• XNCD;
  • X-ray absorption;
  • noradrenaline;
  • L-DOPA;
  • propagator;
  • DFT


  1. Top of page
  2. Abstract

The near carbon K-edge X-ray absorption and circular dichroism spectra of noradrenaline (neutral and protonated forms) and L-DOPA (protonated form) have been determined with use of the complex polarization propagator method in conjunction with Kohn-Sham density functional theory. A Coulomb attenuated exchange-correlation functional and London atomic orbitals have been employed to address the issues of hole-electron interactions and gauge-origin dependence of the magnetic-dipole operator, respectively. Results show that the characteristics of the chromophore part of the circular dichroism spectra are shared for all three considered systems, whereas protonation qualitatively alters the part of the spectrum assigned to the chiral side chain. The comparatively larger spatial separation of chromophore and chiral center in L-DOPA inflicts larger differences in spectral intensities between the chromophore and chiral center part of the circular dichroism spectra. Chirality 21:E13–E19, 2009. © 2009 Wiley-Liss, Inc.


  1. Top of page
  2. Abstract

As shown in this special issue on advances in Chiroptical Methods in Chirality, the study of optical activities in chiral species, provides detailed information about the electronic and conformational structures of biological molecules. As pointed out by Barron,1 electronic transitions in molecules are often localized to chromophores and their immediate intramolecular environments, and, in the absence of chromophores in a molecule, the electronic circular dichroism (ECD) signal will be small, although the nonresonant optical rotation may be significant. So it is thus to be expected that the physical separation between chromophores and chiral centers in molecules will strongly affect the signal strength in ECD spectroscopy.

ECD is typically measured in the visible or ultra-violet regions of the spectrum, involving the low-lying valence and Rydberg states.2–5 The much less exploited counterpart of ECD in the X-ray region is known as X-ray natural circular dichroism (XNCD),6 and one here is concerned with core electronic excitations which, for biological systems, means that the probed excited states are often those at the near K-edges of carbon, nitrogen, and oxygen. In oriented samples, the electric-dipole–electric-quadrupole interaction can dominate the XNCD response, but in randomly oriented samples, when this contribution vanishes, the circular dichroism is governed by the electric-dipole–magnetic-dipole interaction.7–11 We will focus at this latter interaction and view it in perspective of the aforementioned discussion about the dependence of signal response on spatial separation of chromophore and chiral center. Because of the short wavelength of the involved X-rays, the associated electronic transitions are characterized by initial states with a high degree of spatial localization and final states that are more extended, so XNCD is likely to be even more sensitive than ECD toward this separation.

Our interest in this issue stems from a suggestion made to use XNCD as complementary tool to conventional X-ray absorption spectroscopy (XAS) for the characterization of biomolecules used in sensor applications.12, 13 The considered biomolecules have, in this context, been neurotransmitters and amino acids with molecular handles in terms of propanethiol to enable attachment to surfaces. In the present work, we intend to determine the XAS and XNCD spectra of 3,4-dihydroxy-L-phenylalanine (L-DOPA) and noradrenaline (NAd), both for which the near carbon K-edge absorption spectra are dominated by 1s [RIGHTWARDS ARROW] π*-transitions in the respective phenyl units. The phenyl ring is therefore to be considered as the chromophore in both systems, whereas the chiral center is the amine and hydroxyl carbon for L-DOPA and NAd, respectively. In the former (but not the latter) of the two systems, there is a spacer CH2-group in between the chromophore and the chiral center, and we will address the issue of to what extent this spacer group will reduce the XNCD response.

