J. Phys. Chem. 1988, 92, 935-939
935
Tunneling Instability In the Cls-Trans Isomerization Reaction of Hydroxysilylene Akitomo Tachibana,tl Hiroyuki Fueno,+Masahiko Koizumi, Tokio Yamabe,*+t Department of Hydrocarbon Chemistry. Faculty of Engineering, Kyoto University, Kyoto 606,Japan
and Kenichi Fukuit Kyoto Institute of Technology, Kyoto 606, Japan (Received: April 16, 1987; In Final Form: July 20, 1987)
The dynamic bonding character of hydroxysilylene in the cis-trans isomerization reaction is studied in terms of the concept of tunneling instability. Each isomer is identified with a “cell” in the ( 3 N - 6)-dimensional mass-weighted configuration space of molecular “structure”. At low temperature, quantum mechanical instability of the cell structure is brought about via tunneling through the intercell boundary. A remarkable isotope effect of the cell structure is predicted, which is in accord with a novel experimental observation: both trans and cis isomers are detected for HSiOD, but only the trans isomer is detected for HSiOH.
Introduction Recent advances in silicon chemistry have revealed novel bonding character of silicon compounds.’ Theoretical studies of silylene, disilane, disilene, disilyne, and hexasilabenzene have been reported.2 Silanone to silylene isomerization3 and detection of silanone, hydroxysilylene, silanol, and silanoic and sililic acidse6 have been investigated experimentally. Silanone, the dimer of silanone, and hydroxysilylene have been investigated theoretically.Quite recently, the interaction of a silicon atom with a water molecule a t 15 K in a solid argon matrix has been investigated by Ismail et a1.5 Silicon in the triplet ground state reacts with water to form the adduct Si:OH2. After hydrogen transfer, the insertion product hydroxysilylene, HSiOH, is obtained. The ground singlet state of HSiOH is finally obtained by intersystem crossing and is identified by IR spectroscopy. HSiOH has a trans isomer and a cis isomer. Quantum chemical calculation predicts that the trans isomer is slightly more stable than the cis isomer, but the energy difference is very mall.'^,^ In the case of partially deuteriated HSiOD, both trans and cis isomers are detected. On the other hand, only the trans isomer of HSiOH is detected. Why is the trans isomer only detected for HSiOH but not HSiOD? A clear explanation concerning this unusual behavior has not been reported. Both cis and trans isomers should be identified as local minima on the potential energy surface and the barrier which divides the two minima has also been reported theoretically.’ Therefore, the key to solving the unusual difficulty should be the characteristics of the dynamics on the double-well potential energy surface. The reaction dynamics on the double-well potential energy surface itself has received much interest, in particular in connection with the intramolecular proton-exchange reaction’& and hydrogen inversion reaction.Iob This is related to the problem of identification of molecular ”structure+’ in quantum mechanics in terms of both Born-Oppenheimer adiabatic approximation and full quantum mechanical treatment.” The central problem of particular interest is the instability of tunneling.Iob The tunneling instability brings about localization of position probability density leading to the identification of the classical concept of molecular structure. In this connection, we have performed a differential geometrical study of molecular structure in terms of “cell” structure in ( 3 N - 6)-dimensional mass-weighted Riemannian space of nuclear configuration.’* In the present paper, tunneling instability in the cis-trans isomerization reaction of hydroxysilylene is studied. The reaction #Presentaddress: Department of Chemistry, University of North Carolina, Chapell Hill, NC 27514. ‘Also belongs to: Division of Molecular Engineering, Graduate School of En ineering, Kyoto University, Kyoto 606, Japan. ?Also belongs to: Institute for Fundamental Chemistry, 15 Morimoto-cho, Shimogamo, Sakyc-ku, Kyoto 606, Japan.
0022-3654/88/2092-0935$01.50/0
-
scheme is described as follows:
trans-HSiOX (lA’)
cis-HSiOX (lA’);
( X = H or D)
IRC (intrinsic reaction ~ r d i n a t e ) is’ ~used as the unique reaction path. IRC is defined in the curved Riemannian space where the local coordinates are conveniently selected from curvilinear internal coordinates which specify the internal relationship of the constituent nuclei. The metrics of the Riemannian space depends on the mass of the constituent nuclei, and hence the I R C shows a typical isotope effect?a It follows that the double-well potential energy surface along the IRC of the cis-trans isomerization reaction of hydroxysilylene shows a typical isotope effect. The asymmetry of the double-well potential and the corresponding localization of the wave function are in close agreement with the unusual isotope effect of experimental observation.
