vibrational spectroscopy - theory.chem.vt.eduraman spectroscopy cont. by now, we know how to...

Vibrational spectroscopy

Kenneth RuudUniversity of Tromsø

• U

NIV

ERSITETET

•

I TROMSØ

July 3 2015

Outline

Comparing electronic and vibrational spectroscopies

The force fieldInfrared spectroscopy

Raman spectoscopy

AnharmonicitiesVibrational circular dichroism (VCD)Raman optical activity

Coherent anti-Stokes Raman Scattering (CARS)

Comparing electronic and vibrational spectroscopies

So far, response theory has been used largely in the electronic domain

Exceptions were the pure and zero-point vibrational corrections

As for electronic spectroscopies, absorption and scattering processes occur in thevibrational domain (corresponding to infrared energies rather than UV/Vis)

In principle, electronic spectroscopies can be transfered into the vibrationaldomain, creating new spectroscopies

Instrumental limitations in optics and detectors may prevent some methods, butalso enable others

Some notable differences

The vibrational eigenfunctions differ from those of the electronic wave functions

The properties of the vibrational wave functions implies that excitations can ingeneral only occur to the lowest excited vibrational state of a vibrational mode

A frequency scan will record energies corresponding to absorption in differentvibrational modesAs for electronic spectroscopy, the transition moments determines intensities

Note: Also responses in the electron density may induce vibrational transitions(not only the multipole moments)

Transition moments can in principle be determined by the geometry dependenceof the electronic properties (Taylor expansions)

For multiphoton/multidimensional vibrational spectroscopies, analysis of thepoles and residues of the pure vibrational contributions may be morestraightforward

Force field and normal coordinates

We recall that we would use as a starting point a quadratic expansion of theelectronic potential (at the equilibrium geometry)

V = V0 +3N∑

i,j=1

(∂2

∂xi∂xj

)xj xj + . . . = V0 +

3N∑i,j=1

kij xj xj + . . .

We introduce mass-weighted coordinates as qi =√

mi xi

The potential then becomes (V0 is constant and can be ignored)

V =12

∑i,j

Kij qi qj Kij =∂2V∂qi∂qj

The classical energy for the total energy is then

EK =12

3N∑i

q2i +

12

3N∑ij=1

Kij qi qj

Normal coordinates

Solving the equation for the nuclear motion in a quadratic potential much easierif the equation is separable

Introduce normal coordinates Q as the basis which simultaneously diagonalizesthe kinetic energy and the potential

E =12

3N−6∑i

Q2i +

12

3N−6∑i

λi Q2i

The equation is now separable, and we identify the equation for each normalmode as that of the harmonic oscillatorThe total vibrational wave function is a product of harmonic oscillators, one foreach normal mode

ψ =∏

i

ψi (Qi ) E =∑

i

(vi +

12

)~ωi

Note: The total ground-state vibrational wave function is always totallysymmetric

Infrared spectroscopy

When a molecule absorbs light in the UV/Vis region, the absorption crosssection is

Ai→f =πωfi NA

3ε0~c|µfi |2

The key quantity determining the oscillator strength is the dipole transitionmomentIn a similar manner, we may consider a vibrational transition dipole moment fora normal mode k , using as always perturbation theory

〈0 |µ (Q)| n〉 = 〈0 |µ (Re)| kn〉+

3N−6∑k=1

∂µ

∂Qk

∣∣∣∣Re

〈0 |Qk | kn〉+ . . .

The basis for infrared spectroscopy

An alternative approach: Residue analysis

We have throughout this summer school emphasized the strengths of theresponse theory approach

We recall that transition moments can be identified as residues of responsefunctions of different ordersMany (if not all) vibrational spectroscopies can be identified from a residueanalysis of the pure vibrational contributions to the response functions

Let us consider the pure vibrational contribution to the polarizability

[µ2]0,0

=∑

a

∂µα

∂Qa

∂µβ

∂Qa

12ωa

[1

(ωa − ω)+

1(ωa + ω)

]

The poles in this expression represents excitation energies to vibrationallyexcited states, the residues the transition moments

limω→ωk

(ωk − ω)[µ2]0,0

=1

2ωk

(∂µα

∂Qk

)(∂µβ

∂Qk

)

Some important things to note on IR

Gross selection rule: Vibrational modes will only be IR active if the dipolemoment changes during the vibration

Corollary: Molecular vibrations preserving a center of inversion will not be IRactiveWe recall that assuming harmonic oscillator wave functions

〈km |Qk | kn〉 6= 0 m = n ± 1

Specific selection rule: ∆n = ±1

In a molecule with 3N − 6(5) normal coordinates, how do we identify the IRactive modes?

