A Magnetic and Electronic Circular Dichroism Study of Azurin

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A Magnetic and Electronic Circular Dichroism Study of Azurin, Plastocyanin, Cucumber Basic Protein, and Nitrite Reductase Based on Time-Dependent Density Functional Theory Calculations Hristina R. Zhekova, Michael Seth, and Tom Ziegler* Department of Chemistry, UniVersity of Calgary, 2500 UniVersity DriVe NW, Calgary, Alberta, Canada, T2N 1N4 ReceiVed: February 13, 2010; ReVised Manuscript ReceiVed: April 15, 2010

The excitation, circular dichroism, magnetic circular dichroism (MCD) and electron paramagnetic resonance (EPR) spectra of small models of four blue copper proteins are simulated on the TDDFT/BP86 level. X-Ray diffraction geometries are used for the modeling of the blue copper sites in azurin, plastocyanin, cucumber basic protein, and nitrite reductase. Comparison with experimental data reveals that the calculations reproduce most of the qualitative trends of the observed experimental spectra with some discrepancies in the orbital decompositions and the values of the excitation energies, the g| components of the g tensor, and the components of the A tensor. These discrepancies are discussed relative to deficiencies in the time-dependent density functional theory (TDDFT) methodology, as opposed to previous studies which address them as a result of insufficient model size or poor performance of the BP86 functional. In addition, attempts are made to elucidate the correlation between the MCD and EPR signals. I. Introduction Blue copper proteins are metalloenzymes whose biological role is to carry out rapid short and long-range electron transfers.1-7 Azurin participates in the multistep denitrification process of some bacteria as an electron donor to cytochrome c551 and heme-containing nitrite reductase.8,9 Plastocyanin acts as an electron carrier between cytochrome f and P700+ during plant and algae photosynthesis.9 Cucumber basic protein is a member of the phytocyanin family. Its biological function is still unclear.9 Copper-containg nitrite reductase is involved in the bacterial denitrification processes and features intramolecular electron transfer from a blue copper T1 site to an adjacent T2 site where nitrite is reduced to nitric oxide.8 The structure of the blue copper centers has been resolved by X-ray diffraction.1,10-13 In most of the cases, the copper atom is coordinated with 4 ligands in a deformed tetrahedral geometry, although coordination with 5 ligands is also known.14 The four title compounds of the present studysplastocyanin (Pc), azurin (AZA), cucumber basic protein (CBP, also known as plantacyanin), and nitrite reductase (NiR)sfeature the same ligand set (Cys, 2His, Met) (Figure 1). However, the effect of the protein backbone on the active center is different for each of them and results in perturbations of the structures from trigonal pyramidal to tetrahedral in going from AZA and Pc to CBP and NiR. Azurin has an additional fifth ligand (weakly bound Gly) and adopts originally a trigonal bipyramidal configuration. The Gly ligand is neglected in the present study (see below), and the model used has a trigonal pyramidal geometry. In the last two decades the blue copper proteins have been studied extensively with a large number of spectral techniques.1-7,15-17 The geometry and electronic structure of their active sites have been examined with absorption, polarized absorption, circular dichroism, and resonance Raman spectroscopy. X-ray absorption spectroscopy has been used to examine the electronic structure of the ground state of the blue copper proteins. Various studies * Corresponding author: E-mail: [email protected]. Phone: 1-403-2205368. Fax: 1-403-289-9488.

Figure 1. Structural model of the blue copper center used in the present study.

based on electron paramagnetic resonance (EPR) and magnetic circular dichroism (MCD) techniques were conducted to probe the paramagnetic copper sites in the oxidized forms (copper center with a 3d9 electron configuration). In addition, the blue copper centers have been subject to numerous theoretical studies. The chosen models vary in size, complexity, and symmetry.1-7,18-24 The SCF-XR-SW method has been applied to orbital and energy level analysis on models with up to 33 atoms.1-7 Modern DFT with pure and hybrid functionals have been used for geometry optimization,18-24 excitation spectra simulation1-7 and EPR parameters calculations25 on models of 33 or more atoms. Methods based on classical mechanics approaches, such as QM/ MM and MD, have been employed as well to simulate the influence of the remainder of the protein.26-45 CASSCF and CASPT2 studies have been performed for the estimation of different structural parameters19-24 and their effect on the excitation energies of the systems.22-24 Through theory and experiment, insight has been gained on the influence of the ligand set,1-7,19-21,25 the protein backbone,1-7,18-21,28,29,33-35,41,43 and the oxidation state3,18-21 on the properties of the blue copper active sites. Some biologically important characteristics of these compounds (i.e., reduction potentials, reorganization energy, and electron transfer rates) have been evaluated as well.3,18-21,30-32,36-39 Magnetic circular dichroism spectroscopy has been used extensively as an experimental technique to probe the electronic

10.1021/jp101372s  2010 American Chemical Society Published on Web 05/07/2010

TDDFT Analysis of Four Blue Copper Proteins

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structure of the blue copper proteins in their oxidized form. MCD is an important supplement to absorption spectroscopy in experimental studies of metallo-enzymes as it offers additional information about the involvement of d-orbitals in the electronic transitions for these systems. The interpretation of MCD spectra has to some degree been hampered by the lack of methods that could be used to predict from first principle the spectroscopic parameters associated with MCD. This situation has just recently changed by the introduction of methods that can calculate the A,46-48 B,47-52 and C term48,53,54 parameters of MCD theory. We shall here make use of the method developed by Seth et al. and implemented in the ADF program.54,55 This method has already been used for the copper proteins in a preliminary study on the C term parameters of Pc.56 We shall in addition explore the relation between the MCD and EPR spectra of the title compounds. A section of this paper will be dedicated to the analysis of the simulated CD spectra of the aforementioned four models, as no previous theoretical CD studies were found for the blue copper systems. II. Computational Details 1. MCD Theory. MCD is a technique that monitors circular dichroism induced by an external magnetic field.57 It is universal for all substances, including nonchiral ones. It can be observed when circularly polarized light is propagated through a sample positioned within a strong magnetic field parallel to the direction of propagation. In order for the MCD spectrum to be detected, an absorbance difference between left circularly polarized and right circularly polarized light is required. For systems with degenerate ground and/or excited states, the external magnetic field can give rise to a Zeeman splitting that introduces a derivative-shaped A term in the MCD spectra. Furthermore, the magnetic field mixes in all molecules the zerofield wave functions of the ground and excited states, which causes the appearance of the B terms. Finally, temperature dependent C terms can be observed in systems with a spatially degenerate ground state (due to differences in the population of the sublevels caused by the Zeeman splitting) and in systems with a spin degenerate ground state (due to sublevel population differences and spin-orbit coupling). The latter is of great importance for the low-symmetry paramagnetic blue copper sites and yields at low temperature prominent bands that dominate their MCD spectra. We will in the current study simulate C terms for the four blue copper title sites based on TDDFT. Our theoretical results will further be compared to experimental spectra. The fundamental MCD equation used to fit an MCD band is:57

MCD(pω) ) γpωB

∑ J

[( AJ

)

)

1

√πWJ

e-[(ωJ-ω)/WJ]

2

(2)

WJ is an experimental line-width parameter. For better reproduction of the experimental bandwidth, we have chosen the value WJ ) (0.016(pωJ))/(ln 2), where the excitation energy is in atomic units. The same line shape function has been used in the simulation of the theoretical absorption and electronic circular dichroism spectra. The parameters AJ, BJ, and CJ correspond to the A, B, and C terms in MCD spectroscopy. They can be evaluated theoretically based on the TDDFT formalism as implemented in the latest version of the ADF program package.46,49,54 The current study will concentrate on the C terms originating from spin-orbit coupling. The parameter CJ, which is responsible for this MCD activity (and associated with the transition from the ground state A to the excited state J) can be expressed with the following equation:

CJ ) -

4i 3|G|

∑ M2 ∑ εRβγ〈A|MR|J〉(1)γ〈J|Mβ|A〉(0) Rβγ

M

(3) where G is the degeneracy of the field free ground state, M is the spin quantum number, εRβγ is the three-dimensional LeviCivita symbol, and MR and Mβ are the Cartesian components of the electric dipole moment operator. Further, the superscript (1) indicates the integral perturbed to first order in spin-orbit coupling, whereas (0) corresponds to the unperturbed integral. In the present calculations G is 2 (a doublet ground state with one unpaired electron). The spin-orbit coupling is introduced as a first order perturbation to the transition dipole in a specific direction. The perturbed integral can be detailed further as:

〈A|MR |J〉(1)γ ) 〈A(1)γ |MR |J(0)〉 + 〈A(0) |MR |J(1)γ〉

(4)