Method of Calculation The molecular orbital (MO) calculations were carried out with the G A u S S I A N - ~ Oprogram ’~ for the reactants, products, and TS’s ~~
(1) (a) Raabe, G.; Michl, J. Chem. Rev. 1985,85,419 and references cited therein. (b) Luke B. T.; Pople, J. A.; Krogh-Jespersen, M.-B.; Apeloig, Y.; Karni, M.; Chandrasekhar, J.; von Rague Schleyer, P. J . Am. Chem. SOC. 1986, 108, 270 and references cited therein. (2) Raghavachari, K.; Chandrasekhar, J.; Gordon, M. S.;Dykema, K. J. J. Am. Chem. SOC.1984, 106, 5853. Krogh-Jespersen, K. Ibid. 1985, 107, 537. Sax, A.; Olbrich, G. Ibid. 1985,107,4868. Gordon, M. S.;Truong, T. N.; Bonderson, E. K. Ibid. 1986,108, 1421. Kahler, H.-J.; Lischka, H. Chem. Phys. Lett. 1984, 112, 33. Schlegel, H. B. J . Phys. Chem. 1984,88,6254. Clabo. D. A,: Schaefer 111. H. F. J . Chem. Phvs. 1986. 84. 1664. Naease. - . S.;Teramae,’H.; Kudo, T.’Ibid. 1987, 86, 45f3. (3) Barton, T. J.; Hussmann, G. P. J . Am. Chem. SOC.1985, 107, 7581. Linder, L.; Revis, A,; Barton, T. J. Ibid. 1986, 108, 2142. (4) Withnall. R.: Andrews. L. J . Phvs. Chem. 1985, 89, 3261. (5) Ismail, Z. K.; Hauge, R. H.; Frdin, L.; Kauffman, J. W.; Margrave, J. L. J . Chem. Phys. 1982, 77, 1617. (6) Glinski, R. J.; Gole, J. L.; Dixon, D. A. J. Am. Chem. SOC.1985, 107, 5891. (7) (a) Kudo, T.; Nagase, S. J. Phys. Chem. 1984,88,2883. (b) Kudo, T.; Nagase, S. J. Am. Chem. SOC.1985, 107, 2589; Chem. Phys. Lett. 1986, 128, 507. (8) Jaquet, R.; Kutzelnigg, W.; Staemmler, V. Theor. Chim. Acta 1980, 54, 205. (9) (a) Tachibana, A.; Fueno, H.; Yamabe, T. J . Am. Chem. SOC.1986, 108,4546. (b) Tachibana, A.; Koizumi, M.; Teramae, H.; Yamabe, T. J . Am. Chem. SOC.1987,109, 1383. (10) (a) Kunze, K. L.; de la Vega, J. R. J. Am. Chem. SOC.1984, 106, 6528. Hameka, H. F.; de la Vega, J. R. Ibid. 1984, 106, 7703. Busch, J. H.; de la Vega, J. R. Ibid. 1986, 108, 3984. (b) Claverie, P.; Jona-Lasinio, G. Phys. Rev. A 1986, 33, 2245. (11) Woolley, R. G. J . Am. Chem. SOC.1978, 100, 1073. Wilson, E. B. Int. J . Quantum Chem., Quantum Chem. Symp. 1979, 13, 5. Bixon, M. Chem. Phys. 1982, 70, 199; Chem. Phys. Lett. 1982,87, 271. (12) (a) Tachibana, A.; Fukui, K. Theor. Chim. Acta 1979, 51, 189. (b) Tachibana, A,; Fukui, K. Ibid. 1978, 49, 321; 1979, 51, 275; 1980, 57, 81. (13) Fukui, K. J . Phys. Chem. 1970, 74, 4161. Fukui, K.; Kato, S.; Fujimoto, H. J . Am. Chem. SOC.1975, 97, 1. Ishida, K.; Morokuma, K.; Komornicki, A. J . Chem. Phys. 1977, 66, 2153. (14) Pople, J. A,; et al. QCPE 1981, 13, 406.
