Spin-Orbit Coupling Effects in AumPtn Clusters (m + n = 4).

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Spin–Orbit Coupling Effects in Au Pt Clusters (m + n = 4) Norberto Moreno, Franklin Ferraro, Elizabeth Florez, Cacier Zilahy Hadad, and Albeiro Restrepo J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b11397 • Publication Date (Web): 19 Feb 2016 Downloaded from http://pubs.acs.org on February 21, 2016

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The Journal of Physical Chemistry

Spin–Orbit Coupling Effects in AumPtn Clusters (m + n = 4) Norberto Moreno,† Franklin Ferraro,‡ Elizabeth Flórez,¶ C. Z. Hadad,† and Albeiro Restrepo∗,† Instituto de Química, Universidad de Antioquia UdeA, Calle 70 No. 52–21, Medellín, Colombia, Departamento de Ciencias Básicas, Fundación Universitaria Luis Amigó, Transversal 51A No. 67B–90, Medellín, Colombia, and Departamento de Ciencias Básicas, Universidad de Medellín, Carrera 87 No. 30–65, Medellín, Colombia E-mail: [email protected]

Phone: +57 (4) 219 83 32.

∗ To

whom correspondence should be addressed de Antioquia ‡ Fundación Universitaria Luis Amigó ¶ Universidad de Medellín † Universidad

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Abstract A study of Aum Ptn (m + n = 4) clusters with and without spin-orbit (SO) coupling using scalar relativistic (SR) and two component methods with the ZORA Hamiltonian was carried out. We employed the PW91 functional in conjunction with the all electron TZ2P basis set. This paper offers a detailed analysis of the SO effects on the cluster geometries, on the LUMOHOMO gap, on the charge distribution and on the relative energies for each relativistic method. In general, SO coupling led to an energetic rearrangement of the species, to changes in geometries and structural preferences, to changes in the structural identity of the global minimum for the Au3 Pt, AuPt3 and Pt4 case, and to a reduction of relative energies among the clusters, an effect which appears stronger as the amount of Pt increases.

Introduction Among the most important properties of noble metals is their lack of reactivity even in the liquid state. Nonetheless, Gold (Au) and Platinum (Pt) are presently used in a wide variety of technological applications. For example, Au is commonly used in microelectronics. 1,2 In medicine, noble metals have been incorporated for appropriate cancer diagnosis, imaging, and treatment. 3–12 In recent decades, Pt has been used in petroleum cracking as well as in many other industrial processes due to a high catalytic activity. 13–15 Likewise, Au has potential application in catalysis, which has raised great interest as a result of marked selectivity. 16,17 It has recently been discovered that small Au clusters of no more than 13 atoms form rapidly in aqueous solutions at room temperature and act as extremely active catalysts. In fact, these clusters catalyze the ester-assisted intermolecular hydration of alkynes and show turnover frequencies larger than previously reported. 18 These findings generate great enthusiasm and interest in understanding the possible causes of such properties. Additional examples showing that the catalytic activity of Au clusters play important roles in chemical reactions are the CO and glycerol oxidation processes. 19–22

Besides understanding their catalytic activity, theoretical studies of Au and Pt nano– and sub– 2 ACS Paragon Plus Environment

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nanoparticles are motivated by the need of rationalizing experimental observations. For example, there is evidence that hollow cages consisting of Au− 16−18 clusters exist with a diameter of approximately 5.5 Å. 23 The structures of Au7 , Au19 and Au20 have also been experimentally reported, 24 as well as the recent detection and characterization of the Au4 cluster. 25 There have also been several experimental reports involving small Pt clusters in specific reactions and suggestions of synthetic methods to produce clusters of different stoichiometries, such as Pt8−10 15 and Pt12 , Pt28 , Pt60 . 26

Information on bimetallic clusters, which are the focus of this work, is not as abundant as that available for monometallic clusters. Au2 Pt2 , Au3 Pt and AuPt3 structures have been reported along 27–32 with their interactions with CO molecules. 33–35 High adsorption energies into MgO films have also been reported. 35,36 Sensitive issues in the just mentioned theoretical studies are that the corresponding potential energy surfaces (PESs) were not thoroughly explored and that the SO couplings nor the high spin states, which are very relevant for Au/Pt containing clusters, were taken into account.