From a computational perspective, the calculations of XNCD spectra are challenging for several reasons: first, the gauge-origin dependence of the magnetic-dipole operator must be properly treated; second, the relevant excited states will be embedded in a continuum of valence ionized states and therefore difficult resolve, as needed for the evaluation of eq. 1; third, the strong interaction between the hole and electron orbitals causes a contraction of atomic orbital densities for core-excited atoms; fourth, the transitions in K-edge spectroscopy are almost magnetic-dipole forbidden. The first issue is not specific to XNCD but common to general calculations in finite basis sets of magnetic and electric–magnetic response functions. A remedy to this problem is provided by the use of London atomic orbitals14 in conjunction with the natural connection,15 as demonstrated in Ref.16 and as adopted here. The second issue is common to situations in which one is to determine the optical activity in regions of large density of electronic states, which may be the case due to the application of high frequency fields (as in this article) and/or as a consequence of treating a large molecular system. We have previously shown that, for this reason, it may be beneficial to calculate, not the separate rotatory strengths (as done in earlier work on XNCD17, 18) but rather the complex mixed electric-dipole–magnetic-dipole tensor19–21—we will briefly recapitulate this approach in the subsequent section. The third issue is specific to the involvement of core excited states and, in the framework of propagator approaches, it inflicts particularly strong requirements on the treatment of electron correlation.22 The fourth issue is connected with the fact that the initial electronic state in the X-ray induced transition is the atomic 1s-orbital which is an eigenfunction of the magnetic-dipole operator with an eigenvalue that is equal to zero. We will continue the discussion about these issues, and how we choose to deal with them, in the subsequent section.


  1. Top of page
  2. Abstract

The ECD spectral intensity for a transition from the ground state |0〉 to an excited state |n〉 is governed by the rotatory strength5

  • equation image(1)

where equation image and equation image are the electric and magnetic dipole moment operators along the molecular axes α and β, respectively, and the linear absorption intensity for the same transition is governed by the absolute square of the electric-dipole transition moment

  • equation image(2)

The mixed electric-dipole and magnetic-dipole coupling between the ground and the excited state in the rotatory strength eq. 1 means that the observed transitions in ECD spectroscopy must be electric-dipole as well as magnetic-dipole allowed.

For the sake of the argument, let us assume that the ground state is a Hartree-Fock (HF) state and that the excited state is a full configuration interaction (FCI) state (expressed in the canonical orbitals of the ground state), so the relevant magnetic-dipole matrix element becomes

  • equation image

Clearly the dominant contributions in FCI expansions that describe excited states at the near K-edge come from determinants with holes in atomic 1s-orbitals, but because only single excited determinants will contribute in the evaluation of the matrix element and because the atomic 1s-orbital is an eigenfunction of equation image with an eigenvalue that equals zero, the matrix element will vanish altogether. So there can be only two sources to a nonvanishing matrix element, and thereby to an ECD signal, and these are the polarization of the 1s-orbital due to the molecular field and valence excited determinants in the FCI expansion.

We have a fair general understanding of the electron density of core-excited states. It turns out that, in contrast to FCI expansions, an efficient way to express the excited states is to use CI singles (CIS) expansions based on the orbitals of core-ionized states—this approach is known as the static exchange (STEX) method.23–25—and we are then evaluating matrix elements of the type

  • equation image

In this case, the orbitals in the bra-vector are not orthogonal to those in the ket-vector, and the former ones express the flow of electron charge toward the core hole that occur due to the reduced screening of the atomic nucleus (electron relaxation). For example, the singly occupied 1s-orbital in the excited state will be contracted in comparison with the corresponding orbital in the ground state. So, in the STEX approach, this electron relaxation is explicitly taken into account by construction of the wave function, whereas in the FCI approach, it will be accounted for by inclusion of valence excited determinants in the expansion.

In the present work, we will use a time-dependent propagator approach for the determination of the absorption and circular dichroism spectra, and it will share the characteristics regarding orthogonality of ground and excited states with the above FCI example. Based on the discussion up to now, we anticipate that, in the general case, it will be important to include a complete set of electron excitation operators in the construction of the propagator, and we also anticipate that it will be crucial to accurately treat the electron correlation. We will for these reasons adopt the time-dependent density functional theory (DFT) approximation with full inclusion of electron excitation operators equation image (i and s being indices of inactive and secondary orbitals, respectively) and in conjunction with recently developed Coulomb attenuated exchange-correlation functionals.26

In a conventional propagator approach, the matrix elements needed for the evaluation of Rn and Mn would be obtained as residues of the linear response function. This technique requires, however, a resolution of the corresponding eigenvectors of the electronic Hessian, which, as we are dealing with a highly excited states, may become problematic. As an alternative, we have previously proposed that, also in the computational methodology, one focuses directly on the spectral intensities.19–22, 27 For absorption spectra which means that we determine directly the absorption cross section given by28

  • equation image(3)

where α(ω) is the electric-dipole polarizability and ω is the angular frequency of the incident radiation. In this formula, and elsewhere, the summation convention over repeated indices have been adopted, so eq. 3 really refers to a situation of a randomly oriented sample of molecules. The polarization dependence of the absorption is obtained from separate considerations of the three individual Cartesian components of the polarizability tensor.