An exercise in symmetry: Vibrations in CO2

Table : Group multiplication table for the D2h point group.

E C2(z) C2(y) C2(x) i σ(xy) σ(xz) σ(yz)Ag 1 1 1 1 1 1 1 1 x2, y2, z2

B1g 1 1 -1 -1 1 1 -1 -1 Rz , xyB2g 1 -1 1 -1 1 -1 1 -1 Ry , xzB3g 1 -1 -1 1 1 -1 -1 1 Rx , yzAu 1 1 1 1 -1 -1 -1 -1B1u 1 1 -1 -1 -1 -1 1 1 zB2u 1 -1 1 -1 -1 1 -1 1 yB3u 1 -1 -1 1 -1 1 1 -1 x

An exercise in symmetry: Vibrations in CO2

Carbon dioxide has nine nuclear degrees of freedom, of which three correspondto translations and two to rotationsStep 1: Identify the number of Cartesian atomic displacements that transforminto themselves (±) under the symmetry operations of the molecule

E C2(z) C2(y) C2(x) i σ(xy) σ(xz) σ(yz)9 -3 -1 -1 -3 1 3 3

Step 2: Determine the number of functions in each irreducible representation:al = 1

h∑

R χ∗l (R)χ (R)

Ag B1g B2g B3g Au B1u B2u B3u1 0 1 1 0 2 2 2

Vibrations in CO2 cont.

Step 3: Identify and remove translational motion:B1u + B2u + B3u ⇒ 1/0/1/1/0/1/1/1Step 4: Identify and remove rotational motion: B2g + B3g ⇒ 1/0/0/0/0/1/1/1

The four normal modes in CO2 transform as ΓA1 ⊕ ΓB1u ⊕ ΓB2u ⊕ ΓB3u

The components of the dipole moment span ΓB1u ⊕ ΓB2u ⊕ ΓB3u , thus three of thefour vibrations are IR active

Raman spectroscopy

In the Raman process, laser light is directed at a molecule, which scatters thelight (Rayleigh scattering)

Some energy may be absorbed or emitted from the molecule due to “absorption”or “emission” from vibrational states

The scattering within the electronic states is described by the polarizability, andwe will be concerned with transitions in the vibrational manifold⟨

ψk∣∣ααβ∣∣ψl

⟩

Raman spectroscopy cont.

By now, we know how to proceed:Represent the vibrational states as harmonic oscillatorsTaylor expand the geometry dependence of the polarizability tensor

Raman spectroscopy is thus largely governed by matrix elements of the form(Placzek/harmonic approximation)(

∂ααβ

∂Qk

)∣∣∣∣∆Qi =0

⟨ψki|Qk |ψkj

⟩

Residue analysis

lim(ω2+ω3)→ωk

(ωk − [ω2 + ω3])[α

2]0,0

= lim(ω2+ω3)→ωk

(ωk − [ω2 + ω3])∑

a

1

8ωa

(∂ααβ

∂Qa

)(∂αγδ

∂Qa

)[ 1

ωa − (ω2 + ω3)+

1

ωa + (ω2 + ω3)

]

=1

8ωk

(∂ααβ

∂Qk

)(∂αγδ

∂Qk

)

Gross selection rule: The polarizability must change during the vibration

Specific selection rule: ∆vk = ±1

The symmetry analysis of CO2

We recall that the normal coordinates of CO2 transform asΓA1 ⊕ ΓB1u ⊕ ΓB2u ⊕ ΓB3u

The components of the polarizability tensor transform asΓA1 ⊕ ΓB1g ⊕ ΓB2g ⊕ ΓB3g

Thus, only one of the modes (the symmetric stretch) is Raman active

General rule: For molecules with an inversion center, no vibrational mode can beboth IR and Raman active

Comparison to experiment

Detailed analysis of the Raman scattering process shows that the observablequantities depend on experimental setup in most cases(forward/backward/right-angle scattering)L. D. Barron, Molecular Light Scattering and Optical Activity (2204)

The detailed expressions are not important from a computational point of view

The scattering intensities are determined by isotropic and anisotropic invariantsdefined as

α2 =19ααααββ

β (α)2 =12

(3ααβααβ − ααααββ

)The Raman scattering cross section is then proportional to

45α2 + 4β (α)2

Anharmonicity

We discussed in connection with pure and zero-point vibration correction thepossibility of electric and mechanical anharmonicities

