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Molecular Spectroscopy

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Book cover Atoms, Molecules and Optical Physics 2

Part of the book series: Graduate Texts in Physics ((GTP))

Abstract

After a brief introduction in Sect. 5.1 we shall expand our knowledge about rotational (microwave) and vibrational (infrared) spectroscopy in Sects. 5.2 and 5.3, respectively, and supplement it with short excursions into infrared Fourier transform spectroscopy (FTIR) and IR action spectroscopy. In Sect. 5.4 we turn to the spectroscopy of electronic transitions (VIS, UV and VUV) and present a few state-of-the-art methods of modern molecular spectroscopy. In Sect. 5.6 basics of Raman spectroscopy will be developed – a very important spectroscopic art, which may be said to reside in between electronic and vibrational spectroscopy. In Sect. 5.5.4 we illustrate the astonishing capabilities of today’s high resolution spectroscopy with sophisticated methods, as applied to larger, even biologically relevant molecules. Finally, in Sect. 5.8 we introduce the important field of photoelectron spectroscopy.

In Chaps.  3 and  4 we have treated structure and properties of diatomic and polyatomic molecules, together with some basics on rotational and vibrational spectra. Now we shall deepen this first acquaintance and introduce also electronic transitions in molecules. Instrumental to modern spectroscopy are narrow band lasers and synchrotron radiation, covering together with microwave, sub-millimetre and radio frequency sources a spectral range of more than ten decades, ready for any conceivable applications in molecular spectroscopy – for which we shall present selected examples.

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Notes

  1. 1.

    Note that these stick-spectra just communicates molecular line strengths. They do not yet represent absorption spectra (see Sect. 5.2.4 in Vol. 1).

  2. 2.

    Strictly mathematical the following equation is not completely correct: since we back-transform only the real part of the inverse FT, negative frequencies arise … which have to be ignored.

  3. 3.

    We continue to use the spectroscopic notation according to Herzberg as introduced in Chap. 3: lower state double primed ′′, upper state single ′.

  4. 4.

    Obviously, that is not necessarily the case, since a change in electronic structure may also change the symmetry of the system.

  5. 5.

    One has to keep in mind that during the IVR process in an isolated molecule vibrational energy does of course not get lost – as one might infer from the display of the energy terms in Fig. 5.15. Energy (except in optical emission) is just redistributed among the many other vibrational degrees of freedom within the molecule. A flow of energy back into the ‘representative nuclear coordinate’ is – for statistical reasons – the less probable the larger the molecule.

  6. 6.

    In the literature one often finds J for the rotational quantum number, instead of N.

  7. 7.

    Thus the coupling of angular momenta in I2 is most appropriately described as Hund’s case (c), see Sect. 3.6.4. The often used classification by singlet and triplet looses its validity due to the strong spin-orbit splitting. Otherwise the transitions studied here would all be forbidden intercombination lines.

  8. 8.

    As done by Hartmut Hotop (2008) who made these data available for us.

  9. 9.

    We note that the pseudorotation does not occur on a perfect circle. This would only be the case if the potential minima and the saddlepoints would both lie on the same circle.

  10. 10.

    We emphasize that (5.30) holds for Stokes and anti-Stokes lines, since i and f in ħω fi refer here to the initial and final molecular states, respectively. In contrast, in the Jablonsky diagram Fig. 5.32 the indices b and a refer to upper and lower Raman levels, respectively.

  11. 11.

    One easily verifies this by looking up the respective Clebsch-Gordan coefficients.

  12. 12.

    With the exception of pure emission spectroscopy where no incident light is involved.

  13. 13.

    They are measured in units \([ \chi^{(k)} ] =\operatorname{m}^{k-1}\operatorname{V}^{-k+1}\), i.e. only χ (1) is dimensionless. Note that (5.42) is an abbreviation. Explicitly, the components of the polarization vector are

    $$\mathfrak{P}_{i}=\varepsilon_{0} \biggl( \sum _{j}\chi _{ij}^{(1)}E_{j}+ \sum_{jk}\chi_{ijk}^{(2)}E_{j}E_{k}+ \sum_{jk\ell}\chi_{ijk\ell}^{(3)} E_{j}E_{k}E_{\ell}+\cdots \biggr) $$

    for i=x,y,z. Each index in the sums runs over x, y, and z.

  14. 14.

    Unfortunately he still used the old Gaussian esu, strangely in combination with the unit \(\operatorname{V}\). We use here of course SI units.

  15. 15.

