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UA CHEMISTRY 713 - Chapter 2 - ab initio Methods

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Computational Spectroscopy II. ab initio MethodsThe Born-Oppenheimer ApproximationThe Franck-Condon PrincipleIodine oxide (IO) Potential energy curvesSlide 5The Franck-Condon Principle: Polyatomic moleculesSelection rules for electronic spectroscopyThe fate of electronically excited moleculesConical intersectionsElectronic excitations in the orbital approximationQuick review of Slater determinantsHOMO and LUMO molecular orbitalsDifficulties with the Simplest Orbital PictureCI Singles (CIS) for Excited StatesCIS excited state calculations with Spartan (04 or 06)Acrolein UV/Vis by CISAcrolein excited state vibrations by CISSlide 18Slide 19Time-dependent DFT (TDDFT)TDDFT excited state calculation with SpartanAcrolein UV/Vis by TDDFTComparison of Spartan excited state calculationsHigher level methods for excited statesComputational SpectroscopyII. ab initio Methodsfrom part (d) Electronic SpectraChemistry 713Updated: February 20, 2008The Born-Oppenheimer ApproximationFor a given molecular geometry (i.e., fixed nuclear coordinates, R), solve the electronic Schroedinger equation: where He is the whole molecular Hamiltonian except the nuclear kinetic energy and r represents the coordinates for all of the electrons, and e is the electronic wave function. Repeat for a range of molecular geometries R of interest to construct a potential energy surface.The electronic energy En(R) is the potential energy in which the nuclei move.Up to now we have just been concerned about the lowest energy electronic state, n=0.To deal with electronic (UV/vis) spectroscopy, we also need to know some of the higher electronic surfaces (n=1, 2, …) as well.The nuclear motion on each surface can then be solved as a separate step. € Heψe,nr;R( )= EnR( )ψe,nr;R( )QuickTime™ and a decompressorare needed to see this picture.QuickTime™ and a decompressorare needed to see this picture.F.F. Crim, Spectroscopic probes and vibrational state control of chemical reaction dynamics in gases and liquids.Talk WA04, International Symposium on Molecular Spectroscopy, Columbus OH, 2006.http://molspect.chemistry.ohio-state.edu/symposium_61/symposium/Program/WA.html#WA04The Franck-Condon PrincipleIn a diatomic molecule, the potential energy curves are different for lower and upper electronic states.The bond length re changesThe vibrational frequency  changes.Use double prime for lower state (), and single primes for upper state ().Gordon M. Barrow, An Introduction to Molecular Spectroscopy,McGraw-Hill, New York, 1962, fig. 10-1, p. 232.rrerehhIodine oxide (IO) Potential energy curvesThere are many potential energy curves even in a small molecule.Some are attractive;others are repulsiveCurves of the same symmetry don’t cross:“adiabatic” curvesSome result from the crossing of “diabatic” curves, and as a result have peculiar shapes.Notation:“X” denotes the ground stateUpper case letters, A, B, etc., indicate excited states of the same spin multiplicity as the ground state.Lower case letters, a, b, c, etc., indicate excited states of a different multiplicity. (Numbers are not normally used.)The symmetry and spin multiplicity of the state are indicated by a term symbol, such as 2, 4–, etc. S. Roszak, M. Krauss, A. B. Alekseyev, H.-P. Liebermann, and R. J. Buenke, J. Phys. Chem. A, 104 (13), 2999 -3003, 2000. 10.1021/jp994002lr, Fig. 1.The Franck-Condon PrincipleElectronic transitions are “vertical”, that is the nuclei don’t move while the electron(s) are being excited.Because the upper state wavefunctions are shifted from those in the ground state and because the vibrational frequencies are different, changes in the vibrational quantum number accompany the electronic excitation.The relative intensities of the vibrational subbands v  v are given by the squares of overlap integrals, called Franck-Condon factors:If neither the bond length, nor the vibrational frequency change, then the selection rules are v=0.In polyatomic molecules, vibrational progressions occur in vibrational modes for which either the equilibrium position is changes or the frequency is changed.€ ψ′ v ψ ′ ′v 2In polyatomic molecules, vibrational progressions occur in vibrational modes for which either the equilibrium position is changes or the frequency is changed.Therefore, a typical electronic band has a lot of vibrational structure, which extends over a few thousand cm-1.The band origin is the frequency of the v=00 band. The band origins of electronic transitions are what we can most easily calculate with ab initio methods. For large molecules or in the condensed phase, the vibrational structure is heavily overlapped and merges together into a wide unstructured blob (the Franck-Condon envelope).The Franck-Condon Principle:Polyatomic moleculesA spectrum with vibrational progressions45,000 37,000Wavenumber / cm-1BandOrigin Franck-Condonenvelope BenzeneJ. M. Hollas, High resolution Spectroscopy, Butterworths, London, 1982, p 393.Selection rules for electronic spectroscopySpin multiplicity is conserved.Changes in vibrational motion follow the Franck-Condon PrincipleRotational transitions (J=0,1, K=0,1) accompany each electronic+vibrational (vibronic) transition.For molecules with a center of symmetry, the g/u symmetry changes.Nuclear spin states are conserved.Additional rules apply in particular cases.The fate of electronically excited molecules1. Fluorescence: a visible or UV photon is emitted to return the molecule to its ground state.2. Intersystem crossing: radiationless conversion of the energy back to a state of different spin multiplicity. (e.g., singlet to triplet).-Occasionally followed by phosfluorescence: emission of a photon with a change in the spin multiplicity. (VERY weak; a long radiative lifetime.)3. Internal conversion: radiationless conversion of the energy back to the ground state (or other state of the same spin multiplicity).4. A Photochemical reaction-photodissociation, isomerization5. Energy transfer to a nearby moleculeJablonski diagramJ. I. Steinfeld, Molecules and Radiation, MIT Press, Cambridge, MA, 2nd ed, 1985, p 287.Conical intersectionsTwo electronic surfaces can met like two cones touching tip to tip.Widespread throughout electronic spectroscopy.Act like a sink-hole that allows the system to drop through onto a lower


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