\exciting input reference

input schema \exciting input reference input a prefix to be prepended to the output files nonreplace Decides if the groundstate is read from file or recalculated or continued from file. if the IBS correction to the force should be calculated Because calculation of the incomplete basis set (IBS) correction to the force is fairly time-consuming, it can be switched off by setting

 tfibs

 .false.

This correction can then be included only when necessary, i.e. when the atoms are close to equilibrium in a structural relaxation run. set to

 .true.

if the force should be calculated at the end of the self-consistent cycle This variable is automatically set to

 .true.

pre when performing structural optimization. the scissors correction This is the scissors shift applied to states above the Fermi energy. Affects DOS, optics and band structure plots. plot1d specifies sample points along a path. The coordinate space is chosen in the context of the parent A path consists of at least two points and a number of divisions. defines a 2d plot domain defines a 3d plot domain { \bf k} -point and state index pair kstlist is used in the LSJ and wavefunction plot element This is a user-defined list of { \bf k} -point and state index pairs which are those used for plotting wavefunctions and writing { \bf L} , { \bf S} and { \bf J} expectation values. The inputset element can be used to store a set of input elements. It is not used by exciting now but will be usefull eventually. noname noname The input element Is the root element of the exciting input file. XML may contain only one root element. The input element must contain one structure element and one groundstate element. noname Every input file must contain a structure element to specify the domain and the atoms.

Unless explicitly stated otherwise, EXCITING uses atomic units. In this system \hbar=1 , the electron mass m=1 , the Bohr radius a_0=1 and the electron charge e=1 (note that the electron charge is positive, so that the atomic numbers Z are negative). Thus, the atomic unit of length is 0.52917720859(36) \AA, and the atomic unit of energy is the Hartree which equals 27.21138386(68) eV. The unit of the external magnetic fields is defined such that one unit of magnetic field in

exciting.in

equals 1717.2445320376 Tesla. Title of the input file. The structure element contains all structural information such as atoms atom positions and symmetries. This element is used by the spacegroup tool to generate structures and supercells The symmetries element is output from the spacegroup program the values are currently not used in the exciting program defines lattice from a,b,c, and angles noreplace noreplace noreplace number of repeated cells in each direction Herman Mauguin sympol giving the spacegroup hrmg defines the unit cell of the calculation. unit cell is spanned by 3 basevectors that define the lattice coordinates. are the basis vectors or lattice vectors in Bohr. avec scales all the lattice vectors. This is useful for varying the volume. scale allows for a separate scaling of each lattice vector. 1 1 1 means no scaling. (sc1|sc2|sc3) for each atom type (species) a species element is defined containing all the atom positions atomic position in lattice coordinates for atom noname position in lattice coordinates atposl muffin-tin external magnetic field in Cartesian coordinates for atom If present defines ldaplusU parameters for species notaname notaname notaname defines the file from which the species definition is read. It is looked up in the species directory specified by the species path. spfname can be given to simplify visualisation and converters. is ignored by exciting spsymb Is an optional attribute can be given to simplify visualisation and converters. It is not used by exciting noreplace> muffin tin radius this optional parameter allows to override speciesfile or automatic tetemination gives the path to the directory containing the species files sppath has to be set to true if one wants to calculate an isolated molecule. is

true

, then the atomic positions, {\bf a} , are assumed to be in Cartesian coordinates. The lattice vectors are also set up automatically with the i-th lattice vector given by {\bf A}^i=A_i\hat{\bf e}^i, where A_i=\max_{\alpha,\beta}\left|{\bf a}^{\alpha}_i-{\bf a}^{\beta}_i\right| +d_{\rm vac} with \alpha and \beta labeling atoms, and d_{\rm vac} determines the size of the vacuum around the molecule. The last variable is set by the attribute

vacuum

. determines the size of the vacuum around the molecule. vectors with lengths less than this are considered zero. If true automatic determination of the muffin tin radii is allowed. allows the primitive unit cell to be determined automatically from the conventional cell. This is done by searching for lattice vectors among all those which connect atomic sites, and using the three shortest ones which produce a unit cell with non-zero volume. Set to it to "true" if the crystal can be shifted such that the atom closest to the origin is exactly at the origin. The groundstate element is required for anny calculation. Its attributes are the parameters and methods used to calculate the groundstate density. If the element is present calculation is done with spin polarization. spinpol the desired total moment for a FSM calculation. alows to apply a constant B field This is a constant magnetic field applied throughout the entire unit cell and enters the second-variational Hamiltonian as \frac{g_e\alpha}{4}\,\vec{\sigma}\cdot{\bf B}_{\rm ext}, where g_e is the electron g -factor (2.0023193043718). This field is normally used to break spin symmetry for spin-polarised calculations and considered to be infinitesimal with no direct contribution to the total energy. In cases where the magnetic field is finite (for example when computing magnetic response) the external { \bf B} -field energy reported in

