Density Functional Analysis of Geometries and Electronic Structures of

ARTICLE pubs.acs.org/JPCA

Density Functional Analysis of Geometries and Electronic Structures of Gold-Phosphine Clusters. The Case of Au4(PR3)42þ and Au4(μ2-I)2(PR3)4. Sergei A. Ivanov,*,† Indika Arachchige,† and Christine M. Aikens*,‡ † ‡

K771, MPA-CINT, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States Department of Chemistry, Kansas State University, Manhattan, Kansas 66506, United States

bS Supporting Information ABSTRACT: Geometries, ligand binding energies, electronic structure, and excitation spectra are determined for Au4(PR3)42þ and Au4(μ2-I)2(PR3)4 clusters (R = PH3, PMe3, and PPh3). Density functionals including SVWN5, XR, OPBE, LC-ωPBE, TPSS, PBE0, CAM-B3LYP, and SAOP are employed with basis sets ranging from LANL2DZ to SDD to TZVP. Metalmetal and metalligand bond distances are calculated and compared with experiment. The effect of changing the phosphine ligands is assessed for geometries and excitation spectra. Standard DFT and hybrid ONIOM calculations are employed for geometry optimizations with PPh3 groups. The electronic structure of the goldphosphine clusters examined in this work is analyzed in terms of cluster (“superatom”) orbitals and d-band orbitals. Transitions out of the d band are significant in the excitation spectra. The use of different basis sets and DFT functionals leads to noticeable variations in the relative intensities of strong transitions, although the overall spectral profile remains qualitatively unchanged. The replacement of PMe3 with PPh3 changes the nature of the electronic transitions in the cluster due to low-lying π*-orbitals. To reproduce the experimental geometries of clusters with PPh3 ligands, computationally less expensive PH3 or PMe3 ligands are sufficient for geometry optimizations. However, to predict cluster excitation spectra, the full PPh3 ligand must be considered.

’ INTRODUCTION Cationic goldphosphine clusters have been known for decades and have increasingly being used in various applications such as biolabeling, catalysis, or gold nanoparticle precursors.14 Since the early work of Malatesta in 1969,5 a multitude of X-ray crystal structures have been determined for these systems, including Au4(μ2-I)2(PPh3)4,6 Au4(μ2-SnCl3)2(PPh3)4,7 Au4(PtBu)32þ (tBu = tert-butyl),8 Au4(PMes3)42þ (Mes = mesityl),9 Au4(dppm)3I2,10 distorted octahedral Au6C(P(C6H4Me)3)62þ (Me = methyl),11,12 bitetrahedral Au6(PPh3)62þ,13 Au6(PPh3)4(Co(CO)4)22þ,14 Au6(dppp)42þ,15 Au7(PPh3)7þ,14 Au8(PMes3)62þ,9 Au8(PPh3)72þ,14 Au9(dpph)43þ,16 Au11(PR3)7X3 (X = SCN, I, S-4-NC5H4; R = Ph),5,17,18 Au11(PPh3)8Cl2þ,16 Au11(PMePh2)103þ,19 and Au13(PMe2Ph)10Cl23þ,20 and others. All clusters aforementioned (with an exception of Au4(dppm)3I2 and Au6(dppp)42þ) are characterized by the radial bonding of a single donor ligand to each surface gold atom, and by the formal average gold oxidation state below 1, from formal þ1/2 in Au4(PR3)42þ to þ1/4 in Au8(PR3)82þ. Several theoretical studies have examined the electronic structure of these goldphosphine systems. In 1976, using extended-H€uckel calculations, Mingos showed that the orbital picture of clusters such as octahedral Au62þ and Au6(PPh3)62þ is dominated by the overlap of the diffuse metal 6s orbitals forming delocalized r 2011 American Chemical Society

orbitals; due to the small 5d5d overlap, the 5d orbitals form a tight band of orbital energies below the 6s band, whereas the metalphosphorus bonding increases the amount of 6p character in the higher-lying delocalized orbitals.21 In later works, the importance of tangential aurophilic interaction between adjacent gold atoms, especially in the systems with centering gold atom (e.g., Au9(PR3)83þ, Au11L10qþ, Au13L12qþ), has been pointed out: this type of interaction appears to significantly affect the stability of these systems. Pyykk€o and Runeberg calculated the geometric structure of Au42þ and Au4(PH3)42þ using the MP2 level of theory, which partially takes into account the aurophilic nature of AuAu bonding and found that the AuAu bond lengths for Au4(PH3)42þ are in good agreement with the experimental crystal structure of Au4(PtBu3)42þ.22 On the other hand, Calhorda et al., employing MP2 calculations similar to those of the LANL2DZ basis set, predicted longer bond lengths that are likely due to the limitations of the used basis set, which lacks polarization treatment.23 Boca used relativistic and quasi-relativistic CNDO/1 calculations to assess the differences in PH3, PMe3, Received: January 12, 2011 Revised: May 13, 2011 Published: June 16, 2011 8017

dx.doi.org/10.1021/jp200346c | J. Phys. Chem. A 2011, 115, 8017–8031

The Journal of Physical Chemistry A and PtBu3 model ligands and found significant shifts in orbital energies although the geometrical effects were minor.24 Like Au6(PPh3)62þ, the gold 5d levels in this system were also found to be located just below the top of the valence band.24 In 1981, Stone offered a tensor spherical harmonics (TSH) model for boranes and transition metal clusters to rationalize cluster stability and structure; this model uses spherical harmonics in an LCAO-like approach.25 Also in the early 1980s, Knight, Clemenger, de Heer, and others established an electron shell model to explain the observance of particularly stable alkali clusters (for a review, see ref 26). Based significantly on this approach together with the Jellium model, the “superatom” model has been later set forth by H€akkinen and co-workers and applied to goldphosphine as well as goldthiolate clusters and nanoparticles.27 In the superatom picture, metal clusters may be electronically stabilized by the adsorption of ligands, similarly to atomligand complexes. The electron count n of the AuNXMLSz cluster (X = electron-withdrawing or electron-localizing ligand; L = Lewis base type ligand) is calculated as27 n ¼ N Mz If n corresponds to 2, 8, 18, 34, 58, etc., which are “magic” numbers commonly associated with electronic stability in nearly spherical (or highly symmetrical) systems,26 the superatom complex may have special stability. The aufbau rule for filling of these superatomic orbitals is 1S2 | 1P6 | 1D10 | 2S2 1F14 | 2P6 1G18 | and so on, where SPDFG denote the angular momenta of the orbitals.27 When n is not equal to one of these spherical magic numbers, the cluster is expected to undergo a distortion similar to JahnTeller in metal complexes with partially occupied atomic orbitals. For example, the hypothetical “octahedral” Au6(P(C6H4Me)3)62þ cluster would have only partial occupancy of the highest occupied molecular orbital (HOMO) of T1u symmetry (or three triply degenerate superorbitals of P symmetry). The partial occupancy of the HOMO combined with energetically favorable bonding of opposite gold atoms in an octahedron would cause a compression along one of the 4-fold axes reducing the cluster symmetry from Oh to D4h and further to experimentally found D2h (to maintain the maximum possible AuAu contacts)11,21 In this cluster, the highest occupied and lowest unoccupied orbitals can now be viewed as nondegenerate superorbitals with P angular momentum. In contrast, Au11(BINAP)4Cl2þ with 8 electrons has a close-tospherical (incomplete) icosahedral core, where the HOMO becomes a superorbital of P angular momentum and the LUMO of D angular momentum.28 In this work, we undertook a density functional theory (DFT) study of the smallest known gold-phosphine cluster, Au4(PR3)42þ (Figure 1A), and its neutral halogenated analogue, Au4(μ2-I)2(PR3)4 (Figure 1B). The goals of our work were (1) to evaluate the applicability of the superatom model to these small systems within DFT framework, because this model is being used extensively in qualitative analysis of cluster systems, (2) to benchmark the performance of density functionals of different generations and basis sets of varying flexibility in their ability to accurately model cluster molecular structures and absorption spectra, and importantly, (3) to assess the applicability of various ligand models (PH3, PMe3, or PPh3) for the description of real cluster systems. We first report on the results of cluster geometry optimizations and their comparison with experimental data, followed by the predicted metalligand binding energies. In the second part of this work, we present the

ARTICLE

Figure 1. Molecular structures of (A) Au4(PMe3)42þ and (B) Au4(μ2-I)2(PPh3)4 clusters. The clusters’ interiors without CH3 and C6H5 substituents are presented below the corresponding complete structure.

analysis of cluster electronic structure followed by the analysis of calculated absorption spectra of the clusters and the comparison with limited experimental information available. This work provides insights into the physics of the phosphine-stabilized Au4 cluster and suggests model systems and methods that would be effective for determining geometries, binding energies, and excitation energies of related clusters and nanoparticles.

’ COMPUTATIONAL METHODOLOGY The calculations have been performed with commercially available Gaussian0929 and ADF30 computational packages. Several DFT functionals from different levels of density functional theory have been utilized in the current work. Local density approximation (LDA) is represented by the local-exchange-only XR3133 (R = 0.7) and local exchange-correlation SVWN53134 models. Pure DFT generalized gradient approximation (GGA)corrected approach is represented by the OPBE35,36 functional. The hybrid GGA functional family is represented by the very successful PBE0 form3638 with 25% of orbital exchange; its performance is compared with that of the next generation, kinetic-energy density-dependent (meta-GGA) DFT functionals represented by the TPSS39 model, which is a functional that demonstrated good performance in recently reported assessments of gold cluster stability and geometry modeling.40 It is well established4143 that pure GGA and hybrid DFT methods tend to yield elongated bonds relative to experimental structures, while LDA functionals typically lead to close or slightly underestimated bond lengths, so each of these types of functionals is investigated in this study. Previous work on thiolate-protected Au25 nanoparticles43 and phosphine-protected gold clusters44 suggests that GGA, meta-GGA, hybrid, and ab initio (e.g., MP2) levels of theory typically yield longer bond lengths than LDA functionals, which tend to be in good agreement with experiment. Linear-response time-dependent density functional theory (TDDFT) is used to determine excited state energetics and compositions. We have considered the long-range corrected version of the popular B3LYP functional,45,46 namely CAMB3LYP,47 which accounts for long-range exchange effects via 8018

