Self-assembly of nanoscale cuboctahedra by coordination ... - Nature

letters to nature is unfavourable due to the cationic repulsion between two adjacent Pd(II) ions and the electron-withdrawing effects of adjacent Pd(II)± pym bonds on each other. In fact, macrocycles with (Pd(II)±pym)n frameworks (n 3; 4) did not assemble from 2 and 1,3-pyrimidine; instead, oligomers showing broad peaks in NMR were observed. A strong positive cooperative effect of Pd(II)±pym bonds should therefore work in the quantitative assembly of a nanosized capsule structure. The metal-linked dimer 4 and trimer 5 (Fig. 4a, b) may be involved as intermediates in the assembly process of 3, because these species were observed when ligand 1 was titrated with Pd(II) complex 2 in D2O. At 1 : 2 1 : 1 stoichiometry, NMR displayed the high-yield formation of a single product which was assigned to dimer 4 (Fig. 4c). Dimer 4 was isolated as a salt with PF-6 (96% yield) and characterized by NMR, electrospray mass spectrometry (ESI-MS), and elemental analysis. Further addition of 2 into the D2O solution made the spectrum very complex. However, the spectrum again became simpler at 1 : 2 3 : 4 stoichiometry showing 16 singlet signals with a total integral ratio of 36 H (4 H 3 3; 2 H 3 11; 1 H 3 2) in the aromatic region, consistent with the trimer structure of 5 (Fig. 4d). The present results complement our previous synthesis of a corner-sharing octahedron assembling from an exo-tridentate ligand, 1,3,5-tris(4-pyridyl)triazine, and Pd(II) complex 2 (refs 12,15,16). The framework of this octahedron complex has large windows and encloses large guest molecules (for example, as many as four carborane molecules) which can enter or exit through the openings. In contrast, the present edge-sharing hexahedron complex 3 has a closed shell structure, and so should be able to encage large molecules. The encapsulation of large guest molecules by this capsule, as well as guest-templated synthesis of other polyhedra (for example, a regular tetrahedron and an octahedron) are now being studied. M .........................................................................................................................

Methods

Synthesis and physical properties of 3. Ligand 1 (31 mg, 0.10 mmol) was

suspended in an aqueous solution (3 ml) of 2 (96 mg, 0.33 mmol) and the mixture was stirred at ambient temperature for 24 h. Addition of ethanol (10 ml) to the solution precipitated 3 as pale yellow crystals (120 mg, 95%): melting point (m.p.) ,220 8C (decomposed); 1H NMR (500 MHz, D2O tetramethylsilane as external standard) d 2.9±3.3 (m, 72 H), 8.36 (s, 6 H), 8.73 (s, 12 H), 10.18 (s, 12 H), 10.26 (s, 12 H), 10.43 (s, 12 H), 10.50 (s, 6 H), 10.55 (s, 12 H); 13C NMR (125 MHz, D2O) d 47.5 (CH2), 47.6 (CH2) 47.8 (CH2), 125.6 (CH), 127.0 (CH), 130.3 (quaternary carbon, Cq), 131.7 (Cq), 133.4 (Cq), 134.7 (Cq), 157.7 (CH), 158.8 (CH), 159.3 (CH), 159.5 (CH), 160.3 (CH); IR (KBr) 3,209, 1,384, 1,057, 879, 709 cm-1. Elemental analysis: calculated for (C144H216N108O108Pd18×27H2O, C, 22.77; H, 3.56; N, 19.92; found: C, 23.06; H, 3.51; N, 19.60. Synthesis and physical properties of 4. Ligand 1 (12.5 mg, 0.04 mmol) was suspended in dimethyl sulphoxide solution (1.0 ml) of 2 (11.6 mg, 0.04 mmol) and the mixture was stirred for 8.5 h at ambient temperature. The pale yellow solution was added dropwise to a saturated aqueous solution (10 ml) of KPF6 and the resulting white precipitates were ®ltered to give 4 (PF-6 salts) (31.4 mg, 0.019 mmol, 96%): m.p. ,250 8C (decomposed): 1H NMR (500 MHz, D2O) d 2.76 (s, 8 H), 8.25 (s, 4 H), 8.49 (s, 2 H), 9.17 (s, 4 H), 9.21 (s, 2 H), 9.41 (d, J 2:5 Hz, 4 H), 9.71 (s, 4 H), 10.10 (d, J 2:5 Hz, 4 H); IR (KBr) 1,559, 1,421, 1,399, 1,058, 839, 709, 559 cm-1. ESI-MS m/z 1,392.2 (M-PF6), 1,430.9 (M-PF6 CH3 CN), 1,474.0 (M-PF6 2CH3 CN), 1,557.1 (M-PF6 4CH3 CN). Elemental analysis: calcd. for (C18H12N6)2[C2H8N2Pd(PF6)2]2× 5H2O, C, 29.52; H, 3.10; N, 13.77; found: C, 29.19; H, 2.76; N, 13.50. X-ray structural analysis of 3. Ligand 1 (12.5 mg, 0.040 mmol) was suspended in a D2O solution (1 ml) of 2 (34.9 mg, 0.120 mmol), and methanol (14 ml) was added to the mixture. After stirring at ambient temperature for 17 h, diffusion of methanol into the resulting pale yellow solution at 4 8C for 4 d gave yellow single crystals of 3. A single crystal of 3 (0:25 3 0:30 3 0:35 mm) was mounted on a glass ®bre. All measurements were made on a charge coupled device (CCD) plate area detector with graphite monochromated Mo-Ka radiation. The data were collected at 296 K. Crystal data for 3: formula C144H216N108O108Pd18×27H2O, M 7;589:56, hexagonal, space group P63/m (#176), a 23:1688, c Ê V 1585116 AÊ 3 , rcalcd: 1:60 g cm 2 3 , Z 2, F000 7;596, 34:102 A, 796

