Imaginary transition structure

Fujita, S. (1988) Logical perception of ring-opening, ring-closure, and rearrangement reactions based on imaginary transition structures, selection of the essential set of essential rings (ESER).J. Chem. Inf. Comput. Sci., 28, 1-9. 

Fujita defined the concept of imaginary transition structure (ITS) for the description of organic reactions. The ITS is a structural formula obtained by the superposition of the molecules of the reagents and products. The bonds in the ITS are classified into three types out-bonds, bonds appearing only in reagents in-bonds, bonds appearing only in products par-bonds, bonds which are not modified in the reaction. In the graphical representation of the ITS out-bonds are depicted as solid lines with a double bar, in-bonds as. solid lines with a circle, and par-bonds as solid lines. The symbols of the three... 

Figure 9 Types of bonds in imaginary transition structures. Adapted with permission from Ref. 35. Copyright 1986, American Chemical Society...

Schematic representation of some of the lower frequencies in the ion-dipole complex for the Cl + MeCl m and the imaginary frequency of the transition structure, calculated using a 6-31G basis set. 

HyperChem can calculate transition structures with either semi-empirical quantum mechanics methods or the ab initio quantum mechanics method. A transition state search finds the maximum energy along a reaction coordinate on a potential energy surface. It locates the first-order saddle point that is, the structure with only one imaginary frequency, having one negative eigenvalue. 

Imaginary frequencies are listed in the output of a frequency calculation as negative numbers. By definition, a structure which has n imaginary frequencies is an n order saddle point. Thus, ordinary transition structures are usually characterized by one imaginary frequency since they are first-order saddle points. 

One way to do so is to look at the normal mode corresponding to the imaginary frequency and determine whether the displacements that compose it tend to lead in the directions of the structures that you think the transition structure connects. The symmetry of the normal mode is also relevant in some cases (see the following example). Animating the vibrations with a chemical visualization package is often very useful. Another, more accurate way to determine what reactants and products the transition structure coimects is to perform an IRC calculation to follow the reaction path and thereby determine the reactants and products explicity this technique is discussed in Chapter 8. 

A transition state > 1 imaginary frequency The structure is a higher-order saddle point, but is not a transition structure that connects two minima. QST2 may again be of use. Otherwise, examine the normal modes corresponding to the imaginary frequencies. One of them will (hopefully) point toward the reactants and products. Modify the geometry based on the displacements in the other mode(s), and rerun the optimization. 

The frequency job on the middle structure produces one imaginary frequency, indicating that this conformation is a transition structure and not a minimum. But what two minima does it connect Is it the transition structure for the cis-to-trans conversion reaction (i.e. rotation about the C=C bond) ... 

The results of the frequency calculation confirm that the optimized structure is a transition structure, producing one imaginary frequency. The predicted zero-point energy is 0.01774 (after scaling), yielding a total energy of-113.67578 hartrees. 

Optimizing water dimer can be challenging in general, and DFT methods are known to have difficulty with weakly-bound complexes. When your optimization succeeds, make sure that you have found a minimum and not a transition structure by verifying that there are no imaginary frequencies. In the course of developing this exercise, we needed to restart our initial optimization from an improved intermediate step and to use Opt=CalcAII to reach a minimum. 

The frequency calculation of the given transition structure does produce one imaginary frequency, as required for a transition structure. The computed zero point energy is 0.03062 hartrees. When scaled and added to the MP4 total energy, it produces a relative energy of 0.63 kcal moP compared to the starting reactants. 

FIGURE 12. Transition structure for the isomerization of peroxynitrous acid to nitric acid optimized at the B3LYP/6-311- -G(d,p) level of theory. Classical reaction barrier, TS total energy and imaginary frequency (vectors represented by the arrows) are 40.8 kcalmoL (with respect to ds-GS HO—ONO), —280.86143 au and 690i cm, respectively... 

FIGURE 36. Transition structure for the oxidation of ( 113)3 with tricyclic HHO—OH 14 optimized at the B3LYP/6-31+G(d,p) level of theory. Imaginary frequencies are at the B3LYP/6-31G(d) level... 

Nitromethane, CH -NOf. The equilibrium structure of singlet nitromethane has been studied at several levels of theory [3,60,64-71]. Two conformations are possible for nitromethane, staggered (Is) and eclipsed (le), but the eclipsed form has been characterized as a transition structure at MP2/6-31G with an imaginary frequency of 30 cm 1 [3]. Rotation around the H3C-NO2 bond occurs essentially without barrier the estimated value is only 0.01 kcal/mol. This is in accordance with a microwave study, which reports a C-N rotation barrier of only 6 cal/mol [72,73]. The C-N bond length of nitromethane has been estimated with X-ray single crystal diffraction [74], neutron diffraction [46,75], microwave spectroscopy [72,73], MP2/6-31G [3], and B3LYP/6-31+G [71] at respectively 1.449, 1.486, 1.489, 1.485, and 1.491 A, showing that the theoretical estimates compare very well with those determined by experimental methods. The experimentally reported vibrational frequencies of nitromethane... 

---