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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@cobalt78.chem.ucalgary.ca

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- 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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O

C

H

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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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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

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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))

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RPA-type equation system forP, iocc, 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

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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

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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

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- 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

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- 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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(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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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

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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)

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

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Exp. / theor. study [1]

SRexp = 331

SRtheo = 412

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

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*) preliminary Results with ADF Basis IV (no diff.)

[1] TDDFT/Expt. Furche et al., JACS 122 (2000), 1717

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.

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*) BP86 functional, ADF Basis “Vdiff” Triple-z +pol. + diff. basis

- 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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