Ê 99,000 re¯ections measured, mMoKa 11:03 cm 2 1 , lMoKa 0:71069 A; 3,034 observed I . 3:50jI; number of variables 425; R1 0:129; wR2 0:166. Received 16 October 1998; accepted 23 February 1999. 1. Cram, D. J. & Cram, J M. Container Molecules and their Guests (Royal Society of Chemistry, Cambridge, UK, 1994). 2. Cram, D. J., Tanner, M. E. & Thomas, R. The taming of cyclobutadiene. Angew. Chem. Int. Edn Engl. 30, 1024±1027 (1991). 3. Warmuth, R. o-Benzyne: strained alkyne or cumulene?ÐNMR characterization in a molecular container. Angew. Chem. Int. Edn Engl. 36, 1347±1350 (1997). 4. Kang, J. & Rebek, J. Jr Acceleration of a Diels-Alder reaction by a self-assembled molecular capsule. Nature 385, 50±52 (1997). 5. Kang, J., SantamarõÂa, J., Hilmersson, G. & Rebek, J. Jr Self-assembled molecular capsule catalyzes a Diels-Alder reaction. J. Am. Chem. Soc. 120, 7389±7390 (1998). 6. Wyler, R., de Mendoza, J. & Rebek, J. Jr A synthetic cavity assembles through self-complementary hydrogen bonds. Angew. Chem. Int. Edn Engl. 32, 1699±1701 (1993). 7. Rebek, J. Jr Assembly and encapsulation with self-complementary molecules. Chem. Soc. Rev. 25, 255± 264 (1996). 8. Heinz, T., Rudlkevich, D. M. & Rebek, J. Jr Pairwise selection of guests in a cylindrical molecular capsule of nanometre dimensions. Nature 394, 764±766 (1998). 9. MacGillivray, L. R. & Atwood, J. L. A chiral spherical molecular assembly held together by 60 hydrogen bonds. Nature 389, 469±472 (1997). 10. Saalfrank, R. W., Stark, A., Peters, K. & von Schnering, H. G. The ®rst ``adamantoid'' alkaline earth metal chelate complex: synthesis, structure, and reactivity. Angew. Chem. Int. Edn Engl. 27, 851±853 (1988). 11. Boxter, P., Lehn, J.-M., DeCian, A. & Fischer, J. Multicomponent self-assembly: spontaneous formation of a cylindrical complex from ®ve ligands and six metal ions. Angew. Chem. Int. Edn Engl. 32, 69±72 (1993). 12. Fujita, M. et al. Self-assembly of ten molecules into nanometre-sized organic host frameworks. Nature 378, 469±471 (1995). 13. Beissel, T., Power, R. E. & Raymond, K. N. Symmetry-based metal complex cluster formation. Angew. Chem. Int. Edn Engl. 35, 1084±1086 (1996). 14. Hartshorn, C. M. & Steel, P. J. Self-assembly and X-ray structure of a ten-component, threedimensional metallosupramolecular cage. Chem. Commun. 541±542 (1997). 15. Ibukuro, F., Kusukawa, T. & Fujita, M. A thermally switchable molecular lock. Guest-templated synthesis of a kinetically stable nanosized cage. J. Am. Chem. Soc. 120, 8561±8562 (1998). 16. Kusukawa, T. & Fujita, M. Encapsulation of large, neutral molecules in a self-assembled nanocage incorporating six palladium(II) ions. Angew. Chem. Int. Edn Engl. 37, 3142±3144 (1998). 17. Fujita, M. in Comprehensive Supramolecular Chemistry Vol. 9 (eds Sauvage, J.-P. & Hosseini, M. W.) 253±282 (Pergamon, Oxford, 1996). 18. Stang, P. J. & Olenyuk, B. Self-assembly, symmetry, and molecular architecture: coordination as the motif in the rational design of supramolecular metallacyclic polygons and polyhedra. Acc. Chem. Res. 30, 502±518 (1997). 19. Fujita, M. Metal-directed self-assembly of two- and three-dimensional synthetic receptors. Chem. Soc. Rev. 27, 417±425 (1998). 20. Fujita, M., Yazaki, J. & Ogura, K. Preparation of a macrocyclic polynuclear complex, [(en)Pd(4,49bpy)]4(NO3)8, which recognizes an organic molecule in aqueous media. J. Am. Chem. Soc. 112, 5645± 5647 (1990). 21. Fujita, M. & Ogura, K. Supramolecular self-assembly of macrocycles, catenanes, and cages through coordination of pyridine-based ligands to transition metals. Bull. Chem. Soc. Jpn 69, 1471±1482 (1996). Supplementary Information is available on Nature's World-Wide Web site (http://www.nature.com) or as paper copy from the London editorial of®ce of Nature. Acknowledgements. We thank K. Biradha for part of the crystallographic studies. Correspondence and requests for materials should be addressed to M.F. Present address: Department of Applied Chemistry, School of Engineering, Nagoya University, Chikusaku, Nagoya 464-8603, Japan (e-mail: [email protected]).

