Fix various small typographical errors

Author: jryates

docs/docs/user_guide/appendices/utilities.md

@@ -240,7 +240,7 @@ If no options are specified, all the files
 (`mmn, amn, spn, UNK, uHu, uIu`) are considered.
 
 Binary (unformatted Fortran) files are supported, though not
-reccommended, since they are compiler-dependent. A safer choice is to
+recommended, since they are compiler-dependent. A safer choice is to
 use (bigger) formatted files, with options:
 
 `spn_formatted, uiu_formatted, uhu_formatted, unk_formatted`

docs/docs/user_guide/postw90/boltzwann.md

@@ -168,7 +168,7 @@ tensor $\mathrm{\bm{\Sigma}}$ on a grid of energies.
 The first lines are comments (starting with \# characters) which
 describe the content of the file. Then, there is a line for each energy
 $\varepsilon$ on the grid, containing a number of columns. The first is
-the energy $\varepsilon$, the followings are the components if
+the energy $\varepsilon$, the following are the components if
 $\mathrm{\bm{\Sigma}}(\varepsilon)$ in the following order:
 $\Sigma_{xx}$, $\Sigma_{xy}$, $\Sigma_{yy}$, $\Sigma_{xz}$,
 $\Sigma_{yz}$, $\Sigma_{zz}$. If spin decomposition is required (input

docs/docs/user_guide/postw90/gyrotropic.md

@@ -189,6 +189,6 @@ in a Wannier-function basis following Ref. [@yates-prb07].
 ## `gyrotropic_task=-spin`: compute also the spin component of NOA and KME
 
 Unless this task is specified, only the orbital contributions are
-calcuated in NOA and KME, thus contributions from
+calculated in NOA and KME, thus contributions from
 Eqs. $\eqref{eq:m-spin}$
 and $\eqref{eq:B-ac-spin}$ are omitted.

docs/docs/user_guide/postw90/postw90params.md

@@ -1285,7 +1285,7 @@ independent components of $\gamma_{abc}$ (antisymmetric in $ab$): $yzx$,
 $zxy$ ,$xyz$, $yzy$, $yzz$, $zxz$, $xyy$, $xyx$ and $zxx$. For tensors
 $C_{ab}$, $D_{ab}$, $\widetilde D_{ab}$, $K_{ab}$ the symmetric and
 antisymmetric components are writted. Thus, the columns 3 to 11 are
-marked as $xx$, $yy$, $zz$, $xy$, $xz$, $yz$, $x$, $y$, $z$, wich
+marked as $xx$, $yy$, $zz$, $xy$, $xz$, $yz$, $x$, $y$, $z$, which
 correspond ,e.g., for $D_{ab}$ to $D_{xx}$, $D_{yy}$, $D_{zz}$,
 $(D_{xy}+D_{yx})/2$, $(D_{xz}+D_{zx})/2$, $(D_{yz}+D_{zy})/2$,
 $(D_{yz}-D_{zy})/2$, $(D_{zx}-D_{xz})/2$, $(D_{xy}-D_{yx})/2$
@@ -1399,7 +1399,7 @@ For two-dimensional systems, the direction along which the system is
 non-periodic. It can assume the following values: `x` for a 2D system on
 the $yz$ plane, `y` for a 2D system on the $xz$ plane, `z` for a 2D
 system on the $xy$ plane, or `no` for a 3D system with periodicity along
-all threee directions.
+all three directions.
 
 This value is used when calculating the Seebeck coefficient, where the
 electrical conductivity tensor needs to be inverted. If the value is

docs/docs/user_guide/wannier90/files.md

@@ -106,7 +106,7 @@ information.
 
 The header provides some basic information about `wannier90`, the
 authors, the code version and release, and the execution time of the
-current run. The header looks like the following different (the string
+current run. The header looks like the following (the string
 might slightly change across different versions):
 
 ```vi title="Output file"
@@ -196,7 +196,7 @@ plotting.
 
 ### Nearest-neighbour k-points
 
-This part of the output files provides information on the
+This part of the output file provides information on the
 $\mathrm{b}$-vectors and weights chosen to satisfy the condition of
 Eq. [B1](parameters.md#mjx-eqn:eq:B1).
 
@@ -562,7 +562,7 @@ Wannier functions are at the target centres:
 
 After WF have been localised, `wannier90` enters its plotting routines
 (if required). For example, if you have specified an interpolated
-bandstucture:
+bandstructure:
 
 ```vi title="Output file"
  *---------------------------------------------------------------------------*
@@ -816,7 +816,7 @@ the matrix elements of bvector and their weights. The first line gives
 the date and time at which the file was created. The second line states
 the number of k-points and the total number of neighbours for each
 k-point `nntot`. Then all the other lines contain the b-vector (x,y,z)
-coordinate and weigths for each k-points and each of its neighbours.
+coordinate and weights for each k-points and each of its neighbours.
 