It is well known that relativistic effects, especially SO couplings, have very important consequences, 37–47 this is particularly true for systems containing Au and Pt atoms. For example, for Pt4 , it has been found that the inclusion of SO couplings changes the stability order of the isomers, increasing the relative stability of planar structures, but not enough to overcome the tridimensional global minimum. 48 Molecular geometries for group 10 hexafluorides d4 complexes strongly depend on SO coupling, preventing the Jahn–Teller distortion predicted in non–relativistic treatments that erroneously lead to square bipyramidal D4h geometries and diamagnetic materials. It has been shown that only after inclusion of relativistic effects, the experimental octahedral geometries and paramagnetic character of these materials are recovered. 42,44,49

In this work, we conduct exhaustive explorations of the configurations of the Aum Ptn (m + n = 4) clusters in several spin states in order to understand their chemical reactivity and their physico-



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chemical properties. This is an important topic since the behavior of atomic and molecular clusters is mainly dictated by their geometries and since it is well known that for a given PES, chemical and physical processes are not restricted to the lowest energy structure (global minimum).

Theoretical Background The relativistic and non–relativistic Kohn–Sham equations are written as h

i T + V KS ψi = εi ψi

(1)

Where T , the kinetic energy operator, takes a different form under several flavors of relativistic formalism. The zeroth order regular approximation (ZORA) Hamiltonian, written below, is obtained after expanding

E 2c2 −V

on the Dirac Hamiltonian and keeping only the zeroth order

term. 50–53

(2)

H = V +T

c2 H = V +σ · p 2c2 − V

σ ·p

(3)

here, c is the speed of light and σ are the respective Pauli matrices. The potential term in the kinetic energy operator in the Kohn–Sham formalism makes this Hamiltonian electrostatically gauge dependent, leading to distortions in the molecular geometries as a result of non–physical forces between the nuclei. 54 This problem has been overcome in the implementation of ZORA in ADF, 55 where a scaled ZORA method, practically gauge invariant and especially adequate for valence orbitals was developed. 52 As pointed out by Saue, 47 a convenient characteristic of the ZORA


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Hamiltonian is that considering either the average electronic field or the complete Kohn–Sham potential in T , automatically includes SO contributions. In the case of the ZORA SO Hamiltonian, T can be split into two terms, scalar relativistic and relativistic spin–orbit, this decomposition leads to the following expressions of the ZORA Hamiltonian , which were used in our calculations

c2 p 2c2 − V KS

(4)

c2 σ · (~∇V KS × p) (2c2 − V KS )2

(5)

H SR = V + p ·

H SO = H SR +

in H SO , the rightmost term in equation 5 provides the SO coupling contributions.

Computational Details For systems comprising four atoms, a total of seven geometrical patterns, shown in Figure 1, are possible. After optimization without symmetry constraints geometrical distortions may occurr. Each motif for each stoichiometry and for each spin multiplicity (SR cases) was treated in two different ways: (i) using the ZORA SR Hamiltonian (Eq. 4), equilibrium geometries were obtained from the initial guesses in Figure 1 and characterized as true minima by harmonic vibrational frequencies analysis at the PW91 level with the all electron TZ2P basis set, the three lowest spin multiplicities were considered in all cases, except for the Pt4 system, were the lowest five spin multiplicities were accounted for (ii) equilibrium geometries were also obtained and characterized as true minima using the ZORA SO Hamiltonian (Eq. 5). In this way, differences encountered for a particular system are exclusively due to the consideration of SO couplings. Zero–point vibrational energies (ZPE) were incorporated in the calculation of cluster relative energies. The PW91 5 ACS Paragon Plus Environment


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functional has proven to be adequate to treat metallic systems. 30,56 All calculations in this work were carried out using the ADF package. 55 For SR structures the calculations were done using a restricted scheme for singlets and an unrestricted scheme for higher multiplicities. It is necessary to clarify that when we refer to higher multiplicities corresponding to open shell systems, we do it to retain the multiplicity concept while recognizing that the quantum number S is not a good descriptor in a unrestricted single–determinantal framework. For SO structures the calculations have ′

′

been carried out within Kramers restricted or unrestricted schemes. At the same time, Kramers unrestricted calculations were done using the noncollinear aproximation. 46,55

D2h

C2v

D3h

D∞h

Td

D4h

Cs

Figure 1: Initial geometries for Aum Ptn (m + n = 4) clusters. Symmetries for the homonuclear case are included.