INFO.OUT

should be added to the total by hand. This field is applied throughout the entire unit cell. To apply magnetic fields in particular muffin-tins use the

bfcmt

vect ors in the

atoms

block. Collinear calculations are more efficient if the field is applied in the z -direction. if a spin-orbit coupling is required If

spinorb

.true.

, then a \boldsymbol \sigma\cdot{ \bf L} term is added to the second-variational Hamiltonian. . set to

.true.

if a spin-spiral calculation is require Experimental feature for the calculation of spin-spiral states. See

vqlss

for details. the { \bf q} -vector of the spin-spiral state in lattice coordinates Spin-spirals arise from spinor states assumed to be of the form \Psi^{ \bf q}_{ \bf k}({ \bf r})= \left( \begin{array}{c} U^{{\bf q}\uparrow}_{ \bf k}({\bf r})e^{i({ \bf k+q/2})\cdot{ \bf r}} \\ U^{{ \bf q}\downarrow}_{\bf k}({ \bf r})e^{i({\bf k-q/2})\cdot{ \bf r}} \\ \end{array} \right). These are determined using a second-variational approach, and give rise to a magnetisation density of the form {\bf m}^{ \bf q}({ \bf r})=(m_x({\bf r})\cos({ \bf q \cdot r}), m_y({\bf r})\sin({ \bf q \cdot r}),m_z({\bf r})), where m_x , m_y and m_z are lattice periodic. See also

spinprl

. After each iteration the external magnetic fields are multiplied with reducebf. This al- lows for a large external magnetic field at the start of the self-consistent loop to break spin symmetry, while at the end of the loop the field will be effectively zero, i.e. infinitesimal. See bfieldc and atoms. 0 1 2 3 If preset HartreeFock calculation is triggered. energy convergence tolerance Optional configuration options for eigenvector solver. solvertype select the eigenvalue solver for the first variational equation 1 2 3 In the default calculation the matrix is sored in packed form. When using multithreaded BLAS setting this parmeter to false increases efficiency. Tolerance parameter for the ARPACK shift invert solver error tolerance for the first-variational eigenvalues using the LAPACK Solver If present exact exchange calculation is triggered. (experimental) maximum number of iterations when solving the exact exchange integral equations The optimised effective potential is determined using an interative method. [Phys. Rev. Lett. 98, 196405 (2007)]. At the first iteration the step length is set to tauoep(1). Dur- ing subsequent iterations, the step length is scaled by tauoep(2) or tauoep(3), when the residual is increasing or decreasing, respectively. See also maxitoep. If present Reduced Density Matrix Funcional Theory calculation is triggered xc functional. maximum number of self-consistent loops. maximum number of iteration for occupation number optimisation. maximum number of iteration for natural orbital optimisation. step size for occupation numbers. step size for natural orbital coefficients. exponent for the functional. temperature. nonreplace Decides if the groundstate is skipped or recalculated or continued from file. ngridk Number of k grid points along the basis vector directions. This sets the maximum length for the { \bf G}+{ \bf k} vectors, defined as

rgkmax

divided by the smallest muffin-tin radius. If the RMS change in the effective potential and magnetic field is smaller than epspot, then the self-consistent loop is considered converged and exited. For structural optimisation runs this results in the forces being calculated, the atomic positions updated and the loop restarted. See also maxscl. parameters governing the automatic generation of the muffin-tin radii. When @autormt is set to true, the muffin-tin radii are found automatically from the formula R_i\propto 1+\zeta|Z_i|^{1/3}, where Z_i is the atomic number of the $i$th species, \zeta is stored in @rmtapm(1) and the value which governs the distance between the muffin-tins is stored in @rmtapm(2). When @rmtapm(2) =1, the closest muffin-tins will touch. width of the smooth approximation to the Dirac delta function. A smooth approximation to the Dirac delta function is needed to compute the occupancies of the Kohn-Sham states. The variable