May also occur for vibrational transitions, and allow new vibrational bands toappear

From electric anharmonicity, we will for instance have combination bands, inwhich two vibrational modes are excited simultaneously

〈1k 1l |µα| 0k 0l 〉 =

(∂2µα

∂Qk∂Ql

)0〈1k |Qk | 0k 〉〈1l |Ql | 0l 〉

Will in general be weak if it is at all symmetry allowed

Fermi resonances

Mechanical anaharmonicity can also lead to combination bands

⟨2k 0l

∣∣∣V (3)kkl

∣∣∣ 0k 1l

⟩=

12

(∂3V

∂Q2k∂Ql

)0

⟨2k

∣∣∣Q2k

∣∣∣ 0k

⟩〈0l |Ql | 1l 〉

Of particular interest here is when 2ωk ≈ ωl , as happens in CO2

Vibrational analogue of configuration interaction

Weak overtones can steal intensity from an allowed fundamental⇒ 1 strongfundamental and 1 weak overtone replaced by two medium-intensity bandsshifted in energy

Multidimensional vibrational spectroscopiesHigh information content in multidimensional spectroscopies such asDOVE-FWM-2D-IR

〈〈µα;µω1β , µ

ω2γ , µ

ω3δ 〉〉IR =

[µ4]

+[µ2α

](E)+[µ2α

](I)+[α2]

+ [µβ]

W. Zhao and J. C. Wright, Phys. Rev. Lett. 84, 1411 (2000).

Note in particular that leading-order contributions to the odd-order terms[µ2α

]are anharmonicModeling multidimensional and nonlinear vibrational spectroscopies requiresthe evaluation of higher-order energy and property derivatives

Fundamental vibrational frequencies of CH4

M. Ringholm, D. Jonsson, R. Bast, B. Gao, A. J. Thorvaldsen, U. Ekstrom, T. Helgaker and K. Ruud,J. Chem. Phys.140, 034103 (2014).

No symmetry used, degenerate modes identical to within 10−5

B3LYP geometry and harmonic force field both for HF and B3LYP

6-31G works suprisingly well, no basis set effect beyond cc-pVTZ

Minor differences in anharmonicity corrections between HF and B3LYP (7-9% )

Why do analytic derivatives?

The easiest way to calculate energy derivatives would be to use numericaldifferentiation

6N calculations for first derivatives36N2 calculations for second derivatives208N3 calculations for third derivatives

Geometrical derivatives of the dipole moment of hydrogen fluoride at the CCSD/cc-pCVDZ level of theoryin atomic units, bond lengths optimized at the same level of theory (Req = 1.735686661 a.u.).

Computed from ∆R/A(

dµzdR

)R=Req

(d2µzdR2

)R=Req

(d3µzdR3

)R=Req

(d4µzdR4

)R=Req

µz 10−2 -0.31736764 0.17871386 0.763567 0.0750µz 10−3 -0.31741264 0.178712 0.764 . . .µz 10−4 -0.31741309 0.1787 . . . . . .µz 10−5 -0.3174131 0.18 . . . . . .

dµz /dR 10−2 . . . 0.17871606 0.76369391 0.0748442dµz /dR 10−3 . . . 0.17871165 0.763745 0.0714dµz /dR 10−4 . . . 0.17871157 0.7656 . . .dµz /dR 10−5 . . . 0.1787139 0.77 . . .

Fully analytic value -0.317413034 0.17811155 . . . . . .T.-C. Jagau, J. Gauss and K. Ruud, J. Chem. Phys. 139, 154106 (2013).

Numerical derivatives have limited and (non-systematic) numerical precision

Scaling for higher-order derivatives unfavorable

Numerical accuracy also an issue for spectra

1000 1200 1400 1600 1800

harm.

exp. freq.

analytic anharm.

2600 2800 3000 3200 3400

Wavenumber /cm−1

numeric (δx=10−2Å) anharm.

numeric (δx=5.10−3Å) anharm.

numeric (δx=10−3Å) anharm.