Results And Discussion Geometries And Energies A total of 59 well defined minima were located at the scalar relativistic level: 7 for Au4 , 10 for Au3 Pt, 15 for Au2 Pt2 , 13 for AuPt3 and 14 for Pt4 . On the other hand, at the relativistic SO level, a total of 22 minima were found: 3 for Au4 , 5 for Au3 Pt, 6 for Au2 Pt2 , 4 for AuPt3 and 4 for Pt4 . Figure 2, Figure 3, and Figure 4 show the geometries and the corresponding symmetries obtained in each case, lower case labels are included to differentiate motifs belonging to the same point group. Cartesian coordinates for all clusters found in this work can be found in the supporting 6 ACS Paragon Plus Environment

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information. A plot showing the changes in interatomic distances as a result of SO couplings for the comparable structures in both treatments is also included in the SI.

D2h

C2v

D3h

D4h

D2d,a

D2d,b

Td

Cs

Figure 2: Geometrical motifs for Au4 and Pt4 .

C2v,a

C2v,b

C2v,c

C2v,d

C2v,e

C2v, f

D3h

Cs,a

Cs,b

C∞h

C3v

Cs,c

Figure 3: Geometrical motifs for Au3 Pt and AuPt3 Despite the large numbers of electrons (up to 316) in the clusters, despite our systems having odd numbers of electrons and/or open shell electronic structures, and despite the all–electron nature of our approach, the unrestricted calculations seem to be quite reliable as is evidenced from the results plotted in Figure 5. Out of the 59 structures analyzed at the SR level, only 6 of them corresponding to high energy local minima exhibit mild spin contamination (three for Pt4 , two for AuPt3 and one for Au4 ). These results provide strong support for the quality of our calculations and for the most part render multireference calculations in the title systems unnecessary.

Table 1 lists all structures found, their energy ordering and their respective geometrical motif. To 7 ACS Paragon Plus Environment


D2h,a

Cs,a

C2v,a

C2v,b

Cs,b

Cs,c

D2h,b

C2h

C2v,c

Figure 4: Geometrical motifs for Au2 Pt2

22 20 18

2

16 14 12 10

Final

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Au4 Au3Pt Au2Pt2 AuPt3 Pt4

8 6 4 2 0 0

2

4

6

8

10

Initial

12

14

16

18

20

22

2

Figure 5: Spin contamination for Aum Ptn clusters at the SR PW91/TZ2P level. hS2 i = S(S + 1) A total of 59 structures are analyzed, only six of them corresponding to high energy local minima show mild spin contamination.


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the best of our knowledge, a number of the structures are reported here for the first time, or, in some cases, correspond to spin states never reported at the scalar relativistic level, these are marked with asterisks in Table 1. The results in this work suggest that some structures exist with various spin multiplicities in the same geometrical motif.

Table 1 shows that for Au4 in the SR case we found three minima in the singlet state with D2h , C2v , and D4h symmetries. D2h is the lowest energy isomer, which matches the experimentally reported structure 25 and was characterized in other theoretical studies. 29–31,57–61 Two minima in the triplet state with D2h and D3h symmetries and two in the quintet state with D2d and Td symmetries were also located. Generally speaking, the singlets are more stable than the triplets, which in turn are more stable than the quintets. Most structures are planar, with the only 3 dimensional case occurring in the quintet PES. Only three minima with D2h , C2v , and D3h symmetries were found when considering SO, these structures exhibit larger relative energies when compared to the SR case. Interatomic distances (see supporting information) are shortened as a consequence of the inclusion of SO coupling for Au4 clusters. It is important to keep in mind that previous studies involving the Au tetramer limit their scope exclusively to the D2h and C2v isomers in the singlet state, 62 however, we show here that other structures and multiplicities are possible, at least in this single–determinantal frame as a first approximation, and as discussed above, their local minima status does not prevent them to take part in physicochemical processes.

