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Computational Nanoscience at

Laboratory for Simulation and Modeling of Materials

Alvaro Posada-Amarillas

Departamento de Investigación en Física

Universidad de Sonora

Abstract

The computational infrastructure improvement, as well as the theoretical treatment of

materials, has enabled extensive calculations on a variety of physical and chemical systems,

with a striking effect also on biological and materials science applications. At

Departamento de Investigación en Física, computational resources permitted the raising of

Computational Nanoscience as a manner to understand the unique, and sometimes amazing,

properties of nanoscale matter. It is presented in this document the development of

Computational Nanoscience as a research area developed at Laboratory for Simulation and

Modeling of Materials, outlining the main results obtained to date by using high

performance computers, and giving future research perspectives.

1. Origin of Computational Nanoscience at Universidad de Sonora

The intense computational work in physics, chemistry and materials science

worldwide, stimulated a very competitive research activity since the mid 1950's, with

computers playing a main role for understanding a plethora of basic phenomena governing

materials, ranging from nanoscale materials to the bulk. Currently, computer simulation is

recognized as a research activity bridging experimental and theoretical approaches. In silico

experiments prevent expending time and economic resources, providing fanciful outcomes

that give original clues into the knowledge of real materials. Validation of theory through

experiments is the icing on the cake, though.

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In the 1980's, when personal computers became popular, computational work was

eventually incorporated at the Centro de Investigación en Física. The first

theoretical/numerical results on the calculation of the ground and first excited state energy

shifts and optical transition energy for a surface F center, appeared on the Revista

Mexicana de Física, in 1981.1 Professor Angelina Uribe-Araujo, a mathematician working

at Departmento de Física, assisted the authors, professors Alejandro Clark-Bayón,

Marcelino Barboza-Flores, Ricardo Rodríguez-Mijangos and Carlos Ruíz-Mejía, in

performing the model codification and numerical calculations. Since then, computer

simulation and calculation of electronic properties have been carried out intensively at

Universidad de Sonora, and in particular at the Departamento de Investigación en Física.

The approval of funds by CONACYT to the project Computer Simulation of Binary

Metallic Systems, which evolved into the study of homo- and heteroatomic nanoparticles,

promoted research activities on simulation and modeling of materials.

The first article on metal nanoparticles where one of the co-authors was working for

Universidad de Sonora was published in 1993.2 Vibrational properties of nickel

nanoparticles were studied through a combination of theoretical and computational

techniques. In 1996, a series of papers dealing with nickel and gold clusters as well as

liquid and amorphous nickel were published3-5

as part of a doctoral research related to

computer simulation of materials. In 1997 it was proposed the first research project on

computer simulation to get funds from CONACYT, being accepted and obtaining the

assigned funds in 2000. This funding was used, in part, to acquire the first high

performance computer used to carry out calculations on both, computer simulation of liquid

metals and electronic properties calculation of H-doped Si crystal.6,7

2. Evolution of Research Lines

It was in 2003 when the Laboratory for Simulation and Modeling of Materials was

proposed by Dr. Alvaro Posada-Amarillas to the former Head of the Department, Dr.

Germán Campoy Güereña, being leaded since then by Dr. Posada-Amarillas, who has

received Bachelor and Graduate students and Postdocs wishing to acquire additional

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research experience. The current research lines are related to fundamental research on the

study of nanoscale systems, particularly devoted to the search of novel structures by using

global and local optimization methods, and to the understanding of nanomaterials by

quantum chemistry methods. Additionally, this laboratory has facilitated local and external

collaborations, existing at present many active collaborators.

The following is a list of current and past senior scientist collaborators:

Abraham F. Jalbout, Departamento de Investigación en Física, UNISON

Dora J. Borbón-González, Departamento de Matemáticas, UNISON

Ignacio L. Garzón, Instituto de Física, UNAM

Donald H. Galván-Martínez, CNyN, UNAM-Ensenada

Andreas M. Köster, Departamento de Química, CINVESTAV

José M. Cabrera-Trujillo, Facultad de Ciencias, UASLP

Juan M. Montejano-Carrizalez, Instituto de Física, UASLP

Roy L. Johnston, School of Chemistry, University of Birmingham, U.K.