Methanimine, B3LYP/cc-pVTZ calculations, GVPT2/DVPT2 anharmonic corrections

Comparison to experiment, CH4

Mode ωB3LYP νHF νB3LYP νBLYP ωBLYP ωexp νexpcc-pVDZ

1 3146 2977 2988 2906 30682 3025 2887 2892 2817 29543 1530 1484 1488 1451 14944 1309 1264 1268 1233 1275

cc-pVQZ1 3127 2967 2979 2903 3055 3156.8 3022.52 3025 2896 2902 2833 2960 3025.5 2920.93 1558 1510 1514 1481 1524 1582.7 1532.44 1340 1293 1298 1267 1310 1367.4 1308.4


Basis set effect cc-pVDZ to cc-pVQZ for ωB3LYP is 0-31 cm−1: Scaling a poor basisset is not the right solution

Scaling factor B3LYP varies between 0.952-0.972, scaling acceptable foranharmonicities if the basis set is good

ωB3LYP in better agreement with experiment than νBLYP

Unless you have true anharmonic effects (Fermi resonances), first make sureyour basis set and functional is adequate

Comparison to experiment, C2H6


Experimental data: J. L. Duncan, R. A. Kelly, G. D. Nivellini and F. Tullini, J. Mol. Spectro sc. 98, 87 (1983).

Vibrational Circular Dichroism

We recall that circular dichroism was given by the rotatory strength tensor

Rn0αβ ∝ 〈0 |µα| n〉

⟨n∣∣mβ∣∣ 0⟩

Taking the expression into the vibrational domain, using the standard tricks, weobtain

Rk0αβ ∝

⟨0∣∣∣∣∂µα∂Qk

∣∣∣∣ k⟩⟨k∣∣∣∣∂mβ∂Qk

∣∣∣∣ 0⟩Note here that the magnetic (and electric) dipole moment also includes acorresponding nuclear contribution

Problem: The gradient of the magnetic dipole moment will be zero, and thusthere is no VCD intensity

However, this is a consequence of our adoption of the Born–Oppenheimerapproximation

We recall that we get an induced magnetic moment from the molecular rotationdue to the decoupling of the electrons and the nuclei

Vibrationally induced magnetic moment

Let us consider non-Born–Oppenheimer effects from the decoupling of electronsand nuclei during molecular vibrations

We recall that we in the Born–Oppenheimer approximation ignored thecontributions

H(1)N =

∑A,α

1MA

⟨χk′ | PAαχk

⟩δk,k′ PAα + 〈χk′ | TNχk 〉

Let us now consider this as a perturbation to our vibronic wave function with aharmonic-oscillator description of the vibration

ΨpertKk = Ψ

(0)KK + Ψ

(1)Kk = Ψ

(0)KK +

∑(L,l) 6=(0,0)

⟨ΨKk

∣∣Hel + TN∣∣ΨLl

⟩EKk − ELl

ΨLl

The magnetic dipole moment can then be evaluated using this perturbed wavefunction

Vibrationally induced magnetic moment

By evaluating the expression ⟨Ψ

pertKk

∣∣mβ∣∣ΨpertKk

⟩The leading-order, non-vanishing contribution to the vibrationally inducedmagnetic moment (the atomic axial tensor) is

MK ,αβ = IK ,αβ + JK ,αβ

IK ,αβ =

⟨∂Ψel

0

∂RK ,α

∣∣∣∣∣ ∂Ψel0

∂Bβ

⟩∣∣∣∣∣R=R0,B=0

JK ,αβ =i4

∑γ

εαβγZK RKγ

Denoting the dipole gradient (atomic polar tensor) as PK ,αβ , the VCD rotationalstrength for normal mode k is

R (0→ 1)k = Im |PK ·MK |

Comments on VCD

The first observations of VCD was made in the early 70s, and the theoreticalfoundation developed by Stephens in 1985 (J. Phys. Chem. 89, 748 (1985))

VCD gained momentum around the mid 90s due to the development of rigorousab initio methods, and in particular with DFT implementations, and commercialinstrumentationK.L.Bak et al., J. Chem. Phys. 98, 8873 (1993)F. J. Devlin et al., J. Am. Chem. Soc. 118, 6327 (1996)The research group of Stephens has actively calibrated the computationalrequirement, leading to the recommendation of a TZ2P basis with the B3LYP ofB3PW91 functionalsThe method has been approved by the FDA as an experimental method forverifying enantiomeric excess.

An example of the powers of VCD: Troger’s base

Absolute configuration of the (+)-Troger’s base determined to be (R,R) bycircular dichroism (and empirical rules for analysis (octant rule))

X-ray crystallography would however suggest the configuration to be (S,S)?

Can VCD contribute?