Self-assembly of nanoscale cuboctahedra by coordination chemistry Bogdan Olenyuk, Jeffery A. Whiteford, Andreas FechtenkoÈtter & Peter J. Stang Department of Chemistry, University of Utah, Salt Lake City, Utah 84112, USA .........................................................................................................................

Self-assembled polyhedral structures are common in biology. The coats of many viruses, for example, have a structure based on icosahedral symmetry1. The preparation of synthetic polyhedral molecular assemblies represents a challenging problem, but supramolecular chemistry2±4 has now advanced to the point where the task may be addressed. Macromolecular and supramolecular entities of prede®ned geometric shape and with wellde®ned internal environments are potentially important for inclusion phenomena5±8, molecular recognition5,6 and catalysis9. Here we report the use of self-assembly of molecular units driven by coordination to transition-metal ions10 to prepare a cubocta-

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NATURE | VOL 398 | 29 APRIL 1999 | www.nature.com

letters to nature The self-assembly was carried out as summarized in Fig. 2. Slow addition of a dichloromethane solution of 3 at 25 8C to a solution of the transition-metal tris(tri¯ate) in the same solvent resulted in a single highly symmetrical entity with a stoichiometry of 3:2, as determined by integration of the relevant signals in the 1H NMR. The 31P-NMR spectrum of cuboctahedron 5 exhibited only a singlet along with the 195Pt satellites. The product is a robust, hygroscopic microcrystalline solid with a relatively high-temperature decomposition point. This molecule, despite its large molecular mass (26,592.2 Da) and high charge (24+) is remarkably soluble in organic solvents, such as dichloromethane or acetone. A second cuboctahedron was assembled via a different route, where the tridentate angular component 1,3,5-tris(4-pyridylethynyl)benzene (2 in Fig. 1) contained the donor sites, while the bidentate unit, bis(4-[trans-Pt(PPh3)3OTf]phenyl)ketone 411 was selected as the acceptor. The ketone carbon is trigonal, with a 1208 bond angle, but if we account for the large size of the resulting assembly, this 128 distortion can be accommodated by a slight distortion within its subunits. The preparation of 6 was also performed by mixing a solution of the angular ligand 2 with a solution of subunit 4 in dichloromethane (Fig. 2). The 1H and 31P NMR spectra again indicated the formation of a single, highly symmetrical entity. The multinuclear NMR, infrared, elemental analyses and physical properties (solubility, high melting point) of 5 and 6 all are consistent with the design-based cuboctahedral structures. A molecular model of 6 obtained from force-®eld

