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QuantumChemistryandSpectroscopy Text book Engel: Quantum Chemistry and Spectroscopy (3 ed., QCS) or Engel and Reid: Physical Chemistry (3 ed.) Chapter7.Molecularspectroscopy(Engel:QCSchapter 14) Now we have rather good understanding of electronic structure of simple molecules. Now we can start thinking how the molecular spectra will look. Of course every molecule is different and a general discussion is impossible but we can learn a lot form few simple examples. Let us start from O2 molecule. We know it’s ground state. The highest state is the p* and it is degenerated s* --- p* -↑p s thus the ground state is triplet. What kind of molecular excitations the O2 will have. -↑- -↑↓- -↑↓- ↑↓- The first excitation is a singlet state with same orbital as in the ground state. The ground state is marked with 3S g and the excited state as 1Dg . Then in the next excitation the electron is p* -↑p s -↓- -↑↓- -↑↓- ↑↓- still in a singlet state but on different atom orbital. This is marked as 1S + g (Warning the assignment of the states can be Incorrect, I was confused when reading Engel but the labels are correct). The next excitation comes from an electron exited to p* -↑↓p --- -↑↓- -↑↓- s* state. Using Hund’s rule the total spin is 1 and the state is triplet. It is marked with s 3S + . u - ↑↓- This state is very close to O2 dissociation limit. Now it is important that there are several s* -↑- p* -↑-- molecular excited states. This is very --- p -↑↓- -↑↓- s - ↑↓- general feature. Also these states can have different spin states. Next the selections rules are rather complex. First the spin cannot change, DS=0, the angular momentum L can change 0,±1. For homoatomic dimers u ↔ u, g ↔ g transition are forbidden, the u ↔ g transition is allowed. Also the S- ↔ S+ transition is forbidden. (The S- ↔ S- and S+ ↔ react with O2 O2 + hv → 2O∙ S+ transition are allowed). At the end the O2 cannot be exited to any of the bound states. The fist allowed transition is to the 3S-u state. The needed energy is corresponds to radiation of wavelength around 175 – 200 nm. This is a strong UV region. Is the transition to the lower states would be allowed O2 would adsorb at the visible light region and the atmosphere would not be transparent. The O2 cannot dissociate at lower part of the atmosphere but at stratosphere there is much more strong UV-radiation. The dissociated oxygen atoms will molecules to produce ozone, O3. O∙ + O2 + M → O3 + M This is the most important ozone production reaction in the atmosphere. In the energy diagrams the small side marks denote the vibrational levels. Vibrational fine structure in electron spectra The vibration lines can be seen well in the electron spectra. As in the roto-vibrational spectra different quantum states cannot be separated. The transition dipole is now rather complex. We need to deal at the same time the atomic and electronic wave functions. Y = fvib, ground ( R1 ,..RM )jel , ground ( r1..rN ) This is technically rather complex object and now we need to compute the transition dipole. Note that the electrons are excited so the dipole operator affect (mostly) to the electronic wave functions. From the atomic wave functions the overlap integral is relevant. We can assume that the atomic wave functions are close to harmonic oscillator wave functions. òf vib , ground ( R )fvib ,excited ( R ) dR × ò jel , ground ( r1..rN ) mˆjel ,excited ( r1..rN ) d 3r1..d 3rN Note that the selection rule from harmonic oscillator (Dn=±1) is not valid. I do not have a good explanation, but the electrons couple stronger to the electric field. There is also another phenomena which is due to the mass difference between electrons and atoms. The electron transitions are so quick that the atoms do not have time to move. This Franck-Condon principle is general. It is easy to utilize in the potential energy diagrams. When the minima of the potential energy curves are not at the same position, the excitation line goes straight up and the most likely energy excitation is not from vibrational ground state to ground state. The overlap integral can be used to estimate the intensity of the transition òf vib , ground ( R)fvib , excited ( R) dR 2 Note: in the case of O2 the minima were almost at the same position so then the 0 -> 0 transition is the most likely. The side spectra is very useful. From it the molecular vibration connected to the electronic excitation can be determinate. (In many atom molecule it is not easy to know which vibration is really measured.) Fluorescence spectra The Franck-Condon principle is useful in fluorescence spectra. There we are looking both the molecules adsorption and emission spectra, usually at visible or UV-light range. Both the adsorption and emission spectra have several almost equally spaced peaks. The spectra are almost mirror images of each other and emission spectra is higher in energy. The spectra is easy to understand with the energy level diagrams. In the example below the potentials are slightly off-set so the 0 -> 4 peak is more probable. Once the system is at the excited state, S 1, the vibrational states will release energy at IR region. The relaxation to vibrational ground state is rather fast. After