For Au3 Pt at the SR case, we found four minima with Cs and C2v symmetries in the doublet state, four minima with C2v , Cs , and C∞h symmetries in the quadruplet state and two minima with C3v and D3h symmetries in the sextet state. The doublets ended up being more stable than the quadruplets and these, in turn, more stable than the sextets (Table 1). In the SO case, we found five minima with C2v , Cs , and C3v symmetries. As opposed to the Au4 case, here, the inclusion of SO coupling reduced the relative energies among the clusters and in some cases produced geometrical distortions. SO coupling enlarged the range of Au–Au distances and predicted Au–Pt distances that are



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somewhat shorter than in the SR treatment.

In Au2 Pt2 clusters, SR calculations suggest that lower spin multiplicity does not mean greater stability: two minima with C2v and D2h symmetries exist in the singlet state, however, neither of them is the global minimum, which corresponds to a Cs structure found among the seven minima in the triplet state, furthermore, there are three triplets that are more stable than the most stable singlet. Six minima in the quintet state with Cs , C2v , C2h , and D2h symmetries were also located. Consideration of SO leads to six minima with Cs and C2v symmetries with smaller relative energies and smaller Au–Au and Au–Pt distances as well as a shorter range for Pt–Pt distances (Table 1 and supporting information).

For AuPt3 , six minima with C2v , C3v , Cs , and D3h symmetries were located in the doublet state which contain the global minimum. The quadruplet state is populated by four minima of C2v , C3v , and Cs symmetries, two of which are among the most stable clusters. Three minima with C2v and Cs symmetries exist in the sextet state. As in the case of Au2 Pt2 , high spin multiplicity structures lower their energies to the point that they become more stable that some doublets but not enough to overcome the global minimum, producing a scenario where mixed multiplicities are expected for these clusters. In the SO case, we found four minima with C2v , C3v , and Cs symmetries with smaller relative energies and siginficative shortening of the range of Pt–Pt distances.

Another case of high spin multiplicity leading to energetic stabilization is found in Pt4 : the global minimum corresponds to a 3 dimensional Td structure in the triplet state, two additional triplets with C2v and D3h symmetries were found. Our 3 dimensional SR global minimum differs from other non–SO treatments which assigned that role to different C3v 48 and C2v 63 structures. In addition, three minima with D2d , Td , and Cs symmetries were characterized in the singlet state, two minima with C2v and D2d symmetries are present in the quintet state, while four minima with D4h , D2h , Td , and Cs symmetries were found in the septet PES, finally, two minima with D2d and D4h 10 ACS Paragon Plus Environment

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symmetries were located in the nonet state. Interestingly, the lowest singlet is above in energy than triplet, quintet and septet states. Four minima with D2h , D2d , D4h , and C2v symmetries with lower relative energies and smaller range of Pt–Pt distances when compared to their SR counterparts were located upon consideration of SO coupling.

As can be seen in Table 1, high spin states are either the global minimum or are very close in energy to it in the Au2 Pt2 , AuPt3 and Pt4 cases. As shown in Figure 6, energy windows for the clusters are large, but narrowed when considering SO couplings (2.712 to 1.499 eV for Au4 , 3.644 to 0.579 eV for Au3 Pt, 2.426 to 0.326 eV for Au2 Pt2 , 3.108 to 0.311 eV for AuPt3 , and 2.593 to 0.217 eV for Pt4 ).

3.50

Relative Energies (eV)

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3.00 2.50 2.00 1.50 1.00 0.50 0.00

Au4

Au3Pt

Au2Pt2

AuPt3

Pt4

Figure 6: SO effects on relative energies, ∆E0 per cluster. ♦: SR. : SO. Size of diamonds is proportional to spin multiplicity for each structure Consideration of SO coupling in the title clusters allows us to draw five important conclusions from our results: (i) SO coupling reduces the structural complexity of the clusters, allowing fewer minima than the SR treatment, however it is very important to recognize that in the SR treatment, it is possible to optimize the same motif in different spin states while the SO treatment allows the mixing of those states for the same structure. (ii) SO favors planar structures and thus favors



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Table 1: ZPE–corrected relative energies, ∆E, in eV. To help identifying the clusters, we use the M X p notation: X

refers to the stoichiometry. p, the right superscript refers to the relative position with respect to the energy of the global minimum in a given PES. M, the left superscript indicates the initial spin multiplicity for the SR case. * Unreported structure or unreported at a given spin multiplicity. See Figure 2, Figure 3, and Figure 4 for the structural motifs.

