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A: New Tools and Methods in Experiment and Theory

Electrostatics-Assisted Building-up Procedure for Capturing Energy Minima of Metal Clusters: Test Case of Ag Clusters n

Prateek Ahuja, Mohammad Molayem, and Shridhar R. Gadre J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b05601 • Publication Date (Web): 21 Aug 2019 Downloaded from pubs.acs.org on August 25, 2019

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The Journal of Physical Chemistry

Electrostatics-Assisted Building-up Procedure for Capturing Energy Minima of Metal Clusters: Test Case of Agn Clusters Prateek Ahuja,a Mohammad Molayemb and Shridhar R. Gadrec,* a. Department of Chemical Sciences, IISER Mohali, Sector-81, Mohali 140306, India b. Physical and theoretical chemistry, Saarland University, Saarbrücken, Germany c. Interdisciplinary School of Scientific Computing and Department of Chemistry, Savitribai Phule Pune University, Pune 411007, India cEmail

: [email protected], bEmail: [email protected] Abstract

Global geometry optimization of metal clusters is an important problem in nanophysics. The starting geometries of the clusters generated with empirical- or other model potentials, are generally optimized further by density functional theory (DFT)-based energy minimization. For this purpose, several algorithms such as simulated annealing, genetic algorithms, basin hopping etc. are used. Our building-up procedure generates putative lower energy structures of metal (M) clusters, Mn+1, Mn+2 etc. by anchoring one or more metal atoms in the vicinity of the minima of the molecular electrostatic potential (MESP) of Mn. Here we report an application of this method to Agn clusters, for 5  n  20, followed up by DFT-based geometry optimization, generating several lower energy structures than those reported in the literature. New low-energy isomers are obtained by applying the same procedure to the test case of mixed metal clusters, NinAgm, for n+m = 4 and 5. In conclusion, our MESP-based building-up procedure offers a new general methodology for generating lower energy geometries of metal clusters.

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Introduction Clusters are aggregates of atoms or molecules ranging from 10 to 106 atoms1-3 having peculiar properties owing to their finite small sizes. Metal clusters have their own importance4,5 due to the wide range of properties exhibited by them. Understanding the variation in properties of metal clusters, such as ionization potential, binding energy, chemical reactivity, optical and magnetic properties, is of importance for their applications in plasmonics and quantum dots. These properties are dependent on the size, shape and composition of the metal clusters.6,7 The geometric patterns in small metal clusters also serve as the basic building blocks for generating larger clusters. Properties of nanoclusters can be vastly different from those of monomers as well as of the bulk phases. A well-known example is the size-dependent plasmonic behavior of Ag nanocluster, ranging in size from 3.0 to 60nm, which has been studied experimentally8 as well as theoretically.6 Nanoparticles are also found to be useful in biological context. For example, the role of silver nanoparticles as an antibacterial agent has been reported in the literature.9 One of the main issues in the theoretical research on metal clusters is to find or predict the energetically favorable structures for the given cluster size. Exploring geometries of metal clusters, which are local minima on the potential energy surface (PES), is a computeintensive job, since the number of minima increases steeply with the increase in cluster size.10 The geometry optimization and structure generation of large metal clusters has always been a formidable problem because complete sampling of all these minima is obviously not possible. Searching for the lower energy structures from the huge number of trial geometries, generated using intuition or stochastic methods, is a daunting task. Many optimization algorithms have been developed and employed to search the PES for the putative global minima. Jäger et al.11 have summarized various methods used for global optimization of metal clusters and mixed metal clusters. A large number of methods have been developed to find the possible minimum energy structures for a cluster. These include evolutionary algorithms such as genetic algorithms and the basin-hopping algorithm12 which performs a canonical Monte Carlo simulation at constant temperature T on the PES.13-14 Another family of PES search algorithms involves simulated annealing techniques which may be incorporated into Monte Carlo- or molecular dynamics simulation.15-17 Quantum annealing method also belongs to this family of annealing algorithms and employs diffusion, Greens'function method or path-integral Monte Carlo methods for locating the local minima.4,18-20 In