0 1988 American Chemical Society
936 The Journal of Physical Chemistry, Vol. 92, No. 4, 1988
Tachibana et al. trans
H
U
'i
@ =
cis
HSiOH (HSiOD)
93.1
1.494SI
1.506 1 9 7 . 1
%?
"
071
I
\
I
\
i
H
\
/
\
I
I
H
/ H
/ /
*I
\ '
\
10.24*
\ \
'H
(C) Figure 1. Optimized geometries. (a) trans-HSiOH, (b) cis-HSiOH, (c)
-
TS of trans-HSiOH cis-HSiOH and the vector of vibrational mode corresponding to the IRC, in the singlet ground state by HF/3-21G(*), (d) trans-HSiOH, (e) H,SiO, (f) TS of trans-HSiOH H2Si0, in the triplet excited state by MP2/6-31G**. Bond lengths and angles are given in angstroms and degrees, respectively.
-
using the SCF method15with the 3-21G(*)'" basis set. Geometry optimization was performed by using the energy gradient method." The electron correlation energy for each geometry was estimated by double-substituted configuration interaction (CID)'* with the 6-3 1G**'6b basis set, and the Davidson c o r r e ~ t i o nwas ' ~ added to allow for unlinked cluster quadrupole correction (QC) denoted as CID+QC/6-3 lG**//HF/3-2lG(*). The vibrational analysis and IRC were calculated in the SCF level with the HONDOG*O program by use of the 3-21G(*) basis set. In order to compare the singlet ground state and the triplet excited state, geometry optimization of equilibrium points was carried out with the GAUSSIAN-82 program'' using Maller-Plesset second-order perturbation theoryz2with the 6-31G* basis set.16bThe relative energy values between the singlet ground state and the triplet excited state were obtained by Maller-Plesset fourth-order perturbation theory considering the contribution of single, double, triple, and quadrupole substitution^^^ with the 6-31G** basis set, denoted as MP4(SDTQ)/6-3 1G**//MP2/6-3 1G*.
Results and Discussion Geometries and Potential Energy Diagrams. The optimized geometries of the trans isomer, cis isomer, and TS of the reaction (15) Roothaan, C. C. J. Rev. Mod. Phys. 1951, 23, 69. (16) (a) Pietro, W. J.; Francl, M. M.; Hehre, W. J.; DeFrees, D. J.; Pople, J. A.; Binkley, J. S. J . Am. Chem. SOC. 1982,104, 5039. (b) Francl, M. M.; Pietro, W. J.; Herhe, W. J.; Binkley, J. S.; Gordon, M. S.; DeFrees, D. J.; Pople, J. A. J . Chem. Phys. 1982, 77, 3654. (17) Pulay, P. In Modern Theoretical Chemistry; Schaefer, H. F., 111, Ed.; Plenum: New York, 1977; Vol. 4, Chapter 4. (18) Seeger, R.; Krishnan, R.; Pople, J. A. J. Chem. Phys. 1978,68,2519. (19) (a) Langhoff, S. R.; Davidson, E. R. Int. J . Quantum Chem. 1974, 8, 61. (b) Davidson, E.R.; Silver, D. W. Chem. Phys. Lett. 1978, 52, 403. (20) Dupuis, M.; King, H. F. J . Chem. Phys. 1978,68, 3998. (21),Binkley, J. S.; Frisch, M. J.; DeFrees, D. J.; Raghavachari, K.; Whiteside, R. A.; Schlegel, H. B.; Fluder, E. M.; Pople, J. A. "Gaussian 82, Release A version (Sept 1983). An Ab Initio Molecular Orbital Program", Carnegie-Mellon University, Pittsburgh, PA. (22) Pople, J. A.; Binvey, J. S.; Seeger, R.Int. J. Quantum Chem. 1975, 9, 229. Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Int. J. Quantum Chem., Quantum Chem. Symp. 1919, 13, 225. (23) Krishnan, R.; Pople, J. A. Inr. J . Quantum Chem. 1978, 14, 91. Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Ibid. 1978,14,545. Krishnan, R.; Frisch, M. J.; Pople, J. A. J . Chem. Phys. 1980, 72, 4244. Frisch, M. J.; Krishnan, R.; Pople, J. A. Chem. Phys. Lett. 1980, 75, 66.
