Density Functional Study of EPR Parameters and Spin-Density

Jun 26, 2007 - Sebastian Gohr , Peter Hrobárik , Michal Repiský , Stanislav Komorovský , Kenneth Ruud , and Martin Kaupp. The Journal of Physical ...
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8290

J. Phys. Chem. B 2007, 111, 8290-8304

Density Functional Study of EPR Parameters and Spin-Density Distribution of Azurin and Other Blue Copper Proteins Christian Remenyi, Roman Reviakine, and Martin Kaupp* Institut fu¨r Anorganische Chemie, UniVersita¨t Wu¨rzburg, Am Hubland, D-97074 Wu¨rzburg, Germany ReceiVed: March 3, 2007; In Final Form: May 1, 2007

Modern density functional methods have been used to study spin-density distribution, g tensors, as well as Cu and ligand hyperfine tensors for azurin models, for two more blue copper proteins plastocyanin and stellacyanin, and for small model complexes. The aim was to establish a consistent computational protocol that provides a realistic description of the EPR parameters as probes of the spin-density distribution between metal and coordinated ligands in copper proteins. In agreement with earlier conclusions for plastocyanin, hybrid functionals with appreciable exact-exchange admixtures, roughly around 50%, provide the best overall agreement with all parameters. Then the bulk of the spin density is almost equally shared by the copper atom and the sulfur atom of the equatorial cysteine ligand, and the best values are obtained for copper, histidine nitrogen, and cysteine β-proton hyperfine couplings, as well as for g||. Spin-orbit effects on the EPR parameters may be appreciable and have to be treated carefully to obtain agreement with experiment. Most notably, spin-orbit effects on the 65Cu hyperfine coupling tensors in blue copper sites are unusually large compared to more regularly coordinated CuII complexes with similar spin density on copper. In addition to the often emphasized high covalency of the Cu-S(Cys) bond, the characteristically small A|| component of blue copper proteins is shown to derive to a large part from a near-cancellation between negative first-order (Fermi contact and dipolar) and unusually large positive second-order (spin-orbital) contributions. The large spin-orbit effects relate to the distorted tetrahedral structures. Square planar dithiolene complexes with similar spin density on copper exhibit much more negative A|| values, as the cancellation between nonrelativistic and spin-orbit contributions is less complete. Calculations on a selenocysteine-substituted variant of azurin have provided further insight into the relations between bonding and EPR parameters.

Introduction Blue copper proteins (or type I copper proteins) are often considered the prototypical electron-transfer proteins. They are probably among the metalloproteins studied most thoroughly by a host of crystallographic, spectroscopic, and theoretical methods.1-10 One reason is their distorted tetrahedral copper coordination, which has been central to a still-ongoing debate about the role of an “entatic” or “rack” state for the function of metalloproteins.11-14 Additionally, the strong blue color, due to an intense excitation near 600 nm, and a narrow 65Cu hyperfine coupling of the oxidized CuII state are spectroscopic characteristics that have attracted substantial interest.15,16 The hyperfine coupling is related to the mechanistically important question of how the spin density is distributed between the metal and the strongly bound equatorial cysteine ligand. With the aim to establish the electronic structure and spin density of blue copper sites, particularly extended spectroscopic and theoretical studies have been carried out on plastocyanin by Solomon and co-workers and by others.10,17-19 This included optical spectroscopies (including magnetic circular dichroism, MCD), X-ray absorption spectroscopies (XAS) at various frequencies, variable-energy photoelectron spectroscopy (VEPES), electron paramagnetic resonance (EPR), and theoretical treatments ranging all the way from early scattered-wave XR (XR-SW) and semiempirical approaches to state-of-the-art density functional theory (DFT) methods, and even to post* To whom correspondence [email protected].

should

be

addressed.

E-mail:

Hartree-Fock treatments for smaller model systems. Combining the spectroscopic data with various computations, Solomon et al. arrived at a relatively large metal-ligand (Cu-S) covalency and suggested this as the primary reason for the small A|| copper hyperfine splitting and blue color of blue copper proteins. Hybrid density functional methods with an about 38% exact-exchange admixture were indicated to provide the most reliable spindensity distribution. This conclusion was based largely on covalency estimates derived from XAS studies (see ref 10 and references therein) and on adjusting the XR-SW muffin-tin sphere sizes to g tensors; copper K-edge XAS was used to rule out an earlier proposed dx2-y2 - pz hybridization as the reason for the small copper A||. Copper L-edge XAS suggested less spin density on copper than in D4h [CuCl4]2-, and sulfur K-edge XAS indicated 38% cysteine sulfur 3p character in the plastocyanin ground state (45% for azurin). Approximate XR-SW calculations, an early version of DFT, were used to estimate the EPR g tensor. While they confirmed the experimentally observed order g|| > g⊥ > ge, the g|| component and thus the g anisotropy were underestimated by the calculations. This was attributed to a too large metal-ligand covalency in the calculations, associated with too much delocalization of the spin density onto the cysteine ligand. After reducing the muffin-tin sphere sizes around copper arbitrarily, the spin delocalization was reduced, and good agreement with the experimental g tensor was obtained. The resulting spin-density distribution (with slightly more spin on copper than on the cysteine sulfur and slight delocalization onto the two histidine δ-N atoms) was considered adequate and agreed also well with XAS and MCD

10.1021/jp071745v CCC: $37.00 © 2007 American Chemical Society Published on Web 06/26/2007

EPR Parameters and Spin-Density Distribution of Azurin

J. Phys. Chem. B, Vol. 111, No. 28, 2007 8291

Figure 1. Structures of the metal sites of azurin, plastocyanin, and stellacyanin. The protein residues connected directly to copper are shown, with metal-ligand bond lengths. The β-H atoms of Cys112 in azurin are indicated.

data. The large Cu-S covalency was suggested to be the decisive feature of the blue copper proteins compared to more regular copper thiolato complexes, explaining the special spectroscopic characteristics. The obtained “experimental” spin density was used to calibrate more recent computations using state-of-the-art DFT approaches. The above-mentioned hybrid functional with a 38% Hartree-Fock-exchange admixture was the method judged most adequate based on this procedure.10,20 The evidence provided by all of the experiments and computations appears rather compelling, and a relatively large Cu-S covalency is, beyond doubt, an important feature of the blue copper proteins and their function. In view of the fundamental importance of the spin density for the function of these electron-transfer proteins, and of the sensitive dependence of the electronic structure on the theoretical treatment, a direct determination by state-of-the-art quantum chemical methodology of the EPR parameters of the system as faithful probes of the spin-density distribution would be desirable. Notably, such calculations should be able to reconcile the relatively large g anisotropy (which points to appreciable metal-centered spin) with the small copper hyperfine coupling (which has been taken to suggest relatively small metal spin density). Beyond the immediate insight provided for the systems of interest, it is also hoped that such studies will help improve the quantum chemical methodology by showing the limits of the currently applicable approaches (in the present case, hybrid DFT). In this paper, we provide DFT calculations of EPR parameters in blue copper proteins, and we study, in particular, the dependence of the EPR parameters and spin density on the admixture of exact exchange in hybrid density functionals. We will examine g tensors, copper hyperfine tensors, and ligand hyperfine tensors (for the histidine nitrogen and cysteine β-hydrogen nuclei). While computations will be presented on models of azurin, plastocyanin, and stellacyanin (Figure 1), as well as on some smaller model complexes, our main focus will be on azurin. This is the blue copper protein studied most thoroughly by multiple-frequency EPR, as well as by electronnuclear double resonance (ENDOR) and electron-spin-echomodulation (ESEEM) spectroscopies, in particular, by Groenen and co-workers.5-7,21 Previous DFT studies have focused on hyperfine couplings, with rather limited accuracy.22-24 The g tensor of azurin has even been calculated by MRD-CI calculations but with a number of substantial approximations involved (see discussion further below).25 After completion of this work, a QM/MM DFT study of Sinnecker and Neese on optical and EPR properties of plasto-

cyanin appeared.26 Their focus was on the description of the protein environment by QM/MM methods and by continuum solvent models. They restricted themselves to B3LYP calculations. We will make comparison to the results of Sinnecker and Neese where appropriate. Another very recent related thesis work concentrated mainly on ligand hyperfine couplings in azurin.27 Theoretical Formalism The theoretical background of the EPR parameters is covered in detail in various text books.28-33 Here, we summarize only the most relevant points. The g Tensor Calculations. The g tensor will be provided as a correction to the free-electron value ge (in parts per thousand, i.e., in units of 10-3)

g ) ge1 + ∆g

(1)

with ge ) 2.002319. Up to the level of second-order perturbation theory based on the Breit-Pauli Hamiltonian, the g shift ∆g consists of three terms