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the present work, we investigate the structures and energetics of Agn clusters, taken as test examples, employing density functional theory (DFT). Chen et al.21 searched for the low energy isomers of Agn (n < 100). DFT treatment was followed by CCSD(T) calculations performed for n = 3 to 8. Structures up to n ≤ 20 were explored by them employing DFT with benchmarked functionals. Initial geometries, for n < 9, were generated using triangles, squares and tetrahedrons as building blocks and higher isomers of Agn were grown by employing a tree-growth-hybrid genetic algorithm (TGHGA).22 TG-HGA is a combination of two algorithms in which trial structures are generated using the tree-growth algorithm (TGA). TGA grows clusters from small size to the size of interest by taking some pre-defined geometrical parameters such as bond length, change in bond length, maximum number of neighbors and radial expansion parameters. In each step, while changing the parameters, the structures are evaluated and lowest energy structures are carried over to the next step via the use of hybrid genetic algorithm23 (HGA) to search for global minimum. HGA is just an extended form of genetic algorithm24 (GA) which differs in the cluster generation process. GA is based on the principles of natural evolution process such as genetic crossover, mutation etc. The same algorithm is applied in HGA by externally optimizing the structure of metal clusters before the fitness evaluation. Chen et al.21 employed the embedded atom model (EAM) potential25 to calculate total energies for Agn clusters in all the steps of HGA, followed by DFT-based geometry optimization. For silver clusters up to n = 20, the geometries were optimized by them with B3LYP/aug-cc-pVDZPP26-28 level of theory and for n = 21-99, structures were optimized only using the TG-HGA method with the EAM potential. Recently, McKee and Samokhvalov29 investigated neutral, cationic and anionic silver clusters at the M06 level30 employing effective core potential31 (SDD) with ECP28MWB basis set for Ag. M06 has the advantage that it incorporates dispersion correction and has also been parameterized for transition metals. Evolution of structure and electronic properties, such as HOMO-LUMO gap, ionization potential (IP), electron affinity (EA), cohesion energy (Ecoh) etc. were studied and compared for the lowest energy isomer of neutral and charged Agn from n = 2 to 22. In search of low energy structures, McKee and Samokhvalov29 considered the lowest energy neutral silver clusters reported by Chen et al.21 They found that the structures of Agn remain planar upto n = 6, but for n = 7 through 17, they were seen to possess empty cage-like structure. From n = 18-22, the structures of Agn clusters were seen to have one/two silver atoms encapsulated within a cage. Tsuneda32 generated electronic states of the most stable neutral Agn clusters for n = 3 3|Page ACS Paragon Plus Environment


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to 20, by using long-range corrected density functional theory33-35,27 (LC-BLYP) and PBEGGA36 functionals choosing the value of the parameter µ to be 0.330.37 However, no detailed information regarding the method of generating these most stable clusters of silver was provided in Ref. 32. For ground state structures, the HOMO-LUMO gap was calculated by taking the difference between the vertical ionization potential (VIP) and vertical electron affinity (VEA). For excited states, time-dependent Kohn-Sham (TDKS) calculations38 were employed for estimating HOMO-LUMO excitation energy. Molayem et al. searched for the global minimum structures of metal- as well as binary-metal clusters, CumAgn39,40 using the basin–hopping (BH) algorithm12 within the embedded atom model (EAM) potential.25 In EAM, the interatomic interactions are modeled considering any atom as an impurity embedded in a host comprising all the other atoms. The energy of this atom is then a functional of the electron density provided by the other (host) atoms at its position. Thereby, the total energy of the system has a term that is the sum of the embedding energies of its individual atoms. Moreover, a correction due to the core-core interactions must be included. This takes the form of short-ranged pair potentials. Therefore, the functional form of the total energy for an N-atomic system relative to the non-interacting atoms is written as N

E tot   Fi (i )  i 1

1 N  ij (rij ) 2 j1,i j

(1)

Here, Fi(ϕi) is the embedding energy and φij(𝐫𝐢𝐣) is the pair potential between atoms 𝑖 and 𝑗 with an interatomic distance of 𝑟𝑖𝑗. The values of the parameters in embedding functions and also those of the pair potentials were determined by fitting to experimental data of the bulk system, e.g. heat of solution, elastic constants and sublimation as well as vacancy-formation energies. Stability of mixed metal clusters generated from this method was checked using different possible definitions of stability function. Bimetallic CumAgn clusters with n > m were found to be energetically more favorable than those dominated by silver atoms.39 This method was also used for searching the putative global minimum structures for Agn (for n = 2 to 100) clusters.40 A structure comparison was made on silver clusters from different model potentials and their stability emphasized by using a stability function. However, none of these well-developed local optimization techniques can guarantee that the true global minimum structure is indeed captured. To ensure that the lowest energy structure is captured, one needs to sample all the minima on the corresponding PES, which is 4|Page ACS Paragon Plus Environment