swidth

determines the width of the approximate delta function. 0 1 2 3 4 select method to determine the linearization energies. species for which the muffin-tin radius will be used for calculating gkmax. maximum length of |G| for expanding the interstitial density and potential. Defines the number of eigenstates beyond that required for charge neutrality. When running metals it is not known a priori how many states will be below the Fermi energy for each k -point. Setting

nempty

greater than zero allows the additional states to act as a buffer in such cases. Furthermore, magnetic calculations use the first-variational eigenstates as a basis for setting up the second-variational Hamiltonian, and thus

nempty

will determine the size of this basis set. Convergence with respect to this quantity should be checked. when set to

.true.

no symmetries, apart from the identity, are used anywhere in the code. when set to

true

the frozen core approximation is applied, i.e., the core states are fixed to the atomic states. if the k -point set is to be determined automatically Used for the automatic determination of the k -point mesh. If

autokpt

is set to

true

then the mesh sizes will be determined by n_i=\lambda/|{ \bf A}_i|+1 .

reducek

set to

true

if the k -point set is to be reduced with the crystal symmetries. Because calculation of the incomplete basis set (IBS) correction to the force is fairly time- consuming, it can be switched off by setting tfibs to .false. This correction can then be included only when necessary, i.e. when the atoms are close to equilibrium in a structural relaxation run. if the force should be calculated at the end of the self-consistent cycle. angular momentum cut-off for the APW functions. upper limit for te selfconsistency loop. This controls the amount of charge in the unit cell beyond that required to maintain neu-trality. It can be set positive or negative depending on whether electron or hole doping is required. initial band energy step size The initial step length used when searching for the band energy, which is used as the APW linearisation energy. This is done by first searching upwards in energy until the radial wavefunction at the muffin-tin radius is zero. This is the energy at the top of the band, denoted E_{\rm t} . A downward search is now performed from E_{\rm t} until the slope of the radial wavefunction at the muffin-tin radius is zero. This energy, E_{\rm b} , is at the bottom of the band. The band energy is taken as (E_{\rm t}+E_{\rm b})/2 . If either E_{\rm t} or E_{\rm b} cannot be found then the band energy is set to the default value. maximum allowed error in the calculated total charge beyond which a warning message will be issued. smallest occupancy for which a state will contribute to the density. select the mixing (relaxation) scheme for SCF mixtype 1 2 3 initial value for mixing parameter. Used in linear mixing. mixing parameter increase. Used in linear mixing. mixing parameter decrease. Used in linear mixing. Some muffin-tin functions (such as the density) are calculated on a coarse radial mesh and then interpolated onto a fine mesh. This is done for the sake of efficiency. lradstp defines the step size in going from the fine to the coarse radial mesh. If it is too large, loss of precision may occur. lradstp smallest occupancy for which a state will contribute to the density. type of exchange-correlation functional to be used \begin{itemize} \item No exchange-correlation funtional ( E_{\rm xc}\equiv 0 ) \item LDA, Perdew-Zunger/Ceperley-Alder, {\it Phys. Rev. B} 23 , 5048 (1981) \item LSDA, Perdew-Wang/Ceperley-Alder, Phys. Rev. B 45 , 13244 (1992) \item LDA, X-alpha approximation, J. C. Slater, Phys. Rev. 81 , 385 (1951) \item LSDA, von Barth-Hedin, J. Phys. C 5 , 1629 (1972) \\ \item GGA, Perdew-Burke-Ernzerhof, Phys. Rev. Lett. 77 , 3865 (1996) \item GGA, Revised PBE, Zhang-Yang, {\it Phys. Rev. Lett.} 80 , 890 (1998) \item GGA, PBEsol, arXiv:0707.2088v1 (2007) \item GGA, Wu-Cohen exchange (WC06) with PBE correlation, Phys. Rev. B 73 , 235116 (2006) \item GGA, Armiento-Mattsson (AM05) spin-unpolarised functional, {\it Phys. Rev. B} 72 , 085108 (2005) \end{itemize} 2 3 4 5 20 21 22 26 30 -2 1 type of LDA+U method to be used. 0 1 2 3 Any valence states with eigenvalues below evalmin are not occupied and a warning message is issued. angular momentum cut-off for the muffin-tin density and potential. fraction of the muffin-tin radius up to which lmaxinr is used as the angular momentum cut-off. Close to the nucleus, the density and potential is almost spherical and therefore the spherical harmonic expansion can be truncated a low angular momentum. See also fracinr. angular momentum cut-off for the outer-most loop in the hamiltonian and overlap matrix setup. the k-point offset vector in lattice coordinates. order of polynomial for pseudocharge density. damping coefficient for characteristic function. when set to true, source fields are projected out of the exchange-correlation magnetic field. experimental feature. tevecsv is true if second-variational eigenvectors are calculated Normally, the density and potentials are written to the file STATE.OUT only after com- pletion of the self-consistent loop. By setting nwrite to a positive integer the file will be written during the loop every nwrite iterations. ptnucl is true if the nuclei are to be treated as point charges, if .false. ! the nuclei have a finite spherical distribution. The structure optimization element triggers if present a geometry relaxation. <<<<<<< HEAD:xml/excitinginput.xsd atomic position in lattice coordinates for atom noname ======= tructural optimisation run starting from the atomic densities, with atomic positions written to

