摘要:
Are guanine tetrads stabilised by bifurcated hydrogen bonds? An AIM topological analysis of the electronic density Guillaume Louit,a Alexandre Hocquet,*a Mahmoud Ghomi,a Michael Meyerb and Ju�rgen Su�hnelc aLPBC, UMR CNRS 7033, case courrier 138, 4 Place Jussieu, 75252 Paris Cedex 05, France. E-mail: hocquet@lpbc.jussieu.fr bRevotar Biopharmaceuticals AG, Neuendorfstr. 24b, D-16761 Hennigsdorf, Germany. E-mail: m.meyer@revotar-ag.de cBiocomputing Group, Institute of Molecular Biotechnology, Jena Centre for Bioinformatics, Beutenbergstr. 11, D-07745 Jena, Germany. E-mail: jsuehnel@imb-jena.de Received 16th May 2002, Accepted 18th June 2002 Published on the Web 26th June 2002 Following a previous publication (M. Meyer, M. Brandl and J Su� hnel, J. Phys. Chem.A, 2001, 105, 8223–8225) on quantum mechanical calculations of guanine tetrads where the issue of the difference between bifurcated and Hoogsteen conformations was addressed geometrically and energetically, we tackle the problem from the Atoms in Molecules (AIM) point of view of the topological analysis of the electronic density. We provide electronic argumentation to discuss the bifurcated or Hoogsteen issue, from the analysis of density and laplacian at the bond critical point criteria, and from the integration of atomic properties. The Hoogsteen hydrogen bonding network appears to be stronger than the bifurcated one, and benefits more from cooperativity. Introduction Hydrogen bonding plays a pivotal role in biomolecular structure and function.1 In the case of DNA and RNA, hydrogen bonding is one of the most important structural features governing their biological role.2 For guanine tetrads hydrogen bonding networks determine the stability and geometry of different conformations.Guanine tetrads have been investigated by fiber X-ray crystallography from about 40 years ago, even though they have been discovered much earlier.3 Now they are an active area of research again because they are important building blocks of DNA tetraplex structures.4,5 Tetraplex forming sequence motifs occur in telomeres at the ends of linear chromosomes. The proposed function of telomeres is maintenance of the structural integrity of the genome and insurance of complete replication at the chromosome termini. Similar sequence motifs do also occur in regulatory regions of oncogenes. Tetrads play also a role in supra-molecular chemistry, for example, guanosine analogs perform a self-assembly in columnar aggregates in the presence of cations.6 Guanine tetrads have also been investigated by quantum chemical studies.In contrast to experimental crystal and NMR tetraplex-structures, an initial study at Hartree–Fock and B3LYP hybrid density functional predicted that the bases are linked by bifurcated H-bonds between N1-H, N2-H and O6.7 In a subsequent study a Hoogsteen pairing has been found when cations are located in the central cavity formed by the tetrad.8 From these facts it has been concluded that the metal ions change the hydrogen bond pattern in guanine tetrads.In an independent study on guanine tetrads no bifurcated hydrogen bonds have been found.9 It turned out in a further study analysing the discrepancies, that the Hoogsteen structure does not correspond to a local energy minimum at the HF/ 6-311G(d,p) level of theory, whereas the DFT calculations yield minima for both the bifurcated and Hoogsteen H-bond pattern.10 However, the energy difference between the two conformations is very small and thus the relative energy depends on the quantum chemical method adopted. At the B3LYP/DZVP level the bifurcated S4 symmetric structure is the most stable one. At other levels like B3LYP/6-311G(d,p) the Hoogsteen S4 structure is preferred and finally at B3LYP/ 6-3111G(2d,p)//B3LYP/6-311G(d,p) a planar C4h bifurcated structure is most stable.Meanwhile, quantum chemical calculations have been extended to sandwich type complexes formed by two guanine tetrads and a cation11 and to several other tetrads reviewed in ref. 4. Here we analyse the guanine tetrad hydrogen bonds by means of the Atoms In Molecules (AIM) method. The AIM theory has proved itself a valuable tool to conceptually define what is an atom, and above all what is a bond in a quantum calculation of a structure of a molecule.12 The AIM theory has been applied to such systems as van der Waals complexes or hydrogen bond complexes.13 More recently, the concept of hydrogen bonding has been studied with a variety of AIM based descriptors in the cases of C–H…X hydrogen bonding14 and dihydrogen bonding,15 and these two publications defined a set of criteria for hydrogen bonding within the AIM formalism that has eventually been used in nucleic base pairing16 and nucleosides.17 The reader is directed to ref.12 for proper definition of bonding, bond paths, critical points on the basis of electronic density, its gradient and laplacian, and to ref. 17 for a short summary of how it is employed in hydrogen bonding analysis. Using a similar approach in this present paper, we intend to perform an analysis of guanine tetrads hydrogen bonding network: we will address the issue of bifurcated or Hoogsteen hydrogen bonding on the basis of the analysis of the AIM topology of the electronic density, as a complementary study of the energetical one.For an analysis of coopertive effects we studied also bifurcated and Hoogsteen GG dimers for the first time. A series of other GG dimers had been studied previously by Sponer and Hobza.18 94 PhysChemComm, 2002, 5(15), 94–98 This journal is # The Royal Society of Chemistry 2002 DOI: 10.1039/b204736e PaperFig. 1 Chemical structures and atomic numbering for the two studied tetrads. Material and methods Fig. 1 displays the atom numbering and chemical structure of bifurcated and Hoogsteen conformations of guanine tetrads (thereafter referred as G4). The geometries have been optimised at various levels of theory in a previous paper.10 The B3LYP19/6-311G(d,p)20// B3LYP/6-311G(d,p) level has been retained for the analysis of the electronic density, in both C4h (planar) and S4 symmetry group structures (which makes four different geometries, hereafter referred to as G4HoC4h, G4HoS4, G4BiC4h and G4BiS4).To check for basis set consistency, the analysis has also been performed at the B3LYP/DZVP21//B3LYP/DZVP level of theory. Absolute values of the properties are slightly sensitive to basis set change, but variations are quantitatively similar. It has to be noted that the C4h geometries are not true minima, owing to the complete planarity of the molecule, including the amino groups, which are more stable in a pyramidalised form. For comparison, four dimers of guanine (referred as G2) have been optimised at the same level of theory, using the Gaussian 98 software.22 One pair of dimers is planar (Cs symmetry) and the other is not (C1 symmetry). They will be referred to as G2HoCs, G2HoC1, G2BiCs and G2BiC1.The two bifurcated dimers had to be geometrically constrained because no minimum exists at this level of theory. Coordinates of the eight optimised structures are provided for visualisation as a Chime plug in (Fig. 2). The AIM analysis has been performed with the AIM 2000 code,23 with all default options. Integration of atomic properties over the atomic basins have been performed in natural coordinates, with a tolerance of 1024 per integration steps. The radius of the beta sphere used for integration (default value 0.5 a.u.) had sometimes to be set to 0.4 a.u., when the bond critical point (BCP) was too close from the nucleus.Fig. 2 The four tetrads (G4HoC4h, G4HoS4, G4BiC4h and G4BiS4) and four dimers (G2HoCs, G2HoC1, G2BiCs and G2BiC1). Click image or here to access a 3D representation. Eight hydrogen bonding criteria within the AIM formalism have been described in two publications14,15 and applied in previous work.17 The first three criteria are: the existence of a bond path, containing a BCP between the donor hydrogen nucleus and the acceptor, the value of the density r(r) at the BCP and the value of the laplacian of the density at the BCP. These three criteria together with ellipticity and distance to a Ring CriPoint (RCP) will thereafter be referred