    Equation (5.80), Vol. 1 holds for pure, linearly polarized light. If the light is not fully polarized one has to correct for the finite degree of linear polarization \(\mathcal{P}_{12}\) of the source according to (1.101). \(\vert \mathcal{P}_{12}\vert \leq1\) is usually calibrated by the well known angular distributions from rare gases. The observed electron angular distribution is then

    $$ I(\gamma)\propto \bigl[ 1+\beta\mathcal{P}_{12} \bigl( 3 \cos^{2}\gamma-1 \bigr) /2 \bigr] , $$
    (5.48)

    as one may derive using the theory of measurement sketched in Chap. 9.

  16. 16.

    Often the binding energy of the emitted electron W B (γ′′v′′N′′)=−(W I −W γ′′v′′N′′) is communicated. The literature is somewhat ambiguous about the sign. If one refers to the free electron after emission, the electron binding energy is of course negative.

  17. 17.

    We have to use the dynamic relative permittivity (dielectric constant) here, which is much smaller than the static one (ε stat≃80).

  18. 18.

    There is, however, one key difference: anions do not come out of the bottle and have to be specifically prepared, and – as they carry a charge – may also be mass selected prior to the interaction with photons. Specifically for the study of clusters this is an essential advantage compared to neutral cluster beams. They usually have a broad distribution of cluster sizes, and mass selective detection after the interaction process does not really help, since usually very difficult to discriminate against fragments from larger clusters.

  19. 19.

    In these storage devices, originally designed for nuclear physics experiments, events are added up and stored according to their pulse height.

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Authors and Affiliations

  1. Max-Born-Institut für Nichtlineare Optikund Kurzzeitspektroskopie, Berlin, Germany

    Ingolf V. Hertel & Claus-Peter Schulz

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Acronyms and Terminology

AOM:

‘Acousto-optic modulator’, device to modulate and shift the frequency of light by diffraction in a Bragg grating generated by sound waves (usually RF).

BOXCARS:

‘Schematic geometry of a setup for nonlinear spectroscopy’, (see Fig. 5.42).

CARS:

‘Coherent anti-Stokes Raman scattering’, coherent version of Raman scattering.

CCD:

‘Charge coupled device’, semiconductor device typically used for digital imaging (e.g. in electronic cameras).

CFWM:

‘Coherent four wave mixing’, nonlinear optical processes (see Sect. 5.7.1).

conformer:

‘Special kind of isomers (same atomic composition but different molecular structure) having the same sequence of atoms but different geometrical arrangement, such as cis-trans isomers or different alignment with respect to rotation around an axis’, http://en.wikipedia.org/wiki/Conformational_isomerism.

COORS:

‘Common ordinary old Raman scattering’.

CRD:

‘Cavity ring down’, spectrometer (see Sect. 5.5.3).

CSRS:

‘Coherent Stokes Raman scattering’, coherent version of Raman scattering.

CW:

‘Continuous wave’, (as opposed to pulsed) light beam, laser radiation etc.

DF:

‘(laser induced), dispersed fluorescence’.

DFWM:

‘Degenerate four wave mixing’, nonlinear optical process (see Sect. 5.7.1).

DNA:

‘Deoxyribonucleic acid’, large nucleic acid which contains the genetic code according to which living organisms are build.

E1:

‘Electric dipole’, transitions induced by the interaction of an electric dipole with the electric field component of electromagnetic radiation.

EPR:

‘Electron paramagnetic resonance’, spectroscopy, also called electron spin resonance ESR (see Sect. 9.5.2 in Vol. 1).

ESCA:

‘Electron spectroscopy for chemical analysis’, see Sect. 5.51.

ESI:

‘electro spray ionization’, method for bringing very large molecular ions into the gas phase (see Sect. 5.28).

esu:

‘electrostatic units’, old system of unities, equivalent to the Gauss system for electric quantities (see Appendix A.3 in Vol. 1).

EUV:

‘Extreme ultraviolet’, part of the UV spectral range. Wavelengths between \(10\operatorname{nm}\) and \(121\operatorname{nm}\) according to ISO 21348 (2007).

EXAFS:

‘Extended X-ray absorption fine structure’, X-ray absorption by inner shell electrons in a broad energy range above the respective X-ray absorption edge (as opposed to NEXAFS).

FC:

‘Franck-Condon’, introduced an important approximation for optical transition between electronic states (see Sect. 5.4.1).

FDIRS:

‘fluorescent-dip infrared spectroscopy’, (see Zwier 2001).

FEICO:

‘Femtosecond time resolved electron ion coincidence’, see Sect. 5.8.5.

FIR:

‘Far infrared’, spectral range of electromagnetic radiation. Wavelengths between 3 μm and \(1\operatorname{mm}\) according to ISO 21348 (2007).

FPI:

‘Fabry-Pérot interferometer’, for high precision spectroscopy and laser resonators (see Sect. 6.1.2 in Vol. 1).

FT:

‘Fourier transform’, see Appendix I in Vol. 1.

FTIR:

‘Fourier transform infrared spectroscopy’, see Sect. 5.3.2.

