Gold Clusters
1
-8 -4 0 4 8 12 16 20 24 28 32 36 40 44 B are 4PH 3 5PH 3 6PH 3 Au 6 (t) Au 6 (3d) Au 6 (p) Au 6 (dt) -16 -12 -8 -4 0 4 8 12 16 20 B are 4PH 3 5PH 3 6PH 3 7PH 3 Au 8 (3d) Au 8 (h) Au 8 (s) -8 -4 0 4 B are 1PH 3 2PH 3 3PH 3 Au 4 (b) Au 4 (t) Energy (kcal/mol) Isome rs Solvent and Ligand Influence on the Energetics and Optical Transitions in Small Gold Clusters 1 Theoretical Division, 2 Center for Nonlinear Studies, 3 Center for Integrated Nano-Technologies, Los Alamos National Laboratory, New Mexico – 87545, 4 NanoScience Technology Center, University of Central Florida, Orlando, FL 32826 The study of noble metal clusters holds promises for the great advances in materials science as they increasingly form the basis for assembly of nanoarchitectures having specific emergent properties. Recent progress in the synthesis of noble metal nanoclusters, for example, suggests that they will likely permit the manipulation of light at the molecular scale, if only their size and structure can be controlled at the atomic level. Experimental studies alone cannot fully address the fundamental questions about the cluster properties, and as such, theoretical studies can provide invaluable microscopic insight into the electronic structure and dynamics of these nanoclusters. Gold clusters and nanoparticles exhibit a rich array of important electronic, optical, chemical and catalytic properties, which has sparked a huge interest in gold-based systems in several interdisciplinary areas, leading to an explosive growth in the volume of both experimental and theoretical research. Figure - The diatom: an example of biological blueprints for inorganic materials fabrication. To exploit biological specificity to produce highly fluorescent gold (Au) nanoclusters from soluble precursors by using peptide and protein templates to organize metal atoms into a highly ordered structure with novel optical properties. Figure - Predictive design of noble metal nanoclusters. The iterative, a) synthesis, b) characterization (shown as fluorescence correlation spectroscopy), c) theoretical description (showing optical transitions mediated by the excited state dynamics), and d) testing metal LA-UR 09-03153 Au 2 Au 4 (b) Au 4 (t) Au 6 (t) Au 6 (p) Au 6 (dt) Au 6 (3d) Au 8 (s) Au 8 (h) Au 8 (3d) 1L 2L 3L 4L 5L 6L Au 6 (t) Au 6 (p) Au 6 (dt) Au 6 (3d) Geometries of four isomers of Au 6 with ligand attachement from one (top) to full ligation (Last geometry in respective colums). 2.35 2.40 2.45 2.50 2.55 2.60 2.65 B ond L ength (Ǻ ) G old C luster 1L 2L 3L 4L 5L 6L 7L Au 2 Au 4 (b) Au 4 (t) Au 6 (t) Au 6 (p) Au 6 (3d) Au 6 (dt) Au 8 (3d) Au 8 (h) Au 8 (s) 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 B ond L ength (Ǻ ) G old C luster B are 1L 2L 3L 4L 5L 6L 7L Au 2 Au 4 (b) Au 4 (t) Au 6 (t) Au 6 (p) Au 6 (3d) Au 6 (dt) A u 8 (3d) Au 8 (h) Au 8 (s) Bond length variation between gold-gold and gold- ligand bonds in different isomers of small gold clusters, when ligands are attached starting from one to full ligation. Au 2 Au 4 (p ) G03 Total Energy (nm) - 270.9 17 - 541.88 6 1 st Transition Energy (nm) – GS 508.0 30 1049.3 90 NWChem PBE0 B3LYP DFT Total Energy - 270.5 38 - 541.28 3 1 st Transition Energy (nm) – GS 624.7 75 1428.3 06 DFT-ZORA Total Energy - 270.5 54 - 541.31 4 1 st Transition Energy (nm) – GS 625.7 71 1428.3 71 SODFT Total Energy - 270.5 66 - 541.34 4 1 st Transition Energy (nm) – GS 620.4 56 1460.6 44 SODFT-ZORA Total Energy - 270.5 81 - 541.37 5 1 st Transition Energy 620.4 1460.8 Basis set with Polarization functional are required to investigate small gold clusters with ligands. LANL2DZ reproduces