Pd doping, conformational, and charge effects on the dichroic response of a monolayer protected Au38(SR)24 nanocluster

Daniele Toffoli *a, Oscar Baseggio a, Giovanna Fronzoni a, Mauro Stener *a, Alessandro Fortunelli *b and Luca Sementa b
aDipartimento di Scienze Chimiche e Farmaceutiche, Università degli Studi di Trieste, Via Giorgieri 1, 34127 Trieste, Italy. E-mail: toffoli@units.it; stener@units.it
bCNR-ICCOM & IPCF, Consiglio Nazionale delle Ricerche, via Giuseppe Moruzzi 1, 56124, Pisa, Italy. E-mail: alessandro.fortunelli@cnr.it

Received 28th June 2018 , Accepted 14th September 2018

First published on 14th September 2018


TDDFT simulations of the absorption and CD spectra of a Pd2Au36(SC2H4Ph)24 monolayer-protected cluster (MPC) are carried out with the aim of investigating the effects of doping, conformational degrees of freedom of the thiolates’ end-groups, and charge states on the optical and dichroic response of a prototypical MPC species. Clear signatures of Pd doping in both absorption and CD spectra are found to be a consequence of the participation of Pd (4d) states in the ligand-based d-band and on the unoccupied MOs of lower energy. Exploration of conformational space points to a much greater sensitivity of optical rotation to the conformation of the end-groups of the organic monolayer compared to absorption. Finally, the effect of charge is mainly seen as a decreased dependence of the dichroic response on conformation. The agreement between the TDDFT predictions and the available experimental data is good, and enables an assignment of absorption and CD bands to specific classes of one-particle excitations.


1. Introduction

Monolayer Protected Clusters (MPCs) represent a series of systems whose importance is rapidly growing.1 The reasons for the wide interest of the scientific community in this field is twofold: on the one hand there are many questions of fundamental nature which are still open, and on the other hand MPCs are systems with very promising applications, ranging from materials with prescribed optical properties to photocatalysis,2 sensors,3 nanodevices and photovoltaics.4 Clearly, rationalization of their fundamental behaviour is of paramount importance for the design of materials with given properties or characteristics, as advances in applications can be grounded on an improved fundamental understanding. In this respect theory plays a major role, since for MPCs it is difficult to rationalize experimental data without any theoretical tool. This is due to the chemical complexity of these species, with the co-existence of metallic (the metal core), semiconducting (the staple shell), and insulator (typically, the organic residues) components. It is thus difficult using experimental tools only to derive information on the different types of chemical bonds present in these systems, or to understand in depth their optical response, often determined by the coupling between collective effects (plasmons) and molecular-like ligand excitations, thus producing a very intricate physics5–7 – all phenomena which require quantum chemistry approaches for an accurate description. The typical size of many MPC species is however quite challenging for quantum chemistry approaches, since hundreds of atoms are often involved and symmetry is very low or even absent as in the case of the chiral systems considered in the present work. The only method practicable for such large systems and capable of describing the involved, intricate physics is Time Dependent Density Functional Theory (TDDFT). Even if limiting to TDDFT without considering higher-level and computationally more demanding approaches, an efficient algorithm must be properly adopted for any practical application. For example the standard Casida implementation8 is very efficient on large systems only if a very limited number of excitations are extracted (up to a few hundred roots of the Casida matrix). When many excited states are needed for the description of the high-energy portion of the spectrum (usually up to and above 3 eV of photon energy), as it is usually the case for MPCs, it is more convenient to employ alternative schemes, like for example working in the time domain or extracting the spectrum as the imaginary part of the dynamical polarizability.9–11

Once an efficient TDDFT algorithm is available, one can then investigate fundamental problems in the field, and explore the chiro-optical landscape of these systems (i.e., simulate both absorption and circular dichroism spectra) as a function of their many degrees of freedom, such as their structure and composition.12,13 Here we will focus in particular on chirality and its relation with composition (doping) and structure, not simply the static structure but dynamic structure due to sampling of conformational space at finite temperature, which is a less investigated but (as we will see) possibly crucial parameter for MPC species, in analogy with molecular systems.14

Although the importance of chirality in the field of nanoscience is well recognized,15,16 only recently it has been possible to separate successfully MPC enantiomers and characterize them spectroscopically to study their Circular Dichroism (CD) spectra.17,18 The availability of the experimental CD spectrum, together with the structural characterization by means of X-ray diffraction, makes these systems, which combine typical features of metal nanoclusters and molecular compounds, ideal candidates for a thorough theoretical study aimed at rationalizing their optical and dichroic behaviour. In particular, a very important and still partially open question is with regard to the origin of the dichroism, whether it can be ascribed to the metal core, to chiral ligands or to a chiral arrangement of the ligand around the metal core.19,20

Within the field of MPCs a very versatile way to tune their properties consists of alloying the base metal with another one. However, how chiro-optical response is affected by alloying strongly depends on the nature of the alloying element,21–24 on composition (degree of alloying) and on chemical ordering (where alloying atoms are located in the structural framework of the MPC and whether alloying changes this framework), and it is not always easy to have precise information on all these different factors. From this point of view the system on which we will focus our study (Pd2Au36(SC2H4Ph)24) is very well characterized in terms of composition and chemical ordering since the Pd atoms’ positions are well established,25,26 information available only for a very restricted set of systems.