The contributions on the right-hand side of eq 4 correspond to the spin-orbit perturbation to the ground state A and the excited state J, respectively, and can be expressed in terms of a sum over states as:

〈A|MR |J〉(1)γ )

∑

〈K(0) |MR |J(0)〉

K′*A

∑ 〈A(0)|MR|K(0)〉

K*J

γ 〈K(0) |HSO |A(0)〉 + EK - EA

γ 〈J(0) |HSO |K(0)〉 EK - EJ

(5)

-∂fJ(pω - pωJ) + ∂pω CJ BJ + f (pω - pωJ) kT J

(

fJ(ω) )

]

A simplified version of the combined equations 4 and 5 is:

(1)

where γ is a collection of constants, k is the Boltzmann constant, T is the temperature in K, B is the strength of the magnetic field, pω and pωJ are the energies of the incident light and the excitation from the ground state A to an excited state J, and fJ(pω - pωJ) is a line shape function. The line shape function for the present study is a normalized Gaussian function:

CJ ) CGJ + CEJ

(6)

Here CGJ represents the contribution to the total C term CJ originating from mixing due to the spin-orbit coupling between the ground state A and excited states K′ (GS-ES coupling). CEJ is the complementary contribution from mixing between different excited states (ES-ES coupling) K with J. Equation 5 is a sum over states (SOS) expression by nature and allows for a good qualitative description of the effects in

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question. It becomes exact if the summation is over all excitations. However, more accurate results can be obtained by making use of response theory without summing over all excited states (direct method). Both the direct and the SOS formalism are available in ADF. The numerical data shown in Tables 6-9 are obtained mainly from the direct calculations. However, we shall use the SOS formulation in the qualitative analysis. A fourth parameter can be defined and used for comparison with the experimental results. This is the dipole strength DJ:

1 DJ ) 3|A|

∑ |〈A|MR|J〉|2

(7)

R

It is related to the oscillator strength and can be extracted from the absorption spectra. The ratio CJ/DJ is independent of the intensity of the transitions between states A and J and depends only on how strongly the spin-orbit coupling perturbs the two states. Thus, it serves as a tool for the assignment of the MCD bands in terms of ligand field bands (CJ/DJ ∼ 0.1; large spin-orbit coupling) and charge transfer bands (CJ/DJ ∼ 0.01; small spin-orbit coupling). It can be evaluated theoretically with the MCD code implemented in ADF. 2. EPR Theory. EPR is a technique that monitors the absorption of electromagnetic radiation by paramagnetic systems positioned within a static magnetic field.58 The static magnetic field induces a Zeeman splitting of the spin degenerate levels of the samples. In complex systems with more than one unpaired electron and one or more magnetically active nuclei, there are additional interactions that further complicate the energy spectrum. The energy levels for such species can be found as eigenvalues of their spin-Hamiltonian operators. For a system with one magnetically active nucleus and one unpaired electron ˆ (like the blue copper centers) the spin Hamiltonian operator H 58 may be written as:

ˆ ) µBB · g · S - µNB · gN · IN + S · AN · IN H

(8)

where µB and µN are the electronic and nuclear Bohr magnetons, respectively; B is the static external magnetic field; g and gN are the electronic and nuclear g tensors, respectively; S is the electronic spin angular momentum operator; IN is the nuclear spin angular momentum operator; and AN is the hyperfine coupling tensor. The first two terms of eq 8 correspond to the Zeeman splitting of the spin degenerate electronic and nuclear levels due to the static external magnetic field. The last term defines the hyperfine coupling interaction between the electron and nuclear spins. A transition between two levels is possible if the sample is subjected to an oscillating magnetic field, perpendicular to the static magnetic field. The resonance condition for such transition is:

∆E ) hν0

(9)

where ∆E is the energy difference between the two levels and ν0 is the frequency of the oscillating magnetic field. The g tensor, g, from eq 8 is often expressed as:59,60

g ) ge1 + ∆g

(10)

where ∆g is the g-shift tensor, 1 is a unit tensor, and ge is the g factor of an unpaired electron (ge ) 2.0023). The tensor ∆g

is the deviation of g from the free electron value unit tensor ge due to the molecular environment. It accounts for the spin-orbit coupling effects in the systems and can be evaluated from second order perturbation theory:

∆g ∝

〈J|H |A〉

∑ 〈A|L|J〉 EJ -SOEA

(11)

J

Here A and J are the ground and excited states, respectively (with corresponding energies EA and EJ), which are coupled through the spin-orbit coupling operator HSO. L is the orbital momentum operator. Equation 11 is similar to the MCD expression for the C terms (eq 5). The similarity suggests a correlation between the EPR and MCD signals. This correlation has been observed experimentally,61-63 however it is not clear how general it is since the CJ term, in addition to depending on the spin-orbit mixing of ground and excited states (CGJ ) as ∆g does, also depends on the mixing with excited states K through J (CEJ ). The latter dependence is not found for ∆g. The A tensor, AN, from eq 8 is a symmetric matrix that represents the electron-nucleus interactions. It can be divided into an isotropic and an anisotropic part. The isotropic part of the A tensor originates from the unpaired spin density (|ψn(0)|2) at the nucleus and is the result of the spin polarization of the core s-orbitals. It is also known as the contact or Fermi term:58

Acontact ) Acontact ) Acontact ∝ geµBgNµN |ψn(0)| 2 1 2 3

(12) The anisotropic contribution includes the interactions between the nuclear magnetic moment and the spin (dipolar term) or the orbital angular momentum (pseudocontact term) of the electron. In liquid solution the dipolar term averages out to zero, and the isotropic hyperfine coupling constant can be written as:

Aiso )

A1 + A2 + A3 3

(13)

where A1, A2, and A3 components include all of the aforementioned interactions. 3. Computational Parameters. Experimental X-ray diffraction geometries are used throughout.10-13 All calculations employed a spin-unrestricted formalism64 and were performed with TDDFT65,66 as implemented in a modified version of the ADF 2008 program package55,67,68 and the BP86 functional.69-71 The enzyme models were truncated to 18 heavy nuclei with 21 hydrogen atoms added for valence saturation (39 atoms overall). The Gly ligand of Azurin was omitted for comparison with the other three systems. Previous studies with different functionals prove that the effect of the presence of the Gly ligand on the results is insignificant at the BP86 level.25 The positions of the hydrogen atoms were subsequently optimized with a TZ2P basis set, and the heavy nuclei were kept frozen in the crystal configuration. All parameters, associated with excitation, CD, and MCD spectra are calculated within the TDDFT formalism. The dipole-length representation was adopted for the calculations of the oscillator strength and rotatory strength. A scalar ZORA72 approximation was employed for the relativistic effects included in the computation of the rotatory strengths of the CD spectra73,74 and the simulation of the MCD C terms53 at 4.5 K temperature and 4 T magnetic field strength.5,6 The C terms of the lowest



TABLE 1: X-ray Structural Parameters for the Four Blue Copper Centers bonds (Å)

angles (°)

Cu-N1 Cu-N2 Cu-Scys Cu-Smet SmetCuScys SmetCuN1 SmetCuN2 ScysCuN1 ScysCuN2 N1CuN2 SmetCuScysCcys

AZA

Pc

CBP

NiR

2.008 2.075 2.120 3.119 109.5 93.4 78.7 121.6 135.3 100.9 1.8

2.059 1.906 2.067 2.822 109.9 100.6 88.5 121 131.7 97.2 3.2

1.951 1.931 2.155 2.606 110.6 112.1 83.0 110.4 138.1 99.3 6.3

2.063 1.996 2.153 2.550 105.5 131.7 86.6 104.2 136.5 97.0 18.1

20 excitations were calculated with the lowest 50 excitations involved in the qualitative SOS analysis. A TZ2P basis set with a 1s2s2p frozen core was used for Cu, and a DZP basis with a 1s frozen core was adopted for N and C. A 1s2s2p frozen core was employed for S. DZ with no frozen core was used for the hydrogen atoms. The g tensors were obtained with the EPR program75 incorporated into ADF 2008. The A tensor calculations were performed with the ESR module76 of ADF2008 with a full-electron TZ2P basis set (no core formalism). The relativistic effects for the g tensors were based on the Pauli scalar approximation,77-79 and the scalar ZORA approximation was used for the A tensor calculations. Additional MCD and EPR test calculations with a TZ2P basis set for all atoms were carried out as well. The results obtained with TZ2P were virtually identical to those obtained with the smaller basis sets. COSMO80 solvent calculations with ) 4.0 and the smaller basis sets listed above demonstrated that the polarizing effects of the protein environment are negligible in MCD calculations. Hence, the analysis in the present study is based on the results from calculations in vacuum. The computational parameters (basis set) chosen here should also be feasible for comparison with future calculations on bigger and more complicated copper systems. III. Results and Discussion Table 1 and Figure 2 display the variation in the coordination geometry of the identical ligands around copper in the four systems. The geometry perturbation away from a trigonal pyramidal structure (TPS) increases in the order AZA, Pc, CBP, NiR, as explained below. The most pronounced change is the shortening of the long axial Cu-Smet bond. The copper atom is pulled toward the Smet atom and away from the N1N2Scys plane, and the geometry changes from trigonal pyramid-like to a tetrahedron-like conformation through the series AZA, Pc, CBP, and NiR. Another common trend is the rotation of the methionine group with respect to the cysteine residue, marked with the