Cluster 1 (Au

SR

1 4) 1 (Au )2 4 3 (Au )3 4 1 (Au )4 4 3 * (Au4 )5 5 (Au )6 4 5 (Au )7 4 2 (Au Pt)1 3 2 (Au Pt)2 3 2 (Au Pt)3 3 2 (Au Pt)4 3 4 (Au Pt)5 3 4 (Au Pt)6 3 4 (Au Pt)7 3 * 4 (Au3 Pt)8 6 (Au Pt)9 3 * 6 (Au3 Pt)10 * 3 (Au2 Pt2 )1 3 (Au Pt )2 2 2 3 (Au Pt )3 2 2 * 1 (Au2 Pt2 )4 3 (Au Pt )5 2 2 3 (Au Pt )6 2 2 1 (Au Pt )7 2 2 5 (Au Pt )8 2 2 5 (Au Pt )9 2 2 3 (Au Pt )10 2 2 5 (Au Pt )11 2 2 3 (Au Pt )12 2 2 * 5 (Au2 Pt2 )13 5 (Au Pt )14 2 2 * 5 (Au2 Pt2 )15 * 2 (AuPt3 )1 4 (AuPt )2 3 2 (AuPt )3 3 4 (AuPt )4 3 2 (AuPt )5 3 * 4 (AuPt3 )6 * 6 (AuPt3 )7 * 2 (AuPt3 )8 6 (AuPt )9 3 4 (AuPt )10 3 2 (AuPt )11 3 6 (AuPt )12 3 2 * (AuPt3 )13 3 (Pt )1 4 5 (Pt )2 4 * 7 (Pt4 )3 1 (Pt )4 4 3 (Pt )5 4 1 (Pt )6 4 1 (Pt )7 4 5 (Pt )8 4 7 (Pt )9 4 * 7 (Pt4 )10 * 3 (Pt4 )11 7 (Pt )12 4 9 (Pt )13 4 * 9 (Pt4 )14

Motif D2h C2v D2h D4h D3h D2d,b Td Cs,c Cs,a C2v,a C2v,d Cs,c Cs,a C2v,d C∞h C3v D3h Cs,b Cs,a C2v,a C2v,c C2v,b C2v,b D2h,a Cs,a C2v,a D2h,a Cs,c Cs,c D2h,b Cs,c C2h C3v C2v,b C2v,b Cs,b Cs,b C3v C2v,c C2v, f C2v,d C2v,e C2v,e Cs,b D3h Td D2d,b D4h D2d,a C2v Td Cs C2v D2h Td D3h Cs D2d,b D4h

∆E

0.000 0.041 0.674 0.930 1.414 2.684 2.712 0.000 0.208 0.211 0.581 0.879 1.280 1.527 1.791 2.212 3.644 0.000 0.092 0.093 0.264 0.282 0.307 0.685 0.690 0.695 0.741 0.857 1.033 1.108 2.053 2.426 0.000 0.127 0.130 0.166 0.305 0.500 0.508 0.913 1.020 1.039 1.124 1.185 3.108 0.000 0.007 0.135 0.209 0.279 0.283 0.390 0.410 0.673 1.078 1.243 1.360 1.953 2.593