Another general problem, which becomes important when MPCs are made by ligands having some conformational freedom, is that their chiro-optical spectrum, generally recorded at room temperature, is actually the average taken from many structural configurations, each one populated with different probability. This dynamical problem presents a formidable challenge to computational investigation. In this work we take a first step in this direction, that is, we explore the effect of the ligand conformation on the CD spectra of MPCs limiting our study only to a small number of low-lying energy minima, not yet fully exploring the configuration space by molecular dynamics. We believe that this will nevertheless be useful to assess the importance of the ligand configuration in the CD and to identify which spectral optical region is more sensitive to such effects.

Finally also the charge effect on the CD has been considered. This effect is important because it has been shown that the metal core can behave as an electron reservoir, allowing the same cluster to exist in many different charge states.27,28 The charge effect has been found to be weak in the photoabsorption spectra of bare metal clusters;29 however this effect has not yet been studied for CD spectra of MPCs, thus representing an original topic of this work.

The paper is organized as follows: a description of the theoretical method and the computational details are reported in Section 2; results are discussed in Section 3 while conclusions and perspectives are drawn in Section 4.

2. Theoretical method and computational details

CD is defined as the difference between the absorbance of left and right circulary polarized light. For an electronic transition from the ground state |0〉 to the n-th excited state |n〉 and assuming a random orientation of the sample (as it is usual for gas-phase or experiments in solution) we obtain
 
image file: c8cp04107e-t1.tif(1)

In eqn (1)γ is a constant factor, μ and m are, respectively, the electric dipole and the magnetic dipole moment, R0n is the rotatory strength (units of 10−40 esu2 cm2 are used in this paper) while Im means that the imaginary part of the argument must be taken. In turn R0n enters in the following sum-over-states expression for the diagonal elements of the optical rotation tensor, β:

 
image file: c8cp04107e-t2.tif(2)
where the sum is over the complete set of excited states of the molecular system, ω is the photon energy while ω0n is the excitation energy corresponding to the |0〉 → |n〉 transition. The calculation of the photoabsorption and CD spectra is done with the recently developed complex polarizability algorithm, as described in ref. 9–11 and included in the most recent distribution of the ADF suite.30,31 In short, a discretization of the excitation energy spectrum permits one to efficiently carry out the summation over the occupied/virtual orbital pairs (ia) that enters the SOS expression of the non-interacting Kohn–Sham (KS) susceptibility, χKS, which is further represented in the auxiliary basis set of the density fitting functions, thus lowering the dimensions of the matrices involved. From the following expressions, eqn (3)–(6), of the elements of the polarizability (α) and optical rotation (β) tensors, involving electric/magnetic dipole matrix elements and density matrices
 
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the absorption and CD spectra are obtained by taking the imaginary part of eqn (3) and (5) respectively (see also eqn (22) of ref. 11). Detailed expressions for the energy-dependent coefficients sk(ω) and tk(ω), the elements of the density matrices, Pai and image file: c8cp04107e-t7.tif, and of A, L, and b matrices over the auxiliary fit functions are reported in ref. 9–11. Transition contribution maps (TCM32) useful to assist in the analysis of the absorption spectrum are related to the square of Pai as a function of the single-particle KS occupied/virtual energies εi and εa.

Local geometry relaxations at the DFT level and DFT Ab Initio Molecular Dynamics (AIMD) runs were performed using the CP2K code33 which uses a Gaussian/Plane-Wave method (GPW34). Pseudopotentials derived by Goedecker, Teter and Hutter35 were chosen to describe the core electrons of all atoms and DZVP basis sets36 to represent the DFT Kohn–Sham orbitals. Calculations were performed spin-restricted and at the gamma point only. The semi-empirical Grimme-D3 correction37 was added to Perdew–Burke–Ernzerhof (PBE38) exchange and correlation (xc-) functional to take into account dispersion interactions. The cut-off for the auxiliary plane wave representation of the density was 400 Ry. AIMD runs used a time step of 0.5 fs and the temperature was controlled by using Nosé–Hoover chain thermostats.39 Starting from the optimized geometry of Au38(SR)2411 derived in turn from the experimentally determined crystal structure,40–42 two Au atoms in the center of the two Au13 icosahedral units of Au38(SR)24 have been replaced by Pd atoms (we recall that the Au core of the cluster corresponds to a double-icosahedron, see below) and the resulting geometry has been fully optimized. In addition to the fully relaxed structure, three further conformations (hereafter indicated by numbers 2–4) were extracted from an AIMD run at 300 K lasting 10 psec, and on these 4 configurations, fully relaxed at the DFT level, the photoabsorption and CD spectra were calculated. We additionally considered the charged species (with total charge 2−, corresponding to closed-shell electronic configurations) of these four conformations, obtained by vertical electron attachment (i.e., by freezing the cluster coordinates to those of the neutral species). DFT electronic structure calculations revealed that these doubly charged anions can be stable species, so that they have been selected to investigate the effect of charge on the absorption and CD spectra – a topic rarely discussed in the literature of MPCs as it pertains to absorption27 and to the best of our knowledge for the first time here as it pertains to CD.