∆g ) ∆gSO/OZ + ∆gRMC + ∆gGC

(2)

of which the “paramagnetic” second-order spin-orbit/orbital Zeeman cross term, ∆gSO/OZ, dominates (except for extremely small ∆g values).28 Within the coupled-perturbed Kohn-Sham (CPKS) scheme, using (nonlocally implemented) hybrid density functionals and based on unrestricted Kohn-Sham calculations, the Cartesian components ∆guv are computed as

∆gSO/OZ uv

)

R2 2

-

ge

[

occ(R) virt(R)

∑k ∑a

R R R 〈ψRk |hSO V |ψa 〉 〈ψa |F′u|ψk 〉

Rk - Ra

occ(β) virt(β)〈ψβ|hSO|ψβ〉 k V a

∑k ∑a

βk - βa

with

F′u ) l0,u -

2 R

n/2

a0

]

〈ψβa |F′u|ψβk 〉

∑K′k,u k)1

(3)

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Remenyi et al.

lO,u is a spatial component of the orbital Zeeman operator, and K′k is the response exchange operator, whose action on an orbital may be written as

ASO-I K,uv ) 1 2

K′kψ0l (1) )

∫ [ψ′k(1)ψ0k(2) - ψ0k(1)ψ′k(2)]ψ0l (2)r112dr2

-

Additionally, we have computed g tensors for [CuCl4]2- (in D4h vs D2d symmetry) as a first-order property based on relativistic non-collinear two-component Kohn-Sham wave functions using the approach delineated in ref 38. In this method, three spin-polarized two-component SCF calculations with orthogonal orientations of the total (spin plus orbital) magnetization provide each one row of the g matrix. This affords a variational treatment of SO contributions and thus goes beyond the leading-order perturbational treatment described above. These calculations were based on the Douglas-Kroll-Hess (DKH) Hamiltonian39 (see Computational Details below). Hyperfine Tensor Calculations. In the usual nonrelativistic first-order approximation, isotropic hyperfine splittings Aiso(N) correspond to the Fermi contact term AFC

4π 3

βeβNgegN 〈SZ〉-1

R-β Pµ,ν 〈φµ|δ(RN)|φv〉 ∑ µ,ν

(4)

Here, βe is the Bohr magnetron, βN the nuclear magneton, gN is the g value of nucleus N, 〈SZ〉 is the expectation value of the z R-β is the spin-density component of the total electronic spin, Pµ,ν matrix, and the summation runs over all occupied molecular orbitals. The components Adip ij (N) of the anisotropic tensor are given by

1 -1 Adip ij (N) ) βeβNgegN 〈SZ〉 2

1 2〈SZ〉

occ(β) virt(β)

The relativistic mass correction term ∆gRMC and the one-electron part of the gauge correction term ∆gGC are also included in our implementation34,35 (see also refs 36 and 37 for related implementations). In the absence of a nonlocal Hartree-Fock potential (e.g., for GGA functionals like BP86), we end up with an uncoupled system of equations, and F′ reduces to lO (i.e., a0 ) 0).34

Aiso(N) ) AFC )

R geγK 4

a-β 2 Pµ,ν 〈φµ|r-5 ∑ N (rNδij µ,ν

3rN,irN,j) |φν〉 (5) where rN ) r - RN (RN is the position vector of nucleus N). In the rest of this section, we will refer to the metal hyperfine interaction and omit subscript N. The importance of orbital contributions for metal A tensors has been appreciated early on29 and is considered clearly nonnegligible for CuII systems.4,10,40,41 More recent state-of-the-art DFT treatments of spinorbit (SO) effects on A have confirmed this.42-44 Here, we use the second-order perturbation treatment of refs 43 and 44. At the coupled-perturbed Kohn-Sham level, the dominant SO correction term arises as a second-order cross term between the one- and two-electron SO Hamiltonian hSO and the perturbed Fock operator F′

∑k ∑a

×

[

occ(R) virt(R)

∑k ∑a

R R R 〈ψkR|hSO u |ψa 〉 〈ψa |F′V |ψk 〉

Rk - Ra

]

β β β 〈ψβk |hSO u |ψa 〉 〈ψa |F′V|ψk 〉

βk - βa

(6)

where R is the fine-structure constant, γ the gyromagnetic ratio of the nucleus, hSO is explained below, F′ is the perturbed Fock operator, with

F′V ) (lV /r3) -

2 R

n/2

a0

∑ K′V

k)1

where (lV/r3) is a spatial component of the paramagnetic nuclearspin electron-orbit (PSO) operator, and K′V and a0 have the same meaning as discussed near eq 3 for the g tensor (see ref 42 for a related simultaneous CPKS implementation and also refs 43 and 44 for references to earlier work). ψσ and σ are spin-polarized Kohn-Sham orbitals and orbital energies, respectively. For better comparison with experimental values, the SO correction to A (ii denotes principal components) is given in terms of an isotropic pseudocontact (APC) and traceless dipolar (Adip,2) term total dip,2 AK,ii ) APC K + AK,ii

(7)

For the ligand hyperfine couplings, SO contributions were negligible and will not be reported. Computational Details Structural data from high-resolution X-ray diffraction are available for all three sites considered. Blue copper active sites consist of a single copper center coordinated by at least four amino acids (Figure 1); two histidines (coordinated via Nδ) and cysteine (coordinated via sulfur) provide the dominant, approximately trigonal equatorial coordination. In azurin and plastocyanin, one methionine serves as an additional, more weakly bound axial ligand (sulfur coordination); in stellacyanin, the fourth ligand is provided by a glutamine residue (oxygen coordination). A very weakly bound glycine provides a fifth ligand in azurin (Figure 1). The computational models included generally only the amino acid residues directly coordinated to copper. Initial coordinates were taken from crystallographic data in the protein data base PDB 4AZU45 for azurin (from Pseudomonas aeruginosa), 1PLC for plastocyanin46 (from poplar leaves), and 1JER for cucumber stellacyanin.47 The 4AZU contains four independent copper sites in the unit cell. We thus averaged the coordinates, similar to the procedure described by van Gastel et al.25 Keeping the heavy-atom positions fixed, the hydrogen positions were subsequently optimized at the BP86 DFT level48,49 with SVP50 basis sets, using unrestricted Kohn-Sham wave functions and the Gaussian03 program.51 The selenocysteine-substituted azurin lacked experimental X-ray data. Its structure was therefore completely optimized at the BP86/SVP level using the Turbomole 5.652 program. During the optimization process, the axial glycine ligand became detached from the copper center. Therefore, only four substituents were used for selenocysteinesubstituted azurin, selenocysteine, methionine, and two histidines. Comparison of the optimized structure to Cu and Se

