Low-barrier transition states

The Nonmetal Atom Sharing Rule of Low-Barrier Transition States... 

The next section introduces the topological concept of low-barrier transition states through the prevention of formation of shared bonds between reacting surface adsorbates and surface metal atoms. 

Figure 1.22 Structures of high-barrier and low-barrier transition states of surface bond cleavage reactions.

A computational study of the activation of alkane (methane, ethane, propane, and butane) C-H bonds by the metallocarbene homoscorpionate [Cu=C(H)(CC>2CH3)(Tp)] (Fig. 2.133) and [Cu=C(H)(C02CH3)(TpBr3)] has been performed with DFT Becke3LYP calculations. A low-barrier transition state where the key bond-breaking and bond-forming processes take place in a concerted way has been postulated. The transition state has several possible conformations.549... 

A number of advances have led to increased efficiency in particular systems. "Synthetic" mode [23], a KMC treatment of low-barrier transitions, can significantly improve the efficiency in cases where low-barrier events are repeated often. Furthermore, if we know something about the minimum barrier to leave a given state, either because we have visited the state before and have a lower bound on this minimum barrier or because the minimum barrier is supplied a priori, we can accept a transition and leave the state earlier than the time given by Equation (13) (see ref. 24 for details). 

Similarly, several [3 + 2] transition states were identified together with transition states for the rearrangement reaction. The calculation of KIEs was undertaken for the low energy transition states. As an example, the two [3 + 2] transition states with the lowest activation barriers are shown in Fig. 6, together with a comparison between the calculated KIE for the given transition state structures and the experimentally determined KIE. 

In the third step, the carbocation intermediate is captnred by a chloride ion, and the energy barrier for this cation-anion combination is relatively low. The transition state is characterized by partial bond formation between the nncleophile (chloride anion) and the electrophile (fert-bntyl cation). 

The transition from k to on the low-pressure side ean be eonstnieted using iiiidtidimensional unimoleeular rate theory [1, 44], if one knows the barrier height for the reaetion and the vibrational frequeneies of the reaetant and transition state. The transition from to k y ean be deseribed in temis of Kramers theory [45]... 

In the above discussion it was assumed that the barriers are low for transitions between the different confonnations of the fluxional molecule, as depicted in figure A3.12.5 and therefore the transitions occur on a timescale much shorter than the RRKM lifetime. This is the rapid IVR assumption of RRKM theory discussed in section A3.12.2. Accordingly, an initial microcanonical ensemble over all the confonnations decays exponentially. However, for some fluxional molecules, transitions between the different confonnations may be slower than the RRKM rate, giving rise to bottlenecks in the unimolecular dissociation [4, ]. The ensuing lifetime distribution, equation (A3.12.7), will be non-exponential, as is the case for intrinsic non-RRKM dynamics, for an mitial microcanonical ensemble of molecular states. 

For 5=1, the normal transition state theory rate constant is independent of temperature at high temperatures and varies exponentially with temperature in the limit of low temperatures kT small compared with the barrier height U ) as... 

Whereas the barrier for pyramidal inversion is low for second-row elements, the heavier elements have much higher barriers to inversion. The preferred bonding angle at trivalent phosphorus and sulfur is about 100°, and thus a greater distortion is required to reach a planar transition state. Typical barriers for trisubstituted phosphines are BOSS kcal/mol, whereas for sulfoxides the barriers are about 35-45 kcal/mol. Many phosphines and sulfoxides have been isolated in enantiomerically enriched form, and they undergo racemization by pyramidal inversion only at high temperature. ... 

There is another usefiil viewpoint of concerted reactions that is based on the idea that transition states can be classified as aromatic or antiaromatic, just as is the case for ground-state molecules. A stabilized aromatic transition state will lead to a low activation energy, i.e., an allowed reaction. An antiaromatic transition state will result in a high energy barrier and correspond to a forbidden process. The analysis of concerted reactions by this process consists of examining the array of orbitals that would be present in the transition state and classifying the system as aromatic or antiaromatic. 

Examine the transition state for the hydride shift. Calculate the barrier from the more stable initial carbocation. Is the process more facile than typical thermal rearrangements of neutral molecules (.05 to. 08 au or approximately 30-50 kcal/mol) Is the barrier so small (<.02 au or approximately 12 kcal/mol) that it would be impossible to stop the rearrangement even at very low temperature Where is the positive charge in the transition state Examine atomic charges and the electrostatic potential map to tell. Is the name hydride shift appropriate If not, propose a more appropriate name. 

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