A Slater Type Orbitals (STO) basis set of Triple Zeta plus Polarization (TZP) quality together with the asymptotically correct LB94 exchange–correlation potential43 has been employed for the resolution of the Kohn–Sham equations. The exchange–correlation kernel in the TDDFT equations is approximated by ALDA44 taking the derivative of the VWN LDA xc-potential.45 The basis set used in the TDDFT calculations consists of a subset of the ADF fitting functions, chosen after preliminary test calculations as discussed in previous works.9–11 Calculated absorption spectra and rotatory strengths use photon energy with an imaginary part of ωi = 0.15 eV, which leads to a Lorentzian broadening with the same half-width at half-maximum (HWHM). All the calculations have been performed at the scalar relativistic level within the Zero Order Relativistic Approximation (ZORA46). The effect of spin orbit coupling (SOC), although visible in the low-energy part of the absorption spectra taken at low temperature,47 is neglected in the present paper, for computational reasons. This approximation should not affect the main conclusions of the paper since already a reasonably good agreement with the experimentally recorded absorption and CD spectra in the energy region investigated in this work is obtained at the scalar relativistic level (vide infra).

Computed rotatory strengths are invariant under molecular translations when the electric dipole matrix elements are calculated in the velocity gauge, but not for other choices of the gauge if the basis set is not complete.48 We always checked that there is close agreement of oscillator and rotatory strengths obtained with both length and velocity forms of the dipole matrix elements; this as noted above suggests that the basis set used to solve the TDDFT equations ensures convergent results.

3. Results and discussion

The Au38(SC2H4Ph)24 nanocluster is one of the most extensively studied chiral systems in the field of metal clusters because its structure has been precisely determined.40–42 It has a core–shell structure with a symmetric face-fused bi-icosahedral Au23 core and a shell composed of three monomeric (RS–Au–RS) and six dimeric (RS–Au–S(R)–Au–SR) staples.40 The staggered arrangement of the dimeric staples is responsible for the dichroic response of the cluster. Palladium doping has been first achieved by Negishi et al.,25 and shortly thereafter by Barrabés et al.18 Quite interestingly, the Pd doping increases both cluster's stability against core etching by thiols and degradation in solution,25 and flexibility of the Au–S interface as evidenced from the activation parameters of the racemization process.18 Recent DFT total energy calculations25,26 suggest that in the energetically more stable structure the two Au atoms in the center of the Au13 core are replaced by Pd atoms. In this study, focusing on the effects of Pd doping, we therefore constructed the structure of Pd2Au36(SC2H4Ph)24, starting from the optimized geometry of the monometallic gold cluster by substituting the two Au centers of the Au13 core with Pd. Given that carrying out even a partial sampling of the conformational space of the cluster would be a formidable task, due to the large number of conformational degrees of freedom of the thiolates’ lateral chains, and in view of the exploratory nature of this work, we arbitrarily selected four different geometries, of which the first one corresponds to a local energy minimization of the cluster structure in the crystal, while isomers (2–4) are taken as snapshots from the AIMD run (according to the criterion that they correspond to local minima of the potential energy of the cluster as a function of time) and are then fully relaxed at the DFT level. On these 4 different structures we base our subsequent analysis. These four geometries are displayed in Fig. 1, viewed along the X axis of the molecular frame, from which it can be seen that the major differences among them are in the orientation of the phenyl rings. Of these four geometries, the structure with minimum total energy after geometry relaxation is structure 4, while structures 1–3 have a higher energy after relaxation of 0.33 eV, 0.17 eV and 0.40 eV respectively. The fact that the lowest-energy structure does not correspond to the configuration adopted in the crystal is interesting as it is suggestive of a “self-solvation” stabilization mechanism of the ligand shell similar to that discussed for “mushroom” as opposed to “brush” configurations of polymers by de Gennes.49 Cartesian coordinates of all atoms of structures 1–4 are included in the ESI.
image file: c8cp04107e-f1.tif
Fig. 1 The PBE-D3 optimized geometry of the four conformers of the Au36Pd2(C2H4Ph)24 MPC. Views along the X axis of the coordinate system used in the electronic structure calculations. Color code: H atoms are represented in white, C atoms in black, S atoms by small yellow spheres, Au atoms in darker yellow, and Pd atoms in orange.

