The measurement of natural CD7in the X-ray region (XNCD) has developed as a result of the availability of third generation synchrotron sources with insertion devices (helical undulators and Figure 7 The transient charge distributions for the xy!xy* transition of a twisted Mo2L4L04chromo- phore. On rotating the rear set of ligators through an angle of between 0and 45in the counterclockwise direction, the charge distribution is that of a left-handed helix. When the rotation is between 45and 90, the
transition gives rise to a right-handed helical charge displacement.
60
40
20
0
–40 –20
400 500 600 700 800
∆εand ε/102
λ (nm)
δ δ δ δ
xy
xy xy
x – y 2 2
*
Figure 6 The absorption (upper curve) and CD (lower curve) spectra of-[Mo2Cl4(R,R-dppb)2] in MeCN solution.
wigglers) capable of delivering reproducible, high brilliance, photon fluxes with controlled helicity. The X-ray region, with both element specific absorption and the established methods of obtaining structural information from EXAFS and XANES, is clearly an area where the extension of CD spectroscopy provides a new technique for the study of both molecular and crystal structural enantiomorphism. XNCD has been measured in the core excitations of first-row transition metal and lanthanide complexes as well as some main group materials.
2.5.7.2 Theoretical Background
The differences between the origins of CD in core–valence excitations and in valence–valence excitations will now be discussed. The Condon–Eyring sum rule implies that optical activity vanishes at very low and very high energies relative to the excitation energies of an electronic system. However, this does not mean that CD is necessarily small at the extremes of the electromagnetic spectrum. In particular, in the X-ray region the interaction with quadrupole transition moments is enhanced when the dimensions of the electronic displacement are comparable to the wavelength of the radiation (breakdown of the dipole approximation). This allows substantial CD to be derived from the E1–E2 mechanism. This situation pertains in the so-called near-edge absorption (XANES) where multiple scattering of the photoelectron by near neighbor atoms is largely responsible for the structure of the absorption profile, and to preedge excitations with effectively pure quadrupole character (e.g., 1s!3d, 2p!4f).
An important basic feature of X-ray absorption spectroscopy (XAS) is the core nature of the one-electron initial state. Consequently, the transition matrix elements involve integrals which are dominated by the region close to the photo-absorbing atom. The major part of an X-ray edge absorption is, therefore, atomic in nature and contains no chemical structural information. It is the analysis of the small modulations of the edge absorption due to the presence of neighboring atoms that provides structural information (EXAFS). Scattering theoretical methods are com- monly used to describe the propagation of the photo-electron in the neighborhood of the absorber. Conventional EXAFS analysis is applied to energies above100 eV from the ionization threshold where the de Broglie wavelength of the photo-electron is short in comparison to interatomic spacings and the effect of neighbor atoms is largely accounted for by single-scattering events. Below 100 eV (the XANES region), the photo-electron wavelength is comparable to the near-neighbor distances and multiple scattering processes are of significant importance. The analysis of multiple scattering is complicated but it can provide 3D structural information about the neighborhood of a photo-absorber. This contrasts with the single scattering interpretation of EXAFS which gives only a radial distribution function. It is for this last reason that multiple scattering analysis is essential to account for the effects of chirality in XAS.
Table 3 Wave numbers and dissymmetry factors for thexy!xyandxy!x2y2transitions of quadruple- bonded dimolybdenum complexes.
Compound e(xy!xy)
(103cm1) ("/")103 e(xy!x2y2)
(103cm1) ("/")103 Twist
angle() References
-[Mo2Cl4(S,S-dppb)2] 13.7 5.8 21.1 þ7.3 23 48
-[Mo2Br4(S,S-dppb)2] 13.2 3.2 20.7 þ8.5 22 48
-[Mo2Cl4(R-dppp)2] 13.3 þ7.5 21.7 6.7045 48
-[Mo2Br4(R-dppp)2] 12.8 þ3.0 20.8 4.5 045 48
-[Mo2Cl4(R-phenphos)2] 13.2 þ6.0 21.5 6.2 0–45 49
-[Mo2Cl4(S,S-skewphos)2] 13.9 10.8 20.8 þ3.7045 49
-[Mo2Cl4(S-chairphos)2] 14.3 2.0 21.3 þ1.1 0–45 49
[Mo2Cl4(R,R-dach)2] 18.0 þve 22.2 ve 50
-[Mo2Cl4(R,R-DIOP)2] þve 78 46
-[Mo2Cl4(R,R-DIOP)2] ve þ84 46
-[Mo2(MeCO2)2
(S,S-dppb)2]
19.2 þ0.35 25.6 0.32 12 51
-[Mo2Cl4(R-pn)2] 21.0 9.1 27.8 þ1745–90 47
dppb=2,3-bis(diphenylphosphino)butane; dppp=1,2-bis(diphenylphosphino)propane; phenphos=1-phenyl-1,2-bis(diphenylphosphino) ethane; skewphos=2,4-bis(diphenylphosphino)pentane; chairphos=1,3-bis(diphenylphosphino)butane; dach=1,2-diaminocyclohexane;
ve=negative;þve=positive.