Figure 2. Perturbation of the blue copper center: side view (up) and view along the Cu-Scys bond (down).

increase of the SmetCuScysCcys dihedral angle. As a consequence, the SmetCuN1 valence angle increases and the methionine group is tilted toward the second histidine residue (represented by N2 on Figure 2), which further increases the deformation of the copper center away from a TPS geometry. The orbitals involved in the excitations between 5000 and 30 000 cm-1 are shown on Figures S1-S4 (see the Supporting Information) for AZA, Pc, CBP, and NiR, respectively. The corresponding energy diagrams are presented in Figure 3. All four systems have a doublet ground state with an R-electron in the singly occupied molecular orbital (SOMO). All spin-allowed excitations involve β-electron transitions from occupied orbitals to the singly unoccupied molecular orbital (SUMO) of dx2-y2 character on copper. Figure 3 displays occupied levels of the same β-spin as the SUMO. Some transitions from occupied levels of the opposite R-spin to the R-virtual orbitals take place close to and above 30 000 cm-1. They have low intensity and will not be discussed here. The molecular orbitals displayed on Figures S1-S4 have been analyzed previously by Solomon et al.,1-7 and we label them here in the same way according to their composition. We note that such a labeling, although useful, is qualitative. A better picture can be obtained by inspecting the figures. All orbitals are linear combinations of metal and ligand contributions. The SUMO is a Cudx2-y2 orbital with a large contribution from the cysteine residue. It is π-antibonding in nature and features an overlap of the metal dx2-y2 orbital with one of the sulfur lone-pair p orbitals. It is labeled Cudx2-y2-Cysπ. The shorter Cu-Smet bond in CBP and NiR introduces a weak σ-antibonding interaction between dx2-y2 and a p orbital on the Smet atoms. This leads to a destabilization of the SUMO and as a result Cudx2-y2-Cysπ has a higher energy in CBP and NiR compared to Pc (in contradiction to the observations of Solomon et al.5,6). The highest occupied orbitals of β-spin are of ligand origin with a considerable copper participation and will be referred to as the ligand-type orbitals. They might be regarded as the antibonding components of the copper-ligand orbital pairs. The orbitals from the next set are characterized by strong bonding ligand-metal interactions, which are responsible for their stabilization relative to the ligand type orbitals. We shall refer to them as metal-type orbitals. The distinction made here between ligand-metal antibonding ligand-type orbitals and metal-type metal-ligand bonding orbitals is adopted to be consistent with the nomenclature used in previous studies.3-6 In reality it might be more appropriate to talk simply about metal-ligand antibonding and bonding orbitals (as some of the orbital labels suggest) where relative predominance of ligand and metal contributions might depend on the computational method. Also, the orbitals illustrated in Supporting Information Figures S1-S4 are optimized with respect to the ground state as they must since TDDFT is a response theory. Thus, their use in characterizing excited states requires some care, as discussed later. 1. Excitation Spectra. The experimental excitation spectra of the blue copper proteins are characterized by an intense maximum at about 600 nm (hence the blue color of the compounds). In CBP and NiR where the geometry of the classic blue copper center is distorted substantially away from TPS, the most intense band is blue-shifted and that results in a color change from blue to green. Superimposed experimental and calculated excitation spectra for the four systems can be seen in Figure 4, where the intense experimental band is labeled II. The simulated spectra show a good qualitative agreement with

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Figure 3. Order of the calculated energy levels of the four systems (dotted line marks the SUMO).

experiment although all calculated bands especially for AZA and Pc are strongly blue-shifted with respect to the experimental ones, including II. This large shift in the position has been found previously in calculations with similar functionals.2-7 Tables 2-5 give detailed information about the excitations responsible for the simulated excitation signals. As mentioned above, the majority of the occupied metal type orbitals are of lower energies than the occupied frontier ligand type orbitals. We find as a consequence the ligand-metal charge transfer (LMCT) excitations at lower frequencies than the nominal d-to-d transitions. The transition labeled as number 1 takes place at around 5000 cm-1 and is due to an electron promotion from the Met b1 orbitals to the SUMO. It gives rise to the LMCT band L1. Its intensity is fairly low for the classic blue copper sites AZA and Pc, but increases for CBP and NiR. A more intense transition involving the Cysσ + Cudxy orbitals (number 2) can be seen in all four simulated spectra as band L2. It is shifted to shorter wavelengths by going from Pc to NiR. The next few spectral lines involve the two histidine residues and are calculated to be in the range from 14 400 to 16 200 cm-1. Transition No. 3 is a linear combination of one-electron excitations between Hisπ1 (or Hisπ1′) and the SUMO and Cysπ + Cudx2-y2 and the SUMO. Transition No. 4 follows a similar trend, with the addition of some metal to metal exitations mixed with the ligand to metal ones. The band made up of transitions 3 and 4 is labeled L3. A new transition (labeled as x) can be observed close to L3 in the Pc and CBP spectra. It is due to “pure” electron transfer between Hisπ1′ and the SUMO. Hisπ1 as well as some metal d-orbitals with z components are responsible for the last ligand to metal transition (y) in the spectra of AZA and NiR. The overall trend in the aforemen-

tioned LMCT transitions is a moderate shift to the high energy part of the spectra and a slight increase in the intensity as we go through the sites AZA, Pc, CBP, and NiR. We suggest that L1 to L3 in part are responsible for the experimental band III. We note that III with this assignment, in agreement with experiment,5,6 is predicted to increase in intensity from AZA and Pc to CBP and NiR. The first transition from a bonding ligand-metal combination to the SUMO appears at about 17 000 cm-1 (band M1). For AZA, CBP and NiR this excitation involve the dxz and dyz metal orbitals (No. 5). Pc has a similar transition at a higher energy. Transition 5 has in all cases a low calculated intensity. Transition No. 6 occurs between Cudz2 and the SUMO for Pc, CBP, and NiR; and its corresponding band is marked M2 in Figure 4 (B, C, and D). In the case of AZA, the mixing between the d-orbitals with z components yields two separate excitations (q and r at 17 000 and 21 570 cm-1, respectively). The second has the largest oscillation strength (f) in the AZA spectrum and gives rise to band M3, whereas q is part of band M2. We assign M3 in AZA to the experimental band II. Similar mixing of orbital excitations including a Cysπ + Cudx2-y2 excitation is present in transition z (band M3 for Pc, CBP, and NiR). It is responsible for the strongest absorption band in the Pc and CBP spectra and the second most intense ligand field band in the spectrum of NiR. We again assign M3 for these systems to the experimental band II. The most intense band in the NiR spectrum originate from a Cudxy + Cysσ to the SUMO transition (No. 7 at around 23 000 cm-1). For the other three systems excitation 7 has considerable yet lower intensity than r and z. Transition 7 gives rise to band M4 in all four systems, and we assign it in all cases to the experimental band I. In the CBP site its intensity is of the same order as that of excitation z.



Figure 4. Superimposed theoretical and experimental3-6 excitation spectra of AZA (A), Pc (B), CBP (C), and NiR (D).