(+)-(R,R)-Troger’s base: Experimental and theoreticalVCD spectra

A. Aamouche, F. J. Devlin and P. J. Stephens, J. Am. Chem. Soc. 122, 2346 (2000)

Raman Optical ActivityTheoretical foundation developed by Barron and Buckingham inthe early 70s (L. D. Barron and A. D. Buckingham, Mol. Phys. 20 (1971) 1111)

The Raman analogue of VCDCircular Scattering Intensity Differences determined by threetensorsThe electric dipole polarizability

ααβ = 2∑n 6=0

ωn0Re [〈0 |µα| n〉〈n |µβ | 0〉]

ω2n0 − ω2

= −〈〈µα;µβ〉〉ω

The electric dipole–electric quadrupole polarizability

Aαβγ = 2∑n 6=0

ωn0Re [〈0 |µα| n〉〈n |Θβγ | 0〉]

ω2n0 − ω2

= −〈〈µα; Θβγ〉〉ω

The electric dipole–magnetic dipole polarizability

G′αβ = −2∑n 6=0

ωIm [〈0 |µα| n〉〈n |mβ | 0〉]

ω2n0 − ω2

= −i 〈〈µα; mβ〉〉ω

Vibrational matrix elements

In ROA we are interested in the changes in the previouslydefined linear response functions during a vibrational transitionIf we assume the Placzek approximation (double-harmonicapproximation), the relevant quantities can be approximated as

〈ν0 |ααβ | ν1p〉〈ν1p |ααβ | ν0〉 =1

2ωp

(∂ααβ

∂Qp

)∣∣∣∣re

(∂ααβ

∂Qp

)∣∣∣∣re

〈ν0 |ααβ | ν1p〉⟨ν1p∣∣G′αβ∣∣ ν0

⟩=

12ωp

(∂ααβ

∂Qp

)∣∣∣∣re

(∂G′αβ∂Qp

)∣∣∣∣re

〈ν0 |ααβ | ν1p〉〈ν1p |εαγδAγδβ | ν0〉 =1

2ωp

(∂ααβ

∂Qp

)∣∣∣∣re

εαγδ

(∂Aγδβ

∂Qp

)∣∣∣∣re

Scattering Intensity Differences

We will compare our results with the scattering intensitydifference between left and right circularly polarized lightFor scattered light of α polarization

∆α = IRα − IL

α

For the specific cases of right-angle and backscattering, thisequation is reduced to

∆z (90◦) =1c

(6β (G′)2 − 2β (A)2

)∆z (180◦) =

1c

(24β (G′)2

+ 8β (A)2)

Scattering Intensity Differences

The intensity differences are determined using the anisotropicinvariants

β (α)2 =12

(3ααβααβ − ααααββ)

β (G′)2=

12(3ααβG′αβ − αααG′ββ

)β (A)2 =

12ωααβεαγδAγδβ

Implicit summation over repeated indices has been usedFirst ab initio calculations presented in 1990P. L. Polavarapu J. Phys. Chem. 94 8106 (1990)

Calculating ROA spectra

ROA requires the geometrical derivatives of several linearresponse tensor (thus formally a quadratic response function)The most critical component (as is the case for VCD) is anappropriately chosen force field (CIDs less sensitive to thecomputational level)Multilevel computational approaches with specially tailoredbasis sets/force fields is an attractive approach

The powers of ROA: (R)-[2H1, 2H2,2H3]-neopentane

J. Haesler et al., Nature 446, 526 (2007)

ROA: Computational requirements

To include some electron correlation effects, we would like to doDFTWhich basis set and what functional?Test set constructed from:

Five molecules (methyloxirane, glycidol, epichlorhydrine,spiro[2,2]pentane-1,4-diene and σ-[4]-helicene)Three functionals: SVWN, BLYP, and B3LYP6 basis sets: cc-pVDZ, aug-cc-pVDZ, cc-pVTZ,aug-cc-pVTZ, sadlej and a basis by Zuber and Hug(3-21++G plus diffuse p on hydrogens) (G. Zuber and W. Hug,

J. Phys. Chem. A 108 (2004) 2108).90 ROA calculations with up to 21 atoms and 506 basis functionsM. Reiher, V. Liegeois, and K. Ruud. J. Phys. Chem. A, J. Phys. Chem. A 109, 7567 (2005)

The molecules

Analysis of the results

Comparison with experiment difficult due to shape of ROA andRaman bandsDFT/B3LYP using the aug-cc-pVTZ (aug-cc-pVDZ for thehelicene) used as a benchmarkDeviation for a basis set given as