The ECD is given in terms of the extinction coefficient Δε in units of l mol−1 cm−1 as20

  • equation image(4)

where χ, the coupling tensor of the external electric and magnetic fields, and ω are given in atomic units. Both the polarizability and the electric–magnetic coupling tensor are given in terms of a linear response function for which the general sum-over-states expression is given by

  • equation image(5)

where ℏωn are the transition energies between the molecular ground |0〉 and excited states |n〉 and the damping terms γn correspond to the inverse lifetimes of the excited states. If the operators equation image and equation image equal the electric dipole moment operators equation image and equation image, respectively, we obtain the electric-dipole polarizability tensor as equation image. If, on the other hand, operator equation image is replaced with the magnetic dipole moment operator equation image, we obtain the mixed electric-dipole–magnetic-dipole tensor equation image. As is shown in our recent work,20 the real part of χ(ω) is equal to the mixed electric-dipole–magnetic-dipole polarizability G′(ω) given by Barron1 whereas the imaginary part of χ(ω) is found to be related to the optical rotation as demonstrated in Ref.19.

So, the novelty of our computational methodology lies in the formulation and also implementations of the resonant-convergent, but then also complex, linear response function in eq. 5. We have coined this method as the complex polarization propagator (CPP) approach, and we refer the interested readers to Refs.29 and30 for explicit expressions of response functions in the single- and multi-determinant approximations. As mentioned in the introduction, our implementation is based on the use of London atomic orbitals, so that gauge-origin independent results are obtained for the χ-tensor.19


  1. Top of page
  2. Abstract

All calculations are carried out at optimized molecular structures. The geometry optimizations were performed with the Gaussian program31 at the Kohn-Sham DFT level of theory using the hybrid B3LYP32 exchange-correlation functional in conjunction with Dunning's correlation consistent basis sets (cc-pVTZ).33 The property calculations were also performed at the DFT level of theory but with use of the Coulomb attenuated method B3LYP (CAM-B3LYP)26 functional with a parametrization that guarantees a correct asymptotic limit of the Coulomb hole-electron interaction21, 22 (α = 0.19, β = 0.81, and μ = 0.33)—in this case, we adopted the augmented cc-pVDZ (aug-cc-pVDZ) basis set. These calculations were carried out with a modified version of the Dalton program34 that includes an implementation of the CAM-B3LYP functional by Peach et al.35 and an implementation of the CPP approach by Norman et al.29, 30 The relaxation parameters that govern the broadening of the absorption spectra were chosen as γn = 1000 cm−1. To compensate for the self-interaction error in Kohn-Sham DFT, we have applied an overall shift of spectra by +9.6 eV so that the first absorption peak becomes aligned with the lowest experimental K-edge transition in benzene.36


  1. Top of page
  2. Abstract

Molecular Structures

The molecular structure of small neurotransmitters in isolation and solution has been the subject of several studies, and we refer to the work by Baker and Grant for a recent contribution and also a review of previous work.37 For NAd it is predominantly the rotation and arrangement about the C[BOND]C bond in the ethanol-amine side chain (carbons C7 and C8 in Fig. 1) that gives rise to the various conformations. The hydroxyls attached to the phenyl ring can also give rise to different conformers, but an arrangement such as that in Figure 1 with a formed hydrogen bond is the energetically preferred one. So the relevant conformers of NAd can be characterized by the C1[BOND]C7[BOND]C8[BOND]N and O[BOND]C7[BOND]C8[BOND]N dihedral angles that, in Figure 1, are found in anti (A) and gauche (G) formations, respectively. This conformer is for that reason labeled as AG1, in which the additional numeral indicates the formation of a OH[BOND]N hydrogen bond. The AG1 conformer is the one being experimentally observed in gas phase, in spite of its theoretically predicted near degeneracy with the GG1 conformer.38 In line with the experimental finding, we have based our calculations solely on the AG1 conformer. In aqueous solution, the neurotransmitters will become protonated and predominantly reside in the AG conformation,37 and spectroscopic characterizations of the protonated forms of the neurotransmitters can even be carried out in the gas phase.39 We have for these reasons carried out calculations for the AG conformer of NAd also in the protonated form.