J. Christian Schön, Max Planck Institue for Solid State Research, Germany

Alessandro Fortunelli, Consiglio Nazionale delle Ricerche, Italy

And Postdocs:

Roberto Núñez-González, currently at Departamento de Matemáticas, UNISON

Rafael Pacheco-Contreras, currently at Universidad de la Sierra

International collaboration through a research network aimed at the study of

nanoalloys, the COST Action "Nanolloys as Advanced Materials" funded by the European

Union, has underpinned the scientific growth by increasing the research impact of the

investigations developed in this area and providing the means for students and scientists

exchange to work within top level international groups. From this, a significant expansion

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of skills and work methods has been obtained which, to a great extent, have increased

scientific production also making possible the publishing on higher impact factor journals.

This may be regarded as a crucial step in the area growth.

Modified version of a photographic composition representing a section of LSMM and the

high performance computer, Faraday, which has 136 cores shared out as follow: 16 quad

core processors (64 cores) and 12 six core processors (72 cores), all of which are

distributed in several nodes. Additionally, the laboratory has 4 iMac computers each

having 1 quad core processor and 8 GB in RAM. Faraday was acquired through grants

obtained by doctors Felipe Ramos-Mendieta, Jorge A. Gaspar-Armenta and Alvaro

Posada-Amarillas.

It should be mentioned that Faraday is a high performance computer also accessed

by students working for doctors Ramos-Mendieta and Gaspar-Armenta. Some of them are:

Jesús Pablo Lauterio (M.Sc.), Luis Mayoral (M.Sc. and currently a Ph.D. student), Hugo

Borbón (Ph.D. student) and José Manuel Nápoles (Postdoc). They have developed software

for their research or have run installed packages such as Quantum Espresso, for the

calculation of optical properties of relevant materials.

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3. Achievements

Nowadays the Computational Nanoscience area goals contemplate scientific

research, and developing and training of human resources. A number of scientific articles

on mono- and bimetallic nanoparticles have been published; some of them are shown

below:

“Structures and energetics of 98-atoms Pd-Pt nanoalloys: Potential stability of the Leary tetrahedron for

bimetallic nanoparticles”, Lauro Oliver Paz-Borbón, Thomas V. Mortimer-Jones, Roy L. Johnston, Alvaro

Posada-Amarillas, Giovanni Barcaro, and Alessandro Fortunelli, Physical Chemistry Chemical Physics 9,

5202 (2007).

"Structure and stability of Z

XIn (X 9; Z=-1,0,1) clusters. Theoretical insights", A.F. Jalbout, A. Posada-

Amarillas, A. Ordóñez-Campos, G. Moreno-Armenta, D.H. Galván. Chemical Physics Letters 464, 58 (2008).

“Structural insights into 19-atom Pd/Pt nanoparticles: a computational perspective”, D.J. Borbón-González,

R. Pacheco-Contreras, A. Posada-Amarillas, J.C. Schön, R.L. Johnston, and J.M. Montejano-Carrizales,

Journal of Physical Chemistry C 113, 15904 (2009).

“Energetic and structural analysis of 102-atom Pd-Pt nanoparticles: a composition-dependent study”, R.

Pacheco-Contreras, A. Arteaga-Guerrero, D.J. Borbón-González, A. Posada-Amarillas, J.C. Schön and R.L.

Johnston, Journal of Computational and Theoretical Nanoscience 7, 199 (2010).

“Tetrahelix Conformations and Transformation Pathways in Pt1Pd12 Clusters”, Rafael Pacheco-Contreras,

Maribel Dessens-Félix, Dora J. Borbón-González, L. Oliver Paz-Borbón, Roy L. Johnston, J. Christian Schön,

and Alvaro Posada-Amarillas, The Journal of Physical Chemistry A 116, 5235−5239 (2012).

"Structures and electronic properties of neutral (CuS)N clusters (N=1-6): a DFT approach", Octavio J. Juárez-

Sánchez, Nancy Perez-Peralta, Ronaldo Herrera-Urbina, Mario Sanchez, Alvaro Posada-Amarillas, Chemical

Physics Letters, 570, 132-135 (2013).

