Enum OrbProj 

#[repr(u8)]
pub enum OrbProj {
    s = 0,
    px = 1,
    py = 2,
    pz = 3,
    dxy = 4,
    dyz = 5,
    dxz = 6,
    dz2 = 7,
    dx2y2 = 8,
    fz3 = 9,
    fxz2 = 10,
    fyz2 = 11,
    fzx2y2 = 12,
    fxyz = 13,
    fxx23y2 = 14,
    fy3x2y2 = 15,
    sp_1 = 16,
    sp_2 = 17,
    sp2_1 = 18,
    sp2_2 = 19,
    sp2_3 = 20,
    sp3_1 = 21,
    sp3_2 = 22,
    sp3_3 = 23,
    sp3_4 = 24,
    sp3d_1 = 25,
    sp3d_2 = 26,
    sp3d_3 = 27,
    sp3d_4 = 28,
    sp3d_5 = 29,
    sp3d2_1 = 30,
    sp3d2_2 = 31,
    sp3d2_3 = 32,
    sp3d2_4 = 33,
    sp3d2_5 = 34,
    sp3d2_6 = 35,
}

This is the orbital projection

Variants

s = 0

$$\ket{s}=\ket{0,0}$$

px = 1

$$\ket{p_x}=\frac{1}{\sqrt{2}}\lt(\ket{1,-1}-\ket{1,1}\rt)$$

py = 2

$$\ket{p_y}=\frac{i}{\sqrt{2}}\lt(\ket{1,-1}+\ket{1,1}\rt)$$

pz = 3

$$\ket{p_z}=\ket{1,0}$$

dxy = 4

$$\ket{d_{xy}}=-\f{i}{\sqrt{2}}\lt(\ket{2,2}-\ket{2,-2}\rt)$$

dyz = 5

$$\ket{d_{yz}}=-\f{i}{\sqrt{2}}\lt(\ket{2,1}+\ket{2,-1}\rt)$$

dxz = 6

$$\ket{d_{xz}}=-\f{1}{\sqrt{2}}\lt(\ket{2,1}-\ket{2,-1}\rt)$$

dz2 = 7

$$\ket{d_{z^2}}=\ket{2,0}$$

dx2y2 = 8

$$\ket{d_{x^2-y^2}}=\f{1}{\sqrt{2}}\lt(\ket{2,2}+\ket{2,-2}\rt)$$

fz3 = 9

$$\ket{f_{z^3}}=\ket{3,0}$$

fxz2 = 10

$$\ket{f_{xz^2}}=\f{1}{\sqrt{2}}\lt(\ket{3,1}-\ket{3,-1}\rt)$$

fyz2 = 11

$$\ket{f_{yz^2}}=-\f{i}{\sqrt{2}}\lt(\ket{3,1}+\ket{3,-1}\rt)$$

fzx2y2 = 12

$$\ket{f_{z(x^2-y^2)}}=\f{1}{\sqrt{2}}\lt(\ket{3,2}+\ket{3,-2}\rt)$$

fxyz = 13

$$\ket{f_{xyz}}=-\f{i}{\sqrt{2}}\lt(\ket{3,2}-\ket{3,-2}\rt)$$

fxx23y2 = 14

$$\ket{f_{x(x^2-3y^2)}}=\f{1}{\sqrt{2}}\lt(\ket{3,3}-\ket{3,-3}\rt)$$

fy3x2y2 = 15

$$\ket{f_{y(3x^2-y^2)}}=-\f{i}{\sqrt{2}}\lt(\ket{3,3}+\ket{3,-3}\rt)$$

sp_1 = 16

$$\ket{sp_{1}}=\frac{1}{\sqrt{2}}\lt(\ket{s}+\ket{p}\rt)$$

sp_2 = 17

$$\ket{sp_{2}}=\frac{1}{\sqrt{2}}\lt(\ket{s}-\ket{p}\rt)$$

sp2_1 = 18

$$\ket{sp^2_{1}}=\f{1}{\sqrt{3}}\ket{s}-\f{1}{\sqrt{6}}\ket{p_x}+\f{1}{\sqrt{2}}\ket{p_y}$$

sp2_2 = 19

$$\ket{sp^2_{1}}=\f{1}{\sqrt{3}}\ket{s}-\f{1}{\sqrt{6}}\ket{p_x}-\f{1}{\sqrt{2}}\ket{p_y}$$