The composition of the frontier orbitals obtained here with TDDFT (BP86) affords metal-ligand antibonding combinations that are predominantly ligand in character whereas the corresponding bonding combinations are dominated by metal contributions. In the CASSCF calculations the antibonding orbitals are mostly metal centered, whereas the bonding orbitals are of ligand character.22-24 The CASSCF results are in line with the traditional bonding picture for metal-ligand interactions. The difference might in part be due to the fact that the CASSCF method is variational with orbitals optimized for the excited states,81,82 whereas TDDFT is a response theory with orbitals optimized with respect to the ground state.65,66,83-85 We hope in the future to make use of orbitals optimized with respect to excited states rather than the ground state.83 Solomon et al. have used the BP86 functional employed here as well in an earlier study where they found orbital compositions similar to ours.3 However, they modified the nuclear potential on copper in order to get orbitals with a composition more in line with CASSCF. We shall not adopt their procedure here. Keeping in mind possible errors in the composition of our orbitals, we shall next study the MCD, CD, and EPR spectra of our title compounds. 2. MCD Spectra. Tables 6-9 give detailed information about the C terms responsible for the simulated MCD bands. Here, CJ is the overall C term arising from a certain excitation J. CGJ gives the rotationally averaged contribution to CJ from the coupling of the ground state with different excited states

K′. Similarly, CEJ is the averaged contribution to CJ due to the coupling of other excited states (K) with J. The analysis is straightforward and informative especially for the excited states, which can be approximated by a single one-electron excitation. For the other cases where an excited state is the result of two or more one-electron excitations, or where a one-electron excitation contributes to several excited states, more than one excited state (K) may contribute to a certain C term. A comparison between the simulated and experimental MCD spectra has been made in Figure 5. Similarly to the UV spectra, there is a good qualitative agreement between theory and experiment after allowance of a large red shift of the calculated high energy bands, especially for AZA and Pc. The experimental spectra have six C terms (C1 to C6) and we reproduce most of them in the MCD spectra of the four title systems. The experimental C term C1 corresponds to the calculated band a. It is well reproduced in the theoretical spectra. The calculated C term a is small and positive in all cases (with the exception of CBP where the C term a has a comparable intensity to that of the intense bands in the spectrum) and appears at about 5000 cm-1. It originates from the first absorption band L1 and transition 1. In AZA and Pc this C term is governed by the coupling of the ground state with the first excited state as a larger CGJ value is observed. The ES-ES coupling increases gradually and in CBP and NiR it is the dominating contribution. The excited states involved in the coupling with the first excitation (J ) 1) are 2 (for CBP) and 4 and z (for NiR). The

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TABLE 2: Band Labels, Excitation Labels (N), Calculated Excitations Energies (E), Oscillator Strengths (f), Orbitals Involved in the Transitions, and Contributions of the Single Electron Transitions to the Excitations (%) for AZAa fromd

%

f × 103 (R)e

bandb

N

Ec

100

0.06 (-0.29) 0.49 (5.92) 0.91 (0.84) 2.35 (-12.72)

L1 (a′) L2 (n/a) L3 (c′) B4 (c′) (c′)

1

5586

2

bandb

N

Ec

L1 (n/a) L2 (b′) L3 (c′) (c′)

1

5241

Met b1

2

9181

Cysσ-Cudxy

99

3

14 804

4

15 126

(d′)

y

15 802

M1 (d′) M2 (d′)

5

16 873

Hisπ1′ Cysσ-Cudx2-y2 Hisπ1′ Cysπ + Cudx2-y2 Cudz2 Hisπ1 Cudz2 Cudyz

55 34 36 32 23 73 16 85

q

16 959

M3 (e′)

r

21 566

M4 (f′) L4 (g′)

7

23 431

Cudxz Cudz2 Cudyz Cudz2 Cudxz Cysπ + Cudx2-y2 Cudxy + Cysσ

57 21 13 29 27 23 95

8

28 562

Hisπ2

99

M1 (d′) M2 (d′) M3 (e′)

0.57 (0.67) 1.24 (-18.25) 68.16 (25.00)

M4 (f′)

6.00 (-13.28) 1.86 (9.14)

TABLE 3: Band Labels, Excitation Labels (N), Calculated Excitations Energies (E), Oscillator Strengths (f), Orbitals Involved in the Transitions, and Contributions of the Single Electron Transitions to the Excitations (%) for Pca band L1 (n/a) L2 (b′) (n/a) L3 (c1′) (c2′)

M1 (d1′) (d2′) M3 (e′) M4 (f′) L4 (g′)

N

E

%

f × 10 (R)

1

4878

Met b1

100

2

11 009

Cysσ-Cudxy

100

x 3

12 874 14 773

4

16 044

Hisπ1′ Hisπ1 Cysπ + Cudx2-y2 Cysπ + Cudx2-y2 Hisπ1 Cudz2 Cudxz+yz Cudz2

100 74 24 47 22 14 14 82

0.20 (1.27) 1.04 (0.76) 0.18 (-0.37) 0.42 (2.78) 7.12 (-17.41)

97 71 18 98 99

c

from

d

6

16 755

5 z

17 617 22 992

7

24 061

Cudxz-yz Cudxz+yz Cysπ + Cudx2-y2 Cudxy + Cysσ

8

28 319

Hisπ2

%

f × 103 (R)e

Met b1

99

11 077

Cysσ-Cudxy

93

x

14 461

Hisπ1′

98

3

15 951

4

16 263

5

17 237

6

19 151

Hisπ1 Cysπ + Cudx2-y2 Hisπ1 Cysπ + Cudx2-y2 Cudxz Cudxz Cudyz Cudz2

51 34 48 27 13 66 31 94

2.15 (-3.07) 3.80 (0.45) 3.80 (-3.44) 6.22 (-8.70) 4.70 (-17.54)

z

21 219

7

23 569

Cudyz Cysπ Cudxy + Cysσ Cudxz Cudxy + Cysσ

42 22 13 13 87

0.09 (-0.55)

a In brackets are given the band labels and the rotatory strengths (R) for the CD spectrum on Figure 6A. b Assigned labels to the simulated absorption spectrum in Figure 4A. c Excitation energies in cm-1. d All excitations are to the SUMO (Cudx2-y2-Cysπ). e Rotatory strengths in 10-40 cgs.

b

TABLE 4: Band Labels, Excitation Labels (N), Calculated Excitations Energies (E), Oscillator Strengths (f), Orbitals Involved in the Transitions, and Contributions of the Single Electron Transitions to the Excitations (%) for CBPa

3

e

2.82 (17.18) 0.28 (-5.54) 62.33 (2.70) 1.33 (-10.93) 1.39 (4.54)

fromd

1.22 (12.13) 4.03 (13.17) 36.91 (17.78) 18.32 (-40.29)

a In brackets are given the band labels and the rotatory strengths (R) for the CD spectrum on Figure 6C. b Assigned labels to the simulated absorption spectrum in Figure 4C. c See Table 2. d See Table 2. e See Table 2.

TABLE 5: Band Labels, Excitation Labels (N), Calculated Excitations Energies (E), Oscillator Strengths (f), Orbitals Involved in the Transitions, and Contributions of the Single Electron Transitions to the Excitations (%) for NiRa bandb

N

Ec

L1 (a′) L2 (c′) L3 (c′)

1

4782

2

14 075

3

14 878

4

15 699

y

16 226

M1 (d′)

5

16 735

M2 (d′) M3 (e′) M4 (f′) L4 (g′)

6

18 903

z

21 026

7

23 749

8

29 063

(c′)

%

f × 103 (R)e

Met b1

99

Cysσ-Cudxy Cysπ + Cudx2-y2 Hisπ1′ Cysπ + Cudx2-y2 Cysπ + Cudx2-y2 Hisπ1′ Cudxz-yz Hisπ1

86 13 78 14 48 21 18 71

2.15 (-4.98) 12.36 (-23.83) 3.57 (-7.26) 8.54 (-14.03)

Cudxz-yz Cudxz-yz Hisπ1 Cudxz+yz Cudz2

27 44 25 18 90

Cudxz+yz Cudxy + Cysσ Cudxy + Cysσ Cudxz+yz Hisπ2

46 33 66 20 99

fromd

(d′)

1.24 (5.63) 4.92 (23.62) 10.03 (13.45) 13.59 (22.59) 37.09 (-55.25) 1.27 (4.13)

a In brackets are given the band labels and the rotatory strengths (R) for the CD spectrum in Figure 6B. b Assigned labels to the simulated absorption spectrum in Figure 4B. c See Table 2. d See Table 2. e See Table 2.

a In brackets are given the band labels and the rotatory strengths (R) for the CD spectrum on Figure 6D. b Assigned labels to the simulated absorption spectrum in Figure 4D. c See Table 2. d See Table 2. e See Table 2.

transition responsible for the first C term J ) 1 is in our calculations represented by the Met b1 f SUMO one-electron excitation. In the work by Solomon et al.3,5,6 (calculations with BP86 with modified nuclear potential on copper) the first observed C term (C1) is assigned to the Cudz2 f SUMO oneelectron transition. Roos et al. (CASSCF/CASPT2 calculations)

assign it as (Cu-S)σ* to the (Cu-S)π/σ* transition, which, according to our nomenclature, is a Cysσ + Cudxy to SUMO excitation.22,24 Absorption bands L2 and (partially) L3 yield an intense negative C term marked b and a smaller one, again negative,



TABLE 6: Calculated MCD Parameters for AZA C term Ja a b c e f s g

1 2 3 4 y 5 q r 7 8

CJb

CGJ b

K′ a

CEJ b

0.0867 -0.7909 -0.4477 0.3575 -0.0861 0.6350 -2.2531 -1.7367 0.2011 0.5833

0.1381 -1.2235 -0.8058 -0.7280 -0.0694 -0.4331 -0.1716 -4.0344 0.0864 0.7125

1 2

-0.0515 0.4326 0.3581 1.0855 -0.0167 1.0681 -2.0815 2.2977 0.1147 -0.1292

2 8

Ka

TABLE 9: Calculated MCD Parameters for NiR CJ/DJ

0.0332 -0.0676 4 -0.0332 3 0.0105 5, q, 4, 3 -0.0698 q 0.0861 5 -0.1406 7 -0.0025 0.0036 0.0408

a

Assigned labels to the simulated absorption spectrum in Figure 4A. b CJ, CGJ , and CEJ in 103 au.