hedron from 20 tridentate and bidentate subunits in a single step. The cuboctahedron is an archimedean semiregular polyhedron that combines square and triangular faces. Our self-assembled polyhedral capsules, characterized by NMR and electrospray mass spectrometry, are around 5 nanometres in diameter. Figure 1 illustrates our design approach. The shape of a cuboctahedron can be achieved by combining planar tridentate faces with 1088 turning angles via bidentate angular components. As 109.58 is close to 1088, the bidentate angular linking subunit may have a tetrahedral atom connected to a rigid linear donor or acceptor site. The tridentate building unit must, in turn, have three donor or acceptor sites located in one plane at 1208 relative to each other. The ratio of bidentate to tridentate ligands must be 3:2 with a total of 20 appropriate subunits in order to obtain the closed structure. It is also very important for the resulting assembly to be soluble in the reaction medium and most importantly, the product must be thermodynamically stable but kinetically labile, so any errors in the assembly can be self-corrected. The tridentate unit, 1,3,5-tris(49-iodophenyl)ethynylbenzene was prepared from 1,3,5-triethynylbenzene via cross-coupling; the triple oxidative addition of Pt(PPh3)4 into the iodo-phenyl bond was carried out at 95 8C in toluene, then halide abstraction with AgOTf in CD2Cl2 afforded the desired precursor 1 (Fig. 1; OTf indicates tri¯ate, OSO2CF3). The bidentate angular donor unit with the required tetrahedral carbon, 4,49-bispyridylacetal (3 in Fig. 2), was prepared from the known 4,49-bispyridylketone (ref. 11). a

+

b

OTf H

H + I

Ph 3P Pt

I

PPh3

1. Pt(PPh3)4, toluene 95oC, 3 days, 85% 2. AgOTf, CH2Cl 2, rt, 0.5h, 95%

H Pd(PPh3)4, CuI, Et3N THF, rt, 36h, 32%

I

PPh3

Ph3P Pt TfO PPh 3

I

I

Pt Ph3P

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1

c N

120° N

N

Figure 1 The general design scheme for the cuboctahedron. a, Assembly from a

iodophenyl)ethynylbenzene (b) and 1,3,5-tri-(4-pyridyl)ethynylbenzene (c) exem-

combination of bidentate linear and tridentate angular components. 1,3,5-tris(49-

plify tridentate angular components with 1208 directing angles.



797

letters to nature a

Ph3P

PPh3

TfO Pt

OTf Pt

Ph3P

PPh3

+24

=

8 Pt

Ph3P

CH2C l 2, r t, 10 min

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OTf

5 nm

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1 24 -OTf

+ O

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O

= N

N

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5

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+24 8 =

N

CH2Cl 2, r t, 10 min

2 +

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=

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PPh3

Ph3P Pt

Pt T fO

5 nm

Ph3P

PPh3

OTf

4 6

Figure 2 The reaction schemes for the preparation of nanoscopic cuboctahedra 5(a) and 6(b).

Figure 3 Space-®lling model of the cuboctahedron 6 derived from ESFF (Extensable Systematic Force Field) simulations using the Insight II 97.0 software package15.

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simulations12 is presented in Fig. 3. We believe that these macromolecules are the ®rst members of a unique class of arti®cial synthetic assemblies of O-symmetry. The size of 6 was assessed experimentally by measuring its selfdiffusion coef®cient using the pulsed gradient spin echo (PGSE) NMR technique13, widely employed to study aggregation and diffusion data of various chemical and biological assemblies in solution. The self-diffusion coef®cient14 for 6 at 25 8C is 1:92 6 0:072 3 10 2 6 cm2 s 2 1 which gives an experimental hydrodynamic diameter of 5.0 nm, in agreement with predictions based on the force-®eld simulations as well as the size of the component building units. Electrospray ionization mass spectrometry (ESI-MS) was used to identify the respective compositions of 5 and 6. On gentle ionization, the 12+, 13+, 16+ and 18+ species with mass-to-charge ratios (m/z) of 2,067, 1,896, 1,513 and 1,329, respectively, were observed for 5, resulting from the loss of the appropriate number of tri¯ate counterions. Fragmentation of 5 was also observed to a lesser degree, with the main components consisting of several combinations of precursors 1 and 3 with the loss of tri¯ate counterions. Identi®cation of fragments aided in determining coincidental combinations. For example, the peak found at 2,067 m/z was identi®ed as the fragment combination of 2 3 1 3 3 3 with a 3+ charge state resulting from the loss of three tri¯ate counter ions, not simply 5 without 12 tri¯ates (12+ charge state). The composition of 6 was supported by the observation of the 10+, 11+, 12+, 14+, 15+ and 16+ species resulting from the loss of tri¯ate counter ions (m/z 2,456, 2,219, 2,023, 1,713, 1,588 and 1,480, respectively). Additional evidence for 6 was given by the careful