\ \
-0.55*
-9-
Figure 2. Relative energy values by HF/3-21G(*) (full line), HF/321G(*)plus zero-point energies orthogonal to the IRC (dotted line), and
CID+QC/6-31G**//HF/3-21G(*) (dot-dash line). The geometries are the same as Figure 1. The values in parentheses are those of HSiOD. The unit is kcal/mol. TABLE I: Relative Energies AE by
MP4(SDTQ)/6-31GZ*//MP2/6-31G* species AE,kcal/mol trans-HSiOH (singlet) -39.4 trans-HSiOH (triplet) 0.0 TS" (triplet) 41.5 H2Si0 (triplet) 22.6 "The TS of isomerization reaction from trans-HSiOH to HzSiO in its triplet state. are shown in Figure 1. The TS is identified as the structure of a saddle point on the potential energy surface by vibrational analysis. The reaction pathway maintains C, symmetry. The relative energy values of optimized geometries are shown in Figure 2. The activation energy from the trans isomer to the cis isomer by HF/3-21G(*) is 5.47 kcal/mol, and that by CID QC/631G**//HF/3-21G(*) is 10.79 kcal/mol. The activation energy of the isomerization reaction from trans-hydroxysilyleneto silanone is 68.00 kcal/mol,98 which is qualitatively in agreement with the previous theoretical estimate of 63.9 kcal/m01.'~ Because it is much greater than the former value of the cis-trans isomerization reaction, the channel of isomerization to silanone need not be considered. The energy difference between trans-hydroxysilylene in its triplet excited state and its singlet ground state is 39.4 kcal/mol, as shown in Table I. The activation energy of the isomerization reaction from trans-hydroxysilylene to silanone in its triplet state is 47.5 kcal/mol. Therefore, the triplet excited state does not have any influence on the dynamics on the singlet ground state. As shown in Figure 2, the energy difference between the trans isomer and cis isomer by HF/3-21G(*) is 0.38 kcal/mol and that by CID+QC/6-31G**//HF/3-21G(*) is 0.55 kcal/mol. This is very small, and hence the difference in thermodynamic stability at low temperature can hardly be detected. Moreover, the zero-point energies of vibrational modes orthogonal to the IRC
+
Cis-Trans Isomerization Reaction of Hydroxysilylene
6 z 5
h
2 4 w
The Journal of Physical Chemistry, Vol. 92, No. 4, 1988 937
A
-
b:
-
3 -
'
r '
- *
--
-e-
-
m
H Si
=' ='
2 1 -
-' /
0-
-
.
-2
-1
0
2
1
S
fi.bohr
HSiOD
-I
,
o
l
i
l
l
-1.60
-2.40
-
I
OH .
I
-0.80
I
,
I
I
0.80
0.00
,
I
I
2.40
1.60
~
3.20
COOROINRTE I W * B O H R I
/
0
Zl I -2
-1
0
S
1 6 , b o h r
B
2
Figure 3. (A) Born-Oppmheimerpotential energy profde along the IRC and (B) the corrected potential energy profie including zero-point energies orthogonal to the IRC.
