J . Phys. Chem. 1994,98,1942-1944
7942
Gradient Line Reaction Path for an s N 2 Reaction at Neutral Nitrogen Ruslan M. Minyaev Institute of Physical and Organic Chemistry, Rostov State University, Stachka Avenue, 19413, Rostov-on- Don 3441 04, Russia
David J. Wales' University Chemical Laboratories, Lensfield Road, Cambridge CB2 IEW, U.K. Received: June 3, 1994"
The topology of the potential energy surface for the reaction of F- with H2NF has been investigated by ab initio calculations. We find that when steepest descent paths are considered, the fluorine exchange proceeds along a path that includes direct connections between transition states without intervening minima (but with branching points). In accord with theory, symmetry elements are only created and destroyed at stationary points.
SCHEME 1
introduction Recently Biihl and Schaeferl have investigated the mechanism of S N reactions ~ at neutral nitrogen." For example, for
F + H,NF
+
FNH,
F-N-F
+F
the mechanism was described by Scheme 1. The first step is the formation of ion-dipole complex la. Then the system proceeds to the C, transition state (TS) 2 and finally to product, another ion-dipole complex lb, in agreement with experiment.24 However, there is a problem with this scheme: the reaction vector of TS 2 preserves the mirror plane, yet this symmetry element is not present in minimum 1. The reaction path therefore appears to violate the Pearson7-Pechukass theorem, that symmetry elements can only be created or destroyed at stationary points. Here we answer this puzzle in terms of Scheme 2 in which TS 2 and minimum 1 are both directly connected to TS 3, but not to each other. TS 3 is the transition state for F- migration between the two H atoms and was also identified by Biihl and Schaefer.' In the absence of any external fields the gradient lines of the Born-Oppenheimerg potential energy surface (PES) define the local resultant force at any point?JOJ' independent of mass. Scheme 2 is in fact composed of such gradient lines which are steepest descent (SD) paths in non-mass-weighted coordinates. Fukui's intrinsic reaction pathwaylla is analogous but employs a "kinematic" metric tensor;12 we except these two sets of paths to be topologically equivalent. Both are also invariant to the choice of coordinatesystem, as Banerjeeand A d a m have carefully explained.I2 We refer to the complete gradient line network for a given reaction as the gradient line reaction path (GLRP). The advantage of this approach is that gradient lines are well-defined entities,llfJ3 whereas the concept of a minimum-energy pathway,1OJ1J4 although intuitively appealing, can cause difficulties, as discussed below. The complete GLRP of Scheme 2, which is the principal result of this Letter, consists of three different lines. Two of them are equivalent (GL1 and GL1') and correspond to 1,3 F shifts l a 3a IC and l b 3b Id passing through TS's 3a and 3b, respectively. The third gradient line (GL2) connects TS 3a to TS 3b via TS 2. The direct connection of two transition states has been observed before by Windus and Gordon15 for massweighted SD paths in SiHdF- and PH4F and by Ruedenberg and co-workers for the ring opening of cyclopropylideneto allene.16
-
H
-
--
-+
@Abstractpublished in Aduance ACS Abstracts, August 1, 1994.
0022-3654/94/2098-1942%04.50 f 0
pH
F-N
H lb,Cj
11
GL1
N-F
Hq
GL2
e
11
', '*
F'
GLl'
F-N-F
O. H .'
I
I
GL1
11
$1
N-F
H
F'.
,'
lC.CI
The present system provides a further example of such behavior, which may be more common than is generally appreciated.
Method The total energies and geometrical parameters for structures 1-3 calculated in the present work at the SCFIDZP level agree with those obtained by Biihl and Schaefer.' The latter authors have also shown that the stationary points are essentially the same at the SCF/DZP and TZP+/CISD levels' (Table l), and so we have employed the former throughout. The approximate gradient lines were calculated in Cartesian coordinates by displacing transition-state geometries along the two directions corresponding to the (non-mass-weighted) Hessian eigenvector associated with the unique imaginary frequency. Perturbations consisted of adding or subtracting 1150th of the components of the normalized Hessian eigenvector in each case. Pathways were then followed downhill, minimizing the energy using eigenvector-following17(EF) steps with no symmetry 0 1994 American Chemical Society
The Journal of Physical Chemistry. Vol. 98. No. 33. 1994 7943
Letters
Figure 1. Schematic representation of the F--HzNF PES. A simple construction has been used to obtain a threedimensional surface with the same topology as Scheme 2. No attempt has been made to show the branching points.
TABLE 1: Total Energies (EJbartrees), Relative Emergies (AElkcal mol-'). Number of lnagina Frequencies (A), and Values of (be Imaginary Frequencies ?wI/cm+) Cakulatcd for
1 (CI)
Et A
2 (Ca)
i E,
AE A IwI
3 (CJ
E,
AE A
bl
E
-254.4526 O
-254.47403 0
0
-254.43553 24.9 I 601.2 -254.46784 4.6 I 368.6
-254.43459 24.7
-255.08457 24.0
n
n
-255.12885
n-
I
I
-254.46604 5.0
629.0 -255.1 1550 4.6 1
I
0 h n t work. b Reference I . restrictions. Calculations were continued until the maximum step size was