EPR Parameters and Spin-Density Distribution of Azurin EXAFS data53 provides agreement of the Cu-Se distance within 1 pm. The computed Cu-N distances of 207.2 and 204.4 pm appear somewhat too long compared to the Cu EXAFS value of 197(2) pm (and the Se-C distance within the selenocysteine ligand is 199 pm compared to 194 pm from Se EXAFS). Structures of the model complexes [Cu(mnt)2]2- and [CuCl4]2were also fully optimized (the chlorocuprate both in D2d and D4h symmetry). Structural parameters for all optimized models are provided as Supporting Information (Table S1). At the obtained structures, unrestricted Kohn-Sham singlepoint calculations were performed with a (15s11p6d)/[9s7p4d] Cu basis set designed for hyperfine calculations and employed also in our previous studies of 3d complexes.54,55 HuzinagaKutzelnigg-type basis sets BII (sometimes also denoted as IGLO-II)56,57 were used for the ligand atoms S, Se, Cl, O, N, C, and H. Unless noted otherwise, calculations used nonrelativistic wave functions. The following exchange-correlation functionals were compared: (a) the BP86 GGA functional48,49 (without density fitting), (b) the hybrid B3LYP functional58,59 with 20% exact exchange, (c) the hybrid BHLYP functional with 50% exact exchange,58,60 and (d) user-defined three-parameter B3LYPbased hybrid functionals of the general form B88 VWN (1 - a0) ELSD + a0EHF + X X + 0.72EX + EC

(8) 0.81ELYP-VWN C with a0 (indicating the amount of Hartree-Fock exchange admixture) chosen to be 0.30, 0.40, 0.45, 0.50, and 0.60 and, in the following, denoted as B3-xx (with xx ) a0*100; BHLYP is as B3-50 but with the two remaining constants in eq 8 set to 1.0). While most BP86, B3LYP, and BHLYP calculations were done with the Turbomole 5.652 program, the user-defined hybrid functionals were not available in Turbomole, and thus, the Gaussian03 program was used51 to compute the Kohn-Sham orbitals (for B3LYP, differences between Turbomole- and G03based calculations were below ca. 2 ppt for the g tensor component and below 1.5 and 0.7 MHz for metal and nitrogen hyperfine tensors, respectively). Scalar relativistic DKH calculations (with the one-electron Hamiltonian transformed to second order) on azurin were also based on G03, whereas a comparison between one- and two-component DKH calculations on [CuCl4]2was done with the ReSpect code61 for internal consistency (the two-component g tensor methodology of ref 38 has, up to now, only been implemented in ReSpect). The unrestricted Kohn-Sham orbitals obtained with any of these programs were transferred to the MAG-ReSpect property package61 by suitable interface routines.34,35 The atomic meanfield approximation (AMFI)62,63 has been used to compute the matrix elements of the spin-orbit (SO) operator, hSO, in eqs 3 and 6. In calculations based on nonrelativistic wave functions, the AMFI SO integrals were computed at the Breit-Pauli level. In DKH-based calculations, the corresponding first-order transformed DKH SO Hamiltonian39 was used (this holds also for the two-component calculations, where SO coupling is included in the wave function). In g tensor calculations, we employed a common gauge at copper. All HFC tensor results are reported in MHz. Note that in both Turbomole and G03, the hybrid functionals are implemented “in the Hartree-Fock spirit”, that is, with the nonlocal Hartree-Fock potential mixed in. This leads to the above-mentioned coupling terms in magnetic second-order property calculations (see refs 64 and 65 for EPR parameter calculations using localized hybrid potentials within the framework of the optimized effective potential framework).

J. Phys. Chem. B, Vol. 111, No. 28, 2007 8293 Isosurface plots of spin-density distributions and molecular orbitals were done with the Molekel program.66 Mainly Mulliken atomic spin densities will be discussed, but differences to results of natural population analyses are minor ( stellacyanin > 33 azurin (KS orbital energy differences at the BHLYP level are 5.6 > 5.4 > 5.0 eV). The somewhat larger energy denominators in stellacyanin counteract a further pronounced increase of g33, whereas the particularly low g33 of plastocyanin compared to that of the other two sites is partly aided by a larger energy denominator. Most of our calculations neglect scalar relativistic effects. Sinnecker and Neese found for plastocyanin that use of an atomic model potential derived from the scalar relativistic ZORA Hamiltonian (see above) enhanced ∆g33 by ca. 10-15 ppt and ∆g11 and ∆g22 by a few ppt. This brought g33 into somewhat better agreement with experiment but deteriorated agreement for g11 and g22.26 To evaluate the possible importance of scalar relativistic effects for the azurin g tensor, Table 4 includes also B3LYP results obtained with the relativistic DKH Hamiltonian. Due to the shift of spin density from sulfur to the metal, induced by the moderate relativistic contraction of the Cu 4s shell (see above and Table 1), one expects an enhancement of SO effects and thus of g anisotropy. This is confirmed by the calculations (e.g., ∆g33 is enhanced by about 20 ppt), consistent with the ZORA-based results on plastocyanin.26 However, even a moderate increase of the g anisotropy by scalar relativistic effects does not bridge the substantial gap between B3LYP-based results for g33 in azurin and experiment. This suggests that B3LYP does not describe the spin-density distribution accurately enough. Sinnecker and Neese have modeled environmental effects beyond the directly coordinated protein residues using QM/MM approaches for plastocyanin at the B3LYP level.26 While our B3LYP data agree well with their gas-phase results (Table 4), the QM/MM electrostatic contributions enhanced ∆g33 by another ca. 30 ppt (beyond the ca. 20 ppt scalar relativistic effects). The “best” value was about 50 ppt below experiment

J. Phys. Chem. B, Vol. 111, No. 28, 2007 8297 TABLE 5: Comparison of g Shift Components (in Parts Per Thousand) from One- and Two-Component Calculations for [CuCl4]2- a structure D4h

B3LYP 1-comp. 2-comp. BHLYP 1-comp. 2-comp.

D2d

B3LYP 1-comp. 2-comp. BHLYP 1-comp. 2-comp.

∆giso

∆g11

∆g22

∆g33

92.2 (2.09455) 83.6 (2.08596) 187.4 (2.18976) 167.8 (2.17015) 145.3 (2.14762) 125.1 (2.12743) 303.4 (2.30570) 267.0 (2.26931)

50.5 (2.05285) 43.6 (2.04589) 98.6 (2.10089) 82.9 (2.08523) 83.1 (2.08545) 69.8 (2.07208) 186.2 (2.18849) 176.6 (2.17889)

50.6 (2.05294) 43.7 (2.04597) 98.9 (2.10122) 83.2 (2.08551) 83.5 (2.08578) 70.0 (2.07237) 187.0 (2.18931) 177.5 (2.17986)

175.5 (2.17785) 163.7 (2.16602) 364.9 (2.36718) 337.4 (2.33965) 269.3 (2.27163) 235.5 (2.23783) 537.0 (2.53930) 446.8 (2.44917)

a Results from one-component/second-order perturbation and for twocomponent variational DKH treatment. Absolute g values are in parentheses.

(with the remaining error assumed to reflect deficiencies of the functional26). Note that our B3LYP results at nonrelativistic or scalar relativistic DKH levels for azurin deviate much more from the still appreciably larger experimental g33 than corresponding calculations for plastocyanin. It is not expected that environmental effects will be sufficient to provide agreement with experiment at this level. On the other hand, if we accept scalar relativistic or environmental effects of comparable magnitude at the BHLYP level, our results will overshoot the experimental g33 for both azurin and plastocyanin somewhat, and a slightly lower exact-exchange admixture than 50% will be more suitable. Another potential source of errors is the restriction to a leading-order perturbational treatment of SO effects (cf. eq 3). Table 5 shows for [CuCl4]2- at both D4h and D2d symmetries that our two-component treatment, which includes SO coupling variationally (while retaining spin polarization38), reduces all three tensor components compared to the perturbational approach. Overall, the reduction of g33 is much more pronounced for the D2d structure. Two-component calculations on azurin models are currently underway, and the magnitude of higherorder SO effects remains to be evaluated for the g tensors of blue copper sites. The experimental g tensor components for square planar [Cu(mnt)2]2- are g|| ) 2.086 and g⊥ ) 2.02476 and thus exhibit much lower g anisotropy than the blue copper sites, despite the appreciable spin density on copper (cf. Table 3). This suggests that the blue copper sites have better available low-lying excited states, a fact that will be relevant in the context of the copper hyperfine tensors below. We note in passing that our computations on [Cu(mnt)2]2- (cf. Table S2 in Supporting Information) underestimate g|| at the B3LYP level and overshoot it somewhat at the BHLYP level. Isotropic 65Cu Hyperfine Coupling Constants. The second, most interesting EPR probe of spin-density distribution that we evaluated was the copper hyperfine coupling tensors. Together with the blue color, the unusually small A|| component, and a resulting small isotropic coupling Aiso, is the most striking spectroscopic characteristic of blue copper proteins compared to “normal” CuII complexes. A series of experimental and computational studies by Solomon and co-workers10,17,20 (see Introduction) suggested that the small A|| value mainly reflects the unusually large Cu-S(Cys) covalency. Our computational results for blue copper protein models and inorganic complexes

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Remenyi et al.