dx.doi.org/10.1021/jp200346c |J. Phys. Chem. A 2011, 115, 8017–8031

The Journal of Physical Chemistry A Coulomb-attenuating method, together with a long-range corrected version of the ωPBE (HSE) functional (LC-ωPBE).4851 In addition, the asymptotically correct statistical average of orbital potentials (SAOP)52,53 is also used to calculate excitation energies. These methods, which have been developed in the last 12 years and are commercially available, correct the asymptotic behavior of the functionals with a goal of predicting accurate excitation energies. We use several different Gaussian type orbital (GTO) basis sets either uniformly for the whole cluster or as a part of ONIOM hybrid method (vide infra): the relatively small CEP-31G splitvalence ECP basis set by StevensBaschKrauss;54,55 still one of the most commonly used basis set for late transition metals, the LANL2DZ double-ζ quality basis set with the corresponding LANL2 effective core potential (ECP)5658 and D95 V59 allelectron treatment of C and H elements; the more flexible SDD60 triple-ζ quality 18-electron basis set with StuttgartDresden ECP for Au and I and D95 all-electron treatment of P, C, and H; the triple-ζ quality full-electron TZVP55 basis set Ahlrichs et al. with polarization on all atoms was used for P, C, and H atoms combined with valence-electrons only TZVP61 treatment and Def2 ECP treatment of core electrons in Au and I. These basis sets are developed with ECPs that account for scalar relativistic effects. The full-electron TZVP basis set on P, C, and H was used as it is available in Gaussian 09, whereas Def2-TZVP combinations on Au and I were obtained from the basis set exchange.6264 A similar Slater-type orbital triple-ζ plus polarization basis set is implemented in ADF and abbreviated as TZP (all electron) or TZP.4f (a [1s2-4f14] frozen core for Au, a [1s2-4d10] frozen core for I, a [1s2-2p6] frozen core for P, and a [1s2] frozen core for C). In ADF, scalar relativistic effects are incorporated using the zeroth-order regular approximation (ZORA)65 and ZORA-compliant basis sets. Solvation effects were simulated by using implicit CPCM solvation model66,67 as implemented in Gaussian09 and the conductor-like screening model (COSMO)68 in ADF with acetonitrile (CH3CN) or tetrahydrofuran (THF) being solvents of choice. For the calculations of electronic spectra, the following minor simplifications were introduced into the experimental geometries of Au4(PtBu3)42þ [ref 8] and Au4(PMes3)42þ [ref 9]. The former is represented by the Au4(PMe3)42þ cluster with t Bu replaced by CH3 with PC bond distance set at 1.82 Å, the average PC bond in complexes with PMe3 as found in Cambridge Structural Database (instead of the experimental 1.92 Å value for the PC(tBu) bond) and the CH bond distances in CH3 set to 1.096 Å. The latter compound is represented by Au4(PPh3)42þ where each CH3 group of the Mes substituent was replaced by hydrogen at 0.958 Å away from the corresponding carbon. The experimental structure of Au4(μ2-I)2(PPh3)4 [ref 6] was used with no adjustments. To further simplify the calculations involving such a large ligand as PPh3, the hybrid quantum mechanical method ONIOM69 was utilized as implemented in the Gaussian09 package. It combines the calculations with PPh3 ligands at specified lower level of theory (either smaller basis set or universal force field (UFF)70 molecular mechanics method were tested) with calculations of the same metal core with PH3 ligands instead of PPh3 at higher level. The following ONIOM combinations were tested (high level/low level): DFT-LANL2DZ/UFF and DFT-TZVP/ UFF, where DFT stands for a chosen DFT functional. The natural atomic charges and electron populations were elucidated using the NBO-5.0W71 standalone package, because

ARTICLE

NBO-3.0 algorithm implemented in Gaussian 09, as we discovered, unphysically overpopulates 6p atomic orbitals of gold leading to skewed results of natural population analysis.

’ GEOMETRIC ANALYSIS OF Au4(PR3)42þ AND Au4(m2-I)2(PR3)4 CLUSTERS (R = H, Me, Ph) Experimental Geometries. The structures of two clusters with Au4(PR3)42þ stoichiometry have been determined previously by means of single-crystal X-ray analysis, with R = tertbutyl (tBu) [ref 8] or 2,4,6,-trimethylbenzyl (Mes) [ref 9]. In both clusters, the gold core has an idealized Td symmetry with phosphine ligands radially bonded to gold atoms (Figure 1A). In Au4(PtBu3)42þ [ref 8], the metalmetal bond lengths are spread within the 2.7032.730 Å interval with an average of 2.714 Å, and AuP bond distances are determined to be 2.3032.307 Å. The average metalmetal bond length in Au4(PMes3)42þ is slightly longer at 2.734 Å,9 which is likely due to the bulky nature of the PMes3 ligand compared to PtBu3. For the same reason, all AuP bonds in this cluster are also elongated, with three AuP bonds being 2.344 Å and the fourth AuP measured to be 2.389 Å. In contrast to the tetrahedral dicationic Au4(PR3)42þ, the structures of Au4(μ2-X)2(PPh3)4 possess approximate D2d symmetry (Figure 1B). This type of cluster is generated from the tetrahedral Au4(PR3)42þ by the addition of two bridging iodide anions to two AuAu bonds that constitute opposite edges of Au4 tetrahedron. Consequently, goldgold bond lengths between two atoms bridged by the same halide ion, AuAu(base), differ from ones between atoms adjacent to separate halides, AuAu(diag). The AuAu(base) were measured to be 2.648 Å and AuAu(diag) have been measured to vary between 2.771 and 2.829 Å in Au4(μ2-I)2(PPh3)4 [ref 6] with the average of 2.793 Å. The AuP bonds in the same cluster were found to be shorter than ones in the tetrahedral analogue, at 2.293 and 2.289 Å. In the case of X = SnCl3,7 neither AuAu(base) nor AuAu(diag) bonds change significantly and extent on average to 2.635 Å and 2.793 Å, respectively, with AuP bonds being av 2.319 Å. Below we have assessed the performance of different computational approaches to accurately predict bond lengths in both types of clusters, using such model phosphine ligands as phosphine (PH3), trimethylphosphine (PMe3), or triphenylphosphine (PPh3). In addition, we performed the analysis of such factors as the nature of phosphine substituents and the event of cluster halogenations on the cluster geometry. Density Functional and Basis Set Effect on Cluster Geometries. For the DFT functionals examined in this work, optimized AuAu bond lengths (shown in Tables 1 and 2) increase in the following order: SVWN5 < XR < OPBE < LCωPBE < TPSS ≈ PBE0 < CAM-B3LYP. It is noteworthy that this order is independent of the cluster structure considered or the basis set used for calculations. As observed previously,4143 pure GGA and hybrid DFT methods tend to produce elongated bonds relative to experimental structures, while the use of LDA functionals results in better estimation of bond lengths, and our results appear in full agreement with this trend. Also, independently of the basis set or a cluster, the average calculated metal metal bond length increases by 0.070.08 Å as the functional varies from SVWN5 to CAM-B3LYP, with the difference in the prediction of the AuP bond lengths being of a similar magnitude upon the functional change from SVWN5 to CAM-B3LYP: 0.06 Å in Au4(PR3)42þ systems and 0.07 Å in Au4(μ2-I)2(PR3)4 8019


The Journal of Physical Chemistry A

ARTICLE

Table 1. Bond Lengths and Root-Mean-Square (RMS) Values (Å) of Optimized Cluster Structures at Different Levels of Theory for Au4(PH3)42þ, Au4(PMe3)42þ, Au4(μ2-I)2(PH3)4, and Au4(μ2-I)2(PMe3)4 Clusters, and Their Comparison with Experimental Data PBE0 functional: basis set:

TZVP

TZVPa

TPSS TZVP

SVWN5 TZVP

XR TZP.4f

LC-ωPBE TZVP

CAM-B3LYP TZVP

OPBE TZVP

experiment, Å Au4(PtBu3)42þ

Au4(PH3)42þ

Au4(PMes3)42þ

d(AuAu)

2.770

2.763

2.701

2.722

2.757

2.787

2.748

2.714 [ref 8]

2.734 [ref 9]

d(AuP)

2.329

2.342

2.282

2.293

2.323

2.347

2.304

2.305 [ref 8]

2.355 [ref 9]

RMS (Bu)b

0.05

0.04

0.02

0.01

0.04

0.06

0.03

RMS (Mes)c

0.03

0.02

0.05

0.04

0.03

0.04

0.03 Au4(PtBu3)42þ

Au4(PMe3)42þ

Au4(PMes3)42þ

d(AuAu) d(AuP)

2.776 2.338

2.771 2.332

2.767 2.349

2.707 2.293

2.734 2.302

2.762 2.331

2.792 2.354

2.754 2.316

2.714 [ref 8] 2.305 [ref 8]

2.734 [ref 9] 2.355 [ref 9]

1.899 [ref 8]

1.819 [ref 9]

d(PC)

1.826

1.833

1.844

1.811

1.809

1.816

1.826

1.832

RMS (Bu)b

0.05

0.05

0.05

0.01

0.02

0.04

0.07

0.03

RMS (Mes)c

0.03

0.03

0.03

0.04

0.03

0.03

0.04

0.03 Au4(μ2-I)2(PPh3)42þ

Au4(μ2-I)2(PH3)4 d(AuAu), base

2.647

2.645

2.605

2.641

2.634

2.653

2.624

2.648 [ref 6]

d(AuAu), diag

2.877

2.870

2.809

2.803

2.857

2.891

2.861

2.794 [ref 6]

d(AuP)

2.319

2.329

2.273

2.273

2.308

2.345

2.286

2.291 [ref 6]

d(AuI) RMS (Au, P)d

2.917 0.06

2.932 0.05

2.844 0.02

2.941 0.01

2.881 0.04

2.958 0.07

2.881 0.04

2.922, 2.968 [ref 6]

RMS (Au, P, I)e

0.05

0.05

0.06

0.01

0.05

0.06

0.05

d(AuAu), base

2.668

2.663

2.619

2.650

2.681

2.639

Au4(μ2-I)2(PMe3)4 2.645

2.669

Au4(μ2-I)2(PPh3)4 2.648 [ref 6]

d(AuAu), diag

2.832

2.875

2.830

2.766

2.791

2.828

2.853

2.838

2.794 [ref 6]

d(AuP)

