Chapter 6
Recent Advances in Magnetic Circular Dichroism Spectroscopy 1
Downloaded by UNIV OF PITTSBURGH on May 13, 2016 | http://pubs.acs.org Publication Date: June 9, 1998 | doi: 10.1021/bk-1998-0692.ch006
Elizabeth G. Pavel and Edward I. Solomon
Department of Chemistry, Stanford University, Stanford, CA 94305-5080
Magnetic circular dichroism (MCD) spectroscopy has proven to be a useful tool for investigating the electronic and magnetic properties of metal centers in bioinorganic systems. A brief background of this important technique is presented, followed by a discussion of the information available from observed excited-state transitions. Ground -stateelectronic structure information is obtained through variable -temperature, variable-field (VTVH) MCD data, which can be analyzed to extract ground-state sublevel splittings and g values. More recently, the methodology to analyze VTVH MCD data of non-Kramers S = 2 systems has been developed for both negative and positive zero-field splitting. MCD and VTVH MCD have proven particularly valuable for investigating high-spin (S = 2) non-heme Fe sites, which are EPR-silent and have very weak absorption bands. Application of this methodology to non-heme enzymes is presented to demo nstrate how this technique provides active site geometric and electronic structure information which can be used to probe oxygen and substrate reactivity and lend insight into catalytic mechanism. 2+
MCD Theory. Like circular dichroism (CD) spectroscopy, magnetic circular dichroism (MCD) spectroscopy measures the difference between left and right circularly polarized (LCP and RCP) extinction coefficients: Δ ε = e - e = M/cl, where AA is the differential absorption, c is the concentration, and / is the path length. Experimentally, MCD differs from CD by adding a longitudinal magnetic field. While CD activity is restricted to chiral centers, the origin of MCD activity lies in the universal phenomenon known as the Faraday effect, whereby optical activity is induced in all matter when a magnetic field is applied parallel to the direction of the light propagation, and all substances exhibit some form of MCD activity (7). Under the applied magnetic field, electronic levels split so that MCD probes the Zeeman splittings of both the ground and excited states and the selection rules for transitions between these states. Therefore, while CD spectroscopy probes spatial arrangements, MCD spectroscopy applied to bioinorganic systems provides both geometric and electronic structure information for a metal site. LCP
RCP
1
Corresponding author.
©1998 American Chemical Society Solomon and Hodgson; Spectroscopic Methods in Bioinorganic Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1998.
119
120 The standard selection rules for M C D transitions are AM = +1 for L C P and AM = -1 for RCP, where L is the orbital angular momentum. The formalism for M C D intensity using the Rigid Shift model (assuming that the band shape does not change with magnetic field) is given in equation 1 (2-4), L
L
where γ is a collection of spectroscopic constants, β is the Bohr magneton, k is Boltzmann's constant, Η is the applied magnetic field, Τ is the temperature, j(E) is a bandshape function (often approximated as a Gaussian), and df(E)/dE its first derivative. Within this formalism, the M C D intensity has three components, Ά , %, and C , which give rise to and C-terms (4). M C D J3-terms require orbital degeneracy in either the ground (A) or excited (J) state or in both. The quantum mechanical formalism (4) for an j^-term is presented in equation 2, where d is the degeneracy of the ground state, μ = L + 2S is the Zeeman operator for the magnetic field along the z-axis, and m+ = (m ±im )lΛ/2 is the electric dipole transition moment operator. χ
Downloaded by UNIV OF PITTSBURGH on May 13, 2016 | http://pubs.acs.org Publication Date: June 9, 1998 | doi: 10.1021/bk-1998-0692.ch006
0
A
ζ
z
Z
x
* l =^Σ((%μ)-(ΑΚ|Α))
y
{\(A\m_\jf-\(A\m \jf)
(2)
+
j^-terms are distinguished by their derivative bandshape and the fact that their intensity is independent of temperature. C-terms also require orbital degeneracy, but only in the ground state. The formalism for a C-term, shown in equation 3, is similar to that for an Λ-tcrm, except that the Zeeman coupling term for the excited state is now absent. Co =
~ ^Σ(Α\β \Α) ζ
2
(|(ΛΚμ)| - \(A\m \jf)
(3)
+
Note that because equations 2 and 3 contain squares of transition dipole moments, Άand C-terms both require two non-zero perpendicular transition moments. C-terms have absorption bandshapes and intensity which is inversely proportional to the temperature. This temperature dependence arises from differential population of the components of the Zeeman-split ground state: as the population of the lowest-energy component increases with decreasing temperature, the C-term intensity increases. Unlike Ά- and C-terms, M C D iB-terms have no degeneracy requirements and instead arise from field-induced mixing between states. The formalism for a iB-term is given in equation 4, where Κ is some state which mixes with the ground or excited state(s) in a magnetic field. *
=- £
*Σ{
Σ, ^
((A\m_\j)(K\m \A) +
( \m \j){K\m_\A)) A
+
+ Σ %^((Αμ_μ)(/κ|χ)-(Αμ μχ/μ_|ί:))} +
ΚΦΑ
J
iB-terms require that A-+J and A—>Κ (or J-*K) be perpendicularly polarized and that Κ and A (or Κ and J) mix with the Zeeman effect; therefore, iB-terms can occur for an A—>J transition which is polarized along a single direction. Because iB-term intensity
Solomon and Hodgson; Spectroscopic Methods in Bioinorganic Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1998.