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a challenging task even for a medium-sized cluster. Above mentioned facts suggest that it may be useful first to determine the lowest energy structures of smaller metal clusters by DFT-based methods. This may be followed up by growing the clusters further by a stepwise addition of one or more metal atoms, which we shall refer as a systematic building-up procedure for generating structures of metal cluster. For this purpose, we have implemented an electrostatics-based method (EBM), exploiting the topographical features of the molecular electrostatic potential (MESP)41,42 for growing up silver metal clusters as a test example. A similar method has been extensively applied earlier to molecular clusters43-45 with the sole exception of medium-sized lithium clusters.46 In this work,46 the MESP-guided method was tried out for building lithium clusters, Lin, from n = 4 to 58 as a case study. The results obtained from this MESP-guided model for building up of these Lin clusters were found to be in conformity with those reported in the literature. However, this work was only at a proofof-concept level and no exhaustive search for searching minimum energy structures was made. To our knowledge, the method has not been applied to any other metal clusters so far. In the present work, the electrostatics-assisted building-up procedure is applied for generating trial geometries of Agn clusters. A systematic generation of a larger metal cluster is done by introducing m new metal atom(s) near the MESP minima of the precursor clusters, Mn or Mn- to generate trial isomers of M(n+m) clusters for m = 1,2,3 etc. We test our method with Agn clusters. Metal atoms (e.g. Na, Li, Ag, Cu etc.) show a tendency to bind with electronegative elements such as Cl, O etc. Taking a clue from this, in our method, the added Ag atom/s is/are placed in the vicinity of the electron-rich site (negative-valued MESP minima) of the parent Agn cluster for generating the starting geometries of larger clusters, viz. Agn+1, Agn+2 etc. MESP minima of mono-negative clusters, Agn- , are also probed for the addition of Ag+ ion. The rich topographical features of Agn- , are expected to engender some more, geometrically different, trial isomers. In the next section, we describe and illustrate our EBM procedure for generating trial isomers for Agn clusters for n = 5 to 20. Methodology MESP of a molecular system at a reference point r is defined as the amount of work done in bringing a unit positive test charge from infinity to that point. MESP at a point r, is the sum of the respective nuclear and electronic contributions, given by (in a.u.):



V(r )   A

ZA ρ(r ) 3  d r | r  RA | | r  r |

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(2)

where the symbols {ZA} and {RA} denote the nuclear charges and the position vector of the nuclei. The electron density, ρ(r), is the corresponding molecular electron density (MED). The ﬁrst and second terms on the r.h.s. in Eq. (1) represent the contributions of the nuclear and electronic potential, respectively. The MESP value, V(r) at a point r depends on whether the nuclear or electronic effects are dominant at r. This feature makes MESP one of the unique tools for exploring the chemical properties of the system under investigation.47 Topographical information of the scalar field of V(r) can be represented in terms of its critical points (CPs). CPs are the points at which first order partial derivatives of the function vanish, viz.

V(r ) |r rcp  0

(3)

For any three-dimensional function, such as MESP, there can be four types of non-degenerate critical points (CPs). These CPs are characterized by the eigenvalues of the Hessian matrix evaluated at the CP and denoted using the (R, σ) notation, wherein R, the rank, is the number of non-zero eigenvalues of Hessian matrix and σ, the signature, which is algebraic sum of the signs of eigenvalues.48-50 For a function of three variables, the algebraic sum of the eigenvalues can have four values: +3, +1, -1 or -3. Therefore, we get four types of CPs i.e. (3,+3): a local minimum, (3,-3): local maximum, (3,-1) and (3,+1)-type saddle points. The MESP of any neutral molecule is endowed with at least one (3,+3) negative-valued minimum. This minimum refers to the most electron-rich site, amenable to an electrophilic attack.51-53 As discussed earlier, the added Ag atom is positioned in the vicinity of the negative-valued MESP CP of the precursor cluster, say Agn.


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a e

b

g

h

i

j

c

f

d

Fig. 1. The MESP of the lowest energy Ag4 cluster at B3PW91/DGDZVP level of theory with (blue) isosurface of value -0.0102 a.u. Red dots represent positions of MESP minima of value -0.017 a.u. and green dots represent saddle points of value -0.004 a.u. Dots are the positions in the vicinity of which the added Ag atoms are placed. See text for details. The topographical analysis has been carried out for building EBM silver clusters using the DAMQT package.54 DAMQT package works with only spherical functions and can accept the formatted checkpoint (.fchk) Gaussian55 file as an input. Thus the 5d,7f option is included, in input file, in all our calculations. For illustrating our MESP-based building-up procedure, we consider the rhombus-shaped lowest energy Ag4 structure, which was optimized at B3PW9126,56 functional with DGDZVP basis set.57 A pictorial representation of the MESP isosurface of Ag4, along with the corresponding CPs, is shown in Fig. 1. After mapping of all the MESP CPs, the negative-valued ones were filtered for anchoring the added silver atom(s) in their vicinity. This procedure has been followed throughout for building EBM geometries for Agn. For example, to build the possible trial isomers of Ag5, one silver atom is placed at a time at the positions a, f, g…, as marked in Fig. 1. Placing the added Ag atom at a/b/c/d will give geometrically identical isomers of Ag5. Hence only one isomer of them is considered for calculations. Similarly, to build Ag6 from Ag4, a pair of silver atoms is placed in the vicinity of (a,b), (a,c), (b,c) etc. The geometries with new two silver atoms at (a,e), (c,f) etc are omitted because distance between these points is less than the van der Waals diameter for silver. One isomer is picked from the geometrically equivalent isomers formed by placing a pair of silver atoms at positions (a,b) and (c,d). 7|Page ACS Paragon Plus Environment


