3324 29 e5/2u → 30 e5/2g 58 CoreRe - CoreRe

64 u3/2g → 65 u3/2u 18 CoreRe - CoreSe

[Re6(µ3-Se)8Cl6]4−

a 2.80 (2.84†) 442 1.998068 u3/2g → 69 u3/2u 69 CoreRe - CoreRe

30 e5/2u → 31 e5/2g 15 CoreRe + Lig - CoreRe

64 u3/2u → 31 e5/2g 12 Lig - CoreRe

b 2.66 465 0.548268 u3/2g → 69 u3/2u 36 CoreRe - CoreRe

30 e5/2u → 31 e5/2g 28 CoreRe + Lig - CoreRe

68 u3/2g → 31 e5/2u 25 CoreRe - CoreRe

c 2.47 501 0.88999 68 u3/2g → 42 e1/2u 98 CoreRe - CoreRe

[Re6(µ3-Se)8Br6]4−a 2.66 465 2.0655 77 u3/2g → 78 u3/2u 93 CoreRe - CoreRe + Lig

b 2.59 468 0.3551577 u3/2g → 78 u3/2u 54 CoreRe - CoreRe + Lig34 e5/2u → 35 e5/2g 27 CoreRe + Lig - CoreRe

77 u3/2g → 35 e5/2u 10 CoreRe - CoreRe

c 2.32 534 1.1779 77 u3/2g → 47 e1/2u 98 CoreRe - CoreRe + Lig

[Re6(µ3-Se)8I6]4−

a 2.56 (2.58†) 484 2.4050 86 u3/2g → 87 u3/2u 90 CoreRe - CoreRe + Lig

b 2.42 512 0.3568 38 e5/2u → 39 e5/2g 77 Lig - CoreRe

86 u3/2g → 87 u3/2u 15 CoreRe - CoreRe + Lig

c 2.22 556 1.5591 86 u3/2g → 52 e1/2u 97 CoreRe - CoreRe + Lig

†J. Chem. Phys., Vol. 115 N◦ 2 (2001), pp. 726.

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Table S2 : Excitation energies (eV), wavelengths (nm), oscillator strengths (f ) and

orbital assignation for the [Re6(µ3-Te)8X6]4− complexes (X = F−, Cl−, Br−, I−).

Band Energy λ f(x100) Active MOs % Assignation

[Re6(µ3-Te)8F6]4−

a 2.55 485 1.0673 76 u3/2g → 36 e5/2u 48 CoreRe + Lig - Core75 u3/2g → 77 u3/2u 37 CoreRe - Core

b 2.45 505 0.3414 76 u3/2g → 77 u3/2u 86 CoreRe + Lig - Core

c 2.42 511 0.6993 76 u3/2u → 36 e5/2g 96 CoreTe - Core

[Re6(µ3-Te)8Cl6]4−a 2.30 537 0.4141 80 u3/2u → 37 e5/2g 99 CoreRe + Lig - CoreRe

b 2.14 579 0.6772 79 u3/2g → 48 e1/2u 96 CoreRe - CoreRe + Lig

c 2.11 586 0.5436 80 u3/2g → 48 e1/2u 97 CoreRe + Lig - CoreRe

[Re6(µ3-Te)8Br6]4−

a 2.22 556 1.6695 89 u3/2g → 90 u3/2u 88 CoreTe + Lig - Core + Lig88 u3/2g → 90 u3/2u 11 Core - Core + Lig

b 1.99 621 0.6209 88 u3/2g → 53 e1/2u 98 Core - Core + Lig

c 1.95 635 0.9143 89 u3/2g → 53 e1/2u 99 CoreTe + Lig - Core + Lig

[Re6(µ3-Te)8I6]4−a 2.10 590 1.3382 98 u3/2g → 99 u3/2u 91 Core + Lig - Core + Lig

b 1.91 647 0.7220 97 u3/2g → 58 e1/2u 98 Core + Lig - Core + Lig

c 1.83 675 1.1250 98 u3/2g → 58 e1/2u 99 Core + Lig - Core + Lig

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