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Figure 1. Molecular structures and atomic labeling of the neutral forms of L-DOPA (left) and noradrenaline (right) in S-configurations. [Color figure can be viewed in the online issue, which is available at]

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The conformer of L-DOPA, which is illustrated in Figure 1, has anti and gauche formations of the C1[BOND]C7[BOND]C8[BOND]C9 and C1[BOND]C7[BOND]C8[BOND]N dihedral angles, respectively, and a NH[BOND]O hydrogen bond. This AG conformer is, at the B3LYP/cc-pVTZ level of theory, found to be lower in energy than both the GA conformer as well as the corresponding AG conformer with a NH[BOND]OH hydrogen bond, and we have restricted our property calculations to include only this conformer.

XAS Spectra

The molecules span the nonsymmetric C1 point group and our calculations refer to the S-enantiomers. We have chosen to place the phenyl rings in the xy-plane for the study of the polarization dependence of the X-ray absorption. Common to all molecules is that the first few peaks in the carbon near-edge X-ray absorption fine structure (NEXAFS) spectra will be dominating and correspond to 1s [RIGHTWARDS ARROW] π* transitions in the phenyl ring, and these bands will of course, with our choice of coordinate system, be strongly polarized along the z-direction. In other words, the dominating contribution to the cross section in eq. 3 will come from the imaginary part of αzz, and which thus illustrates the role of polarization in the CPP approach. The other piece of information that is normally extracted from theoretical calculations of X-ray absorption spectra is the atomic localization of the initial electronic states in the absorption process. In a separate state approach, such as the STEX method, one computes separately and adds the contributions to the overall absorption spectrum from final electronic states with core holes localized at specific symmetry independent atoms, which, in turn, is hampering for work on large systems of low symmetry. The CPP approach, on the other hand, is well suited for this task, and the computational issues are the same regardless of the frequency of the perturbation. However, as the excited states are never explicitly formed, one cannot directly associate peaks in the absorption spectrum to atoms in the molecule. But the calculation of the response function is separated into two steps: (i) the solving of a linear response equation for the so-called response vector N(ω) (eq. 18 of Ref. 29) and (ii) the formation of the response function value (eqs. 33 and 34 of Ref.29). Each element of N(ω) refers to a specific electron excitation operator equation image, and what we do to address the issue of atomic spectral contributions is to determine the relative contributions to N(ω) from separate inactive orbitals (i.e., we perform a contraction over the set of virtual orbitals). As complete channel interaction is accounted for, spectral bands will, in this procedure be associated with symmetry independent atoms on a percentage scale.

To a first approximation, one expects that there will appear two separate main bands in the NEXAFS spectra of NAd and L-DOPA associated the dihydroxy-phenyl unit (the chromophore). The first of these bands should be due to carbons C1, C2, C5, and C6 and the second band to the hydroxyl carbons C3 and C4. Of course, as none of the carbons are entirely equivalent, there will also be small splittings within each of these two main bands. The first absorption band is for all systems found in the energy region between 284 to 286 eV. The spectrum of NAd, which is depicted in the upper panel of Figure 2, shows a small splitting of the first band giving rise to a shoulder to the right of the main peak. This shoulder is associated with carbon C1 and the main peak with carbons C2, C5, and C6. For the protonated NAd+ (see Fig. 3), and even more pronounced so for L-DOPA+ (see Fig. 4), this splitting becomes larger and a left shoulder appears due to carbon C5. With the current choice of resolution (γ = 1000 cm−1), there is no observable splitting of the second band in the spectra of NAd and L-DOPA+, but, for NAd+, a splitting of about 0.1 eV can be seen (the peak due to C4 being lower in energy than that due to C3). In all cases, the second band is found in the energy region between 286 and 287 eV, and the average separation of the main bands is more or less constant and equal to some 1.7 eV.

