Ligand and Solvent Effects on the Structural and Optical Properties of Au13L83+ Clusters: a Density Functional Theory Study

Density functional theory (DFT) calculations have been performed to develop a systematic structural analysis of Au₁₃L₈³⁺, where L = SCH₃, SeCH₃, SCH₂OCH₃ and S(CH₂)₂NH₂, in order to examine the influence of different ligands. Binding energy calculations indicate that the gold core is more stabilized by the ligand in the following sequence S(CH₂)₂NH₂ > SCH₂OCH₃ > SeCH₃ > SCH₃. Natural bond orbital (NBO) analysis describes the interaction between the gold and the ligands, showing that the strongest electron donation occurs from a lone pair orbital on the sulfur and selenium atoms to the antibonding acceptor σ^* (Au-S) and σ^* (Au-Se) orbitals, respectively. The NBO analysis allowed to understand the origin of enhanced stability of the [Au₁₃(S(CH₂)₂NH₂)₈]³⁺. Time-dependent DFT (TDDFT) calculations have been performed to simulate the optical absorption spectra of Au₁₃L₈³⁺ in gas phase and under the effect of solvents with different polarities. The absorption spectrum of [Au₁₃(S(CH₂)₂NH₂)₈]³⁺ shows a spectral profile that differs considerably from the others in gas phase and which is strongly affected by the solvent.

Keywords:
gold clusters; DFT calculations; optical spectrum; solvent effect

Authorship

Edna S. Machado

Departamento de Química, Universidade Federal de Sergipe, Av. Marechal Rondon, s/n, Jardim Rosa Elze, 49100-000 São Cristóvão-SE, BrazilUniversidade Federal de SergipeBrazilSão Cristóvão, SE, BrazilDepartamento de Química, Universidade Federal de Sergipe, Av. Marechal Rondon, s/n, Jardim Rosa Elze, 49100-000 São Cristóvão-SE, Brazil

http://orcid.org/0000-0002-3482-1590

Nailton M. Rodrigues

Marcus V. A. Prado

Departamento de Física, Universidade Federal de Sergipe, Av. Marechal Rondon, s/n, Jardim Rosa Elze, 49100-000 São Cristóvão-SE, BrazilUniversidade Federal de SergipeBrazilSão Cristóvão, SE, BrazilDepartamento de Física, Universidade Federal de Sergipe, Av. Marechal Rondon, s/n, Jardim Rosa Elze, 49100-000 São Cristóvão-SE, Brazil

José D. L. Dutra

Nivan B. da Costa Júnior

Viviane C. Felicíssimo ^** e-mail: felicissimo@ufs.br

* e-mail: felicissimo@ufs.br

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables

Figures (5)
Tables (2)

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Figure 1
Optimized structures of (a) [Au₁₃(SCH₃)₈]³⁺; (b) [Au₁₃(SeCH₃)₈]³⁺; (c) [Au₁₃(SCH₂OCH₃)₈]³⁺; (d) [Au₁₃(S(CH₂)₂NH₂)₈]³⁺ in gas phase. Color labels: yellow: Au, pink: S, green: Se, orange: C, red: O, blue: N and white: H.

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Figure 2
NBO orbitals associated with charge transfer analysis in [Au₁₃(SCH₃)₈]³⁺.

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Figure 3
Theoretical absorption spectrum and the respective Kohn-Sham (KS) orbital level diagram of (A) [Au₁₃(SCH₃)₈]³⁺; (B) [Au₁₃(SeCH₃)₈]³⁺; (C) [Au₁₃(SCH₂OCH₃)₈]³⁺ and (D) [Au₁₃(S(CH₂)₂NH₂)₈]³⁺ clusters. Each KS orbital is drawn to indicate the relative contributions (line length with color labels) of the atomic orbitals. The orbital symmetry is indicated within O_h point group for (A) and (B) and within D4h point group for (C) and (D). The quasi-degenerate KS orbitals in D4h symmetry are grouped according to the O_h correlation table: a_2u + e_u → t_t1u, b_2g + e_g → t_2g and b_1g + a_1g → e_g. The energy values of each peak are specified in the absorption spectra.

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Figure 4
Molecular orbitals with the respective energies and symmetries of (a) [Au₁₃(SCH₃)₈]³⁺; (b) [Au₁₃(SeCH₃)₈]³⁺; (c) [Au₁₃(SCH₂OCH₃)₈]³⁺; (d) [Au₁₃S(CH₂)₂NH₂)₈]³⁺ clusters. The orbital symmetry is indicated within O_h point group for (a) and (b) and within D4h point group for (c) and (d). The quasi-degenerate KS orbitals in D_4h symmetry are grouped according to the O_h correlation table: a_2u + e_u → t_t1u, b_2g + e_g → t_2g and b_1g + a_1g → e_g. An average energy is indicated for the quasi-degenerate KS orbitals in D4h symmetry.

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Figure 5
Optical absorption spectra in gas phase and under the effect of different solvents (A) [Au₁₃(SCH₃)₈]³⁺; (B) [Au₁₃(SeCH₃)₈]³⁺; (C) [Au₁₃(SCH₂OCH₃)₈]³⁺; (D) [Au₁₃(S(CH₂)₂NH₂)₈]³⁺ clusters.

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Table 1
Structural parameters (bond lengths and bond angles) of the Au₁₃L₈³⁺ clusters and their binding energies (Eb)

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Table 2
Donor-acceptor natural bond orbital interactions in the Au₁₃L₈³⁺ clusters and their second-order perturbation stabilization energies (E(2))

Figure 1 Optimized structures of (a) [Au₁₃(SCH₃)₈]³⁺; (b) [Au₁₃(SeCH₃)₈]³⁺; (c) [Au₁₃(SCH₂OCH₃)₈]³⁺; (d) [Au₁₃(S(CH₂)₂NH₂)₈]³⁺ in gas phase. Color labels: yellow: Au, pink: S, green: Se, orange: C, red: O, blue: N and white: H.