TABLE 7: Calculated MCD Parameters for Pc C term a b c d e f g

J

a

1 2 x 3 4 6 5 z 7 8

b

CJ

CGJ b

K′

0.0746 -1.6489 0.0363 -0.4986 3.4742 -4.8304 -0.2726 -0.6460 -0.0031 0.4881

0.1545 -2.0526 0.0126 -0.2988 -1.7473 -0.7960 0.0878 -3.4722 -0.0490 0.4863

1 2

5 7 2

a

CEJ b

K

-0.0799 0.4037 0.0237 -0.1998 5.2215 -4.0344 -0.3605 2.8262 0.0459 0.0019

a

4 4 6 4, 5 6, 4 7, 2, 6 z

CJ/DJ 0.0081 -0.0797 0.0117 -0.0710 0.0356 -0.1307 -0.0779 -0.0011 -0.0003 0.0453

a

Assigned labels to the simulated absorption spectrum in Figure 4B. b CJ, CGJ , and CEJ in 103 au.

TABLE 8: Calculated MCD Parameters for CBP C term Ja a b c d e f u V

1 2 x 3 4 5 6 z 7

CJb

CGJ b

K′ a

CEJ b

0.9013 -2.3167 -0.4113 0.5235 0.3056 -1.8248 -1.2946 -0.4151 -0.1786

0.4018 -1.9685 -0.1391 -0.6789 -0.1938 -0.9052 -1.1072 -1.5712 -0.8750

1 2 x

0.4994 -0.3483 -0.2722 1.2023 0.4994 -0.9197 -0.1874 1.1562 0.6964

7

Ka

CJ/DJ

2 0.0107 4, 3, z, 6, 1 -0.0307 3 -0.0137 6 0.0061 6, 3, 2 0.0048 6 -0.1170 -0.0280 6 -0.0011 -0.0010

a

Assigned labels to the simulated absorption spectrum in Figure 4C. b CJ, CGJ , and CEJ in 103 au.

marked c in the theoretical spectra. They correspond to the broad and “shallow” negative band C2 observed experimentally. The corresponding transitions are 2 for band b and 3 (in AZA and Pc) or x (in CBP) for band c. The dominating contribution for band b comes from the coupling of the ground state with the second excited state. GS-ES coupling governs the C terms c for AZA and Pc as well, unlike in the case of CBP where the ES-ES coupling between the second excited state and a number of energetically close excited states yields the major contribution to the C term. The intensity of both bands a and b is overestimated in CBP. We fail to reproduce the negative term C2 in the NiR spectrum. According to our calculations, the C term C2 is due to excitations from the ligand orbitals Cysσ + Cudxy, Cysπ + Cudx2-y2, Hisπ1, or Hisπ1′ to the SUMO. Solomon et al. assign this band as a Cudxy to SUMO excitation. Roos et al. assign the corresponding band from the excitation spectrum as Cu3dz2 f (Cu-S)π/σ* (Met b1 to SUMO in our nomenclature). The experimental C terms C3 and C4 form a derivative shaped pseudo A term that is very characteristic for the MCD

C term a d e

f l m g

Ja

CJb

CGJ b

K′ a

CEJ b

Ka

CJ/DJ

1 2 3 4 y 5 6 z 7 8

0.3158 1.2403 0.6436 -3.1522 -3.4389 -1.1333 -1.1625 2.9272 -1.2524 0.3156

-0.3910 -1.3244 -0.5800 -1.0139 -0.9231 -1.0542 -1.7013 1.1630 -1.7186 0.7283

1 2

0.7068 2.5646 1.2235 -2.1382 -2.5158 -0.0791 0.5388 1.7642 0.4662 -0.4126

4, z 4 4 2 4

0.0032 0.0064 0.0122 -0.0264 -0.2051 -0.0176 -0.0010 0.0206 -0.0036 0.0330

8

6

a

Assigned labels to the simulated absorption spectrum in Figure 4D. b CJ, CGJ , and CEJ in 103 au.

spectra of the blue copper proteins. These bands can be observed also in the simulated spectra and are marked as d and e, respectively. The only exception is AZA, where the positive C term d is missing. However, from the data in Table 6 one can see that the corresponding positive C term parameters do exist. The C term due to transition 4 cannot be seen in the spectrum as a result of the overlap with the more intense negative C term due to transition 3. The positive C term (d) from the d,e pair is less intense and originates from the L3 absorption band and transition 4 for AZA, and Pc, and 3 and 4 for CBP. In the case of NiR this band is the result of the overlap of the C terms arising from L2 and L3 and also involves transition 2. The negative C term e is the first C term based on the ligand field transitions (5, 6, y, q, and z in the different systems) from the absorption band M1. This part of the MCD spectrum is governed by ES-ES coupling as the majority of CEJ values are much larger than their CGJ counterparts. For AZA and Pc the coupling is between the closest excited states (3 with 4; 5 with q and vice versa for AZA and 4 with 6 and vice versa for Pc). However, the C terms for CBP and NiR introduce coupling between some nonadjacent excited states (3 with 6 or 4 with 6). In the assignment of the positive band some copper d orbitals with z components can be added to the orbital mixture of the excitations responsible for bands b and c. The negative C term e is due to excitations involving the copper d orbitals with z components, as per Solomon et al.3,5,6 and Roos et al.22,24 The intense negative band e is followed by another negative band f in all four simulated MCD spectra. It originates from the ligand field absorption band M2 and appears also in the experimental spectra as the C term C5. For AZA and Pc this C term is due to the most intense transitions in the simulated absorption spectrasr and z, respectively. These transitions correspond also to the most intense absorption bands M3 in the experimental spectra. In CBP and NiR it is due to the weak transition 6. Actually, in the case of CBP there is an additional weak negative C term in the simulated MCD spectra (marked as u). It is unique for this system and originates from the most intense absorption band M3 and its underlying transition z. Here C term C5 comes from the overlap of f and u. The dominating contributions to this C term are due to the GS-ES coupling. Once again, the orbitals involved in the formation of C term C5 are the copper orbitals with z components with some participation of Cysπ + Cudx2-y2. In refs 3, 5, and 6 this band is assigned as a Cysπ to SUMO transition. Roos et al. describe it as a (Cu-S)π to (Cu-S)π/σ* transition (Cysπ + Cudx2-y2 to SUMO in our nomenclature). The last C term observed in the experimental spectra, C6, is broad, not very intense, and positive. The corresponding calculated bands are s and g in AZA, g in Pc, V and g in CBP

6316


Zhekova et al.

Figure 5. Superimposed theoretical and experimental3-6 MCD spectra of AZA (A), Pc (B), CBP (C), and NiR (D).