to as ‘‘BCP’’ criteria.DE, and DrH. All these criteria are defined in detail in ref. 17. The procedure thus implies a reference molecule: a ‘‘monomer’’ in which the atoms involved in the hydrogen bonding are unbound. In this work, this free monomer is a guanine molecule, optimised at the same level of theory. To check for accuracy of the integration of atomic properties, the laplacian of each integrated atomic basin (which is supposed to integrate to zero in a perfect integration) has been calculated.24 Its value The five other criteria deal with variation of five atomic properties (namely atomic charge q(H), atomic polarization moment M(H), atomic volume v(H), atomic energy E(H) and atomic radius r(H) of the hydrogen atom upon formation of the hydrogen bond.They will thereafter be named Dq, DM, Dv, 95 PhysChemComm, 2002, 5(15), 94–98is always inferior to 1.2.1023 a.u. which guaranties that every integrated property variation encountered in this study is well above significance threshold. Mutual penetration is defined as DrH 1 DrX, i.e. the sum of the variations of atomic radii of H (the hydrogen bond donor atom, namely H1 and H2) and X (the acceptor atom, namely N7 and O6) upon complexation. All those criteria (namely Dq, DM, Dv, DE, DrH, DrX) will thereafter be referred to as ‘‘two molecules’’ criteria. Results and discussion 1 Bonding as evidenced by the molecular graph The most immediate evidence of bonding within the AIM formalism is the existence of a bond path between two atoms and a bond critical point (BCP) in the middle of the path.The molecular graph (i.e. the ensemble of bond paths connecting atoms) can be visualized in Fig. 3. On the basis of the bond paths, the Lewis scheme of each guanine molecule is respected in tetrads and dimers. Fig. 3 molecular graph of the C4h Hoogsteen (Fig. 3a) and C4h bifurcated (Fig. 3b) tetrad with hydrogen bond distances in a°ngstro�ms densities at the BCPs in 1022 a.u. Figures in parentheses correspond to the C4h structure, the others correspond to the S4 one, as pictured in ref. 10. Small red dots represent Bond Critical Points (BCP). Small yellow dots depict Ring Critical Points (RCP). 96 PhysChemComm, 2002, 5(15), 94–98 Fig. 4 detail of the C4h Hoogsteen (Fig. 4a) and C4h bifurcated (Fig.4b) tetrad, including isodensity contours (thin lines), bond paths and interatomic surfaces. Black dots represent atoms. Red squares depict Bond Critical Points (BCP). Yellow triangles indicate Ring Critical Points (RCP). Intermolecular interactions are also characterised: in Hoogsteen conformations, both classic Hoogsteen H1…O6 and H2…N7 intermolecular hydrogen bonds are present (see detail in Fig. 4a). In bifurcated conformations, the scheme is more surprising, because of the existence of the H2…N7 interaction in both G4 bifurcated structures, in addition to the H1…O6 and H2…O6 interactions (Fig. 4b). In bond path terms, the differ- ences between the two conformations are thus the presence of a bond path between H2 and O6 in the bifurcated conformation, thus parting the ring formed by classic Hoogsteen hydrogen bonds (Fig.4a) in two (Fig. 4b), as shown by the presence of two RCPs and a BCP (Fig. 4b), instead of one RCP (Fig. 4a). This means that not only the acceptor O6 is involved in a double interaction: it is also the case of the donor H2. This kind of double interaction has been investigated and named as a ‘‘three centered’’ interaction.25 In the bifurcated dimers, this bond path exists in the non-planar C1 conformation, but not in the Cs planar one. It has to be noted that these two optimised structures (and only these ones) were geometrically constrained to ensure a bifurcated scheme of interaction. Its analysis is thus less reliable.It has also to be noted that the N2…H7 bond path exists even for the Hoogsteen conformation at the B3LYP/ DZVP level of theory, but the values of density, laplacian and ellipticity prevent consideration of the interaction as a hydrogen bond.Table 1 Density, density laplacian, ellipticity and distance to RCP BR) at Bond Critical Points between hydrogen bond