the trends with one family of ligands. Ligands increase the energies and oscillator strengths of 1 st transition of gold clusters. Solvation effects partially simulate the effect of ligands on 1 st transition energy for bare clusters. For ligated clusters solvation does not change 1 st transition energy significantly but has a prominent effect on the oscillator strength. Spin-orbit and ZORA relativistic effects do not significantly change Considered DFT functionals of different classes are consistent both qualitatively and quantitatively. Ligand binding leads to the stabilization of more planar isomers of Au 4 and Au 6 . No size scaling was revealed as judged by the 1 st transition energy from Au 2 to Au 8 . Increase in number of ligands around the metal core reduces the metal-ligand binding energy as expected. Ligands significantly effect the cluster geometries. Neutral gold clusters form stable bonds with primary and tertiary Isomers of small gold clusters (Au 2 , Au 4 , Au 6 and Au 8 ) Relative energies for different isomers of small gold clusters with ligands. Comparison displays variations starting from saturated isomer with least number of ligands to the saturated siomer with most number of ligands. The lowest energy isomer is taken as reference structure (zero energy) for comparison. DFT function als • SVWN5 • PBEPBE • TPSSTPSS • B3LYP • CAM-B3LYP • LANL2DZ • LAN2DZ+P • def2-SVP • def2-TZVP • def2-QZVP • Gaussian 03/09 • Turbomol • NWChem 5.1 • Model - CPCM • Solvent - Methanol Basis Set Solvati on Softwar e Theoretical Details Excited State Properties - TDDFT D FT FunctionalBinding E nergy (kcal/m ol)Bond Lengths(A) SVW N 5 64.14 2.49 PBEPBE 50.03 2.55 TPSSTPSS 50.58 2.54 B3LYP 43.20 2.57 CAM -B3LYP 41.62 2.55 E xp * 53.00 2.47 SVW N 5 67.72 2.49 PBEPBE 53.33 2.55 TPSSTPSS 54.39 2.53 B3LYP 41.14 2.57 CAM -B3LYP 45.61 2.55 Solvated (M ethanol) Au2 Bonding energies and bond lengths of Au 2 calculated with different (5 generations) DFT functionals compared with experimental data. Representative geometries of Au 2 and Au 4 cluster with ligand attached as PMe 3 , (a) Au 2 (PMe 3 ) 2 , (b) Au 4 (PMe 3 ) 2 , (c) Au 4 (PMe 3 ) 4 , (d) Au 4 (NMe 3 ) 4 . *K ordiset. al., Journal of Chemical Physics , 1974 , 61, 5114. -62 -52 -42 -32 -22 -12 NH 3 NM e 3 PH 3 PM e 3 Au 2 L 2 / m ol) -62 -52 -42 -32 -22 -12 NH 3 NM e 3 PH 3 PM e 3 Au 4 L 2 EnergyperLigand (kcal -62 -52 -42 -32 -22 -12 SVW N5 PBE TPSS B3LYP CAM -B3LYP NH 3 NM e 3 PH 3 PM e 3 Au 4 L 4 Binding TypeofLigand -44 -39 -34 -29 -24 -19 -14 NH 3 NM e 3 PH 3 PM e 3 Au 2 L 2 / m ol) -44 -39 -34 -29 -24 -19 -14 NH 3 NM e 3 PH 3 PM e 3 Au 4 L 2 EnergyperLigand (kcal -44 -39 -34 -29 -24 -19 -14 LANL2DZ LANL2DZ-P SVP TZVP Q ZVP TZVP (sol) NH 3 NM e 3 PH 3 PM e 3 Au 4 L 4 TypeofLigand Binding Binding energies per ligand in kcal/mol for geometries of Au 2 and Au 4 in partial and fully ligated forms determined using various DFT functionals (left, TZVP basis set has been used for all calculations) and various basis sets (right, TPSS functional has been used for all calculations). BENCHMARKING 2.0 2.5 3.0 3.5 NH3 NM e3 PH3 PM e3 NH 3 NM e 3 PH 3 PM e 3 Au 4 L 2 1.5 2.0 2.5 3.0 SVW N5 PBEPBE TPSSTPSS B3LYP CAM -B3LYP NH 3 NM e 3 PH 3 PM e 3 Au 4 L 4 3.0 3.5 4.0 4.5 5.0 NH3 NM e3 PH 3 PM e3 NH 3 NM e 3 PH 3 PM e 3 Au 2 L 2 2.0 2.5 3.0 3.5 NH3 NM e3 PH3 PM e3 NH 3 NM e 3 PH 3 PM e 3 Au 4 L 2 1.5 2.0 2.5 3.0 PM e3 SVW N5 PBEPBE TPSSTPSS B3LYP CAM -B3LYP NH 3 NM e 3 PH 3 PM e 3 Au 4 L 4 3.0 3.5 4.0 4.5 5.0 NH 3 NM e 3 PH 3 PM e 3 Au 2 L 2 1 st Transition Energy (eV) Type of Ligand SODFT and ZORA corrections for Au 2 and Au 4 (p) bare clusters. Oscillator