are added to the Fbm-Oppenheimer potential energy. The energy difference is 0.51 kcal/mol for HSiOH and 0.54 kcal/mol for HSiOD, and the isotope effect cannot be identified significantly. Analysis of ZRC. The potential energy profile along the IRC of the cis-trans isomerization reaction is shown in Figure 3A. The number on the abscissa indicates the IRC: the origin corresponds to the TS, the negative side corresponds to the ce1112of the trans isomer, and the positive side corresponds to the cell of the cis isomer. The isotope effect can be clearly seen in the cell of the trans isomer and is scarcely seen in the cell of the cis isomer. The changes of geometry along the IRC are shown in Figure 4. All the bond lengths are almost fixed in the course of the reaction. The bond angles are also fixed, except for the angle LSiOH. Therefore, the cis-trans isomerization reaction path may be regarded as a one-dimensional path corresponding purely to the SOH bending vibration. The frequency changes of the vibrational modes orthogonal to the reaction path as a function of the IRC are shown in Figure 5 . The vibrational modes orthogonal to the IRC are obtained by diagonalizing the projected force constant matrix24projecting out the degrees of freedom of the IRC, overall translations, and rotations. The frequencies of all modes, including the OH stretching mode possessing an isotope effect, are almost constant. Again, the one-dimensionality of the reaction path is demonstrated. The vibrational modes orthogonal to the reaction coordinate are considered purely bath modes which should not contribute significantly to the dynamics along the reaction coordinate. The potential energy profile including the zero-point vibrational energies orthogonal to the IRC is shown in Figure 3B. The isotope effect can be clearly seen in the cell of the trans isomer and is (24) Miller, W. H.; Handy, N. C.; Adams, J. E. J. Chem. Phys. 1980. 72, 99. Gray, S.K.;Miller, W.H.; Yamaguchi, Y.; Schaefer 111, H. F.Ibid. 1980, 73, 2733. Kato, S.;Morokuma, K. Ibid. 1980, 73, 3900. Yamashita, K.; Yamabe, T.; Fukui, K . Chem. Phys. Lett. 1981, 84, 123. Yamashita, K.; Yamabe, T. Int. J. Quantum Chem., Quantum Chem. Symp. 1983.17, 177.
I
I
--2.40
I
-1.60
I
I
I
I
I
I
I
0.00
-0.80
COOROINRTE
I
I
I
1
2.40
1.60
3.20
1
[&iiOtiR
Figure 4. Changes of geometries along the IRC: (A) bond length and (B) bond angle. Circle and triangle correspond to HSiOH and HSiOD,
respectively.
4800;
'i h -4000:
HSi str.
w
Si0 stt.
0 -12 . 4 0
I
,
-1.60
I
1
-0.80
I
I
,
(1.00
COOROINRTE
[
,
0.80
1
I
1.60
L/RMU.BOHAI
I
I
2.10
I
I
1.20
Figure 5. Frequencies of the vibrational modes orthogonal to the IRC, as a function of the reaction coordinate s.
scarcely seen in the cell of the cis isomer. It follows that the isotope effect of the cell structure is under the control of the large-amplitude vibrational motion of the hydrogen atom of OH along the
I
938
Tachibana et al.
The Journal of Physical Chemistry, Vol. 92, No. 4, 1988
5 900
800
700
...
600
5 30 HSiOH
Us100
DSIOH
-
DSIOD
Figure 6. Frequencies of the vibrational modes in the direction of the IRC for trans-HSiOH (dotted line) and cis-HSiOH (full line) and the
isotope effects.
Q
/ ,
Figure 7. Model of double-well potential.
a
IRC. This is nothing but the SiOH bending vibration at each equilibrium point which has the least vibrational frequency maintaining the C, symmetry of HSiOH. It should be noted that by the stable limit theorem12athe vibrational mode corresponding to the IRC has the least vibrational frequency at the equilibrium point. The isotope effect of the SiOH bending vibration which corresponds to the IRC is shown in Figure 6. The frequencies of trans isomers are greater than those of cis isomers in all cases. This tendency is also found in the work of Kudo and N a g a ~ e , ' ~ which corresponds to the experimental results of Ismail et This indicates that the trans isomer is more tight than the cis isomer. The frequency difference between the trans isomer and cis isomer of HSiOH is larger than that of HSiOD. This is caused by the isotope effect which is remarkable for the trans isomer rather than for the cis isomer, as shown in Figure 3; that is, the potential energy surface is symmetric for HSiOD and largely asymmetric for HSiOH. We will discuss the asymmetry in the next section in order to get information on the global aspect of isomerization. Tunneling Instability and Localization of Wave Function. The asymmetry of the potential energy surface of HSiOH is mainly due to the expansion of the cell of the trans isomer. Therefore, the vibrational wave function of HSiOH localizes greatly in the cell of the trans isomer, probably corresponding to the fact that only the trans isomer is observed in the case of HSiOH. In order to examine the general features of the localization problem, a simplified model potential is used as shown in Figure 7. Each cell is represented by a square well potential and is separated from each other by the intercell boundary. At low temperature, cis-trans isomerization occurs by tunneling through the intercell boundary. The localization of the wave function is a function of the asymmetry of the potential. In harmony with the present situation, the diameter a of the cell of the trans isomer will be enlarged, and the stabilization energy A will also be introduced for the cell of the trans isomer. The wave functions are defined separately for each region as $b, and $, corresponding to the regions (-a Is I0),(0 Is Ib ) , and ( b Is Ib c), respectively, and are easily obtained by a standard method as presented in the Appendix. Regional probability, denoted as Pa, Pb3 P,, may be defined as follows:
+
Pa + Pb
+ P, = 1
The situation Pa = P, may correspnd to the model of HSiOD, and P, > P, to the model of HSiOH. Since this is a crude model for the purpose of demonstration of localization, a quantitative correlation with the present situation
21
2.2
':
Figure 0.1 8. Contour of P, at an interval of 5% as a function of a and A.