acceptors and 100*e 100*r 100*2(r) BR 1.42 1.53 7.08 5.55 1.06 1.03 4.92 5.53 8.98 8.99 6.18 7.07 12.21 12.63 9.48 9.89 2.36 2.26 1.52 1.65 3.33 3.53 2.19 2.45 1.72 1.40 0.83 2.27 6.75 6.97 7.49 8.20 1.89 1.90 2.16 2.34 4.79 5.69 69.92 5.95 6.02 1.45 (d hydrogen bond donors (all units are atomic units) Interaction H1…O4 G2HoC1 G2HoCs G2BiC1 G2BiCs G4HoC4h G4HoS4 G4BiC4h G4BiS4 H2…O6 G2BiC1 G2BiCs G4BiC4h G4BiS4 H2…N7 G2HoC1 G2HoCs G2BiC1 G2BiCs G4HoC4h G4HoS4 G4BiC4h G4BiS4 1.86 1.84 0.45 No BCP 2.53 2.40 0.88 0.69 5.42 5.14 13.44 29.71 7.86 7.48 2.88 2.22 (H) d1.49 1.54 1.60 1.60 0.62 1.18 0.96 10.1 10.1 6.7 7.4 13.4 13.7 10.1 10.3 7.9 8.4 8.9 8.4 11.2 10.8 12.3 12.8 2 Analysis of intermolecular interactions of dimers The results of the analysis are listed in Tables 1 and 2.On the basis of the analysis of the density and laplacian at the bond critical points (‘‘BCP’’ criteria, Table 1) and the integration of the atomic properties of H1 and H2 (‘‘two molecules’’ criteria, Table 2), all intermolecular bonds possess critical point and integrated properties in the range defined as a hydrogen bond.According to this analysis, the Hoogsteen interaction may be viewed as a very strong H1…O6 bond plus a strong H2…N7 bond. The bifurcated interaction may be viewed as a strong H2…O6 bond plus a medium H1…O6 bond plus a feeble H2…N7 bond. The high ellipticity of this last bond has to be noted, and its (relative) short distance to the closest RCP too. These two last factors, and the fact that the interaction does not show a bond path in the planar conformation cast doubt on the energetical significance of this interaction. This doubt cannot be confirmed by the ‘‘two molecules’’ criteria, as the integration Table 2 ‘‘Two molecules’’ criteria: H1 and H2 atomic basin integrated properties and H1 and H2 and O4 and N7 bond radii.rHf represents the radius of the hydrogen atom in the hydrogen bond free structure. rHb is the radius of the same atom bound through the hydrogen bond. For each atomic property X, DX represents the difference of the property between the hydrogen bound molecule and the hydrogen bond free molecule. L is the value of the laplacian, integrated over the hydrogen atomic basin (all units are atomic units) (H) Hydrogen atom q(H) Dq M DM v Dv 1 HGuanine G2HoC1 G2HoCs G2BiC1 G2BiCs G4HoC4h G4HoS4 G4BiC4h 30.3 20.2 20.2 23.6 22.9 16.9 16.6 20.2 20.0 0.169 0.125 0.124 0.137 0.135 0.109 0.108 0.123 0.123 0.400 0.462 0.463 0.440 0.444 0.505 0.507 0.481 0.481 0.044 0.045 0.032 0.034 0.060 0.061 0.046 0.046 0.062 0.063 0.040 0.044 0.105 0.107 0.081 0.081 G4BiS4 2 HGuanine G2HoC1 G2HoCs G2BiC1 G2BiCs G4HoC4h G4HoS4 G4BiC4h 31.1 23.2 22.7 22.2 22.7 19.9 20.3 18.8 19.3 0.170 0.139 0.137 0.137 0.135 0.127 0.129 0.129 0.129 0.379 0.436 0.449 0.441 0.452 0.478 0.473 0.473 0.472 0.031 0.033 0.033 0.035 0.043 0.041 0.041 0.041 0.057 0.070 0.062 0.073 0.099 0.094 0.094 0.093 G4BiS4 of H2, in the bifurcated conformation, involves two hydrogen bonds in only one hydrogen atom, so the influence of one hydrogen bond is diluted in the other.L(H) 20.0001 20.0001 20.0011 20.0001 20.0011 20.0002 20.0012 0.0001 3 Analysis of intermolecular interactions of tetrads Results are also listed in Tables 1 and 2, for comparison. On the basis of the same analysis of ‘‘BCP’’ and ‘‘two molecules’’ criteria, a strengthening of hydrogen bonding is noted when passing from dimer to tetrad. The H2…N7 densities are about three times smaller in the bifurcated conformation than in the Hoogsteen structure (Table 1). But the H2…N7 interaction, while still not very strong, is certainly more significant in the tetrad than in the dimer, especially in the C4h conformaon. At least, it exists in every symmetry group.All other interactions, defined as true hydrogen bonds in dimers, show even stronger hydrogen bond characteristics in tetrads. This strengthening may certainly be linked to a cooperativity effect in hydrogen bonding, which is known to be energetically significant in chained hydrogen bondings, in particular in formamide chains,26 which are structurally very similar to