TABLE 6: Computed and Experimental 65Cu HFC Tensors (in Megahertz)a

Aiso azurin

BP86

B3-40

-64.9

B3-45

-62.2

BHLYP -36.8

plastocyanin BP86

-10 -73.7

B3LYP -71.8 BHLYP -51.9 exptlb stellacyanin BP86

-22 -42.0

B3LYP -28.4 BHLYP 31.0 exptlb

AFC

-72.6 -228.4 -160.0

B3LYP -67.3

exptlb

A11, A22, A33

5

3.5 7.0 -224.5 6.4 16.1 -235.6 13.0 27.8 -260.0 28.8 44.8 -251.9 61.1 80.3 (-)161 66 66 -250.9 3.5 26.3 -258.6 4.0 39.0 -293.9 31.5 106.8 (-)185 60 60 -215.1 17.6 71.4 -210.3 28.4 96.7 -223.4 94.4 222.2 (-)167 87 96

APC

T11, T22, T33

87.4 -238.1

-179.1 111.8 -222.0 157.1 -241.0 178.8 -264.8 228.0

117.0 121.1 -267.7 129.1 138.6 -332.1 160.7 171.4 -378.2 182.8 195.3 -444.1 211.2 232.9

Adip,2 11 , Adip,2 22 , Adip,2 33

Aiso

82.8 [CuCl4]2(D4h) -40.8 -41.9 111.5 -53.8 -57.7 162.8 -79.0 -83.8 181.2 -87.7 -93.5 229.8 [CuCl4]2(D2d) -109.0 -120.8

-143.5

69.8 -242.4 65.4 107.3 -30.2 135.1 -35.2 -166.1 94.3 -279.0 92.5 116.6 -40.9 162.3 -51.5 -237.8 185.9 -426.4 185.0 [Cu(mnt)2]2158.8 -74.5 267.6 -110.5

-125.3

83.3 -246.8 74.0 84.0 -24.4 162.8 -49.6 -145.4 117.0 -291.6 110.4 93.2 -36.3 198.4 -74.1 -213.1 244.1 -477.6 226.5 124.1 -60.7 353.5 -165.8

BP86

A11, A22, A33

AFC

-153.2 -409.9 -241.5

APC

T11, T22, T33

88.2 -341.1

Adip,2 11 , Adip,2 22 , Adip,2 33 84.4

-24.9 170.6 -42.2 -24.9 170.6 -42.2 B3LYP -182.1 -470.3 -311.3 129.2 -409.3 121.1 -38.1 204.7 -60.6 -38.1 204.7 -60.6 BHLYP -152.2 -480.5 -383.7 231.5 -545.1 216.8 12.0 272.6 -108.4 12.0 272.6 -108.4 exptlc -95 (-)491 103 103 BP86 -57.7 -284.6 -187.8 130.1 -341.0 114.0 55.8 55.8 B3LYP -42.6 -312.4 92.3 92.3 BHLYP 21.0 -287.6 175.2 175.2 exptld (+67)e (-)70 +135 +135 BP86 -163.6 -384.8 -55.7 -50.4 B3LYP -213.2 -474.9 -84.7 -79.9 -605.0 BHLYP -268.3 -100.7 -99.2 -482 exptl76 -238 -117 -114

170.5 -57.0 170.5 -57.0 -249.0 206.4 -424.1 154.3 212.1 -77.1 212.1 -77.1 -304.0 324.9 -566.8 258.3 283.4 -129.1 283.4 -129.1

-203.0

39.4 -256.0 126.1 129.9 -272.0 58.8 -314.1 155.3 158.7 -434.7 -379.4 111.1 215.9 218.8

34.8 -16.6 -18.2 52.3 -25.5 -26.8 98.0 -48.2 -49.7

a All-electron results. A FC and APC denote the isotropic first-order iso is the total isotropic value, and Aii represents the total tensor components. A Fermi contact and the second-order pseudocontact (spin-orbit) contributions, respectively. T and Adip,2 denote, respectively, the first-order nonrelativistic and second-order spin-orbit anisotropic tensors. b From Cu ENDOR.2 c From K2PdCl4(Cu) crystals with square planar CuCl4 symmetry.84 d From Cs2ZnCl4(Cu) crystals.41 e Assuming a negative A||.

in Table 6 indicate, however, that rationalization by a particularly small copper spin density alone is an oversimplification. The discussion is complicated somewhat by the large dependence of the quantitative results on the exact-exchange admixture. Given that we found the overall best agreement with spindensity distribution and EPR parameters at relatively large fractions of exact exchange (see above and also the nitrogen and proton hyperfine tensors below), we will base our detailed rationalization mainly on the BHLYP data (using somewhat lower values than 50% exact exchange, e.g., the 38% favored by Solomon and co-workers, would not alter the main conclusions). Our previous experience with EPR parameter calculations for transition-metal complexes suggests that the relative magnitude of the different contributions to the copper hyperfine tensors will be modeled reasonably well at this computational level (note the absence of spin contamination). Let us start with azurin, for which the most extensive comparison of functionals has been carried out (Table 6). We

concentrate first on Aiso (note that the “experimental” data given for the blue copper proteins are 1/3 of the trace of the hyperfine tensor, based on the assumption that A⊥ > 0, a choice which is consistent with a variety of experimental and computational data). The overall isotropic hyperfine coupling starts out appreciably negative for the BP86 GGA functional and grows to less negative values with larger Hartree-Fock exchange admixtures a0. How can this be reconciled with increasing metal spin density along the same series of functionals (cf. Table 1)? Closer examination of the first- and second-order contributions indicates that the first-order Fermi contact term AFC is substantially negative already with BP86 and turns even more negative with increasing a0. This is the expected trend, as the negative spin density at the copper nucleus arises from spin polarization of the 2s (large negative contribution) and 3s (smaller positive contribution) core shells by the unpaired spin density in the copper 3d orbitals.41,54,55 Thus, the increased spin density on copper with increasing a0 causes a more negative AFC value.