 ## `seedname_wsvec.dat`
 

docs/docs/user_guide/wannier90/library_mode.md

@@ -40,7 +40,7 @@ which is non-zero in case of error.  This allows the calling code to ignore
 errors in the Wannier90 library or to exit using the calling program's own error
 handling mechanism.  Synchronisation of error state across MPI ranks is
 performed prior to all MPI operations.  Error handling internally adopts the
-strategy developed by [Bálint Aradi](https://github.com/aradi/errorfx)
+strategy developed by [Bálint Aradi](https://github.com/aradi/errorfx).
 
 Section [Using the Library](#using-the-library) provides detailed instructions
 on using the library interface.
@@ -72,7 +72,7 @@ projections (Ref. [@marzari-prb97], Eq. (62); Ref. [@souza-prb01], Eq. (22))
 ```
 
 The library exposes a number of functions via a Fortran module that should be
-*use*d.  Use follows the following steps:
+*use*d.  Use follows these steps:
 
 1. create an instance of the [library data structure](#lib_common_type)
 2. set necessary control parameters/flags/options using
@@ -89,12 +89,12 @@ The library exposes a number of functions via a Fortran module that should be
 8. obtain the finite difference neighbour BZ offsets using
    [w90_get_gkpb](#w90_get_gkpb)
 9. (optionally) get projector definition corresponding to input string
-   [w90_get_proj](#w90_get_gkpb)
+   [w90_get_proj](#w90_get_proj)
 10. calculate projections and overlap
 11. pass pointers to $U$, $M$, $U^{opt}$ and (if disentangling) eigenvalue
     matrices using [w90_set_eigval](#w90_set_eigval),
 [w90_set_u_matrix](#w90_set_u_matrix), etc
-12. initial projections, $A$, should be stored in the u_opt matrix
+12. initial projections, $A$, should be stored in the $U^{opt}$ matrix
 13. if disentangling is required, call [w90_disentangle](#w90_disentangle)
 14. prepare for MLWF algorithm by projecting $M$, $U^{opt}$ onto subspace by
     calling [w90_project_overlap](#w90_project_overlap)

docs/docs/user_guide/wannier90/methodology.md

@@ -39,7 +39,7 @@ $$
 
 The total spread
 can be decomposed into a gauge invariant term $\Omega_{\rm I}$ plus a
-term ${\tilde \Omega}$ that is dependant on the gauge choice
+term ${\tilde \Omega}$ that is dependent on the gauge choice
 $\mathbf{U}^{(\mathbf{k})}$. ${\tilde \Omega}$ can be further divided
 into terms diagonal and off-diagonal in the WF basis, $\Omega_{\rm D}$
 and $\Omega_{\rm OD}$,
@@ -77,7 +77,7 @@ $$
 $$
 
 The MV method
-minimises the gauge dependent spread $\tilde{\Omega}$ with respect the
+minimises the gauge dependent spread $\tilde{\Omega}$ with respect to the
 set of $\mathbf{U}^{(\mathbf{k})}$ to obtain MLWF.
 
 `wannier90` requires two ingredients from an initial electronic

docs/docs/user_guide/wannier90/notes_interpolations.md

@@ -5,7 +5,7 @@ In `wannier90` v.2.1, a new flag `use_ws_distance` has been introduced
 `.false.` reproduces the "standard" behavior of `wannier90` in v.2.0.1
 and earlier, while setting it to `.true.` changes the interpolation
 method as described below. In general, this allows a smoother
-interpolation, helps reducing (a bit) the number of $k-$points required
+interpolation, helps reduce (a bit) the number of $k-$points required
 for interpolation, and reproduces the band structure of large supercells
 sampled at $\Gamma$ only (setting it to `.false.` produces instead flat
 bands, which might instead be the intended behaviour for small molecules
@@ -16,7 +16,7 @@ $w_{n\mathrm{\rm{R}}}(\mathrm{\rm{r}})$ that we build from
 $N\times M\times L$ $k-$points are actually periodic over a supercell of
 size $N\times M\times L$, but when you use them to interpolate you want
 them to be *zero* outside this supercell. In 1D it is pretty obvious
-want we mean here, but in 3D what you really want that they are zero
+what we mean here, but in 3D what you really want is that they are zero
 outside the Wigner--Seitz cell of the $N\times M\times L$ superlattice.
 
