2424
J. Phys. Chem. B 2000, 104, 2424-2431
Interactions of the Rubredoxin Redox Site Analogue [Fe(SCH3)4]2- with Water: An Ab Initio Quantum Chemistry Study John B. Koerner and Toshiko Ichiye* Departments of Biochemistry/Biophysics and Chemistry, Washington State UniVersity, Pullman, Washington 99164-4660 ReceiVed: July 26, 1999; In Final Form: December 23, 1999
Water has been found to interact with the redox site of rubredoxin by molecular dynamics simulations, resonance Raman spectroscopy, and X-ray crystallographic structure determination. Since this should have a large effect on its electron-transfer properties, the nature of this interaction is important to characterize. Here, the interaction of [Fe(SCH3)4]2-, a redox site analogue for reduced rubredoxin, with a water molecule was investigated using ab initio calculations. Two different conformations of the analogue and different orientations of the incoming water were examined. Geometry optimizations at the unrestricted Hartree-Fock and second-order Møller-Plesset levels reveal hydrogen bonds donated from the water molecule to the sulfurs of the analogue. Calculated binding energies, which are similar at all computational levels even after correcting for basis set superposition error, indicate that the orientation in which each hydrogen of the water interacts with a separate sulfur is preferred to that in which a single hydrogen points toward the analogue. In addition, an enthalpically unfavorable trigonal-bipyramidal type adduct was found in which the water oxygen interacts directly with the iron but only at the lowest computational level. Atom-centered partial charges, by both Mulliken’s and electrostatic potential fitting methods, and geometries of the redox site show only slight changes upon complexation. This indicates that both electronic and geometric polarization of the analogue by the water was small, although there was some localized electronic polarization of the sulfurs near the incoming water. On the other hand, both electronic and geometric polarization of the water by the analogue were seen: the dipole moment of the water molecule increased by about 20% over that for an isolated water, with about one-quarter of this increase attributed to a more acute H-O-H angle. These results are also important in modeling the interaction of the water and the redox site in classical molecular dynamics simulations of rubredoxin and other iron-sulfur proteins.
1. Introduction Water molecules near the active site of metalloproteins can play a role in their function. In metalloenzymes, water can enhance the binding of the reactant, reduce the transition state energy, or facilitate release of the products.1-5 Interaction of water with the active site has also been seen in proteins involved in oxidation/reduction reactions. For instance, nuclear magnetic resonance studies show changes in the number and location of water molecules, including a so-called catalytically important water, near the redox site of cytochrome c upon changes in redox state.6 These changes were postulated to have significant roles in setting the solvent reorganization energy associated with electron transfer. The redox potential of electron-transfer proteins is determined by both the intrinsic redox potential, which includes the energetics of the metal redox site, and the extrinsic redox potential, which includes the effects of the surrounding protein matrix and solvent. However, the distinction between intrinsic and extrinsic redox potentials can become ambiguous due to the strong interaction of the active metal with the environment; the metal may affect the electronic properties of the nearby protein and solvent, and also the protein and/or solvent may affect the electronic properties of the metal site. More simply, the orientation and distance of a highly polar water molecule * To whom all correspondence should be addressed.
with respect to the redox site will affect the electrostatic potential at the redox site. The iron-sulfur protein rubredoxin contains the one-iron site, [1Fe], in which the iron is tetrahedrally coordinated to four cysteinyl sulfurs. Several analogues of the [1Fe] site have been synthesized and their redox potentials measured, as reviewed elsewhere.7 In addition, several electronic structure studies have been performed on iron-sulfur sites, as reviewed elsewhere.8 In particular, two recent studies have determined electrostatic potential (ESP) or “partial” charges for use in classical electrostatic calculations by density functional theory9 and by unrestricted Hartree-Fock methods.10 Moreover, the latter study determined that the partial charges and ionization potentials of the [1Fe] site are invariant with respect to changes in the dihedral angles of the site. All of these studies have been in vacuo or in a continuum dielectric environment. However, our previous molecular dynamics simulations of reduced rubredoxin in aqueous solution, using partial charges on the Fe-S site from X-R electronic structure calculations,11 indicate that solvent water can enter the protein close to the redox site.12 This has been confirmed in resonance Raman studies of ferredoxin13 and rubredoxin [J. Sanders-Loehr, personal communication] in which deuterium is exchanged with the cysteinyl hydrogens and, very recently, in an X-ray crystallographic study in which water is present very near the redox site in the reduced but not the oxidized
10.1021/jp9925785 CCC: $19.00 © 2000 American Chemical Society Published on Web 02/18/2000
Interactions of [Fe(SCH3)4]2- with Water
J. Phys. Chem. B, Vol. 104, No. 10, 2000 2425