2.325

2.315

2.336

2.279

2.278

2.314

2.346

2.300

2.291 [ref 6]

d(AuI)f

2.947 3.148

2.906

3.068

2.950 3.020

2.976 3.003

2.994 2.947

3.096

2.956

2.922, 2.968 [ref 6]

d(PC)

1.834

1.836

1.852

1.820

1.821

1.823

1.832

1.841

1.825 [ref 6]

RMS (Au, P)d RMS (Au, P, I)e

0.03 0.06

0.05 0.05

0.04 0.07

0.02 0.03

0.01 0.03

0.03 0.03

0.05 0.09

0.03 0.02

a

ONIOM approach was used: PBE0/TZVP level for Au4P4/Au4P4I2 core and UFF for methyl groups of Au4(PMe3)42þ and Au4(μ2-I)2(PMe3)4. RMS is calculated on the basis of experimental values for Au4(PtBu3)42þ.8 c RMS is calculated on the basis of experimental values for Au4(PMes3)42þ.9 d RMS is calculated with values for AuAu and AuP bonds only. e RMS is calculated with values for AuAu, AuP, and AuI bonds. f Geometry optimizations of Au4(μ2-I)2(PMe3)4 with certain DFT functionals result in unequal AuI bonding to the same halogen atom. b

clusters. The performance of two tested long-range corrected functionals does not point to any particular trend: LC-ωPBE geometric results are positioned between those of pure DFT and hybrid DFT functionals and CAM-B3LYP produces the longest bonds obtained in our study. Overall, the average metalmetal separation in considered clusters appears to be only moderately sensitive to DFT functional used in geometry optimizations, with bond length variations comprising 23% of the bond length value. The TPSS functional was considered for its notable reported performance in estimation of metalligand binding energies. As can be concluded from presented geometry optimization results, the performance of TPSS is practically identical to that of PBE0. Although it has been reported prior that the “work horse” of basis sets for heavy metals, LANL2DZ, lacks the necessary flexibility to accurately describe the bonding between metal and light elements of ligands, it is still widely used in similar calculations and the assessment of its performance in the cluster system of interest is warranted. From the obtained geometry optimization results it follows that the increase in the basis set

flexibility from LANL2DZ to SDD to TZVP yields a small systematic decrease in goldgold bonding of tetrahedral Au4(PR3)42þ clusters, by 0.01 Å overall. In contrast, the AuP bonds are more sensitive to the basis set used, decreasing by 0.03 Å as double-ζ quality LANL2DZ is replaced by the triple-ζ quality SDD; these bond lengths further decrease by 0.07 Å as the polarization treatment improves from SDD to TZVP. The PC bonds in Au4(PMe3)42þ systems shorten by ∼0.045 Å upon the basis set improvement from LANL2DZ to TZVP. All reported changes are practically independent of the DFT functional used. In contrast to the AuAu bond shortening in Au4(PR3)42þ when the TZVP basis set is used, its use in Au4(μ2-I)2(PR3)4 cluster calculations causes AuAu bonds to slightly elongate by an average of 0.01 Å. At the same time, gold-ligand bonds shorten by av 0.1 Å mainly due to the introduction of polarization functions in TZVP, again with almost no dependence on the DFT functional used. Compared to clusters with PH3 and PMe3 ligands, the PPh3 analogues are much more computationally expensive to treat 8020



ARTICLE

Table 2. Selected Geometric Parameters and Root-Mean-Square (RMS) Values (Å) for Structures of Au4(PPh3)42þ and Au4(μ2-I)2(PPh3)4 Optimized at Different Levels of Theorya Au4(PPh3)42þ [ref 9]

basis set d functional PBE0

Au, P, I

C, H

d

Au4(μ2-I)2(PPh3)4 [ref 6]

d

d

d

d

d

d

RMS

RMS

(AuAu) (AuP) (PC) RMS (AuAu) base (AuAu) diag. (AuP) (AuI) (PC) (Au, P) (Au, P, I)

LANL2DZb LANL2DZb

2.777

2.403

1.858

0.05

2.664

2.852

2.424

3.062

1.867

0.10

0.10

LANL2DZ CEP-31Gb

UFF CEP-31Gb

2.758 2.757

2.405 2.396

1.824 1.868

0.04 0.03

2.622 2.657

2.867 2.841

2.421 2.407

3.023 3.020

1.827 1.878

0.10 0.08

0.09 0.08

TZVP

UFF

2.749

2.315

1.817

0.03

2.639

2.895

2.318

2.897

1.822

0.11

0.05

LANL2DZb LANL2DZb

2.709

2.354

1.849

0.02

2.610

2.805

2.370

2.986

1.861

0.05

0.05

LANL2DZ

UFF

2.695

2.367

1.834

0.03

2.573

2.828

2.374

2.947

1.841

0.07

0.07

TZVP

UFF

2.684

2.274

1.825

0.06

2.601

2.825

2.276

2.835

1.829

0.04

0.07

XR

TZP.4fb

TZP.4fb

2.745

2.324

1.815

0.02

2.656

2.793

2.290

2.990

1.827

0.03

0.04

LC-ωPBE

LANL2DZ

UFF

2.746

2.399

1.820

0.03

2.611

2.856

2.411

2.958

1.824

0.09

0.08

TZVP CAM-B3LYP LANL2DZ

UFF UFF

2.736 2.779

2.311 2.423

1.814 1.821

0.03 0.06

2.628 2.636

2.872 2.884

2.309 2.447

2.861 3.053

1.817 1.824

0.06 0.12

0.07 0.12

UFF

SVWN5

TZVP OPBE

experiment

2.765

2.332

1.814

0.03

2.644

2.912

2.341

2.929

1.818

0.09

0.08

LANL2DZb LANL2DZb

2.754

2.399

1.873

0.03

2.646

2.843

2.434

3.080

1.883

0.10

0.11

LANL2DZ

UFF

2.732

2.392

1.827

0.02

2.587

2.841

2.419

3.130

1.829

0.10

0.21

TZVP

UFF

2.725

2.289

1.822

0.04

2.620

2.878

2.288

2.869

1.826

0.06

0.07

2.734

2.355

1.819

2.648

2.794

2.291

2.955

1.825

a

Basis sets used for heavy (Au, P, and I) and light (C, H) atoms are indicated separately. b Conventional (non-ONIOM, one basis set for all atoms) approach.

with a single good-quality basis set. On the other hand, the majority of known gold clusters are stabilized predominantly with aromatic phosphines, and to model the experimental systems, either explicit treatment of PPh3 ligands is needed or a simpler model ligand is needed to simulate the influence of PPh3. R€osch and others have previously shown that for Au(I) complexes, the use of PMe3 ligands in calculations to model PPh3 is sufficient to capture main trends and geometric and energetic description of a system of interest.72 To extend these findings onto cationic gold clusters, we undertook explicit calculations with PPh3 ligands for all atoms of the studied clusters using XR/TZP.4f and several functionals with the LANL2DZ basis set as well as calculations using ONIOM method (see Computational Methodology). The XR/TZP.4f geometries are found to be in good agreement with experiment, with RMS values of 0.02 Å for Au4(PPh3)42þ and 0.04 Å for Au4(μ2-I)2(PPh3)4. Conventional calculations with LANL2DZ show RMS values of 0.020.05 Å for Au4(PPh3)42þ and 0.050.11 Å for Au4(μ2-I)2(PPh3)4 (Table 2). We have performed geometry optimizations of Au4(PPh3)42þ using the ONIOM approach with the LANL2DZ basis set used for the cluster core and the smaller CEP-31G basis set or UFF used for phenyl groups at the PBE0, SVWN5, and OPBE levels of theory. The results were compared to calculations that employ the LANL2DZ basis set for the whole cluster (Tables 2 and S2, Supporting Information). In addition, we performed ONIOM calculations with TZVP treatment of a cluster core with UFF or CEP-31G treatment of phenyl substituents using five DFT functionals. In addition, to compare the performance of the ONIOM approach with calculations with all-atom TZVP basis, we also utilized ONIOM approach with TPSS and PBE0 functionals in geometry optimization of Au4(PMe3)42þ and Au4(μ2-I)2(PMe3)4. In general, ONIOM calculations with LANL2DZ/UFF treatment of phenyl groups lead to AuAu and PC bonds shrinking up to 0.02 and 0.045 Å,

respectively, when the OPBE functional is used and only to 0.005 and 0.015 Å, respectively, upon SVWN5 use. No systematic trend in AuP bond length changes is noticed, but the unsigned length difference is below 0.01 Å. Although the all-atom calculations using the LANL2DZ basis set lead to good agreement with experiment, our results indicate that the ONIOM approach provides a similar or even better description at a fraction of a cost. Indeed, with the exception of SVWN5, the other four DFT functionals used with the ONIOM method gave rise to either equivalent or somewhat better agreement of modeled geometries with available experimental structures when compared to the explicit calculations with LANL2DZ basis set. As we have discussed above, LANL2DZ leads to overestimated metalmetal and especially metalligand bonding, while the more flexible TZVP basis set corrects the overestimation. The same trend is observed in the ONIOM approach. The good agreement of ONIOM-optimized geometries with experimental data arises from the fact that alkyl or aryl substituents on phosphorus in phosphines provide mostly steric shielding to the cluster core without significant influence on electron density distribution within the Au4P4 framework. Because of the limited electronic influence of the substituents on the cluster core, the simplified description by molecular mechanics is sufficient to result in acceptable accuracy of the whole structure description. In further studies of larger gold clusters with bulky ligands, we would recommend use of the TZVP/UFF or an equivalent hybrid combination for structure optimizations. Attempts to use different basis sets for different parts of the system (such as LANL2DZ for Au and P and 3-21G for C and H atoms) were not found to be advantageous to the ONIOM approach, mostly due to wave function and structure convergence problems that erased the time gains due to smaller number of basis set functions. It is important to point out that the ONIOM approach was also beneficial when the PMe3 ligand was used. Geometries of 8021