GEOMETRY.OUT

. >>>>>>> 0e4cdde6f89434702cbce7aee38bfe95334ba215:xml/excitinginput.xsd convergence tolerance for the forces during a structural optimisation run. the step size to be used for structural optimisation

The position of atom \alpha is updated on step m of a structural optimisation run using {\bf r}_{\alpha}^{m+1}={\bf r}_{\alpha}^m+\tau_{\alpha}^m \left({ \bf F}_{\alpha}^m+{ \bf F}_{\alpha}^{m-1}\right), where \tau_{\alpha} is set to

tau0atm

for m=0 , and incremented by the same amount if the atom is moving in the same direction between steps. If the direction changes then \tau_{\alpha} is reset to

tau0atm

. <<<<<<< HEAD:xml/excitinginput.xsd If present defines ldaplusU parameters for species notaname notaname notaname defines the file from which the species definition is read. It is looked up in the species directory specified by the species path. spfname can be given to simplify visualisation and converters. is ignored by exciting spsymb Is an optional attribute can be given to simplify visualisation and converters. It is not used by exciting noreplace> muffin tin radius this optional parameter allows to override speciesfile or automatic tetemination ======= Resumption of structural optimisation run using density in

STATE.OUT

but with positions from

exciting.in

. >>>>>>> 0e4cdde6f89434702cbce7aee38bfe95334ba215:xml/excitinginput.xsd Properties listed in this element can be calculated from the groundstate. It works also from a saved state from a previous run. If present a banstructure is calculated. Create a bandstructure. Must contain plot1d element for bandstructure path. value to shift bandgap. Band structure plot which includes angular momentum characters for every atom. wavefunction plot. Plot the wave function at a set of kpoints List of kpoints of which the wave functions should be plotted. If present a DOS calculation is started.

DOS and optics plots require integrals of the kind g(\omega_i)=\frac{\Omega}{(2\pi)^3}\int_{\rm BZ} f({ \bf k}) \delta(\omega_i-e({\bf k}))d{ \bf k}. These are calculated by first interpolating the functions e({ \bf k}) and f({ \bf k}) with the trilinear method on a much finer mesh whose size is determined by

ngrdos

. Then the \omega -dependent histogram of the integrand is accumulated over the fine mesh. If the output function is noisy then either

ngrdos

should be increased or

nwdos

decreased. Alternatively, the output function can be artificially smoothed up to a level given by

