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WIREs Comput Mol Sci
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Circular dichroism: electronic

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First‐principles calculations of electronic circular dichroism (ECD) are widely used to determine absolute configurations of chiral molecules. In addition, ECD is a sensitive probe for the three‐dimensional molecular structure, making ECD calculations a useful tool to study conformational changes. In this review, we explain the origin of ECD and optical activity using response theory. While the quantum‐mechanical underpinnings of ECD have been known for a long time, efficient electronic structure methods for ECD calculations on molecules with more than 10–20 atoms have become widely available only in the past decade. We review the most popular methods for ECD calculation, focusing on time‐dependent density functional theory. Although single‐point vertical ECD calculations yield useful accuracy for conformationally rigid systems, inclusion of finite‐temperature effects is necessary for flexible molecules. The scope and limitations of modern ECD calculations are illustrated by applications to helicenes, fullerenes, iso‐schizozygane alkaloids, paracyclophanes, β‐lactams, and transition metal complexes. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 00 1–17 DOI: 10.1002/wcms.55

This article is categorized under:

  • Electronic Structure Theory > Density Functional Theory
Figure 1.

Left‐circularly polarized light propagating in z‐direction. The plotted electric field vectors rotate in the x–y plane, describing a left‐handed helix. The magnetic field vector (not shown) is perpendicular to the electric field vector.

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Figure 2.

Experimental ECD spectrum of trans‐(2S,3S)‐dimethyloxirane (solid) together with calculated ECD spectra3 of the (2S,3S) and the (2R,3R) enantiomers. (Theoretical data reprinted with permission from Ref 3. Copyright 2002 American Institute of Physics. Experimental data reprinted with permission from Ref 2. Copyright 1994 Elsevier.)

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Figure 3.

Qualitative behavior of real and imaginary part of G(ω) close to an excitation energy Ω0n.

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Figure 4.

Comparison of TDDFT67 and experimental128 circular dichroism spectra for (M)‐7 helicene with the three different density functionals B2LYP, B2PLYP,66 and B3LYP along with the TZVP basis set. (Reprinted with permission from Ref 67. Copyright 2007 American Institute of Physics.)

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Figure 5.

Experimental ECD spectrum129 of D2‐C84 compared to simulations using a semiempirical method130 and TDDFT131(BP86/aug‐SVP). The absolute configuration of the fullerene is fA in the old129 and C in the new IUPAC132 nomenclature. ε denotes the molar decadic absorption coefficient, R the rotatory strength. Calculated Δε values from TDDFT were scaled by 1/14 to match the experimental intensities. (Data reprinted with permission from Ref 131. Copyright 2002 American Chemical Society. CNDO/S data reprinted with permission from Ref 130. Copyright 1997 Elsevier.)

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Figure 6.

Iso‐schizogamine and iso‐schizogaline.

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Figure 7.

[2.2]paracyclophane‐ketimine derivative featuring planar and central chirality.

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Figure 8.

Structures of the low‐energy conformers of the (Rp,R) and (Rp,S) diastereomers. (Reprinted with permission from Ref 118. Copyright 2009 American Chemical Society.)

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Figure 9.

Experimental electronic circular dichroism (ECD) of a pair of diastereomers recorded in toluene is compared to corresponding theoretical spectra from time‐dependent density functional theory (TDDFT) response calculations PBE hybrid functional/split‐valence plus polarization basis set. Solvent effects are included using COSMO (see the section Solvent Effects). Calculated spectra were scaled with a factor 0.5. Root mean square linewidth for Gaussian broadening is 0.15eV (see section Temperature Effects). The predicted difference in the absolute intensities of the lowest‐energy band is present in the measured spectra. (Reprinted with permission from Ref 118. Copyright 2009 American Chemical Society.)

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Figure 10.

Computed and measured electronic circular dichroism (ECD) of the tautomeric forms (Rp,S) ‐arom and (Rp,S)‐quino of the studied [2.2]paracyclophane‐ketimine derivative (Figure 7). The less polar solvent favors the less polar ortho‐hydroquinone‐imine whereas the more polar solvent promotes the ortho‐quinone‐enamine tautomer. Computed spectra were obtained from time‐dependent density functional theory (TDDFT) (PBE hybrid/SVP) response calculations. Root mean square linewidths are 0.15eV for the aromatic tautomer and 0.30eV for the quinoidal tautomer (see the section Temperature Effects). Theoretical spectra are scaled by a factor 0.45. (Reprinted with permission from Ref 118. Copyright 2009 American Chemical Society.)

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Figure 11.

Tautomeric equilibrium explaining the observed solvatochromism. arom is the ortho‐hydroquinone‐imine form and quino is the ortho‐quinone‐enamine form.

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Figure 12.

Boltzmann‐weighted superposition of the computed ortho‐quinone enamine and ortho‐hydroquinone‐imine electronic circular dichroism (ECD) spectra versus ECD spectrum of the (Rp,S) diastereomer recorded in chloroform. Computed circular dichroism spectra from time‐dependent density functional theory (TDDFT) (PBE hybrid/SVP) calculations, scaled by a factor 0.5. Conformer energies for Boltzmann‐factors were computed including solvent effects through COSMO (see section Solvent Effects). For details see Ref 118. (Reprinted with permission from Ref 118. Copyright 2009 American Chemical Society.)

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Figure 13.

The investigated (6R,7S)‐7‐((1R)‐1‐hydroxyethyl)‐8‐oxo‐1‐aza‐bicyclo[4.2.0]octane.

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Figure 14.

Computed structure of the cepham analog (see Figure 13) and its simulated electronic circular dichroism (ECD) spectrum at 0 K and 350 K compared to experiment. The 0 K curve corresponds to the conformer shown, whereas the 350 K curve is the result of MD simulation. ε is the molar decadic absorption coefficient, λ the wavelength, and R the computed rotatory strength. The experimental spectrum was recorded in acetonitrile at room temperature. See Ref 96 for details. (Data reprinted with permission from Ref 96. Copyright 2007 Wiley‐VCH Verlag GmbH & Co.)

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Figure 15.

Δ‐ and Λ‐configuration of [Co(en)3]3+.

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