J. Phys. Chem. 1989, 93, 7560-7562
7560
Vlnylldene Radlcai Cation: A Slzable Barrier to Unimolecular Rearrangement to the Acetylene Radical Catlon Tracy P. Hamilton and Henry F. Schaefer III* Center for Computational Quantum Chemistry,t University of Georgia, Athens, Georgia 30602 (Received: July 24, 1989)
The activation energy for isomerizationof the lowest electronic state (2B1)of the radical cation of vinylidene to the 211uacetylene radical cation is predicted to be about 10 kcal/mol by high-level ab initio theory. Thus, the 2BIcation is metastable and may be observable. This is in conflict with conclusions based on previous theoretical results but apparently in agreement with two recent experimental studies employing collisional activation mass spectrometry.
Introduction
Singlet vinylidene has been the subject of theoretical and experimental study for some time, and not without controversy. The general consensus is that the classical barrier for the rearrangement of vinylidene via 1,Zhydrogen migration to acetylene is very small: H,C=C H-C=C-H (1) The best theoretical estimate for the classical barrier is about 3 kcal/mol.’ Other electronic states of vinylidene may have large barriers to rearrangement. The 2B2ground state of the vinylidene anion is easily generated experimentally2 and is predicted to be m e t a ~ t a b l e ~with - ~ respect to acetylene anion, which undergoes autodetachment of the electron. Experiments have also shown the existence of the 3B2and 3A2electronic states of vinylidene,6 most definitively by photoionization of the vinylidene anion. The 3B2state was predicted in 1978 by ab initio methods to have a substantial activation energy for isomerization to acetylene.’ The earliest experimental paper that mentions H2CC+ as a possible product concerned the decomposition of “[3]radialene”,* an isomer of C & , . Two recent letters reported the charge reversal of H2CC- to H2CC+,9,10with evidence for H2CC+coming from collisional activation mass spectrometry. In the latter paper, reference was made to two ab initio papers4v5as obtaining a nearly zero barrier for rearrangement of 2BI H2CCf to 211,, HCCH’. Some low-level theoretical results also appear in tabular form in the Carnegie-Mellon archives.” In ref 4, the transition state was not explicitly considered, and the correlation diagram from *BI to 211uwas drawn without a barrier. In ref 5, transition-state geometries were optimized by using a 4-31G basis set at the unrestricted Hartree-Fock self-consistent-field (SCF) level only. When electron correlation techniques and more complete basis sets were used at these geometries, the activation energy went from 21.3 to -0.5 kcal/mol! In light of these results, the activation barrier for the lowest cation state, ,B,, will be studied with high-level ab initio theory, as well as the energy difference between the 2B, ground state of the vinylidene cation and the 211uground state of the acetylene radical cation. -+
Figure 1. Geometry of the 2A‘‘ transition state for the rearrangement of 2B, H2CC+ to 211u HCCH+.
