Molecular Spectroscopy 박영동 교수

Atomic Spectroscopy Brief

Hydrogen Atom Spin-Orbit Interaction

Hydrogen Atom The magnetic field can be expressed in terms of the orbital angular momentum L: This corresponds to an internal magnetic field on the electron of about 0.4 Tesla.

Hydrogen Atom At the heart of the process is the exchange force by which charges interact by the exchange of photons (the exchange force model of the electromagnetic force). There can be a self interaction of the electron by exchange of a photon as sketched in the Feynman diagram at left. This "smears out" the electron position over a range of about 0.1 fermi (Bohr radius = 52,900 fermis). This causes the electron spin g-factor to be slightly different from 2. There is also a slight weakening of the force on the electron when it is very close to the nucleus, causing the 2s electron (which has penetration all the way to the nucleus) to be slightly higher in energy than the 2p(1/2) electron.

Sodium D-lines The Fraunhofer lines are a set of spectral lines named for the German physicist Joseph von Fraunhofer (1787–1826). The lines were originally observed as dark features (absorption lines) in the optical spectrum of the Sun. He labeled the lines with letters from A to K.

5688.205 5688.193 5682.633

The Zeeman Effect The Zeeman effect is the splitting of a spectral line into several components in the presence of a static magnetic field. Zeeman effect splits mJ levels into 10 lines

Lithium 1s22s1← 1s2nl1 Figure 7.5 Four series in the emission spectrum of lithium Figure 7.6 Grotrian diagram for lithium

7.2 Electronic spectroscopy of diatomic molecules 7.2.1.1 Homonuclear diatomic molecules LCAO-MO Condition 1: The energies of the AOs must be comparable. Condition 2: The AOs should overlap as much as possible. Condition 3: The AOs must have the same symmetry properties with respect to certain symmetry elements of the molecule.

Figure 7.13 Formation of molecular orbitals from 1s, 2s, and 2p atomic orbitals for O2 and F2 for Li2 to N2

7.2.2 Classification of electronic states Figure 7.16 (a) Hund’s case (a) and (b) Hund’s case (c) coupling of orbital and electron spin angular momenta in a diatomic molecule

7.2.3 Electronic selection rules Σ-Σ, Π-Σ,Δ-Π Δ -Σ, Φ-Π Rule 2: the selection rule breaks down as the nuclear charge increases. Rule 3: Rule 4: Σ+-Σ+, Σ--Σ- This is relevant only for Σ-Σ transitions Rule 5: 𝚺 𝒖 + − 𝚺 𝒈 + , 𝚷 𝒖 − 𝚺 𝒈 + 𝚺 𝒈 + − 𝚺 𝒈 + , 𝚷 𝒖 − 𝚺 𝒖 −

이원자분자 그림 1. 상태로부터 높은 에너지 상태로 일어나는 전자 흡수 전이의 진동 구조

Franck-Condon Principle 그림 2. 이원자 분자의 퍼텐설 에너지 곡선, 진동 에너지 준위 및 진동 파동함수의 제곱 그림 3. 두 전자-진동 상태들 사이에 일어나는 수직 전이들

그림 4. 윗 전자 상태와 아랫 전자 상태의 핵간 거리의 차이와 그 때의 전자-진동 스펙트럼 그림 5. 전자 들뜸에 의한 분해. 들뜬상태가 (a) 안정할 때와 (b)불안정할 때.

그림 6-9 불안정한 상태와 교차하는 안정한 윗 상태로 전이가 일어날 때 先解雜가 생길 수 있다. 그림 6-5 전자 들뜸에 의한 분해. 들뜬상태가 (a) 안정할 때와 (b)불안정할 때.

Figure 7.23 Dissociation energies D’0 and D”0 may be obtained from 𝜈 𝑙𝑖𝑚𝑖𝑡 , the wavenumber of the onset of a continuum in a progression in I2

7.2.6 Rotational fine structure 7.2.6.1 1Σ - 1Σ electronic and vibronic transitions Figure 7.25 Rotational fine structure of a 1Σ+-1Σ+ electronic or vibronic transition in a diatomic molecule for which r’e > r”e. The g and u subscripts and the s and a labels apply only to a homonuclear molecule: the +, -, e and f labels can be ignored

The A1Σ+-X1Σ+ electronic transition of CuH Figure 7.26 The A1Σ+-X1Σ+ electronic transition of CuH in absorption. Lines marked with a cross are not due to CuH.

7.2.6.2 1Π - 1Σ electronic and vibronic transitions Figure 7.27 Resultant J of the rotational angular momentum R and the component, Λ ℏ, of the orbital angular momentum Figure 7.28 Rotational fine structure of a 1Π - 1Σ electronic or vibronic transition in a diatomic molecule for which r’e > r”e. The g and u subscripts and s and a labels apply only to a homonuclear molecule

7.3 Electronic spectroscopy of polyatomic molecules 7.3.1.1 AH2 molecules 1s atomic orbitals on the hydrogen atoms in AH2 7.3.1.1(b) ∠HAH=90° 7.3.1.1(a) ∠HAH=180°

7.3 Electronic spectroscopy of polyatomic molecules 7.3.1.1 AH2 molecules 7.3.1.1(b) ∠HAH=90° 7.3.1.1(a) ∠HAH=180° Figure 7.31 Walsh molecular orbital diagram for AH2 molecules

Table 7.8 Ground and excited configurations of some AH2 molecules

7.3.1.2 Formaldehyde (H2CO) Ground state: : … (1b1)2(2b2)2 𝑋 1 𝐴 1 Figure 7.33 The 1b1(π), 2b1(π*) and 2b2(n) molecular orbitals in formaldehyde Ground state: : … (1b1)2(2b2)2 𝑋 1 𝐴 1 1st Excited state: : … (1b1)2(2b2)1(2b1)1 𝑎 3 𝐴 2 or 𝐴 1 𝐴 2

그림 6-11 포름알데하이드의 분자 오비탈들의 상대적 에너지

Fig. 2.1. Energy levels of molecular orbitals in formaldehyde (HOMO: Highest Occupied Molecular Orbitals; LUMO: Lowest Unoccupied Molecular Orbitals) and possible electronic transitions.