(g is not shown on the spectrum as its corresponding C term parameter appears after 30 000 cm-1), and l, m and g in NiR from the overlap of the last ligand field bands M4 (and M3 in the case of NiR) and the following LMCT band L4. C6 is most intense in NiR where the calculated C term parameter originating from transition z yields a large maximum (l) in the simulated spectrum. Once again the GS-ES coupling contributions dominate this part of the MCD spectra with two exceptions. Band l features considerable coupling between the close excited states z and 6, which yields a CEJ value bigger than CGJ . Band s also has a slightly larger CEJ . We assign this C term mainly to excitations from Cudxy + Cysσ and Hisπ2 to the SUMO, whereas in Solomon’s works it is assigned as a Cysσ to SUMO transition. According to Roos et al., the corresponding excitation band is due to a (Cu-S)σ to (Cu-S)π/σ* transition (or Cudxy + Cysσ to SUMO based on our nomenclature). The CJ/DJ ratios for all calculated C terms of the four systems are presented in Tables 6-9 as well. They are commonly used in experimental studies5,6 to facilitate the assignment of the MCD bands. CJ/DJ ratios of ca. 0.1 or larger are indirect experimental evidence for a substantial interaction between the states involved in the C term formation due to spin-orbit coupling. They can therefore be attributed to ligand-field transitions. Charge transfer bands are characterized by a smaller CJ/DJ ratio (around 0.01). Based on this criterion, AZA and Pc both have four “ligand field” bands with CJ/DJ ratios close to 0.1 in agreement with the studies of Solomon et al.5,6 However, these four bands are not concentrated at the low energy side of the spectrum as

experimentally, but are mixed among the charge transfer excitations and are observed at higher energies. We underestimate the magnitudes of the CJ/DJ ratios in all cases. CBP and NiR feature a single “ligand field” band. The remaining bands have CJ/DJ ratios lower than 0.1. The decrease in the calculated CJ/DJ values for the “ligand field” bands is consistent with experiment, where the CJ/DJ ratios for CBP and NiR are considerably smaller than those of the classic blue copper site Pc.5,6 Combined with the aforementioned CJ/DJ underestimation by the calculations this may lead to calculated values around 0.01 even in the case of a ligand field band. The low theoretically predicted CJ/DJ values are due to the large ligand character of the orbitals involved in the transitions. The largest calculated CJ/DJ ratios are observed for bands, resulting from excitations from orbitals of considerable metal character to the LUMO. Generally, we reproduce well the qualitative trends of the experimental MCD spectra after allowance for a red shift of the calculated excitation energies, although no such artificial shift was introduced in the spectra in Figures 4-6. Preliminary studies with several GGA functionals (BLYP, PBE, PW91) yielded similar orbital arrangement and decompositions as the ones calculated with BP86 and are not reported here. The use of hybrid functionals does not improve significantly the comparison with experiment.3,26 The inclusion of the protein backbone in QM/MM calculations with B3LYP results in orbital decompositions similar to experiment.26 However, even in this case the discrepancies between the theoretical and experimental excitation energies are only partially eliminated. We believe



Figure 6. Superimposed theoretical and experimental3-6 CD spectra of AZA (A), Pc (B), CBP (C), and NiR (D).

that the overestimation of the calculated excitation energies is due to shortcomings of the TDDFT methodology83-85 as implied by the aforementioned comparisons with previous studies (TDDFT3,5,6,26 and CASSCF/CASPT222,24). TDDFT does not account for the relaxation of the canonical orbitals used in the calculations. Such a relaxation would decrease the excitation energies without affecting considerably the oscillator strengths. Thus, the intensity ratios of the calculated bands would be kept relatively unchanged while the bands themselves would be shifted to energy values closer to the experimentally determined ones.83 3. EPR Spectra. One of the characteristic features of the blue copper sites is the small A|| copper hyperfine splitting in the EPR signal of the oxidized centers compared to that of the “regular” copper compounds1-7 like CuCl42-. Table 10 shows the theoretical and experimental values of the A tensor components (A1, A2, and A3) and the isotropic hyperfine coupling constant (Aiso, calculated as (A1 + A2 + A3)/3 for the four title systems and CuCl24 ). The classic blue copper centers AZA and Pc feature an almost axial EPR spectrum with a very small difference between the first two components of g (g1 and g2) (see below, Table 11).3-6 The EPR spectra of CBP and NiR are rhombic (larger difference between g1 and g2). The experimentally observed A|| components are represented by the calculated A1 (or Az) parameters, and A2 and A3 are the components of A⊥ when an axial signal is present. The experimental A|| values are considered negative, whereas A⊥ are positive in all cases as suggested by various theoretical and experimental

TABLE 10: Calculated and Experimentala Copper A Tensor Components for the Four Title Systems and CuCl42b

A tensor components

model

A1

A2

A3

Aiso

AZA Pc CBP NiR CuCl24

-122 (-54) -113 (-63) -92 (-58) -70 (-73) -175 (-164)

-4 (22) ∼0 (20) ∼0 (5) 13 (0) -8 (34)

1 (22) 11 (20) 44 (63) 63 (58) -8 (34)

-42 (-3) -34 (-8) -16 (-3) 2 (-5) -64 (-32)

a Experimental values for A tensor components of AZA,15 Pc,15 CBP,16 and NiR17 in parenthesis. b A tensor components in 10-4 cm-1.

studies.3-7,15-17,25-27 Generally |A1| is larger than |A2| and |A3|, with a small |A2| value, which is a trend observed both theoretically and experimentally. The only exception is in the EPR spectrum of CBP where |A1| and |A3| are very close (measured difference of 5 × 10-4 cm-1). The calculated A1 values of the classic blue copper sites AZA and Pc are more negative than the corresponding experimental ones but are still smaller than the calculated A1 component of CuCl42-. However, the experimental observation that A|| of the blue copper centers are more than two times smaller than A||3 of CuCl42- is not reproduced in the cases of AZA, CBP, and Pc. Consequently, the large negative A1 parameters lead to a significant discrepancy between the theoretical and experimental Aiso values. A1 and Aiso for CBP and NiR are in a better agreement with the experimental results. As the copper hyperfine coupling constant

6318


Zhekova et al. TABLE 12: Calculated Contributions to ∆gnoW′ (n ) 1, 3), As Well As Maximal ∆goW′, and Total ∆g° in AZA

TABLE 11: Calculated and Experimentala g Tensor Components for the Four Title Systems g tensor components model AZA Pc CBP NiR

g2

g1 2.03 2.03 2.03 2.02

(2.04) (2.05) (2.02) (2.02)

2.05 2.06 2.05 2.05

(2.06) (2.06) (2.09) (2.06)

g3 2.10 2.08 2.09 2.09

(2.27) (2.23) (2.20) (2.19)

a Experimental values for g tensor components of AZA,16a Pc3, CBP,16b and NiR17 in parenthesis.

occ.a

b,c ∆goV′ 1

b,c ∆goV′ 2

b,c ∆goV′ 3

max ∆goV′ c,d

total ∆g° c,e

Cudxy + Cysσ Cudyz Cudxz Cysπ + Cudx2-y2 Hisπ1′ Cudz2

2007 30 384 73 -60 1780 3334

4770 2189 14 024 12 105 5871 261

58 306 582 980 290 2553 6466

21 695 11 051 5026 4111 3401 3354

23 455 12 262 5739 5133 4678 4316

a oV′ Contributing occupied orbital to ∆goV′ n , ∆g , and ∆g°. Contributions to ∆goV′ from coupling between o and V′ ) SUMO. n c oV′ d ∆goV′ ∆goV′ ) (1/3)(∆goV′ + ∆goV′ + n , ∆g , and ∆g° in ppm. 1 2 e Vir oV oV oV ∆goV′ 3 ). ∆g° )(1/3)∑V (∆g1 + ∆g2 + ∆g3 ). b

reflects the spin distribution around the copper atom, the overestimation in |A1| can be attributed to the overestimation of the covalency of the Cu-Scys bond that was detected in all spectral simulations of the present study (see the sections on excitation energies, MCD, g tensors, and CD). This discrepancy between the calculated and experimental |A1| values has been observed previously in other theoretical EPR studies with similar functionals25 and in B3LYP QM/MM calculations on the EPR parameters of plastocyanin.26 The ij component of the ∆g tensor (eq. 10) may be written as a sum of contributions:

∆gij ) ∆gijp + ∆gijd

(14)

Here ∆gdij is the diamagnetic term and ∆gpij is the paramagnetic part of the g-shift tensor. For the title systems, the diamagnetic contribution to ∆g is much smaller than the paramagnetic one and can be neglected in the qualitative analysis. The paramagnetic contribution can be broken into two parts:

∆gijp ) ∆gijoV + ∆gijoo

(15)