In EBM, the number of trial geometries is based on the number of negative-valued MESP CPs for a given cluster, say N and the number of the Ag atoms to be added, say M. The total number of trial isomers will be equal to or less than NCM, since the Ag atoms are added selectively in the vicinity of only some of the lower-valued MESP minima. We have also considered the closely spaced 2nd lowest or the 3rd lowest energy isomer for producing more trial geometries. Consequently, the number of geometries increases but this number is very small in comparison to the thousands of isomers, for a particular n, generated from other methods. These geometries are optimized at B3PW91/DGDZVP level of theory26,56-57 by employing the GAUSSIAN09 package.55 We compare our minimum energy structures obtained from EBM with those obtained from BHM up to n = 20. MESP of the molecular anions has been explored extensively by Gadre and coworkers.58-60 It has been shown that anions possess a rich MESP topography with several negative-valued CPs lying on a zero flux surface in the exterior region. The most negative MESP CPs were exploited for anchoring the metal cations around the anions.61-62 Thus, it is natural to explore topography of Agn― to build higher clusters by a suitable addition of positively charged Ag moieties to generate Agn+1, Agn+2 etc. The following section compares the structures generated from EBM with the corresponding isomers obtained from other methods. Energies of the optimized EBM Agn clusters are compared with the lowest energy isomers optimized at B3PW91/DGDZVP level.26,56-57 EBM silver clusters are also optimized at B3LYP/aug-cc-pVDZ-PP,26-28 M06/SDD with the ECP28MWB basis set for Ag30,31 and LC-BLYP/LANL2DZ level of theory33-35,27,63 and compared wih their counterparts. The choice of the level of theory is based upon the structures reported in literature (see Ref. 21,32 and 40) as the most stable ones at that level of theory. Computations of EBM metal and mixed-metal clusters have been carried out on a 24core machine with Intel Xeon E5-2960 processor in IISER Mohali and computations of BHM metal and mixed-metal clusters40 were carried out at the University of Saarland. Results and Discussion: a. Minimum energy silver clusters from BHM, Agn, n = 5 to 20. Molayem et al.40 searched for the global minimum energy structures of Agn clusters, for n = 2-100 using EAM potential25 in combination with BHM.12 Structural properties of these 8|Page ACS Paragon Plus Environment

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clusters, such as their growth patterns, stability etc. have been studied extensively. Low energy isomers were compared with corresponding isomers of copper, nickel and mixed metal clusters (CumAgn, NimAgn).40 Isomers of the Ag6 and Ag7 clusters are found to be in octahedral and pentagonal bipyramidal structure respectively and for Ag12, Ag13, Ag14 and Ag19 the minimum energy isomers turn out to be the variants of icosahedral structure. BHM-generated minimum energy Agn clusters, n = 5-20 found by Molayem et al.26,56 were further optimized by employing B3PW91 functional in conjunction with DGDZVP57 basis

set.

To

circumvent

convergence

issues,

“opt=(vtight,maxcycles=500)

integral=ultrafine” parameters available in GAUSSIAN software,55 were used. Calculations were performed for the high spin states (2S+1=4 when n is odd and 2S+1=3 when n is even) as well as low spin states (2S+1=2 when n is odd and 2S+1=1 when n is even). On analyzing the results, it was found that the low-spin isomers are generally lower in energy than their high-spin counterparts, with the exception of Ag10, Ag15 and Ag16. Optimized coordinates and energies of BHM Agn clusters are reported in Table TS1 and TS9 respectively in SI. In the next section, we compare the B3PW91 energies of the isomers generated by using BHM with the corresponding EBM ones. b. Comparison of Agn clusters generated by EBM and BHM methods As an illustration of the MESP-based building-up procedure for generation of structures, we consider the lowest energy D2h structure of Ag4 (cf. Fig. 1) reported in earlier theoretical and experimental studies21,64 as the starting point. We build starting structures by placing atoms at vicinity of CPs of Ag4, as discussed above, for building trial structures of Ag5, Ag6 and Ag7. This exercise has been performed for generating structurally different isomers of Agn (n = 5-20). For Agn (n = 5-9) clusters generated using EBM, the structure and energy of the low energy isomers match the corresponding results obtained using BHM. Similar result is observed for Ag17. Since we focus on locating missing minimum energy structures, we report here only the lower energy ones as compared to BHM. Energies (in a.u.) of our EBM-based clusters are compared with corresponding BHM-ones in Table TS1 in Supporting Information. Low energy isomers of Ag9 and Ag8 were used for generating trial isomers for Ag10. Out of 13 trial isomers, the most stable structure from EBM turned out to be of D2d symmetry whereas the BHM-based40 low energy isomer of Ag10 has Cs symmetry. Both structures, generated from EBM and BHM, were optimized at B3PW91/DGDZVP level of theory 9|Page ACS Paragon Plus Environment