포름알데히드의 전자전이 스펙트럼 전자 배치 대칭종 바닥상태로부터의 전이 모멘트 [내부 전자](π)2(n)2 A1 B2 [내부 전자](π)(n)2(σ*) B1

포름알데히드의 전자전이 스펙트럼 λmax (nm) Oscillator strength Assignment 오비탈 변화 윗상태 선택 규칙 170 0.5 π→π* 1A1 허용됨 180 0.02 n→σ* 1B2 280 4×10-4 n→π* 1A2 대칭에 의해 금지됨 350 10-5 3A2 대칭과 스핀 다중도에 의해 금지됨

Benzene, D6h Γ 𝜓 𝑒 0 = 𝑒 1𝑔 × 𝑒 2𝑢 = 𝐵 1𝑢 + 𝐵 2𝑢 + 𝐸 1𝑢 Ground state : … (1a2u)2(1e1g)4 𝑋 1 𝐴 1𝑔 1st Excited state: … (1a2u)2(1e1g)3(1e2u)1 Γ 𝜓 𝑒 0 = 𝑒 1𝑔 × 𝑒 2𝑢 = 𝐵 1𝑢 + 𝐵 2𝑢 + 𝐸 1𝑢 𝑎 3 𝐵 1𝑢 , 𝑏 3 𝐸 1𝑢 , 𝑐 3 𝐵 2𝑢 , or 𝐴 1 𝐵 2𝑢 , 𝐵 1 𝐵 1𝑢 , 𝐶 1 𝐸 1𝑢 , Figure 7.36 Hückel molecular orbitals in benzene

Benzene, D6h

그림 6-15 (a) 벤젠의 260 nm 띠 (b) 벤젠의 𝐵 0 0 띠 50 cm-1 500 cm-1 10 cm-1 그림 6-15 (a) 벤젠의 260 nm 띠 (b) 벤젠의 𝐵 0 0 띠

FIG. 2. Comparison between the measured rotational structure of the 6 0 1 band (upper traces in a and b) and a spectrum simulation (lower traces therein) for different magnifications. The calculation is based upon a rotational temperature of 25 K and parameters determined in this work. The band origin could be evaluated to 38 606.098(2) cm-1 by evaluation of the iodine spectrum which was recorded simultaneously. In c the observed linewidth together with the sampling of the spectrum is visible. 10 cm-1 0.1 cm-1 M. Okruss, R. Muller, and A. Hese, J. Molec. Spectrosc. 193, 293(1999) 0.01 cm-1

Molecules and Radiation: An Introduction to Modern Molecular Spectroscopy ... By Jeffrey I. Steinfeld

7.1 Indicate which of the following electronic transitions are forbidden in a diatomic molecule, stating which selection rules result in the forbidden character:

7.2 How would the components of a 3Δg electronic state be described in the case (c) coupling approximation?

7.3 Derive the states which arise from the following electron configurations: C2 : : :(σu*2s)2 (πu2p)3 (σg2p)1 NO : : :(σ2p)1 (π 2p)4 (π*2p)2 CO : : :(σ*2s)1 (π2p)4 (σ2p)2 (π*2p)1 B2 : : :(σu*2s)2 (πu2p)1 (πg*2p)1 What is the ground state of B2?

7.5 Sketch potential energy curves for the following states of CdH, Br2 and CH, given their internuclear distances re, and suggest qualitative intensity distributions in the v” = 0 progressions for transitions between the states observed in absorption:

7.6 Measure, approximately, the wavenumbers of the P-branch and R-branch rotational transitions in the 0–0 band of the A1Σ+ – X1Σ+ electronic transition of CuH in Figure 7.26 and hence obtain values for r0 in the A and X states, neglecting centrifugal distortion.

7.7 Discuss, briefly, the valence molecular orbitals of AlH2 and the shape of the molecule in the ground and first excited singlet states. Al: 3s23p1

7.8 For formaldehyde give the lowest MO configuration resulting from a π*–π promotion and deduce the resulting states. 7.9 Show how the determinant Equation (7.107) gives the results in Equation (7.109).

7.10 Write down the crystal field orbital configurations of the following transition metal complexes: [Cu(H2O)6]2+, [V(H2O)6]3+, [Mn(H2O)6]2+ –high spin, [Co(NH3)6]3+ –low spin. Explain why [Mn(H2O)6]2+ is colourless. 7.11 A 1B3g - 1 Ag electronic transition in a molecule belonging to the D2h point group is forbidden. What are the possible symmetry species of a vibration X which would result in the X10 and X01 transitions being allowed?

7.12 Show that the following electronic transitions: (a) 1E - 1A1 in methyl fluoride; (b) 1A”2 - 1A’1 in 1,3,5-trichlorobenzene; (c) 1B2 - 1A1 in allene (CH2=C=CH2); are allowed, determine the direction of the transition moment and state the rotational selection rules that apply.