Article pubs.acs.org/JPCA
Bonding in Nitroxide Spin Labels from Interactions
14
N Electric−Quadrupole
Derek Marsh* Max-Planck-Institut für biophysikalische Chemie, Am Fassberg 11, 37077 Göttingen, Germany Memphys, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark ABSTRACT: Nitrogen nuclear electric quadrupole couplings from FT-EPR of nitroxide spin labels can be used to deduce the covalent transfer πc in the N−O π-bond, and ionicities iσ(NO) and iσ(NC) of the N−O and N−C σ-bonds, if they are combined with the unpaired spin density on the nitrogen ρNπ obtained from the dipolar hyperfine couplings. Application to EPR data from an analogue of the MTSSL nitroxide that is used in site-directed spin-labeling demonstrates how environmental polarity and hydrogen bonding are reflected in the bonding parameters of the C−NO−C spin label moiety. Several recent publications erroneously claim to have deduced three independent bonding parameters from nitrogen quadrupole couplings alone.
R
ecently, 14N electric−quadrupole interactions have been determined with high precision for nitroxides commonly used in spin labeling, by using FT-EPR methods.1−3 These offer the possibility to characterize chemical bonding of the nitroxide group in terms of the electron occupations, nx, ny, and nz, of the nitrogen 2px, 2py, and 2pz orbitals.4,5 To satisfy Laplace’s equation, the electric field gradient tensor is traceless, and therefore the quadrupole tensor alone is insufficient to specify the bonding fully. However, the magnetic dipole component of the N-hyperfine coupling provides a further parameter that is related directly to the unpaired spin density ρNπ on the nitrogen atom, and therefore completes characterization of the C−NO− C bonding. Here, I concentrate on the pyrroline nitroxide PYMeOH (2,2,5,5-tetramethylpyrroline-1-oxyl-3-methylhydroxy). This forms the core of the methane thiosulfonate spin label MTSSL that is used routinely in site-directed spin labeling studies.6,7 Conventionally for nitroxides, the z-axis is the symmetry axis of the 2p-orbital that forms the pπ-bond, which contains the unpaired electron, and the x-axis lies along the N−O bond. In magnetic resonance, the quadrupole coupling tensor, P, of a nucleus with spin I ≥ 1 is defined by the principal elements:
Pii =
A p-orbital has axial symmetry about its unique axis. Therefore, the components (qxx,qyy,qzz) of the traceless field gradient from a pz-electron are 1 qxx(pz ) = qyy(pz ) = − qzz(pz ) 2
Equivalent expressions hold for a px- and a py-electron by permuting the indices. In an isolated atom, the directions i are equivalent, and qii(pi) is simply the field gradient along the symmetry axis of a nitrogen 2p-orbital, q2p,N. The net electric field gradient along principal direction i is the sum of contributions from the three 2p-orbitals: qii = nxqii(px ) + nyqii(py ) + nzqii(pz )
⎛ ⎞ 1 qzz = ⎜nz − (nx + ny)⎟q2p,N ⎝ ⎠ 2
(4)
Correspondingly, the asymmetry in the field gradient is given by qxx − qyy = (3/2)(nx − ny)q2p,N
(5)
Equations 4 and 5 characterize the field gradient completely, because Laplace’s equation requires that qxx + qyy + qzz = 0 for p-electrons, which have a node at the nucleus. Thus, only two independent parameters are available from the quadrupole
(1)
where qii are the principal elements of the electric field gradient at the nucleus, Q is the nuclear quadrupole moment, and i ≡ x,y,z. Both qii and Q are scaled by the elementary charge, e. The electric field gradient is contributed solely by the valence pelectrons, because s-orbitals and closed shells are spherically symmetric. © 2015 American Chemical Society
(3)
where nx, ny, and nz are the numbers of electrons in the nitrogen 2px, 2py, and 2pz-orbitals, respectively. From eqs 2 and 3, the field gradient in the principal z-direction becomes
e 2qiiQ 2I(2I − 1)
(2)
Received: December 22, 2014 Revised: January 9, 2015 Published: January 9, 2015 919
DOI: 10.1021/jp512764w J. Phys. Chem. A 2015, 119, 919−921
Article
The Journal of Physical Chemistry A
Table 1. Nitrogen 2p-Orbital Occupation Numbers, nx, ny, and nz; Covalent Transfer, πc, in the Nitroxide 2pzπ Bond; and Ionicities, iσ, of the N−O and N−C σ-Bonds nx PYMeOH/o-Terphenyl 1.10 ± 0.01 PYMeOH/Glycerola 1.08 ± 0.01 a
ny
nz
πc ≡ ρNπ
iσ(NO)
iσ(NC)
1.18 ± 0.01
1.445 ± 0.002
0.555 ± 0.002
0.05 ± 0.03
0.18 ± 0.01
1.18 ± 0.01
1.396 ± 0.002
0.604 ± 0.002
0.01 ± 0.03
0.18 ± 0.01
a
2,2,5,5-Tetramethylpyrroline-1-oxyl-3-methylhydroxy in o-terphenyl or glycerol at 180 K. EPR data are from ref 1.