"Determination of the energy landscape of Pd12Pt1 using a combined Genetic Algorithm and Threshold

Method", R. Pacheco-Contreras, Dora J. Borbón-González, M. Dessens-Félix, R. L. Johnston, J. C. Schön, M.

Jansen, Alvaro Posada-Amarillas, RSC Advances, 3, 11571–11579 (2013).

"Structural Motifs of Bimetallic Pt101−xAux Nanoclusters", Maribel Dessens-Félix, Rafael Pacheco-Contreras,

Giovanni Barcaro, Luca Sementa, Alessandro Fortunelli, and Alvaro Posada-Amarillas, Journal of Physical

Chemistry C 117, 20967−20974 (2013).

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A number of novel structures have been found using a basin hopping code designed

to search for minimum energy structures through the global exploration of the potential

energy hypersurface (atomic bonding model), some of which are part of Ph. D. thesis

results by Maribel Dessens-Félix, from the Programa de Posgrado en Ciencias de

Materiales, Universidad de Sonora. The next figure exhibits a few of the lowest energy

structures each having different chemical composition.

Au101

Pt41Au60

Pt60Au41

Pt101

Figure 1. Four representative lowest energy structures of clusters PtxAu101-x obtained by

varying chemical composition.

Another global search strategy, the threshold energy method, provided us with a

deeper understanding of isomeric spiral and biplanar structures. A major contributor on

these findings was Dr. Rafael Pacheco-Contreras, currently at Universidad de la Sierra. In

this study we found chirality as a fingerprint of these structures. Chirality is a geometric

structural characteristic which means that the structure is not super-imposable to its mirror

image by means of pure translations and/or rotations only. Figure 2 shows part of these

spiral and biplanar chiral isomers.

Left-handed spiral

Right-handed spiral

BP0

BP1

Figure 2. Typical spiral and biplanar structures obtained through the threshold method. BP

stands for biplanar.

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Finally, to emphasize the role played by composition and number of atoms, Dr.

Dora J. Borbón-González suggested the existence of Pt-based dodecahedral clusters. A vast

search over several bimetallic clusters was performed, succeeding in finding these platonic

solid clusters after using a set of parameters for Pt-Cu clusters investigated by Josafat

Guerrero-Jordan in his M. Sc. in Physics thesis. Figure 3 shows one of these structures. It is

worth mentioning that dodecahedral structures have recently been experimentally obtained

as core structures in thiolated nanoparticles.

Dodecahedral core-shell cluster

Figure 3. A dodecahedral cluster obtained by optimizing an empirical model potential.

Density Functional theory (DFT) has also been utilized in our laboratory. A

theoretical calculation of the structural properties of a neutral Pt1Pd12 cluster was performed

by Maribel Dessens-Félix as part of her M.Sc. thesis on Materials Science, using DFT to

search for the minimum energy structure. The structural reoptimization and frequency

analysis were performed within the generalized gradient approximation (GGA) employing

the PBE exchange-correlation functional. Structural distortion of the reoptimized cluster

was attributed to a Jahn-Teller effect.

Figure 4. Local distortion is produced as an effect of electron correlation, as well as an

increase of cluster size. Initial structure was obtained from a genetic algorithm (GA).

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Recently, copper sulfide clusters were studied by Octavio J. Juárez-Sánchez, a Ph.

D. student at Programa de Posgrado en Ciencias de Materiales, Universidad de Sonora,

using a combined Empirical Potential-DFT approach to locate ground state structures,

focusing on those structures behaving as semiconducting nanoparticles. Our theoretical

results are expected to drive experiments in the tailoring of novel, promising nanomaterials

for producing energy by taking advantage of photocatalysis. A 12-atom copper sulfide

cluster is shown below.

Figure 5. Most stable structure of a copper sulfide cluster. The calculated HOMO-LUMO

gap indicates that this nanoparticle is a semiconductor.

