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Density Functional Implementation of the Computation of Chiroptical Molecular Properties

Density Functional Implementation of the Computation of Chiroptical Molecular Properties . With Applications to the Computation of CD Spectra. Jochen Autschbach & Tom Ziegler, University of Calgary, Dept. of Chemistry University Drive 2500, Calgary, Canada, T2N-1N4

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Density Functional Implementation of the Computation of Chiroptical Molecular Properties

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  1. Density Functional Implementation of the Computation of Chiroptical Molecular Properties With Applications to the Computation of CD Spectra Jochen Autschbach & Tom Ziegler, University of Calgary, Dept. of Chemistry University Drive 2500, Calgary, Canada, T2N-1N4 Email: jochen@cobalt78.chem.ucalgary.ca 1

  2. Motivation • Almost all biochemically relevant substances are optically active • CD (circular dichroism) and ORD (optical rotation dispersion) spectroscopy are important methods in experimental research • Interpretation of spectra can be difficult, overlapping CD bands obscure the spectra … Prediction of chiroptical properties by first- principles quantum chemical methods will be an important tool to asssist chemical and biochemical research and enhance our under- standing of optical activity 2

  3. O C H 3 Methodology Quantifying Optical Activity Light-Wave interacts with a chiral molecule or electric dipole moment in a time-dependent magnetic field (B of light wave) magnetic dipole moment in a time-dependent electric field (E of light wave) b is the optical rotation parameter perturbed electric & magnetic moments 3

  4. Methodology Excitation Frequencieswl0 Sum-Over-States formalism yields Rotatory StrengthsRl0 electric transition dipole magnetic transition dipole frequency dependent optical rotation para- meter  ORD spectra Related to the CD spectrum 4

  5. Methodology Frequency dependent electron density change (after FT) Direct computation of b and R with TDDFT • = molecular orbitals, occupation # 0 or 1 Fourier-transformed density matrix due to the perturbation (E(t) or B(t)) 5

  6. Methodology RPA-type equation system forP, iocc, a virt Direct computation of b and R with TDDFT X = vector containing all (ai) elements, etc… matrix elements of the external perturbation,(w-dependent Hamiltonian due to E(t) or B(t)) A,B are matrices. They contain of the response of the system due to the perturbation (first-order Coulomb and XC potential) We use the ALDA Kernel (first-order VWN potential) for XC 6

  7. Methodology Definitions: Direct computation of b and R with TDDFT The F’s are the eigenvectors of W, wl2 its eigenvalues (wl= excitation frequencies) Skipping a few lines of straightforward algebra,we obtain 7

  8. Methodology Comparison with the Sum-Over-States Formula yields for R0l Direct computation of b and R with TDDFT Therefore consistent with definition of oscillator strength in TDDFT, obtained as 8

  9. Implementation into ADF • Excitation energies and oscillator strengths al-ready available in the Amsterdam Density Functional Code (ADF, see www.scm.com) • Only Maimatrix elements additionally needed for Rotatory Strengths (wl, D, S, Fl already available) • Computation of Mai by numerical integration • Abelian chiral symmetry groups currently sup-ported for computation of CD spectra (C1, C2, D2) • Implementation for b in progress (follows the available implementation for frequency dependent polarizabilities 9

  10. Implementation into ADF • Additionally, the velocity representations for the rotatory and oscillator strengths have been implemented (matrix elements ai) • Velocity form of R is origin-independent • Differences between Rm and R typically ~ 15% for moderate accuracy settings in the computations • Computationally efficient, reasonable accuracy for many applications • Suitable Slater basis sets with diffuse functions need to be developed for routine applications 10

  11. Applications (R)-Methyloxirane [1] TD LDA: Yabana & Bertsch, PRA 60 (1999), 1271 [2] MR-CI: Carnell et al., CPL 180 (1991), 477 a) BP86 triple-zeta + diff. Slater basis b) SAOP potential 11

  12. Applications ADF CD Spectra simulation *) Exp. spectrum / MR-CI simulation [1] (S,S)-Dimethyloxirane Rcalc = 7.6 Rexp. = 9.5 calc. predicts large neg. R for this excitation low lying Rydberg excitations, sensitive to basis set size / functional good agreement with exp. and MR-CI study for R of the 1st excitation DE for GGA ~ 1eV too small, but well reproduced with SAOP potential [1] Carnell et al., CPL 179 (1994), 385 12 *) Assumed linewidth proportional to E (approx. 0.15 eV), Gaussians centered at excitation energies reproducing R , ADF Basis “Vdiff” (triple-z + pol. + diff)

  13. Applications C=O ~290 nm (4.4 eV) p-p* transition Cyclohexanone Derivatives [1] CNDO: Pao & Santry, JACS 88 (1966), 4157. [2] Extended Hückel: Hoffmann & Gould,JACS 92 (1970), 1813. a) Numbered hydrogens substituted with methyl groups. Same geometries used than in [1],[2] b) BP86, triple-zeta Slater basis, numbers in parentheses: SAOP functional, SAOP R’s almost identical c) As quoted in [1]. Exp. values are computed from ORD spectra d) magnitude not known 13

  14. Exp. / theor. study [1] SRexp = 331 SRtheo = 412 Applications ADF CD Spectra simulation *) Hexahelicene Shape of the spectrum equivalent to the TDDFT and exp. spectra published in [1] magnitude of R‘s smaller than exp., in particular for the short-wavelength excitations (TDDFT in [1] has too large R ‘s for the “B” band, too small for “E” band) GGA / SAOP yield qualitatively similar results 14 *) preliminary Results with ADF Basis IV (no diff.) [1] TDDFT/Expt. Furche et al., JACS 122 (2000), 1717

  15. Applications SAOP yields com-parable DE thanGGA Exp. spectra quali-tatively well repro-duced, for 1a,1bmagnitudes for Dealso comparableto experiment (+)Band at ~260 nm for 2 much strongerin the simulations(low experimental resolution ?) Blue shift for 1b isnot reproduced Exp. Spectra [1] Chloro-methyl-aziridines ADF simulation *) 2 1b 1a GGA, shifted +0.7 eV [1] in heptane, Shustov et al., JACS 110 (1988), 1719. 15 *) BP86 functional, ADF Basis “Vdiff” Triple-z +pol. + diff. basis

  16. Summary and Outlook • Rotatory strengths are very sensitive to basis set size and the chosen density functional • GGA excitation energies are systematically too low. The SAOP potential is quite accurate for small hydrocarbon molecules with large basis sets, but not so accurate for 3rd row elements. Standard GGAs yield comparable results for these elements. • Qualitative features of the experimental CD spectra are well reproduced in particular for low lying excitations. • Solvent effects can be important in order to achieve realistic simulations of CD spectra. Currently, solvent effects are neglected. • Implementation for ORD spectra in progress 16

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