state of rubredoxin.14 Thus, it is critical to determine the nature of the interaction of the Fe-S site with a water molecule to assess the redox properties of rubredoxin accurately. One important aspect is how well these interactions can be modeled for classical molecular mechanics simulations. For instance, whether these interactions can be described as simple van der Waals and/or electrostatic (including hydrogen bonding) must be determined. In particular, it is important to understand the extent of electronic polarization of water by the redox site and vice versa. The goal of this study is to determine the nature of the interaction of the [1Fe] site with a single water molecule using quantum mechanical calculations. Whereas the previous study was of the [1Fe] site alone,10 here the focus is on its interactions with the water molecule. The reduced state is examined since in the previous molecular dynamics simulations12 and the X-ray crystal structure,14 the close interaction of water with the redox state was seen for the reduced state of rubredoxin. The preferred geometries of the water are studied with respect to different conformations of the [1Fe] site, which were chosen as representative of the rubredoxin redox site and as representative of analogue in solution conformation in which the iron is most exposed to solvent. Also, several details of the electronic structural features of this model system are examined to determine the nature of the interaction of [1Fe] and water. In addition, the effects of water on the partial charge distribution of the [1Fe] site are studied and the degree of polarization of the water by the [1Fe] site is calculated by examining the geometric and electronic changes of the water molecule. 2. Computational Details a. Models. The model for the active site of rubredoxin and its synthetic analogues consists of four methiolate ligands surrounding a central iron atom as in our earlier study.10 The four methiolate sulfurs form a tetrahedron surrounding the central iron atom (Figure 1) with the four faces of the sulfur tetrahedron being designated by the three numbered sulfurs composing the face. For example, the face made up of S2, S3, and S4 is designated S2:S3:S4. The carbons attached to the sulfurs of a face can be oriented either cis or trans with respect to that face. For instance, when C1 is trans to S2, it is cis with respect to S1:S3:S4 and vice versa. A given face is most buried when its carbons are cis and most exposed when its carbons are trans. The two conformations of the analogue examined here are structures 1 and 2 (Figure 1), which were selected from the previously reported set of five.10 Structure 1 was chosen as an idealization of the geometry of the redox site of rubredoxin. Structure 2 was chosen as a representative of a conformation that an analogue with freely rotating alkyl groups might adopt, which has the iron most exposed to the solvent. The two structures differ by a 180° rotation about a single Fe-S bond, thus altering the position of ligand 1 so that the S1:S3:S4 face is blocked by the alkyl group in conformation 1 but is fully exposed in conformation 2. For the analogue alone, conformation 1 possesses C2V symmetry while conformation 2 possesses a mirror plane (Cs). The conformations of the water plus analogue complexes are denoted by a boldface arabic numeral for the analogue conformation followed by a boldface italics letter for the water orientation. In all cases, the water is approaching the S1:S3:S4 face. The water has the hydrogens pointing toward the analogue in conformations a and b and away from the analogue in conformation c. Furthermore, the water is constrained to lie either entirely within the mirror plane of symmetry (a and c) or perpendicular to the mirror plane of
Figure 1. Schematic of the interaction of the analogue [Fe(SCH3)4]2in conformations 1 and 2 with water molecules in the plane, a and c, and perpendicular to the plane, b, are also shown.
symmetry (b); thus, the complexes examined have Cs symmetry regardless of whether the analogue is in conformation 1 or 2. b. Electronic Structure Calculations. The reduced form of the model is examined here, which has a net charge of 2- so that the iron is formally Fe(II). The electronic state was matched to experiment, which shows a quintet state for the reduced complex.15 Since the high spin states of these complexes were examined, unrestricted Hartree-Fock calculations (UHF) were carried out using the Gaussian 9216 and GAMESS17 electronic structure packages. The MP2 calculations, which were all carried out using Gaussian 92, utilized the frozen core approximation. Two different basis sets were implemented for these calculations. The first (BSI) was a relatively small basis set, while the second (BSII) was much larger. The consistency of the results indicates that BSII was sufficient. BSI utilizes an effective core potential (ECP) on the iron and the sulfurs. Both of these pseudopotentials remove the 1s, 2s, and 2p electrons from explicit consideration. In addition, the associated bases were used, for both iron and sulfur, which were contracted to give a double-ζ basis in the valence region. For iron, they took the form (341/311/41) while the sulfur basis was contracted to give (21/21).18,19 The C atoms of the ligands and the O and H atoms associated with the water used the standard 3-21G basis,20 while the methyl hydrogens of the ligands were represented with the smaller STO-3G basis.21,22 BSII consists of the (14s9p5d) primitive set of Wachters23 for the iron, which was modified in the following way. The last s exponent was changed to 0.298. Two p functions were added with exponents of 0.231 and 0.0899. Wachters’ d exponents were supplanted with the 6d set calculated by Rappe
2426 J. Phys. Chem. B, Vol. 104, No. 10, 2000 et al.24 These exponents were contracted in the following manner: (5111111111/41111111/411). This was the TZV (“triple-ζ valence”) basis set in the GAMESS library.17 The same basis set for the S, C, and H atoms of the ligands used in BSI was employed here, but the S atom was augmented with a d function (ζ ) 0.85). The basis set for the water molecule was changed to the Dunning-Hay split-valence set with an added d function on the oxygen (ζ ) 0.65).25 These primitives were contracted according to (721/41/1) for the oxygen and (3/ 1) for the hydrogens. In the previous study,10 a third basis set was also studied that was the same as BSII with an f polarization function (ζ ) 1.339) added to the iron.26 However, the earlier studies indicated that the properties examined here are relatively insensitive to the added f function. Three sets of calculations were performed: UHF calculations were performed using BSI and BSII, and an MP2 