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Figure 2. XAS and XNCD spectra of neutral noradrenaline at the near carbon K-edge. The spectra have been shifted by +9.6 eV. Atomic labeling of the XAS spectrum is made in agreement with Figure 1 and peak assignments of the XNCD spectrum are in accordance with Table 1. [Color figure can be viewed in the online issue, which is available at]

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thumbnail image

Figure 3. XAS and XNCD spectra of protonated noradrenaline at the near carbon K-edge. The spectra have been shifted by +9.6 eV. Atomic labeling of the XAS spectrum is made in agreement with Figure 1 and peak assignments of the XNCD spectrum are in accordance with Table 1. [Color figure can be viewed in the online issue, which is available at]

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thumbnail image

Figure 4. XAS and XNCD spectra of protonated L-DOPA at the near carbon K-edge. The spectra have been shifted by +9.6 eV. Atomic labeling of the XAS spectrum is made in agreement with Figure 1 and peak assignments of the XNCD spectrum are in accordance with Table 1. [Color figure can be viewed in the online issue, which is available at]

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If we turn focus to the ethanol-amine side chain (containing the chiral center), the absorption bands in NAd associated with carbons C7 and C8 fall in the energy region between 287.5 and 288.5 eV (the peak due to C8 appears as a left shoulder to that due to C7, see Fig. 2). In contrast to the phenyl part of the spectra, the ethanol-amine parts of the absorption spectra are strongly shifted by protonation. In the spectrum of NAd+ in Figure 3, we see that the peak associated with C8 appears almost as a shoulder to the peak of the hydroxyl carbons C3 and C4, and the peak associated with C7 is shifted toward lower energy by some 0.4 eV and is found around 287.6 eV. It is clear that the absorption in the ethanol-amine side chain can be quite well separated from that of the dihydroxy-phenyl by considering the polarization dependence. For instance, a substantial part of the intensity of the C7 peak at 287.6 eV in the spectrum of NAd+ is due absorption of radiation polarized in the z-direction, see the dashed curve in the upper panel of Figure 3. This z-polarized part of the absorption has a peak at 287.5 eV, which is due to a Rydberg transition from carbons C1, C2, and C6 and which thus is near degenerate with the valence state due to carbon C7.

XNCD Spectra

As illustrated in the work on the C84 fullerene,40 XNCD spectra may in comparison with XAS spectra provide a better resolution of the excited states due to the fact that the circular dichroism (but not the absorption) can take on positive as well as negative values. As seen in the absorption spectra, the first band is due to the four nonhydroxyl carbons of the chromophore and in this band three peaks can be discerned for NAd+ (see Fig. 3) and L-DOPA+ (see Fig. 4) but only two for NAd (see Fig. 2). In view of the XNCD spectra presented in the lower panel of the respective figures, it becomes clear that the transition due to carbon C5 has negative dichroism (Peak 0), the near degenerate transitions due to C2 and C6 have positive dichroism (Peak 1), and the transition due to C1 has negative dichroism (Peak 2). For NAd, the dichroism of the C5 transition is not seen because it overlaps with that of C2 and C6, but for the other two molecules it does appear.

In comparison with the first main absorption band, the assignment of the XNCD spectra of the second main absorption band is somewhat more complicated. Absorption peaks due to hydroxyl carbons C3 and C4 are near degenerate, but, from a detailed analysis of the response vector, we see that, as we pass through the band from lower to higher energies, the weight goes from a dominance of C4 to C3. In the XNCD spectrum for NAd in Figure 2, these two transitions are no more clearly separated. At about 286.6 eV, we note first a positive dichroism that is due to the C4 transition (Peak 4) and which then is followed by a negative dichroism due to the C3 transition (Peak 5). Next to the C3 transition (at about 287.0 eV), however, yet another state with positive dichroism is visible in the XNCD spectrum (Peak 6). In hindsight one can discern a very weak shoulder to the right of the corresponding absorption peak in the upper panel of Figure 2 and which is due to xy-polarized absorption. Having identified this transition, an assignment of it to carbon C8 can be made. In the second absorption band of NAd+, the contributions from C3 and C4 are slightly splitted. The C4 transition (occurring at lower energy) gives rise to positive dichroism in accordance with the situation for the neutral NAd (Peak 4 in Fig. 3). The XNCD signal from the C3 transition, however, is not observable in the spectrum, or possibly overlapping the C4 signal.

In the second absorption band of L-DOPA+, we again see both the positive dichroism of the C4 transition as well as the negative dichroism of the C3 transition (Peaks 4 and 5 in Fig. 4).