 The best way to impose this condition is to check that every real-space
@@ -28,13 +28,13 @@ distances are between Wannier functions which are not centred on
 $\mathrm{\rm{R}}=0$. Hence, when you want to consider the matrix element
 of a generic operator $\mathrm{\rm{O}}$ (i.e., the Hamiltonian)
 $\langle w_{i\mathrm{\rm{0}}}(\mathrm{\rm{r}})|\mathrm{\rm{O}}|w_{j\mathrm{\rm{R}}}(\mathrm{\rm{r}})\rangle$
-you must take in account that the centre $\mathrm{\rm{\tau}}_i$ of
+you must take into account that the centre $\mathrm{\rm{\tau}}_i$ of
 $w_{i\mathrm{\rm{0}}}(\mathrm{\rm{r}})$ may be very far away from
 $\mathrm{\rm{0}}$ and the centre $\mathrm{\rm{\tau}}_j$ of
 $w_{j\mathrm{\rm{R}}}(\mathrm{\rm{r}})$ may be very far away from
 $\mathrm{\rm{R}}$.
 
-There are many way to find the shortest possible distance between
+There are many ways to find the shortest possible distance between
 $w_{i\mathrm{\rm{0}}}(\mathrm{\rm{r}})$ and
 $w_{j\mathrm{\rm{R}}}(\mathrm{\rm{r}}-\mathrm{\rm{R}})$, the one used
 here is to consider the distance
@@ -70,7 +70,7 @@ actual centres of the Wannier functions. Using the centres of the
 unit-cell to which the Wannier functions belong is not enough (but is
 easier, and saves you one index).
 
-Point 3 is not stricly necessary, but using it helps enforcing the
+Point 3 is not strictly necessary, but using it helps enforcing the
 symmetry of the system in the resulting band structure. You will get
 some small but evident symmetry breaking in the band plots if you just
 pick one of the equivalent $\mathrm{\rm{\tilde R}}$ vectors.
@@ -81,11 +81,11 @@ a molecule carefully placed in the periodic cell).
 
 In some other cases, the effect may exist but be imperceptible. E.g., if
 you use a very fine grid of $k-$points, even if you don't centre each
-functions perfectly, the periodic copies will still be so far away that
-the change in centre applied with $\tt use\_ws\_distance$ does not
+function perfectly, the periodic copies will still be so far away that
+the change in centre applied with `use_ws_distance` does not
 matter.
 
-When instead you use few $k-$points, activating the
-$\tt use\_ws\_distance$ may help a lot in avoiding spurious oscillations
+When instead you use few $k-$points, activating `use_ws_distance` may
+help a lot in avoiding spurious oscillations
 of the band structure even when the Wannier functions are well
 converged.

docs/docs/user_guide/wannier90/parameters.md

@@ -54,7 +54,7 @@ strings: `T`, `true`, `.true.`.
 
 For further examples see Section
 [Master input file: `seedname.win`](sample_inputs.md#winfile)
-and the the `wannier90` Tutorial.
+and the `wannier90` Tutorial.
 
 ## Keyword List
 
@@ -65,7 +65,7 @@ and the the `wannier90` Tutorial.
 <!-- markdownlint-enable MD013 -->
 
 `seedname.win` file keywords defining the system. Argument types are
-represented by, I for a integer, R for a real number, P for a physical
+represented by, I for an integer, R for a real number, P for a physical
 value, L for a logical value and S for a text string.
 
 - `atoms_cart` and `atoms_frac` may not both be defined in the same input file.
@@ -77,9 +77,9 @@ value, L for a logical value and S for a text string.
 <!-- markdownlint-enable MD013 -->
 
 `seedname.win` file keywords defining job control. Argument types are
-represented by, I for a integer, R for a real number, P for a physical
+represented by, I for an integer, R for a real number, P for a physical
 value, L for a logical value and S for a text string.
-translate_home_cell only relevant if `write_xyz` is `.true.`
+translate_home_cell is only relevant if `write_xyz` is `.true.`
 
 ### Disentanglement Parameters
 
@@ -88,7 +88,7 @@ translate_home_cell only relevant if `write_xyz` is `.true.`
 <!-- markdownlint-enable MD013 -->
 
 `seedname.win` file keywords controlling the disentanglement. Argument