calculation was performed using BSI. The binding energies of the [1Fe]water complex were calculated with respect to the sum of the isolated fragments. Basis set superposition errors (BSSE) were estimated for these systems by counterpoise (CP) calculations, and the problem associated with choosing representative fragments to obtain the CP correction is well documented.27 For the MP2 calculation using BSI, the BSSE were the same as for the UHF using BSI, thus avoiding problems associated with BSSE at the correlated level.28 c. Electrostatic Potential Properties. The net “partial charges” on each atom were obtained from the BSI optimized geometries and wave functions of the systems by both Mulliken population analysis and by fitting the electrostatic potential (i.e., ESP charges) using CHELPG. The latter calculations on the UHF wave functions used the GAMESS package, while those on the MP2 wave functions used the Gaussian 92 package. The electrostatic potential at points spaced on a cubic grid (0.5 Å apart in the GAMESS calculations and 0.3 Å apart for Gaussian) was determined for all points within a shell surrounding the molecule. The outer boundary of the shell was 5.0 Å in GAMESS and 2.8 Å in Gaussian from any atom in the molecule, while the inner boundary was defined by the van der Waals radii of the atoms in the molecule, which for all calculations are those proposed by Breneman and Wiberg: S, 2.0 Å; C, 1.5 Å; O, 1.75 Å; H, 1.45 Å; Fe, 1.8 Å (the default value). In the GAMESS calculations, the total charge and Cartesian components of the dipole and quadrupole moment were constrained to those determined from the electronic wave function whereas for Gaussian, only the charge and dipole were constrained. 3. Results and Discussion a. Molecular Geometries and Basis Sets. Separate geometry optimizations of the [1Fe] site and of the water were first examined to determine the dependence of the results on basis set and level of calculation. The basis sets selected (see Methods section) represent a compromise between two competing factors. Accurate electrostatic moments are needed to study the electronic polarization of the molecules, which can be achieved by increasing the number of basis functions or the electron correlation contained within a calculation. However, an unbalanced basis set for any fragment must be avoided when examining the quantum mechanical interaction between molecules. Given these considerations, the general strategy was that rather modest basis sets were chosen for the nonmetal atoms, i.e., the ligands and the water, even though water has been studied with much higher basis sets in order to keep the calculations tractable for studies of multiple conformations of the complex. For these atoms, the variation between BSI and
Koerner and Ichiye TABLE 1: Comparison of Absolute Energies, Optimized Geometries, Partial Charges, and Dipole Moments of H2O at Different Basis Sets and Levels of Calculation method
absolute energya
geometryb OH HOH
UHF/BSI
-76.01093 0.951
112.6
MP2/BSI
-76.13535 0.978
110.8
UHF/BSII -76.03524 0.947
106.5
exptl
-76.48d,e
0.957e 104.5e
electrostatic momentsc Mulliken CHELPG QM qO qH µ qO qH µ qO qH µ µe
-0.799 0.398 2.03 -0.754 0.377 2.01 -0.856 0.428 2.33
-1.010 0.505 2.56 -0.942 0.471 2.52f -0.843 0.422 2.29 1.87
2.53 2.52 2.26
a Absolute energies in au. b Bond lengths in angstroms and bond angles in degrees. c Charges in units of electron charge; dipole moments in Debyes. d Estimated HF energy is -76.068 au. e Reference 31, p 431. f Constrained to the quantum mechanically determined value.
BSII was the inclusion of d polarization functions for the sulfurs. For the iron, which is of central interest, both an effective core potential with an associated basis that is double-ζ in the valence shell (BSI) and a full core basis that is triple-ζ in the valence shell (BSII) were examined. From the previous study, the differences between BSI and BSII were small for the analogue except that BSII led to better geometries. Results for MP2 calculations using BSI (designated MP2/BSI) as in the previous study10 are included for reference. Although geometries using very small basis sets are not improved by the introduction of correlation,29 the Fe-S bond length does improve (Fe and S are both double-ζ). Moreover, MP2 tends to overestimate electron correlation more with larger basis sets.29 The previous study indicates that the higher basis set is preferable to the lower with correlational effects included. Geometries and electronic properties for an isolated water molecule have been studied by many workers.30 Several different basis sets were examined here and compared to experiment31 (Table 1). In terms of bond lengths, the UHF calculations using BSI and BSII (designated as UHF/BSI and UHF/BSII, respectively) both give accuracies within 0.01 Å of the experimental structure, but the MP2/BSI are actually worse than the UHF/ BSI. The H-O-H angle is markedly improved upon going from BSI to BSII at the UHF level, but the MP2/BSI calculation is only slightly better than UHF/BSI. Mulliken charges for the UHF/BSI and MP2/BSI calculations give a less polarized picture of the bonding than for UHF/BSII. BSI fortuitously gives a Mulliken dipole moment closer to the experimental gas-phase value of 1.84 D. The partial charges from the UHF calculations determined from the ESP fits gave dipole moments that were very close to the quantum mechanically determined values, while the charges from the MP2 calculations were constrained to the correlated quantum mechanical dipoles. While the MP2/ BSI calculations did not show improvement in the dipole moment over UHF/BSI, the UHF/BSII showed a marked decrease toward the experimentally determined value. Thus, UHF/BSII gives the best properties for an isolated water molecule and is balanced with respect to the basis set used for the [1Fe] site. The isolated [1Fe] site has been studied in detail elsewhere;10 thus, only selected geometric parameters for the optimized isolated [1Fe] site are summarized here and compared to experiment32 (1 + H2O and 2 + H2O in Table 2a). For both conformations 1 and 2, the geometries are quite similar to each other and the energies are within 0.1 kcal/mol of each other. The error in the Fe-S bond lengths determined at the UHF level using BSI is quite large, about 0.2 Å, but predictable.33,34