The Journal of Physical Chemistry A Au4(PMe3)42þ and Au4(μ2-I)2(PMe3)4 obtained with all-atom TZVP treatment and TZVP/UFF ONIOM approach using the PBE0 functional were practically identical (Table 1). As such, we expect that in larger metal cluster systems, where use of PMe3 may be computationally expensive, the ONIOM approach with an accurate basis set used for metal and phosphorus atoms and UFF treatment of C and H atoms will provide a good alternative. Geometrical Changes Produced by Cluster Halogenation. The comparison of experimental structures of Au4(PMes3)42þ and Au4(μ2-I)2(PPh3)4 reveals that the addition of two iodide anions breaks the tetrahedral symmetry of the Au42þ core by stretching the Au4 tetrahedron along one of its C2 axes. The two AuAu bonds that become perpendicular to the axis, AuAu (base), contract by almost 0.1 Å due to the bridging binding of I. The four AuAu bonds that are positioned alongside of the axis, AuAu(diag), extend by 0.06 Å. It is noteworthy that AuP bonds slightly shorten upon cluster halogenations, from av 2.355 Å (in Au4(PMes3)42þ) or av 2.305 Å (in Au4(PtBu3)42þ) to av 2.291 Å in Au4(μ2-I)2(PPh3)4, despite the neutralization of the positive charge on the Au4 cluster. Similar changes are observed in the model clusters as well. Regardless of the DFT functional utilized with a polarized triple-ζ basis set (TZVP or TZP.4f) for the structure optimization, AuP bonds shorten by av 0.01 Å in PH3- and PMe3-protected halogenated clusters compared to their tetrahedral analogues and no AuP bond shortening is apparent in optimized cluster structures with PPh3 which is likely due to interligand steric repulsion. Influence of the Phosphine Ligand on Gold Cluster Structure. As nucleophilicity of a phosphine ligand increases upon the change from PH3 to PMe3, one would expect the shortening of AuP bonds due to the increase in the strength of ligand bonding and that, in turn, should cause slight elongation of AuAu bonds in cluster core. Metalmetal bond elongation is indeed observed upon the ligand change: the use of TZVP basis set gives rise to the uniform elongation of 0.0050.006 Å independent of the DFT functional. The elongation predicted at the XR/TZP.4f level of theory is a little longer, at 0.012 Å. In the halogenated cluster, Au4(μ2-I)2(PR3)4, regardless of the basis set and DFT functional used, the PH3-to-PMe3 substitution causes AuAu(base) bonds to elongate and AuAu(diag) bonds to shorten. The use of TZVP produces an average elongation of AuAu(base) bond of 0.02 Å and an average shortening of AuAu(diag) bond of 0.04 Å. Ligand substitution also gives rise to significant elongation of AuI bonds: 0.12 Å for TZVP, and 0.05 Å for TZP.4f. Because the binding of more nucleophilic PMe3 increases the amount of electron density donated to the gold core (as is manifested by the decrease in the natural charge on gold atoms), it leads to the weakening and elongation of AuI bond, which is also confirmed by the bond energy calculations (vide infra). In turn, the weakening of the AuI bond will lead to the elongation of AuAu(base) contact, because the AuAu(base) bond length is significantly dependent on the strength of AuI interaction. The TZVP-based calculations lead to AuP bonds becoming consistently longer upon the phosphine substitution (by ca. 0.008 Å), and the extent of the bond elongation is inversely proportional to the AuP bond length value independently of DFT functional. Such behavior of AuP bonds is likely caused by increased steric repulsion between ligands as PH3 is being substituted with PMe3, leading to the AuP bond elongation. Comparison of experimental bond lengths in Au4(PtBu3)42þ and Au4(PMes3)42þ reveals that the introduction of the bulkier ligand, PMes3, with a Tolman angle of 212°, leads

ARTICLE

to the increase in AuAu and AuP bond distances by 0.02 and 0.05 Å, respectively, compared to the less crowded PtBu3, with a Tolman angle of 182°. This is in agreement with the trends observed above for the calculated geometries of Au4(PH3)42þ and Au4(PMe3)42þ. The substitution of PH3 with PPh3 ligands was tested using two LDA functionals (SVWN5 and XR), one pure GGA functional (OPBE), and one hybrid functional (PBE0) (Table 2) and overall leads to increased AuAu(base) bond lengths, decreased AuAu(diag) bond lengths, and slightly elongated AuI bonds. This observation is consistent with increased metalligand bonding for PPh3 ligands compared to PH3 and is confirmed by the bonding energy calculations below. Comparison with Experimental Structures. For comparison of optimized structures with experimentally known ones, the root-mean-square (RMS) value for each structure is calculated on the basis of AuAu and AuL bond lengths (eq 1): nhX RMS ¼ ni ðdexp, i ðAuAuÞ dcalc, i ðAuAuÞÞ2 þ

X

i o1=2 nj ðdexp, j ðAuLÞ dcalc, i ðAuLÞÞ2 =N

ð1Þ

where ni is the number of bonds of type i, dexp,i is the experimental value of bond of type i, and N is the total number of bonds considered. The variations of AuI bond lengths in optimized structures of Au4(μ2-I)2(PR3)4 clusters were significantly larger compared to variations of AuAu and AuP bonds (Tables 1 and 2). To compare RMS values for both types of clusters considered, with and without the halogen, we have included only AuAu and AuP bonds in RMS calculations for Au 4 (μ2 -I)2 (PR 3 )4 . First of all, RMS values for both types of clusters with the same phosphine substituents, PH3 or PMe3, are similar regardless of basis set and DFT functional used, especially for dicationic Au4(PR3)42þ. As discussed above, the LANL2DZ basis set is not flexible enough to well describe bonding with significant polarization contribution (e.g., AuP bonds) and its replacement with the more flexible TZVP basis significantly improves the metalligand bond length predictions. Indeed, RMS values decrease by more than a factor of 2 upon the basis set switch (Table S1, Supporting Information). As follows from the comparison of RMS values, the Au4(PH3)42þ model cluster describes the geometry of the Au4(PMes3)42þ experimental cluster better than that of Au4(PtBu3)42þ, with RMS values being lower across all DFT functionals used. Surprisingly, even the Au4(PMe3)42þ model cluster describes the geometry of Au4(PMes3)42þ better than that of chemically similar Au4(PtBu3)42þ. It is likely that the relatively noncrowded PMe3 is not large enough to simulate the steric influence of bulky PtBu3. The known effect of LDA functionals to produce shorter bonds compared to pure or hybrid DFT functionals4143 is also observed in our calculations, giving rise to a factor of 2 or 3 decrease in RMS values from SVWN5 or XR calculations compared to the other four functionals. Overall, the metalmetal and metalligand bond lengths of the dicationic cluster, Au4(PR3)42þ, can easily be predicted when SVWN5 or XR functionals are used, even with the relatively small LANL2DZ basis set (in the case of the SVWN5 functional), although the performance of XR/TZP.4f appears to be the best. In the case of the halogenated cluster, the polarization effects are important for correct description of metalligand bonding, so the use of the TZVP basis set is warranted, and LDA functionals 8022



ARTICLE

Table 3. MetalLigand Binding Energies BE (kcal/mol) Calculated for Au4(PR3)42þ and Au4(μ2-I)2(PR3)4 (R = H, Me, Ph) Clusters basis set

Au4(μ2-I)2(PH3)4 Au4(PH3)42þ

functional PBE0

Au, I, P

C, H

BE(AuPH3) BE(AuPMe3)

LANL2DZ

LANL2DZ

60.4

78.1

TZVP

TZVP

60.5

84.1

38.9

51.0

TZVP(CH3CN)a TZVP(CH3CN)a TPSS

TZVP

UFF

TZVP

TZVP

TZVP(CH3CN)a TZVP(CH3CN)a

SVWN5

LC-ωPBE

OPBE

QCISD(T)

132.0 112.0 6.2 131.5

68.8

TZP.4f

TZP.4f

74.4

98.3

LANL2DZ

LANL2DZ

59.1

76.4

TZVP

TZVP

102.3

37.1

146.1

49.2

128.8

41.8

146.5

54.6

126.8

43.1

25.4

55.4

20.1

39.2

139.9

52.2

118.0

28.7

131.3

38.7

116.6

69.5 101.0

61.3

83.4

33.7

136.6

44.7

114.5

39.0

50.6

33.3

11.4

43.2

7.8

24.7

128.6

34.3

113.2

51.5 58.0

75.4

48.8

59.0

80.6

28.3

131.5

38.9

109.4

36.2

32.6

28.5

7.2

38.2

3.2

19.9

124.2

28.5

104.4

25.88

127.4

34.9

104.1

20.2

5.7

35.5

32.3

132.3

TZVP

UFF

LANL2DZ

LANL2DZ

54.6

73.2

TZVP

TZVP

60.2

80.8

TZVP

6.9

11.4

9.1

54.0

TZVP

41.1

38.6

UFF

UFF

11.5

44.0

TZVP

TZVP

31.2 51.8

11.6

97.4


115.2 112.7

29.4

102.9

TZVP

36.1 41.3

49.5

80.2


131.7 138.5

37.8 76.7

CAM-B3LYP TZVP

26.6 30.6

38.1

TZVP

LANL2DZ

BE

132.2

LANL2DZ

LANL2DZ

BE

28.7

TZVP

UFF

BE

74.9

34.7 48.6 64.9

Au4(μ2-I)2(PPh3)4 BE

BE

(AuPH3) (AuI) (AuPMe3) (AuI) (AuPR3) (AuI)

82.8

LANL2DZ

TZVP

81.0

BE

Au4(μ2-I)2(PMe3)4

63.3

UFF


Au4(PPh3)42þ BE(AuPPh3)b

44.6

TZVP

TZVP(CH3CN)a TZVP(CH3CN)a XR

Au4(PMe3)4

2þ

36.6

110.0

16.8

128.4

56.5

133.7

28.7

141.6

55.3

118.9

19.9

128.7

14.2

123.6

25.0

93.7

12.2

123.3

a Structures were optimized in CH3CN (CPCM model). b SCF energy in CH3CN of Au4(PPh3)42þ with gas-phase optimized geometry was used to estimate the ligand binding energy.

again lead to the best agreement between the experimental and optimized structures. It appears that the explicit use of PPh3 ligands in predicting cluster geometries is not necessary because it does not improve the final result or even gives rise to less accurate geometrical parameters. Although the XR/TZP.4f method still provides the best description, the calculations with triphenylphosphine become rather expensive without improvement in geometry prediction results.