strengths for these cluster calculations are zero. LUMO HOMO Au 2 (NMe 3 ) 2 CAM-B3LYP =4.816 eV f=0.128 =0.96424 TPSS =4.407 eV f=0.000 =0.98933 Au 4 (PMe 3 ) 2 (Sol) CAM-B3LYP =3.206 eV f=0.733 =0.94561 TPSS =2.700 eV f=0.003 =0.99798 Au 4 (NMe 3 ) 4 CAM-B3LYP =2.728 eV f=0.000 = 0.99137 TPSS =2.482 eV f=0.054 = 0.99336 Lowest energy state molecular orbitals for ligated Au 2 and Au 4 with CAM-B3LYP and TPSS. Figure showing different lowest states corresponding to the use of different DFT functionals for TDDFT absorption calculations. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Au 2 Au 4 Au 6 Au 8 Au 6 (t) Au 6 (p) Au 6 (dt) Au 6 (3d) Au 2 Au 4 (b) Au 4 (t) Au 8 (3d) Au 8 (s) 1 st transition energy (eV) for geometries of Au 2 and Au 4 in partial and fully ligated forms determined using various DFT functionals with (right) and without solvent (left) 1 st transition energy of several lowest energy isomers of small gold clusters (Au 2 -Au 8 ) Optical Properties Geometry & Energetics
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Transcript of Gold Clusters
-8-4048
121620242832364044
Au6(t) Au6(3d) Au6(p) Au6(dt)
Bare4PH35PH36PH3
Bare
4PH3
5PH3
6PH3
Au6(t) Au6(3d) Au6(p) Au6(dt)
-16-12-8-4048
121620
Au8(3d) Au8(h) Au8(s)
Bare4PH35PH36PH37PH3
Bare
4PH3
5PH3
6PH3
7PH3
Au8(3d) Au8(h) Au8(s)
-8
-4
0
4
Au4(b) Au4(t)
Bare
1PH3
2PH3
3PH3
Bare
1PH3
2PH3
3PH3
Au4(b) Au4(t)
En
erg
y (k
cal/
mol)
Isomers
Solvent and Ligand Influence on the Energetics and
Optical Transitions in Small Gold Clusters1Theoretical Division, 2Center for Nonlinear Studies, 3Center for Integrated Nano-Technologies, Los Alamos National Laboratory, New Mexico – 87545, 4NanoScience Technology Center, University of
Central Florida, Orlando, FL 32826The study of noble metal clusters holds promises for the great advances in materials science as they increasingly form the basis for assembly of nanoarchitectures having specific emergent properties. Recent progress in the synthesis of noble metal nanoclusters, for example, suggests that they will likely permit the manipulation of light at the molecular scale, if only their size and structure can be controlled at the atomic level. Experimental studies alone cannot fully address the fundamental questions about the cluster properties, and as such, theoretical studies can provide invaluable microscopic insight into the electronic structure and dynamics of these nanoclusters. Gold clusters and nanoparticles exhibit a rich array of important electronic, optical, chemical and catalytic properties, which has sparked a huge interest in gold-based systems in several interdisciplinary areas, leading to an explosive growth in the volume of both experimental and theoretical research.
Figure - The diatom: an example of biological blueprints for inorganic materials fabrication. To exploit biological specificity to produce highly fluorescent gold (Au) nanoclusters from soluble precursors by using peptide and protein templates to organize metal atoms into a highly ordered structure with novel optical properties.
Figure - Predictive design of noble metal nanoclusters. The iterative, a) synthesis, b) characterization (shown as fluorescence correlation spectroscopy), c) theoretical description (showing optical transitions mediated by the excited state dynamics), and d) applications testing of fluorescent metal nanoclusters.
LA-UR 09-03153
Au2 Au4(b) Au4(t) Au6(t) Au6(p)
Au6(dt) Au6(3d) Au8(s) Au8(h) Au8(3d)
1L
2L
3L
4L
5L
6L
Au6(t) Au6(p) Au6(dt) Au6(3d)
Geometries of four isomers of Au6 with ligand attachement from one (top) to full ligation (Last geometry in respective colums).
