## 6.2.1.2. UPDATING FREE LATTICES

next, previous Section / Table of Contents / Index Option [U] selected from the lattice option menu L, see Sec. 6.2.1, allows you to update or redefine a free lattice definition (lattice code = +/-10) including Bravais lattices, see Sec. 6.2.1.1, selected before. The lattice update submenu LU reads =========================================================== Update free lattice: [L]atvec [B]asvec [?,]esc ===================================================== 62 == and allows you to modify both the lattice (periodicity) vectors and the lattice basis. > [L] selected from submenu LU shows the present lattice vectors ============================================================ Lattice vectors (Xyz) : x1 y1 z1 x2 y2 z2 x3 y3 z3 Update lattice vectors: [L]update [?,]esc ====================================================== 63 == from which one can redefine all three lattice vectors R1, R2, R3 analogous to the input in the free lattice definition [J] of submenu L (select [L]). Selecting [,] returns to submenu LU. > [B] selected from submenu LU lists definitions of all nc atoms in the unit cell of the present lattice by their lattice basis vectors (x,y,z), atomic radii rad, and nuclear charges nuc togeter with the lattice basis update menu LUB reading ======================================================================== nc atom(s) : X Y Z , RAD , NUC Xyz,R,Id( 1)= xb1 yb1 zb1 , rad1 , nuc1 ... Xyz,R,Id( nc)= xbnc ybnc zbnc , radnc , nucnc Update lattice basis: [N]ew [A]dd [D]el [M]od [S]ymm [L]ist [?,]esc ================================================================== 64 == where this atom listing has to be initiated for nc > 10 by answering the prompt nc atoms [L]ist [?,]esc with [L]. (Selecting [,] in this menu will show submenu LUB without the atom listing.) Some of the above lattice basis vector lines may read Xyz,R,Id(i )= xb yb zb , rad , nuc => ieq which indicates that basis vectors i and ieq are translationally equivalent. Equivalent atoms should be removed from the lattice basis, see option [D] below. > > [N] selected from submenu LUB redefines the full set of atoms inside the elementary cell repeating the input sequence of the lattice basis described above (see option [J] of submenu L) after which BALSAC returns to submenu LU. > > [A] selected from submenu LUB adds an atom to the present lattice basis definition. The prompt Add basis atom : [R]el [A]bs [?,]esc allows you to define the position of the additional atom in absolute cartesian coordinates (select [A]) where Atom nc+1 ( X, Y, Z, RAD, NUC) : asks for cartesian coordinates (x,y,z), an atomic radius rad, and a nuclear charge nuc. Alternatively, the coordinates of the additional atom may be given in multiples of the lattice vectors (select [R]), see above, where Atom nc+1 (Q1,Q2,Q3, RAD, NUC) : asks for the relative coordinates (q1,q2,q3), the atomic radius rad, and the nuclear charge nuc. After successful input BALSAC shows the present basis vector definition returns to submenu LUB. > > [D] selected from submenu LUB deletes an atom from the present lattice basis definition. The prompt Delete basis atom no. (0=esc) : asks for an appropriate atom number nd from the listing of submenu LUB (a dummy number "0" will cancel the delete process). Then a confirm prompt [C]onfirm delete [?,]esc deletes atom nd (select [C]) or cancels deleting (select [,]) after which BALSAC shows the present basis vector set definition and returns to submenu LUB. > > [M] selected from submenu LUB modifies an existing atom definition of the lattice basis. The prompt Modify basis atom no. (0=esc) : asks for an appropriate atom number m from the listing of submenu LUB (a dummy number "0" will cancel the modification process) after which the present definition of atom nm (in absolute and relative coordinates) shows as Xyz,R,Id( m)= xbm ybm zbm , radm , nucm Qrel = q1 q2 q3 and the prompt Modify coordinates : [R]el [A]bs [?,]esc allows you to redefine atom m in exactly the same way as explained for the addition of an atom to the basis set, see option [A] of submenu LUB. > > [S] selected from submenu LUB allows you to impose point symmetries on the lattice basis set. The basis will be completed by adding equivalent atoms (if needed) to achieve the required symmetry. Further, coinciding/equivalent atoms produced by previous group operations may be removed with the present option. The basis symmetry menu LUBS reads ==================================================================== Basis symmetry: [C]axis [M]irror [I]nvers [R]educe [D]max(dc) [?,]esc ============================================================== 82 == allowing to define an n-fold rotation axis, a mirror plane, inversion symmetry, and to reduce the lattice basis by removing coinciding/equivalent atoms. The value dc determines the the present coincidence distance which is the maximum distance between two atoms to be considered to coincide in the above point symmetry transformations. Note that new atoms generated from the symmetry transformation will be translated such that they lie inside the parallel epipeth spanned by the lattice vectors. However, the symmetry operation will not be applied iteratively to new atoms. > > > [C] selected from submenu LUBS defines a rotation axis by an origin (x,y,z) (on the axis), a direction vector (xd,yd,zd), and an order N. The prompt Rotation origin NC,X,Y,Z ("-1,0,0,0"=esc) : asks for four numbers defining the rotation origin given either in absolute coordinates (0,x,y,z) or denoting the center of an existing basis atom na by (na,0,0,0). Dummy input "-1,0,0,0" returns immediately to submenu LUBS. Then the prompt Rotation axis, order (X,Y,Z, N) : asks for four numbers defining the direction vector components (xd,yd,zd) and the order N of the rotation axis. The direction vector does not need to be normalized. Further, note that BALSAC allows any local N-fold rotation axis while only orders N= 2, 3, 4, 6 are compatible with translational symmetry. > > > [M] selected from submenu LUBS defines a mirror plane by an origin (x,y,z) (on the plane) and a plane normal vector (xn,yn,zn). The prompt Mirror origin NC,X,Y,Z ("-1,0,0,0"=esc) : asks for four numbers defining the mirror plane origin given either in absolute coordinates (0,x,y,z) or denoting the center of an existing basis atom na by (na,0,0,0). Dummy input "-1,0,0,0" returns immediately to submenu LUBS. Then the prompt Mirror plane normal (X,Y,Z) : asks for three numbers defining the vector components (xn,yn,zn) of the plane normal. The normal vector does not need to be normalized. > > > [I] selected from submenu LUBS defines an inversion center by its origin (x,y,z). The prompt Inversion origin NC,X,Y,Z ("-1,0,0,0"=esc) : asks for four numbers defining the inversion origin given either in absolute coordinates (0,x,y,z) or denoting the center of an existing basis atom na by (na,0,0,0). Dummy input "-1,0,0,0" returns immediately to submenu LUBS. After successful definition of the symmetry the respective operation is applied to all basis atoms and new atoms are added to the set if needed which is concluded by Symmetry checked, no new atoms if the symmetry operation did not result in new atoms or by Symmetry operation yields nn new atom(s) if nn new atoms have been generated by the symmetry operation and BALSAC returns to the lattice basis update menu LUB. If a new atom generated by the symmetry operation coincides with an existing basis atom (within the limit given by the coincidence distance, see below) the new atom will not be included in the basis. For coinciding atoms of different nuclear charge a warning WARNING: symmetry copy of XX atom (n1) and YY atom (n2) coincide no or partial symmetry applied to atom no. n1 will be issued where n1 denotes the number of the basis atom (XX its element name) where the symmetry operation was applied and n2 is the number of the existing basis atom (YY its element name). > > > [R] selected from submenu LUBS checks all atoms of the lattice basis to fit inside the lattice unit cell allowing you to translate lattice basis vectors accordingly. Further, all atoms are checked for coincidence and can be discarded if needed. Two atoms are considered to coincide if their relative distance (after translational reduction inside the elementary cell) is smaller than a limit given by the coincidence distance which can be set freely, see below. For each atom outside the lattice unit cell a prompt Xyz,R,Id( nn) : x y z , rad , nuc Qrel : q1 q2 q3 Coordinates: [R]educe [A]utored [S]kipall [?,]esc appears where nn gives the atom pointer, (x,y,z) denotes its position, rad its atom radius, and nuc its nuclear charge (element name). Selecting option [R] reduces the coordinates of atom nn by adding multiples of the lattice vectors to fit inside the unit cell where 0 < qi < 1 for i = 1,2,3. [A] continues in automatic reduce mode where all following atoms are translated inside the unit cell without prompting. [S] leaves all following atom coordinates unchanged without prompting atoms outside the unit cell. [,] leaves the coordinates of the present atom unchanged. For each pair of coinciding atoms a prompt Xyz,R,Id( n1) : x y z , rad1 , nuc1 Xyz,R,Id( n2) : x y z , rad2 , nuc2 Discard atom: [F]irst [S]econd [A]utosec [?,]esc appears where n1/2 gives the atom pointers of the two atoms, (x,y,z) denotes their (identical) positions, rad1/2 their atom radii, and nuc1/2 their nuclear charges (element names). Selecting option [F] removes the first atom of the pair, atom no. n1 (lower number), from the cluster. [S] removes the second atom of the pair, atom no. n2 (higher number), from the cluster. [A] continues in automatic discard mode where of all pairs of coinciding atoms the second, no. n2 (higher number), is discarded without prompting. [,] stops the search for coinciding atoms returning to the lattice basis update submenu LUB. The coincidence/equivalence check is concluded by the message nr atom(s) coordinate reduced, np atom(s) equivalent, nrem removed giving the number nr of atoms translated inside the unit cell, the number np of pairs of coinciding atoms, and the number nrem of atoms removed from the lattice basis. If coincidence checking was interrupted by selecting [,] above the number np may be smaller than the actual number of coincidence pairs of the lattice basis. Note that the atom translation and removal of this option is final and cannot be undone. > > > [D] selected from submenu LUBS resets the coincidence distance which is the maximum distance between two atoms to be considered to coincide in the above symmetry transformations. The prompt Atom coincidence distance ( dc) : shows the present value of the coincidence distance (default = 0.01) and asks for a new value after which BALSAC returns to submenu LUBS. > > > [,] selected from submenu LUBS returns to the lattice basis update submenu LUB. > > [L] selected from submenu LUB lists the complete lattice basis definition as shown above and returns to the lattice basis update submenu LUB. > > [,] selected from submenu LUB returns to the lattice update submenu LU. > [,] selected from submenu LU returns to the BALSAC/LATTICE main option menu, see Sec. 6.2.0, or if the lattice is built from scratch asks for the global lattice scaling constant, see below. next, previous Section / Table of Contents / Index