The assignments made up to this point for the XNCD spectra cover the valence transitions of the chromophore (which is common to the systems under investigation), where the remaining part of the spectra will be dominated by dichroism in the respective side chains. It is these low-lying transitions that lie at the heart of the present investigation and which address the issue of the dependence of the circular dichroism signal on the separation of chromophores and chiral centers. But it is also interesting to point out the dichroism of transitions belonging to the carbons of the chiral centers—for NAd the chiral center is C7 whereas for L-DOPA it is C8 (see Fig. 1). The XNCD responses at the transition frequencies of the chiral centers are, not surprisingly, strong in comparison with those associated with the chromophore transitions. For NAd, the dichroism of the C7 transition at around 288 eV is negative with an absolute value that is about twice as large as the dichroism of the strongest chromophore transition (the ratio is 2.3 see Table 1). The dichroism is a very sensitive probe of protonation as can been by a comparison of the spectrum for NAd to that of NAd+. For NAd+, the dichroism peak of the C7 transition is found around 287.7 eV and it is positive (see Fig. 3). There is an overall reduction in signal strength upon protonation, and the ratio of signal strengths between chiral center and strongest chromophore transitions is for NAd+ circa 1.8. We have deliberately used identical axes scalings in the respective plots for the systems under investigation to allow for direct visual comparisons of spectra. This choice means, however, that the XNCD response of the chiral center in L-DOPA+ exceeds the bounding box of the figure, see the signal at 288.3 eV in Figure 4. In this case, the ratio of signal intensities for the chiral center and the strongest chromophore amounts to 10.6.

Table I. Excitation energies (eV) and extinction coefficients Δε (l mol−1 cm−1) for the near K-edge XNCD spectra of NAd, NAd+, and L-DOPA+
  1. The peak numbering is made in accordance with the labels used in Figures 2, 3, and 4.

0  284.671−0.17284.639−0.40
10288.358−1.04  287.750−2.42
11    288.099−2.97
12    288.3509.75


  1. Top of page
  2. Abstract

The X-ray absorption and circular dichroism spectra of NAd (in neutral and protonated forms) and L-DOPA (in protonated form) have been determined with use of the CPP approach in conjunction with Kohn-Sham DFT. The main absorption peaks at the near carbon K-edge are due to the dihydroxy-phenyl ring, which therefore is referred to as the chromophore unit and which is spatially separated from the respective chiral centers. This work is aimed at comparing the XNCD spectra in view of the different chromophore-to-chiral center separations.

The parts of the absorption and dichroism spectra that are due to the chromophore show characteristic features that are common to all three systems. In the analysis of X-ray absorption spectra this is something well-known and due to the localized character of these electronic transitions, and one can at times interpret absorption spectra in terms of a building-block principle. But, for the studied X-ray circular dichroism spectra, the situation is in principle quite different. Because, even though the electronic transitions at play are the same as in the absorption spectrum, there is also a dependence on the coupling to the chiral center of the side chain, and the electronic structure of the side chain changes significantly on protonation and of course completely in going from NAd to L-DOPA.

The XNCD response is largest for the electronic transitions that can be assigned to the carbon of the chiral center. Even for NAd, where the amine is separated from the chiral center by a CH2-group, the act of protonation largely affects the dichroism of the chiral center. In fact, protonation will reverse the sign of the dichroism of the lowest electronic transition in the chiral center, changing it from being negative for the S-enantiomer of NAd to becoming positive for the corresponding enantiomer of NAd+.

When comparing the circular dichroism for the first electronic transition of the respective chiral centers with the strongest dichroism of the chromophore transitions, it is found that, for NAd and NAd+, the intensity ratio amounts to about two whereas, for L-DOPA+, the ratio amounts to about 10. Our interpretation of this difference in ratios is that it directly connects to the existence of a spacer CH2-unit in L-DOPA between the chromophore and the chiral center.