nsmdos

. This is the number of successive 3-point averages to be applied to the function g . spin-quantisation axis in Cartesian coordinates used when plotting the spin-resolved DOS (z-axis by default) When lmirep is set to true, the spherical harmonic basis is transformed into one in which the site symmetries are block diagonal. Band characters determined from the density ma- trix expressed in this basis correspond to irreducible representations, and allow the partial DOS to be resolved into physically relevant contributions, for example eg and t2g . number of frequency/energy points in the DOS effective k-point mesh size to be used for Brillouin zone integration. level of smoothing applied to DOS/optics output integer 0 frequency/energy window for the DOS or optics plot wdos Output L, S and J expectation values. i th { \bf k} -point and state pair Compute the effective mass tensor at the k -point given by vklem. The size of the k-vector displacement used when calculating numerical derivatives for the effective mass tensor. the number of k-vector displacements in each direction around vklem when computing the numerical derivatives for the effective mass tensor. the k-point in lattice coordinates at which to compute the effective mass tensors. Plot the charge density exchange-correlation and Coulomb potential plots. electron localisation function (ELF) plot of magnetisation vector field plot of exchange-correlation magnetic vector field writes the elsectric field to file. plot of he gradient of the magnetic vector field. writes fermisurface data to file. number of states to be included in the Fermi surface plot file Calculation of electric field gradient (EFG), contact charge Linear optical response tensor. the components of the first- or second-order optical tensor to be calculated noname q-vector in lattice coordinates for calculating ELNES Coulomb pseudopotential, μ*, used in the McMillan-Allen-Dynes equation Phonon frequencies and eigen vectors for an arbitrary q-point. The phonon element must contain one or more q-point elements Phonon density of states.

no special blocks required

Phonon dispersion plot. nonreplace Decides if the phonon calculation is skipped or recalculated or continued from file. ngridq Number of q grid points along the basis vector directions.