Finally, to investigate the effects of the nature of thiolates’ lateral chains on both absorption and dichroic parameter we also considered a simplified model of the Pd2Au36(SC2H4Ph)24 MPC with the –C2H4Ph moiety replaced by methyl groups. This simplification is a widespread practice to save computational time in the calculation of MPCs’ structure and dynamics, but can sometimes hinder a precise comparison with the experimental data and/or impact the reliability of numerical predictions of spectroscopic properties.50

In the following discussion, we will first analyse the effect of Pd doping on the electronic structure of the Pd2Au36(SC2H4Ph)24 MPC with reference to structure 1. We will assign all major spectral features visible in the theoretical CD spectrum to specific orbital excitations and briefly discuss the comparison with the available experimental data. We will then analyse the effect of the conformational degrees of freedom on both the CD and absorption spectra, by studying the evolution of the more prominent spectral features along the sequence of structures 1–4. The effect of the MPC's charge on these observables is subsequently analysed. The charge state of the MPCs can vary depending on several conditions such as the environment, synthesis protocol, or investigative techniques.27,28

To put the following discussion in perspective, we briefly summarize the electronic structure and the major features of the absorption and CD spectra of the parent monometallic Au38 cluster, recently calculated by adopting the same computational protocol used in this work.11 The calculated HOMO–LUMO energy gap of 0.96 eV is consistent with the experimental estimate of the optical absorption edge of 0.92 eV obtained in ref. 51. The absorption spectrum displays a characteristic peak at 2.0 eV which qualitatively agrees with the computed TDDFT value of 1.75 eV, and is assigned to correspond to a manifold of single-particle excitations of the type HOMO−n → LUMO+n with n = 2, 3 and 4. HOMO and HOMO−1 are degenerate and can be described as a linear combination of Au(sp) and S(3p) AOs, while lowest energy virtual orbitals have major Au(sp) contributions with minor weights of S(3p) AOs.11 The most prominently resolved structures in the experimental CD spectrum involve two positive peaks at around 345 and 394 nm in qualitative agreement with the TDDFT results. We note here and in the following that well known deficiencies in the LB94 exchange–correlation potential used in our computational protocol tend to shift the spectral features to lower energies compared to the experiment.50

3.1 Electronic structure of the Pd2Au36(SC2H4Ph)24 MPC and assignment of its CD spectrum

Fig. 2 reports a plot of the frontier MOs for the Pd2Au36(SC2H4Ph)24 MPC geometry 1, while a KS energy level diagram is reported in Scheme S1 of the ESI. The DFT HOMO–LUMO gap is 0.21 eV and it is in agreement with the DFT estimate of the gap in the Pd2Au36(SC6H13)24 MPC (0.23 eV[thin space (1/6-em)]28). Since the states involved are mainly localized on the Au–S interface of the MPCs, this value is accordingly found rather independent of the nature of the thiolates’ end groups. The Pd 4d states contribute to the low-lying virtual MOs (LUMO+1, LUMO+2, see Scheme S1 of the ESI), which are well separated from the LUMO (about 0.7 eV), while the C(2p) states of the aromatic thiolate's tails are located some 2.0 eV at higher energy. The HOMO is singly degenerate, is contributed by Au(6s) and S(3p) AOs, and has a similar composition in terms of AOs of the LUMO. Pd 4d AOs contribute to occupied MOs that span quite a large energy range within the Au 5d band, and of mixed nature with contributions of S(3p) and C(2p) AOs (ligand-based d band). From the eigenvalues of the KS MOs, it is anticipated that a band-gap opening could be obtained by vertical electron attachment, in line with that found recently in the Pt2Au36(SC6H13)24 MPC.28
image file: c8cp04107e-f2.tif
Fig. 2 Plot of frontier KS MOs for Au36Pd2(SR)24, geometry 1. Isosurfaces are plotted with the ADFview program, using a contour value of 0.005 bohr−3/2. Different colors are used to denote opposite signs of the orbitals.

The experimental absorption and CD spectra, taken from ref. 26, are reported in Fig. 3, together with the TDDFT results from this work. In the panels we include all spectra corresponding to the four conformers of the Pd2Au36(SR)24 MPC considered in this work, together with the theoretical profiles for a model Au36Pd2(SR)24 cluster (model 1) where thiolates’ –CH2CH2Ph tails are replaced by –CH3 groups, to analyze the validity of predictions based on simplified ligands, as commonly done in the literature. Computed and experimental intensities have been divided by the square of the corresponding excitation energy, to enhance the features present in the lower energy part of the absorption spectrum.


image file: c8cp04107e-f3.tif
Fig. 3 Upper panel: Absorption spectra. Comparison between the TDDFT spectra of the four conformers of Au36Pd2(SR)24 neutral clusters and experimental data. Model 1 refers to the Au36Pd2(SR)24 cluster (geometry 1) with thiolates’ tails replaced by –CH3 groups. Theoretical intensity is in units of eV−2. The right y axis refers to the experimental data (a.u. eV−2). Lower panel: CD spectra. The experimental data are taken from ref. 26.