letters to nature analysis of the fragmentation data containing expected combinations of precursors 3 and 4. The coordination-driven self-assembly process described here facilitates the ready formation of single-molecule, highly symmetrical, static, non-dissociating ultra®ne particles by simple mixing of predesigned, readily available components. This provides rapid access to supramolecular ensembles that are much larger than any classical synthetic macrocycles known at present. M .........................................................................................................................

Methods

Preparation. A 5-ml round-bottom ¯ask in a glovebox was charged either

with 1,3,5-tris[4-(trans-Pt(PPh3)2OTf) phenylethynyl] benzene 1 (30 mg, 0.01 mmol) for cuboctahedron 5 or with bis(4-[trans-Pt(PPh3)3I]phenyl) ketone 2 (30 mg, 0.007 mmol) in 2 ml of CD2Cl2. Then, a solution of 4,49bispyridylacetal 3 (3.5 mg, 0.015 mmol) in 2 ml of CD2Cl2 was added dropwise to the solution of 1 or 1,3,5-tris(49-pyridylethynyl)benzene 4 (3.2 mg, 0.011 mmol) was added to 2, resulting in the solutions of cuboctahedrons 5 or 6, respectively. The products were isolated by solvent removal in vacuo. Yields: 33.5 mg (99%) for 5 or 32 mg (98%) for 6. Characterization. The identity and purity of the products of self-assembly and their precursors was con®rmed by 1H, 31P{1H}, 13C{1H} and 19F NMR, IR, ESIMS and elemental analyses: see Supplementary Information. PGSE technique. A Stejscal-Tanner pulse sequence was used13. The diffusion coef®cients for both 5 and 6 were determined using 31P resonances in dichloromethane-acetone mixtures at 25 8C on the Z-gradient probe capable of producing pulsed ®eld gradients of nearly 200 G cm-1. The molecular size was determined from the effective hydrodynamic radius R, related to the effective hydrodynamic volume Vm as V m 4p=3R3 . R is calculated from the Stokes±Einstein equation, D kB T=6pRh, where D is the diffusion coef®cient, kB is the Boltzmann constant, T is the absolute temperature, and h is the viscosity of the liquid through which the species is diffusing14. ESI-MS technique. Samples of 5 and 6 were dissolved in acetone (10± 20 ng ml-1) and injected via syringe pump (100-ml syringe) into a Micromass Quatro II mass spectrometer with ionization performed under electrospray conditions (¯ow rate, 7.7 ml min-1; capillary voltage, 3.0 kV; cone, 47 V; extractor, 27 V). About 15 individual scans were averaged for the mass spectrum. The calibration of the mass range 500±3,000 atomic mass units was done with a 1:1 mixture of an isopropanol:water solution of NaI (2 mg ml-1) and CsI (0.01 mg ml-1). A table of ESI-MS data for 5 and 6 is available; see Supplementary Information. Received 12 November 1998; accepted 26 February 1999. 1. Horne, R. W. Virus Structure (Academic, New York, 1974). 2. Lehn, J.-M., Atwood, J. L., Davis, J. E. D., MacNicol, D. D. & VoÈgtle, F. (eds) Comprehensive Supramolecular Chemistry Vol. I±II (Pergamon, Oxford, 1996). 3. Lehn, J.-M. Supramolecular Chemistry: Concepts and Perspectives (VCH, Weinheim, 1995). 4. Stoddard, J. F. (ed.) Monographs in Supramolecular Chemistry (Royal Society of Chemistry, Cambridge, 1989, 1991, 1994±1996). 5. Fujita, M. et al. Self-assembly of ten molecules into nanometre-sized organic host frameworks. Nature 378, 469±471 (1995). 6. Cram, D. J. & Cram, J. M. Container Molecules and Their Guests (Royal Society of Chemistry, Cambridge, 1994). 7. Cram, D. J., Tanner, M. E. & Thomas, R. The taming of cyclobutane. Angew. Chem. Int. Edn Engl. 30, 1024±1027 (1991). 8. Meissner, R. S., Mendoza, J. D. & Rebek, J. Jr Autoencapsulation through intermolecular forces: a synthetic self-assembling spherical complex. Science 270, 1485±1488 (1995). 9. Kang, J. & Rebek, J. Jr Acceleration of a Diels-Alder reactions by a self-assembled molecular capsule. Nature 385, 50±52 (1997). 10. Stang, P. J. & Olenyuk, B. Self-assembly, symmetry and molecular architecture: Coordination as the motif in the rational design of supramolecular metallacyclic polygons and polyhedra. Acc. Chem. Res. 30, 502±518 (1997). 11. Persky, N. E., Manna, J. & Stang, P. J. Molecular architecture via coordination: Self-assembly of nanoscale platinum containing molecular hexagons. J. Am. Chem. Soc. Soc. 119, 4777±4778 (1997). 12. Dinur, U. & Hagler, A. T. in Reviews of Computational Chemistry II (eds Lipkwowitz, K. B. & Boyd, D. B.) Ch. 4 (VCH, New York, 1991). 13. Stejskal, E. O. & Tanner, J. E. Spin diffusion measurements: spin echoes in the presence of a timedependent ®eld gradient. J. Chem. Phys. 42, 288±292 (1965). 14. Hansen, J. P. & McDonald, I. R. Theory of Simple Liquids (Academic, London, 1976). 15. Insight II 97.0 (Molecular Simulations Inc., San Diego, CA, 26 Jan 1998). Supplementary information is available on Nature's World -Wide Web site (http://www.nature.com) or as paper copy from the London editorial of®ce of Nature. Acknowledgements. This work was supported by the National Science Foundation and the National Institutes of Health. Correspondence and requests for materials should be addressed to P.J.S. (e-mail: stang@chemistry. chem.utah.edu).