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  2. Abstract
  • 1
    Barron LD. Molecular light scattering and optical activity. Cambridge: Cambridge University Press; 2004.
  • 2
    Hirst JD,Collella K,Gilbert ATB. Electronic circular dichroism of proteins from first-principles calculations. J Phys Chem B 2003; 107: 1181311819.
  • 3
    Fukuyama T,Matsuo K,Gekko K. Vacuum-ultraviolet electronic circular dichroism of L-alanine in aqueous solution investigated by time-dependent density functional theory. J Phys Chem A 2005; 109: 69286933.
  • 4
    McCann DM,Stephens PJ. Determination of absolute configuration using density functional theory calculations of optical rotation and electronic circular dichroism: chiral alkenes. J Org Chem 2006; 71: 60746098.
  • 5
    BerovaN,NakanishiK,WoodyRW, editors. Circular dichroism: principles and applications. New York: Wiley-VCH, Inc.; 2004.
  • 6
    Nakagawa K,Kaneko F,Ohta Y,Tanaka M,Kitada T,Agui A,Fujii F,Yokoya A,Yagi-Watanabe K,Yamada T. Natural circular dichroism of amino acid films observed in soft X-ray and VUV region using polarizing undulator. J Electron Spectrosc Relat Phenom 2005; 144–147: 271273.
  • 7
    Goulon J,Goulon-Ginet C,Rogalev A,Gotte V,Malgrange C,Brouder C,Natoli CR. X-ray natural circular dichroism in a uniaxial gyrotropic single crystal of LiIO3. J Chem Phys 1998; 108: 63946403.
  • 8
    Alagna L,Prosperi T,Turchini S,Goulon J,Rogalev A,Goulon-Ginet C,Natoli CR,Peacock RD,Stewart B. X-ray natural circular dichroism. Phys Rev Lett 1998; 80: 47994802.
  • 9
    Stewart B,Peacock RD,Alagna L,Prosperi T,Turchini S,Goulon J,Rogalev A,Goulon-Ginet C. Circular dichroism at the edge: large X-ray natural CD in the 1s [RIGHTWARDS ARROW] 3d pre-edge feature of 2[Co(en)3Cl3]·NaCl6·H2O. J Am Chem Soc 1999; 121: 1023310234.
  • 10
    Carra P,Benoist R. X-ray natural circular dichroism. Phys Rev B 2000; 62: R7703R7706.
  • 11
    Peacock RD,Stewart B. Natural circular dichroism in X-ray spectroscopy. J Phys Chem B 2001; 105: 351360.
  • 12
    Petoral RMJr.,Uvdal K. XPS and NEXAFS study of tyrosine-terminated propanethiol assembled on gold. J Electron Spectrosc Relat Phenom 2003; 128: 159164.
  • 13
    Petoral RMJr.,Uvdal K. Structural investigation of 3,4-dihydroxyphenylalanine-terminated propanethiol assembled on gold. J Phys Chem B 2003; 107: 1339613402.
  • 14
    London F. Théorie quantique des courants interatomiques dans les combinaisons aromatiques. J Phys Radium 1937; 8: 397409.
  • 15
    Olsen J,Bak KL,Ruud K,Helgaker T,Jørgensen P. Orbital connections for perturbation-dependent basis-sets. Theor Chem Acc 1995; 90: 421439.
  • 16
    Helgaker T,Ruud K,Bak KL,Jørgensen P,Olsen J. Basis-set convergence and correlation-effects in vibrational circular-dichroism calculations using London atomic orbitals. Faraday Discuss 1994; 99: 165180.
  • 17
    Plashkevych O,Carravetta V,Vahtras O,Ågren H. Theoretical study of X-ray circular dichroism of amino acids. Chem Phys 1998; 232: 4962.
  • 18
    Carravetta V,Plachkevytch O,Vahtras O,Ågren H. Ordinary and rotatory intensities for X-ray absorption at the C-1s edge of organic chiral molecules, propylene oxide and trans-1,2-dimethylcyclopropane. Chem Phys Lett 1997; 275: 7078.
  • 19
    Norman P,Ruud K,Helgaker T. Density-functional theory calculations of optical rotatory dispersion in the nonresonant and resonant frequency regions. J Chem Phys 2004; 120: 50275035.
  • 20
    Jiemchooroj A,Norman P. Electronic circular dichroism spectra from the complex polarization propagator. J Chem Phys 2007; 126: 134102134108.
  • 21
    Jiemchooroj A,Ekström U,Norman P. Near-edge X-ray absorption and natural circular dichroism spectra of L-alanine: a theoretical study based on the complex polarization propagator approach. J Chem Phys 2007; 127: 165104165111.
