POAV

class sknano.core.atoms.POAV(atom)

Bases: sknano.core.meta.BaseClass

Base class for POAV analysis.

Parameters:atom (Atom) – Atom instance.

Attributes

A	Magnitude of $\mathbf{v}_{\pi}$.
H	Altitude of tetrahedron.
R1	Bond 1 Vector length.
R2	Bond 2 Vector length.
R3	Bond 3 Vector length.
T	$\frac{1}{6}$ the volume of the tetrahedron defined by Vectors V1, V2, and V3.
V1	$\mathbf{v}_1$ unit Vector
V2	$\mathbf{v}_2$ unit Vector
V3	$\mathbf{v}_3$ unit Vector
Vpi	$\mathbf{v}_{\pi}$ unit Vector
Vv1v2v3	Volume of the parallelepiped defined by Vectors v1, v2, and v3.
fmtstr	Format string.
misalignment_angles	List of misalignment $\phi_{i}$ angles.
pyramidalization_angles	List of pyramidalization $\theta_{P}$ angles.
reciprocal_v1	Reciprocal Vector $\mathbf{v}_1^{*}$.
reciprocal_v2	Reciprocal Vector $\mathbf{v}_2^{*}$.
reciprocal_v3	Reciprocal Vector $\mathbf{v}_3^{*}$.
sigma_pi_angles	List of $\theta_{\sigma-\pi}$ angles.
t	$\frac{1}{6}$ the volume of the tetrahedron defined by Vectors v1, v2, and v3.
v1	Vector $\mathbf{v}_1$ directed along the $\sigma$-orbital to the nearest-neighbor Atom in Bond 1.
v2	Vector $\mathbf{v}_2$ directed along the $\sigma$-orbital to the nearest-neighbor Atom in Bond 2.
v3	Vector $\mathbf{v}_3$ directed along the $\sigma$-orbital to the nearest-neighbor Atom in Bond 3.
vpi	General $\pi$-orbital axis vector ($\mathbf{v}_{\pi}$) formed by the terminii of Vectors Vectors v1, v2, and v3.

Methods

POAVdict([rad2deg])	Return dictionary of POAV class attributes.
todict()	Return dict of constructor parameters.

Attributes Summary

A	Magnitude of $\mathbf{v}_{\pi}$.
H	Altitude of tetrahedron.
R1	Bond 1 Vector length.
R2	Bond 2 Vector length.
R3	Bond 3 Vector length.
T	$\frac{1}{6}$ the volume of the tetrahedron defined by Vectors V1, V2, and V3.
V1	$\mathbf{v}_1$ unit Vector
V2	$\mathbf{v}_2$ unit Vector
V3	$\mathbf{v}_3$ unit Vector
Vpi	$\mathbf{v}_{\pi}$ unit Vector
Vv1v2v3	Volume of the parallelepiped defined by Vectors v1, v2, and v3.
misalignment_angles	List of misalignment $\phi_{i}$ angles.
pyramidalization_angles	List of pyramidalization $\theta_{P}$ angles.
reciprocal_v1	Reciprocal Vector $\mathbf{v}_1^{*}$.
reciprocal_v2	Reciprocal Vector $\mathbf{v}_2^{*}$.
reciprocal_v3	Reciprocal Vector $\mathbf{v}_3^{*}$.
sigma_pi_angles	List of $\theta_{\sigma-\pi}$ angles.
t	$\frac{1}{6}$ the volume of the tetrahedron defined by Vectors v1, v2, and v3.
v1	Vector $\mathbf{v}_1$ directed along the $\sigma$-orbital to the nearest-neighbor Atom in Bond 1.
v2	Vector $\mathbf{v}_2$ directed along the $\sigma$-orbital to the nearest-neighbor Atom in Bond 2.
v3	Vector $\mathbf{v}_3$ directed along the $\sigma$-orbital to the nearest-neighbor Atom in Bond 3.
vpi	General $\pi$-orbital axis vector ($\mathbf{v}_{\pi}$) formed by the terminii of Vectors Vectors v1, v2, and v3.