EPR Parameters and Spin-Density Distribution of Azurin At the same time, however, the pseudocontact term, APC (i.e., the second-order SO correction to Aiso), is significant and positive already at the BP86 level and increases even more dramatically in absolute value with increasing a0 than AFC. As a result, Aiso turns less negative and arrives at a very small absolute value at the BHLYP level (still about 27 MHz too negative compared to experiment). It is well-known that spinorbital contributions tend to be nonnegligible for copper HFCs.4,10,41 However, the most recent DFT calculations indicated that the positive APC contributions amount only to about 30-50% of the (negative) AFC terms in typical square planar or square pyramidal CuII systems.42,44 Obviously, APC plays a much larger role for azurin, in particular when relatively large exact-exchange admixtures to the functional are accepted. Results for plastocyanin and stellacyanin exhibit similar trends as those for azurin, albeit with overall slightly more and less negative Aiso, respectively, consistent with the experimental data (Table 6). Thus, the compensation between negative AFC and positive APC plays an important role for the small Aiso in blue copper proteins! Previous comparisons were often made with [CuCl4]2- (at both D4h and D2d structures).10,41 This suggested the larger Cu-S covalency and thus lower copper spin density in the blue copper sites to account for the narrow hyperfine splittings. Our calculations clearly confirm the more negative AFC for [CuCl4]2(Table 6), particularly for the D4h structure (cf. also the larger spin densities on copper, Table 3). APC contributions (and SO contributions to the anisotropy; see below) for [CuCl4]2- in D4h symmetry incidentally tend to compare well with those computed for the blue copper models (cf. BHLYP results in Table 6). Tetrahedrally distorted (D2d) [CuCl4]2- exhibits larger SO contributions but a less negative AFC (cf. extensive previous discussions of this fact in refs 40 and 41). We feel that a full discussion of the low copper hyperfine coupling in blue copper sites needs to appreciate also the trigonal (or distorted tetrahedral or trigonal bipyramidal) coordination of copper and the presence of low-lying excited states, in analogy to the discussion40,41 for [CuCl4]2-. We should thus compare also to regularly coordinated systems with more covalently bonded ligands such as thiolates. Therefore, Table 6 includes data for the bisdithiolene complex [Cu(mnt)2]2-, which exhibits square planar coordination of copper and an even slightly lower spin density on copper than the blue copper models (cf. Table 3 and also Figure 3). Again, both the negative AFC and the positive APC increase with an increasing exactexchange admixture in the functional. At the BHLYP level, the computed Aiso is in fair agreement with experiment and has become appreciably more negative than that in the three blue copper model systems (Table 6). This is due, in almost equal parts, to a more negative AFC and to a less positive APC. The large AFC is an effect of a large valence shell spin polarization of the 4s orbital (see below). The small APC indicates the fact that no appropriate low-lying excited states enhance the SO contributions, in contrast to the tetrahedrally distorted blue copper sites (see below for further discussion). This situation is thus similar to the above comparison between [CuCl4]2- at the D4h versus D2d symmetry. We may conclude that the low isotropic copper hyperfine coupling in blue copper proteins reflects not only a relatively large covalency and thus low spin density on copper but also the distorted tetrahedral coordination, which gives rise to low-lying excited states and thus to particularly large SO (“orbital dipolar”) contributions to the hyperfine coupling. This nicely confirms an earlier systematic experimental comparison77 between various copper (II) com-

J. Phys. Chem. B, Vol. 111, No. 28, 2007 8299 TABLE 7: MO Contributions to AFC(Cu) (in Megahertz)a azurin plastocyanin stellacyanin [Cu(mnt)2]2[CuCl4]2- D4h [CuCl4]2- D2d c

AFC

1s

2s

3s

-264.8 -237.8 -213.1 -379.4 -383.7 -304.0

-21.2 -18.8 -22.1 -22.6 -26.6 -26.9

-607.8 -594.2 -670.3 -609.0 -743.7 -773.2

454.6 455.1 499.4 482.3 543.8 549.1

Σ CSb

Σ VSc

-174.4 -90.4 -157.9 -79.9 -193.0 -23.1 -149.3 -230.1 -226.5 -157.2 -251.0 -53.0

a Results at the BHLYP level. b Sum of all core-shell contributions. Sum of all valence-shell contributions.

plexes with comparable ligand sets but with coordination either closer to square planar or to tetrahedrally distorted. In all cases, tetrahedral distortion led to larger g|| components but to lower A||. Notably, this was also observed for sulfur coordination.77 While dithiolene ligands are sometimes considered a special case (“L-L interactions” are often invoked), in our experience, the delocalized backbone of the chelate ligand makes them mainly poorer π donors78,79 than saturated thiolates like cysteinyl. The individual Cu-S covalency in [Cu(mnt)2]2- is thus lower than that for Cu-S(Cys) in blue copper sites, but the fact that four Cu-S bonds are present renders the Cu spin density comparable (Table 3 and Figure 3), and we regard this system as a proper reference point. Comparison between the three different blue copper protein sites shows that AFC does not follow the expected trend; the copper spin density, FR-β(Cu), increases from plastocyanin over azurin to stellacyanin (Table 3). One would therefore expect that stellacyanin shows the most negative AFC, but the opposite is the case. Analysis of MO contributions reveals a crucial role of valence shell (VS) spin polarization (Table 7); the usually dominant contributions55 of the core-shell 2s and 3s spin polarization on AFC would indeed follow the order expected from the spin densities (Table 3) and provide the most negative AFC for stellacyanin (Table 7). However, this trend is overcompensated by the also negative, unusually large valence shell contributions, which are most pronounced for azurin and plastocyanin. Closer analysis indicates that these contributions arise from valence orbitals with some Cu 4s character. Table 8 shows natural atomic orbital (NAO) occupation numbers and spin populations of the metal 4s and 3d orbitals in the blue copper protein models. It is clear that stellacyanin exhibits much smaller 4s spin polarization than the other two systems. While the 3d spin population (Table 8) is, of course, much larger, the effect of a given 4s spin on AFC is much more pronounced due to the nonzero amplitude of the 4s AO at the nuclear position (whereas the 3d spin affects the spin density at the nucleus only indirectly via spin polarization of the 2s and 3s core shells;54,55 Table 7). The 4s spin populations arise both from some 4s character of the SOMO in the low-symmetry blue copper sites and from spin polarization of a number of doubly occupied valence MOs. The structural dependence of the valence shell contributions to AFC may be seen clearly for the comparison between [CuCl4]2- at D4h versus D2d symmetry (Table 7). While the distorted structure exhibits more spin density on copper and thus a more negative core-shell contribution, the more negative valence shell contributions render AFC considerably more negative for the square planar structure. Qualitatively, this agrees with a previous analysis at the XR-SW level with adjusted sphere sizes41 (our BHLYP results produce overall larger spin polarization and much larger negative valence shell contributions). Similarly, the particularly large valence shell contribution for

8300 J. Phys. Chem. B, Vol. 111, No. 28, 2007

Remenyi et al.

TABLE 8: NAO Occupation Numbers and Spin Populations (in Parentheses) of the Metal 4s and 3d Orbitalsa BP86 azurin plastocyanin stellacyanin [Cu(mnt)2]2a

4s 3d 4s 3d 4s 3d 4s 3d

0.417 (-0.0077) 9.603 (0.2995) 0.446 (-0.0070) 9.775 (0.2896) 0.403 (-0.0051) 9.589 (0.3120) 0.543 (-0.0119) 9.618 (0.2732)

B3LYP 0.370 (-0.0085) 9.591 (0.3294) 0.406 (-0.0082) 9.825 (0.3310) 0.367 (-0.0062) 9.566 (0.3658) 0.509 (-0.0165) 9.587 (0.3466)

BHLYP 0.354 (-0.0086) 9.414 (0.5800) 0.382 (-0.0089) 9.873 (0.5415) 0.360 (-0.0040) 9.308 (0.6572) 0.479 (-0.0207) 9.451 (0.5099)

From natural population analyses (NPA).85

Figure 5. Orbitals relevant for g33 and for the second-order SO contribution to A11 (see text).

