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.