δ (I) =

∑p

∣∣I trialp − Iref

p

∣∣∑p

∣∣Irefp∣∣

We also note the number of modes with incorrect signExperimental data kindly provided by prof. Werner Hug(University of Fribourg, Switzerland)

S-methyloxirane

M. Reiher, V. Liegeois, and K. Ruud. J. Phys. Chem. A 109, 7567 (2005)

(M)-spiro-[2,2]pentane-1,4-diene

M. Reiher, V. Liegeois, and K. Ruud, J. Phys. Chem. A 109, 7567 (2005)

ROA requirements

There appears to be no alternative to aug-cc-pVDZSadlej may work, but unreliableThe basis set of Zuber and Hug may work if used with a properforce fieldBLYP can in many cases be an alternative to B3LYP→ allows forefficient density-fitting (RI) techniquesBased on the assumption B3LYP is the best functional

M. Reiher, V. Liegeois, and K. Ruud. J. Phys. Chem. A, A 109, 7567 (2005)

Vibrational mode selection

Idea: Calculate relevant normal modes onlyMode-tracking—Selective calculation of vibrational frequenciesand normal modes from eigenpairs of the Hessian matrixthrough subspace iteration.Instead of

[H− λµ]Qµ = 0

solve

[H− λ(i)µ ]Q(i)

µ = r(i)µ

iteratively for a few eigenpairs by a Davidson-type calculation.

M. Reiher, J. Neugebauer, J. Chem. Phys. 118 2003, 1634–1641

(R,R)-Dialanine: ROA intensities

Intensities for amide I and amide II modes

Full (calculated) spectrum:

Frequency region 1371–1502 cm−1

AKIRA converges within 4 iterations→ 24 additional single-pointscalculations→ compared to full analysis: 24+6 = 30 vs. 138 points

Coherent anti-Stokes Raman Scattering

Enhances the Raman signal by tuning two lasers to be in resonance with avibrational excitation

Determined by the second hyperpolarizability tensor

γα;β,γ,δ (− (2ω1 − ω2) ;ω1, ω1,−ω2)

If ω1 − ω2 corresponds to a resonance in the IR region, the tensor is dominatedproducts of vibrational matrix elements of the kind

〈0 |α (ωσ)| k〉〈k |α (ωτ )| 0〉

We have used the resolution of the identity when summing over vibrationalstates for an electronic excited states

Coherent anti-Stokes Raman scattering

Assuming the double-harmonic approximation we can writethese matrix elements as

〈ν0 |ααβ (ωσ)| ν1p〉〈ν1p |ααβ (ωτ )| ν0〉 =1

2ωp

(∂ααβ

∂Qp

)∣∣∣∣re

(∂ααβ

∂Qp

)∣∣∣∣re

The CARS signals are thus determined by the same tensors asthe Raman intensityHowever, the intensity a mixture of electronic and vibrationalhyperpolarizability contributions, since

I ∝ |γ|2 =[(γR

v + γIv

)+ γe

]2=(γR

v

)2+ 2γR

v γe + (γe)2 +(γI

v

)2.

A. J. Thorvaldsen, L. Ferrighi, K. Ruud, H. Agren, S. Coriani, P. Jørgensen, Phys. Chem. Chem. Phys. 11, 2293 (2009)

Computational details

Geometries and force fields calculated using B3LYP/cc-pVDZ

Polarizability derivatives calculated using Hartree–Fock and the cc-pVDZ basisset

ANTHRACENE TETRACENE

CHRYSENE

PYRENE1,2 BENZANTHRACENE

PERYLENEBENZO(E)PYRENE

BENZO(A)PYRENE

BENZO(GHI)PERYLENECORONENE

Pyrene

After lineshape analysis

Demonstrating the different selectivity: Benzonitrile

A. Mohammed et al., Chem. Phys. Lett. 485, 320 (2010)

Concluding remarks

Many absorption processes occuring in the electronic domain will have ananalogous process in the vibrational domain

Scattering processes may however also allow for new interaction mechanisms

The vibrational domain provides a wealth of information, with up to 3N − 6responses for a molecule with N atoms

Multiphoton processes in the vibrational domain opens for the possibility fordetailed information about a molecule to be obtainedVCD and ROA are both powerful methods for determining the absoluteconfiguration of chiral molecules when used in conjunction with theoreticalcalculationsMost critical computational success factor: The quality of the force field

vibrational spectroscopy - theory.chem.vt.eduraman spectroscopy cont. by now, we know how to...

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