Cluster (Au4 )1 (Au4 )2 * (Au4 )3

SO

Motif

∆E

D2h C2v D3h

0.000 0.144 1.499

(Au3 Pt)1 (Au3 Pt)2 * (Au3 Pt)3 (Au3 Pt)4 (Au3 Pt)5

C2v,b C2v,a Cs,b C3v C2v,d

0.000 0.187 0.300 0.475 0.579

* (Au2 Pt2 )1 (Au2 Pt2 )2 (Au2 Pt2 )3 (Au2 Pt2 )4 (Au2 Pt2 )5 * (Au2 Pt2 )6

Cs,b Cs,a Cs,c C2v,b C2v,a C2v,c

0.000 0.014 0.098 0.220 0.262 0.326

(AuPt3 )1 (AuPt3 )2 * (AuPt3 )3 * (AuPt3 )4

C2v,d C2v,b C3v Cs,a

0.000 0.253 0.280 0.311

(Pt4 )1 (Pt4 )2 (Pt4 )3 (Pt4 )4

D2h D2d,b D4h C2v

0.000 0.056 0.112 0.217


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planar global minima. (iii) Au–Au distances are shortened in most cases when SO is considered (details in the supporting information). Au–Pt distances are also shortened in Au2 Pt2 , but depend on specific connectivity, those distances are shortened or enlarged in Au3 Pt and in AuPt3 . Pt–Pt distances also depend on specific connectivity. (iv) Inclusion of SO changes the structural identity of the global minimum for the Au3 Pt, AuPt3 and Pt4 cases. (v) Inclusion of SO coupling reduces energy differences among isomers.

Mulliken Charges And Spin Densities Mulliken charges and spin densities for all clusters found in this work are in the supporting information.

For Au4 , some charge polarization is observed, electrons are driven mainly towards peripheral atoms in D2h , C2v , and D3h structures. For some structures, 1 (Au4 )4 , 5 (Au4 )6 , 5 (Au4 )7 , the charge on each atom is zero showing no charge transfer. When SO is considered, the charge on atoms decreases slightly, perhaps due to an increase in the covalency. For open-shell structures at the SR level, the spin density accounts for unpaired electrons corresponding to the initial multiplicity. This spin density is correlated to the most negatively charged atoms.

Charge polarization is also observed in Au3 Pt. In general, the charges on atoms are small, extreme cases approaching –0.12, Au atoms being more negatively charged than Pt atoms, except for a few exceptions of peripheral Pt atoms. When SO is considered, the negative charge on atoms decreases for the C2v,a structure, but for C3v and C2v,d structures, larger negative charges are observed. The largest spin density is located on Pt atoms, which accounts for unpaired electrons corresponding to the initial multiplicity.

For Au2 Pt2 , the magnitudes of negative charge on all atoms do not exceed 0.13, the most extreme case. The largest negative charges are on peripheral atoms, however there are some structures 13 ACS Paragon Plus Environment


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where centralized Pt atoms have the highest negative charge, for example those belonging to C2v,a and C2v,c motifs. The largest spin density is located on Pt atoms for all structures. Even smaller negative charges are observed when considering SO, on Cs,a , Cs,b , C2v,b and, C2v,c motifs, however, for Cs,c and C2v,a structures, larger charges are actually observed.

An interesting observation is that the high Pt content in AuPt3 clusters reverses the direction of charge transfer, namely, Au atoms become generally positive while Pt atoms become negative. All atoms exhibit charges smaller than 0.14, the extreme case. For structures belonging to the C3v motif an accumulation of negative charge on Pt atoms is seen, except for 4 (AuPt3 )6 where Au is negatively charged. When SO is considered the charge transfer decreases for C3v and C2v,b structures, while for C2v,d the charge transfer increases. The largest spin density is located on Pt atoms and accounts for unpaired electrons corresponding to the initial multiplicity.

For Pt4 , the magnitude of charge on all atoms is smaller than 0.15. For structures belonging to the Td , D2d,a and, D4h motifs, the charge on each atom is zero and the spin density is the same, resembling the unpaired electrons corresponding to the initial multiplicity. For others motifs, the charge is preferably located on peripheral atoms. For structures with inhomogeneous spin density, it can be seen that the spin densities are located on the negatively charged atoms, except for 3 (Pt4 )11 and 9 (Pt4 )13 . Furthermore, when SO is considered the charge transfer increases.

Finally, we state that in most clusters, Pt atoms have higher spin densities with a few exceptions. Furthermore 2 (Au3 Pt)4 , 3 (Au2 Pt2 )6 , 2 (AuPt3 )1 , 2 (AuPt3 )3 , 2 (AuPt3 )8 , 2 (AuPt3 )13 and, 2 (AuPt3 )11 structures have negative spin density on some atoms showing both beta spin electrons and spin polarization. As a general rule, Au atoms are charged more negatively than Pt atoms, except for AuPt3 clusters and for cases of peripheral Pt atoms.


