Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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: [email protected] 1 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 firstprinciples quantum chemical methods will be an important tool to asssist chemical and biochemical research and enhance our understanding of optical activity 2 Methodology Quantifying Optical Activity Light-Wave interacts with a chiral molecule electric dipole moment in a time-dependent magnetic field (B of light wave) perturbed electric & magnetic moments ' B c t O or m CH3 magnetic dipole moment in a time-dependent electric field (E of light wave) ; m' E c t is the optical rotation parameter 3 Methodology Sum-Over-States formalism yields 2c R 0 2 2 3 0 frequency dependent optical rotation parameter ORD spectra Excitation Frequencies 0 Rotatory Strengths R0 R 0 Im( 0 m0 ) electric magnetic Related to transition transition the CD dipole dipole spectrum R0 const. dE E CD Band 4 Methodology Direct computation of and R with TDDFT Frequency dependent electron density change (after FT) ' ( ) Pia ( ) i i * a = molecular orbitals, occupation # 0 or 1 a Pia () Pai* () Fourier-transformed density matrix due to the perturbation (E(t) or B(t)) occ virt X ai Pai Yai Pia ' ( ) (X ai Yai ) (er )ai i a occ virt e m' ( ) (Xai Yai ) ( r pˆ ) ai 2c i a 5 Methodology Direct computation of and R with TDDFT RPA-type equation system for P, iocc, a virt A B 1 0X V X = vector containing B A 0 1 Y W all (ai) elements, etc… Wai Via matrix elements of the external perturbation, (-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 Methodology Direct computation of and R with TDDFT 1 Definitions: S (A B) F F [ ] 2 2 2 2 1 1 / 2 ; S (A B)S 1/ 2 The F’s are the eigenvectors of , 2 its eigenvalues (= excitation frequencies) Skipping a few lines of straightforward algebra,we obtain 2 Im( DS 1/ 2 1 1/ 2 [ ] S M) Dai (er )ai dipole moment matrix elements e Mai ( r pˆ ) magnetic moment matrix elements 2c 7 Methodology Direct computation of and R with TDDFT Comparison with the Sum-Over-States Formula yields for R0 1 / 2 R0 Im( DS 1/ 2 F F S M) Therefore 0 1 / 2 DS 1 / 2 F 1/ 2 m0 MS 3 /2 F consistent with definition of oscillator strength in TDDFT, obtained as 2 f 0 3 | DS 1/ 2 2 F | 8 Implementation into ADF Excitation energies and oscillator strengths already available in the Amsterdam Density Functional Code (ADF, see www.scm.com) Only Mai matrix elements additionally needed for Rotatory Strengths (, D, S, F already available) Computation of Mai by numerical integration Abelian chiral symmetry groups currently supported for computation of CD spectra (C1, C2, D2) Implementation for in progress (follows the available implementation for frequency dependent polarizabilities 9 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 R 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 Applications H (R)-Methyloxirane Excit. 1 E/eV f R/1040cgs 2-4 <E>/eV Sf SR/1040cg s H O H CH3 ADF ADF Other Other Expt. GGA a) SAOP b) Ref [1] Ref [2] Ref [2] 6.05 0.011 7.11 0.013 6.0 0.012 6.4 7.12 0.0004 0.025 -10.2 6.59 -13.4 7.69 -23.0 6.5 -2.66 7.3 0.047 +9.75 0.061 +14.7 0.044 +23.0 0.0012 0.062 +2.24 11.8 [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 -11.8 7.75 11 Applications H (S,S)-Dimethyloxirane ADF CD Spectra simulation *) O H3C CH3 H Exp. spectrum / MR-CI simulation [1] 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 E for GGA ~ 1eV too small, but well reproduced with SAOP potential [1] Carnell et al., CPL 179 (1994), 385 *) Assumed linewidth proportional to E (approx. 0.15 eV), Gaussians centered at excitation energies reproducing R , ADF Basis “Vdiff” (triple-z + pol. + diff) 12 Applications H14 O Cyclohexanone Derivatives H7 C=O ~290 nm (4.4 eV) pp* transition H? CH3 a) Ecalc/eV H13 H10 H11 H8 H9 Rcalc R Other R Other R Expt. GGA b) Ref [1] Ref [2] Ref [1] c) none H7 3.94 (4.3) b) 0 0 0 0 3.96 (4.3) 0.27 0.00 9.92 +(small) H9 3.96 (4.3) -1.39 -2.26 -15.11 - d) H7H13 3.96 (4.3) +1.46 +3.6 +5.53 +1.7 H7H13H8 3.99 (4.3) +4.36 +5.3 +6.36 +6.2 H12 [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 Applications Hexahelicene ADF CD Spectra simulation *) Exp. / theor. study [1] SRtheo = 412 SRexp = 331 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 *) preliminary Results with ADF Basis IV (no diff.) [1] TDDFT/Expt. Furche et al., JACS 122 (2000), 1717 14 Applications Chloro-methyl-aziridines ADF simulation *) Exp. Spectra [1] CH3 2 N CH3 Cl CH3 N Cl 1b CH3 Cl N 1a GGA, shifted +0.7 eV SAOP yields comparable E than GGA Exp. spectra qualitatively well reproduced, for 1a,1b magni tudes for also comparable to experiment (+)Band at ~260 nm for 2 much stronger in the simulations (low experimental resolution ?) Blue shift for 1b is not reproduced [1] in heptane, Shustov et al., JACS 110 (1988), 1719. *) BP86 functional, ADF Basis “Vdiff” Triple-z +pol. + diff. basis 15 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