## What are models? What are simulations?

Materials are complex systems and the equations that describe the physical and chemical behaviour of real systems are often too complicated to be solved easily. In order to save computer time, which is a precious and limited resource, the description of phenomena has to be simplified. Fortunately, often not all the details need to be taken into account in order to reproduce and predict experimental results. Key assumptions about reality can be made ignoring the complexity that is not necessary to describe the given situation. These approximations are called models.

Simulations consist of the implementation of the model in a computational code and the numerical methods that are used to solve equations.

Ref. L. Rosso; A.F. de Baas (2012), "What makes a material function? Let me compute the ways..."

## What are the benefits of simulation?

· **Save costs **by identifying new materials for new products

· **Reduce time-to-market **of novel materials and R&D acceleration

· **Understand results **of measurements

· Provide guidelines to design **effective materials **for specific applications

· **Analysis and characterisation **of material properties that are not accesible experimentally

· **Study **physical and chemical **phenomena **for every point in the sample at every time

## What are the main types of electronic models?

1.1.-Ab initio quantum mechanical (or first principle) models

- Hartree-Fock (HF) method
- Higher level ab initio method
- Density Funcional Theory

1.2.- Many body models and effective Hamiltonians

- Nearly-free electron models
- Pseudopotentials
- Semi-empirical tigh binding potential (TB) model
- Hubbard model
- k·p effective Hamiltonian
- Polarisable continuum model
- Envelope function approximation for continuous media

1.3.- Quantum mechanical in response to time dependent fields

- TD-DFT and TD(Spin)DFT
- The time-dependent
- k·p-model
- Other time dependent models

1.4.- Statistical charge transport model

- Semi-classical drift-diffusion model
- Percolation models

## What are the main types of atomistic models?

2.1.-Molecular Mechanics

2.2.- Statistical Mechanics models: Molecular Dynamics (MD)

- Cassical Molecular Dynamics
- Ab initio molecular dynamics
- Quantum mechanics/molecular mechanics (QM/MM)

2.3.- Statistical Mechanics models: Monte Carlo molecular models

2.4.- Atomistic Spin models

2.5.-Statistical Mechanics for atomistic systems

- Langevin Dynamic method for magnetic spin systems
- Semi-classical non-equilibrium spin transport model
- Statistical transport model at atomistic level

Ref. L. Rosso; A.F. de Baas (2012), "What makes a material function? Let me compute the ways..."

## What is SIESTA?

**SIESTA** (Spanish Initiative for Electronic Simulations with Thousands of Atoms) is both a method and its computer program implementation, to perform efficient electronic structure calculations and *ab initio* molecular dynamics simulations of molecules and solids.

Information and credits on: http://www.icmab.es/siesta/

## Which are the main characteristics of SIESTA?

The characteristics of DFT code SIESTA are:

- It uses the standard Kohn-Sham self-consistent density functional method in the local density (LDA-LSD) or generalized gradient (GGA) approximations.

- It uses norm-conserving pseudopotentials in their fully nonlocal (Kleinman-Bylander) form.

- It uses atomic orbitals as a basis set, allowing unlimited multiple-zeta and angular mo- menta, polarization and on-site orbitals. Finite-support basis sets are the key for calculating the Hamiltonian and overlap matrices in O(N) operations.

- Projects the electron wavefunctions and density onto a real-space grid in order to calculate the Hartree and exchange-correlation potentials and their matrix elements.

- Besides the standard Rayleigh-Ritz eigenstate method, it allows the use of localized linear combinations of the occupied orbitals (valence-bond or Wannier-like functions), making the computer time and memory scale linearly with the number of atoms. Simulations with several hundred atoms are feasible with modest workstations.

- It is written in Fortran 95 and memory is allocated dynamically. It may be compiled for serial or parallel execution (under MPI).

## Which are the strengths of SIESTA?

The use of linear combination of numerical atomic orbitals makes SIESTA a flexible an efficient DFT code. SIESTA is able to produce very fast calculations with small basis sets, allowing computing systems with a thousand of atoms. At the same time, the use of more complete and accurate bases allows to achieve accuracies comparable to those of standard plane waves calculations, still at an advantageous computational cost.

## What is ANT?

**ANT** (Atomistic NanoTransport) is a software package to compute the electrical current in atomically defined nanostructures. At present, ANT software package is composed of the independent codes, ANT.G, ANT.1D and ANT.U.