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employing the above mentioned keywords. EBM-based Ag10 isomer was generated from the lowest energy Ag9 isomer and, on DFT-optimization, is found to be lower by 13.23 kcal/mol (low spin state) than the corresponding BHM one. The relative stability (i.e. how much lower in energy is the EBM cluster from the corresponding literature ones) of EBM-based clusters vis-à-vis the BHM ones are reported in Table 1 and the corresponding energies (in a.u.) are given in Table TS1 in SI.

A

B

Fig. 2. (A) The MESP of the lowest energy Ag10 cluster optimized at B3PW91/DGDZVP level of theory depicting isosurface value of -0.007 a.u. Bigger isosurface indicates deep minimum at that position. (B) The MESP CPs of Ag10 isomer. Red and green dots represent (3,+3) and (3,+1) CPs respectively. Marked red CPs are the deepest minima of value -0.021 a.u. Unmarked red CPs are less deeper MESP minima with value of -0.008 a.u. See text for details. This low-energy Ag10 isomer is employed for production of trial geometries of higher clusters, viz. Ag11, Ag12, Ag13 etc. by adding 1, 2 and 3 Ag atoms respectively. A pictorial representation of MESP and its CPs for the lowest energy isomer of Ag10 is shown in Fig. 2. MESP CPs of the lowest energy isomers of Ag8, Ag9, Ag10 etc. were similarly employed for generating guess isomers of Ag11, Ag12 and Ag13 by adding appropriate number of Ag atoms. Minimum energy isomer of Ag11 is generated from the low energy high-spin isomer of Ag9 and is lower by 13.48 kcal/mol vis-à-vis the corresponding BHM-one (see Table 1 and TS1). The newly generated Ag12 and Ag13 isomers were lower by about 20.2 and 12.98 kcal/mol respectively (cf. Table 1 and TS1). Both the lowest energy EBM-isomers were formed from

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the lowest energy Ag11 isomer. The structures of the lowest energy isomers of Ag11, Ag12 and Ag13 are shown in Fig. 3.

Ag11

Ag12

Ag13

Fig. 3. The new minimum energy isomers of Ag11, Ag12 and Ag13 generated using EBM, optimized at B3PW91/DGDZVP level of theory. See text for details. For n = 14, 15 and 16, we found new isomers generated from the corresponding low energy precursors of Ag13, Ag14 and Ag15 to be lower (than those generated using the BHM) by about 23.44, 6.86 and 6.93 kcal/mol respectively (see Table 1 and TS1). For n = 18, 19 and 20 clusters, more than 50 trial geometries were generated and optimized, leading to the energies lower by 13.08, 13.44 and 14.63 kcal/mol respectively from the BHM ones (cf. Table 1 and TS1). All these isomers were generated from the lowest energy isomer of Ag17. The same lowest energy isomer of Ag19 is obtained from Ag17 by adding 2 Ag atoms. Similarly, identical Ag20 isomer is obtained from Ag17 and Ag18 by adding 3 and 2 Ag atoms respectively. This shows that our method also works for the simultaneous addition of multiple Ag atoms. The optimized coordinates of only the new minimum energy structures of Agn clusters are given in Table TS4 in Supporting Information. Structures of the respective new minimum energy isomers are shown in Fig. 4.



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Ag14

Ag15

Ag16

Ag18

Ag19

Ag20

Fig. 4. New minimum energy structures of Ag14, Ag15, Ag16, Ag18, Ag19 and Ag20 located using EBM, optimized at B3PW91/DGDZVP level of theory. See text for details. We have also built more isomers of neutral Agm by anchoring desired number of appropriately positively charged Ag atoms, at the CPs of Agn- . In this strategy, the Agnstructure was further optimized by taking optimized coordinates of neutral Agn and the same building-up procedure, discussed previously, has been followed. As per our expectation, this strategy successfully located some new low energy isomers, as compared to the corresponding BHM ones for Ag12, Ag14 and Ag16. This serves as a proof-of-concept confirming that the anionic metal clusters can yield many lower energy isomers than those - , with given by BHM. In the case of Ag12, we located a new isomer from topography of Ag11

the relative stability of 22.14 kcal/mol (of -62394.83783 a.u. energy) which is even lower by about 1.93 kcal/mol (see Table 1) when compared to our best Ag12 isomer of energy 62394.83474 a.u. generated using the neutral Agn clusters (cf. TS1).