Figure 2 NBO orbitals associated with charge transfer analysis in [Au₁₃(SCH₃)₈]³⁺.

Figure 3 Theoretical absorption spectrum and the respective Kohn-Sham (KS) orbital level diagram of (A) [Au₁₃(SCH₃)₈]³⁺; (B) [Au₁₃(SeCH₃)₈]³⁺; (C) [Au₁₃(SCH₂OCH₃)₈]³⁺ and (D) [Au₁₃(S(CH₂)₂NH₂)₈]³⁺ clusters. Each KS orbital is drawn to indicate the relative contributions (line length with color labels) of the atomic orbitals. The orbital symmetry is indicated within O_h point group for (A) and (B) and within D4h point group for (C) and (D). The quasi-degenerate KS orbitals in D4h symmetry are grouped according to the O_h correlation table: a_2u + e_u → t_t1u, b_2g + e_g → t_2g and b_1g + a_1g → e_g. The energy values of each peak are specified in the absorption spectra.

Figure 4 Molecular orbitals with the respective energies and symmetries of (a) [Au₁₃(SCH₃)₈]³⁺; (b) [Au₁₃(SeCH₃)₈]³⁺; (c) [Au₁₃(SCH₂OCH₃)₈]³⁺; (d) [Au₁₃S(CH₂)₂NH₂)₈]³⁺ clusters. The orbital symmetry is indicated within O_h point group for (a) and (b) and within D4h point group for (c) and (d). The quasi-degenerate KS orbitals in D_4h symmetry are grouped according to the O_h correlation table: a_2u + e_u → t_t1u, b_2g + e_g → t_2g and b_1g + a_1g → e_g. An average energy is indicated for the quasi-degenerate KS orbitals in D4h symmetry.

Figure 5 Optical absorption spectra in gas phase and under the effect of different solvents (A) [Au₁₃(SCH₃)₈]³⁺; (B) [Au₁₃(SeCH₃)₈]³⁺; (C) [Au₁₃(SCH₂OCH₃)₈]³⁺; (D) [Au₁₃(S(CH₂)₂NH₂)₈]³⁺ clusters.

Table 1 Structural parameters (bond lengths and bond angles) of the Au₁₃L₈³⁺ clusters and their binding energies (Eb)

Parameter	Au₁₃L₈³⁺
Parameter	L = SCH₃	L = SeCH₃	L = SCH₂OCH₃	L = S(CH₂)₂NH₂
r(Au_c–Au_s) / Å	3.642 ± 0.003	3.819 ± 0.002	3.636 ± 0.001	3.643 ± 0.000
r(Au_s–Au_s) / Å	3.642 ± 0.001	3.819 ± 0.001	3.627 ± 0.000	3.625 ± 0.003
r(Au_s–S) / Å	2.390 ± 0.000		2.385 ± 0.000	2.385 ± 0.000
r(Au_s–Se) / Å		2.487 ± 0.000
r(S–C) / Å	1.846 ± 0.002		1.868 ± 0.000	1.865 ± 0.000
r(Se–C) / Å		1.987 ± 0.000
∠ (Au_s–S–Au_s) / degree	99.292 ± 0.031		98.973 ± 0.015	98.841 ± 0.001
∠ (Au_s–Se–Au_s) / degree		100.270 ± 0.034
∠ (Au_s–S–C_s) / degree	118.391 ± 0.105		117.017 ± 0.075	119.235 ± 0.001
∠ (Au_s–Se–C_s) / degree		117.623 ± 0.048
E_b / eV	−3.05	−3.10	−3.15	−3.20

Au_c: central gold atom; Au_s: surrounding gold atom.

Table 2 Donor-acceptor natural bond orbital interactions in the Au₁₃L₈³⁺ clusters and their second-order perturbation stabilization energies (E(2))

Au₁₃L₈³⁺	Charge transfer	E(2) / (kcal mol^-1)
L = SCH₃	$n_{s} \to σ_{{Au}_{s} - S}^{*}$	49.36
	$σ_{{Au}_{s} - S} \to n_{{Au}_{c}}^{*}$	13.68
	$n_{s} \to n_{{Au}_{s}}^{*}$	9.56
L = SeCH₃	$n_{Se} \to σ_{{Au}_{s} - Se}^{*}$	54.78
	$σ_{{Au}_{s} - Se} \to n_{{Au}_{c}}^{*}$	20.19
	$n_{Se} \to n_{{Au}_{c}}^{*}$	13.85
L = SCH₂OCH₃	$n_{s} \to σ_{{Au}_{s} - S}^{*}$	67.95
	$σ_{{Au}_{s} - S} \to n_{{Au}_{c}}^{*}$	19.07
	$n_{s} \to n_{{Au}_{s}}^{*}$	10.66
L = S(CH₂)₂NH₂	$n_{s} \to σ_{{Au}_{s} - S}^{*}$	68.95
	$σ_{{Au}_{s} - S} \to n_{{Au}_{x}}^{*}$	20.28
	$n_{s} \to n_{{Au}_{s}}^{*}$	11.12

Au_c: central gold atom; Au_s: surrounding gold atom; n, n*, σ and σ*: refers, respectively, to the lone pair, empty lone pair, bonding and antibonding orbitals.

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Ligand and Solvent Effects on the Structural and Optical Properties of Au13L83+ Clusters: a Density Functional Theory Study

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[1] * e-mail: felicissimo@ufs.br