The effective screening medium (ESM) method is a first-principles computational method for charged or biased systems consisting of a slab [81,82,83,84]. In this method, a 2-dimensional periodic and 1-dimensional optional boundary conditions are imposed on a model cell (Fig. 37(a)), and the Poisson's equation is solved under those set of boundary conditions by using the Green's function method. An isolated slab, charged slab, and a slab under an uniform electric field can be treated by introducing the following combinations of semi-infinite media (ESMs).

- (a) Isolated slab: vacuum (relative permittivity ) + vacuum
- (b) Charged slab: vacuum + ideal metal (relative permittivity
)
- (c) Slab under an electric filed: ideal metal + ideal metal

- The a-axis of the cell is perpendicular to the
**b**-**c**plane and is parallel to the x-axis. - Two periodic boundary conditions are set in y- and z-axis directions
- ESMs are placed at the cell-boundaries (x = 0 and a).
- The origin of the x-axis is set at the cell boundary.
- A fractional coordinate for x-axis is designated between 0 and 1.

A calculation based on an ESM-method can be performed by the following keyword:

ESM.switch on3 # off, on1=v|v|v, on2=m|v|m, on3=v|v|m, on4=on2+EF ESM.buffer.range 4.5 # default=10.0 (ang),where on1, on2, on3, and on4 represent combinations of ESMs, 'vacuum + vacuum', 'ideal metal + ideal metal', 'vacuum + ideal metal', and 'ideal metal + ideal metal under an electric field', respectively. The keyword 'ESM.buffer.range' indicates the width of a exclusive region for atoms with ESM (unit is Å), which is necessary in order to prevent overlaps between wave functions and ESM.

- ESM.switch = on1:
Both ESM (I) and (II) are semi-infinite vacuum media. In this case, note that the total charge of a calculation system should be neutral. The keyword 'scf.system.charge' should be set to be zero.

- ESM.switch = on2:
Both ESM (I) and (II) are semi-infinite ideal-metal media. One can deal with charged systems. The keyword 'scf.system.charge' can be set to be a finite value.

- ESM.switch = on3:
ESM (I) and (II) are a semi-infinite vacuum and ideal metal medium, respectively. One can deal with charged systems. The keyword 'scf.system.charge' can be set to be a finite value.

- ESM.switch = on4:
An electric field is imposed on the system with the same combination of ESMs to 'on2'. By using the following keyword, one can impose a uniform electric field on a calculation system;

ESM.potential.diff 1.0 # default=0.0 (eV),

where one inputs a potential difference between two semi-infinite ideal-metal media with reference to the bottom ideal metal (unit is eV). The electric filed is decided by the length of the cell, a, and the potential difference. - In case of MD calculations with the ESM method:
One can implement MD calculations of solid surface-liquid interface systems with any combinations of ESMs. A surface-model slab and a liquid region should be located as shown in Fig. 37(b). In order to restrict liquid molecules within a given region, an cubic barrier potential can be introduced by using the following keyword (see Fig. 37(b)):

ESM.wall.position 6.0 # default=10.0 (ang) ESM.wall.height 100.0 # default=100.0 (eV),

where 'ESM.wall.position' denotes the distance between the upper edge of the cell and the origin of the barrier potential, , and 'ESM.wall.height' is the height of the potential (value of potential energy) at (Å). It is also recommended to fix positions of atoms on the bottom of a surface-model slab during a MD run.