’ LIGAND BINDING ENERGIES IN TETRANUCLEAR GOLD CLUSTERS The ligand binding energies are calculated according to the following equations: In Au4 ðPR 3 Þ4 2þ : BEðAuPÞ ¼ ð¼ÞjEðAu4 ðPR 3 Þ4 2þ Þ EðAu4 2þ Þ 4EðPR 3 Þj

ð2Þ

In Au4 ðμ2 -IÞ2 ðPR 3 Þ4 : BEðAuPÞ ¼ ð¼ÞjEðAu4 ðμ2 -IÞ2 ðPR 3 Þ4 Þ

EðAu4 I2 Þ 4EðPR 3 Þj

ð3aÞ

BEðAuIÞ ¼ ð½ÞjEðAu4 ðμ2 -IÞ2 ðPR 3 Þ4 Þ EðAu4 ðPR 3 Þ4 2þ Þ 2EðI Þj

ð3bÞ

With an exception of the SVWN5 functional, the remaining DFT functionals predict similar values for PH3 and PMe3 binding in Au4(PR3)42þ and Au4(μ2-I)2(PR3)4 clusters: PH3 binding is calculated to be in the ranges 5560 and 2029 kcal/mol per ligand, respectively, and PMe3 binding is estimated in the ranges 7378 and 2839 kcal/mol per ligand, respectively, with the LANL2DZ basis set (Table 3). As expected for an LDA functional, the use of the SVWN5 functional results in higher ligand binding energies; for the two clusters of interest, Au4(PR3)42þ and Au4(μ2-I)2(PR3)4, the binding energy is 19 and 12 kcal/mol per ligand more, respectively, for PH3 binding, and 22 and 15 kcal/mol per ligand, respectively, for PMe3 binding, compared to the average binding energies calculated from the results of the other four DFT functionals. The use of more flexible TZVP basis set compared to the relatively small LANL2DZ increases the predicted phosphine bonding energy by the similar value of 67 kcal/mol per ligand for both PH3 and PMe3 binding. However, these values constitute up to 10% of ligand binding energy in Au4(PR3)42þ and up to 30% in Au4(μ2-I)2(PR3)4. The LDA overbinding energy value remains relatively unchanged upon the LANL2DZ to TZVP switch. To gauge the performance of DFT calculations in predicting the ligand binding energies, we have performed the ligand binding calculations for Au4(PH3)42þ and Au4(μ2-I)2(PH3)4 clusters employing the ab initio MP4SDQ, QCISD, and QCISD(T) methods with TZVP basis set using the 8023



ARTICLE

Figure 2. Molecular orbital diagrams for Au42þ, Au4(PH3)42þ, and Au4(μ2-I)2(PH3)4 cluster models calculated at CAM-B3LYP/TZVP level of theory. Occupied orbitals are shown in gray or black; the unoccupied orbitals, in red. The cluster (superatom) orbitals are identified by their angular momentum in bold italics. Gold atomic orbitals contributing to the corresponding cluster orbital are shown in parentheses. Unmarked molecular orbitals with higher than 90% contribution of gold 5d AOs are shown in light gray (d band). Contribution from ligand orbitals is indicated with L. Color code: Au, orange; I, brown; P, green; H, cyan.

geometries obtained at PBE0/TZVP level of theory. This combined approach in which post-HF methods are used to calculate the energy of a system that was optimized at the DFT level is widely accepted for large molecular systems where geometry optimizations with post-HF methods are computationally prohibitive. As follows from the presented results in Table 3 and Table S3 (Supporting Information), performance of all non-LDA DFT functionals agrees well with prediction of highlevel ab initio methods: e.g., the phosphine binding energy to Au42þ is predicted to be 64.9 kcal/mol per ligand by QCISD(T)/TZVP//PBE0/TZVP approach, which is at most only 10% higher than values predicted by DFT calculations. Out of the tested DFT functionals, TPSS functional has provided the closest ligand binding values to the reference QCISD(T)/TZVP method, with LC-ωPBE functional being the close second. Unscreened positive charge on Au4(PR3)42þ gives rise to more than a factor of 2 stronger ligand binding compared to the corresponding neutral Au4(μ2-I)2(PR3)4 for both R = PH3 and PMe3. At the same time, the higher nucleophilicity of PMe3 compared to PH3 results in stronger binding of the former to both clusters by 3040%. The binding of PPh3 in Au4(PPh3)42þ is only 35% stronger than that of PMe3 when the LANL2DZ basis set is used together with PBE0, SVWN5, and OPBE. This finding is also consistent with previous estimates of ligand binding to Auþ cations or similar gold species.7275 The utilization of ONIOM methods yields only half the binding energy when LANL2DZ or TZVP are combined with the UFF description (Table 3). Consequently, despite our demonstration that the TZVP/UFF combination is an excellent alternative to LANL2DZ or all-atom TZVP geometry optimizations involving large phosphines, this combination is not acceptable

for the binding energy estimation, so more computationally expensive all-atom basis set approaches should be considered. The calculation of ligand binding energies in solvent is similar to that in the gas phase, except that geometries of all species were optimized in the presence of solvent before their potential energies are used in eqs 2, 3a, and 3b. The geometries of Au4(PPh3)42þ and Au4(μ2-I)2(PPh3)4 were not optimized in solvent, but rather the solvation energies were calculated on the basis of the gas-phase optimized geometries. We believe this approach is acceptable due to expected minimal interaction of such hydrophobic ligands as PPh3 with polar environment of CH3CN. The introduction of implicit solvation into bond energy calculations leads to ∼40% energy reduction of phosphine binding to the dicationic cluster. The percentage of the energy reduction appears to be independent of the basis set used or DFT functional used. It is also apparent that the nature of the phosphine ligand minimally affects the bond energy reduction as well. For instance, at the PBE0/TZVP level of theory, the binding energy of a phosphine to Au42þ in CH3CN decreases from 60.5 kcal/mol per ligand to only 38.9 kcal/mol per ligand in the case of PH3, and from 84.1 kcal/mol/ligand to 51.0 kcal/mol per ligand in the case of PMe3; the energy reduction constituted 36% and 39%, respectively, for PH3 and PMe3 phosphines. Because the energy of phosphine binding to Au42þ core in a solvent can be estimated from the corresponding gas-phase binding energy corrected only by solvation energies of the core and the cluster (assuming very small solvation energy of a large free phosphine in polar solvent), BEsolv ðAuPÞ ¼ BEgas ðAuPÞ ΔEsolv ðAu4 2þ Þ þ ΔEsolv ðAu4 ðPR 3 Þ4 2þ Þ 8024

ð4Þ


The Journal of Physical Chemistry A the phosphine binding energy lowering becomes expected due to the solvent stabilization of the charged core. In addition, the solvation energy of the cluster with bulkier phosphines is lower than that with PH3, which should further increase the difference between BEsolv and BEgas whereas their ratio might stay unchanged. On the other hand, the phosphine binding in the halogenated cluster, Au4(μ2-I)2(PR3)4 appears practically unaffected by solvation: binding energies change only within 13 kcal/mol per ligand. As such, the solvent effect on ligand binding is expected to play a crucial role in the case of charged gold clusters and can be neglected in calculations involving large phosphine binding to neutral species. Unlike the goldphosphine bonding, binding of two unscreened I anions in vacuum to Au4(PR3)42þ dication is an extremely favorable process with ligand binding energies calculated to be in the range of 100130 kcal/mol per ligand. However, the introduction of solvent reduces iodide binding energies by more than an order of magnitude and brings them significantly below ones for the goldphosphine interactions: e.g., at the PBE0/TZVP level of theory in CH3CN, the iodide binding to Au4(PH3)42þ decreases from 138.5 kcal/mol per ligand (in vacuum) to 11.5 kcal/mol per ligand and, similarly, from 112.7 to 6.9 kcal/mol per ligand in the case of I binding to Au4(PMe3)42þ.

’ ELECTRONIC STRUCTURE OF TETRAHEDRAL GOLD CLUSTERS The electronic structure in the tetrahedral goldphosphine clusters under consideration can simplistically be viewed as originating from the interaction between electrons of Au(6s) atomic orbitals, one orbital from each gold atom. Consequently, in clusters such as Au4(PR3)42þ and Au4(μ2-X)2(PR3)4 where only two 6s valence electrons would be responsible for the metalmetal bonding, the highest occupied molecular orbitals (HOMOs) would be expected to be “superatom” S orbitals (or S cluster orbitals) in which all four Au(6s) atomic orbitals (AOs) have the same phase, while the lowest unoccupied orbitals (LUMOs) would be the cluster P orbitals. In the realistic case of these gold clusters, the 5d6s hybridization of gold AOs complicates the analysis of occupied molecular orbitals and the involvement of Au(6p) AOs affects the makeup of empty MOs. To qualitatively estimate the degree of the difference between the realistic picture of cluster molecular orbitals and the simplistic 6sorbital-only interaction model, we analyzed the makeup of the molecular orbitals for the clusters of interest starting with the bare Au42þ cluster core.

Electronic Structure of the Au42þ Tetrahedral Cluster Core. A KohnSham (KS) single-electron orbital diagram of

the cluster core is presented in Figure 2. Unlike the model prediction, where the HOMO is expected to be the S(6s) superatom orbital, the HOMO of Au42þ is found to be triply degenerate with T1 symmetry and composed of a combination of Au(5d) AOs without significant admixing of Au(6s) orbitals. The superatom S orbital of A1 symmetry with predominant contribution from Au(6s) AOs, denoted S(6s), is either HOMO 2 (when calculated at CAM-B3LYP/Def2-TZVP//SVWN5/ LANL2DZ level) or HOMO8 (using SAOP/TZP method). Orbitals below HOMO2 make up the 5d band of the cluster with the lowest orbital of the band being fully symmetric and composed primarily of 5dz2 AOs of four gold atoms. At the SAOP/TZP level of theory, the S cluster orbital lies 1.3 eV below the bottom of the 5d band. At all levels of theory, the LUMO