The experimental absorption spectrum displays a rise in intensity at about 1.5 eV, followed by a broad maximum at 2.0 eV. Other broad bands have maxima located at 3.0 eV and 3.75 eV of photon energy. The TDDFT absorption spectrum of the Pd2Au36(SCH2CH2Ph)24 nanomolecule shows a modest dependence on the particular conformation of the thiolates’ end-groups, as can be noticed from an inspection of the upper panel of Fig. 3 where the theoretical profiles corresponding to geometries 1–4 are almost superimposable. Focusing our attention on the computed absorption spectrum relative to geometry 1, well defined absorption features fall at 1.7 eV, 2.3 eV, 2.7 eV and 4.0 eV of photon energy. We tentatively assign the latter to the prominent absorption band visible at around 3.8 eV in the experimental UV-Vis spectrum. It is important to notice that, although our conformational sampling is minimal, the conformational degrees of freedom seem not to affect the MPCs’ absorption to an extent sufficient to bring theory and experiment in quantitative agreement. Since the absorption spectrum is not much sensitive to the conformational degrees of freedom of the ligand end-groups we are led to attribute the observed discrepancies between theory and experiment, which make the agreement only semi-quantitative, partially to the known deficiencies of the LB94 xc-potential here employed, which tend to shift absorption bands to lower energy compared to the experiment, and partially to the effects of the environment (experimental UV-vis spectra are recorded in solution) which are neglected in the computational model. We also note that a full account of the chemical structure of the end groups of the protecting organic monolayer is necessary to obtain a better agreement with the experiment in the high energy region of the optical spectrum. In fact, the replacement of the thiolates’ end groups by –CH3 groups determines a decrease of absorption intensity starting from about 2.0 eV of photon energy, but the main structures of the absorption TDDFT spectrum described above are still present with this simplified model, although further shifted in energy. This is in line with the observations that the nature of the ligands significantly affects the optical response of the cluster, as evidenced from the comparison of computed absorption spectra that use simplified models for the ligands (e.g. where complex aliphatic end groups are modeled with –CH3 or simply hydrogens) and calculations on the full ligand's structure.50,52 The results of the present work and of ref. 50 clearly show that the presence of the aromatic rings has a strong influence on the computed absorption spectrum for energies above 2.0–2.5 eV of photon energy due to the coupling of ligand-based excitations (that fall around 4.0–4.5 eV for the organic monolayer) with electronic excitations of the Au–S framework. This further points to the need of considering the full structure of MPCs in theoretical calculations aimed at a quantitative agreement with the experimental data.

The dichroic response, here evaluated in terms of the CD dispersion profiles, is instead much more sensitive to the conformation of the organic monolayer's end groups. With reference to the TDDFT CD profile corresponding to geometry 1, relatively intense CD bands with positive polarity are found at 1.71 eV, 2.55 eV, and 3.45 eV, while bands with negative polarity are found at 2.06 eV, 2.30 eV, 2.91 eV, 4.08 eV and 4.59 eV. TCM plots for selected excitation energies corresponding to bands observed in the theoretical CD spectrum are reported in Fig. 4. TCM plots are 2D representations of the excited state expansion in terms of 1h–1p configurations: each excited determinant corresponds to a point in the plane, the value on the X axis corresponds to the occupied orbital energy (εi) while the value on the Y axis corresponds to the unoccupied orbital energy (εa). For each excited determinant, a 2D Gaussian function (with FWHM = 0.12 eV) is added, with a weight proportional to its coefficient in the excited-state expansion. With the aid of Scheme S1 of the ESI and the TCM maps reported in Fig. 4, we can assign the CD absorption at 1.71 eV to transitions from the ligand-based d band (with significant Pd(4d) AOs contributions) to the LUMO. Similar 1h1p configurations contribute to the band at 2.06 eV while transitions from the same initial states to the LUMO+1 are responsible for the CD band at 2.55 eV. For higher excitation energies, a larger number of 1h1p excited configurations contribute significantly to the excited state wave function. For example, the band at 2.91 eV carries contributions of 1h1p interband Au(5d), Pd(4d) → Au(sp) transitions together with excitations from MOs mainly located at the Au–S interface to MOs mainly located on the ligand's aromatic moieties. An even larger number of 1h–1p states are seen to contribute to the CD bands at 3.45 eV and 4.08 eV. Note that the more intense 1h1p contributing configurations lie along the diagonal of the plots (corresponding to the equation εaεi = ω). However, from the TCM plots off-diagonal contributions with much lower intensity are also discernible, which add to these excitations a partial (very small) collective (plasmonic) character. In going along the series 1 → 4 of conformations, we note a similarity in the CD dispersion curves of 1–2 and 3–4 in the low-energy range. Overall, the same number of bands characterizes the CD spectra of all conformers, albeit with maxima and minima at slightly different energies. A close inspection of the TCM plots (not included) for energies corresponding to the stationary points of the corresponding CD spectra reveals a general common nature of the underlying 1h1p excited determinants contributing to the final wave function, and already discussed above.


image file: c8cp04107e-f4.tif
Fig. 4 TCM analysis of Au36Pd2(C2H4Ph)24, geometry 1, at selected excitation energies. X and Y axes refer to KS occupied and virtual orbitals’ eigenvalues respectively. Dotted lines obey the equation εaεi = ω, where ω is the photon energy.