2.35
2.40
2.45
2.50
2.55
2.60
2.65
Au2 Au4(b) Au4(t) Au6(t) Au6(p) Au6(3d) Au6(dt) Au8(3d) Au8(h) Au8(s)
Bon
d L
ength
(Ǻ)
Gold Cluster
1L
2L
3L
4L
5L
6L
7L
Au2 Au4(b) Au4(t) Au6(t) Au6(p) Au6(3d) Au6(dt) Au8(3d) Au8(h) Au8(s)
2.50
2.55
2.60
2.65
2.70
2.75
2.80
2.85
2.90
Au2 Au4(b) Au4(t) Au6(t) Au6(p) Au6(3d) Au6(dt) Au8(3d) Au8(h) Au8(s)
Bon
d L
ength
(Ǻ)
Gold Cluster
Bare1L2L3L4L5L6L7L
Au2 Au4(b) Au4(t) Au6(t) Au6(p) Au6(3d) Au6(dt) Au8(3d) Au8(h) Au8(s)
Bond length variation between gold-gold and gold-ligand bonds in different isomers of small gold clusters, when ligands are attached starting from one to full ligation.
Au2
Au4(p)
G03
Total Energy (nm)-
270.917
-541.88
6
1st Transition Energy (nm) – GS
508.030
1049.390
NWChem
PBE0 B3LYP
DFT
Total Energy-
270.538
-541.28
3
1st Transition Energy (nm) – GS
624.775
1428.306
DFT-ZORA
Total Energy-
270.554
-541.31
4
1st Transition Energy (nm) – GS
625.771
1428.371
SODFT
Total Energy-
270.566
-541.34
4
1st Transition Energy (nm) – GS
620.456
1460.644
SODFT-ZORA
Total Energy-
270.581
-541.37
5
1st Transition Energy (nm) – GS
620.477
1460.890 Basis set with Polarization functional are required to investigate small gold clusters
with ligands. LANL2DZ reproduces the trends with one family of ligands. Ligands increase the energies and oscillator strengths of 1st transition of gold
clusters. Solvation effects partially simulate the effect of ligands on 1st transition energy for
bare clusters. For ligatedclusters solvation does not change 1st transition energy significantly but has a prominent effect on the oscillator strength.
Spin-orbit and ZORA relativistic effects do not significantly change energy for bare gold clusters considered.
Counter poise correction as well have small effect on energies (binding energy/mol).
Considered DFT functionals of different classes are consistent both qualitatively and quantitatively.
Ligand binding leads to the stabilization of more planar isomers of Au4 and Au6. No size scaling was revealed as judged by the 1st transition energy from Au2 to
Au8. Increase in number of ligands around the metal core reduces the metal-ligand
binding energy as expected. Ligands significantly effect the cluster geometries. Neutral gold clusters form stable bonds with primary and tertiary amine ligands,
which is in contrast to cationic gold cluster, which are stabilized with phosphenes only.
Number of ligands binding to a gold cluster largely depends upon cluster geometry.
Isomers of small gold clusters (Au2, Au4, Au6 and Au8)Relative energies for different isomers of small gold clusters with ligands. Comparison displays variations starting from saturated isomer with least number of ligands to the saturated siomer with most number of ligands. The lowest energy isomer is taken as reference structure (zero energy) for comparison.
DFT function
als
• SVWN5 • PBEPBE • TPSSTPS
S • B3LYP • CAM-
B3LYP
• LANL2DZ• LAN2DZ+
P• def2-SVP• def2-
TZVP• def2-
QZVP
• Gaussian 03/09
• Turbomol• NWChem
5.1
• Model -CPCM
• Solvent - Methanol
Basis Set
Solvation
Software
Theoretical Details
Excited State Properties - TDDFT
DFT Functional Binding Energy (kcal/ mol) Bond Lengths (A)
SVWN5 64.14 2.49PBEPBE 50.03 2.55TPSSTPSS 50.58 2.54
B3LYP 43.20 2.57CAM-B3LYP 41.62 2.55
Exp* 53.00 2.47
SVWN5 67.72 2.49PBEPBE 53.33 2.55TPSSTPSS 54.39 2.53B3LYP 41.14 2.57CAM-B3LYP 45.61 2.55
Solvated (Methanol)
Au2
Bonding energies and bond lengths of Au2 calculated with different (5 generations) DFT functionals compared with experimental data.
