J. Phys. Chem. 1994,98, 6955-6960
6955
A Theoretical Study of Stationary Structures for the Addition of Azide Anion to Tetrofuranosides: Modeling the Kinetic and Thermodynamic Controls by Solvent Effects J. And&,' S. Bohm,? and V. Moliner Departament de Cihcies Experimentals, Universitat Jaume I, Apartat 242, 12080 Castellb, Spain
E. Silla and I. Tu& Departament de QuSmica-Fisica, Universitat de Valencia, 461 00 Burjassot, Valencia, Spain Received: November 18, 1993; In Final Form: March 22, 1994'
The reaction mechanisms for the addition of azide anion to methyl 2,3-dideoxy-2,3-epimino-a-~-erythrofuranoside (I), methyl 2,3-anhydro-c~-~-erythrofuranoside (11), and methyl 2,3-anhydro-B-~-erythrofuranoside (111) were investigated with ab initio molecular orbital methods at the HF/3-21G level. A detailed characterization of the potential energy surface in vacuo allows us to localize stationary points and the possible reaction pathways. The solvent effects are discussed by means of a polarizable continuum model. The results indicate that the inclusion of solvent effects changes the order of stability of both products in I and 11, and of both transition states in 11. The results of I11 are qualitatively invariant in uacuo and in solvent. These findings suggest that a thermodynamic and kinetic controls take place in the addition process mechanism that would help explain the experimental data.
Introduction Saccharides with an oxirane, thiirane, and aziridine ring are interesting and useful types of derivatives in sugar chemistry. The presence of a three-membered ring is responsible for these compounds remarkable reactivity. They are often used in the synthesis of amino-, halogen-, thio-, and branched-chain saccharides, many of which are biologically active, especially as antiviral and antitumor agents.14 Even simple nucleosides with three-memberedrings are biologically active; e.g. 1-(2,3-anhydro@-D-lyxofuranosyl)thymineis a selective inhibitor for reverse tran~criptase.~Recently, a similar compound, 3'-azido-3'deoxythymidine (AZT), has raised interest due to its activity against the human T-lymphotropicvirus (HTLV-III/LAV, also known as HIV), based on the presence of these three-membered rings.6~~ Nevertheless, the molecular mechanism of blocking HIV replication by these new drugs is still unknown. The stereochemistry of the nucleophilic opening of threemembered rings plays a key role in the chemistry of these compounds. However, contemporary experimental knowledge does not allow reliable qualitative and quantitative predictions to be made about the furanoside three-membered-ring cleavage. In particular, the three possible saccharides that are presented in Figure 1-methyl tetrofuranosides, i.e. methyl 2,3-dideoxy2,3-epimino-a-~-erythrofuranoside (I), methyl 2,3-anhydro-aL-erythrofuranoside (11), and methyl 2,3-anhydro-j3-~-erythrofuranoside (111)-present differences in the reactivity of C3 and C4 centers with respect to the nucleophilic attack of the azide anionas Experimental results have proved that in the case of I the ratio of products P1 and P2 is 3:1, respectively (in DMF). In 11, the ratio of products P1 and P2 is 4:1, respectively (1:4 mixture of water-ethanol), while in the I11 model only the P1 stereoisomer is obtained. The ratio of products P1 and P2, experimentally obtained by the anti nucleophilic attack of the azide anion that produces the three-membered-ring cleavage, remains obscure.8 Therefore, the aim of this paper is to carry out a theoretical study and make an exhaustive analysis and characterization of stationary points on the potential energy surface (PES) in the f Permanent address: Department of Organic Chemistry, Institute of Chemical Technology, 166 28 Prague 6, Czech Republic. Abstract published in Advance ACS Abstracts, June 1, 1994.
reaction mechanismsof the nucleophilicattackof the azide anion on I-111, in order to address the following points. The first hurdle is to determine the reaction mechanism that corresponds to the minimum energy path that connects the minimum of reactants and products and passes through the transition state (TS) structures on the PES9 In this path the height of the barrier that exists between the reactant and TS is correlated to the rate of each different pathway (kineticcontrol), while the relativeenergy reactants and products is correlated to equilibrium parameters (thermodynamic control). The second is how the soluts-solvent interactions affect the different barrier heights and relative energies of products, taking into account that ionic structures take part in the reaction paths. In fact, the differential stabilization of the different stationary points in both reaction pathways can treat one of them favorably, sometimes altering the relative energy orderi0and, consequently,possibly changing the ratio of products of the reaction.
Methods and Computing Procedures Ab initio calculations were carried out by use of the MONSTERGAUSS*iand GAUSSIAN 9212programs. The molecular structures of all stationary points have been determined at the HF/3-21G13 basis set level. The use of larger basis sets, diffuse functions, and the correlation energy in the solvent-anion interaction problems has been shown to be important.14 However, the size of our molecular system makes it impossible to carry out these calculations. Geometry optimizations and transition state searches were performed with the aid of analytically determined gradients.I5J6 The OC subroutine was employed in the search for these stationary points.17 For the TS, a simple rationale behind the construction of a trial structure is to start searching directly in the quadratic zone with the help of the PES. The exact characterization of the TS was achieved by the utiilization of a simple algorithm,'* in which the set of coordinates describing the system is separated into two: (41) and (q,), where (4,)is the control space set which is responsible for the unique negative eigenvaluein the respective force constant matrix connectedwith the variables that form the transition vector.I9 The remaining coordinates, (qJ, are called the complementary space set. First we optimized the complementary space using the OC method to
QQ22-3654/94/2098-6955%04.5Q/O 0 1994 American Chemical Society
And& et al.
6956 The Journal of Physical Chemistry, Vol. 98, No. 28, 1994
P1
3 : l
c;)'"' NaN3
P2
+
4.W H
N3
N3 P1
4 : l
P2
"3
OMe
___)c q. EOH
OMe
N3
Pl
Figure 1. Model reactions.
explore the energy hypersurfacejust around the above the saddle point. As a second step, a complete optimization with the use of the VAOS method20was achieved for the complete space of all variables. Finally, the nature of each stationary point was established by calculating analytically and diagonalizing the matrix of energy second derivatives to determine the number of imaginary frequencies, zero for a local minimum and one for a transition state. We use the FREQ subroutine as contained in the GAUSSIAN 92program in order to request the vibrationary frequencies calculation. Intrinsic reaction coordinate (IRC) calculations21-23 have been carried out in order to verify the path that links reactants (R) and products (P)via the putative TS obtained. The optimizations were terminated after the overall average gradient length had been reduced to