ARTICLE

orbital of the cluster is triply degenerate of T2 symmetry and represents three superatom orbitals of P type composed of Au(6s) atomic orbitals, P(6s). The unoccupied orbitals above LUMO can be assigned to the superatom orbitals with increasing nodality and involvement of Au(6p) AOs: 2S(6sp) (symmetry: A1), D(6p)(EþT2), F(6p)(A1þT1þT2) and so on. Generally, to analyze the makeup of donating and accepting orbitals in electronic transitions in the clusters, it is beneficial to consider cluster’s natural transition orbitals (NTOs)76 rather than MOs. Transition orbitals represent the wave functions of an electron and a hole underlying a specific optical excitation. The analysis of electronic transitions using NTOs in the clusters of interest reveals that electron and hole NTOs can be relatively easily mapped onto a single pair of corresponding one-electron KS molecular orbitals; as such, the conventional description of an excitation from a donor to acceptor molecular orbitals is appropriate in our case (Figure 3A). The lowest electronic transition at the CAM-B3LYP/Def2-TZVP//SVWN5/LANL2DZ level can be assigned as 96% of 5d-P(6s) (HOMOLUMO) transition (Figure 3A). In general, all but one electronic transition below 9 eV with nonzero oscillator strength in Au42þ can be considered to originate on consecutively lower occupied orbitals starting with the HOMO and the excitation occurs primarily onto P(6s) (LUMO). The first strong excitation (f = 0.13) at 5.27 eV can be assigned primarily to S(6s)-to-P(6s) transition, followed by two weak excitations at 5.96 and 6.43 eV originating from different combinations of gold 5d AOs to P(6s). This trend holds until 8.64 eV, where the transition again originates from the HOMO but the excitation occurs to the doubly degenerate E orbital, D(6p) (LUMOþ2) (Figure 3). Electronic Changes in Au42þ Cluster Core upon Ligation. The coordination of four PH3 ligands leads to hybridization of each ligand’s lone pair with the 5d6sp manifold of gold AOs in the Au42þ core, thereby causing some mixing of triply degenerate P(6s) (LUMO) with a P-like orbital arising from the 5d Au AOs (HOMO4). It leads to destabilization of the latter and results in a triply degenerate HOMO1 orbital of P(5d6s) type while preserving the P(6s) superatom orbital as LUMO (Figure 2). In addition, the ligand coordination substantially lowers the 2S(6sp) (LUMOþ1) orbital of bare Au42þ so it becomes the HOMO in Au4(PH3)42þ. In addition to mainly Au(6sp) character, this orbital also possesses contributions from Au(5d) and P(3p) AOs. According to NTO analysis, all allowed electronic transitions under 8 eV involve excitations from the 56 highest occupied orbitals onto the triply degenerate P(6sp) (LUMO, T2 symmetry) (Figure 3B). The lowest transition at 5.03 eV can be viewed as originating primarily from P(5d6s) (HOMO1) onto LUMO. The ligated cluster exhibits five strong (f > 0.1) electronic transitions under 8 eV. The lowest strong transition (f = 0.22) at 5.6 eV may be viewed as an excitation from the mixture of S(5d6s) (HOMO5) and Au(5d) (HOMO2, HOMO3) to LUMO. The next even-stronger transition (f = 0.47) at 6.1 eV from the combination of HOMO and HOMO2 onto LUMO is followed by the excitation from HOMO5 and HOMO6 onto LUMO at 7.1 eV and from HOMO1 and HOMO2 onto LUMOþ1 at 7.4 eV and, last, by the transition involving HOMO þ (HOMO1) excitations onto P(6sp) þ D(6p) þ ligand-based MOs at 7.9 eV(Figure 3B). The addition of two iodide anions to Au4(PH3)42þ further alters the makeup of molecular orbitals for the cluster thereby complicating the correlation of newly produced MOs with ones of the parent cluster Au4(PH3)42þ (Figure 2). Iodine 5p atomic 8025



Figure 3. Calculated TD spectra of (A) Au42þ, (B) Au4(PH3)42þ, and (C) Au4(μ2-I)2(PH3)4 at the CAM-B3LYP/TZVP level. Cluster geometries were optimized at the SVWN5/LANL2DZ level.

orbitals primarily make up six occupied frontier molecular orbitals including two pairs of doubly degenerate MOs, from HOMO3 to HOMO. As such, the superatom S(6sp) orbital becomes HOMO4. In the case of HOMO3 and HOMO, where the main contribution comes from two I(5pz) AOs, there is also significant mixing of Au(5d) AOs. In doubly degenerate HOMO2 and HOMO1, the contribution of gold atomic orbitals is minimal and the orbitals are primarily composed of 5px or 5py AOs of iodine. The introduction of iodine ions also leads to the partial removal of the LUMO 3-fold degeneracy in Au4(PH3)42þ (due to the lowering of molecular symmetry from Td to D2d), causing the destabilization of superatom Pz(6s) orbital by the antibonding mixing of I(5pz) AOs (Figure 2). Unlike transitions in Au42þ and Au4(PH3)42þ, the electronic transitions in the halogenated cluster appear to involve the full

ARTICLE

manifold of occupied orbitals and many low-lying empty orbitals. The lowest transition in Au4(μ2-I)2(PH3)4 can be assigned to I(5p) (HOMO)-to-Px,y(6sp) (LUMO) excitation at 3.4 eV with low oscillator strength of 0.031. The first two strong transitions (f = 0.49 and 0.32) originate from iodine 5p AOs (from HOMO to HOMO2) and the excitations promote an electron to Px,y,z(6sp) (LUMO and LUMOþ1), at 4.4 and 4.7 eV, respectively. The weak S(6sp)P(6sp) (Au-to-Au) transition appears at 5.4 eV (f = 0.04). Some transitions above ∼5.5 eV can be categorized as excitations from iodine onto phosphine ligands. For instance, the third strong transition (f = 0.12) still originates from iodine-based HOMO and HOMO1 and the electron is promoted onto phosphinelocalized LUMOþ3 and LUMOþ4 at 5.5 eV. The remaining two strong transitions under 6 eV originate primarily from S(6sp) (HOMO4) orbital onto Pz(6s)(LUMOþ1) combined with phosphine-based LUMOþ3 and LUMOþ4 (Figure 3C). The initial electron configuration of bare Au 4 2þof 6s 0.55 5d9.92 6p0.03 indicates minimal involvement of Au(6p) AOs into binding of the cluster and almost no mixing of Au(5d) AOs. The ligation with PH3 alters the electron configuration in two ways. First, the nucleophilic ligands donate extra electron density onto Au 6s AOs, which is manifested by the significant increase in the corresponding orbital occupancies: from 0.55 to 0.93 on 6s AOs without affecting 6p AOs of gold. Second, the ligands also assist 6s5d mixing of gold AOs that leads to a slight electron density depletion on gold 5d orbitals, from 9.92 to 9.84. Overall, the gold electronic configuration in Au4(PH3)42þ cluster, namely 6s0.935d9.846p0.026d0.02, points to the buildup of 0.30e on each gold atom in the ligated cluster. This conclusion can also be drawn from the natural population analysis partial atomic charge calculation that puts þ0.19 charge on each gold in the ligated cluster, compared to þ0.50 in bare Au42þ. Additional ligation of two iodide ions only slightly perturbs the electron density on the cluster core. The partial charge on each gold atom minimally increases from þ0.19 to þ0.22 due to withdrawal of total 0.09e from Au(6s) AOs, which is likely caused by Au(6s)I(5s) electron repulsion. Although an overall 0.58e is transferred from two iodide anions onto the Au4(PH3)42þ cluster upon ligation (charge on I changes from 1.0 to 0.71), the transfer affects only PH3 ligands which charge decreases from þ0.31 to þ0.13. Ligand Influence on Cluster Electronic Transition. The substitution of PH3 with the more realistic PMe3 in both Au4(PH3)42þ and Au4(μ2-I)2(PH3)4 does not significantly alter the clusters’ absorption spectra. As expected for clusters with more nucleophilic PMe3, the HOMOLUMO gap of both types of PMe3-substituted clusters decreases as the buildup of electron density from donor ligands in the cluster core destabilizes occupied orbitals compared to those in more electron-deficient PH3ligated analogues. As such, almost uniform red shift of 0.25 0.5 eV is observed in the absorption spectrum of the PMe3ligated cluster compared to its simpler analogues (Figure 3). In the case of Au4(μ2-I)2(PH3)4, the substitution leads to the systematic decrease in oscillator strengths of many transitions, proportional to the contribution of ligand MOs involved in the transition. This effect has also been observed in calculations involving small neutral gold clusters.77 In Au4(μ2-I)2(PMe3)4 clusters, the two strong transitions (f > 0.2), which occur at 4.66 and 4.89 eV, can be assigned to the excitations from I(5p)þAu(5d) orbitals onto the superatom P orbital, which is still centered on Au and I atoms. 8026



ARTICLE

Figure 4. Comparison of theoretical absorption spectra for Au4(μ2-I)2(PR3)4 (R = Me, Ph) with (A) the experimental spectrum of Au4(μ2-I)2(PPh3)4 in THF with energies of relevant spectral features (eV). Theoretical TD absorption spectra are calculated for (B) Au4(μ2-I)2(PMe3)4 and (C) Au4(μ2-I)2(PPh3)4 in vacuum. The level of geometry optimization and TD calculation is indicated on the corresponding panel. The DFT functional used for TD calculations is indicated next to each spectrum together with band transition energies (eV). The energy of the lowest transition is indicated in bold italics. Transitions were not calculated in the energy range shaded in gray.

The replacement of PMe3 with PPh3 changes the nature of electronic transitions in the cluster. While the transitions in PH3- and PMe3-ligated clusters would mostly originate within the manifold of occupied cluster MOs and the excitation would occur to the lowest few unoccupied orbitals, the situation is reversed in PPh3-ligated clusters, both dicationic and halogenated. Multiple delocalized bonds of phenyl substituents in PPh3 give rise to low-lying π*-orbitals thereby increasing the density of unoccupied states close to the cluster’s LUMO. As such,

the low-energy electronic excitations in Au4(PPh3)42þ and Au4(μ2-I)2(PPh3)4 originate on few highest occupied orbitals and occur to the manifold of low-lying empty MOs that are composed of primarily PPh3 π*-orbitals with very little contribution from metal MOs. Because most of the low-lying electronic transitions can be classified as metal-to-ligand excitations, their intensities are relatively low. The most intense transitions in the PPh3-ligated clusters still can be assigned to the metalmetal excitations, but they are no longer the lowest transitions in 8027