TABLE 13: Calculated Contributions to ∆gnoW′ (n ) 1, 3), As Well As Maximal ∆goW′, and Total ∆g° in Pc occ.a

a ∆goV′ 1

a ∆goV′ 2

a ∆goV′ 3

max ∆goV′ a

total ∆g° a

Cudxy + Cysσ Cudz2 Cudxz-yz Cysπ + Cudx2-y2 Cudxz+yz Cysσ-Cudxy

3802 13 789 9231 6239 6337 484

2023 9691 6628 9153 5882 -1137

53726 456 6662 -90 12 4671

19 850 7979 7507 5101 4077 1339

21 976 9678 9237 6668 5299 3927

a

TABLE 14: Calculated Contributions to ∆gnoW′ (n ) 1, 3), as Well As Maximal ∆goW′, and Total ∆g° in CBP occ.a

a ∆goV′ 1

a ∆goV′ 2

a ∆goV′ 3

max ∆goV′ a

total ∆g° a

Cudxy + Cysσ Cudxz Cudyz Cysπ + Cudx2-y2 Cudz2

499 22 913 21 902 468 1816

8584 5458 5306 4200 833

58676 1792 573 2955 2852

22 586 10 054 9261 2541 1834

24 688 11 757 10 804 4945 4239

a

The first term on the right-hand side of eq 15 comes from the magnetic coupling between pairs of occupied and virtual orbitals, whereas the second one is due to the coupling between different occupied orbitals.75 The ∆goV ij term due to the β-electrons represents the dominating contribution to ∆gpij, hence all other sources will be omitted from the qualitative analysis. The predominant role played by the β-electrons stems from the fact that we have chosen the SUMO to be of β-spin. That is, the SUMO of β-spin is the only virtual orbital that contributes significantly to ∆goV ij , and it can only couple magnetically with occupied orbitals of the same spin. A comparison between the calculated and experimental g tensor components is made in Table 11. The calculated values for g1 and g2 are in a very good agreement with experiment. The third component, g3, corresponds to the experimental parameter g|| (or gz). The large difference between the calculated and experimental values for g3 has been observed before in theoretical studies with similar functionals and basis sets.25 It is also present in studies based on the XR-SW methodology3 and hybrid functionals as B3LYP.25,26 It is attributed to the overestimation of the covalency of the Cu-Scys bond3 or to deficiencies of the available DFT functionals.25,26 In addition, the g3 component proves sensitive to the amount of Hartree-Fock exchange included in the calculations as shown by studies on the EPR parameters of blue copper proteins based on the BHLYP and a series of modified B3LYP functionals.26 50% Hartree-Fock exchange in BHLYP and B3LYP yields theoretical values of g3 in good agreement with experiment but overestimates g1 and g2.

See Table 12.

See Table 12.

TABLE 15: Calculated Contributions to ∆gnoW′ (n ) 1, 3), As Well As Maximal ∆goW′, and Total ∆g° in NiR occ.a

a ∆goV′ 1

a ∆goV′ 2

a ∆goV′ 3

max ∆goV′ a

total ∆g° a

Cudxy + Cysσ Cudxz+yz Cudxz-yz Cysσ-Cudxy Cudz2

7968 32 491 18 916 7 -25

6344 931 3285 2807 7860

45 554 1240 628 6940 160

19 955 11 554 7610 3251 2665

21 775 13 407 9913 5536 4511

a

See Table 12.

Tables 12-15 display the contributions ∆gnoV′ (n ) 1, 3) to ∆gn from the coupling between occupied orbital o of β-spin and v′ ) SUMO, also of β-spin. Shown in addition is 1 oV oV ∆goV ) (∆goV 1 + ∆g2 + ∆g3 ) 3

(16)

as well as the total contribution to ∆g from the coupling between o and all virtual orbitals:

∆go )

1 3

Vir

∑ (∆goV1 + ∆goV2 + ∆goV3 )

(17)

V

Contributions to the ∆g tensor come from many couplings between the SUMO and metal-containing orbitals as well as a

TDDFT Analysis of Four Blue Copper Proteins few couplings between the SUMO and ligand-based orbitals. The largest contribution to the ∆g tensor involves ∆g3oV′ and comes for all four compounds from the coupling of the lowest metal-type orbital (Cudxy + Cysσ) with the SUMO. It results in a value for the g3 component that is larger than those for g1 and g2. The second largest contribution to ∆g involves ∆g1oV′ and to some degree ∆goV′ 2 . It is a result of the magnetic coupling between the SUMO and one of the metal d-orbitals with a z component (Cudyz in AZA, Cudz2 in Pc, Cudxz in CBP, and Cudxz+yz in NiR). Another d-orbital with a z component (Cudxz in AZA, Cudxz-yz in Pc and NiR, and Cudyz in CBP) is responsible for the third largest contribution. However, this time the magnetic coupling contributes to either g1 (in Pc, CBP, and NiR) or g2 (in AZA). The fourth largest contribution is cysteine based in all four systems. The occupied orbitals involved in the magnetic coupling with the SUMO are Cysπ + Cudx2-y2 (in AZA, Pc, and CBP, with a contribution to g2) and Cysσ-Cudxy (in NiR, with a small contribution to g3). A ligand orbital, this time based on one of the histidine residues is responsible for the fifth largest ∆go value in AZA, but it cannot be seen in any of the other three systems. The remaining d-orbitals with a z component (Cudz2 in AZA, CBP, and NiR and Cudxz+yz in Pc) yield contributions in different gn components for the different systems. In Pc the coupling between the Cysσ-Cudxy and the SUMO appears as the final considerable ∆go value and is smaller than those for the other three systems. Numerous additional contributions, smaller than the ones listed in Tables 12-15 are included in the gn values presented in Table 10, but they are neglected here in the qualitative analysis. Because the EPR signal comes from the GS-ES coupling, and MCD as well probes GS-ES mixing (in addition to ES-ES interactions), one might expect some correlation between EPR and MCD spectra as anticipated previously.61-63 As we noted above, some bands of the MCD spectra for the four title systems are governed by the GS-ES contributions. The exceptions are the characteristic bands d and e for all four systems, and bands s in AZA and l in NiR where CEJ > CGJ . Comparison between the orbitals responsible for the EPR and MCD activity proves that most of the orbitals involved in the MCD signals are involved in the EPR signals as well. Moreover, in all cases, the orbitals that yield the large CEJ values are also responsible for the large ∆go contributions to ∆g and participate in the formation of the MCD bands d, e, s, and l. These are all metal orbitals with z-components, as well as some of the cysteine (Cysπ + Cudx2-y2 and Cysσ-Cudxy) and histidine-based (Hisπ1′) orbitals. They are also involved in various MCD bands that show larger GS-ES than ES-ES coupling (f in all systems except AZA; m, u, and V). The orbital whose coupling with the SUMO results in the largest ∆goV′ contribution, Cudxy + Cysσ actually yields a CEJ value comparable to CGJ , with the exception of NiR, where CGJ is much larger than CEJ . The ligand-to-metal charge-transfer bands a, b, c, and g are not accounted for well by the EPR, as the majority of the occupied orbitals (Met b1, Cysσ-Cudxy, Hisπ1′, Hisπ1, and Hisπ2) participating in their underlying transitions are not among those responsible for the largest g-shifts. We have shown that the GS-ES couplings that dominate the EPR spectrum for some transitions also dominate contributions to the MCD spectrum. However, the correlation is in general only qualitative at best. We conclude our analysis of the EPR calculations by noting that deviation of the theoretical g3 value compared to the experiment (Table 11) is likely due to an underestimation of the contribution to g3 from the coupling between the SUMO and Cudxy + Cysσ as the result of a too large contribution from

J. Phys. Chem. A, Vol. 114, No. 21, 2010 6319 Cysσ to Cudxy + Cysσ.5,6,22,24 Furthermore, we do not reproduce the experimental trend of a reduction in g3 from AZA to NiR. 4. CD Spectra. The four blue copper sites used in this study are of C1 symmetry and are therefore chiral and potentially CD active. This chirality is kept in our 39 atoms models (based on the real crystal geometries), since no symmetry limitations were employed during the calculations. Figure 6 displays the superimposed simulated and experimental CD spectra of the four title systems. The numerical data pertaining to the theoretical CD spectra is presented in Tables 2-5. R is the rotatory strength in 10-40 cgs. It is a measure of the difference in absorbance of right and left circularly polarized light and can be expressed as a scalar product of the electric transition dipole moment and the magnetic transition dipole moment:86

RAJ ) Im[〈A|M|J〉 · 〈J|m|A〉]