a + b is fixed at 3.2 and b changes from 1.2 to 1.0, while the other parameters c and h are fixed. The unit of Pa is %. Let the unit of energy be kcal/mol, then the unit of coordinates becomes 1.704 IRC unit = 1.704 (amu)'/2.bohr for a corresponding particle of mass 1.O.
is not so exactly introduced. Indeed, the local curvature of potential energy at the stable equilibrium point, i.e., at the center of the cell, and the global feature of the cell is not so well-parametrized by the square well model. Let the unit of energy be chosen as kcal/mol in the model potential; then the unit of coordinate becomes 1.704 times the IRC unit = 1.704 (amu)1/2.bohr for the corresponding particle of mass 1.O. If we assume the symmetric double-well cell structure for HSiOD, then for the set of parameters ( h = 5.0, a = c = 2.0, b = 1.2) we obtain the set of zero-point energies (0.897) which may be comparable to h = 5.73 of the present calculation (see Figure 3) with E = 0.805 (= (1/2)563.2 cm-') of the experimental ob~ervation.~ The following type of asymmetry is taken into account: a b is fixed at 3.2 and b changes from 1.2 to 1.0, while the other parameters c and h are fixed. The stabilization energy A is also the origin of asymmetry. The contour of Pa as a function of a and A is shown in Figure 8. Suppose that only one isomer is observed if Pa is more than 90; then a should be larger than 2.07 if A is nearly equal to 0. This situation is likely to occur for HSiOH even though it is impossible for HSiOD. This corresponds to the fact that only the trans isomer is observed for HSiOH.
+
Concluding Remarks Tunneling instability in the cis-trans isomerization reaction of hydroxysilylene is studied by using IRC as the unique reaction coordinate. The difference in the hydrogen movement at different cells of the double-well potential brings about the zharacteristic asymmetry of the cell structure. The effect on the asymmetry due to the zero-point energy orthogonal to the reaction coordinate does not work so drastically. The character of the asymmetry
J. Phys. Chem. 1988,92,939-945 is then purely one-dimensional. The asymmetry due to the difference in expansion of the cell is effective for the localization of the wave function. The tunneling instability mechanism in the novel isotope effect of hydroxysilylene is in close agreement with experimental ob~ervation.~Further study in this direction of research is expected in the future.
+ b + c)
J., = C sin @(-s
( b Is I b
+ c)
where a = [2(E
+ A)]'/*, A=-
Acknowledgment. This work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education of Japan, for which the authors express their gratitude. The numerical calculations were carried out a t the Data Processing Center of Kyoto University and the Computer Center of the Institute for Molecular Science (IMS). Appendix. The Wave Function of the Square Well Potential The wave function for a corresponding particle of mass 1.O of the square well potential as shown in Figure 7 may be written as follows: (-a Is I0) J /=, A sin a(s a)
939
@ = (2E)'/', e = [2(h - E ) ] ' / 2
2e B sin aa(a cot aa - e )
B'= - a cot aa + e B a cot aa - e
c=
-(
1 sin Bc
dtb
- a cot aa
a cot aa
+ e e'') B -e
The energy eigenvalue E is determined by the boundary condition a t the intercell boundary and is defined by the root of f(E)= 0, where
+
J/b
= Be-"
+ Bk'
(0 IS 5 b)
Registry No. HSiOH, 83892-34-6; HSiOD, 83892-35-7; H2Si0, 22755-01-7; Dz, 7782-39-0.