the hydrogen bonding network of tetrads. They are both good candidates for Resonance Assisted Hydrogen Bonding,27 like malonaldehyde. The variation in ‘‘BCP’’ criteria makes G4 hydrogen bonds comparable to the molecules studied in ref. 27 and the spectacular variation in ‘‘two molecules’’ criteria observed in our study (and not realised in other works, to our knowledge) incites us to investigate more deeply the concept of Resonance Assisted Hydrogen Bonding.28 Furthermore, this strengthening is more quantitative in the Hoogsteen conformation than in the bifurcated one, worsening the difference of stability in favour of the Hoogsteen structure.It does not seem to be particularly enhanced by complete planarity, though: no significant difference is found in favour of the C4h symmetry with respect to the S4 one. If we compare S4 and C4h structures, properties vary 4h to S4, we can according to geometrical variation. From C observe that: —There is a compensation for the Hoogsteen conformation: the H1…O6 bond is stronger and the H2…N7 bond is weaker. This corresponds to a shorter H1…O6 bond and a longer H2…N7 bond.— The bifurcated hydrogen bond network seems stronger in Hb rXf rXb rHf DrX DrH 2E(H) DE r 3.36 3.36 3.36 3.36 3.36 3.36 3.36 3.36 3.36 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 0.466 0.436 0.434 0.447 0.447 0.410 0.410 0.425 0.425 1.10 1.00 0.86 0.91 1.14 1.16 1.02 1.04 2.26 2.36 2.50 2.45 2.22 2.20 2.34 2.32 1.05 1.04 0.83 0.88 1.20 1.22 1.01 1.03 1.32 1.33 1.54 1.49 1.17 1.15 1.36 1.34 0.030 0.032 0.019 0.019 0.056 0.056 0.041 0.041 2.42 2.42 2.42 2.42 2.42 2.42 2.42 2.42 2.42 0.479 0.446 0.439 0.447 0.442 0.420 0.423 0.428 0.429 0.98 0.98 0.86 0.87 1.12 1.09 0.89 0.93 3.62 3.62 3.36 3.36 3.62 3.62 3.36 3.36 2.64 2.64 2.50 2.49 2.50 2.53 2.47 2.43 0.95 0.96 0.95 0.95 1.11 1.09 1.01 1.05 1.45 1.44 1.45 1.45 1.31 1.33 1.41 1.37 0.033 0.040 0.032 0.037 0.059 0.056 0.051 0.050 20.0002 20.0004 20.0001 20.0002 20.0012 20.0012 20.0013 0.0001 97 PhysChemComm, 2002, 5(15), 94–98the S4 symmetry: the H1…O6 bond is stronger and the H2…O6 bond is stronger too (and both bonds are shorter).It has to be said that these effects of symmetry change are noticeable in the analysis of the BCP criteria but much less obvious in the analysis of the ‘‘two molecules’’ criteria. We can thus safely infer that the cooperativity effect that favours the Hoogsteen conformation is certainly more important than the effect of change of symmetry.Conclusions On the basis of the information provided by the analysis of the topology of the electronic density, the networking of hydrogen bonding of guanine tetrads is more efficient in the Hoogsteen conformation. It seems also more strengthened with the cooperativity effect from dimer to tetrad in the Hoogsteen conformation. The network of intramolecular hydrogen bonding thus favours the Hoogsteen tetrad, with respect to the bifurcated tetrad. Also, the bifurcated tetrad hydrogen bonding network seems to be slightly stronger in the S4 symmetry while no trend is revealed for the Hoogsteen conformation. It can then be concluded that reasons for relative stability of bifurcated and Hoogsteen, as revealed by the previous energetical study, have to be found in another piece of argumentation in favour of the bifurcated conformation, like lesser repulsion of central oxygen atoms (which are more distant), especially in the C4h symmetry. A bifurcated conformation could then be anticipated to be disfavoured in a metal interacting tetrad, as surmised by metallated tetrad calculations.9,11 Strictly speaking in hydrogen bonding terms, our study reveals unambiguously that hydrogen bonds are weaker in bifurcated structures than in Hoogsteen guanine tetrads, a conclusion that could not be drawn on energetical arguments (because energetical arguments are global and not local), neither in geometrical arguments because of the complexity of the network of hydrogen bonding.To extend this study, this tool will then be used in metallated tetrads in order to assess how the presence of the metal affects the hydrogen bonding network. Acknowledgement Friedrich Biegler-Ko� nig and the University of Bielefeld for making available the AIM2000 program,23 IDRIS and CINES for providing time and space for calculations, are kindly acknowledged. References 1 G. A. Jeffrey and W. Saenger, Hydrogen Bonding in Biological Structures, Springer, Berlin, 1991. 