Interactions of [Fe(SCH3)4]2- with Water
J. Phys. Chem. B, Vol. 104, No. 10, 2000 2427
TABLE 2: Optimized Geometries and Relative Energies of Conformations 1 and 2 as Isolated Fragments (1 + H2O, 2 + H2O) and Interacting with Water (1a, 1b, 2a, 2b, 2c) at Different Computation Levels Using Different Basis Setsa method UHF/BSI
MP2/BSI
UHF/BSII
experimentf
property
1 + H2O
1a
1b
2 + H2O
2a
2b
2c
Erelc (Fe-S)avg (S-C)avg (O-H)avg H-O-H Ereld (Fe-S)avg (S-C)avg (O-H)avg H-O-H Erele Fe-S1 Fe-S2 Fe-S3,4 S1-C1 S2-C2 S3,4-C3,4 S1-Fe-S2 S1-Fe-S3,4 S2-Fe-S3,4 S3-Fe-S4 Fe-S1-C1 Fe-S2-C2 Fe-S3,4-C3,4 O-H1 O-H2 H-O-H (Fe-S)avg (S-C)avg O-H H-O-H
18.8 2.57 1.91 0.95 112.6 20.9 2.52 1.94 0.98 110.8 18.1 2.540 2.540 2.543 1.852 1.852 1.852 107.57 110.68 110.68 106.58 99.86 99.86 102.42 0.947 0.947 106.53 2.36 1.81 0.957 104.5
6.0 2.56 1.91 0.95 107.8 7.4 2.51 1.94 0.98 105.8 6.7 2.540 2.524 2.535 1.850 1.851 1.851 106.49 111.22 113.67 100.65 102.46 100.37 104.45 0.948 0.951 102.23
0.0 2.57 1.91 0.96 108.4 0.6 2.51 1.94 0.99 106.7 0.0 2.525 2.521 2.556 1.850 1.851 1.849 109.17 109.69 112.74 102.64 101.92 100.29 101.71 0.954 0.954 102.66
18.7 2.58 1.91 0.95 112.6 22.2 2.52 1.94 0.98 110.8 18.0 2.562 2.551 2.539 1.851 1.851 1.851 106.50 111.86 109.26 108.05 101.85 99.44 100.22 0.947 0.947 106.53 2.36 1.81 0.957 104.5
4.1 2.56 1.91 0.96 108.9 5.4 2.51 1.94 0.98 106.6 4.4 2.571 2.537 2.524 1.845 1.851 1.851 105.64 109.85 111.85 107.78 104.98 99.82 100.65 0.955 0.949 102.90
0.9 2.57 1.91 0.96 108.4 0.0 2.51 1.94 0.99 106.3 1.7 2.538 2.528 2.553 1.851 1.851 1.850 107.31 111.29 112.03 102.94 101.27 99.79 103.83 0.954 0.954 102.56
22.8 2.66 1.91 0.95
a Energies in kcal/mol, bond lengths in angstroms, and bond angles in degrees. c Energy calculated relative to 1b, which has an absolute energy of -395.86012 au. d Energy calculated relative to 2b, which has an absolute energy of -396.61097 au. e Energy calculated relative to 1b, which has an absolute energy of -1535.75493 au. f Experimental measurements for H2O from ref 31, p 431. Other values from ref 32.
Including electron correlation at the MP2 level consistently reduced the error by 0.05 Å. On the other hand, at the MP2 level, the S-C bond lengths are farther from the experimental values by 0.03 Å. Not surprisingly, a larger basis set also reduced the error from the UHF/BSI level; the Fe-S bonds determined at the UHF/BSII level are shorter by 0.03 Å. The S-Fe-S and Fe-S-C bond angles were reasonable (not shown, see ref 10), the average S-Fe-S angles being nearly the expected tetrahedral angle of 109.5° in all cases and the Fe-S-C angles being approximately 102° much like that found in many inorganic salts.35-37 The optimized geometries of the complexes with different basis sets and levels were compared (Table 2). In general, the molecular geometries of each species do not differ much from the isolated species and the basis set dependence of the trends between different conformations is small. Thus, only abbreviated results are shown for the UHF/BSI and MP2/BSI calculations. The relative geometry of the [1Fe] site and the water shows some basis set dependence. Moreover, the trends in the relative geometries between the conformations are similar at each computational level. The MP2 results show a decrease in distance between the [1Fe] and the water over both the UHF/ BSI and UHF/BSII results, which are generally in agreement with each other. One notable exception is conformation 2a, in which the Fe‚‚‚O distance expands from 4.42 to 4.81 Å upon going from BSI to BSII due to the correction by the d polarization function of BSII for an underestimation of the lone pair-lone pair repulsion between the S and O at the BSI level. b. The [1Fe] Site-Water Interaction. The [1Fe] site-water interaction can be examined by studying optimized geometries (Table 2, Figure 2) for the complexes 1a 1b, 2a, and 2b, which
are formed from the interaction of the [1Fe] site in conformations 1 and 2 with the water molecule in the a and b orientations (Figure 1). Conformation 2c, in which the water is oriented differently, is discussed separately. The interaction in the complexes gives rise to slight changes in the internal geometry of both the [1Fe] site and the water (Table 2a). Among the bond lengths of either component of the complex, the maximum change in any bond length is 0.01 Å. On the other hand, the H-O-H bond angle shows slight compression of about 4-5° in the complex at all the levels tested, indicating a geometric polarization of the water molecule. At all of the computational levels tested, the interaction between the iron and the water molecule in 1a, 1b, 2a, and 2b can be described as a weak van der Waals type. For all of these complexes, the Fe‚‚‚O distance is rather large, from 4 to 5 Å (Table 3). The dependence on the orientation of the water can be seen in that the Fe‚‚‚O distance is 0.3-0.4 Å farther away in the a relative to the b conformation. On the other hand, the water is able to come much closer to the sulfurs and the S‚‚‚H distances are highly conformation-dependent (Table 3) so that apparently it forms different O-H‚‚‚S hydrogen bonds depending on the conformation. For the a conformation, where the plane of the water molecule is parallel to the S1-Fe-S2 plane, the interactions of the water with the sulfurs is governed by the alkyl group from ligand 1. For complex 1a, where the alkyl group blocks the face of the approaching water molecule, the S1‚‚‚H1 distance is large (over 4 Å) and the water is rotated so that the H1 is actually closer to S3 (and by symmetry, S4). In addition, H2 is even closer to S3 and S4 and may form a very weak bifurcated hydrogen bond to the two. However, when the alkyl group is rotated by 180° in complex 2a, H1 of the water
2428 J. Phys. Chem. B, Vol. 104, No. 10, 2000
Koerner and Ichiye
Figure 3. Ball-and-stick figure of the analogue in conformation 2c showing selected geometrical parameters from the UHF optimizations using BSI (bond lengths in angstroms and bond angles in degrees).
