Transition state initial guesses

Note that no gradients are used and this method is not computationally as demanding as other methods. However, it often yields a stmcture with two or more negative eigenvalues and it inherently assumes a simple reaction with one transition state. For these reasons, most computer programs have excluded this option for better search schemes. 

The quadratic synchronous method or QST is another method proposed by Halgren and Lipscomb (1977). QST is an improvement of the LST approach in that it searches for a maximum along a parabola connecting reactants and products, instead of a line. That is, in the orthogonal optimization step, the constraint of constant path coordinates is applied by appropriately displacing each resultant structure along a 3-point interpolation, or QST, 

The LST and QST calculations do not actually locate a proper transition state but aim to arrive at structures sufficiently close to it. Ideally, the resulting configuration would lie within the quadratic basin of the first order saddle point and be suitable for input to subsequent transition state searches. However, the synchronous transit methods often yield structures with more than one negative eigenvalue. 

The choice of the constrained internal coordinate relies heavily on chemical intuition and experience. Consequently, the method has not yet been incorporated in most available quantum chemical programs and perhaps never will be. Despite this, studies have used this procedure with much success. One can construct a software interface to currently existing programs that would effect the constrained optimization algorithm in a semi-automated manner. 

Constrained optimization has the advantage of finding intermediates that may have been overlooked, giving a more detailed picture of the topology of the PES. Furthermore, constrained optimizations often provide better starting guesses for transition state searches. Failure to find a transition state in the forward direction may be solved by locating it in the reverse direction. This also serves as an internal check to see if the reactants and products do correspond to each other and may lead to the discovery of new minima. 

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When this initial guess is poor, you need a more sophisticated—albeit more expensive—means of generating the force constants. This is especially important for transition state optimizations. Gaussian provides a variety of alternate ways of generating them. Here are some of the most useful associated keywords consult the Gaussian User s Reference for a full description of their use ... 

An iteration scheme is used to numerically solve this minimization condition to obtain Peq(r) at the selected temperature, pore width, and chemical potential. For simple geometric pore shapes such as slits or cylinders, the local density is a function of one spatial coordinate only (the coordinate normal to the adsorbent surface) and an efficient solution of Eq. (29) is possible. The adsorption and desorption branches of the isotherm can be constructed in a manner analogous to that used for GCMC simulation. The chemical potential is increased or decreased sequentially, and the solution for the local density profile at previous value of fx is used as the initial guess for the density profile at the next value of /z. The chemical potential at which the equilibrium phase transition occurs is identified as the value of /z for which the liquid and vapor states have the same grand potential. 

The simplest approach for determining the transition state might just be an initial guess at the structure based on chemical intuition or symmetry constraints. Somewhat better is using a transition state that has been obtained at the intended level of calculation for a simpler system, or alternatively saving computation time by... 

Hehre noted that current semiempirical methods sometimes give very poor descriptions of [geometries of] reaction transition states Hehre, Chapter 3) and Houk and co-workers stated that semiempirical methods. .. are not adequate for the calculation of organic transition structures (Wiest, Montiel, and Houk, op. cit.). Despite this, it can be fruitful to use a fast semiempirical method such as AMI in a preliminary investigation of a potential-energy surface to get initial estimates of transition-state structures. Each semiempirical structure is then used as the initial guess in an ab initio calculation of the transition-state geometry. Such a procedure can save considerable computational time Hehre, Section 3.3). 

Truong and Truhlar (1990) obtained initial transition state guesses drawn from a novel interpolation technique inspired by Hammond s postulate. These were subsequently optimized to true transition states. The calculations were performed to the MP-SAC2//MP2/6-311G(3d,2p) level. The rate constants were determined using TST and the zero theory interpolation model, wherein the rate constant is equal to the product of the TST rate constant and the zero-order interpolation of the zero-curvature ground... 

Flow can we understand these simple results Could we have predicted them a priori It turns out that the r on of the potential surface that corresponds to the 2 + 2 addition is virtually identical to the 2 + 2 cycloaddition of two ethylenes. During the initial phase of the reaction four of the electrons in benzene become passive in a butadiene-like structure. But this might have been one s intuitive guess anyway. Further, one can find synchronous structures, both transition states and conical intersections, for the direct addition of ethylene to form the meta- and para- structures but it transpires that these are quite h h in energy. 

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