Methods Summary

POAVdict([rad2deg])	Return dictionary of POAV class attributes.
todict()	Return dict of constructor parameters.

Attributes Documentation

A

Magnitude of $\mathbf{v}_{\pi}$.

H

Altitude of tetrahedron.

R1

Bond 1 Vector length.

R2

Bond 2 Vector length.

R3

Bond 3 Vector length.

T

$\frac{1}{6}$ the volume of the tetrahedron defined by Vectors V1, V2, and V3.

$$T = \frac{|\mathbf{V}_1\cdot(\mathbf{V}_2\times\mathbf{V}_3)|}{6}$$

V1

$\mathbf{v}_1$ unit Vector

$$\mathbf{V}_1\equiv\frac{\mathbf{v}_1}{|\mathbf{v}_1|}$$

V2

$\mathbf{v}_2$ unit Vector

$$\mathbf{V}_2\equiv\frac{\mathbf{v}_2}{|\mathbf{v}_2|}$$

V3

$\mathbf{v}_3$ unit Vector

$$\mathbf{V}_3\equiv\frac{\mathbf{v}_3}{|\mathbf{v}_3|}$$

Vpi

$\mathbf{v}_{\pi}$ unit Vector

Returns the $\pi$-orbital axis vector ($\mathbf{v}_{\pi}$) unit vector.

$$\mathbf{V}_{\pi} = \frac{\mathbf{v}_{\pi}}{|\mathbf{v}_{\pi}|}$$

Vv1v2v3

Volume of the parallelepiped defined by Vectors v1, v2, and v3.

Computes the scalar triple product of vectors $\mathbf{v}_1$, $\mathbf{v}_2$, and $\mathbf{v}_3$:

$$V_{v_1v_2v_3} = |\mathbf{v}_1\cdot(\mathbf{v}_2\times\mathbf{v}_3)|$$

misalignment_angles

List of misalignment $\phi_{i}$ angles.

pyramidalization_angles

List of pyramidalization $\theta_{P}$ angles.

reciprocal_v1

Reciprocal Vector $\mathbf{v}_1^{*}$.

Defined as:

$$\mathbf{v}_1^{*} = \frac{\mathbf{v}_2\times\mathbf{v}_3} {|\mathbf{v}_1\cdot(\mathbf{v}_2\times\mathbf{v}_3)|}$$

reciprocal_v2

Reciprocal Vector $\mathbf{v}_2^{*}$.

Defined as:

$$\mathbf{v}_2^{*} = \frac{\mathbf{v}_3\times\mathbf{v}_1} {|\mathbf{v}_1\cdot(\mathbf{v}_2\times\mathbf{v}_3)|}$$

reciprocal_v3

Reciprocal Vector $\mathbf{v}_3^{*}$.

Defined as:

$$\mathbf{v}_3^{*} = \frac{\mathbf{v}_1\times\mathbf{v}_2} {|\mathbf{v}_1\cdot(\mathbf{v}_2\times\mathbf{v}_3)|}$$

sigma_pi_angles

List of $\theta_{\sigma-\pi}$ angles.

t

$\frac{1}{6}$ the volume of the tetrahedron defined by Vectors v1, v2, and v3.

$$t = \frac{|\mathbf{v}_1\cdot(\mathbf{v}_2\times\mathbf{v}_3)|}{6}$$

v1

Vector $\mathbf{v}_1$ directed along the $\sigma$-orbital to the nearest-neighbor Atom in Bond 1.

v2

Vector $\mathbf{v}_2$ directed along the $\sigma$-orbital to the nearest-neighbor Atom in Bond 2.

v3

Vector $\mathbf{v}_3$ directed along the $\sigma$-orbital to the nearest-neighbor Atom in Bond 3.

vpi

General $\pi$-orbital axis vector ($\mathbf{v}_{\pi}$) formed by the terminii of Vectors Vectors v1, v2, and v3.

$$\mathbf{v}_{\pi} = \mathbf{v}_1 + \mathbf{v}_2\ + \mathbf{v}_3$$

Methods Documentation

POAVdict(rad2deg=False)

Return dictionary of POAV class attributes.

todict()

Return dict of constructor parameters.