Hydration of Methylated and Nonmethylated B-DNA and 2-DNA1 Pui Shing HoJt Gary J. Quigley,*+Robert F. Tilton Jr.: and Alexander Richt Departments of Biology and Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (Received: April 23, 1987; In Final Form: August 17, 1987)
The water-accessiblearea of DNA with a sequence of alternating guanine and cytosine residues has been calculated for both right-handed B-DNA and left-handed Z-DNA. Comparing the values for DNA that is unmethylated and that methylated on the 5-position of cytosine we find that methylation of B-DNA increases the solvent-accessiblearea whereas methylation of Z-DNA decreases the solvent-accessiblearea. This is largely due to the methyl group blocking a region otherwise accessible to the solvent. Relative energies of hydration have been calculated by adopting approximations initially developed for the hydration of proteins. These show a significant increase in hydration energy for methylation of B-DNA compared to its unmethylated form. However, only a slight increase is noted for the methylation of Z-DNA compared to its unmethylated form. This may play a role in explaining the fact that, for the methylated polymer, Z-DNA is the stable form in a physiological salt solution, while B-DNA is the stable form in the unmethylated polymer.
Introduction One of the more striking conformational changes in macromolecules is the conversion of the right-handed form (B-DNA) to its left-handed Z-DNA form (reviewed in Rich, 1984'). This interconversion is strongly influenced by a number of factors, including negative supercoiling and the ionic environment. It is also influenced by chemical modification such as methylation of cytosine base a t position 5 . There is a growing awareness that the nature of the aqueous environment surrounding a biological macromolecule also plays a significant role in determining its conformation.2 Our ability to assess the contributions of water interactions toward the stability of any particular conformation in a rigorously analytical manner, however, is restricted by the lack of information on the structure of the immediate hydration layers around macromolecules. Only a limited number of proteins2g3and nucleic acid sequence^^,^ produce crystals that diffract to a resolution high enough to provide reliable data on solvent structure (better than 1.5-2 A). 'Department of Biology. *Current address: Department of Biochemistry and Biophysics, Oregon State University, Corvallis, OR 9733 1 . t Department of Chemistry. Current address: Department of Molecular Biology, Scripps Clinic, La Jolla, CA 92037. Dedication: This paper is dedicated to the memory of Massimo Simonetta of Milan, Italy.
Recently, semiempirical approaches have been used to describe the influence of hydration on macromolecular conformations at the atomic level. In these methods, the degree to which a protein or nucleic acid polymer is hydrated can be estimated by calculating the surface of the molecule that is exposed to water.68 Thus analysis of the water-accessible surface of transfer R N A and of the right-handed A and B forms of D N A has contributed to our understanding of how dehydrating conditions may favor one conformation of a polynucleotide over another.' Eisenberg and McLachlad have extended this strategy by weighting the calculated surfaces areas with thermodynamic parameters that describe the hydration energies of hydrophilic, hydrophobic, and charged surfaces. These solvation energies for molecular surfaces were derived from experimental values for transferring an amino (1) Rich, A.; Nordheim, A.; Wang, A. H.-J. Annu. Rev.Biorhem. 1984, 53, 791-846.
(2) Teeter, M. M. Proc. Narl. Acad. Sei. USA 1984, 81, 6014-6018. (3) Poulos, T. L.; Finzel, B. C. Protein, Peptide Reu. 1984, 4, 115-171. (4) Wang, A. H.-J.; Quigley, G. J.; Kolpak, F. J.; Crawford, J. L.; van Boom, J. H.; van der Marel, G.; Rich, A. Nature (London) 1979, 282, 680-686. (5) Wing, R.; Drew, H.; Takano, T.; Broka, C.; Tanaka, S.; Itakura, K.; Dickerson, R. Nature (London) 1980, 287, 755-758. (6) Langmuir, I. Colloid Symp. Monogr. 1925, 3, 48-75. (7) Alden, C. J.; Kim, S. H. J . Mol. Biol. 1979, 132, 411-434. (8) Eisenberg, D.; McLachlan, A. D. Nature (London) 1986, 319, 199-203.
0022-3654/88/2092-0939$01.50/0 0 1988 American Chemical Society