FWHM:

‘Full width at half maximum’.

FWM:

‘Four wave mixing’, nonlinear optical processes (see Sect. 5.7.1).

HFS:

‘Hyperfine structure’, splitting of atomic and molecular energy levels due to interactions of the active electron with the atomic nucleus (Chap. 9 in Vol. 1).

HHG:

‘High harmonic generation’, in intense laser fields.

HITRAN:

‘High-resolution transmission molecular absorption database’, http://www.cfa.harvard.edu/hitran (Rothman et al. 2009).

IAS:

‘Infrared action spectroscopy’, special method to detect infrared absorption by particle detection (see Sect. 5.3.3).

IC:

‘Internal conversion’, radiationless transition between different electronic states (see Sect. 5.4.3).

iPEPICO:

‘Imaging photoelectron-photoion coincidence spectroscopy’, see also PEPICO, Sect. 5.8.5.

IR:

‘Infrared’, spectral range of electromagnetic radiation. Wavelengths between \(760\operatorname{nm}\) and \(1\operatorname{mm}\) according to ISO 21348 (2007).

ISC:

‘Intersystem crossing’, radiationless transition between states with different total spin, typically between singlet and triplet states (see Chap. 5, Fig. 5.15).

isomer:

‘Molecules with the same atomic composition but different molecular structure’, http://en.wikipedia.org/wiki/Isomer.

isosceles triangle:

‘Triangle with two equal sides’, has two varieties: acute (all angles are <90∘) and obtuse (one angles is >90∘).

isotopologue:

‘Molecules that differ only in their isotopic composition’, http://en.wikipedia.org/wiki/Isotopologue.

isotopomer:

‘Molecules with the same number of isotopes of each element but differ in their position within the molecule’, http://en.wikipedia.org/wiki/Isotopomers.

IVR:

‘Intra molecular vibrational energy redistribution’, excess vibrational energy in one mode of a polyatomic molecule is redistributed among other vibrational modes.

JT:

‘Jahn and Teller’, have first treated in 1937 the symmetry breaking effect, now referred to by their names.

JTE:

‘Jahn-Teller effect’, symmetry breaking effect first treated by Jahn and Teller in 1937.

KETOF:

‘Kinetic energy analysis by time of flight’, method for determining fragmentation energies after dissociative ionization.

LIF:

‘Laser induced fluorescence’, radiation emitted from a quantum system after excitation by laser radiation (see Sect. 5.5.1).

M1:

‘Magnetic dipole’, transitions induced by the interaction of a magnetic dipole with the magnetic field component of electromagnetic radiation.

MALDI:

‘Matrix assisted laser desorption ionization’, method for bringing very large molecular ions into the gas phase (see Sect. 5.28).

MATI:

‘Mass analyzed threshold ionization’, see Sect. 5.8.3.

MB:

‘Molecular beam’.

MCA:

‘Multi channel analyzer’, electronic device, storing pulses according to their pulse height (originally used in nuclear physics).

MCP:

‘Multi channel plate’, electron multiplier with many amplifying elements.

MIR:

‘Middle infrared’, spectral range of electromagnetic radiation. Wavelengths between 1.4 μm and 3 μm according to ISO 21348 (2007).

MO:

‘Molecular orbital’, single electron wave function in a molecule; typically the basis for a rigorous molecular structure calculation.

MRCI:

‘Multi reference configuration interaction’, high quality quantum chemical method for computing molecular potentials.

MW:

‘Microwave’, range of the electromagnetic spectrum. In spectroscopy MW usually refers to wavelengths from \(1\operatorname{mm}\) to \(1\operatorname{m}\) corresponding to frequencies between \(0.3\operatorname{GHz}\) to \(300\operatorname{GHz}\); ISO 21348 (2007) defines it as the wavelength range between \(1\operatorname{mm}\) to \(15\operatorname{mm}\).

MWFT:

‘Microwave Fourier transform’, spectrometer (see Sect. 5.2).

NEXAFS:

‘Near edge X-ray fine structure absorption, also XANES’, X-ray absorption by inner shell electrons close to the respective X-ray absorption edge.

NIR:

‘Near infrared’, spectral range of electromagnetic radiation. Wavelengths between \(760\operatorname{nm}\) and 1.4 μm according to ISO 21348 (2007).

NIST:

‘National institute of standards and technology’, located at Gaithersburg (MD) and Boulder (CO), USA. http://www.nist.gov/index.html.

NMR:

‘Nuclear magnetic resonance’, spectroscopy, a rather universal spectroscopic method for identifying molecules (see Sect. 9.5.3 in Vol. 1).

ODE:

‘Ordinary differential equation’.

OMA:

‘Optical multichannel analyzer’, spectrometer which allows simultaneous registration of a whole spectrum.