The Journal of Physical Chemistry A energy and are almost not present within first 100 electronic transitions we analyzed. DFT Functional and Basis Set Dependence. From obtained results it is clearly established that the expansion of the basis set from relatively small LANL2DZ to polarization-included triple-ζ quality Def2-TZVP or TZP minimally affects relative intensities of predicted electronic transitions: the spectrum profile does not change upon the basis set expansion and the expansion expectedly and uniformly lowers the energies of intense transitions by 0.150.17 eV, regardless of DFT functional or type of phosphine. Because of the uniformity in the energy shift and no change in relative intensities of electronic transitions, we would expect that calculations performed even with relatively inexpensive LANL2DZ basis set with the consecutive red-shift of calculated transitions by 0.150.16 eV should generate results quantitatively similar to ones produced by much more expensive Def2-TZVP or TZP.4f basis sets. Conversely to the relative insensitivity of cluster absorption spectra to the used basis set, the calculated electronic transitions demonstrate stronger dependence on the utilized DFT functional. As established previously, pure DFT functionals tend to underestimate the HOMOLUMO gap in molecules,78 while HartreeFock (HF) overestimates it. In agreement with this commonly accepted trend, SVWN5 and OPBE functionals used in our work produced the most red-shifted spectra compared to PBE0 (the GGA hybrid DFT with 25% contribution of “exact” exchange) or long-range corrected LC-ωPBE and CAM-B3LYP, in which HF treatment is incorporated at long distances (together with exact exchange in hybrid B3LYP). The use of different DFT functionals also brings about the noticeable variations in the relative intensities of strong transitions, although the overall spectral profile remains qualitatively unchanged. Comparison to Experimental Spectrum. The experimental spectrum of Au4(μ2-I)2(PPh3)4 in THF is presented in Figure 4A. The only prominent feature of the experimental spectrum is a peak at 2.94 eV with a tail of lower-energy transitions at 2.32.5 eV. Using the second-derivative method, several more higher-energy bands could be identified on the spectrum, the most prominent being at 3.78, 4.09, 4.37, 4.51, and 4.63 eV. In the same figure we present calculated TD spectra obtained at different theoretical levels for Au4(μ2-I)2(PR3)4 structures (panels B and C for R = Me and Ph, respectively) in vacuum with 0.2 eV Gaussian broadening. Due to high computational cost, the energies and intensities for only first 120 transitions were calculated, which span the energy interval ∼2.5 eV. For uniformity of spectra presentation in the Figure 4, the energy range in which electronic transitions were not calculated is shaded in gray. As follows from the comparison of the experimental spectrum with calculated ones for gas-phase Au4(μ2-I)2(PPh3)4, SAOP/ TZP and SVWN5/LANL2DZ perform the best to give the closest agreement between the experimental and calculated absorption spectra: both methods qualitatively reproduce the profile of the experimental spectrum at low energies and predict the envelope of transitions with average position just 0.2 eV lower than the experimentally observed at 2.94 eV. The hybrid and long-range corrected functionals tend to overestimate the energy of electronic transitions up to 1.3 eV (for the LC-ωPBE functional). According to the analysis of the spectral transitions that we believe contribute to the experimental peak at 2.94 eV, they have metal-to-ligand Au(5d) f π*(Ph) character. Because of the nature of these transitions, it appears unlikely that the

ARTICLE

Figure 5. Comparison of theoretical TD absorption spectra calculated for the experimental geometry of Au4(μ2-I)2(PPh3)4 [ref 6] at (A) SVWN5/LANL2DZ and (B) SAOP/TZP levels of theory in vacuum and in THF with energies of relevant spectral features (eV). The energy of the lowest transition is shown in bold italics. Transitions were not calculated in the energy range shaded in gray.

modeling of the experimental spectrum using TD spectrum of less expensive Au4(μ2-I)2(PMe3)4 will result in an accurate spectral profile. Indeed, the comparison of TD spectra calculated for Au4(μ2-I)2(PMe3)4 (Figure 4B) and Au4(μ2-I)2(PPh3)4 (Figure 4C) at the same levels of theory reveals significant qualitative differences between corresponding spectra. Calculated absorption spectra for PMe3-analogues systematically blueshift by 0.30.6 eV compared to that of corresponding PPh3ligated clusters. The smallest shift is observed when either of two long-range corrected DFT functionals was used. Figure 5 features the TD spectra of Au4(μ2-I)2(PPh3)4 at SVWN5/LANL2DZ (Figure 5A) and SAOP/TZP (Figure 5B) levels of theory calculated in the gas phase and in tetrahydrofuran. Taking the solvent into account systematically blue-shifts electronic transitions and improves even further the agreement between calculated and experimental spectra. The SAOP/TZP method performed the best among methods studied in this work, with less-expensive SVWN5/LANL2DZ model chemistry being a close second. Given the observation that the use of TZVP basis set red-shifts the energy of electronic transitions by ∼0.15 eV, the use of SVWN5/TZVP model chemistry will likely match the SAOP/TZP approach in modeling the experimental spectrum of studied gold clusters. We also emphasize that the use of solvent in TD spectra calculations is important even for a neutral cluster such as Au4(μ2-I)2(PPh3)4, as it correctly adjusts the electronic transition energies of gas-phase molecule from being too low compared to the experimentally data.

’ CONCLUSION We have demonstrated the applicability of the DFT approach for accurate modeling of gold-phosphine cluster geometries and absorption spectra and for the analysis of clusters’ electronic structures. 8028


The Journal of Physical Chemistry A 1. The average calculated metalmetal and metalligand bond lengths in Au4(PR3)42þ and Au4(μ2-I)2(PR3)4 systems increase by 0.070.08 Å (23% of the bond length) independent of the basis set as the functional varies in the following order: SVWN5 < XR < OPBE < LC-ωPBE < TPSS ≈ PBE0 < CAM-B3LYP. From the comparison of RMS values for calculated bond lengths at different levels of theory, the LDA (XR or SVWN5) geometries appear in best agreement with experiment. The recent long-range corrected DFT functionals produce systematically elongated metalmetal and metalligand bonds and are not recommended. The use of larger basis sets only partially remedies the shortcomings of used DFT functionals. While an increase in the basis set flexibility from LANL2DZ to SDD to TZVP yields a small systematic decrease in metal metal bond distances of these clusters (by 0.01 Å overall), the metalligand bonds appear to be more sensitive to the basis set used (due to significant polarization contribution to metalligand bonding) and vary by as much as 0.12 Å with the basis set change. 2. As the nucleophilicity of a phosphine ligand increases from PH3 to PMe3, AuP bonds shorten due to the stronger metalligand bonds in turn leading to elongation of all metalmetal bonds in the Au4(PR3)42þ cluster and of iodide-bridged metalmetal bonds in the Au4(μ2-I)2(PR3)4 cluster. The replacement of PH3 with PPh3 also shortens AuP bonds in both clusters while the AuAu bonds are practically unaffected in Au4(PR3)42þ. In the Au4(μ2-I)2(PR3)4 cluster, substitution of phosphine by triphenylphosphine leads to increased AuAu(base) bond lengths, decreased AuAu(diag) bond lengths, and slightly elongated AuI bonds. The observations are consistent with increased metalligand bonding for PPh3 ligands compared to PH3. 3. ONIOM calculations can be effectively employed for geometry optimizations with PPh3 groups with the best combination found to be the triple-ζ treatment of metal core combined with universal force field treatment of the ligands, TZVP/UFF. Although this combination is recommended for geometries due to its computational efficiency and modeling accuracy, it is not acceptable for ligand binding energy calculations. 4. Au4(PR3)42þ has more than a factor of 2 stronger ligand binding compared to the corresponding neutral Au4(μ2-I)2(PR3)4 for both R = PH3 and PMe3, which is attributed to unscreened positive charge on the former. The higher nucleophilicity of PMe3 compared to PH3 results in stronger binding of the former to both clusters by 3040% whereas the binding of PPh3 in Au4(PPh3)42þ is only 35% stronger than that of PMe3. GGA and hybrid DFT calculations are in good agreement with QCISD(T) calculations, whereas LDA functionals expectedly overestimate the binding. Implicit solvation reduces the AuP binding energies in the cationic clusters, whereas the halogenated clusters are essentially unaffected. On the other hand, the AuI bonding energies are dramatically affected by the solvation and decrease by more than an order of magnitude in solventincluded non-LDA calculations. As such, the energetics of charge-neutralizing metalligand binding should not be evaluated only on the basis of gas-phase calculations. 5. The electronic structure of the goldphosphine clusters examined in this work can be analyzed in terms of cluster

ARTICLE

(aka superatom) orbitals that stem mostly from the interaction between Au(6s) atomic orbitals. The manifold of occupied orbitals contains several superatom orbitals of Slike character, which differ by the type of contributing atomic orbitals, either 5d^z2 or 6sp orbitals of Au. The first unoccupied orbitals indeed have P-like symmetry, as would be expected from the superatom model. This set of P orbitals is triply degenerate in the tetrahedral Au4(PR3)42þ system but is split in the Au4(μ2-I)2(PR3)4 cluster due to symmetry lowering, and the orbitals are composed primarily of 6s and 6p atomic orbitals of the metal. In the case of the dicationic cluster, the S(6sp) orbital represents the HOMO, whereas in its halogenated analogue, due to the lone pairs of iodine, S(6sp) orbital becomes HOMO4. 6. Transitions out of the d band are significant in the excitation spectra. The use of different basis sets and DFT functionals leads to noticeable variations in the relative intensities of strong transitions, although the overall spectral profile remains qualitatively unchanged. The replacement of PMe3 with PPh3 changes the nature of the electronic transitions in the cluster due to low-lying π*-orbitals. In the experimental excitation spectra, the principal observed peak at 2.94 eV comprises an envelope of several Au(5d) f π*(Ph) transitions. Because of the nature of this peak, modeling of the experimental spectrum with TD spectra calculated on the basis of Au4(μ2-I)2(PH3)4 or Au4(μ2-I)2(PMe3)4 structures will result in inaccurate spectral profiles, and the inclusion of full PPh3 ligand in calculations is needed.

’ ASSOCIATED CONTENT

bS

Supporting Information. Full versions of Tables 13 are presented in the Supporting Information section as Tables S1S3, respectively. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: S.A.I., [email protected]; C.M.A., [email protected].