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Table 1. Relative stability (in kcal/mol) of low lying Agn isomers, generated using electrostatic binding method (EBM), w.r.t. the isomers generated from other methods. The level of theory in each case is given in footnote. The EBM calculations are done at the same level of theory of the reference methods. See text for details. Δ𝐄𝐚𝐁𝐇𝐌 Δ𝐄𝐛𝐓𝐆 ― 𝐇𝐆𝐀 Δ𝐄𝐜𝐌𝐜𝐊𝐞𝐞 Δ𝐄𝐝𝐓𝐬𝐮𝐧𝐞𝐝𝐚 System Ag8 Ag9 Ag10 Ag11 Ag12 Ag13 Ag14 Ag15 Ag16 Ag17 Ag18 Ag19 Ag20 a)

13.23 13.48 20.20 (22.14)e 12.98 23.44 6.86 6.93 13.08 13.44 14.63

5.91 -

10.18 -

5.26 1.56 15.29 3.46

24.47 14.46 10.55 3.10 -

1.51 1.96e -

1.90 10.85 2.16 1.39 -

B3PW91/DGDZVP, b) B3LYP/aug-cc-pVDZ-PP, c) M06/SDD-ECP28MWB, d) LC-BLYP/LANL2DZ level

e) Employing anionic starting clusters

From the above results, we conclude that EBM is successful in the capturing minimum energy isomer by processing 50 to 60 trial geometries. This shows the efficacy of our EBM method for locating minimum energy isomers, even in the case of metal clusters. In next subsections, we compare our EBM-based Agn clusters with their counterparts reported in the literature using different DFT functionals and basis sets. c. Comparison of Agn clusters generated by EBM and TG-HGA We now compare our EBM-based Agn clusters with the those reported by Chen et al.21 using TG-HGA, which were optimized by employing the B3LYP26,27 functional with aug-ccpVDZ-PP28 basis set. It was found21 that for all n, TG-HGA-based Agn clusters in low spin states (2S+1=2 for odd n and 2S+1=1 for even n) are minimum in energy. Optimizing all the trial isomers, generated for comparison with TG-HGA ones, for finding energy minima at a different level of theory is a cumbersome job. In this case, we selected the three lowest energy structures (called henceforth as ‘three best structures’) optimized at B3PW91/DGDZVP level for n = 5 through 20 and these best structures were considered for further optimization at B3LYP/aug-cc-pVDZ-PP level theory in low spin state. 13 | P a g e ACS Paragon Plus Environment


For n = 5-9, we found exactly identical low energy isomer as given by TG-HGA.21 Energies of only newer and lower energy isomers generated by EBM method vis-à-vis those reported in Ref. 21 are shown in table TS1 and optimized coordinates are given in Table TS5 in SI file. For n = 10, the three best isomers from subsection b, optimized at B3PW91/DGDZVP level, were chosen for calculations at B3LYP/aug-cc-pVDZ-PP level. The minimum energy isomer of Ag10 is obtained from the lowest energy structure of Ag10 in subsection b and is found to be lower by about 5.91 kcal/mol (see Table 1 and TS1) from the lowest energy Ag10 isomer reported in Ref. 21. A similar trend is observed in the case of Ag14 and Ag15 i.e. the lowest energy isomers of Ag14 and Ag15 from subsection b give new lowest energy isomers which are lower by about 24.47 and 14.46 kcal/mol (see Table 1 and TS1) of their TG-HGA-based counterparts. In the case of Ag16 and Ag18, the third best Ag16 and Ag18 energy isomer from subsection b is found to be minimum energy isomer on optimization at B3LYP/aug-cc-pVDZ-PP level. These isomers are lower by 10.55 and 3.1 kcal/mol (see Table 1 and TS1) respectively vis-àvis those reported by Chen et al.21 From the above results, we conclude that our electrostatics-assisted method is efficient for locating some new minimum energy structures which are somehow missed out by TG-HGA. In the next subsections, we compare the stability of EBM isomers with the lowest energy Agn isomers at a different level of theory reported by McKee et al.29 and Tsuneda et al.32

d. Comparison with the most stable isomers reported in Ref. 29 McKee and Samokhvalov29 studied the evolution in structure and properties of neutral and charged silver clusters, Agn, for n = 2 through 22. DFT-based studies were carried out by them on the lowest energy structures using M06 level30 with effective core potential31 (SDD) with ECP28MWB basis set for Ag. Keywords “iop(2/17=3,2/18=3,5/13=1)” and “int=ultrafine” were used29 while performing these calculations. DFT calculations were performed by us on the geometries generated by EBM for Agn, n = 5 to 20, at the same level of theory, using the above mentioned keywords in GAUSSIAN09 package.55 The energies of the EBM-based structures are compared with their counterparts in Ref. 29 and are tabulated in Table TS2 in the SI file.