basis appended a single set off functions to carbon (af(C)= 0.8) and improved the hydrogen atom basis to Dunning’s triple split contraction15 plus two sets of polarization functions [a,(H) = 1.5, 0.3751 plus a single set of d functions [ad(H) = 1.0)]. This large basis will be named TZ2P+f and can be designated C(9s5~2dlf/5~3p2dlf), H(4s2pld/3s2pld). The more complete sets of functions on hydrogens were used because of the radical changes in bonding to hydrogen in the transition state ( H is bridging). All of the basis sets were constructed from Cartesian Gaussians. For SCF optimized structures, analytic second derivativesI6were evaluated to characterize the stationary points as minima or transition states. Vibrational frequencies were not obtained for the CISD stationary points. Final comparisons of energies were made using the Davidson correction” for approximating con(1) Carrington, T.; Hubbard, L. M.; Schaefer, H. F.; Miller, W. H. J . Chem. Phys. 1984, 80, 4347. Gallo, M. M.; Hamilton, T. P.; Schaefer, H. F. To be submitted for publication. (2) Dawson, J. H. J.; Jennings, K. R. Ado. Mass Spectrom. 1974,6, 797. (3) Chandrasekhar, J.; Kahn, R. A.; Schleyer, P. von R. Chem. Phys. Lett. 1982, 85, 493. (4) Rosmus, P.; Botschwina, P.; Maier, J. P. Chem. Phys. Lett. 1981,84, 71. ( 5 ) Frenking, G. Chem. Phys. Lett. 1983, 100, 484. (6) Laufer, A. H. J. Chem. Phys. 1980,73,49; 1982,76,945; Chem. Phys. Left. 1983,94, 240. Burnett, S. M.; Stevens, A. E.; Feigerle, C. S.; Lineberger, W. C. Chem. Phys. Lett. 1983, 100, 124. Ervin, K. M.; Ho, J.; Lineberger,
W. C. Submitted for publication in J. Chem. Phys. The characteristics of these triplet states of vinylidene were earlier predicted theoretically by: OsGeometries were optimized by using analytic gradients at both amura, Y.; Schaefer, H. F. Chem. Phys. Letf. 1981, 79, 412. the restricted open-shell SCFI2 and at the singly and doubly (7) Conrad, M. P.; Schaefer, H. F. J. Am. Chem. Soc. 1978,100,7820. (8) Bally, T.; Baumghrtel, H.; Biichler, U.;Haselbach, E.; Lohr, W.; substituted configuration interaction (CISD)13 levels of theory. Maier, J. P.; Vogt, J. Helv. Chim. Acta 1978, 61, 741. Most of the work was done utilizing a basis set made from the Holmes, J. L.; Szulejko, J. E. Chem. Phys. Lett. 1984, 107, 301. Huzinaga-Dunning set of double-{ contracted G a ~ s s i a n s ~ ~ J ~ (9) (10) Siilzle, D.; Schwarz, H. Chem. Phys. Letr. 1989, 156, 397. augmented by polarization functions ( a d ( C )= 0.75, a,(H) = (11) Whiteside, R. A.; Frisch, M. J.; Pople, J. A. Carnegie-Mellon Quantum Chemistry Archive, 3rd ed.; Carnegie-Mellon University: Pitts0.75). This basis will be called DZP and may be designated as burgh, 1983. C(9s5pld/4s2pld), H(4slp/2slp). A second basis set improved (12) Gcddard, J. D.; Handy, N. C.; Schaefer, H. F. J . Chem. Phys. 1979,
Theoretical Methods
the description of the carbon atoms to C(9s5p2d/5s3p2d) using Dunning’s triple split contracti~n’~ and q ( C ) = 1.5, 0.375. This basis set will be referred to loosely as TZZP, even though the hydrogen basis is still at the DZP level and the carbon basis is not truly triple (for the valence electrons. The third and largest ‘Contribution CCQC No. 59.
71, 1525. (13) Brooks, B. R.; Laidig, W. D.; Saxe, P.; Goddard, J. D.; Yamaguchi, Y.; Schaefer, H. F. J. Chem. Phys. 1980,72,4652. Rice, J. E.; Amos, R.D.; Handy, N. C.; Lee, T. J.; Schaefer, H. F. J . Chem. Phys. 1986, 85, 963. (14) Huzinaga, S. J . Chem. Phys. 1965, 42, 1293. (15) Dunning, T. H. J. Chem. Phys. 1970, 53, 2823. (16) Saxe, P.; Yamaguchi, Y.; Schaefer, H. F. J . Chem. Phys. 1982, 77, 5641.