76 Chiral Molecules Spectroscopy
The optical activity invalenceexcitations of chiral metal complexes has been effectively treated using the model of an achiral chromophore (metal ion) in a chiral environment (ligands) and this model appears also appropriate for XAS in view of the core nature of the initial orbital state. The zero-order electric and magnetic transition moments arise from different transitions and must be mixed by some chiral environmental potential (V*). Considering the case of a lanthanide ion, and taking the electric dipole transitions for the L2,3 edge as 2p!d, a first-order perturbation expression for the rotational strength looks like:
RImh2pjmjfdihfdjVjfp0ihfp0jmj2pi ð10ị The problem is with the magnetic dipole transition moment,hp0|m|2pi, which vanishes in the zeroth approximation. The magnetic dipole selection rule |l|=0, allows the transition from 2p to thenpand continuum"pstates but, sincemis a pure angular operator it cannot connect states which are radially orthogonal. This results in the |n|=0 selection rule for bound states and also clearly forbids 2p!"p except via core-hole relaxation.
The E1–M1 mechanism is even more restrictive for K-edge or L1-edge spectra. Magnetic dipole transitions are forbidden from s-orbitals so the only possible source of magnetic dipole intensity involves 1s–2p-orbital mixing in addition to core-hole relaxation. This may account for XNCD in light atom systems but is unlikely to be significant for transition metals or lanthanides.
In all XNCD measured so far, it has been found that the predominant contribution to X-ray optical activity is from the E1–E2 mechanism. The reason for this is that the E1–M1 contribution depends on the possibility of a significant magnetic dipole transition probability and this is strongly forbidden in core excitations due to the radial orthogonality of core with valence and continuum states. This orthogonality is partially removed due to relaxation of the core-hole excited state, but this is not very effective and in the cases studied so far there is no definite evidence of pseudoscalar XNCD.
The appearance of E1–E2 optical activity is restricted to those symmetry groups in which the components of a second rank odd-parity tensor are totally symmetric.5 As pointed out by Jerphagnon and Chemla,59optical activity may be observed even in nonenantiomorphous systems due to the nonpseudoscalar parts of the optical activity tensor—only enantiomorphous crystal classes having a nonvanishing pseudoscalar part.
Table 4 shows the occurrence of the pseudoscalar, vector, and second rank odd-parity (pseudodeviator) parts of the optical activity tensor in the noncentrosymmetric crystallographic point groups.
2.5.7.3Measurements
XNCD spectra were first measured for uniaxial single crystals of Na3Nd(digly)32NaBF46H2O (digly=2,20-oxydiacetate) (Nd L2, L3 edges)5 (Figure 8) and {Co(en)3Cl3}2NaCl6H2O (Co K edge)6 (Figure 9) where the lanthanide and the transition metal occupy chiral coordination sites, and for the ionic crystal LiIO3(IL1,L2,L3edges)60in which the achiral iodate anions are helically arranged. The XANES part of the XNCD shows CD corresponding to chiral multiple scattering paths of the photoelectron. In addition, both the NdIII(Figure 8) and CoIII(Figure 9)
Table 4 Irreducible components of the optical activity tensor for the noncentrosymmetric crystallographic point groups.
Crystal class Pseudoscalar Vector Pseudodeviator
O,T 3 0 0
D3,D4,D6 3 0 3
C1,C2,C3,C4,C6 3 3 3
D2 3 0 3
S4,D2d 0 0 3
Cs,C2v 0 3 3
C3v,C4v,C6v 0 3 0
Td,D3h,C3h 0 0 0
compounds show quadrupole-allowed preedge features (2p!4f for Nd and 1s!3d for Co) which have exceptionally large Kuhn dissymmetry factors. The theory of XNCD shows that the CD is due to the interference between allowed electric dipole and electric quadrupole transition moments (E1–E2 mechanism).
Subsequent to the first measurements, KTiOPO4, a gyrotropic crystal of the nonenantio- morphous mm2 crystal class, has been studied61 and the predictions of Jerphagnon and Chemla59 have been confirmed. Tellurium L1-edge XNCD61 in-TeO2 is dominated by chiral multiple scattering paths of the type TeO1O2Te involving the nearest oxygen neigh- bors. A range of trigonal complexes of the first transition series have been studied in uniaxial crystals, with measurements on biaxial faces confirming the expectations of the E1–E2 mechanism.62