couplings. To determine the three orbital occupancies nx, ny, and nz, we need an additional parameter. This is provided by the unpaired spin density on the nitrogen, ρNπ , which we get from the nitrogen hyperfine coupling. The 2pzπ-bond that contains the unpaired electron in a nitroxide radical is established by transferring covalent electron density πc from the doubly occupied nitrogen 2pz-orbital to the corresponding singly occupied 2pz-orbital on the oxygen. Thus, the net occupation number for the nitrogen pz-orbital is nz = 2 − πc
hybrid orbitals that are directed along the N−C bonds, the three mutually orthogonal nitrogen valence orbitals are
ΔAdip
2p,N
1 (nx + ny) 2
1 r3
2p,N
(12)
ψN − C = as|s⟩ −
1 − 2as2 1 |px ⟩ + |p ⟩ 2 2 y
(13)
1 θCNC = 2
1 1 − 2as2
(14)
Taking θCNC = 115.0° from the closely related pyrroline nitroxide MTSSL,12 the s-electron admixture in PYMeOH is a2s = 0.297. We quantify the population imbalance of the two shared electrons in a σ-bond by the fractional ionic character iσ of the covalent bond,5 where positive values correspond to electron excess on the nitrogen. The population of the ψN−O orbital is 1 + iσ(NO), and that of each ψN−C orbital is 1 + iσ(NC). From eqs 12 and 13, the electron population of the nitrogen py-orbital thus becomes
(7)
ny = 1 + iσ (NC)
(15)
Correspondingly, from eqs 11−13, that for the nitrogen pxorbital is nx = 1 + 2as2iσ (NO) + (1 − 2as2)iσ (NC)
(9)
(16)
where iσ(NO) is the ionicity of the N−O bond, and iσ(NC) is that of an N−C bond. Table 1 gives the nitrogen 2p-orbital occupancies for PYMeOH in hydrophobic and protic media. These values come from the experimental 14N hyperfine and quadrupole tensors of samples in o-terphenyl and glycerol glasses, respectively.1 Corresponding values for the degree of covalent transfer and ionicities are also listed in Table 1. The values of iσ(NC) approach the empirical prediction from electronegativities of halogen-containing compounds:13 iσ(NC) = (1/2)(XN − XC) = 0.25. Those of iσ(NO) are much lower, in accord with the relative electronegativities of carbon and oxygen, although the sign does not reverse, which might be a feature specific to free radicals. The positive charge on the nitrogen becomes c+ = πc − iσ(NO)−2iσ(NC) = 0.14 ± 0.03 in o-terphenyl and increases to 0.24 ± 0.03 in glycerol. Empirically correcting for the charge on the nitrogen atom by replacing P2p,N with P2p,N(1 + εc+), where the shielding factor is ε = 0.30
where P2p,N ≡ (1/2)e2q2p,NQ is the value of Pzz for a 14N nitrogen 2p-orbital. To obtain the electric field gradient q2p,N for a nitrogen atom, we must average over the 2p-orbital:4 q2p,N = ⟨3 cos2 θ − 1⟩p
1 − 2as2 1 |px ⟩ − |p ⟩ 2 2 y
tan
(8)
(Pxx − Pyy)/P2p,N = 3/2(nx − ny)
ψN − C = as|s⟩ −
Because p-orbitals transform like Cartesian vectors,11 the coefficients of |px⟩ and |py⟩ in eqs 12 and 13 are the projections on the x- and y-axes. Therefore, the angle θCNC between the two N−C bonds is given by
where g and gN are the electron and nuclear g-values, respectively, βe is the Bohr magneton, and βN is the nuclear magneton. The angular average in eq 7 is ⟨3 cos2 θ − 1⟩p = 4/5 for a p-electron. From self-consistent field calculations for nitrogen, the radial average is ⟨1/r3⟩2p,N = 2.093 × 1025 cm−3,9,10 and eq 7 becomes ΔAdip = (143.4 MHz) × ρNπ . Knowing nz from eq 6, we can now use the quadrupole couplings to obtain the occupancies, nx and ny, of the two other p-orbitals. From eqs 1, 4, and 5, the principal values of the quadrupole tensor become: Pzz /P2p,N = nz −