Signature of recent climate change in frequencies of natural atmospheric circulation regimes S. Corti*, F. Molteni*³ & T. N. Palmer² * CINECA-Interuniversity Computing Centre, Via Magnanelli 6/3, 40033 Casalecchio di Reno, Bologna, Italy ² European Centre for Medium-Range Weather Forecasts, Shin®eld Park, Reading, RG2 9AX, UK .........................................................................................................................

A crucial question in the global-warming debate concerns the extent to which recent climate change is caused by anthropogenic forcing or is a manifestation of natural climate variability1. It is commonly thought that the climate response to anthropogenic forcing should be distinct from the patterns of natural climate variability. But, on the basis of studies of nonlinear chaotic models with preferred states or `regimes', it has been argued2,3 that the spatial patterns of the response to anthropogenic forcing may in fact project principally onto modes of natural climate variability. Here we use atmospheric circulation data from the Northern Hemisphere to show that recent climate change can be interpreted in terms of changes in the frequency of occurrence of natural atmospheric circulation regimes. We conclude that recent Northern Hemisphere warming may be more directly related to the thermal structure of these circulation regimes than to any anthropogenic forcing pattern itself. Conversely, the fact that observed climate change projects onto natural patterns cannot be used as evidence of no anthropogenic effect on climate. These results may help explain possible differences between trends in surface temperature and satellite-based temperature in the free atmosphere4±6. Our climate can be thought of as a nonlinear dynamical system with a chaotic attractor. Let us imagine that the anthropogenic in¯uence on climate (for example, from increased atmospheric concentration of CO2) can be represented by a weak imposed forcing on this dynamical system. Because of the nonlinearity of the underlying system, its sensitivity to this forcing will vary with location on the attractor; in regions of strong local instability7 the system may be sensitive to the imposed forcing, but in regions of stability the system will be relatively insensitive. This notion can be demonstrated on the chaotic Lorenz8 system which has two dominant regimes. Irregular ¯uctuations between these regimes characterize the model's principal mode of internal variability. Largely independent of the details of the imposed forcing, the response of the Lorenz system to an imposed forcing is associated with an increase in the probability density function (PDF) associated with one regime, and a decrease in the PDF associated with the other regime (Fig. 1). (In the unforced Lorenz model, the PDF has the same value at both centroids.) By contrast, the locations of the regimes' centroids in phase space are largely unaffected by the imposed forcing. This can be understood by noting that the centroids of the regimes are phase-space regions of relative stability; the system is sensitive to the imposed forcing in a region of the attractor between the two centroids. If this picture were applicable to the real climate system, it would imply that anthropogenically forced changes in climate would project primarily onto the principal patterns of natural variability, even though such natural variability may occur predominantly on ³ Present address: The Abdus Salam International Centre for Theoretical Physics, PO Box 586, 34100 Trieste, Italy.


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