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The relative stability of EBM-based clusters with their counterparts, in Ref. 29, is shown in Table 1 and the corresponding energies (in a.u.) are given in Table TS2 in SI. Optimized geometries of these low energy isomers are in Table TS6 in SI file. In the case of Ag10 and Ag16, the optimized coordinates of Ag10 and Ag16, from subsection b, were employed for further calculations at above mentioned level of theory. We found our new low energy Ag10 and Ag16 EBM-isomers are lower by about 10.18 and 1.51 kcal/mol (cf. Table 1 and TS2) vis-à-vis those reported in Ref. 29. MESP topography of Agn- is substantially different from that of its neutral counterpart, viz. Agn. For the larger clusters, we just ran only single point calculations by putting one negative charge on EBM-optimized clusters and followed same procedure for building the starting geometries. For Ag19, we found that the Ag19 isomer generated from the MESP ― topography of Ag16 , generates a lower energy isomer (by about 1.96 kcal/mol) than its

counterpart generated by neutral Agn clusters reported in Table 1. For the remaining cases, our EBM-based clusters yield results identical to those reported in Ref. 29 except Ag9 and Ag20. e. Comparison with the most stable isomers reported in Ref. 32 Recently,32 a theoretical investigation has been done on the most stable Agn clusters using LC-BLYP/LANL2DZ level of theory.33-35,27,58 Coordinates of these most stable geometries for Agn, n = 5-20, were supplied by Dr. Tsuneda and were used for obtaining ETsuneda. (cf. Table TS2). We followed same strategy, as discussed in subsections b and c, by taking lowest three minimum energy EBM silver clusters, n = 5 through 20, at the same level of theory. On a comparison, we found some new and more stable clusters. Energy comparison of these isomers with the reported ones32 is shown in Table TS2 in SI. For Ag8 and Ag9, our method engendered lower energy isomers (lower by 5.26 and 1.56 kcal/mol respectively) as compared to those reported in Ref. 32 (see Table 1 and TS2). For Ag10, we have a still better isomer which is lower by about 15.29 kcal/mol (cf. Table 1 and TS2). Probably enough search has not been made for finding the most stable structure of Ag10 employed in Ref. 32. For Ag11 and Ag12, we have isomers lower by about 3.46 and 1.9 kcal/mol (cf. Table 1 and TS2) vis-à-vis those in Ref. 32, but for Ag13, we found an isomer lower by about 10.85 kcal/mol (cf. Table 1 and TS2) than that in Ref. 32. On going further, we found that the EBM-based Ag18 and Ag19 low energy isomers are marginally lower (by 2.16 and 1.39 15 | P a g e ACS Paragon Plus Environment


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kcal/mol respectively) vis-à-vis those reported in Ref. 32 (cf. Table 1 and TS2). The optimized geometries of all new low energy Agn clusters, at this level of theory, are reported in Table TS7 is Supporting Information file. f. Test application of EBM to mixed metal clusters. Encouraged by the success of our building-up procedure to Agn clusters, we venture to try it out on mixed metal clusters, NinAgm (n+m = 4, 5), as a beginning case study. The buildingup procedure discussed above has been followed for generating trial isomers of these mixed metal clusters. A given parent cluster (e.g. Ag2Ni2) can be used for generating isomers of different stoichiometry by a suitable addition of some metal atoms. The MESP isosurface of Ni2Ag2 cluster along with its CPs is shown in Fig. 5. Isomers of Ni2Ag3 and Ni3Ag2 are generated by adding one Ag and Ni atom respectively to this Ni2Ag2 cluster. The building-up procedure described above is followed up for generating isomers of all possible stoichiometries of NimAgn, (n+m = 4, 5) clusters. These isomers were optimized at B3PW91/DGDZVP level. Energy comparison of selected new EBM generated minimum energy isomers and BHM generated40 isomers is shown in Table TS3 in SI.

e a

b

f

g c

h

i d

Fig. 5. MESP of the lowest energy Ni2Ag2 cluster at B3PW91/DGDZVP level theory with (blue) isosurface of value -0.020 a.u. Red dots a, b, c, d are MESP minima of value -0.0293 a.u. Green dot e has MESP of -0.0199 a.u. and dots with label f, g, h, i have -0.0125 a.u. MESP value. The Ag/Ni atoms are added in the vicinity of these CPs. See text for details.