Figure 2. Ball-and-stick figures of the analogues in conformations (a) 2a and (b) 2b showing selected geometrical parameters from the UHF optimizations using BSII (bond lengths in angstroms and bond angles in degrees).
TABLE 3: Interaction Properties of Conformations 1 and 2 Interacting with Water (1a, 1b, 2a, 2b, 2c) at Different Computational Levels Using Different Basis Setsa method
property
UHF/BSI Ebind Ebind - BSSE Fe‚‚‚O S3,4‚‚‚O S3‚‚‚H1 S4‚‚‚H1 S3‚‚‚H2 S4‚‚‚H2 S1‚‚‚H1 MP2/BSI Ebind Ebind - BSSE Fe‚‚‚O S3,4‚‚‚O S3‚‚‚H1 S4‚‚‚H1 S3‚‚‚H2 S4‚‚‚H2 S1‚‚‚H1 UHF/BSII Ebind Ebind - BSSE Fe‚‚‚O S3,4‚‚‚O S3‚‚‚H1 S4‚‚‚H1 S3‚‚‚H2 S4‚‚‚H2 S1‚‚‚H1
1a
1b
2a
-12.8 -11.6 4.678 4.018 3.826 3.826 3.447 3.447 4.369 -13.5 -12.3 4.425 3.936 3.743 3.743 3.339 3.339 4.087 -11.5 -10.1 4.647 4.047 3.881 3.881 3.396 3.396 4.261
-18.8 -17.3 4.292 3.571 2.690 3.681 3.681 2.690 4.831 -20.2 -18.7 3.911 3.455 2.542 3.576 3.576 2.542 4.419 -18.1 -16.5 4.279 3.572 2.680 3.624 3.624 2.680 4.747
-14.6 -13.3 4.421 4.729 4.678 4.678 4.019 4.019 2.570 -16.8 -15.5 4.044 4.341 4.395 4.395 3.565 3.565 2.516 -13.5 -12.5 4.809 5.262 5.071 5.071 4.550 4.550 2.542
2b
2c
-17.8 +4.1 -16.8 4.249 2.258 3.565 3.303 2.686 4.017 3.675 4.017 3.675 3.390 2.686 3.390 4.883 2.637 -22.2 -21.2 3.776 3.473 3.597 3.597 2.554 2.554 4.072 -16.2 -14.7 4.279 3.573 2.681 3.624 3.624 2.681 4.862
a Energies in kcal/mol, bond lengths in angstroms, and bond angles in degrees.
molecule approaches closely to S1 (about 2.5 Å) apparently form a hydrogen bond. On the other hand, for the b conformation where the plane of the water molecule is perpendicular to the
S1-Fe-S2 plane, the S1‚‚‚H1 (and by symmetry, S1‚‚‚H2) distance (over 4 Å) is relatively unaffected by the orientation of the methyl ligand associated with S1 so that this distance is very similar for 1b and 2b. For the b conformation, H1 is closer to S3 (and by symmetry, H2 is closer to S4) at a distance of about 2.6 Å. The presence of the short S‚‚‚H distances may indicate hydrogen bonds, which is presently being studied.38 For both the UHF calculations, each of the two interactions in 1b and 2b is weaker than the S1‚‚‚H1 interaction in 2a, as indicated by the slightly longer (about 0.2 Å) S‚‚‚H distance, while the MP2 calculations the interaction appears similar in magnitude. Structure 2c represents a very different interaction between the water and the [1Fe] site, namely, a covalent iron-water interaction with an Fe-O bond length of 2.26 Å (Table 2, Figure 3). The crowding of the Fe coordination sphere also gives rise to an increase in the average Fe-S bond length from 2.58 in the isolated [1Fe] site to 2.66 Å in the complex. Complex 2c appears to be a trigonal-bipyramidal adduct. However, complex 2c was obtained at the UHF level with BSI, and no converged results could be obtained at the higher level. The relative energies, Erel, of the complexes (1a, 1b, 2a, 2b) and of the sums of the two isolated fragments (1 + H2O, 2 + H2O) were also calculated (Table 2a). At all three computational levels, there is virtually no difference in Erel between conformations 1 and 2 as isolated fragments.10 The binding energies of the complexes, Ebind, with and without BSSE corrections were also calculated (Table 2b). Note that the BSSE corrections for the MP2 calculations are the same as those in the UHF/BSI calculations. In addition, the inclusion of more basis functions upon going to BSII makes little difference in the BSSE correction. For complex 2a, Ebind is roughly -13.0 kcal/mol due to the relatively strong interaction of the partial negative charge of S1, with the partial positive charge on the H1 of water. For conformation 1a, where the alkyl group blocks the approach of the water to S1, the somewhat smaller Ebind of about -11 kcal/mol is due to a modest stabilization from the interaction of the other water hydrogen, H2, with S3 and S4 of the [1Fe] site. For conformations 1b and 2b, each hydrogen interacts with a sulfur, i.e., S3 with the water H1 and S4 with the water H2, with an Ebind of -17.0 kcal/mol. The interaction is relatively weaker per interaction than in complex 2a so that the energies are not pairwise additive. On the whole, the presence of two S‚‚‚H interactions, even though weaker, in the b orientation of the water leads to the most stable interaction. In addition,
Interactions of [Fe(SCH3)4]2- with Water
J. Phys. Chem. B, Vol. 104, No. 10, 2000 2429
TABLE 4: Mulliken and CHELPG Charges for Conformations 1 and 2 Calculated at the UHF Level Using BSII charge
atom
Mulliken Fe S1 (H3C)1 S2 (H3C)2 S3,4 (H3C)3,4 O H1 H2 CHELPG Fe S1 (H3C)1 S2 (H3C)2 S3,4 (H3C)3,4 O H1 H2
TABLE 5: Mulliken and CHELPG Electrostatic Moments for Water Both Isolated and Interacting with Conformations 1 and 2 Calculated at the UHF Level Using BSII
1 + H2O
1a
1b
2 + H2O
2a
2b
charges
atom
H2O
1a