(11)
2
This creates unpaired electron spin density on the nitrogen that is equal to the covalent transfer from the nitrogen pz-orbital, that is, πc ≡ ρNπ . A consistent value for πc comes from the dipolar hyperfine anisotropy ΔAdip = Azz − (1/2)(Axx + Ayy). This is related to the unpaired spin density on the nitrogen ρNπ by (see, e.g., ref 8): ρπN
1 − 2as2 |s⟩ +
1
(6)
3 1 = gβegNβN⟨3 cos2 θ − 1⟩p 3 2 r
2as2 |px ⟩
ψN − O =
(10)
where the angular and radial averages are the same as those used in calculating the dipolar hyperfine anisotropy in eq 7. With a quadrupole moment Q = 2.044 × 10−26 cm2 for 14N, we then find that P2p,N = −6.0 MHz. Finally, we relate the electron occupancies nx and ny to the imbalance of electron pairing in the N−O and N−C σ-bonds of the trigonal nitrogen. In terms of σ-bonding orbitals, the electron configuration of the central nitrogen is 1s22(sp2)x2(sp2)C12(sp2)C22pz2, where the three sp2-orbitals are singly occupied. If a2s is the fraction of s-electron character in the 920
DOI: 10.1021/jp512764w J. Phys. Chem. A 2015, 119, 919−921
Article
The Journal of Physical Chemistry A for nitrogen,5,14 reduces these values to c+ = 0.10 and 0.19, respectively, with only small changes in the other quantities. The effective group electronegativity, Xg, of the nitroxide orbital to which the oxygen is bonded is defined from the empirical relationship by Xg = XO + 2iσ(NO). This yields Xg ≈ 3.6 ± 0.1, which is considerably larger than the averaged value of 3.0 for nitrogen, because of the net positive charge on the latter. Comparing the two sets of values in Table 1, we see that the greatest sensitivity to polarity and proticity comes from the increase in covalent transfer in the π-bond, followed by a decrease in ionicity of the N−O σ-bond. Both have the effect of increasing the electric dipole of the N−O bond. The N−C σbonds, on the other hand, remain unaffected. From the charge transfer from nitrogen to oxygen, we can predict the electric dipole moment of the N−O bond: pel = e(πc − iσ (NO))rNO
(3) Nalepa, A.; Möbius, K.; Lubitz, W.; Savitsky, A. High-Field ELDOR-Detected NMR Study of a Nitroxide Radical in Disordered Solids: Towards Characterization of Heterogeneity of Microenvironments in Spin-Labeled Systems. J. Magn. Reson. 2014, 242, 203−213. (4) Townes, C. H.; Dailey, B. P. Determination of Electronic Structure of Molecules From Nuclear Quadrupole Effects. J. Chem. Phys. 1949, 17, 782−796. (5) Dailey, B. P.; Townes, C. H. The Ionic Character of Diatomic Molecules. J. Chem. Phys. 1955, 23, 118−123. (6) Hubbell, W. L.; Lopez, C. J.; Altenbach, C.; Yang, Z. Technological Advances in Site-Directed Spin Labeling of Proteins. Curr. Opin. Struct. Biol. 2013, 23, 725−733. (7) Hubbell, W. L.; Altenbach, C. Investigation of Structure and Dynamics in Membrane Proteins Using Site-Directed Spin Labeling. Curr. Opin. Struct. Biol. 1994, 4, 566−573. (8) Carrington, A.; McLachlan, A. D. Introduction to Magnetic Resonance with Applications to Chemistry and Chemical Physics, 2nd ed.; Harper and Row: New York, 1969. (9) Whiffen, D. H. Information