3. Available Computational Tools

3.1 Molecular Dynamics8

The Newton’s equations of motion are solved using any available numerical

integration algorithm with a time step which assures total energy conservation. The initial

values of the system's atomic coordinates are provided and the initial momenta are chosen

from a Maxwell-Boltzmann distribution of velocities according to the initial simulation

temperature. The simulation proceeds through a time loop until the total simulation time is

reached. Initialization, equilibration and production are the 3 typical simulation stages

needed to unravel structural and dynamical properties of physical systems. It is necessary a

model empirical potential from which forces are obtained, thus the integration scheme

provides values of acceleration, velocity and coordinates at each time-step. Sometimes a

local optimization method is needed to eliminate the thermal motion effect, obtaining a set

of typical 3-D structures characterizing the energy landscape of the system's

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thermodynamic phase. This dynamical approach allows us to change the thermal state

simply by a velocity-scaling procedure.

3.2 Genetic Algorithm9

This is a global search strategy based on evolutionary principles to find the optimal

individual. When applied to the structural determination of the lowest energy nanoparticle,

the configuration of the individual, a nanoparticle, is expressed by atomic coordinates.

Many of these configurations are randomly generated to form a generation which evolves

according to natural selection rules. In the Darwinian approach, energy is evaluated and

compared after performing local optimizations over each cluster. Those having the lowest

energy are singled out for mating to build a new generation with optimal individuals. This

procedure is repeated until the pre-defined number of generations is reached or the energy

convergence criterion has been met. Fitness is defined in terms of an empirical potential

function modeling interatomic bonding.

3.3 Basin Hopping10

The basin hopping algorithm has been extensively utilized since the pioneering

work by J. P. K. Doye and D. Wales as a stochastic search strategy to explore hypersurfaces

of cluster systems, and applied to atomic clusters with manageable interaction potential

models. Despite its simplicity, this method has proven to be an effective strategy to study

several systems described by empirical potentials. It is based on a mathematical

transformation of the function that models the potential energy to be explored, which is

transformed into a collection of interpenetrating staircases. For each nanoparticle's

chemical composition optimizations can be started from random configurations, increasing

the likelihood of unveiling their structural complexity by generating a vast number of initial

configurations. The basin hopping method requires assigning a definite number of Monte

Carlo steps.

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3.4 The Threshold Energy Method11

This is a Monte Carlo based approach which makes use of random walks below a

sequence of prescribed energy lids combined with stochastic quenches. This method

requires a low-energy configuration usually obtained from other optimization techniques as

initial input. Starting from the global or a local minimum, random walks are carried out

through the configurational space, under the constraint that a given energy threshold is not

exceeded accepting all moves that fulfill this criterion. After a certain number of steps the

system is relaxed into one neighboring minimum. Several stochastic quenches are usually

carried out from the same point in order to determine whether the walker is inside a basin

or in a transition region. By performing several Monte Carlo runs at different energy lid

values, energy barriers separating the accepted global minimum from other minimum

energy structures can be estimated. Such a set of runs is repeated starting from many local

minima on the landscape to carefully explore the potential energy surface landscape.

3.5 Density Functional Theory12,13

This methodology has evolved since the 1960's, when Hohenberg and Kohn, and

later Kohn and Sham, established the mathematical basis for studying quantum systems

through the use of electron density functionals. A set of Kohn-Sham equations is obtained

by applying the variational theorem to minimize the energy functional, which is solved

using exchange-correlation functionals to appropriate model the physical system under

study. After a self-consistent procedure leading to obtain the electron density which

minimizes the energy, energy eigenvalues and Kohn-Sham orbitals are obtained from

which physical or chemical properties are calculated by using computer packages.

4. Theses on Atomic Clusters and Crystals

4.1 Concluded

"Cálculo ab initio del gap en halogenuros alcalinos", Margarita Franco Ortiz, Licenciatura

en Física. February 2004.

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"Propiedades estructurales y estabilidad en cúmulos de oro, plata y cobre", Johann Omar

Zazueta Sánchez, Licenciatura en Física, June 2005.

"Estudio Teórico-Experimental de la densidad de estados electrónicos en la vecindad de la

banda de conducción en cristales de KCl:Cu+ y KCl:In

+", Margarita Franco Ortiz, Maestría

en Ciencias (Física), April 2006.

“Estudio de propiedades electrónicas y estructurales mediante método Kohn-Sham DFT

para nanoaleaciones de 13 átomos de Pdn-mPtm", Maribel Dessens Félix, Maestría en

Ciencias de Materiales, November 2009.