0022-3654/89/2093-7560$01.50/00 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 22, 1989 7561
Letters TABLE I: Absolute (in hartrees) and Relative Energies (in kcal/mol) for *B1Vinylidene Cation, Transition State, and *& Acetylene cation4 TZ2P TZ2P+f DZP TZ2P DZP SCF SCF CISD CISD -76.416 43 -76.625 92 -76.424 66 -76.649 59 (33.5) (38.8) (35.7) (42.1) (+Q) -76.644 73 -76.670 20 (38.9) (42.2) ts -76.37676 -76.589 55 -76.38744 -76.624 13 (58.4) (56.0) (59.1) (58.1) (+Q) -76.61 9 46 -76.646 59 (54.8) (57.0) 'nu -76.46979 -76.687 75 -76.481 55 -76.71676 (0.0) (0.0) (0.0) (0.0) (+Q) -76.706 76 -76.737 48 (0.0) (0.0)
2B,
SCF -76.428 02 (36.6) -76.391 67 (59.4) -76.486 32 (0.0)
'Relative energies are in parentheses. The entries labeled +Q applied the Davidson correction for quadruple excitations to the CISD energies. All of the coefficients, C,, of the S C F configurations in the CISD wave functions were in the range of 0.951-0.956.
TABLE II: Harmonic Vibrational Frequencies (in cm-l) for the SCF ODtimized Cation Structures DZP SCF' TZ2P S C F TZ2P+f S C F 2BI
3332 3213 1570 1320 968 68 1
3274 3163 1555 1310 974 664
3287 3176 1559 1316 975 658
tS
3372 2422 1717 957 559 1061i
3341 2359 1716 974 628 1060i
3359 2369 1719 979 629 1053i
3528 3419 2049 864b 835b 797' 736'
3506 3393 2042 897b 854b 823' 777'
3522 3409 2045 901b 860b 823' 789'
2nu
'These frequencies correspond to the energetically lower lying component of the Renner-Teller pair of potential surfaces. bThese frequencies refer to the energetically higher lying component of the Renner-Teller pair of potential surfaces. 'The DZ+P S C F frequencies may be estimated to lie about 10% above the true (unknown) fundamentals.
tributions to C I from quadruple excitations [CISD(+Q)].
Results and Discussion The energies for the 2B1vinylidene catioq2A" transition state, and the 211uacetylene cation are given in Table I. The most obvious points to note are that the basis set effects are very small
beyond the DZP level and that the contributions of CISD to the relative energies are nearly constant for these basis sets. Judging from the fact that basis set effects are very similar for SCF, CISD, and CISD(+Q), the effect off functions will be to lower the barrier by about 0.5 kcal/mol. Adding this and a zero point vibrational energy (ZPVE) correction of 2.7 kcal/mol (from D Z P SCF vibrational frequencies that were simply scaled by a factor of 0.9) results in an activation energy of 11.6 kcal/mol. Table I1 lists the SCF harmonic vibrational frequencies for each SCF optimized stationary point. This easily places the vinylidene cation in the realm of being (maybe not so easily) observable. The energy difference between the vinylidene and acetylene cations, with a correction of 1.5 kcal/mol for f functions and ZPVE correction of -1.6 kcal/mol added to the TZ2P CISD(+Q) value, is estimated to be near 42 kcal/mol. It must be pointed out that the 211ustate was examined in DZhsymmetry and that the S C F method was constrained to singly occupy the b3u orbital. The symmetry is therefore not precisely of spatial ll character. Moreover, when one K component is doubly occupied and the other is singly occupied, the bending vibrational frequencies are no longer degenerate, and this is a manifestation of the Renner-Teller splitting.I8 The DZP S C F bending frequencies in neutral acetylene are 858 and 767 cm-' whereas in the acetylene cation they are split to 797, 736 cm-' (energetically lower lying component of the Renner-Teller pair of potential surfaces) and 864, 835 cm-' (higher lying component). This is similar to the splitting seen in a previous multireference SCF and CISD study19of CzHz+ that demonstrated the Renner-Teller splitting to be of the type referred to as type A,'* Table 111reports