Computational chemistry determination stationary points

One of the most significant advances made in applied quantum chemistry in the past 20 years is the development of computationally workable schemes based on the analytical energy derivatives able to determine stationary points, transition states, high-order saddle points, and conical intersections on multidimensional PES. The determination of equilibrium geometries, transition states, and reaction paths on ground-state potentials has become almost a routine at many levels of calculation (SCF, MP2, DFT, MC-SCF, CCSD, Cl) for molecular systems of chemical interest. 

Advances in computational chemistry allow for the determination of stationary points by various approximations to the Schrodinger equation [4,35 43], Complete discussions and excellent reviews of the different methods can be found in the literature [6,33,44,45]. Over the years, the Diels-Alder reaction between 1,3-butadiene and ethylene has become a prototype reaction to evaluate the accuracy of many different levels of theory. A level of theory involves the specific combination of a computational method and basis set. For example, the RHF/3-21G level of theory involves the restricted Flartree-Fock method with the 3-21G basis set. Ken Flouk and his research group have pioneered many ideas concerning the fundamental ideas of pericyclic reactions by combining theory and experiment [3,4,37,38,46 48], For the Diels-Alder... 

This chapter deals with two very important aspects of modern ab initio computational chemistry the determination of molecular structure and the calculation, and visualization, of vibrational spectra. The two things are intimately related as, once a molecular geometry has been found (as a stationary point on a potential energy surface at whatever level of theory is being used) it has to be characterized, which usually means that it has to be confirmed that the structure is a genuine minimum. This of course is done by vibrational analysis, i.e., by computing the vibrational frequencies and checking that they are all real. 

A key factor in our ability to understand complex systems is the coming of age of modern computational chemistry. It is the fast motion of the electrons that determines the forces that act on the nuclei. Quantum chemistry provides the methods for analyzing electronic structure and thereby allows the determination of the equilibrium configuration for the nuclei and the energy of the electrons at that point. In the same compntation we can also determine the forces at that point and not only the potential. This allows the computation of the frequencies for the vibrations about the stable equilibrium. Next, methods have been introduced that enable us to follow the line of steepest descent from reactants to products and, in particular, to determine the stationary points along that route, and the forces at those points. Our ability to do so provides us with the means for quantitative understanding of the dynamics. 

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