-types are represented by, I for a integer, R for a real number, P for a
+types are represented by, I for an integer, R for a real number, P for a
 physical value, L for a logical value and S for a text string.
 
 ### Wannierise Parameters
@@ -98,7 +98,7 @@ physical value, L for a logical value and S for a text string.
 <!-- markdownlint-enable MD013 -->
 
 `seedname.win` file keywords controlling the wannierisation. Argument
-types are represented by, I for a integer, R for a real number, P for a
+types are represented by, I for an integer, R for a real number, P for a
 physical value, L for a logical value and S for a text string.
 
 - `fixed_step` and `trial_step` may not both be defined in the same input
@@ -114,7 +114,7 @@ file.
 <!-- markdownlint-enable MD013 -->
 
 `seedname.win` file keywords controlling the plotting. Argument types
-are represented by, I for a integer, R for a real number, P for a
+are represented by, I for an integer, R for a real number, P for a
 physical value, L for a logical value and S for a text string.
 
 - `wannier_plot_radius` only applies when `wannier_plot_format` is `cube`.
@@ -126,7 +126,7 @@ physical value, L for a logical value and S for a text string.
 <!-- markdownlint-enable MD013 -->
 
 `seedname.win` file keywords controlling transport. Argument types are
-represented by, I for a integer, R for a real number, P for a physical
+represented by, I for an integer, R for a real number, P for a physical
 value, L for a logical value and S for a text string.
 
 ## System
@@ -259,8 +259,8 @@ end kpoints
 There is no default.
 
 !!! note
-    There is an utility provided with `wannier90`, called
-    `kmesh.pl`, which helps to generate the explicit list of $k$ points
+    There is a utility provided with `wannier90`, called
+    `kmesh.pl`, which helps to generate the explicit list of $k$-points
     required by `wannier90`. See Sec. [`kmesh.pl`](../appendices/utilities.md#kmeshpl).
 
 ### `logical :: gamma_only`
@@ -362,14 +362,14 @@ also if the k-points do not describe a regular mesh.
 
 ### `real(kind=dp) :: kmesh_tol`
 
-Two kpoints belong to the same shell if the distance between them is
+Two k-points belong to the same shell if the distance between them is
 less than `kmesh_tol`. Units are Ang.
 
 The default value is 0.000001 Ang.
 
 ### `integer :: higher_order_n`
 
-Specifies the order of finite-difference(FD) formula. The default is 1.
+Specifies the order of finite-difference (FD) formula. The default is 1.
 Assuming the first-order FD uses #1, #3 shells for neighbors,
 then the n-th-order FD also includes 2, 3, ..., n times #1, #3 shells.
 A very high value of n may require larger `search_shells`.
@@ -449,7 +449,7 @@ No default.
 
 ### `integer :: exclude_bands(:)`
 
-A k-point independent list of states to excluded from the calculation of
+A k-point independent list of states to exclude from the calculation of
 the overlap matrices; for example to select only valence states, or
 ignore semi-core states. This keyword is passed to the first-principles
 code via the `seedname.nnkp` file. For example, to exclude bands 2, 6,
@@ -761,7 +761,7 @@ The default value is 1.0E-10
 
 Whether or not to use preconditioning to speed up the minimization of
 the spreads. This is based on the same idea as the classical
-Tetter-Payne-Allan preconditionning for DFT and dampens the
+Teter-Payne-Allan preconditioning for DFT and dampens the
 high-frequency oscillations of the gradient due to contributions from
 large real lattice vectors. It is useful when the optimization is slow,
 especially on fine grids. When `optimisation<3`, this uses a slower
@@ -1338,7 +1338,7 @@ The default value is `false`.
 
 ### `logical :: write_bvec`
 
-If `write_bvec = true`, then the the matrix elements of
+If `write_bvec = true`, then the matrix elements of
 bvector and their weights will be written to a file `seedname.bvec`.
 
 The default value is `false`.