reduceq

set to

true

if the q -point set is to be reduced with the crystal symmetries. Phonon calculations are performed by constructing a supercell corresponding to a particular {\bf q} -vector and making a small periodic displacement of the atoms. The magnitude of this displacement is given by deltaph. This should not be made too large, as anharmonic terms could then become significant, neither should it be too small as this can introduce numerical error. If this element is present with valid configuration, the macroscopic dielectric function and related spectroscopic quantities in the linear regime are calculated through either time-dependent DFT (TDDFT) or the Bethe-Salpeter equation (BSE). dftrans,ndftrans intraband is true if the intraband term is to be added to the optical matrix (q=0) true if to consider the anti-resonant part for the dielectric function true if to consider the anti-resonant part for the BSE-derived xc-kernels split parameter for degeneracy in energy differences of BSE-derived kernel true if analytic continuation from the imaginary axis to the real axis is to be performed number of energy intervals (on imaginary axis) for analytic continuation true if Lindhard like function is calculated (trivial matrix elements) smallest energy difference for which the square of its inverse will be considered in the Kohn-Sham response function angular momentum cutoff for Rayleigh expansion of exponential factor for ALDA-kernel alpha-parameter for the static long range contribution (LRC) model xc kernel alpha-parameter for the dynamical long range contribution (LRC) model xc kernel beta-parameter for the dynamical long range contribution (LRC) model xc kernel treatment of macroscopic dielectric function for {\bf Q} -point outside of Brillouin zone. A value of 0 uses the full {\bf Q} and and the ({\bf 0},{\bf 0}) component of the microscopic dielectric matrix is used. A value of 1 invokes a decomposition {\bf Q}={\bf q}+{\bf G}_{\bf q} and and the ({\bf Q}_{\bf q},{\bf Q}_{\bf q}) component of the microscopic dielectric matrix is used. defines which xc kernel is to be used 0 1 2 3 4 5 7 8 true if the TDDFT calculation is to be resumed starting from a new xc kernel. nonreplace nosymscr nosym is true if no symmetry information should be used ngridkscr k-point grid sizes reducekscr reducek is true if k-points are to be reduced (with crystal symmetries) vkloffscr k-point offset rgkmaxscr smallest muffin-tin radius times gkmax nemptyscr number of empty states defines which screening is used nosymbse reducekbse reducek is true if k-points are to be reduced (with crystal symmetries) vkloffbse k-point offset rgkmaxbse smallest muffin-tin radius times gkmax defines how the screened Coulomb interaction matrix is to be averaged (important for the singular terms) true if the body of the screened Coulomb interaction is to be averaged (q=0) true if the head of the screened Coulomb interaction is to be averaged (q!=0) true if the wings of the screened Coulomb interaction is to be averaged (q!=0) true if the body of the screened Coulomb interaction is to be averaged (q!=0) angular momentum cutoff of the spherical harmonics expansion of the dielectric matrix number of points used for the Lebedev-Laikov grids (must be selected according to Ref.LebLaik) nbfbse,nafbse number of states below and above the Fermi level nbfce,nafce defines which parts of the BSE Hamiltonian are to be considered finite momentum transfer { \bf G}+{ \bf q} vector vgqlmt,nqptmt true if tetrahedron method is used for the k-space integration in the Kohn-Sham response function tetrakordexc tetracw1k tetraqweights number of points to be sampled linearly inside the energy interval energy interval for the density of states noreplace noreplace 301 Calculate eigenvectors, -values and occupancies 310 Calculate frequency-dependent weights for convolutions using the linear tetrahedron method 320 Calculate momentum matrix elements 330 Calculate q-dependent matrix elements 340 Calculate the Kohn-Sham response function checked in the code ! 345 Calculate the Kohn-Sham response function taking into account the rigid shift of the BSE diagonal. This is not a duplicate task, as the task-Nr. is referenced. checked in the code ! 350 Set up simple xc-kernels, solve Dyson's equation for the full polarizability and determine the macroscopic dielectric function and other spectroscopic quantities. 401 Calculate eigenvectors, -values and occupancies for screening 410 Calculate frequency-dependent weights for convolutions using the linear tetrahedron method for screening 420 Calculate momentum matrix elements for screening 430 Calculate RPA screening (ignoring scissor's shift) 440 Calculate direct term of BSE Hamiltonian 441 Calculate exchange term of BSE Hamiltonian 445 Bethe-Salpeter equation 450 Calculate frequency dependent xc-kernel drived from the Bethe-Salpeter equation in first order 23 estimate bandgap from regular grid 120 calculate momentum matrix elements (legacy) 121 linear optics (legacy) 321 ASCII output of momentum matrix elements 322 convert momentum matrix elements file to old format 331 ASCII output of q-dependent matrix elements 335 calculate matrix elements of the plane wave (simple version for checking) 339 check relation between matr. el. of exp. and mom. matr. el. 341 ASCII output of Kohn Sham response function 342 binary output of Kohn Sham response function 396 convolute dielectric function from tetrahedron method with Lorentzian 398 check ALDA kernel 451 BSE-kernel, straight forward version 499 degub routine of xs-part 700 estimate disk-space, cpu-time and memory requirements 701 test timing 999 debug routine main part of code 900 generate STATE.xml file from STATE.OUT file 901 generate STATE.OUT file from STATE.xml file 910 display Information about STATE.OUT file 911 display Information about STATE.xml file Type of matrix element generation (band-combinations). Should only be referenced for experimental features. true if also off-diagonal tensor elements for the interacting response function are to be calculated maximum angular momentum for APW functions for q-dependent matrix elements maximum angular momentum for Rayleigh expansion of {\bf q} -dependent plane wave factor energy cutoff for the unoccupied states in the Kohn-Sahm response function and screening Lorentzian broadening for all spectra true if energy outputs are in eV Should TDDFT be used or BSE True if only symmorphic space-group operations are to be considered, i.e. only symmetries without non-primitive translations are allowed. if true, a fast method to calculate APW-lo, lo-APW and lo-lo parts of the momentum matrix elements in the muffin-tin is used. if true, a fast method to calculate APW-lo, lo-APW and lo-lo parts of the {\bf q} -dependent matrix elements in the muffin-tin is used. |G+q| cutoff for Kohn-Sham response function, screening and for expansion of Coulomb potential nosymxs nosym is true if no symmetry information should be used ngridkxs k-point grid sizes vkloffxs k-point offset reducekxs reducek is true if k-points are to be reduced (with crystal symmetries) ngridqxs q-point grid sizes reduceqxs reducek is true if q-points are to be reduced (with crystal symmetries) rgkmaxxs smallest muffin-tin radius times gkmax swidthxs width of the smooth approximation to the Dirac delta function lmaxapwxs angular momentum cut-off for the APW functions lmaxmatxs angular momentum cut-off for the outer-most loop in the hamiltonian and overlap matrix setup nemptyxs number of empty states scissors correction This is the path to scratch space where the eigenvector files EVECFV.OUT, EVECSV.OUT and OCCSV.OUT will be written. If the local directory is accessed via a network then scrpath can be set to a directory on a local disk The id is a unique identifier in an input set. The inputset element is currently not used by the exciting code. The depends attribute can be used to specify a dependence from another simulation in the same input set. The inputset element is currently not used by the exciting code. a q-point is given in reciprocal space coordinates