The agreement between the TDDFT predictions and the experimentally recorded CD spectrum is quite satisfying, keeping in mind the deficiencies of the computational model discussed above in the case of the absorption spectrum. The rather broad bands, with opposite polarities, peaking at 2.06 eV and in the interval 2.6–3.0 eV have counterparts in the theoretical profiles although shifted by about 0.3–0.6 eV at lower energy, due to the over-attractive character of the LB94 xc potential. Their sign is however correctly reproduced. The more intense features of the experimental CD spectrum are the broad positive band extending in the energy interval 3.1–4.0 eV and the negative band with minimum at 4.7 eV and its side-band at 4.2 eV. These features are all reproduced, with the correct sign, by the TDDFT calculations, although with a narrower envelope and slightly shifted to lower energy. The negative side-band at 4.2 eV is not reproduced by the model structure, implying that the ligands’ structure plays a role in determining the finer structure of this broad high-energy band.

To get qualitative insights into the local nature of excitations responsible for the most prominent absorption and CD bands, in analogy to what has been done to analyse absorption spectra,7 we here also introduce a fragment projection analysis of computed CD spectra. This analysis basically entails a partition of the system into two or more separate subsystems and a projection of each given transition onto such fragments. This CD fragment projection analysis has been mentioned in a concurrent review article,53 but we here use it systematically for the first time and provide complete working formulae. Suppose our system is divided into two fragments, M and L (in this work M = Au, Pd and L = S, C, H atoms). From the normalization condition we get

 
image file: c8cp04107e-t8.tif(7)
 
image file: c8cp04107e-t9.tif(8)
 
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where indices λ, μ run over the basis set, Cμi are expansion coefficients of the i-th KS MO, Sλμ are the overlap matrix elements, and F = L or M. The desired projection of the CD response onto fragment contributions is then given by the following expression:53
 
image file: c8cp04107e-t11.tif(10)
where F, G = M or L.

At the outset one would anticipate that such a fragment contribution analysis would be less revealing in cases where a large number of 1h1p excitations of different nature contribute to the excited n-electron state. To investigate this issue, we report in Fig. 5 the fragment decomposition of the absorption spectrum (left panel) and of the CD spectrum (right panel) for Au36Pd2(SR)24, geometry 1, whereas similar plots for the other three geometries of the MPC are reported in the ESI (Fig. S1–S3). From an analysis of the plots we can draw the following conclusions. In absorption, all M → M, L → M, M → L, and L → L contributions are equally important in the optical region (excitation energies ≤3 eV); we note here that the Au–S interface region contributes to both M (Au) and L (S) regions, but clearly a different partitioning scheme where M = Au, Pd, S would decrease the M → L and L → L contributions. For higher excitation energies M → L and L → L contributions dominate. This is also in line with the discussion made above on numerical predictions based on simplified structural models of MPCs, especially in the UV region of the spectrum. Concerning the CD spectrum the situation is less clear-cut, especially in energy regions where cancellations among the various M → M, L → M, M → L, and L → L terms occur. From the plots reported in Fig. 5 and in the ESI it appears that these energy regions are ubiquitous and somewhat geometry-dependent. With reference to the right panel of Fig. 5, we can however see that M → L and L → L “localized” transitions contribute to the CD bands at 1.71 eV, 4.08 eV and 4.58 eV, while M → M and L → M contributions are mostly responsible for the appearance of the CD bands of (+) polarity at 2.45 and 3.45 eV.


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Fig. 5 Fragment decomposition of the absorption spectrum (left panel) and the CD spectrum (right panel) for Au36Pd2(SR)24, geometry 1. M = Au, Pd; L = S, C, H.

A different, complementary analysis is afforded by an examination of individual component maps of rotatory strengths (ICM-RS) plots, which have been introduced very recently.54 Starting from eqn (5) and using eqn (22) of ref. 11 we can write the following expression for the z component of the rotatory strength:

 
image file: c8cp04107e-t12.tif(11)
where ε corresponds to a Lorentzian energy broadening and ω is the photon energy. Similar expressions hold for the other Cartesian components. One can then construct 2D or 3D plots (ICM-RS plots) of the (real part of) the product of image file: c8cp04107e-t13.tif as a function of the single-particle KS occupied/virtual energies εi and εa at a given excitation energy (its integral over the εiεa domain gives then the rotatory strength). The motivation in using this quantity in addition to TCM maps is that while the latter are directly connected with the nature of the excited-state wave function, the former can give complementary information on the mechanisms responsible for the chiro-optical response of the system (see discussion in ref. 54). In particular, as can be seen from Fig. S4 of the ESI, where the dispersion curve of the rotatory strength for the Au36Pd2(SR)24 cluster, geometry 1, is decomposed into its x, y and z Cartesian components, the isotropically averaged CD results mainly from a cancellation between its x and y components which have opposite signs in the whole photon energy region investigated. It is therefore interesting to inspect ICM-RS maps corresponding to these two Cartesian components for a selection of excitation energies. We chose to focus on the high-energy region portion of the CD spectrum, where the most intense features appear in the experimental spectrum. We considered three excitation energies (3.45 eV, 4.08 eV and 4.59 eV) and show both 2D and 3D ICM-RS maps in Fig. 6. For all three excitation energies considered in the figure, the presence of destructive interference effects among contributions relative to the x and y Cartesian components is clearly displayed. Focusing for the moment on the ICM-RS (3.45 eV, x or y polarizations) maps, displayed in the first column of Fig. 6, one notices that the main contributions, more spread in energy and negative for the x component and more “localized” and positive for the y component, arise from single-particle excitations localized in the diagonal (points for which εaεi = ω) and correspond to excitations from occupied orbitals with metal (Pd(4d) and Au(6s,5d)) and S(3p) AOs contributions to MOs localized on the ligands and/or on the Au, S interface. However off-diagonal contributions (lower region of the εiεa domain) are clearly visible in both ICM-RS Cartesian components which interfere destructively although the cancellation is not complete. A similar observation can be made for the other two excitation energies investigated. In all cases most off-diagonal terms that interfere are restricted to the lower region and those interference effects are mostly among x and y Cartesian components and not due to interference among different excitations within a given polarization axis. For increasing excitation energies, positive (y Cartesian component) and negative (x Cartesian component) contributions along the diagonal are spread in energy and the corresponding 1h1p excitations involve occupied and virtual MOs that are either delocalized on the organic monolayer end-tails, interfacial Au–S states and states with appreciable Pd(4d) character. This is also in line with the general observation that for complex systems many 1h1p excitations contribute to the dichroic response.


image file: c8cp04107e-f6.tif
Fig. 6 TDDFT ICM-RS (ω, x or y) plots at three different excitation energies (in eV) for the Au36Pd2(SR)24 cluster, geometry 1. For each excitation energy/cartesian component both 3D plots (upper panels) and 2D projections (lower panels) are given.

3.2 Effects of the excess negative charge

The excess charge on MPCs can vary depending on the environmental conditions or it can be tuned electrochemically.27,28 It is therefore instructive to investigate the combined effect of excess negative charge and conformation on the dichroic response of the cluster. In the following we consider only vertical 2-electron attachment, i.e., keeping the geometry frozen to that of the neutral species. A plot of the frontier MOs for the Pd2Au36(SC2H4Ph)242− MPC, geometry 1, is reported in Fig. S5 of ESI while a Kohn–Sham energy level diagram is displayed in Scheme S2 (ESI). A visual comparison between Fig. S5 of the ESI and Fig. 2, where the plots of the frontier KS MOs for the neutral MPC are reported, reveals that the low-lying virtual MOs of the charged cluster have more contributions of C(2p) AOs of the phenyl rings, even if they are still mostly localized on the Au–S cluster's shell. The calculated DFT HOMO–LUMO gap is 0.56 eV and the effect of the vertical electron attachment is therefore an opening of the band-gap. The Pd 4d states contribute to the low-lying virtual MOs (LUMO, LUMO+1). The HOMO−n (n = 0, 1, 2) have a similar nature of mixed Au(6s) and S(3p) AOs. Before examining in detail the effect of conformational degrees of freedom on the dichroic response of the charged MPCs, we proceed as before, with an assignment of the most prominent calculated CD bands for the charged MPC geometry 1. A similar assignment then carries over to the CD spectra of the other geometries considered (see Fig. 7 and 8). In the 200–1200 nm range of the CD spectrum, prominent bands are at 285 nm (4.34 eV), 348 nm (3.55 eV), 426 nm (2.91 eV), 486 nm (2.55 eV) and 548 nm (2.26 eV), with alternating polarity. TCM plots calculated at the corresponding excitation energies are reported in Fig. S6 of the ESI. We see that at each excitation energy many 1h1p configurations contribute, so for each case we will only consider the few more intense ones. For all excitation energies, and for many contributing excited 1h1p determinants, the occupied MOs are in the so-called “ligand-based” d band (since these orbitals arise mainly from contributions of Au 5d and S 3p AOs), to which, at variance with the monometallic MPC, also Pd 4d AOs strongly contribute. Among others, final MOs are LUMO and LUMO+1 for the CD bands at 426 nm, 486 nm and 548 nm, even if 1h1p configurations with final states localized on the thiolates’ aromatic end-groups also contribute. The number of excited 1h1p configurations contributing to the excited state wave function for the CD signals at 285 nm and 348 nm becomes very large although strong contributions of excitations to MOs localized on the ligands can be singled out from the plots.
image file: c8cp04107e-f7.tif
Fig. 7 Upper panels: Absorption spectra. Comparison between the TDDFT spectra of Au38 and the four conformers of Au36Pd2 neutral MPCs (left). Similar comparison, but for the charged species (right). Model refers to the Au36Pd2 cluster (geometry 1) with thiol tails replaced by –CH3 groups. Lower panels: CD spectra for the neutral (left) and charged (right) MPCs.

image file: c8cp04107e-f8.tif
Fig. 8 Effect of charge on the CD spectra of all conformers of Au36Pd2(SC2H4Ph)24 considered in this work. A comparison with the CD spectrum of the Au38(SC2H4Ph)24 MPC is also added for geometry 1.