"Computational modelling of nanoalloys", Josafat Guerrero Jordan, Maestría en Ciencias

(Física), December 2012.

"Cálculo de propiedades estructurales y dinámicas de metales líquidos por medio de

simulación computacional", Efrain Urrutia Bañuelos, Doctorado en Ciencias (Física). June

2003.

"Determinación de los mecanismos de formación de nanopartículas de plata sintetizadas en

etilén glicol utilizando caracterización teórica y experimental de la banda del plasmón",

Ángel Slistan Grijalva, Doctorado en Ciencias de Materiales, April 2005.

“Paisaje de energía de nanopartículas bimetálicas”, Rafael Pacheco Contreras, Doctorado

en Ciencias (Física), June 2010.

4.2 Underway*

Alvaro Posada-Borbón, Licenciatura en Física, Thesis defense: December 2013.

Maribel Dessens-Félix, Doctor en Ciencias de Materiales, Thesis defense: January 2014.

José Octavio Juárez-Sánchez, Doctor en Ciencias de Materiales, Thesis defense: March

2014.

*All dates are tentative.

5. Future Work

With the available resources at LSMM, it is possible to give a suitable response to

the new questions posed by the technological necessity of new (nano) materials. The

threshold method can be used to study thermal stability of medium-size mono- and

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bimetallic nanoparticles; basin hopping and genetic algorithms might aid in providing new

candidate structures to be used in more advanced theoretical schemes; and DFT strategies

can be used to explore additional chemical properties of more complex bi- and

multimetallic structures. Also, new strategies are feasible to implement with the aim of

elucidating new and fascinating basic phenomena leading to the computational design of

nanomaterials by means of state-of-the-art methodologies. Nobel Prize in Chemistry 2013

has highlighted the important role played by computer simulation and modeling of

materials. New discoveries on nanoscale materials are now made possible by modern

computers.

References

1. "The F Band of a Surface F Center", A. Clark B., M. Barboza F., R. Rodríguez M. and C.

Ruiz Mejía, Rev. Mex. Fís. 28, 29 (1981).

2. “Vibrational properties of nickel and gold clusters”, S. Carnalla, A. Posada and I.L.

Garzón, Nanostruct. Mater. 3, 385, 1993.

3. “Microstructural analysis of simulated liquid and amorphous nickel”, Alvaro Posada-

Amarillas and Ignacio L. Garzón, Phys. Rev. B 53, 8363(1996).

4. “Vibrational analysis of Nin clusters”, Alvaro Posada-Amarillas and Ignacio L. Garzón,

Phys. Rev. B 54, 10362(1996).

5. “Structural and vibrational analysis of amorphous Au55 clusters”, Ignacio L. Garzón and

Alvaro Posada-Amarillas, Phys. Rev. B 54, 11796(1996).

6. “Temperature effect on the local order of liquid Ni, Ag and Pb: A molecular dynamics

study”, E. Urrutia-Bañuelos, A. Posada-Amarillas, I.L. Garzón, Phys. Rev. B 66, 144205

(2002).

7. "Concentration-dependent study of electronic and optical properties of c-Si and c-Si:H",

R. Núñez-González, A. Posada-Amarillas, D. H. Galván, and A. Reyes-Serrato, physica

status solidi (b) 248, 1712 (2011).

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8. "Phase Transition for a Hard Sphere System", B. J. Alder and T. E. Wainwright, J.

Chem. Phys. 27, 1208 (1957).

9. "Molecular Geometry Optimization with a Genetic Algorithm", D. M. Deaven and K. M.

Ho, Phys. Rev. Lett. 75, 288 (1995).

10. "Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-

Jones Clusters Containing up to 110 Atoms", D. J. Wales, J. P. K. Doye, J. Phys. Chem. A

101, 5111 (1997).

11. "Studying the energy hypersurface of continuous systems - the threshold algorithm", J.

C. Schön, H. Putz and M. Jansen, J. Phys.: Condens. Matter. 8, 143 (1996).

12. "Inhomogeneous Electron Gas", P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964).

13. "Self-Consistent Equations Including Exchange and Correlation Effects", W. Kohn, L.

J. Sham, Phys. Rev. 140, A1133 (1965).

November 2013