  • 22
    Ekström U,Norman P. X-ray absorption spectra from the resonant-convergent first-order polarization propagator approach. Phys Rev A 2006; 74: 042722042728.
  • 23
    Ågren H,Carravetta V,Vahtras O,Petterson LGM. Direct, atomic orbital, static exchange calculations of photoabsorption spectra of large molecules and clusters. Chem Phys Lett 1994; 222: 7581.
  • 24
    Ågren H,Carravetta V,Vahtras O,Petterson LGM. Direct SCF direct static-exchange calculations of electronic spectra. Theor Chem Acc 1997; 97: 1440.
  • 25
    Ekström U,Norman P,Carravetta V. The relativistic four-component static-exchange approximation for core excitation processes in molecules. Phys Rev A 2006; 73: 022501022509.
  • 26
    Yanai T,Tew DP,Handy NC. A new hybrid exchange-correlation functional using the Coulomb-attenuating method. Chem Phys Lett 2004; 393: 5157.
  • 27
    Ekström U,Norman P,Carravetta V,Ågren H. Polarization propagator for X-ray spectra. Phys Rev Lett 2006; 97: 143001143004.
  • 28
    Boyd RW. Nonlinear optics, 2 ed. San Diego: Academic Press; 2003.
  • 29
    Norman P,Bishop DM,Jensen H,Aa J,Oddershede J. Near-resonant absorption in the time-dependent self-consistent field and multi-configurational self-consistent field approximations. J Chem Phys 2001; 115: 1032310334.
  • 30
    Norman P,Bishop DM,Jensen H,Aa J,Oddershede J. Nonlinear response theory with relaxation: the first hyperpolarizability. J Chem Phys 2005; 123: 194103194120.
  • 31
    Frisch MJ,Trucks GW,Schlegel HB,Scuseria GE,Robb MA,Cheeseman JR,Montgomery JAJr.,Vreven T,Kudin KN,Burant JC,Millam JM,Iyengar SS,Tomasi J,Barone V,Mennucci B,Cossi M,Scalmani G,Rega N,Petersson GA,Nakatsuji H,Hada M,Ehara M,Toyota K,Fukuda R,Hasegawa J,Ishida M,Nakajima T,Honda Y,Kitao O,Nakai H,Klene M,Li X,Knox JE,Hratchian HP,Cross JB,Adamo C,Jaramillo J,Gomperts R,Stratmann RE,Yazyev O,Austin AJ,Cammi R,Pomelli C,Ochterski JW,Ayala PY,Morokuma K,Voth GA,Salvador P,Dannenberg JJ,Zakrzewski VG,Dapprich S,Daniels AD,Strain MC,Farkas O,Malick DK,Rabuck AD,Raghavachari K,Foresman JB,Ortiz JV,Cui Q,Baboul AG,Clifford S,Cioslowski J,Stefanov BB,Liu G,Liashenko A,Piskorz P,Komaromi I,Martin RL,Fox DJ,Keith T,Al-Laham MA,Peng CY,Nanayakkara A,Challacombe M,Gill PMW,Johnson B,Chen W,Wong MW,Gonzalez C,Pople JA. Gaussian 03, Revision B05. Pittsburgh, PA: Gaussian, Inc.; 2003.
  • 32
    Becke AD. Density-functional thermochemistry. III. The role of exact exchange. J Chem Phys 1993; 98: 56485652.
  • 33
    Dunning TH,Jr. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J Chem Phys 1989; 90: 10071023.
  • 34
    Dalton, a molecular electronic structure program, release 2.0 (2005). Available at 2005.
  • 35
    Peach MJG,Helgaker T,Salek P,Keal TW,Lutnæs OB,Tozer DJ,Handy NC. Assessment of a Coulomb-attenuated exchange-correlation energy functional. Phys Chem Chem Phys 2006; 8: 558562.
  • 36
    Hitchcock AP,Fischer P,Gedanken A,Robin MB. Antibonding σ* valence MOs in the inner-shell and outer-shell spectra of the fluorobenzenes. J Phys Chem 1987; 91: 531540.
  • 37
    Baker CM,Grant GH. The effect of solvation on biomolecular conformation: 2-amino-1-phenylethanol. J Phys Chem B 2007; 111: 99409954.
  • 38
    van Mourik T. On the relative stability of two noradrenaline conformers. Chem Phys Lett 2005; 414: 364368.
  • 39
    Macleod NA,Simons JP. Protonated neurotransmitters in the gas-phase: clusters of 2-aminoethanol with phenol. Phys Chem Chem Phys 2003; 5: 11231129.
  • 40
    Jiemchooroj A,Norman P. X-ray absorption and natural circular dichroism spectra of C84: a theoretical study using the complex polarization propagator approach. J Chem Phys 2008; 128: 234304234307.