Low energy isomer of Ni2Ag2 is generated by placing one nickel atom near minima of Ni1Ag2 whereas Ni3Ag2 is formed by adding one silver and one nickel atom, simultaneously, 16 | P a g e ACS Paragon Plus Environment

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near the minima positions of minimum energy isomer of Ni1Ag2. New minimum energy Ni2Ag2 and Ni3Ag2 isomers are lower by about 5.32 and 6.10 kcal/mol (see Table TS3) when compared with their BHM-generated counterparts.40 Optimized coordinates of EBM-based and BHM-based lower energy structures are reported in Table TS9 and TS10 respectively in SI. Thus, the above discussed results show that our building-up procedure is also successful in locating missing minimum energy isomers for mixed metal clusters. Conclusion In the present work, an application of electrostatic potential for metal clusters has been explored for generating minimum energy structures of metal silver clusters, Agn (n = 5-20). New geometries were made by introducing m new silver atoms at vicinity of CPs, where m = 1, 2, 3… etc. DFT-based energy minimization has been employed on MESP generated clusters and new minimum energy isomers were located with 50-60 trial isomers. The advantage of using EBM is the latter’s ability to locate minimum energy structures using a small number of trial isomers whereas other stochastic methods like BHM and TG-HGA requires large number of trial isomers for each n (5 ≤ n ≤ 20). We located 10 (Ag10, Ag11, Ag12, Ag13, Ag14, Ag15, Ag16, Ag18, Ag19, Ag20) and 5 (Ag10, Ag14, Ag15, Ag16, Ag18) new lowest energy structures when compared with lowest energy clusters of BHM and TG-HGA methods (Ref. 21) respectively. Similarly, we engendered three (Ag10, Ag16, Ag19) minimum energy structures when compared with the clusters studied by McKee et al. (Ref. 29) and eight (Ag8, Ag9, Ag10, Ag11, Ag12, Ag13, Ag18, Ag19) new most stable isomers when compared with the clusters reported in Ref. 32 by Tsuneda. The sucess of our work is seen from Table 1 showing the relative stability of our EBM clusters when compared with the low energy clusters obtained from other methods. We also explored EBM on mixed metal clusters NinAgm (for n+m = 4 and 5) using the MESP topography of mixed metal clusters which is different from its analogues of metal clusters. We followed the same procedure for placing Ni and Ag atoms near negative-valued MESP CPs for growing mixed metal clusters. We attempted for all possible stoichiometries and found some energetically new isomers in the case of mixed-metal clusters as well. For larger metal clusters, e.g. Agn, one can opt from one of the following three ways of generating low energy isomers. (a) When co-ordinates of the minimum energy isomers of Mn (e.g. Ag20) are available, then one can build, as shown in our work, Ag21, Ag22, Ag23 etc. by adding 1, 2 or 3 Ag atoms to the lowest, 2nd or 3rd lowest energy isomers. 17 | P a g e ACS Paragon Plus Environment


(b) The co-ordinates of the smaller cluster/s are not for building larger clusters. For example, for building Ag40 when the co-ordinates of DFT based optimized clusters such as Ag39 or Ag38 are not available, but the geometry of the nearest smaller cluster, say Ag35 is available. In this case, one can generate potentially low energy isomers by placing 5 Ag atoms, at a time, at the lowest MESP minima positions, followed by geometry optimization. (c) If the DFT-optimized geometries of smaller Agn isomers are not available, a limited number of low energy isomers of Ag37, Ag38, Ag39 etc. can be generated from stochastic methods using empirical potentials. These could be DFT-optimized and MESP CPs of them utilized for getting the starting structures of Ag40, say. Our EBM, being a building-up procedure, has this advantage. We conclude that our electrostatics-based building-up procedure is general, simple to implement and provides a systematic stepwise procedure for generating metal and mixed metal clusters. The number of trial isomers is rather small in comparison to the number of isomers required for other methods. The efficiency of the method is tested extensively by generating potential minimum energy structures for Agn clusters and optimizing them at four different levels of theory. We also found some new lower energy isomers for NinAgm clusters by using a similar strategy. The results indicate that our general and simple building-up method has a great potential for locating new minimum energy structures for metal- and mixed-metal clusters and needs to be explored further for other metal- and mixed-metal clusters. Supporting Information The supporting Information is available free of charge on the ACS Publications website at DOI: ________ . Energy tables (in a.u.), Cartesian coordinates (in Angstroms) and employed keywords of low-lying metal and mixed-metal clusters, viz. Agn and NinAgm, at all four different level of theories. Acknowledgments PA thanks IISER Mohali for research fellowship and infrastructure. Dr. P. Balanarayan, IISER Mohali, is acknowledged for timely discussions and computational support. We thank Professor Michael McKee and Dr. Tsuneda for providing the employed keywords and optimized geometries, respectively for silver clusters. We are thankful to Subodh Khire, SPPU, Pune and laboratory members from IISER Mohali for help and discussions.


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Test Case of Agn Clusters - ACS Publications

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