Frequencies, imaginary

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. 

The situation simplifies when V Q) is a parabola, since the mean position of the particle now behaves as a classical coordinate. For the parabolic barrier (1.5) the total system consisting of particle and bath is represented by a multidimensional harmonic potential, and all one should do is diagonalize it. On doing so, one finds a single unstable mode with imaginary frequency iA and a spectrum of normal modes orthogonal to this coordinate. The quantity A is the renormalized parabolic barrier frequency which replaces in a. multidimensional theory. In order to calculate... 

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. 

If applicable, the program notes that there is an imaginary frequency present just prior to the frequency and normal modes output, and the first frequency value is less than zero. Log files may be searched for this line as a quick check for imaginary frequencies. 

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 minimum 0 imaginary frequencies The structure is a minimum. Compare the energy to that of other isomers if you are looking for the global minimum. 

A minimum > 1 imaginary frequencies The structure is a saddle point, not a minimum. Continue searching for a minimum (try unconstraining the molecular symmetry or distorting the molecule along the normal mode corresponding to the imaginary frequency). 

A transition state 1 imaginary frequency The structure is a true transition state. Determine if the structure connects the correct reactants and products by examining the imaginary frequency s normal mode or by-performing an IRC calculation. 

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. 

All of the optimizations are successful. The frequency jobs for the two forms where the H-C-C-H dihedral angle is 0° produce no imaginary frequencies, and the cis form is lower in energy than the trans form by about 0.63 kcal/mole. 

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) ... 

Note that the magnitude of the imaginary frequency is not very large (-226), indicating that the geometric distortion desired by the molecule is modest. The... 

This table gives the displacements for the normal mode corresponding to the imaginary frequency in terms of redundant internal coordinates (several zero-valued coordinates have been eliminated). The most significant values in this list are for the dihedral angles D1 through D6. When we examine the standard orientation, we realize that such motion corresponds to a rotation of the methyl group. 

Neither frequency job produces any imaginary frequencies, indicating that both structures are minima. A quick way to check for this is to search the output file for the string imagin such a search indicates that there is no matching line in the file. 

So]ots ji A frequency job on the optimized structure for planar vinyl amine will produce one imaginary frequency. This indicates that it is a transition state, not a minimum... 

In order to find the minimum, we look at the normal mode associated with the imaginary frequency. Here are the displacements ... 

Solution The optimization of 3-fluoropropene leads to a minimum on the PES, indicated by the fact that the frequency calculation results in no imaginary frequencies. 

The transition state optimization (Opt=(TS,CakFC)) of the structure on the right converges in 12 steps. The UHF frequency calculation finds one imaginary frequency. Here is the associated normal mode ... 

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. 

Unfortunately, the frequency job finds an imaginary frequency, indicating that this structure is not a minimum. Here are the displacements corresponding to this frequency ... 

The frequency job for this structure finds no imaginary frequencies, confirming that it is a minimum. 

The frequency job confirms that this structure is a rninimum, finding no imaginary frequencies. Here are the predicted frequencies, compared to the experimental values given earlier ... 

Energy minima have all real frequencies, while molecules with one or more imaginary frequencies are not minima. 

Transition states have a single imaginary frequency which corresponds to the reaction coordinate. 

Dimethylborane+propene Cl depicts the transition state for addition of dimethylborane onto the terminal alkene carbon of propene. Examine and describe the vibration with the imaginary frequency. Which bonds stretch and compress the most What simultaneous changes in bonding are implied by these motions Simultaneously display the highest-occupied molecular orbital (HOMO) of propene and the lowest-unoccupied molecular orbital (LUMO) of dimethylborane. Is the overall geometry of the transition state consistent with constructive overlap between the two Explain. 

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