Static quantum chemical calculations approach

The idea of constrained dynamics performed for a set of points along such a reaction path , i.e. for a set of fixed values of the reaction coordinate, A, is not specific to MD. Similar approaches have been commonly used in computational studies based on static quantum-chemical calculations. Such approaches are known as linear transit calculations, reaction path scans, etc. A set of constrained geometry optimizations with the constraint driving the system from reactants to products is a popular way to bracket a transition state, for instance. 

In this section we will present results of ab initio molecular dynamics simulations performed for more complex chemical reactions. Catalytic copolymerization of a-olefins with polar group containing monomers, chosen here as an example, is a complex process involving many elementary reactions. While for many aspects of such a process the standard approach by static quantum chemical calculations performed for the crucial reaction intermediates provides often sufficient information, for some aspects it is necessary to go beyond static computations. In the case of the process presented here, MD was priceless in exploring the potential energy surfaces for a few elementary reactions that were especially difficult for a static approach, due to a large number of alternative transition states and thus, alternative reaction pathways.77... 

Ab initio correlated or so-called post Hartree-Fock methods provide a proper description of dispersion forces. Unfortunately, these methods are computationally limited to systems with few atoms. Only few CCSD(T) calculations of very small ionic liquid systems were reported so far. Second-order Moller Plesset perturbation theory (MP2) might be also a suitable ab initio method to study ionic liquids. Recent developments have made this approach available for systems with hundreds of atoms. However, calculations of medium sized ionic liquid systems need still enormous computational resources. Thus, MP2 and similar approaches seem to be limited to static quantum chemical calculations and are still too expensive for ab initio molecular dynamics simulations over an appropriate system size and time frame. 

The parameters of Hamiltonians (1) and (2) are determined in our approach by pure theoretical way using different quantum chemical models and calculations unlike the traditional fitting the experimental thermodynamic and dielectric data. Our method of the many-pseudospin clusters [ 1,4] seems to be the most reliable way of determination. The latter are obtained in this case within the static approximation from the system of equations for a typical crystal fragment (cluster) for all possible proton distributions on H-bonds. The left-hand side of any equation expresses the cluster total energy in terms of Jy, while the right-hand side is determined by means of the quantum chemical calculation of this energy. 

One of the main advantages of the MD over the static quantum chemical approaches is that it can be utilized to directly determine the reaction free energy barriers, as it explicitly includes entropic effects. An estimation of the free energy via a normal (static) DFT approach requires frequency calculations that are relatively expensive for large molecular systems. Such an approach assumes in addition the harmonic (normal mode) approximation, which breaks down for processes where weak intermolecular forces dominate.10... 

In order to be able to describe kinetic phenomena in terms of the statistical methods, the knowledge of the critical configuration on the PES is needed as well as the eigenvalues of all the nonelectronic degrees of freedom of the system in the transition state. As shown in the previous sections, information on the critical configurations is the subject of quantum chemical calculations within the static approach. 

In other cases [166, 167] literature values for (supposedly) fc(w) taken from quantum chemical calculations were used to separate the Ag and Aj contributions. While this is in principle preferred over the first approach, the use of computational data leads to questions concerning their reliability, as low-level data might easily deteriorate the accuracy of the quadrupole moments obtained in this way. In addition, there has been some confusion in the earlier literature concerning the hyperpolarizability correction term / ( >). In the original papers by Buckingham and coworkers [134, 168] this term was called B and was referred to as a quadrupole hyperpolarizability. This was apparently misunderstood and led to the incorrect use of the averaged static dipole-dipole-quadrupole hyperpolarizability correction term instead of in the determination of the quadrupole moment [166, 167]. 

Compared to ordinary quantum chemical approaches, the AIMD free-energy calculations have significant advantage as entropic effects and anharmonicity are explicitly included in the calculation. In contrast, a normal static DFT procedure requires that the vibrational entropy be added via harmonic frequency calculations and the computational demands may be quite substantial for large molecular systems. Furthermore, the harmonic approximation may not even be valid in situations where weak interactions are dominant. 

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