the geometrical parameters for the optimized structures. The effect of CISD is to lengthen the C-C bonds by 0.02 A and the C-H distances by 0.01 A, while changing the bond angles very little. Comparison of these structures with those of the analogous neutral singlet ground states' shows the effect of removing one of the .rr electrons: increasing the C-C distance by 0.09,0.06, and 0.04 in the vinylidene, bridging, and acetylene isomers, respectively. The DZP SCF values for the neutral species are included in Table 111 for comparison. Otherwise, the neutral and cationic species are very similar. This carries over into the energetics, as the M ' s for the isomerization of 2B1 HzCC+ are within 1 kcal/mol of the AE's between the 'Al HzCC and lZg+ HCCH. However, the barriers to isomerization differ by 7 kcal/mol, a significant amount considering that the neutral barrier is only about 3 kcal/mol. The presence of a substantial barrier in the 3B2(and presumably the 3A2)states of HzCC can be postulated to arise from repulsion between the singly occupied 2b2 orbital and a migrating hydride-like H.20 This nonbonding orbital on the terminal carbon of vinylidene is unoccupied in the 'A, state, and the barrier is low. The extra barrier height for ZB1over that of 'A, is probably due to the longer distance between the carbon atoms to be traversed by the migrating H. The above qualitative suggestion of a sizable barrier for 3A2is at variance with an analysis by Harding?' which predicts a low barrier. After this work was completed, we learned of two other papers submitted on the vinylidene c a t i ~ n . ~These z ~ ~ papers also included
!I
TABLE III: Bond Lengths (in A) and Angles (in deg) for the *B1Vinylidene Cation, Transition State, and *nuAcetylene Cation; Geometries for the Neutral Species at the DZP SCF Levels of Theory C2H2+ TZ2P SCF 1.3737 1.0867 121.0
TZ2P CISD 1.3855 1.0957 120.5
TZ2P+f S C F 1.3734 1.0856 120.7
DZP SCF
1.3849 1.0890 120.8
DZP CISD 1.4023 1.0989 120.4
1.3080 1.4337 1.0855 127.3 54.1
1.3330 1.4114 1.0953 127.8 55.1
1.2965 1.4301 1.0785 127.2 54.9
1.3162 1.4042 1.0878 127.4 56.2
1.2964 1.4323 1.0776 127.4 54.5
1.2429 1.4674 1.0679 130.0 50.5
1.2338 1.0773
1.2589 1.0857
1.2232 1.0697
1.2423 1.0776
1.2234 1.0690
1.1912 1.0616
DZP SCF IBI
c-c
ts
c-c
C-H H-C-H C2-H3
C2-H4 H-C-H C 1-C2-H3
2n"
c-c C-H
C2H2
1.2993 1.0804 120.2
J. Phys. Chem. 1989, 93, 7562-7570
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research on the 4Azand zAI states. Our preliminary work on these states showed that the 4A2HzCC cation (with a singly occupied 2bz orbital) has a very high activation energy for rearrangement and that the 2AI barrier is nearly zero at the DZP CISD level of theory. This is in good agreement with the results in a preprint from Baker.22 The 2AIstate suffers badly from spin contamination (17) Langhoff, S.R.; Davidson, E. R. Inr. J . Quantum Chem. 1974,8, 61. (18) Lee,T. J.: Fox, D. J.; Schaefer, H. F.; Pitzer, R. M. J. Chem. Phys. 1984, 81, 356. (19) Lee, T. J.; Rice, J. E.; Schaefer, H. F. J . Chem. Phys. 1987,86,3051.
(20) Ha, T. K.; Nguyen, M.-T.; Hendrickx, M.; Vanquickenborne, L. G. Chem. Phys. Leu. 1983, 96, 267. (21) Harding, L. B. J . Am. Chem. SOC.1981, 103, 7469. (22) Baker, J. Chem. Phys. Lerr. 1989, 159, 447. (23) Frenking, G. Submitted for publication in Chem. Phys. Lett.
in Baker’s work (based on the unrestricted Hartree-Fock method), and extrapolation of his values leads to the 2Bl state being 7 kcal/mol higher than zAl. This is compared to our ZBI state predicted to be. below ZAlby 2 kcal/mol using DZP CISD, making the order of these states problematic. Our activation energy for the 2BI 211urearrangement converged to a value 3.6 kcal/mol higher than that from Baker’s highest level of theory.