Representative geometries of Au2 and Au4 cluster with ligand attached as PMe3, (a) Au2(PMe3)2, (b) Au4(PMe3)2, (c) Au4(PMe3)4, (d) Au4(NMe3)4.
* Kordis et. al., Journal of Chemical Physics, 1974, 61, 5114.
-62
-52
-42
-32
-22
-12
NH3 NMe3 PH3 PMe3NH3 NMe3 PH3 PMe3
Au2L2
/ m
ol)
-62
-52
-42
-32
-22
-12
NH3 NMe3 PH3 PMe3NH3 NMe3 PH3 PMe3
Au4L2
Ener
gy p
er Li
gand
(kc
al
-62
-52
-42
-32
-22
-12
NH3 NMe3 PH3 PMe3
SVWN5 PBETPSS B3LYPCAM-B3LYP
NH3 NMe3 PH3 PMe3
Au4L4
Bind
ing
Type of Ligand
-44
-39
-34
-29
-24
-19
-14
NH3 NMe3 PH3 PMe3NH3 NMe3 PH3 PMe3
Au2L2
/ m
ol)
-44
-39
-34
-29
-24
-19
-14
NH3 NMe3 PH3 PMe3NH3 NMe3 PH3 PMe3
Au4L2
Ener
gy p
er Li
gand
(kc
al
-44
-39
-34
-29
-24
-19
-14
NH3 NMe3 PH3 PMe3
LANL2DZ LANL2DZ-PSVP TZVPQZVP TZVP (sol)
NH3 NMe3 PH3 PMe3
Au4L4
Type of Ligand
Bind
ing
Binding energies per ligand in kcal/mol for geometries of Au2 and Au4 in partial and fully ligated forms determined using various DFT functionals (left, TZVP basis set has been used for all calculations) and various basis sets (right, TPSS functional has been used for all calculations).
BENCHMARKING
2.0
2.5
3.0
3.5
NH3 NMe3 PH3 PMe3 NH3 NMe3 PH3 PMe3
Au4L2
1.5
2.0
2.5
3.0
NH3 NMe3 PH3 PMe3
SVWN5PBEPBETPSSTPSSB3LYPCAM-B3LYP
NH3 NMe3 PH3 PMe3
Au4L4
3.0
3.5
4.0
4.5
5.0
NH3 NMe3 PH3 PMe3 NH3 NMe3 PH3 PMe3
Au2L2
2.0
2.5
3.0
3.5
NH3 NMe3 PH3 PMe3 NH3 NMe3 PH3 PMe3
Au4L2
1.5
2.0
2.5
3.0
NH3 NMe3 PH3 PMe3
SVWN5PBEPBETPSSTPSSB3LYPCAM-B3LYP
NH3 NMe3 PH3 PMe3
Au4L4
3.0
3.5
4.0
4.5
5.0
NH3 NMe3 PH3 PMe3 NH3 NMe3 PH3 PMe3
Au2L2
1st T
ran
siti
on
E
nerg
y (e
V)
Type of Ligand
SODFT and ZORA corrections for Au2 and Au4(p) bare clusters. Oscillator strengths for these cluster calculations are zero.
LUMO HOMO
Au2(NMe3)2
CAM-B3LYP =4.816 eV f=0.128
=0.96424
TPSS =4.407 eV f=0.000
=0.98933
Au4(PMe3)2
(Sol)
CAM-B3LYP =3.206 eV f=0.733
=0.94561
TPSS =2.700 eV f=0.003
=0.99798
Au4(NMe3)4
CAM-B3LYP =2.728 eV f=0.000
= 0.99137
TPSS =2.482 eV f=0.054
= 0.99336
Lowest energy state molecular orbitals for ligated Au2 and Au4 with CAM-B3LYP and TPSS. Figure showing different lowest states corresponding to the use of different DFT functionals for TDDFT absorption calculations.
Au2
Au4(t)
Au6(t)
Au8(d)
Au6(d)
Au6(d1)
Au4(p)
Au6(p)
Au8(t)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Au2 Au4 Au6 Au8Au2 Au4 Au6 Au8
Au6(t)
Au6(p)
Au6(dt)
Au6(3d)
Au2
Au4(b)
Au4(t)
Au8(3d)
Au8(s)
1st transition energy (eV) for geometries of Au2 and Au4 in partial and fully ligated forms determined using various DFT functionals with (right) and without solvent (left)
1st transition energy of several lowest energy isomers of small gold clusters (Au2-Au8)
Optical Properties
Geometry & Energetics
