Density Functional Implementation of the Computation of Chiroptical Molecular Properties

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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_at_cobalt78.chem.ucalgary.ca
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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
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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
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Methodology

• Sum-Over-States formalism yields

Excitation Frequencies wl0
Rotatory Strengths Rl0
electric transition dipole
magnetic transition dipole
frequency dependent optical rotation para- meter
? ORD spectra
Related to the CD spectrum
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Methodology

• Direct computation of b and R with TDDFT

Frequency dependent electron density change
(after FT)

• molecular orbitals,
• occupation 0 or 1

Fourier-transformed density matrix due to the
perturbation (E(t) or B(t))
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Methodology

• Direct computation of b and R with TDDFT

RPA-type equation system for P, i?occ, a? virt
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
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Methodology

• Direct computation of b and R with TDDFT

Definitions
The Fs are the eigenvectors of W, wl2 its
eigenvalues (wl excitation frequencies)
Skipping a few lines of straightforward
algebra,we obtain
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Methodology

• Direct computation of b and R with TDDFT

Comparison with the Sum-Over-States Formula
yields for R0l
Therefore
consistent with definition of oscillator strength
in TDDFT, obtained as
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Implementation into ADF

• Excitation energies and oscillator strengths
  al-ready available in the Amsterdam Density
  Functional Code (ADF, see www.scm.com)
• Only Mai matrix 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

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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

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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
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Applications

• (S,S)-Dimethyloxirane

ADF CD Spectra simulation )
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
• DE for GGA 1eV too small, but well reproduced
  with SAOP potential

1 Carnell et al., CPL 179 (1994), 385
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) Assumed linewidth proportional to ?E (approx.
0.15 eV), Gaussians centered at excitation
energies reproducing R , ADF Basis Vdiff
(triple-z pol. diff)
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Applications

• Cyclohexanone Derivatives

CO 290 nm (4.4 eV) p-p transition
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
Rs almost identical c) As quoted in 1. Exp.
values are computed from ORD spectra d)
magnitude not known
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Applications

• Hexahelicene

ADF CD Spectra simulation )

• Shape of the spectrum equivalent to the TDDFT and
  exp. spectra published in 1
• magnitude of Rs 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

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1 TDDFT/Expt. Furche et al., JACS 122 (2000),
1717
) preliminary Results with ADF Basis IV (no
diff.)
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Applications

• Chloro-methyl-aziridines

• 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
ADF simulation )
2
1b
1a
GGA, shifted 0.7 eV
1 in heptane, Shustov et al., JACS 110 (1988),
1719.
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) BP86 functional, ADF Basis Vdiff Triple-z
pol. diff. basis
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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

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