## Which are the characteristics of ANT?

**ANT** combines self-consistent field electronic calculations (typically Density Functional Theory), Landauer transport and the (non-equilibrium) Greens functions formalisms.

**ANT.G**

Code designed as a generic computational tool with application in nanoelectronics. It provides an excellent compromise between computational cost and electronic structure definition as long as the aim is to compare with experiments where the precise atomic structure of the electrodes is not relevant or defined with precision.

Straightforward use of ANT.G include the computation of the zero-bias conductance (or, alternatively, the electrical current under an applied bias voltage) of a variety of nanoscale systems such as molecular bridges or simply metallic atomic contacts as those created with scanning tunneling microscope or break junction techniques. The use of ANT.G may be naturally extended to the computation of scanning tunnelling spectroscopy and the simulation of scanning tunnelling and electrostatic force microscopy.

The technical specifications are:

-Interface to the quantum chemistry GAUSSIAN03/09 code for practical implementation of the embedded cluster approach, associated with the use of parameterized tight-binding (TB) Bethe lattice model, see Figure 1.

-The electrodes are modelled by parameterized TB Bethe (BL) lattices. The model is generated by connecting a site with N nearest-neighbors in directions that can be those of a particular crystalline lattice.

-The electronic structure of the infinite system is calculated self-consistently only within a finite-size region (the scattering or device region containing the nanoconstriction or molecule) while the electronic structure of the rest of the system (i.e., the two bulk electrodes) is fixed from the very beginning to that of a simplified parameterized BL model.

-It has been thoroughly tested with PGI compilers on various 32- and 64-bit platforms.

Figure 1. Diagram illustrating the self-consistent procedure for calculating the electronic structure in the embedded cluster approach as implemented in ANT.G. The central aspects of the used approach and of the one-body Green’s function and Landauer formalisms are given in D. Jacob and J. J. Palacios, J. Chem. Phys. 134,044118 (2011).

**ANT.1D**

Software specifically designed for the computation of the conductance at zero bias voltage in quasi-one-dimensional systems such as atomic chains, nanowires, carbon nanotubes, graphene nanoribbons, etc., which may present a disordered central region where scattering takes place. Other systems without an underlying one-dimensional symmetry such as molecular bridges can also be computed with ANT.1D by modeling the electrodes as finite-section quasi-one-dimensional wires.

ANT.1D is more demanding than ANT.G from the computational point of view, but presents the advantage of expanding the range of applicability of transport calculations to situations where the electrodes have a well-defined atomic structure.

The technical specifications are:

-Practical implementation of the super-cell approach, where the electrodes are described by perfect nanowires, to calculate the electronic structure of the device and the leads, see Figure 2.

-In the super-cell approach, the model for the leads consists of semi-infinite nanowires with finite cross-section where the electronic structure is described at the same computational level as that of the device.

-It is written in Fortran 95 and memory is allocated dynamically. It may be compiled for serial or parallel execution (under MPI).

-The interface with the CRYSTAL03 and CRYSTAL06 code is written in ANSI C++, and has been tested with the gnu C++ compiler on various 32- and 64-bit platforms

Figure 2. Illustration of the super-cell approach to calculate the electronic structure of the device and of the leads: (a) One-dimensional periodic system to calculate the electronic structure of the device region. (b) and (c): Infinite nanowires to calculate the electronic structure of the left (L) and right (R) semi-infinite leads. (d) Sketch of the setup of the physical system: The device region (D) is suspended between two semi-infinite leads L and R. Further details of the method are given in D. Jacob and J. J. Palacios, J. Chem. Phys. 134,044118 (2011).

**ANT.U**

This code is specifically designed for the computation of the conductance at zero bias voltage in, e.g., graphene-based systems using a one-orbital minimal model and on-site interactions (Hubbard model).

ANT.U is an easy-to-use program for the study of spin transport in 1D systems (fundamentally graphene-based systems like nanoribbons and nanotubes) which applies the Landauer formalism to tight-binding Hamiltonians with a local Coulomb interaction (U).

The local Coulomb potential is obtained self-consistently using the mean-field Hubbard model.

## What are the software packages used by SIMUNE?

SIMUNE offers the software based solution that best fits the needs of our customers.