the molecule is at state S1 vibrational ground state it can relax back to S0 state. This relaxation can end to different vibrational states. Time scales of the different processes. Note that the fluorescence process have to be much slower than the vibrational processes. From: http://micro.magnet.fsu.edu/primer/techniques/fluoresce nce/fluorescenceintro.html The fluorescence spectroscopy is very useful in biology and it has several every day applications. One of the most common are the fluorescent lights. Inside of these lamps are mercury vapor that emits mild UV light. The fluorescent material on the lamps surface will turn the UV lights to white light. These lamps are more energy efficient than normal light bulbs. Also the color of the light can be tuned with different fluorescent materials. Some of the least pleasant light comes from tubes containing the older, halophosphate-type phosphors (chemical formula Ca5(PO4)3(F, Cl):Sb3+, Mn2+). From: https://en.wikipedia.org/wiki/Fluorescent_lamp Chromophores All chemical molecules adsorb at some wave length, mostly at UV. But we are interested of chemical groups that adsorbs are (near) visible range. These are usually called chromophores. As an example we can look C=O group in formaldehyde H2CO. The carbon is sp2 hybridized, two of the hybrid orbital form the C-H s-bonds and one will participate to the C=O bond. The sp2 orbital and O:2pz orbital will form a s-bond. The px orbitals from the C and O will form a p-bond and the electron pair on the O:py orbital does not interact much with the carbon, it is marked with n O. (The O:2s orbital does not interact much with the C.) (2sO)2(sCH1)2(sCH2)2(sCO)2(pCO)2(nO)2(pCO*)0 Now we have the electronic structure of C=O group. The transition rules are again rather complex but the lowest transition is n → p* the next one is p → p*, and the highest one is s → s* . There is also the triplet states. The description is mostly valid to any C=O group. Below is a table of few common chromophores. As one can see most of them are on the UV range. Well we know that, most of organic compounds are transparent. And UV radiation, especially strong UV, will broke most molecules. (Visible light 400 -700 nm.) The table contain the lowest excitation and there are other transitions higher in energy. The chromophores below are simple but nature is full of more complex chromophores. One very interesting class is conjugated pbond systems, like beta-carotene and 11-cis-retinal. The 11-cisretinal is the prime molecule responsible in vision. In retinal it is important that is changes its shape in the excitation. The long p-bonded systems have adsorption at longer wave lengths. This can be understood using the Huckel model. We can solve the Huckel matric for longer p-bonded chain and we will see that the NxN matrix − ℎ 0 0 0 0 ℎ − ℎ 0 0 0 0 ℎ − ℎ 0 0 0 0 ℎ − ℎ 0 … … .. .. … .. 0 0 0 0 ℎ − =0 Will have solution of En= H11 + 2h cos(np/(N+1)). When N is large we will have several states in the range of H11 ± 2h. Half of them are occupied and for even N the HOMO-LUMO gap is 2h [cos(Np/(2(N+1))- cos((N+2)p/(2(N+1))] ≈ 4h/(N+1) so the gap shrinks when the N increases retinal From: https://en.wikipedia.org/wiki/Chromophore Carotene Last also the metal complexes are often colorful and basis of many pigments. Blood’s red color comes from the iron porphyrin. Many of these pigments are toxic due to the metal. · · · · · · · · · · Cadmium pigments: cadmium yellow, cadmium red, cadmium green, cadmium orange, cadmium sulfoselenide Chromium pigments: chrome yellow and chrome green Cobalt pigments: cobalt violet, cobalt blue, cerulean blue, aureolin (cobalt yellow) Copper pigments: Azurite, Han purple, Han blue, Egyptian blue, Malachite, Paris green, Phthalocyanine Blue BN, Phthalocyanine Green G, verdigris, viridian Iron oxide pigments: sanguine, caput mortuum, oxide red, red ochre, Venetian red, Prussian blue Lead pigments: lead white, cremnitz white, Naples yellow, red lead, lead-tin-yellow Manganese pigments: manganese violet Mercury pigments: vermilion Titanium pigments: titanium yellow, titanium beige, titanium white, titanium black Zinc pigments: zinc white, zinc ferrite Phthalo blue (from: https://en.wikipedia.org/wiki/Pigment) Problem: what might be the transition in metals that give them color. Phosphorence spectra If the ground state is a singlet state the excited state is also a singlet but the (with heavier elements) there can be transition from the excited singlet state to triplet state. Only small fraction of the molecules will make the singlet -> triplet transition but then the triplet state is very stable. The transition T1 state to the ground state can take minutes. The phosphorence phenomena is used commonly to illuminate the clock hands even when they are not illuminated. Applications of fluorescence Fluorescence has become a very useful tool for biological samples. In those (different) fluorescensing molecules are attached to the samples and they can be imagined with very high accuracy (Nobel Prize 2014). It is important that the fluorophores can be attach to different parts of the samples, like the nucleus of the cell, or cancer cells, etc.. From: https://en.wikipedia.org/wiki/Fluorescence_microscope