A Comparative Analysis of Various Quantum Chemical Methods and Strategies for Complex Reaction Pathway Calculations and Modeling

Introduction:

On the most basic and fundamental level, reaction pathways are the processes or steps by which reactants go through elementary steps to be converted into products. Reaction pathways thus allow for scientists to understand the evolution of the system — such as through the potential energy and chemical kinetics of the system — which serves in better predicting the products, determining the mechanism, and avoiding undesirable by-products (1). These elementary pathways — i.e., reactions that transition solely from reactants to products — are only a small piece of reaction pathways overall, as complex reactions are arguably even more prevalent. Complex reaction pathways are composed of a multitude of different elementary reaction steps that create an intricate outcome due to the several transition steps (2). Currently, the topics of reaction pathways are of particular interest to chemists in the fields of chemical kinetics and physical chemistry. Thus, this paper will seek to discuss the current techniques and strategies to compute the pathways, and how they may be further expanded in the future for optimal knowledge of such phenomena. 

Current Methods for Pathway Calculations:

Advances in current modeling and computational technology are starting to make it possible for better understanding uniquely complex reaction pathways. However, the current strategy base is not yet to such a revolutionary point, which makes it increasingly imperative to evaluate current methods so that new technology can be better optimized.

One of the most common methods is the Density Functional Theory (DFT), which focuses on calculating molecular electronic structures and reaction pathways through elucidating electron densities as in place of wavelengths. By analyzing the physical properties, DFT therefore allows for more accurate and realistic modeling of chemical reactions (3). Currently there exist many different derivatives of DFT, such as time-dependent DFT (TDDFT), which allows for better modeling and calculations for chemical reactions in highly excited states. Indeed, TDDFT is able to compute highly excited pathways and reactions with ease and accuracy due to its revolutionary approach of using the basic variable n(r,t), which represents one-body electron densities (4). Standard DFT variants and derivatives do not use the one-body densities, which means that it is optimal for ground state energies. Traditional DFT methods are very commonly employed due to its efficiency and effectiveness. One study elucidated this through deriving two reaction pathways for the decomposition of HCOOH (formic acid) with noble metals in both a gaseous and aqueous state. The study found that the DFT modeling provided insight into how to properly develop novel heterogeneous catalysts that produce “CO-free H2 at near ambient temperatures” in future experiments or research (5). Overall, the applications of traditional DFT and its derivatives proves its worth as the most commonly used modeling and computational theory for chemical pathways.

Another type of commonly used computational method is the Hartree-Fock Theory. In the context of chemical reactions and pathways, HF calculations elucidate the overall energy and density of a molecule (5). This proves to be incredibly useful in computational models for chemical phenomena due to the ability for researchers to understand the excitation energies that will occur in a reaction and how molecules will bond together with their electron shells. Hartree-Fock calculations have been improved upon in recent years, as seen through the development of post-HF theories, which seek to improve the ignorance original HF methods had to electron correlation — the inner force (beyond the mean field approximation) of the electron system that, when it has gained strength, can reduce conductivity (6). Original HF methods clearly affect the computational modeling of reaction pathways as they do not take into account how a reaction with high excitation energies may not actually behave the way it was modeled to. Thus, the establishment of post-HF methods can reveal the electron correlations in a diverse array of reactions through possibly correcting the single determinant approximation, which approximates electronic wavefunctions in Hartree-Fock methods. Another way that has been experimented is through introducing correlation energy, which is the difference between the exact energy and Hartree-Fock energies (7-8). Regardless, post-Hartree-Fock methods are proven to be much more reliable than their forefathers, due to the ability for post-HF methods to correct factors previously ignored.

Table 1. Describes and summarizes the limitations of previously discussed methods to compute and calculate chemical pathways (7, 9-10)

Computational Methods	Limitations
Density Functional Theory	The delocalization error and static correlation error from commonplace approximations.
Hartree-Fock Theory	Accuracy of solving HF equations is determined by the expansion basis, which can negatively affect the approximations; solving HF equations leads only to an approximate wavefunction, not a solution to the Schrodinger equation. The system is therefore limited to represent some chemical pathways.
Post-Hartree-Fock Theories	Complete reliance on basis sets, which are functions used to visualize an electronic wavefunction for digital computation. Also, there is poor scaling in the digital system that is maintained by high costs.

Future Possibilities:

Recognizing the current limitations can lead scientists to create much more extensive and accurate modeling and computational systems to create a visual representation of chemical pathways. One suggestion would be to expand research regarding quantum chemical algorithms that operate in real time. One research group has explored this possibility through synthesizing many mathematical models (such as the Roothaan-Hall equation) with HF and DFT knowledge. They were able to find that real-time quantum algorithms are possible and can be expanded further (11). Furthermore, such possibilities will allow for more comprehensive simulations of reaction pathways in tangent with novel haptic systems. Overall, the future for this kind of technology is bright and ought to be experimented with on a larger, more diverse scale.

Conclusion:

By intersecting computational chemistry with physical and quantum chemistry, scientists have the ability to model chemical pathways with extreme efficacy. As a result, this will allow for a better understanding of chemical systems and the steps they undergo to react in a wide array of systems. Expanding the current technology will expand the current knowledge base also.

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