Geometry Optimization,
Frequency and IR
Calculation
Geometry Optimization
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●
A B 3N-5 = 1 V(R) = E(R)
V(R1
,R2
,R3
,...,RN
) = E(R1
,R2
,R3
,...,RN
)
Potential Energy
Surface (PES)
∂ ∂
∂ ∂ ∂ ∂
●
●
●
● ∂ … ∂ ∂
●
●
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IR spectroscopy
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Wavenumber
ṽ 𝜆
𝜈 𝜆
ṽ 𝜆
ṽ
Normal modes of vibrations
●
●
○
○
●
○
○
●
Model for describing vibrations between atoms
●
●
○
○ Ṽ 𝜋
Quantum harmonic oscillator
●
○ 𝜈
○ …
○ 𝜈 𝜈 𝜈 𝜈 …
𝜟𝝂
𝜈 ⇾ 𝜈 𝜈 ⇾ 𝜈
Anharmonic oscillator
●
● − − −
●
● 𝜟𝝂
● 𝜈 ⇾ 𝜈
●
○ 𝜈 ⇾ 𝜈
○ 𝜈 ⇾ 𝜈 …
●
○ 𝜈 ⇾ 𝜈
○ 𝜈 ⇾ 𝜈
Diatomic oscillator
●
●
○ ṽ 𝜋 √ 𝜇
○
○ 𝜇
●
○
○
○
○
Task (I)
● − ＝ ≡
●
○ −
○ ＝
○ ≡
Task (II)
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○ https://cccbdb.nist.gov/vibscalejust.asp
Task (III)
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https://www.basissetexchange.org/
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Homework