# ⚖️ Comparing Similar Words

Compare words that are similar and may be confused with each other.

# Tech

## Parameter, Configuration, Argument

• Parameter: to a function

• Configuration: to an application

• Argument: to a CLI command

# Science

## Polygon Rule, Huckel's Rule, bonding and antibonding

molecular orbitals (MOs), aromaticity

### How to utilize the Polygon Rule and Huckel's Rule in practice:

`For a 6 annulene:    By Polygon Rule: it has floorToOddNumber(6/2) =>  bonding MOs.     By Huckel's Rule: 6 = 4* + 2 => suggests AROMATIC    ( - 1)/2 = `

※ remember that annulene is only applicable to the annulenes.

### How to interpret aromaticity in terms of MO Theory:

Consider cyclohexane (C6H12):

`    Originally, each carbon atom has 2 p e-'s - that's 6*2 = 12 pi e-'s in total.    According to the Polygon Rule: Its "energy diagram" should be a hexagon, opening 6*2 spots for e-'s to settle in.    ∵12 pi e-'s = 12 spots in the polygon ∴The polygon should appear "all occupied", including all the bonding and anti-bonding "MOs".    We noticed that the cyclohexane has no pi bond. (Does "anti-bonding" mean "canceling the bonding effect of the bonding MOs"?)`

Now consider the annulene (a.k.a. "benzene"):

`    One of the requirements for Huckel's Rule suggests that the molecule should have a continuous cyclic repetition of pattern "C-C=C", which actually reduces 1 e- from each C.    So, the total amount of pi e-'s in benzene = 6*2 - 6*1 = 6    It's just enough to fill up all the 3 bonding MOs.    (We observed 3 pi bonds in the benzene molecule. Does this suggests a "bonding MO" represents a pi bond in the molecule?)`

Now consider cyclohexa-1,3-diene (benzene with one C=C bond reduced by H atoms):

`    2 additional pi e-'s compared to benzene    [Polygon Rule] the 2 additional e-'s are placed separately on the 2 degenerate LUMOs in the benzene diagram. Imagine these 2 e-'s are placed together in one of these LUMOs - an anti-aromatic MO is filled, so the molecule structure should have one pi bond less than benzene - and it truly is so.    [Huckel's Rule] 8 = 2*4 ===suggests===> anti-aromacitiy <===because that=== we are having 2 MOs with only 1 e- in each (can be proven by Polygon Rule), which makes up a "di-radical" structure.`

### Conclusion

`The bonding/anti-bonding of the MOs - gives the amount of pi bonds in the molecule (just atom-and-atom bonds; not "pi conjugated system"):    a filled bonding MO suggest one more pi bond        a filled anti-bonding MO suggest one less pi bond   The Aromaticity - all about the stability and reactive electrons:     anti-aromaticity: has lone e-'s. They are likely to escape/grab e-'s from other molecules (a.k.a. "reactive"), thus making it very hard for this molecule to stay itself (a.k.a. "unstable").    aromaticity: has no lone e-'s. Every pi e- are paired in the MOs ,leaving no e-'s wandering about and causing troubles. It's not likely that this molecule change its structure, thus it has a high stability.`

## Resonance and Inductive Effects

There are two main electronic effects that substituents can exert:

• RESONANCE effects are those that occur through the p system and can be represented by resonance structures. These can be either electron donating (e.g. -OMe) where p electrons are pushed toward the arene or electron withdrawing (e.g. -C=O) where p electrons are drawn away from the arene.

• INDUCTIVE effects are those that occur through the s system due to electronegativity type effects. These too can be either electron donating (e.g. -Me) where s electrons are pushed toward the arene or electron withdrawing (e.g. -CF3, +NR3) where s electrons are drawn away from the arene.

## "Thermodynamic reaction control" v.s. "Kinetic reaction control"

### COMMON PROPERTIES

decide the composition of the product mixture of a reaction when:

• competing pathways lead to different products

• the reaction conditions influence the selectivity

### Thermodynamic reaction control

• Favors the thermodynamic product - the one with the lower internal energy.

• Advantage in competition: product is more stable (due to lower U).

• favored in lower temperature (where the Ea barrier cannot be easily overcome).

• goes the thermodynamically-controlled pathway

• e.g.: 1,4-addition of HBr to Dienes

### Kinetic reaction control

• Favors the kinetic product - the one with the lower kinetic energy.

• Advantage in competition: goes faster (due to lower Ea).

• favored in high temperature (where the Ea barrier can be easily overcome).

• goes the kinetically-controlled pathway

• e.g.: 1,2-addition of HBr to Dienes

## Eigenvectors v.s. eigenvalues

English
Mandarin Chinese
English

For rhyming, the "feature vector" is hereinafter referred to as "eigenvector".

The eigenvectors and eigenvalues are used to describe a linear transformation.

The eigenvector describes the direction in which the direction does not change after the linear transformation is applied. The eigenvalues describe how much the vector will be stretched/compressed (as a scaling factor) in the direction above (the one that does not change direction after the linear transformation).

in case

• V and W are finite dimensional, and

• There are selected bases in these spaces,

Then: all linear transformations from V to W can be represented as matrices.

Under certain conditions (such as a linear transformation whose matrix form is a real symmetric matrix), the eigenvectors and eigenvalues can fully represent a linear transformation.

Mandarin Chinese

• V 和 W 是有限维的，并且

• 在这些空间中有选择好的基，