[Cu(mnt)2]2- renders AFC for this square planar complex significantly more negative than that for the blue copper sites (Table 7). In summary, stellacyanin has the largest (positive) Cu 3d spin population of the three blue copper sites evaluated but nevertheless exhibits the least negative AFC. This is due to a larger (negative) 4s spin population in plastocyanin and in azurin. Already the AFC contribution to Aiso alone, even without the complication of a large positive APC term (see above), is thus strongly structure dependent and not easily interpreted in terms of the absolute spin density on copper. Anisotropic 65Cu Hyperfine Tensors. Turning to the spectroscopically most relevant A|| components (which are, of course, to a large extent reflected in the Aiso values), we have to examine how AFC, APC, T|| (T11), and the SO contribution dip,2 Adip,2 || (A11 ) behave. Agreement with experimental values is less favorable for A|| (cf. A11 in nonaxial cases) than for Aiso (Table 6), as the computed values tend to come out too negative (the same has been noted by Sinnecker and Neese for plastocyanin at the B3LYP level26). At the BHLYP level, there is obviously some error compensation between the too negative A|| (A11) and the somewhat too positive A⊥ (A22, A33) components when computing Aiso. Nevertheless, the conclusions drawn above for the origin of the small Aiso in blue copper sites apply analogously to A||; in addition to the already discussed compensation between negative AFC and positive APC, which becomes more complete with an increasing exact-exchange admixture, we find a similar compensation between a negative first-order dipolar contribution T11 and a positive anisotropic SO term Adip,2 11 . As the former remains larger than the latter at all levels, the overall anisotropic part of A|| is generally negative (the small negative Aiso makes only a moderate additional contribution to A||). It is difficult to assess the origin of the too negative A|| at the BHLYP level. A small part of it arises from a too negative Aiso, but the other part must come either from a too negative first-order dipolar or from an insufficiently positive second-order SO contribution. Due to the partial compensation

between the dependencies of the various first- and second-order contributions on the functional, the overall trend of A|| with the functional remains surprisingly weak for all three blue copper sites studied here. The dependence of the A⊥ components on the functional is actually somewhat more notable. As pointed out by Sinnecker and Neese,26 the quality of the computed SO contributions is related to the quality of the corresponding g tensor components, as similar couplings dominate these terms (see Figure 5 and discussion below). Given that we find a need for a relatively large exact-exchange admixture to reproduce the large g33 component (see above), it is thus not surprising than, for example, that BHLYP gives a larger APC and Adip,2 11 the B3LYP functional. We may again compare the situation for “regular” and “distorted” structures. The much more negative A|| of [CuCl4]2in D4h symmetry compared to D2d symmetry (Table 6) is predominantly due to the negative Aiso contribution (caused partly by a more negative AFC but mostly by a less positive APC; see above) and only to a small extent to a more negative anisotropic contribution. The BHLYP values agree qualitatively with data measured for salts with regular or distorted anions, whereas a quantitative comparison should probably not be attempted in view of the neglected crystal environmental effects. Compared to the earlier XR-SW calculations with adjusted sphere sizes,41 our results provide qualitatively similar trends (Table S3 in Supporting Information). The increase of the SO contributions to A|| from D4h to D2d is somewhat less pronounced, whereas our BHLYP computations provide a clearer reduction of the AFC contributions. The particularly negative A|| in the “normal” CuII reference thiolato complex [Cu(mnt)2]2- arises to almost equal parts from the negative Aiso (due to incomplete compensation between AFC and APC; see above) and from incomplete cancellation between T11 and a relatively small anisotropic SO contribution Adip,2 11 (Table 6). The picture obtained for Aiso may thus be extended to A||; the narrower hyperfine splittings compared to those of the [CuCl4]2- salts do reflect the lower copper spin density in

EPR Parameters and Spin-Density Distribution of Azurin TABLE 9: 14N Hyperfine Coupling Tensors (in Megahertz) of Histidine δ-N Atoms in Azurin BP86 B3LYP BHLYP exptl7

His46 His117 His46 His117 His46 His117 His46 His117

Aiso

A11

A22

A33

13.4 18.8 13.3 19.6 16.8 23.8 18.1 25.1

11.9 16.7 11.8 17.5 15.1 21.2 17.2 23.6

12.1 17.2 12.1 18.1 15.5 22.2 18.0 24.0

16.2 22.6 16.0 23.3 19.9 27.9 19.1 27.8

J. Phys. Chem. B, Vol. 111, No. 28, 2007 8301 TABLE 10: 1H Hyperfine Coupling Tensors (in Megahertz) of Cysteine β-H Atoms in Azurina BP86 B3LYP BHLYP exptlb exptld

the blue copper sites. However, the comparison with the more covalent dithiolene complex with Cu-S bonding strongly emphasizes the importance of positive SO contributions at the distorted tetrahedral compared to regular square planar structures. This seems a point that has been insufficiently appreciated up to now. Large SO effects on the copper hyperfine tensors at the distorted tetrahedral structures appear to arise mainly from the presence of low-lying excited states. Why are the SO effects so large here? Viewing the SO contributions as a second-order response property, we may infer from the computational formalism (eq 6) that their increased role in the distorted blue copper sites (or for D2d [CuCl4]2-) arises mainly from the presence of appropriate low-lying excited states that are mixed in by SO coupling. This is confirmed by our MO excitation analyses (Figure 5; cf. eq 6). The dominant positive SO contributions to A|| (or A11) arise from two β f β couplings of the doubly occupied MOs with the Cu-S(Cys) π-antibonding SOMO. The HOMO-8 is the Cu-S(Cys) σ-bonding MO involving the dx2-y2 orbital on Cu. The same HOMO-8 f SOMO coupling provides the dominant contribution (confirmed to be about 75% in our calculations) to g33, which is oriented collinear with A11 (see below). The second contribution is provided by coupling from the corresponding σ-antibonding HOMO-1 to the SOMO (Figure 5). The previous discussion40,41 for [CuCl4]2may thus be carried over to an appreciable extent to a comparison between blue copper sites and complexes with comparably covalent metal-ligand bonds but more regular structures. Ligand Hyperfine Couplings in Azurin. As additional EPR probes of the spin-density distributions in azurin at different degrees of the exact-exchange admixture to the functional, we examine the hyperfine tensors of the coordinating Nδ atoms of the equatorial histidine ligands (Table 9), as well as the β-proton hyperfine couplings of the cysteine ligand (Table 10). In agreement with experimental assignment and previous calculations,22,23 we find both isotropic and anisotropic 14N HFC components to be more positive for His117 than those for His46 (Table 9). Comparison with experiment shows that both BP86 and B3LYP results reproduce the near-axiality of the tensor reasonably well, but both are generally too low. Only at the BHLYP level are the experimental values approached with reasonable accuracy. We note, however, that in QM/MM calculations on plastocyanin, Sinnecker and Neese found electrostatic effects due to the larger protein environment to enhance the Nδ HFCs to some extent26 (a similar effect was also found in the GGA-based calculations on azurin models by Moon et al.23). This has to be kept in mind when judging the performance of different functionals. As the Mulliken spin densities on these nitrogen atoms are low and depend only moderately on the exact-exchange admixture (cf. Table 1), the computed trends mainly reflect the trend in the spin density at the nearby copper atom.

exptle

Ha Hb Ha Hb Ha Hb Ha Hb Ha Hb Ha Hb

Aiso

T11

T22

T33

45.2 52.6 43.0 47.4 25.2 26.2 20.8

-3.4 -3.3 -3.3 -3.2 -2.7 -2.4 -2.2c -2.9c

-1.6 -1.7 -1.8 -1.9 -1.5 -1.6 -0.7c +0.8c

+5.0 +5.0 +5.1 +5.1 +4.2 +4.0 +2.3c +2.0c

22.2 18 23

a See Figure 1a. b From 2H ENDOR at 95 GHz80 (recalculated to the nuclear g value of 1H). c Anisotropic tensor components in the principal axis system of the g tensor (not fully comparable to the computed A tensor principal components). d From a proton ENDOR line at 95 GHz (at g⊥).81 e From proton ENDOR at 35 GHz.3

