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PSCF v1.1
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Commands - pscf_pc (Up/Prev) Commands - pscf_pg (Next)
THE WRITE_STARS command accepted by pscf_pc and pscf_pg programs writes a compact report of information about the stars of wavevectors that are related by space group symmetries. A more detailed report that contains information about individual wavevectors within each such star may be obtained by invoking the WRITE_WAVES command.
Conceptual background : As background, before reading this description of the output of the WRITE_STARS, we strongly recommend that users read the discussion of the relationships between "stars" and basis functions given in the documentation of the basis file format. Users who would like a more complete discussion can also consult appendices that discuss crystallographic space group symmetry operations and symmetry-adapted bases.
For users who examine the source code : The format of this report is defined by the outputStars function of class template Basis<int D>, which is defined in the file src/pscf/crystal/Basis.tpp.
The file created by the WRITE_STARS command contains a header section similar to that used for field files, followed by a long data section. The last line of the header section contains the value for N_basis, which is equal to both the total number of uncancelled stars and the number of independent basis functions in the symmetry-adapated Fourier expansion used by the program that wrote the file.
The data section contains one line per uncancelled star. Stars are listed in order of increasing eigenvalue of the Laplacian as computed using the unit cell parameters that were available when the basis was constructed. A large section of the data section that has been removed from this example, as indicated by vertical dots.
The format of each row of the data section is as follows
in which:
The indices beginId and endId list indices of waves in an ordered list of all waves, including those that belong to cancelled stars, in which the waves that belong to a particular star are listed as a consecutive block with indices beginId, ...., endId - 1. Only non-cancelled stars are listed in this file format.
Stars are listed in this file output in order of increasing starId. Pairs of open stars that are related to each other by inversion are always assigned sequential values for the starId, and thus always appear sequentially in this format, with the star with starInvert = +1 listed first.
An example of the file created by a WRITE_STARS command is shown below for a system with space group \( I a\overline{3} d \), or PSCF space group identifier I_a_-3_d. This is the space group of the double gyroid phase of a diblock copolymer. Because this space group is centrosymmetric (i.e., has an inversion center), all stars are closed under inversion, and so a value of starInvert = 0 is thus listed for every star. An example of the output file created by the MAKE_WAVES command for the same system is shown here.
Because \( I a \overline{3} \) space group has an inversion center, every star of this space group is closed under inversion. For this reason, a value of starInvert = 0 is listed for every star in this example.
An example of the file created by a WRITE_STARS command is shown below for a triblock copolymer system with space group \( I 4_{1} 3 2 \), or PSCF space group identifier I_41_3_2. This is the space group of the alternating gyroid phase of an ABC triblock copolymer.
Unlike the space group of the double gyroid, this space group is not centrosymmetric. As a result, the stars of this space group can include open as well as closed stars. Open stars of a non-centrosymmetric group always exist in pairs that are related by inversion - the wavevectors in one member of the pair are just the inverses of the wavevectors in the other.
By convention, open stars that are related by inversion are always assigned consecutive indices. The first member of each such pair is assigned a value of starInvert = 1, while the second is assigned a value starInvert = -1. These pairs of open stars thus show up as consecutive rows with starInvert values of 1 and -1, in that order. The first such pair in this listing is the pair with basisId values 6 and 7, starId values 14 and 15. By convention, characteristic waves of stars that are related by inversion are chosen to be inverses of one another. Consistent with this, these two stars have characteristic waves {3 2 -1} and {-3 -2 1}, respectively.
All of the rows in this file in which starInvert = 0 are associated with starts that are closed under inversion despite the fact that this symmetry group does not contain an inversion symmetry operation.
Commands - pscf_pc (Up/Prev) Commands - pscf_pg (Next)
1.9.5