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LUMO–HOMO gaps LUMO–HOMO gaps for the global minima are listed in Table 2. A lowering of this gap is evident as a consequence of the SO coupling. Thus, the clusters, at least in their lowest energy forms become softer, this has serious implications regarding the reactivity of these clusters, because the maximum hardness principle states that harder systems reduce their chemical reactivity. 64 It appears that by not considering SO couplings, the reactivity of the Aum Ptn clusters is grossly underestimated. Notice that Table 2 only considers the global minima on each PES whose identity is changed by the SO calculations, thus HOMO–LUMO gaps in the two treatments actually correspond to different structures in some cases.

Table 2: ∆ELUMO−HOMO (eV) for the global minima in each stoichiometry.

Cluster Au4 Au3 Pt Au2 Pt2 AuPt3 Pt4

∆ELUMO−HOMO SR 1.01 1.16 1.05 0.66 0.71

SO 1.00 0.36 0.09 0.16 0.20

Frontier orbitals shown in Figure 7 suggest that for the cases were the identity of the global minimum is not altered by inclusion of SO, Au4 and Au2 Pt2 , the compositions and shapes of the HOMO and LUMO are slightly altered. It is also seen in Figure 7 that increasing the amount of Pt leads to higher nucleophilicity and electrophilicity at Pt sites as revealed by higher local concentrations of frontier orbitals at Pt atoms. This observation is consistent with the above statements that relate high local concentrations of charge and spin density (HOMOs) at peripheral atoms in Au4 and Pt4 clusters, while the electrophilic power for the same systems is related to high local concentrations of LUMOs at centralized atoms. Detailed contributions from atomic orbitals to frontier molecular orbitals in the SR case for all clusters is listed in the supporting information.



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Cluster

HOMO SR

LUMO SR

HOMO SO

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LUMO SO

Au4

Au3 Pt Au2 Pt2 AuPt3 Pt4 Figure 7: HOMO and LUMO orbitals for global minima.

Pt Content Pt–Pt interatomic distances (see supporting information) are generally smaller than Au–Pt distances and those, in turn, are smaller than Au–Au distances. SO coupling introduced mild changes in atom–atom distances, however, it is evident that these changes are dependent on the Pt content: going from Au4 to Au3 Pt and then to Au2 Pt2 results in larger Au–Au distances for both SR and SO cases. Au–Pt distances in Au3 Pt, Au2 Pt2 and AuPt3 are not as sensitive to the Pt content. Pt–Pt distances decreased slightly in going from Au2 Pt2 to AuPt3 and to Pt4 .

As seen in Figure 6, for the SR case, there is a clear energy separation between different spin multiplicities in Au4 and in Au3 Pt. For these clusters, the structures with lower multiplicities, namely singlets and doublets, are more stable than triplets and quadruplets, and these, in turn are more stable than quintets and sextets. However, increasing the amount of Pt causes the high multiplicities to substantially lower their relative energies, to the point that for Au2 Pt2 , the lowest energy structures are triplets followed by singlets and then quintets. For AuPt3 , the stability mixing 16 ACS Paragon Plus Environment

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of structures with different multiplicities is evident, and finally, for Pt4 , this effect is stronger where a triplet structure is the global minimum closely followed by a quintet 0.007 eV above. Thus, our results clearly show that a larger amounts of Pt lead to a mixing of similar structures with different spin states. Increasing the content of Pt caused both the SR and SO treatments to reduce energy ranges for particular stoichiometries. As mentioned above, this effect is more pronounced for the SO case. Increasing the amount of Pt reduces the LUMO-HOMO gap, thus increasing the reactivity of the clusters (it is well known that Au is not as reactive as Pt 65,66 ).

Summary, Conclusions And Perspectives In this work, we report for the first time a number of structures previously unnoticed in the literature for the Aum Ptn (m + n = 4) clusters and show that the inclusion of SO couplings is pivotal for proper description of their physical and chemical properties. Considering the SO coupling in the title clusters (i) reduced the range of relative energies and changed the energetic ordering of the clusters, except of Au4 , (ii) In some cases changed the identity of the global minimum, favoring planar over 3 dimensional structures, (iii) reduced the LUMO-HOMO gap of the global minimum on each PES, enhancing their reactivity and therefore improving their ability to act as catalyst. Increasing the Pt content (i) reduced relative energies among structures on each PES, (ii) shuffled the stability orders among different spin multiplicities at the SR level, (iii) reduced the LUMOHOMO gap of the most global minima.