A large dependence on the functional is also observed for the cysteine β-proton HFCs, for which a variety of experimental data is available3,80,81 (this holds only for the isotropic value; the smaller anisotropy is less well defined; cf. footnote c to Table 10). At the BP86 or B3LYP level, a far too large spin density on the cysteine ligand leads to very large isotropic HFCs. In contrast, the BHLYP results are only slightly above experiment and show a smaller splitting between the Ha and Hb protons (cf. Figure 1), consistent with conclusions from the most recent 2H ENDOR experiments.80 The trends in the S(Cys) spin densities (cf. Table 1) are thus reflected in the β-hydrogen hyperfine couplings. QM/MM calculations indicate some decrease of the cysteine β-proton HFCs due to the protein environmental effects,23,26 but the changes do not appear large enough to bring the B3LYP results into agreement with the substantially lower experimental values. The present results for the ligand hyperfine couplings provide further confirmations that hybrid functionals with relatively large a0’s provide a better description of the overall spin-density distribution in blue copper sites than standard BP86 or B3LYP levels,10 and we may base our discussion of the g tensor and the copper hyperfine tensor upon results with such hybrid functionals. Tensor Orientations. The computed orientations of the g tensor and of the two histidine Nδ HFC tensors for azurin are indicated in Figure 6. The Cu HFC tensor is not shown. Its A11 component is covariant with g33 (i.e., pointing roughly perpendicular to the equatorial plane), consistent with the above MO excitation analysis. A22 and A33 may be obtained by rotating g11 and g22, respectively, by 45° within the equatorial plane. In contrast to the magnitude of the tensor components (see above), the tensor orientations depend very little on the functional. The histidine Nδ HFC tensors are characterized by the largest component (A33) being along the N-Cu bond and A22 being perpendicular to the histidine ring plane. This indicates that most of the spin density associated with the Nδ HFC is along the N-Cu σ bond and not in the π bonds of the imidazole ring.7,82 The EPR Parameters of a Selenocysteine-Substituted Azurin. The recent EPR spectroscopic study of a selenocysteinesubstituted synthetic azurin analogue53 (SeCys-azurin) provides additional insight into the relations between equatorial coordination and EPR parameters in azurin. It was found experimentally that g33 was lower, and A|| was more negative in the selenocysteine-modified azurin than in the wild-type (WT) case.53 This is confirmed by the computational results for a geometry-

8302 J. Phys. Chem. B, Vol. 111, No. 28, 2007

Remenyi et al. TABLE 13: 65Cu Hyperfine Coupling Tensor (in Megahertz) in SeCys-Azurina

Aiso exptlb

-77.3

BP86

-79.5

B3LYP

-82.4

BHLYP

-63.1

A11, A22, A33 -310.0 24.8 53.4 -268.5 -22.7 52.7 -298.5 -12.6 63.9 -307.4 6.3 111.6

AFC

APC

-122.6

43.1

-133.5

51.1

-192.2

129.1

T11, T22, T33

Adip,2 11 , Adip,2 22 , Adip,2 33

-187.5 37.3 150.2 -204.5 41.4 163.0 -311.8 61.9 249.8

58.9 -2.5 -56.4 74.2 -1.7 -72.5 114.7 -18.3 -96.4

aA iso is the total isotropic value, and Aii represents the total tensor components. AFC and APC denote the isotropic first-order Fermi contact and second-order pseudocontact (spin-orbit) contributions, respectively. T and Adip,2 denote, respectively, the first-order nonrelativistic and second-order spin-orbit anisotropic tensors. b Frozen solution Q-band measurements.53

Figure 6. Orientation of the g tensor and the histidine Nδ HFC tensors for azurin.

TABLE 11: The g Shifts for SeCys-Azurin (in Parts Per Thousand), with Absolute g Values in Parentheses exptla BP86 B3LYP BHLYP a

∆giso

∆g11

∆g22

∆g33

∆g33 - ∆g11

126.3 (2.1286) 135.1 (2.1376) 151.5 (2.1538) 166.7 (2.1691)

42.5 (2.0448) 31.9 (2.0344) 36.1 (2.0384) 56.9 (2.0592)

103.3 (2.1056) 127.0 (2.1293) 140.0 (2.1423) 176.3 (2.1786)

233.1 (2.2354) 246.5 (2.2491) 278.6 (2.2809) 267.0 (2.2693)

188.6 214.6 242.5 210.1

Frozen solution (50 K) Q-band measurements.53

TABLE 12: Breakdown of the ∆gSO/OZ Contribution of the g Shift Tensor (in Parts Per Thousand) into Cu and S/Se Contributionsa in WT Azurin and SeCys-Azurin S/Se (from cysteine/ selenocysteine)

Cu ∆g11 azurin

BP86 B3LYP BHLYP SeCys-azurin BP86 B3LYP BHLYP

∆g22

∆g33

34.4 43.7 78.3 39.4 50.0 102.5 80.0 94.0 283.9 28.8 75.4 23.0 32.9 89.3 27.0 49.6 106.1 151.4

∆g11 ∆g22 0.2 0.4 0.7 3.1 3.5 7.7

∆g33

16.6 26.3 17.8 25.5 10.0 4.7 51.4 223.4 50.2 251.9 69.0 115.1

a AMFI-SO operators used only for the indicated atoms. The common gauge was on the metal center. The general axes of the individual ∆gSO/OZ contributions were transformed to the principal axes of the total g tensor.

optimized four-coordinate model (cf. Computational Details) of the SeCys-azurin site (Tables 11 and 13). We start with the g tensor. In contrast to the WT case, BP86 results do already reproduce the g tensor reasonably well, and the hybrid functionals tend to overshoot. The lower g33 and larger g22 (that is, the lower anisotropy and larger rhombicity) compared to WT azurin are reproduced. Dependence on the exact-exchange admixture is less pronounced than for the WT case (cf. Tables 3 and 11), consistent with the reduced dependence of the spin-density distribution found for a four-

coordinate model of WT azurin (cf. Table 2). The spin-density distribution in SeCys-azurin exhibits around 30% spin on Cu and around 60% on Se, essentially for all functionals studied, although the trend is toward less spin density on Se with increased exact exchange. The lower coordination (and possibly the long Cu-Se distance of 230 pm) thus renders the two sets of calculations more difficult to compare. Interestingly, comparison of individual atomic SO contributions to ∆gSO/OZ for WT azurin and SeCys-azurin (Table 12) shows pronounced differences; in the WT case, the dominant SO contributions come clearly from Cu, whereas sulfur SO contributions are only moderate. The Cu contributions increase with the exact-exchange admixture due to a larger localization of spin density at the metal (see above). In SeCys-azurin, the Cu contributions increase also with an increasing exact-exchange admixture, but they remain generally appreciably smaller than those in the WT case (Table 12). Now, Se-based SO coupling contributes comparable amounts to ∆g33, with a pronounced decrease with an increasing exact-exchange admixture. The overall lower dependence on the functional compared to the WT results from a compensation between the trends of the Cu and Se SO contributions! The influence of the functional on the Cu HFC tensor is also less pronounced than that in the WT system (Table 13). The largest A11 component is reproduced reasonably well, whereas the rhombicity of the tensor appears overestimated. In any case, the calculations confirm the experimental observation of a more negative A|| in the SeCys-azurin than that in the WT case, which is reflected also in a more negative Aiso. As can be seen from Table 13 (cf. also Table 5 for WT azurin), this is not due to a more negative AFC but to a less positive APC. Apparently, the low-lying excited states that render g33, as well as the SO contribution to A||, large and positive in WT azurin (see above) contribute less in the SeCys-azurin case. This allows us to reconcile the lower g anisotropy with the larger magnitude of A||. The latter would be hard to understand if the SO contributions to the HFC tensor were not as important as they are. Conclusions The direct computation of g tensors, as well as 65Cu, histidine 1 δ, and cysteine β- H hyperfine tensors for models of azurin, together with results for plastocyanin and stellacyanin and some