1b
2a
2b
0.728 -0.463 -0.217 -0.463 -0.217 -0.464 -0.220 -0.856 0.428 0.428 1.371 -0.839 0.002 -0.839 0.002 -0.879 0.029 -0.843 0.422 0.422
0.688 -0.444 -0.222 -0.449 -0.216 -0.453 -0.215 -0.912 0.435 0.456 1.179 -0.764 0.045 -0.750 -0.014 -0.794 -0.007 -0.997 0.401 0.502
0.714 -0.454 -0.207 -0.447 -0.214 -0.457 -0.207 -0.954 0.445 0.445 1.161 -0.824 0.047 -0.805 0.034 -0.777 0.020 -1.028 0.465 0.465
0.733 -0.466 -0.218 -0.473 -0.216 -0.460 -0.220 -0.856 0.428 0.428 1.174 -0.898 0.124 -0.912 0.086 -0.807 0.020 -0.843 0.422 0.422
0.718 -0.477 -0.203 -0.461 -0.216 -0.450 -0.214 -0.928 0.459 0.437 1.080 -0.765 0.100 -0.880 0.087 -0.738 -0.017 -0.928 0.388 0.427
0.711 -0.448 -0.215 -0.452 -0.213 -0.455 -0.206 -0.955 0.447 0.447 1.213 -0.868 0.117 -0.923 0.082 -0.764 0.007 -0.966 0.430 0.430
Mulliken
qO µ µgeom θ φ qO µ µgeom θ φ
-0.856 2.33 2.33
-0.912 2.61 2.45 1.8 179.0 -0.997 2.88 2.42 8.0 174.8
-0.954 2.73 2.45 0 171.8 -1.028 2.94 2.42 0 171.8
-0.928 2.64 2.44 2.0 175.2 -0.928 2.65 2.41 3.2 179.5
-0.955 2.74 2.45 0 172.0 -0.966 2.77 2.42 0 172.0
complex 2c can be classified as a trapped intermediate since Ebind is +4.1 kcal/mol. c. Electrostatic Potential Properties and Polarization Effects. The Mulliken and CHELPG charges were calculated for all structures (Table 4). The Mulliken charges are less polar than the CHEPLG charges, which are constrained to match the actual dipole moment of the wave function. The magnitude of the Mulliken charges is generally considered to be unreliable because of the basis set dependence, which was also noted specifically for the [1Fe] site in earlier work.10 For either method, there is little variation in the charges whether comparing the isolated fragments or among the complexes, although this variation is less pronounced for the Mulliken charges than the CHELPG charges. For instance, the charge on the Fe in the complex ranges over 0.04e in the Mulliken charges, whereas it ranges over 0.29e in the CHELPG charges. This relative homogeneity in the Mulliken charges, and the apparently spurious changes in the CHELPG charge on the buried Fe atom in the [1Fe] site has been noted before.10 Since it is difficult to fit a buried charge as is necessary in the CHELPG method, and since Mulliken’s method is based on dividing the electron density between atoms in a standard though arbitrary manner, the conformational variance of charges was viewed to be more accurately predicted by Mulliken’s method. However, the magnitudes were viewed to be more accurately predicted by CHELPG, because the moments are constrained to the correct values (see Methods), with more symmetric, more open structures being the most accurate. The use of RESP or SVD methods may lead to fewer problems with buried charges; however, the CHELPG results presented here are consistent with previous work.10 Despite the relatively small changes, certain trends in the changes can be seen in all complexes. Among these is the increased polarization of the water molecule upon coordination to the complex. In the complex, the oxygen atom always has an increased negative charge and the water hydrogens also have increased positive charges; however, the latter is to a lesser degree leaving a net excess negative charge on the water molecule. Also, the charge distribution on the water hydrogens is dependent on the conformation of the [1Fe] site that it interacts with. For the a conformations where the two water hydrogens have different interactions, there are different charges on the water hydrogens for both types of charge determination. This
CHELPG
-0.843 2.29 2.29
asymmetry of the charges in the water hydrogens is most evident in conformation 2a, where there is one hydrogen closely approaching a sulfur and another is farther away. Interestingly, the Mulliken and CHELPG charges predict the opposite pattern in the charge distribution among the water hydrogens for conformation 2a, whereas they predict the same pattern for conformation 1a. The close approach of the water to the [1Fe] site also polarizes the electron density of the sulfurs associated with the close contact in the complex in that the charges on the sulfurs decrease in magnitude slightly upon association with the water. The trends seen are quite similar regardless of conformations or method used to obtain the charges. The exceptions are that for conformation 2a, Mulliken charges predict an increase in negative charge on S1 and that for conformation 2b, CHELPG predicts an increase in negative charge on S2. Another measure of the extent of the polarization of the water molecule by the [1Fe] is to compare the dipole moment of the uncoordinated water molecule to that found in the complex (Table 5). However, in the presence of [1Fe], there is an excess negative monopole, qexcess, on the water