(18)

where M and m are the electric and magnetic dipole moment operators, respectively; and A and J stand for the ground and excited states, respectively. Once again, our calculations reproduce well the qualitative trends of the experimental spectra after allowance for a large red shift of the calculated excitation energies in the two classical blue copper systems AZA and Pc. The experimental spectra have six bands (B1 to B6) and we find theoretical analogues for most of them. B1 is a small negative band, visible in the experimental CD spectra of CBP and NiR. It does not appear in the experimental CD spectrum of AZA in the onset between 5000 and 30 000 cm-1. In the spectrum of Pc, its intensity is negligible. Band B1 corresponds to the theoretically computed band a′, and its underlying transition is No. 1 (from Met b1 to the SUMO). Transition 2 (Cysσ-Cudxy to the SUMO) yields a small positive band in the spectra of AZA and Pc, which correspond to the experimental maximum B2. In the theoretical spectrum of CBP this band is not visible due to its low rotatory strength. In NiR, transition 2 gives rise to a CD signal with a large negative rotatory strength and participates in the formation of the complex theoretical band c′. Band c′ is intense and negative for all four systems and corresponds to B3 in the experimental spectra. Its underlying excitations are mostly from the ligand orbitals Cysσ + Cudxy, Cysπ + Cudx2-y2, Hisπ1, or Hisπ1′ to the SUMO. Some copper d-orbitals with z components are involved in these excitations as well. In AZA and Pc band c′ is due to transitions 3 and 4, which have rotatory strengths of the opposite sign. In Pc, the energy difference between transitions 3 and 4 is large enough to split band c′ into a small positive band c1′ and a larger negative band c2′. The broad experimental maximum B4 appears in the ligand field part of the spectrum and corresponds to the theoretical bands d′ and e′. The underlying excitations are from the three copper d-orbitals with z components to the SUMO. For CBP and NiR, transitions 5, 6, and z all result in CD signals with positive rotatory strengths. In the case of AZA transition q yields an intense negative band d′, while transition r participates in the formation of the positive band e′ with higher rotatory strength than d′. In the theoretical CD spectrum of Pc a splitting of band d′ into bands d1′ and d2′ of opposite signs can be observed. The last ligand field excitation (from Cudxy + Cysσ to the SUMO) gives rise in all four cases to a CD band f′ with a negative rotatory strength. For CBP and NiR this is the most

6320


intense CD signal. Band f′ corresponds to the experimental minimum B5. A positive band of charge transfer character can be observed close to 30 000 cm-1 in the theoretical CD spectra of the four models. It is due to transition 8 (between Hisπ2 and the SUMO) and corresponds to the experimental band B6. IV. Concluding Remarks Despite the long-lasting interest of the scientific community in the blue copper proteins, their optical and magnetic properties still pose challenges for both theoreticians and experimentalists. Recent computational codes, based on modern DFT, may be of great help for the determination of the orbital interactions responsible for the spectroscopic characteristics of these systems. In addition, the large amount of experimental and theoretical data accumulated on the blue copper sites, as well as their small size, make them good targets for the evaluation of methodology deficiencies and the performance of newly developed computational methods. Here we have presented extensive TDDFT studies on the excitation, MCD, EPR, and CD parameters of small models of the four blue copper proteins azurin, plastocyanin, cucumber basic protein, and nitrite reductase. Comparison with experimental data has been made throughout. Generally, we reproduce well most of the qualitative trends of the experimentally determined excitation, MCD, and CD spectra (alternation of minima and maxima, intensity ratios of the bands, etc.). A large blue-shift is observed for most of the calculated bands compared to experiment, and the ligand field excitations appear at higher energies than the charge transfer ones. Orbital analysis reveals that the highest occupied orbitals are of predominantly ligand character. The discrepancies in the bands positions and the orbital decompositions compared to traditional ligand field theory have been observed previously in other studies with similar functionals and is characteristic for the TDDFT methodology. The blue shifts of the calculated excitation energies are most profound in the cases of Pc and AZA, whereas in the cases of CBP and NiR a better agreement between theory and experiment is achieved. The blue-shift of the bands has been attributed to the covalency overestimation of the bonds around the metal center (in particular the Cu-Scys bond) by BP86. Previous studies have aimed to solve this problem by adjustment of the Cu effective nuclear charge in BP86 calculations on small models, inclusion of the protein environment through QM/MM calculations, and treatment with hybrid functionals. QM/MM calculations with B3LYP on plastocyanin lead to spin distribution comparable with the experimentally determined one.26 However the corresponding excitation energies were still considerably blue-shifted, proving that the problem is most probably intrinsic to the approximate TDDFT methodology as a first-order response theory. A better fit between the theoretical and experimental excitation energies might be obtained if the orbitals used in the spectral simulations are allowed to undergo relaxation (i.e., are optimized with respect to excited states instead of the ground state as in the conventional TDDFT). Relaxation would not affect strongly the intensities of the calculated bands but would lower the energy of the excited states relative to the ground state. As a result, it would not change significantly the qualitative appearance of the spectra while adjusting the excitation energies to values closer to experiment. We hope that we will be able to elucidate further these problems in our future studies. The simulations of the EPR parameters show a noticeable difference between the calculated and the experimentally measured g3 (gz or g||) component of the g-tensor, which is once

Zhekova et al. again attributed in previous studies to the covalency overestimation of the Cu-Scys bond. Upon addition of the protein environment in QM/MM B3LYP studies, the spin distribution around the metal atom is corrected, but the discrepancy in the g3 values is still present. It can be moderated with the inclusion of large amounts of Hartree-Fock exchange in hybrid functionals as BHLYP and modified B3LYP. Nevertheless, the g1 and g2 values are reproduced well in our calculations. The characteristic small A|| hyperfine coupling splittings of the blue copper proteins are overestimated (again, the overestimation is the largest for the classic blue copper sites AZA and Pc) but are still considerably smaller than A|| of the “regular” planar compound CuCl42-. A qualitative analysis has been performed on the correlation between MCD and EPR signals based on eqs 5 and 11. We have shown that most of the metal orbitals responsible for the intense bands in the MCD spectra of the four title systems are also involved in the largest contributions to the EPR g-tensors. This “EPR active” orbitals participate in both GS-ES and ESES coupling, proving that EPR can account for some of the MCD activity. However, the correlation is less straightforward than what is suggested by eqs 5 and 11. The qualitative picture is complicated further by the fact that some ligand orbitals yield relatively intense bands in the MCD spectra but do not contribute significantly to the EPR spectrum. Acknowledgment. This work has been supported financially by the National Sciences and Engineering Research Council of Canada (NSERC). Some of the calculations presented here made use of the Western Canada Research Grid computing resources. T. Z. would like to thank the Canadian Government for a Canada Research Chair. Supporting Information Available: Figures, detailed description, and tables with the orbital decompositions of the orbitals of AZA, Pc, CBP, and NiR used in the spectral analysis. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Solomon, E. I.; Baldwin, M. J.; Lowery, M. D. Chem. ReV. 1992, 92, 521. (2) Solomon, E. I.; LaCroix, L. B.; Randall, D. W. Pure Appl. Chem. 1998, 70, 799. (3) Solomon, E. I.; Szilagyi, R. K.; DeBeer George, S.; Basumallick, L. Chem. ReV. 2004, 104, 419. (4) Solomon, E. I.; Hare, J. W.; Dooley, D. M.; Dawson, J. H.; Stephens, P. J.; Gray, H. B. J. Am. Chem. Soc. 1980, 102, 168. (5) LaCroix, L. B.; Randall, D. W.; Nersissian, A. M.; Hoitink, C. W. G.; Canters, G. W.; Valentine, J. S.; Solomon, E. I. J. Am. Chem. Soc. 1998, 120, 9621. (6) LaCroix, L. B.; Shadle, S. E.; Wang, Y.; Averill, B. A.; Hedman, B.; Hodgson, K. O.; Solomon, E. I. J. Am. Chem. Soc. 1996, 118, 7755. (7) Solomon, E. I. Inorg. Chem. 2006, 45, 8012. (8) Ghosh, S.; Dey, A.; Sun, Y.; Scholes, C. P.; Solomon, E. I. J. Am. Chem. Soc. 2009, 131, 277. (9) Adman, E. T. In AdV. Protein Chem.; Anfinsen, C. B., Richards, F. M., Edsall, J. T., Eisenberg D. S., Eds.; Academic Press, Inc: San Diego, 1991; Vol. 42; p 145. (10) Baker, E. N. J. Mol. Biol. 1988, 203, 1071. (11) Guss, J. M.; Bartunik, H. D.; Freeman, H. C. Acta Crystallogr. B 1992, 48, 790. (12) Guss, J. M.; Merritt, E. A.; Phizackerley, R. P.; Freeman, H. C. J. Mol. Biol. 1996, 262, 686. (13) Adman, E. T.; Godden, J. W.; Turley, S. J. Biol. Chem. 1995, 270, 27458. (14) Gray, H. B.; Malmstro¨m, B. G.; Williams, R. J. P. J. Biol. Inorg. Chem. 2000, 5, 551. (15) Roberts, J. E.; Cline, J. F.; Lum, V.; Freeman, H.; Gray, H. B.; Peisach, J.; Reinhammar, B.; Hoffman, B. M. J. Am. Chem. Soc. 1984, 106, 5324.

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A Magnetic and Electronic Circular Dichroism Study of Azurin

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