14N

EPR Parameters and Spin-Density Distribution of Azurin model complexes, by state-of-the-art density functional methods has provided additional insight into the important spin-density distributions of blue copper protein electron-transfer sites. The EPR parameter calculations with hybrid functionals agree with the conclusions of Solomon and co-workers10,20 that such functionals require larger exact-exchange admixtures than standard functionals (e.g., BP86 or B3LYP) to provide an accurate description of the spin-density distribution in blue copper sites. Solomon et al. have recommended a functional with 38% exact exchange based on a variety of measurements of the spin density (mainly XAS spectroscopy). We have focused on the slightly more common BHLYP functional with 50% exact exchange, which appears to provide a reasonable compromise for EPR parameters in azurin; the sensitive g33 g tensor component is approached well at this level. The spin density on copper comes out slightly larger than that given by some experimental measures. Nitrogen hyperfine couplings of the histidine ligands are still somewhat too low, and cysteine β-H hyperfine couplings are slightly too large. The g11 and g22 g tensor components are overestimated somewhat, and we will have to investigate higher-order spin-orbit contributions in this context. Scalar relativistic effects have been studied in one instance. While they do shift some spin density from the cysteine ligand to copper,26 the effect on spin density and EPR parameters tends to be less than the differences between different hybrid functionals. The same holds for potential long-range electrostatic influences from the protein, which have been neglected here. We see, therefore, that deficiencies of the available functionals are the main bottleneck in reproducing the EPR parameters reliably. Clearly, a more quantitative description of EPR parameters and spin-density distributions in such complex transition-metal systems as blue copper sites by DFT methods will require improved exchange-correlation functionals (as, e.g., a position-dependent exact-exchange admixture69-71). We had to refine previous rationalizations for the small Cu A|| hyperfine splitting in blue copper sites based on the large Cu-S(Cys) covalency (and thus small spin density on copper). When compared to regularly coordinated complexes with sulfur ligands and similar covalency (and equally low spin density on copper), the blue copper sites exhibit far larger positive spinorbit contributions to the hyperfine coupling, which together with the less negative Fermi contact term (and a negative spindipolar term) give rise to the characteristic, extremely narrow splitting. The same structural dependence of the copper hyperfine splitting is also found when comparing [CuCl4]2- at the D4h square planar versus D2d tetrahedrally distorted structures10,41 (see also Table 5), and it is consistent with earlier systematic experimental EPR comparisons between square planar and tetrahedrally distorted CuII systems with a variety of ligands.77 The distorted, essentially trigonal structure of the blue copper sites and the equatorially coordinated cysteine ligand provide access to low-lying excited states that spin-orbit couple strongly to the ground state. Both the large g anisotropy (large g||) and the large spin-orbit contributions to the Cu hyperfine coupling (related to the small Cu A|| and Aiso) derive from these strong couplings. Overall, only the consideration of unusually large SO effects on Cu hyperfine couplings allows reconciliation between relatively large g anisotropies and the small hyperfine couplings in blue copper proteins. Of course, the trigonal structures of the blue copper sites are, in turn, related to the pronounced π covalency of the Cu-S(Cys) bond.13,14 Studies on a selenocysteine-substituted azurin analogue have provided additional information on the relations between structure, bonding, and EPR parameters in blue copper protein

J. Phys. Chem. B, Vol. 111, No. 28, 2007 8303 sites. A number of further insights have been obtained by the direct comparison between models for the blue copper sites in azurin, plastocyanin, and stellacyanin, for example, on interrelations between spin-density distributions with g tensors and Cu hyperfine tensors. Acknowledgment. We are grateful to E. Groenen (Leiden) and M. van Gastel (Mu¨lheim) for suggesting this study and for fruitful discussions. This work has been supported by Deutsche Forschungsgemeinschaft and by the graduate college “Modern methods of magnetic resonance” at Universita¨t Stuttgart. C.R. thanks Studienstiftung des Deutschen Volkes for a doctoral scholarship. Supporting Information Available: Table S1 gives Cartesian coordinates of the (fully or partially) optimized structures. Table S2 provides g tensor data for [Cu(mnt)2]2-. Table S3 compares analyses of Cu hyperfine tensors for [CuCl4]2- at the BHLYP level with earlier XR-SW results. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Roberts, J. E.; Brown, T. G.; Hoffman, B. M.; Peisach, J. J. Am. Chem. Soc. 1980, 102, 825. (2) Roberts, J. E.; Cline, J. F.; Lum, V.; Gray, H. B.; Freeman, H.; Peisach, J.; Reinhammar, B.; Hoffman, B. M. J. Am. Chem. Soc. 1984, 106, 5324. (3) Werst, M. M.; Davoust, C. E.; Hoffman, B. M. J. Am. Chem. Soc. 1991, 113, 1533. (4) Solomon, E. I.; Baldwin, M. J.; Lowery, M. D. Chem. ReV. 1992, 92, 521. (5) Coremans, J. W. A.; Poluektov, O. G.; Groenen, E. J. J.; Canters, G. W.; Nar, H.; Messerschmidt, A. J. Am. Chem. Soc. 1994, 116, 3097. (6) Coremans, J. W. A.; Poluektov, O. G.; Groenen, E. J. J.; Canters, G. W.; Nar, H.; Messerschmidt, A. J. Am. Chem. Soc. 1996, 118, 12141. (7) Coremans, J. W. A.; Poluektov, O. G.; Groenen, E. J. J.; Canters, G. W.; Nar, H.; Messerschmidt, A. J. Am. Chem. Soc. 1997, 119, 4726. (8) Bertini, I.; Ciurli, S.; Dikiy, A.; Gasanov, R.; Luchinat, C.; Martini, G.; Safarov, N. J. Am. Chem. Soc. 1999, 121, 2037. (9) Bertini, I.; Fernandez, C. O.; Karlsson, B. G.; Leckner, J.; Luchinat, C.; Malmstroem, B. G.; Nersissian, A. M.; Pierattelli, R.; Shipp, E.; Valentine, J. S.; Vila, A. J. J. Am. Chem. Soc. 2000, 122, 3701. (10) Solomon, E. I.; Szilagyi, R. K.; DeBeer, G. S.; Basumallick, L. Chem. ReV. 2004, 104, 419. (11) Malmstrom, B. G. Eur. J. Biochem. 1994, 223, 711. (12) Williams, R. J. P. Eur. J. Biochem. 1995, 234, 363. (13) Ryde, U.; Olsson, M. H. M.; Pierloot, K.; Roos, B. O. J. Mol. Biol. 1996, 261, 586. (14) Ryde, U.; Olsson, M. H. M. Int. J. Quantum Chem. 2001, 81, 335. (15) Sykes, A. G. AdV. Inorg. Chem. 1991, 36, 377. (16) Adman, E. T. AdV. Protein Chem. 1991, 42, 145. (17) Shadle, S. E.; Penner-Hahn, J. E.; Schugar, H. J.; Hedman, B.; Hodgson, K. O.; Solomon, E. I. J. Am. Chem. Soc. 1993, 115, 767. (18) Penfield, K. W.; Gewirth, A. A.; Solomon, E. I. J. Am. Chem. Soc. 1985, 107, 4519. (19) Penfield, K. W.; Gay, R. R.; Himmelwright, R. S.; Eickman, N. C.; Norris, V. A.; Freeman, H. C.; Solomon, E. I. J. Am. Chem. Soc. 1981, 103, 4382. (20) Szilagyi, R. K.; Metz, M.; Solomon, E. I. J. Phys. Chem. A 2002, 106, 2994. (21) Coremans, J. W. A. W-Band Electron Spin Echo Spectroscopy of Azurin. Ph.D. Thesis, Leiden University, Leiden, The Netherlands, 1996. (22) Jaszewski, A. R.; Jezierska, J. Chem. Phys. Lett. 2001, 343, 571. (23) Moon, S.; Patchkovskii, S.; Salahub, D. R. THEOCHEM 2003, 632, 287. (24) Sugimori, K.; Shuku, T.; Sugiyama, A.; Nagao, H.; Sakurai, T.; Nishikawa, K. Polyhedron 2005, 24, 2671. (25) van Gastel, M.; Coremans, J. W. A.; Sommerdijk, H.; van Hemert, M. C.; Groenen, E. J. J. J. Am. Chem. Soc. 2002, 124, 2035. (26) Sinnecker, S.; Neese, F. J. Comput. Chem. 2006, 27, 1463. (27) Telyatnyk, L. G. Density Functional Studies of EPR and NMR Parameters of Paramagnetic Systems. Ph.D. Thesis, KTH Stockholm, Sweden, 2006. (28) Harriman, J. E. Theoretical Foundations of Electron Spin Resonance; Academic Press: New York, 1978. (29) Abragam, A.; Bleaney, B. Electron Paramagnetic Resonance of Transition Ions; Clarendon Press: Oxford, 1970.

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