A comparative analysis of absorption and dichroic response of both neutral and charged clusters can be done with reference to Fig. 7. A close inspection of the figure reveals that the main effect of the presence of an excess negative charge on the clusters is to somewhat “quench” the dependence of the CD dispersion on the particular conformation (compare the two lower panels in Fig. 7). The reason for this effect can be traced back to a decrease of off-diagonal 1h–1p contributions brought about by an increase in Coulomb screening at higher electron density, as apparent from a comparison of Fig. 4 and Fig. S6 (ESI). The effect of the excess charge on the molar circular dichroism for each different geometry of the Pd2Au36(SR)24 MPC considered in this work is further analyzed in Fig. 8. For all four geometries, the dichroic response of the MPC is affected by the presence of an excess charge mainly in the 400–800 nm wavelength range, but the induced electronic effects do not alter in a substantial way the qualitative behavior of the CD profiles of the neutral species. It is also worth noticing that in the same wavelength range major quantitative differences with the CD spectrum of the monometallic MPC are found (upper left panel of Fig. 7) concerning the polarity of the CD bands that fall in this wavelength range.

4. Conclusions

In this work we have analysed the effect of Pd doping on the electronic structure and optical response of the Au38(SC2H4Ph)24 monolayer-protected cluster (MPC). TDDFT calculations of the absorption and CD spectra of Pd2Au36(SC2H4Ph)24 have been carried out by using a recently developed complex polarizability algorithm9–11 with the aim of investigating the effects of Pd doping, the conformational degree of freedom of the thiolates’ end groups, and the excess charge on the optical and dichroic response of the Au38(SC2H4Ph)24 MPC. Pd doping clearly affects the electronic structure and therefore the spectroscopic features of the Au38(SC2H4Ph)24 cluster. This is mainly due to the localization of Pd (4d) states in the ligand-based d band and on the virtual MOs of lower energy. Clear signatures of Pd doping are visible both in absorption and in CD dispersion spectra. A limited conformational sampling as carried out here points out to a much greater sensitivity of the optical rotation to the specific conformation of the end-groups of the organic monolayer, as compared to the absorption. The effect is apparent in energy shifts of the most intense CD bands. This is an important aspect that should be taken into account when quantitative agreement with experiments (mostly done on solvated systems) is sought. A complete account of the impact of the conformational degrees of freedom on absorption and CD spectra should entail sampling (e.g. via molecular dynamics) the accessible configuration space followed by the calculation of the spectrum by TDDFT at each snapshot, with a final Boltzmann average of all the spectra so obtained. Obviously such a computational scheme is not presently feasible for such large systems, thus highlighting the need to develop efficient procedures based on minimal sampling,55 or multilevel approaches.56 The effect of the excess charge is mainly seen as a lower dependence of the dichroic response on conformational sampling, due to a decrease of off-diagonal 1h–1p contributions brought about by an increase in Coulomb screening at higher electron density.

The agreement between the TDDFT predictions and the available experimental data is qualitatively good, and enabled us an assignment of absorption and CD bands to specific classes of one-particle excitations. The agreement is however not quantitative and points to the importance of both the nature of the environment and the large conformational degrees of freedom of the organic monolayer end groups in determining the spectroscopic properties of this interesting class of materials.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Computational support from the CINECA supercomputing centre within the ISCRA-C program (awards: HP10CP65P9 and HP10B89V25) and through the convenzione Università degli Studi di Trieste and CINECA is gratefully acknowledged. Computational research by A. F. was performed using EMSL, a DOE Office of Science User Facility sponsored by the Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory, and PNNL Institutional Computing at Pacific Northwest National Laboratory. This work has been supported by MIUR (Programmi di Ricerca di Interesse Nazionale PRIN 2010) of Italy, Finanziamento per ricerca di ateneo, FRA 2015 and FRA 2016 of the Università degli Studi di Trieste.

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Footnote

Electronic supplementary information (ESI) available: Kohn–Sham energy level diagrams for geometry 1 for both neutral and charged MPCs. Fragment decomposition of the absorption and CD spectra for all geometries and charge states not included in the manuscript. TCM analysis for geometry 1 (charged state). Decomposition of the CD spectrum of the Au36Pd2(SR)24 cluster, geometry 1, into its x- y- z-Cartesian components. Atomic coordinates for geometries 1–4 in xyz format. See DOI: 10.1039/c8cp04107e

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