-
Acknowledgment. This research was supported by the U S . Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Fundamental Interactions Branch, Grant DE-FG09-87ER13811. We are grateful to Dr. J. Baker for a preprint and correspondence. We also thank Professor Michael A. Duncan, Ms. Mary Gallo, and Dr. Brian F. Yates for useful discussions.
FEATURE ARTICLE Stability of Lyotropic Phases wlth Curved Interfaces Sol M. Gruner Department of Physics, Princeton University, Princeton, New Jersey 08544 (Received: January 6. 1989; In Final Form: May 1, 1989) The diverse structural forms of lipid-water phases are representative of those found in many lyotropic and amphiphilic systems. These structures consist of interfaces which divide the material into hydrophobic and hydrophilic volumes. The net result of a very complex set of intermolecular interactions is that the interfaces behave as surfaces endowed with a spontaneous curvature and whose separations are subject to constraints of molecular lengths and component densities. Phase transitions which result in an abrupt change of the curvature of the interfaces may be understood phenomenologically as a competition between the elastic energy of bending the interfaces and energies resulting from the constraints of interfacial separation. The application of this approach is reviewed for transitions between lamellar, hexagonally packed cylindrical, close-packed spherical, and bicontinuous cubic structures of diacyl biomembrane lipids. It is shown that the structural dimensions and phase transitions of the lipid mesomorphs may be largely understood in terms of the phenomenological model. The existence of a spontaneous curvature associated with the lipid monolayers of bilayers implies that biomembranes exist in a state of compositionally controlled elastic stress which may provide a chemically nonspecific rationale for the types of lipids found in cell membranes. A discussion is given of the evidence that membrane proteins are functionally sensitive to the elastic stress. The article concludes with a summary of related outstanding problems.
Introduction At high concentrations in water, polar biomembrane lipids form liquid crystalline structures with an astonishing degree of geometrical complexity. Consider, for example, one of the cubic phases of glycerol monooleate-water mixtures (Figure 1); this is but one of the many liquid crystalline phases seen in the phase diagram of this system. The structure consists of two mutually interpenetrating, but separate, mesh works of water channels separated by a multiply connected bilayer wall of monooleate molecules organized on a three-dimensionally periodic cubic 1attice.l This structure spontaneously self-assembles upon mixing of the constituents. Further, although the monooleate headgroups are confined to the hydrophobic-water interface and the water to the water channels, the molecules are in every other way in a fluid form and randomly diffuse over many unit cells of the structure each second. Even more remarkably, this structured liquid has unit cell dimensions considerably larger than the size of any of the constituent molecules even though there are no long-range forces present. What are the physical principles which control the structure of this and many other amphiphilic systems? (1) Longley, W.; McIntosh, T. J. Nature 1983, 303, 612.
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As discussed in this article, in the past 5 years a surprisingly simple picture of the forces which are involved has emerged and has potent implications for areas as diverse as catalysis and biomembranes. The lyotropic mesomorphism exhibited by glycerol monooleate is shared by many of the polar lipids commonly found in biomembranes. The word lyotropic indicates that the structures and phases which are formed are a function of the ratios of the constituent molecules, such as the water-to-lipid ratio, as well as the temperature and pressure. Mesomorphism, from the Greek mesa, or middle, indicates that there is a sequence of thermodynamically distinct phases sandwiched between the low-temperature solid phase and the high-temperature isotropic fluid phase. Typically, these mesophases are liquid crystalline; i.e., they simultaneously exhibit aspects of crystalline periodicity and liquidlike molecular diffusibility. An example of the phase sequence observed in a biomembrane-water mixture as a function of temperature is shown in Figure 2. Depending on the system chosen, the same phase sequence may be observed as a function of salt concentration, pressure, ratios of the constituent lipids, or pH. More generally, homologous sequences of similar structures are seen in diverse systems which exhibit amphipathic character, such as diblock copolymers. In the case of the diblock copolymers, lyotropic 0 1989 American Chemical Society
