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XtalOpt is a free and truly open source evolutionary algorithm designed for a priori crystal structure prediction.

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XtalOpt is implemented as an extension to the Avogadro molecular editor.

Check out a few of the features:

User Interface Mutation Operators

Screenshot of Avogadro visualizing a 16 x TiO₂ cell.

User Interface

Structure Limits

Optimization Settings

Search Settings

Progress

• As XtalOpt performs the search, the progress table continuously updates, providing information about each structure.
• In the figure we see individuals in various stages of completion:
  • One structure XtalOpt displays is optimized (in blue), another structure has been automatically marked as a duplicate (dark green) and removed from the breeding pool, yet another structure is currently undergoing a local optimization (light green), while another structure is waiting to be optimized (light blue).
• Other useful information is displayed about each structure, such as the time spent in optimization, the optimized enthalpy, the cell volume, spacegroup, and each structure’s ancestory (i.e. parent(s) and parameters for the evolutionary operator that generated it).
• A status bar on the bottom of the window shows the number of structures that are optimized, running, and failing at any given time.
• This information is visible regardless of which tab is currently being viewed.
• An additional feature of the progress table is the ability to immediately visualize any of the individuals in the Avogadro main window – simply clicking on a row in this table will display the three-dimensional structure in Avogadro, where it can be visualized, modified, or exported.
• If the user would like to add a bit of “intelligent design” to the evolutionary process, a structure can be modified and then resubmitted using a context (right-click) menu from the progress table.
• The context menu provides tools to (un)kill a structure, resubmit for local optimization at an arbitrary optimization step, or replace a problematic structure with a new, random individual.

The "Progress" tab

Plot

• Another visualization and analysis tool available during the search is the interactive plot.
• Allows investigation of various trends in the search by plotting a point for each individual.
• Each point can be plotted based upon structure number, generation number, enthalpy, energy, PV enthalpy term, lattice parameters, or cell volume on either axis.
• Further information is available by labeling the points with the individual’s spacegroup number, Hermann-Mauguin spacegroup symbol, enthalpy, energy, PV term, volume, generation, or index number.
• The plot is also interactive; zooming and panning are possible using simple mouse controls.
• Clicking on a structure’s point in the plot will load it in the main Avogadro window, allowing all the same functionality as described above in the progress table section.

Mutation Operators

Strain

• The strain operator allows XtalOpt to mutate the unit cell parameters, but not the fractional positions of the atoms.
• One can multiply the cell row vectors by the symmetric voight matrix, as shown below,

  \centering \vec{\textrm{v}}_{\textrm{new}} = \vec{\textrm{v}} \begin{bmatrix} 1+\varepsilon_{11} & \frac{\varepsilon_{12}}{2} & \frac{\varepsilon_{13}}{2} \\ \frac{\varepsilon_{12}}{2} & 1+\varepsilon_{22} & \frac{\varepsilon_{32}}{2} \\ \frac{\varepsilon_{13}}{2} & \frac{\varepsilon_{23}}{2} & 1+\varepsilon_{33} \end{bmatrix}

  where ε_i,j is a random selected value, taken from a zero-centered normal distribution.

Exchange

• Exchange is the simpliest operator that exchanges two atoms of different types in a cell.

Ripple

• The ripple operator acts as a periodic displacement of the atomic coordinates in a cell.
• A random axis is chosen (for this example the z axis will be chosen) and the atoms along this axis are shifted by an amount, \Delta z, where the new coordinate along that axis will be z_{new} = z + \Delta z.
• The displacement along the axis chosen is dependent on atomic placement in the orthogonal plane (x and y axes for this example) following the formula:
  

  \Delta z = \rho\cos(2\pi\mu x+\theta_{x})\cos(2\pi\eta y+\theta_{y})~~~~~\mu\in\mathbb{Z},~\eta\in\mathbb{Z}

• In this equation:
  • \rho is the maximum displacement of an atom along the axis.
  • \mu and \eta determines the number of cosine waves in the orthogonal directions.
  • \theta_{x} and \theta_{y} are randomly chosen values between 0 and 2\pi that specify the strength of the ripple in various areas of the cell.

Crossover

• The crossover, or "cut and splice", operator is the equivalent of breeding in biology of breeding in which two parents are combined to form an offspring.
• This is the only operator in XtalOpt that requires two parents to generate an offspring.
• For XtalOpt's implentation, two parents are selected from the breeding pool.
• The atoms in both parent structures are randomly reflected and rotated to avoid biasing one given orientation.
• Each newly mutated parent is then "cut" to form the two halves of what will be the offspring structure.
• Finally, the two halves are "spliced" together.
• This occurs through first joining the atomic positions in fractional coordinates.
• The cell dimensions are defined through random weighting of each of the parents' cell vectors.