’ ACKNOWLEDGMENT C.M.A. is grateful to the Air Force Office of Scientific Research (AFOSR) and the Defense Advanced Research Projects Agency (DARPA) for funding under Grant FA9550-09-1-0451. S.A.I. and I.A. also acknowledge support of the Los Alamos National Laboratory Directed Research LDRD-DR program. This work was partially performed at the Center for Integrated Nanotechnologies, a U.S. Department of Energy, Office of Basic Energy Sciences user facility at Los Alamos National Laboratory (Contract DE-AC52-06NA25396) and Sandia National Laboratories (Contract DE-AC04-94AL85000). ’ REFERENCES (1) Safer, D.; Bolinger, L.; Leigh, J. S., Jr. J. Inorg. Biochem. 1986, 26, 77. (2) Jahn, W. J. Struct. Biol. 1999, 127, 106. (3) Yuan, Y.; Asakura, K.; Kozlova, A. P.; Wan, H.; Tsai, K.; Iwasawa, Y. Catal. Today 1998, 44, 333–342. 8029


The Journal of Physical Chemistry A (4) Omary, M. A.; Rawashdeh-Omary, M. A.; Chusuei, C. C.; Fackler, J. P., Jr.; Bagus, P. S. J. Chem. Phys. 2001, 114, 10695. (5) McPartlin, M.; Mason, R.; Malatesta, L. Chem. Commun. 1969, 334. (6) Demartin, F.; Manassero, M.; Naldini, L.; Ruggeri, R.; Sansoni, M. J. Chem. Soc., Chem. Commun. 1981, 222. (7) Mingos, D. M. P.; Powell, H. R.; Stolberg, T. L. Trans. Met. Chem. 1992, 17, 334–337. (8) Zeller, E.; Beruda, H.; Schmidbaur, H. Inorg. Chem. 1993, 32, 3203–3204. (9) Yang, Y.; Sharp, P. R. J. Am. Chem. Soc. 1994, 116, 6983–6984. (10) van der Velden, J. W. A.; Bour, J. J.; Pet, R.; Bosman, W. P.; Noordik, J. H. Inorg. Chem. 1983, 22, 3112–3115. (11) Bellon, P.; Manassero, M.; Sansoni, M. J. Chem. Soc., Dalton Trans. 1973, 2423–2427. (12) Scherbaum, F.; Grohmann, A.; Huber, B.; Kr€uger, C.; Schmidbaur, H. Angew. Chem., Int. Ed. 1988, 27, 1544–1546. (13) Briant, C. E.; Hall, K. P.; Mingos, D. M. P. J. Organomet. Chem. 1983, 254, C18–C20. (14) van der Velden, J. W. A.; Bour, J. J.; Bosman, W. P.; Noordik, J. H. Inorg. Chem. 1983, 22, 1913–1918. (15) van der Velden, J. W. A.; Bour, J. J.; Steggerda, J. J.; Beurskens, P. T.; Roseboom, M.; Noordik, J. H. Inorg. Chem. 1981, 21, 4321–4324. (16) Schulz-Dobrick, M.; Jansen, M. Z. Anorg. Allg. Chem. 2007, 633, 2326. (17) Bellon, P.; Manassero, M.; Sansoni, M. J. Chem. Soc., Dalton Trans. 1972, 1481. (18) Nunokawa, K.; Onaka, S.; Ito, M.; Horibe, M.; Yonezawa, T.; Nishihara, H.; Ozeki, T.; Chiba, H.; Watase, S.; Nakamoto, M. J. Organomet. Chem. 2006, 691, 638. (19) Copley, R. C. B.; Mingos, D. M. P. J. Chem. Soc., Dalton Trans. 1996, 479. (20) Briant, C. E.; Theobald, B. R. C.; White, J. W.; Bell, L. K.; Mingos, D. M. P.; Welch, A. J. J. Chem. Soc., Chem. Commun. 1981, 5, 201–202. (21) Mingos, D. M. P. J. Chem. Soc., Dalton Trans. 1976, 1163–1169. (22) Pyykk€o, P.; Runeberg, N. J. Chem. Soc., Chem. Commun. 1993, 1812–1813. (23) Calhorda, M. J.; Crespo, O.; Gimeno, M. C.; Jones, P. G.; Laguna, A.; Lopez-de-Luzuriaga, J. M.; Perez, J. L.; Ram on, M. A.; Veiros, L. F. Inorg. Chem. 2000, 39, 4280–4285. (24) Boca, R. J. Chem. Soc., Dalton Trans. 1994, 2061–2064. (25) Stone, A. J. Inorg. Chem. 1981, 20, 563–571. (26) de Heer, W. A. Rev. Mod. Phys. 1993, 65, 611–676. (27) Walter, M.; Akola, J.; Lopez-Acevedo, O.; Jadzinsky, P. D.; Calero, G.; Ackerson, C. J.; Whetten, R. L.; Gr€onbeck, H.; H€akkinen, H. Proc. Nat. Acad. Sci. U. S. A. 2008, 105, 9157–9162. (28) Provorse, M. R.; Aikens, C. M. J. Am. Chem. Soc. 2010, 132, 1302–1310. (29) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, N. J.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, € Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; S.; Daniels, A. D.; Farkas, O.; Fox, D. Gaussian09; Gaussian Inc.: Wallingford, CT, 2009. (30) te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; et al. J. Comput. Chem. 2001, 22, 931. (31) Hohenberg, H.; Kohn, W. Phys. Rev. 1964, 136, B864–B871. (32) Kohn, W.; Sham, L. J. Phys. Rev. 1965, 140, A1133–A1138.

ARTICLE

(33) Slater, J. C. The Self-Consistent Field for Molecular and Solids, Quantum Theory of Molecular and Solids; McGraw-Hill: New York, 1974; Vol. 4. (34) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200. (35) Handy, N. C.; Cohen, A. J. Mol. Phys. 2001, 99, 403. (36) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. (37) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1997, 78, 1396. (38) Adamo, C.; Barone, V. J. Chem. Phys. 1999, 110, 6158–6169. (39) Perdew, J. P.; Tao, J.; Staroverov, V. N.; Scuseria, G. E. Phys. Rev. Lett. 2003, 91, 146401. (40) Shi, Y.-K.; Li, Z. H.; Fan, K.-N. J. Phys. Chem. A 2010, 114, 10297–10308. (41) R€ osch, N.; Nasluzov, V. A. Chem. Phys. 1996, 210, 415. (42) H€aberlen, O. D.; Chung, S.-C.; Stener, M.; R€ osch, N. J. Chem. Phys. 1997, 106, 5189. (43) Aikens, C. M. J. Phys. Chem. A 2009, 113, 10811–10817. (44) Goel, S.; Velizhanin, K. A.; Piryatinski, A.; Tretiak, S.; Ivanov, S. A. J. Phys. Chem. Lett. 2010, 1, 927–931. (45) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (46) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785. (47) Yanai, T.; Tew, D.; Handy, N. C. Chem. Phys. Lett. 2004, 393, 51–57. (48) Tawada, Y.; Tsuneda, T.; Yanagisawa, S.; Yanai, T.; Hirao, K. J. Chem. Phys. 2004, 120, 8425. (49) Vydrov, O. A.; Heyd, J.; Krukau, A.; Scuseria, G. E. J. Chem. Phys. 2006, 125, 074106. (50) Vydrov, O. A.; Scuseria, G. E. J. Chem. Phys. 2006, 125, 234109. (51) Vydrov, O. A.; Scuseria, G. E.; Perdew, J. P. J. Chem. Phys. 2007, 126, 154109. (52) Gritsenko, O. V.; Schipper, P. R. T.; Baerends, E. J. Chem. Phys. Lett. 1999, 302, 199. (53) Schipper, P. R. T.; Gritsenko, O. V.; van Gisbergen, S. J. A.; Baerends, E. J. J. Chem. Phys. 2000, 112, 1344–1352. (54) Stevens, W. J.; Basch, H.; Krauss, M. J. Chem. Phys. 1984, 81, 6026. (55) Stevens, W. J.; Krauss, M.; Basch, H.; Jasien, P. G. Can. J. Chem. 1992, 70, 612. (56) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 270–283. (57) Wadt, W. R.; Hay, P. J. J. Chem. Phys. 1985, 82, 284–298. (58) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 299–310. (59) Modern Theoretical Chemistry; Dunning, T. H., Jr.; Hay, P. J., Eds.; Plenum: New York, 1976; Vol. 3. (60) Kuechle, W.; Dolg, M.; Stoll, H.; Preuss, H. Mol. Phys. 1991, 74, 1245. (61) Weigend, F.; Ahlrichs, R. Phys. Chem. Chem. Phys. 2005, 7, 3297–3305. (62) (63) Feller, D. J. Comput. Chem. 1996, 17, 1571–1586. (64) Schuchardt, K. L.; Didier, B. T.; Elsethagan, T.; Sun, L.; Gurumoorthi, V.; Chase, J.; Li, J.; Windus, T. L. J. Chem. Inf. Model. 2007, 47, 1045–1052. (65) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1993, 99, 4597. (66) Barone, V.; Cossi, M. J. Phys. Chem. A 1998, 102, 1995–2001. (67) Cossi, M.; Rega, N.; Scalmani, G.; Barone, V. J. Comput. Chem. 2003, 24, 669–681. (68) Klamt, A.; Sch€u€urmann, G. J. Chem. Soc., Perkin Trans. 1993, II, 799. (69) Dapprich, S.; Komaromi, I.; Byun, K. S.; Morokuma, K.; Frisch, M. J. J. Mol. Struct. (THEOCHEM) 1999, 462, 1–21. (70) Rappe, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A., III; Skiff, W. M. J. Am. Chem. Soc. 1992, 114, 10024–10035. (71) Glendening, E. D.; Reed, A. E.; Carpenter, J. E.; Weinhold, F. NBO Version 3.0. (72) H€aberlen, O. D.; Chung, S.-C.; R€osch, N. Int. J. Quantum Chem. 1994, S28, 595–610. 8030



ARTICLE

(73) H€aberlen, O. D.; R€osch, N. J. Phys. Chem. 1993, 97, 4970–4973. (74) Schwerdtfeger, P.; Hermann, H. L.; Schmidbaur, H. Inorg. Chem. 2003, 42, 1334–1342. (75) Li, J.; Wang, S.-G. J. Mol. Model. 2010, 16, 505–512. (76) Martin, R. L. J. Chem. Phys. 2003, 118, 4775–4777. (77) Goel, S.; Velizhanin, K. A.; Piryatinski, A.; Ivanov, S. A.; Tretiak, S. ACS Nano 2011 submitted for publication. (78) von Barth, U. Phys. Scr. 2004, T109, 9–39.

’ NOTE ADDED AFTER ASAP PUBLICATION This article posted ASAP on June 16, 2011. Equations 3a and 4 have been revised. The correct version posted on June 21, 2011.

8031


Density Functional Analysis of Geometries and Electronic Structures of

Recommend Documents