sp2_3 = 20

$$\ket{sp^2_{1}}=\f{1}{\sqrt{3}}\ket{s}+\f{2}{\sqrt{6}}\ket{p_x}$$

sp3_1 = 21

$$\ket{sp^3_{1}}=\frac{1}{2}\lt(\ket{s}+\ket{p_x}+\ket{p_y}+\ket{p_z}\rt)$$

sp3_2 = 22

$$\ket{sp^3_{2}}=\frac{1}{2}\lt(\ket{s}+\ket{p_x}-\ket{p_y}-\ket{p_z}\rt)$$

sp3_3 = 23

$$\ket{sp^3_{3}}=\frac{1}{2}\lt(\ket{s}-\ket{p_x}+\ket{p_y}-\ket{p_z}\rt)$$

sp3_4 = 24

$$\ket{sp^3_{4}}=\frac{1}{2}\lt(\ket{s}-\ket{p_x}-\ket{p_y}+\ket{p_z}\rt)$$

sp3d_1 = 25

$$\ket{sp^3d_{1}}=\f{1}{\sqrt{3}}\ket{s}-\f{1}{\sqrt{6}}\ket{p_x}+\f{1}{\sqrt{2}}\ket{p_y}$$

sp3d_2 = 26

$$\ket{sp^3d_{2}}=\f{1}{\sqrt{3}}\ket{s}-\f{1}{\sqrt{6}}\ket{p_x}-\f{1}{\sqrt{2}}\ket{p_y}$$

sp3d_3 = 27

$$\ket{sp^3d_{3}}=\f{1}{\sqrt{3}}\ket{s}+\f{2}{\sqrt{6}}\ket{p_x}$$

sp3d_4 = 28

$$\ket{sp^3d_{4}}=\f{1}{\sqrt{2}}\lt(\ket{p_z}+\ket{d_{z^2}}\rt)$$

sp3d_5 = 29

$$\ket{sp^3d_{5}}=-\f{1}{\sqrt{2}}\lt(\ket{p_z}-\ket{d_{z^2}}\rt)$$

sp3d2_1 = 30

$$\ket{sp^3d^2_{1}}=\frac{1}{\sqrt{6}}\ket{s}-\f{1}{\sqrt{2}}\ket{p_x}-\f{1}{\sqrt{12}}\ket{d_{z^2}}+\f{1}{2}\ket{d_{x^2-y^2}}$$

sp3d2_2 = 31

$$\ket{sp^3d^2_{2}}=\frac{1}{\sqrt{6}}\ket{s}+\f{1}{\sqrt{2}}\ket{p_x}-\f{1}{\sqrt{12}}\ket{d_{z^2}}+\f{1}{2}\ket{d_{x^2-y^2}}$$

sp3d2_3 = 32

$$\ket{sp^3d^2_{3}}=\frac{1}{\sqrt{6}}\ket{s}-\f{1}{\sqrt{2}}\ket{p_x}-\f{1}{\sqrt{12}}\ket{d_{z^2}}-\f{1}{2}\ket{d_{x^2-y^2}}$$

sp3d2_4 = 33

$$\ket{sp^3d^2_{4}}=\frac{1}{\sqrt{6}}\ket{s}+\f{1}{\sqrt{2}}\ket{p_x}-\f{1}{\sqrt{12}}\ket{d_{z^2}}-\f{1}{2}\ket{d_{x^2-y^2}}$$

sp3d2_5 = 34

$$\ket{sp^3d^2_{5}}=\frac{1}{\sqrt{6}}\ket{s}-\f{1}{\sqrt{2}}\ket{p_z}+\f{1}{\sqrt{3}}\ket{d_{z^2}}$$

sp3d2_6 = 35

$$\ket{sp^3d^2_{6}}=\frac{1}{\sqrt{6}}\ket{s}+\f{1}{\sqrt{2}}\ket{p_z}+\f{1}{\sqrt{3}}\ket{d_{z^2}}$$

Implementations

impl OrbProj

pub fn from_str(s: &str) -> Result<Self>

pub fn to_quantum_number(&self) -> Result<Array1<Complex<f64>>>

这个函数是将 \ket{px},\ket{py},\ket{pz} 等原子轨道基转化为以 l,m 为基的函数的. 它输入一个原子轨道比如 $\ket{px}$, 输出一个 array![Complex;16], 表示 $$[\ket{0,0},\ket{1,-1},\ket{1,0},\ket{1,1},\ket{2,-2},\cdots,\ket{3,3}]$$

Trait Implementations

impl Clone for OrbProj

fn clone(&self) -> OrbProj

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for OrbProj

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for OrbProj

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for OrbProj

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl PartialEq for OrbProj

fn eq(&self, other: &OrbProj) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Serialize for OrbProj

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl Copy for OrbProj

impl StructuralPartialEq for OrbProj