Derived From Anisotropic Hyperfine Couplings. J. Chim. Phys. 1964, 61, 1589−1591. (10) Clementi, E.; Roothaan, C. C. J.; Yoshimine, M. Accurate Analytical Self-Consistent Field Functions for Atoms. II. Lowest Configurations of the Neutral First Row Atoms. Phys. Rev. 1962, 127, 1618−1620. (11) Coulson, C. A. Valence; Clarendon Press: Oxford, 1952. (12) Zielke, V.; Eickmeier, H.; Hideg, K.; Reuter, H.; Steinhoff, H. J. A Commonly Used Spin Label: S-(2,2,5,5-Tetramethyl-1-Oxyl-Δ3Pyrrolin-3-ylmethyl) Methanethiosulfonate. Acta Crystallogr., Sect. B 2008, 64, o586−o589. (13) Gordy, W. Introductory Paper - Quadrupole Couplings, Dipole Moments and the Chemical Bond. Discuss. Faraday Soc. 1955, 14−29. (14) Gordy, W.; Cook, R. L. Microwave Molecular Spectra. Techniques of Chemistry; Wiley Interscience: New York, 1984. (15) Vasserman, A. M.; Buchachenko, A. L.; Rozantsev, E. G.; Neiman, M. B. Dipole Moments of Molecules and Radicals. Di-TertButyl Nitrogen Oxide. J. Struct. Chem. 1965, 6, 445−446. (16) Tanjaroon, C.; Subramanian, R.; Karunatilaka, C.; Kukolich, S. G. Microwave Measurements of 14N and D Quadrupole Coupling for (Z)-2-Hydroxypyridine and 2-Pyridone Tautomers. J. Phys. Chem. A 2004, 108, 9531−9539. (17) Bird, R. G.; Neill, J. L.; Alstadt, V. J.; Young, J. W.; Pate, B. H.; Pratt, D. W. Ground State 14N Quadrupole Couplings in the Microwave Spectra of N,N′-Dimethylaniline and 4,4′-Dimethylaminobenzonitrile. J. Phys. Chem. A 2011, 115, 9392−9298. (18) Betz, T.; Zinn, S.; Graneek, J. B.; Schnell, M. Nuclear Quadrupole Coupling Constants of Two Chemically Distinct Nitrogen Atoms in 4-Aminobenzonitrile. J. Phys. Chem. A 2014, 118, 5164− 5169.
(17)
Taking the N−O bond length rNO = 1.2767 × 10−8 cm for MTSSL,12 we get pel = 3.0 ± 0.2 D in o-terphenyl. This is of a magnitude similar to the experimental estimate of Δpel = 2.4 ± 0.1 D for the contribution to the total dipole moment from the N−O bond.15 In the case of nitrogen quadrupole couplings determined by rotational spectroscopy for nonparamagnetic molecules, we lack the additional parameter provided by EPR, and it is not possible to characterize the bonding parameters uniquely when the nitrogen is bonded to a third atom. In several recent studies, three independent parameters, iσ(NC), iσ(NX), and πc, have been derived from nitrogen quadrupole couplings alone.16−18 (In ref 18, the H−N−H angle θHNH, and hence as, is determined from DFT calculations, because this is not available from X-ray diffraction.) The reason appears to be that iσ(NC) was erroneously identified with as2, which specifies the sp2 hybridization of the nitrogen valence orbitals. This quantity is completely determined by the C−N−C bond angle, and unrelated to the degree of ionic transfer in the N−C σ-bonds. A further independent parameter is required, for which the textbook solution is to estimate iσ(NC) from differences in electronegativity (see ref 14, p 776).
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS I thank Christian Griesinger and the Department of NMRbased structural biology (MPI), and the Hans Christian Andersen Foundation (SDU) for financial assistance.
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REFERENCES
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DOI: 10.1021/jp512764w J. Phys. Chem. A 2015, 119, 919−921