2 W. Saenger, Principles of Nucleic Acid Structure, ed. C. R. Cantor, Springer-Verlag, New York, 1984. 3 W. Guschlbauer, J. F. Chantot and D. Thiele, J.Biomol. Struct. Dyn., 1990, 3, 491–511. 4 J. Su� hnel, Biopolymers (NAS), 2002, 61, 32–51; M. Meyer and J. Su� hnel, Base Polyad Motifs in Nucleic Acids, in Computational Chemistry: Reviews of Current Trends, ed. J. Leszczynski, World Scientific, River Edge, NJ, vol. 8, in press. 98 PhysChemComm, 2002, 5(15), 94–98 5 D. J. Patel, S. Bouaziz, A. Kettanim and Y. Wang, Structures of guanine-rich and cytosine-rich quadruplexes formed in vitro by telomeric, centromeric and triplet repeat disease DNA sequences, in Oxford Handbook of Nucleic Acid Structure, ed. S. Neidle, Oxford, 1999, pp. 389–453. 6 E. Mezzina, P. Mariani, R. Itri, S. Masiero, S. Pieraaccini, G. P. Spada, F. Spinozzi, J. T. Davis and G. Gottarelli, Chem. Eur. J., 2002, 7, 388–395.7 J. Gu and J. Leszczynski, Chem. Pys. Lett., 1999, 311, 209–214. 8 J. Gu and J. Leszczynski, J. Phys. Chem. A, 2000, 104, 6308– 9 M. Meyer, M. Brandl and J. Su� hnel, J. Comput. Chem., 2001, 22, 6313. 109–124. 10 M. Meyer, M. Brandl and J. Su� hnel, J. Phys. Chem. A, 2001, 105, 8223–8225. 11 J. Gu and J. Leszczynski, J. Phys. Chem. A, 2002, 106, 529–532. 12 R. F. W. Bader, Atoms In Molecules. A Quantum Theory, Clarendon, Oxford, 1990. 13 M. T. Carroll and R. F. W. Bader, Mol. Phys., 1988, 65, 695. 14 U. Koch and P. L. A. Popelier, J. Phys. Chem., 1995, 99, 9747. 15 P. L. A. Popelier, J. Phys. Chem. A, 1998, 102, 1873. 16 P. Hobza, J. Sponer, E. Cubero, M. Orozco and F. Luque, J. Phys. Chem. B, 2000, 104, 6286–6292; J. Munoz, J.Sponer, P. Hobza, M. Orozco and F. J. Luque, J. Phys. Chem. B, 2001, 105(25), 6051–6060. 17 A. Hocquet, Phys. Chem. Chem. Phys., 2001, 3, 3192–3199; G. Louit, A. Hocquet and M. Ghomi, Phys. Chem. Chem. Phys., 2002, 4 (DOI: 10.1039/b201339h). 18 J. Sponer, J. Leszczynski and P. Hobza, J. Phys. Chem., 1996, 100, 1965–1974. 19 A. D. Becke, J. Chem. Phys. A, 1993, 98, 5648; B. Miehlich, A. Savin, H. Stoll and H. Preuss, Chem. Phys. Lett., 1989, 157, 200; C. Lee, W. Yang and R. G. Parr, Phys. Rev. B, 1988, 37, 785; S. H. Vosko, L. Wilk and M. Nusair, Can. J. Phys., 1980, 58, 1200. 20 R. Krishnan, Y. Binkley, R. Seeger and J. Pople, J. Chem. Phys., 1980, 72, 650–654; R. Ditchfield, W. J. Hehre and J. A. Pople, J. Chem. Phys., 1971, 54, 724; W.J. Hehre, R. Ditchfield and J. A. Pople, J. Chem. Phys., 1972, 56, 2257; P. C. Hariharan and J. A. Pople, Mol. Phys., 1974, 27, 209; M. S. Gordon, Chem. Phys. Lett., 1980, 76, 163; P. C. Hariharan and J. A. Pople, Theor. Chim. Acta, 1973, 28, 213; M. J. Frisch, J. A. Pople and J. S. Binkley, J. Chem. Phys., 1984, 80, 3265. 21 N. Godbout, D. R. Salahub, J. Andzelm and E. Wimmer, Can. J. Chem., 1992, 70, 560–571. 22 M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery, Jr., R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam, A. D. Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adifford, J. Ochterski, G. A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. Cioslowski, J. V. Ortiz, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, J. L. Andres, C. Gonzalez, M. Head-Gordon, E. S. Replogle and J. A. Pople, Gaussian 98, Gaussian, Inc., Pittsburgh, PA, 1998. 23 F. Biegler-Ko� nig, J. Scho�nbohm and D. Bayles, J. Comput. Chem., 2001, 22, 545–559. 24 F. M. Aicken and P. L. A. Popelier, Can. J. Chem., 2000, 78, 415. 25 I. Rozas, I. Alkorta and J. Elguero, J. Phys. Chem. A, 1998, 102, 9925–9932. 26 N. Kobko, L. Paraskevas, E. del Rio and J. J. Dannenberg, J. Am. Chem. Soc., 2001, 123, 4348–4349. 27 S. J. Grabowski, J. Mol. Struct., 2001, 562, 137–143. 28 G. Louit and A. Hocquet, to be publis
ISSN:1460-2733
DOI:10.1039/b204736e
出版商:RSC
年代:2002
数据来源: RSC