About OpenMX

OpenMX (Open source package for Material eXplorer) is a software package for nano-scale material simulations based on density functional theories (DFT) [1], norm-conserving pseudopotentials [2,20,21], and pseudo-atomic localized basis functions [23]. Since the code is designed for the realization of large-scale ab initio calculations on parallel computers, it is anticipated that OpenMX can be a useful and powerful tool for nano-scale material sciences in a wide variety of systems such as bio-materials, carbon nanotubes, magnetic materials, and nanoscale conductors. The distribution of the program package and the source codes follow the practice of the GNU General Public License (GPL) [47], and they are downloadable from http:http://www.openmx-square.org/

Features and capabilities of OpenMX Ver. 3.5 are as follows:

• Total energy and forces by cluster, band, and O($N$) methods
• Local density approximation (LDA, LSDA) [2,3,4] and generalized gradient approximation (GGA) [5] to the exchange-correlation potential
• Norm-conserving pseudopotentials [2,20,21]
• Variationally optimized pseudo-atomic basis functions [23]
• Fully and scalar relativistic treatment within pseudopotential scheme [10,19,13]
• Non-collinear DFT [6,7,8,9]
• Constraint DFT for non-collinear spin and orbital orientation [11]
• Collinear LDA+U and non-collinear LDA+U methods [16]
• Macroscopic polarization by Berry's phase [12]
• Divide-conquer (DC) method [28], generalized DC method, and Krylov subspace method for O($N$) eigenvalue solver
• Simple, RMM-DIIS [31], GR-Pulay [30], Kerker [32], and RMM-DIIS with Kerker's metric [31] charge mixing schemes
• Exchange coupling parameter [14,15]
• Optical conductivity
• Charge doping
• Uniform electric field
• Full and constrained geometry optimization
• Electric transport calculation by a non-equilibrium Green's function method
• Construction of maximally localized wannier functions
• NVE ensemble molecular dynamics
• NVT ensemble molecular dynamics by a velocity scaling [17] and the Nose-Hoover methods [18]
• Mulliken, Voronoi, and ESP fitting analysis of charge and spin densities
• Analysis of wave functions and electron (spin) densities
• Dispersion analysis by the band calculation
• Density of states (DOS) and projected DOS
• Flexible data format for the input
• Completely dynamic memory allocation
• Parallel execution by Message Passing Interface (MPI)
• Parallel execution by OpenMP
• Useful user interface for developers
• Evaluation of two-center integrals using Fourier transformation [27]
• Evaluation of three-center integrals by a projector expansion method [24]
• Solution of Poisson's equation using FFT [26]

Considerable functionalities are available for calculations of physical properties such as magnetic, dielectric, electric transport properties as listed above. Not only conventional diagonalization schemes are provided for clusters, molecules, slab, and solids, but also linear scaling methods are supported as the eigenvalue solver. Three calculation parts in OpenMX are mainly time-consuming:

• Evaluation of Hamiltonian matrix elements
• Solution of Poisson's equation
• Diagonalization of the generalized secular equation

For the first and second parts, the computational time always scales as O($N$) and O($N{\rm log}(N)$) for any eigenvalue solver, where $N$ is the number of atoms, basis functions, or grid points. When the conventional diagonalization scheme (cluster and band methods) is used, the computational time for the third part scales as O($N^3$). On the other hand, the O($N$) methods can solve the eigenvalue problem in O($N$) operation in exchange for accuracy. For large scale calculations parallel execution by MPI or OpenMX is supported for parallel machines. The hybrid parallelization by OpenMP/MPI is also supported which is suitable for PC cluster consisting of multicore processors. All work arrays in the program codes are dynamically allocated with the minimum memory size required by an input file. The execution environment is unix and linux. For the execution of OpenMX, you are required to possess pseudo-atomic basis orbitals and pseudopotentials. These input data can be calculated using ADPACK which is a program package for atomic density functional calculations. Conveniently, the data for several elements and ADPACK are available from a web site (http://www.openmx-square.org/). We are continuously working toward development. Motivated contributors who want to develop the open source codes are welcome. If so, the contact information is available in the above website.