qexcess ) qO + qH1 + qH2 where the subscripts on the right-hand side denote the atom. Therefore, the excess negative monopole can be considered to be due to a gain of electron density on the hydrogens from the redox site sulfur totaling qexcess in charge. Thus, here the moments are broken into a monopole of qexcess on the hydrogens and a dipole of qO on the oxygen and -qO on the hydrogens. Since the charge of -qO is spread between both hydrogens, the charges on the hydrogens are increased by a total of -qexcess proportionate to qH1 and qH2 until they reached a total of -qO. These charges, which are referred to as q′H1 and q′H2, are thus given by
(
q′Hi ) qHi 1 -
)
-qHiqO qexcess ) qH1 + qH2 qH 1 + q H 2
For the Mulliken charges, the dipole increases by 0.3 D for the a conformations and by 0.4 D for the b conformations. The CHELPG charges exhibit an even greater increase in the dipole moment of the water molecule of about 0.5-0.6 D but, although the a versus b pattern is evident, the trends are less clear than with the Mulliken charges due to the more erratic nature of the CHELPG charges. The changes underlying the increased dipole moment when the water is close to the [1Fe] site are both an increase in charge density on the oxygen and hydrogens and a ∼4° decrease in the H-O-H angle (Table 1). The geometric effects can be separated by calculating the dipole moment with the water
2430 J. Phys. Chem. B, Vol. 104, No. 10, 2000
Figure 4. Schematic drawing of an asymmetric water molecule showing (a) the orientation of the dipole with respect to hydrogens, (b) the orientation of the dipole with respect to the geometric bisector of the H-O-H angle, and (c) the orientation of the dipole with respect to the Fe.
geometry in the complex but with the partial charges of the isolated water molecule, which is referred to as µgeom. Comparing µgeom with the total dipole moment µ shows geometric effects account for about a quarter of the increase in dipole moment (Table 4). The balance is due to the increase in charge density, negative on the oxygens and positive on the hydrogens. The water molecule itself is symmetric in 1b and 2b, but is asymmetric in 1a and 2a; that is, the OH bond lengths are not equal (Figure 4). One measure of the degree of asymmetry is the angle θ between the dipole moment and the geometric bisector of the H-O-H angle (Figure 2). θ is small in the Mulliken charge distributions, while the CHELPG method predicts greater shifts from the geometric bisector due to the nonhomogeneous distribution of the charges on the water hydrogens. The orientation of the dipole moment of the water with respect to the [1Fe] site can be measured by φ, the angle between the oxygen, iron, and internuclear vector of the water dipole moment (Figure 4). Examination of φ shows that, for all conformations, the water is far enough away from the Fe to have its dipole approximately pointing toward the Fe in this negatively charged complex. 4. Conclusions Quantum mechanical calculations on the [1Fe] site interacting with a water molecule indicate hydrogen bonding interactions between the sulfurs and the water and a weak van der Waals type of interaction between the iron and the water at all levels tested. This interaction is predicted to be slightly stronger at the MP2 level than at the UHF level using the same basis set (BSI) as indicated by a shorter Fe‚‚‚O distance and slightly more negative binding energies. UHF calculations using a larger basis set (BSII) reveal no significant differences from the results obtained using an ECP on the iron (BSI) with the exception of orientational differences when the water hydrogen bonds to one of the ligand sulfurs. While a strong interaction is made when the water forms a single hydrogen bond to one redox site sulfur, the most energetically favored orientation is when each water hydrogen forms a hydrogen bond to a separate redox site sulfur. The degree of polarization of each molecule by the other was also studied. The partial charge distributions on the [1Fe] changed little upon coordination of the water in the complex
Koerner and Ichiye from that found in its isolated state. Nonetheless, a slight predictable polarization occurred among the sulfurs participating in the hydrogen bonding to the water molecule. Moreover, both electronic and geometric polarization was seen in the water molecule. Mulliken’s method and the CHELPG ESP fitting procedures provide different but complementary information about atom-centered partial charges. Mulliken charges are wellknown to be highly basis set dependent, and thus, the magnitudes are not reliable. Here, the Mulliken charges were less polar than CHELPG charges and the dipole moments of the CHELPG charges were constrained to match the actual moments of the electron distribution. However, here, as in earlier calculations,10 the CHELPG charges appeared overly