121
is inversely proportional to the energy separation between the mixing states (AE^ or Δ Ε ) and most mixing states are at much higher energy, iB-terms have an absorption bandshape and their intensity is generally weak, temperature-independent, and linear with field. However, if AE^ is small and on the order of kT, there can be differential population between A and Κ which gives rise to a temperature-dependent ίΒ-term. Since the observed M C D spectrum can be a combination of Ά-, *B-, and C-terms, it is worth considering their relative intensities. The Ά : ίΒ : C intensity ratio is (1/T) : (1/ΔΕ) : (1/kT), where Γ is the transition full-width-at-half-height, AE is the energy separation between mixing states, and kT is Boltzmann's constant times the experimental temperature. For transition metal complexes, a typical bandwidth is Γ « 1000 cm" and a typical energy separation is AE ~ 10,000 cm for a temperatureindependent ίΒ-term. At room temperature, kT ~ 200 cm" so that Ά.Ώ.Ο ~ 10 : 1 : 50 and C-terms contribute most to the M C D intensity. At liquid helium temperatures, kT « 3 cm" and Ά : ίΒ : C « 10 : 1 : 3300. Thus at the low temperatures where much bioinorganic spectroscopy is performed, C-terms fully dominate the M C D spectrum. Μ
1
1
Downloaded by UNIV OF PITTSBURGH on May 13, 2016 | http://pubs.acs.org Publication Date: June 9, 1998 | doi: 10.1021/bk-1998-0692.ch006
1
Excited State Information. C-terms require ground-state orbital degeneracy, yet metal sites in biology often have not orbital, but rather spin degeneracy. The selection rules for M C D require that AM = ±1 and also that AM = 0. Therefore, with only spin degeneracy in the ground state, non-zero C-term intensity can only occur via spin-orbit coupling. (MCD selec tion rules are often given as AMj = ±1, taking into account this spin-orbit coupling mechanism.) When considering the excited state information content, it is convenient to divide metalloprotein sites into two categories: those with high symmetry, and thus possible excited-state orbital degeneracy, and those with low symmetry. High-symmetry metalloenzyme systems are those with approximate C , C , or 5 axes, such as heme and iron-sulfur centers. In these cases, it is possible to have orbitally degenerate excited states which are xy-polarized and thus satisfy the C-term condition of two non-zero perpendicular transition dipole moments. The orbital angular momentum of the excited state will spin-orbit couple with the spin degeneracy to split the excited state, as demonstrated in Figure 1 for the case of an S = 1/2 system with an M = 0 ground state and an M = ±1 excited state. As shown in Figure 1, there will be one C-term to the lower-energy component of the spinorbit-split excited state and a second C-term to the higher-energy component which is oppositely signed. The resulting M C D signal is a pseudo- J3.-term, composed of equal and opposite C-terms (4). The energy splitting between the two C-terms gives the in-state spin-orbit coupling (A), and the sign of the pseudo-^L-term, defined to be that of the higher-energy component, gives insight into the one-electron orbitals involved in the transition (5). Many metal sites in proteins are highly distorted and have low symmetry so that there is no orbital degeneracy in the excited states. In these cases, the M C D transitions are electric dipole allowed, but with the transition moment polarized in only one direction. The C-term intensity formalism can be rewritten in terms of the electric dipole transition moments, M . (/ = x, y, z), and the components of the g tensor, g ., as given in equation 5(6). L
S
3
L
4
4
L
{
C
0
- g (M M ) z
x
y
+ g (M M ) y
x
z
+ g (M M ) x
y
z
(5)
From equation 5, it is clear that two perpendicular transition moments are required for C-term intensity. With all transitions polarized in only one direction, the only way to obtain a second perpendicular polarization component is through spin-orbit coupling (7). Spin-orbit coupling between two excited states which are close in energy
Solomon and Hodgson; Spectroscopic Methods in Bioinorganic Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1998.
122 produces a pseudo-J3L-term, as described above. Spin-orbit coupling over all excited states will produce equal and opposite C-terms which sum to zero intensity. Non-zero C-term intensity summed over excited states for low symmetry sites must therefore arise from spin-orbit mixing into the ground state (8). Because spin-orbit coupling governs the C-term intensity, the magnitude of the spin-orbit coupling parameter (ζ) can provide insight into relative intensities. Spinorbit coupling is much stronger for metals (for example, ζ(Οι ) « 830 cm" , ζ ( Ρ β ) « 4 0 0 cm" , ζ(Ρε ) « 460 cm" ) than for biologically relevant ligands (ζ(Ο,Ν) « 60-70 cm" , £(S) « 325 cm" ). From these values, one expects that metalbased excited states will be more spin-orbit-mixed than ligand-based states; therefore d-»d transitions will exhibit a larger MCD intensity relative to the absorption intensity than will charge transfer transitions. The ratio of MCD to absorption intensities is often expressed as C /(D (equation 6), where (D is the dipole strength as defined in equation 7 and can be obtained from the experimental lowtemperature absorption spectrum. 2+
2+
1
3+
1
1
Downloaded by UNIV OF PITTSBURGH on May 13, 2016 | http://pubs.acs.org Publication Date: June 9, 1998 | doi: 10.1021/bk-1998-0692.ch006
0
C
_
0