Our results are very comprehensive regarding cluster geometries, charges and analysis of frontier orbitals that not only match what is currently found in the scientific literature, 25,29–32 but considerably extend the scope of available knowledge in fundamental aspects of the problem. However, our work should only be considered a valuable first step towards a rigorous treatment because some aspects of the problem fall outside the scope of this work, most prominently, the possible



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multideterminantal character of some of the structures reported here.

ACKNOWLEDGMENTS Partial funding for this work was provided by Universidad de Antioquia via “Estrategia de sostenibilidad” and by CODI project 10170. N.M. thanks Colciencias for a graduate scholarship.

Supporting Information: Cartesian coordinates, Mulliken charges and, spin densities for all clusters found in this work. For all structures calculated at the SR level, we also include the open shells and frontier orbital contributions as well as the hS2 i value. Comparison of interatomic distances in both SR and SO treatments is also provided.

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Graphical Abstract: Relativistic effects change many properties, including the identity of some global minima (top) and relative energies (bottom). Gold atoms in yellow and platinum atoms in blue


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Comparative study of small boron, silicon and germanium clusters: B(m)Si(n) and B(m)Ge(n) (m + n = 2-4).

Photoelectron spectroscopy and ab initio calculations of small SinSm⁻ (n = 1,2; m = 1-4) clusters.

Theoretical study of nascent solvation in Ni+ (benzene)m, m = 3 and 4, clusters.

A novel concept for the synthesis of multiply doped gold clusters [(M@Au(n)M'(m))L(k)](q+).

Photoelectron imaging and photodissociation of ozonide in O3(-)⋅(O2)n (n = 1-4) clusters.

Promoting effect of Co in Ni(m)Co(n) (m + n = 4) bimetallic electrocatalysts for methanol oxidation reaction.

Formation of neutral In(m)C(n) clusters under C60 ion bombardment of indium.

Ligand Field Strength Mediates Electron Delocalization in Octahedral [((H)L)2Fe6(L')m](n+) Clusters.

Excited states of OH-(H₂O)n clusters for n = 1-4: an ab initio study.

Identification of hyperhalogens in Ag(n)(BO2)(m) (n = 1-3, m = 1-2) clusters: anion photoelectron spectroscopy and density functional calculations.

Vibrational spectra and structures of bare and Xe-tagged cationic Si(n)O(m)⁺ clusters.

Bulk size crystal growth, spectroscopic, dielectric and surface studies of 4-N,N-dimethylamino-4-N'-methylstilbazolium m-nitrobenzenesulfonate (DSMNS): A potential THz crystal of stilbazolium family.

Different pharmacology of N-desmethylclozapine at human and rat M2 and M 4 mAChRs in neocortex.

Infrared spectroscopy of protonated trimethylamine-(benzene)(n) (n = 1-4) as model clusters of the quaternary ammonium-aromatic ring interaction.

On the structural landscape in endohedral silicon and germanium clusters, M@Si12 and M@Ge12.

O,N,N-pincer ligand effects on oxidatively induced carbon-chlorine coupling reactions at palladium.

Double aromaticity in transition metal centered double-ring boron clusters M@B2n (M = Ti, Cr, Fe, Ni, Zn; n = 6, 7, 8).

Structures and energetics of (MgCO3)n clusters (n ≤ 16).

Sterically controlled self-assembly of tetrahedral M(6)L(4) cages via cationic N-donor ligands.

S-P coupling induced unusual open-shell metal clusters.

Triphosphine-supported bimetallic Au(I)-M(I) (M = Ag, Cu) alkynyl clusters.

Global minimum Pt(13)M(20) (M = Ag, Au, Cu, Pd) dodecahedral core-shell clusters.

Exploration of the Structural, Electronic and Tunable Magnetic Properties of Cu₄M (M = Sc-Ni) Clusters.

Why are the {Cu4N4} rings in copper(I) phosphinimide clusters [Cu{μ-N = PR3}]4 (R = NMe3 or Ph) planar?