AtomicOrbitals

	Core NanoLanguage elements
Core NanoLanguage elements	basisSetParameters

Name

AtomicOrbitals — Available basis sets in ATK

Synopsis

Namespace: ATK.KohnSham or ATK.TwoProbe

Description

ATK solves the Kohn-Sham equations by expanding the wave functions using localized, numerical orbitals as basis sets [2]. Five different types of basis sets are available, and they are listed below in order of increasing size and accuracy. In most practical cases, experience has shown that the DoubleZetaPolarized basis set gives very good accuracy, but for large systems with e.g. many transition metal atoms this basis set might be too big to fit in the computer memory.

The following AtomicOrbitals objects are singleton values that take no options nor return any values:

SingleZeta; least accurate; a single basis orbital for each valence orbital
SingleZetaPolarized; SingleZeta plus one basis orbital for the first unoccupied shell
DoubleZeta; two basis orbitals for each valence orbital
DoubleZetaPolarized; DoubleZeta plus one basis orbital for the first unoccupied shell
DoubleZetaDoublePolarized; most accurate; DoubleZeta and two basis orbitals for the first unoccupied shell

The SingleZeta basis set covers the valence configuration, which contains all open shells and, in some cases, also some high-energy closed shells (such as the d shell in transition metals).

Usage examples

Set the basis size for all elements to the DoubleZeta basis set

basis_set_parameters = basisSetParameters(type=DoubleZeta)

Specify a smaller basis set for Hydrogen elements than the default basis set.

my_basis = basisSetParameters(
    type=SingleZeta,
    element=Hydrogen
    )
my_method = KohnShamMethod(
    basis_set_parameters=my_basis,
    exchange_correlation_type=GGA.PBE
    )

Generating the basis set

Using the basisSetParameters() method of NanoLanguage, it is possible to customize the predefined basis sets supplied with ATK. In the following subsections we will describe how these parameters affect the basis sets.

Please see basisSetParameters() for a presentation of the various parameters that control the basis functions within the basis set.

Single Zeta Orbitals

The basis functions are found by solving the radial Schrödinger equation for the atom with a confinement potential. The confinement potential is defined by the parameters, $V_0$ , $r_{\mathrm{inn}}$ and $r_c$ through the equation

$\displaystyle V_{\mathrm{conf}}(r) = \begin{cases} 0 & \mathrm{if} r < r_{\mathrm{inn}} \\ V_0 \; \frac{\exp[\frac{-1}{(r-r_{\mathrm{inn}})}]}{(r_c-r)} & \mathrm{if} r_{\mathrm{inn}} < r < r_c\\ \infty & \mathrm{if} r_c < r \end{cases}$

Double Zeta Orbitals

The double zeta orbital is constructed through a procedure reminiscent of the splitting of a Gaussian basis set. The split orbital is obtained by constructing an analytical basis orbital that matches the first zeta orbital smoothly at the radius $r^{\mathrm{split}}$ . The functional form used for the split orbital is

$\phi_{l}^{2 \zeta}(r) = \begin{cases} r^l(a_l-b_l r^2) & \mathrm{if} r < r_l^{\mathrm{split}} \\ \phi_{l}^{1 \zeta}(r) & \mathrm{if} r \ge r_l^{\mathrm{split}} \end{cases}$

The radius $r^{\mathrm{split}}$ is determined by specifying the norm of the split orbital using the split_norm argument of the basisSetParameters() method.

Polarization Orbitals

The polarization orbitals have higher angular momentum than the valence orbitals. In ATK such orbitals are generated by perturbing the single zeta orbitals by an electric field, and extracting the $l+1$ component of the perturbed orbital.

The lower part of the plot shows the 14 0 45e09236e8f293f5565707e3bbf241d4 l=0 effective potential for hydrogen (dashed) with the soft confinement potential (solid). The upper part shows the lowest occupied state of the confined potential (solid line), and the atomic 9 0 2786d53c1122848ae6431398d6be7767 s -wave function is indicated by the dashed curve. The dotted curve shows the solution with energy shift 0.01 Rydberg. The position of the first node of this solution defines the position of 9 3 f5b9dfb293fbb1edbb2d00d790c0c6f2 r_c .

Figure 64: The lower part of the plot shows the $l=0$ effective potential for hydrogen (dashed) with the soft confinement potential (solid). The upper part shows the lowest occupied state of the confined potential (solid line), and the atomic $s$ -wave function is indicated by the dashed curve. The dotted curve shows the solution with energy shift 0.01 Rydberg. The position of the first node of this solution defines the position of $r_c$ .

Notes

One can inspect which type of orbitals that are included in the basis set for a particular atom in the system by running the self-consistent calculation with verbosity level larger than or equal to 9.

Further examples


Core NanoLanguage elements		basisSetParameters