dependent on conformation especially for buried charges. Thus, the magnitude of CHELPG charges appears most useful for ESP calculations, but Mulliken charges give a better picture of conformational dependency. As a whole, the homogeneity in the Mulliken partial charges for the [1Fe] site regardless of conformation indicate that including polarization effects for the [1Fe] site in calculations using classical electrostatic potentials will not be necessary. However, the polarization of water by the [1Fe] site in the more highly charged reduced state as seen in the 1628% increase in the dipole moment, of which about a quarter is due to geometric changes, may require addition of polarization effects for the water. Acknowledgment. This research was supported by a grant from the National Institutes of Health (GM45303) and by a grant from the Pittsburgh Center (MCB950005P), sponsored by the National Science Foundation, for time on their CRAY C90 and DEC Alpha Supercluster. We also thank the Maui High Performance Computing Center for the generous allocation of computer time on their IBM SP high performance parallel computer. References and Notes (1) Aqvist, J.; Warshel, A. J. Am. Chem. Soc. 1990, 112, 2860. (2) Merz, K. M., Jr.; Hoffmann, R.; Dewar, M. J. S. J. Am. Chem. Soc. 1989, 111, 5636. (3) Liang, J.-Y.; Lipscomb, W. N. Biochemistry 1988, 27, 8676. (4) Liang, J.-Y.; Lipscomb, W. N. Int. J. Quantum Chem. 1989, 36, 299. (5) Shen, J.; Subramaniam, S.; Wong, C. F.; McCammon, J. A. Biopolymers 1989, 28, 2085. (6) Qi, P. X.; Urbauer, J. L.; Fuentes, E. J.; Leopold, M. F.; Wand, J. A. Struct. Biol. 1994, 1, 378. (7) Holm, R. H.; Ibers, J. A. In Iron-Sulfur Proteins; Lovenberg, W., Ed.; Academic Press: New York, 1977; Vol. 3, p 205. (8) Noodleman, L.; Case, D. A. AdV. Inorg. Chem. 1992, 38, 423. (9) Mouesca, J.-M.; Chen, J. L.; Noodleman, L.; Bashford, D.; Case, D. A. J. Am. Chem. Soc. 1994, 116, 11898. (10) Koerner, J. B.; Ichiye, T. J. Phys. Chem. B 1997, 101, 3633. (11) Noodleman, L.; Norman, J. G., Jr.; Osborne, J. H.; Aizman, A.; Case, D. A. J. Am. Chem. Soc. 1985, 107, 3418. (12) Yelle, R. B.; Park, N. S.; Ichiye, T. Proteins 1995, 22, 154. (13) Backes, G.; Mino, Y.; Loehr, T. M.; Meyer, T. E.; Cusanovich, M. A.; Sweeney, W. V.; Adman, E. T.; Sander-Loehr, J. J. Am. Chem. Soc. 1991, 113, 2055. (14) Min, T.; Kang, C.; Eidsness, M. K.; Ichiye, T. Unpublished results. (15) Phillips, W. D.; Poe, M.; Weiher, J. F.; McDonald, C. C. Nature 1970, 227, 574. (16) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92; Gaussian, Inc.: Pittsburgh, PA, 1992. (17) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Jensen, J. H.; Koseki, S.; Gordon, M. W.; Nguyen, K. A.; Windus, T. L.; Elbert, S. T. QCPE Bull. 1990, 10, 52. (18) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 284.
Interactions of [Fe(SCH3)4]2- with Water (19) Wadt, W. R.; Hay, P. J. J. Chem. Phys. 1985, 82, 284. (20) Binkley, J. S.; Pople, J. A.; Hehre, W. J. J. Am. Chem. Soc. 1980, 102, 939. (21) Collins, J. B.; Schleyer, P. v. R.; Binkley, J. S.; Pople, J. A. J. Chem. Phys. 1976, 64, 5142. (22) Hehre, W. J.; Stewart, R. F.; Pople, J. A. J. Chem. Phys. 1969, 51, 2657. (23) Wachters, A. J. H. J. Chem. Phys. 1970, 52, 1033. (24) Rappe, A. K.; Smedley, T. A.; Goddard, W. A., III J. Phys. Chem. 1981, 85, 2607. (25) Curtiss, L. A.; Halley, J. W.; Hautman, J.; Rahman, A. J. Chem. Phys. 1987, 86, 2319. (26) Bach, R. D.; Su, M.-D.; Andres, J. L.; Schlegel, H. B. J. Am. Chem. Soc. 1993, 115, 8763. (27) Turi, L.; Dannenberg, J. J. J. Phys. Chem. 1993, 97, 2488. (28) Cook, D. B.; Sordo, J. A.; Sordo, T. L. Int. J. Quantum Chem. 1993, 48, 375. (29) Feller, D.; Davidson, E. R. In ReViews in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; VCH Publishers: New York, 1990; p 1.
J. Phys. Chem. B, Vol. 104, No. 10, 2000 2431 (30) Kern, C. W.; Karplus, M. In Water: A ComprehensiVe Treatise.; Franks, F., Ed.; Plenum Press: New York, 1972; Vol. 1: The Physics and Physical Chemistry of Water, p 21. (31) Levine, I. N. Quantum Chemistry, 4th ed.; Prentice Hall: Englewood Cliffs, NJ, 1991. (32) Lane, R. W.; Ibers, J. A.; Frankel, R. B.; Papaefthymiou, G. C.; Holm, R. H. J. Am. Chem. Soc. 1977, 99, 84. (33) Luthi, H. P.; Siegbahn, P. E. M.; Almlof, J.; Aegri, K. F., Jr.; Heiberg, A. Chem. Phys. Lett. 1984, 111, 1. (34) Taylor, T. E.; Hall, M. B. Chem. Phys. Lett. 1985, 114, 338. (35) Calhourda, M. J.; Carrondo, M. A. A. F. d. C. T.; Dias, A. R.; Frazao, C. F.; Hursthouse, M. B.; Martinho Simoes, J. A.; Teixeira, C. Inorg. Chem. 1988, 27, 2513. (36) Darensbourg, M. Y.; Silva, R.; Reibenspies, J.; Prout, C. K. Organometallics 1989, 8, 1315. (37) Darensbourg, M. Y.; Bischoff, C. J.; Houliston, S. A.; Pala, M.; Reibenspies, J. J. Am. Chem. Soc. 1990, 112, 6905. (38) Beck, B. W.; Koerner, J. B.; Yelle, R. B.; Ichiye, T. Unpublished results.