OODR:

‘Optical-optical double resonance’, spectroscopy with two photons, one kept fixed on a resonance transition, one tuning another part of the spectrum.

PEPICO:

‘Photoelectron-photoion coincidence spectroscopy’, method to correlate a photoelectron with one specific fragment ion (see Sect. 5.8.5).

PES:

‘Photoelectron spectroscopy’, see Sect. 5.8.

PFI:

‘Pulsed field ionization’, electrons are extracted from the ionization volume with some time delay.

PJTE:

‘Pseudo-Jahn-Teller effect’, vibronic coupling for nearly degenerate molecular states, leading to symmetry breaking.

R2PI:

‘also RTPI, resonantly enhanced two-photon ionization spectroscopy’, special version of REMPI.

REMPI:

‘Resonantly enhanced multi-photon ionization’, ionization of atoms or molecules by several photons with one resonant intermediate state.

RF:

‘Radio frequency’, range of the electromagnetic spectrum. Technically, one includes frequencies from \(3\operatorname{kHz}\) up to \(300\operatorname{GHz}\) or wavelengths from \(100\operatorname{km}\) to \(1\operatorname{mm}\); ISO 21348 (2007) defines the RF wavelengths from \(100\operatorname{m}\) to \(0.1\operatorname{mm}\); in spectroscopy RF usually refers to \(100\operatorname{kHz}\) up to some \(\operatorname{GHz}\).

RIDIRS:

‘Resonant ion dip infrared spectroscopy’, (see Zwier 2001).

RTPI:

‘also R2PI, resonantly enhanced two-photon ionization spectroscopy’, special version of REMPI.

SEM:

‘Secondary electron multiplier’, see Appendix B.1.

SEP:

‘Stimulated emission pumping’, special kind of two colour resonant four wave mixing (see TC-RFWM).

SERS:

‘Surface enhanced Raman spectroscopy’.

SI:

‘Système international d’unités’, international system of units (m, kg, s, A, K, mol, cd), for details see the website of the Bureau International des Poids et Mésure http://www.bipm.org/en/si/ or NIST http://physics.nist.gov/cuu/Units/index.html.

TAC:

‘Time to amplitude converter’, electronic device, same as time to height converter.

tautomer:

‘Special isomers which readily interconvert by moving single atoms (e.g. H) or atomic groups’, http://en.wikipedia.org/wiki/Tautomer.

TC-RFWM:

‘Two colour resonant four wave mixing’, nonlinear optical process (see Sect. 5.7.1).

TDC:

‘Time to digital converter’, electronic device.

TOF:

‘Time of flight’, measurement to determine velocities of charged particles, and consequently their energies (if the mass to charge ratio is known) or their mass to charge ratio (if their energy is known).

TPEPICO:

‘Threshold photoelectron-photoion coincidence spectroscopy’, method to correlate photoelectrons of nearly zero kinetic energy with one specific fragment ion (see Sect. 5.8.5).

TPES:

‘Threshold photoelectron spectroscopy’, PES of only those electrons which are emitted with nearly vanishing kinetic energy, i.e. at threshold of the process studied.

UPS:

‘Ultraviolet photoelectron spectroscopy’.

UV:

‘Ultraviolet’, spectral range of electromagnetic radiation. Wavelengths between \(100\operatorname{nm}\) and \(400\operatorname{nm}\) according to ISO 21348 (2007).

VIS:

‘Visible’, spectral range of electromagnetic radiation. Wavelengths between \(380\operatorname{nm}\) and \(760\operatorname{nm}\) according to ISO 21348 (2007).

VMI:

‘Velocity map imaging’, experimental method for registration (and visualization) of particle velocities as a function of their angular distribution (see Appendix B).

VUV:

‘Vacuum ultraviolet’, spectral range of electromagnetic radiation. part of the UV spectral range. Wavelengths between \(10\operatorname{nm}\) and \(200\operatorname{nm}\) according to ISO 21348 (2007).

XANES:

‘X-ray absorption near edge spectroscopy, also NEXAFS’, X-ray absorption by inner shell electrons close to the respective X-ray absorption edge.

XAS:

‘X-ray absorption spectroscopy’, Used for to study the electronic states of inner shell electrons.

XPS:

‘X-ray photoelectron spectroscopy’, see Sect. 5.8.1.

XUV:

‘Soft x-ray (sometimes also extreme UV)’, spectral wavelength range between \(0.1\operatorname{nm}\) and \(10\operatorname{nm}\) according to ISO 21348 (2007), sometimes up to \(40\operatorname{nm}\).

ZEKE:

‘Zero kinetic energy’, photoelectron spectroscopy (see Sect. 5.8.3).

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Hertel, I.V., Schulz, CP. (2015). Molecular Spectroscopy. In: Atoms, Molecules and Optical Physics 2. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54313-5_5

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