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The foremost issues of chemistry are to discover new molecules and reactions and to develop useful substances for society and the environment. If new molecules or reactions can be theoretically predicted before experiments, it would help to accelerate development, reduce the risk of failure, and consequently save on investment of effort, energy and money. Theoretical chemistry is often used to obtain rational explanations for chemical phenomena observed in experiments; for example, it can provide a mechanism for a chemical reaction. It can also be used to predict chemical structures and their properties, even if it is difficult or impossible to access them, for example, for molecules in interstellar space. Furthermore, it could pave the way for discovery of new chemistry.

The basic mathematical equations that can describe chemical phenomena were discovered about 100 years ago in quantum mechanics (QM). Nevertheless, chemical phenomena are generally too complicated to be described by a straightforward application of these equations, and so it seemed that most of the chemical problems could not be theoretically solved based on QM. However, scientists have attempted to apply QM in chemistry, made a lot of efforts to overcome the difficulties, and established quantum chemistry (QC), which is a major discipline of theoretical chemistry. The development of computer technology has also helped to increase the number and range of targets which can be treated with QC methods. QC has become an essential approach to study chemical problems at the end of the 20th century.

However, there was an obstacle when applying QM to basic questions of chemistry: what kinds of isomers can be produced from a given atomic composition, how are the isomers converted into one another and how are the isomers decomposed into smaller species, or, conversely, how are they made from smaller species? It was thought to be almost impossible to solve these problems based on QM when the size of molecular systems exceeds three atoms. One had to wait for more breakthroughs to go beyond the limitation.

The difficulty comes from a combinatorial explosion. Fundamental theoretical approaches to treat chemical structures and reactions calculated from QM are based on the potential energy surface (PES), which is a function of nuclear coordinates. A point on a PES corresponding to the potential energy of one set of fixed nuclear positions can be obtained by solving the equations of electronic structure, and this calculation is repeated for each point on the PES by changing the nuclear positions. An N-atom system has 3N – 6 degrees of freedom, with a corresponding dimensional PES. The total number of sampling points for an N-atom system is M(3N – 6), where M is the number of points along one dimension. Thus, the total number of points exponentially increases as the size of molecules becomes larger. For example, when M = 100, the total number of points is 106 for a three-atom system, 1012 for a four-atom system and 1048 for a ten-atom system. Therefore, for such a coarse sampling on lattice points, the calculation time for a ten-atom system, even by using advanced computer technology, can be estimated to be more than 1040 years, which far exceeds the time from the Big Bang to the present (approximately 1010 years).

Despite these difficulties, scientists have attempted to surpass the limitations and achieved breakthroughs for more efficient exploration of PESs. These new methods can provide a better and wider landscape of reaction pathway maps even for a system with more than three atoms.

This book focuses on the methods and their applications for exploration of PESs based on QM (QM-PES). It outlines the theory, basic techniques and state-of-the-art methods in Chapters 1 and 2. Some applications of these methods are demonstrated in Chapters 3 and 4, including applications of exploration for chemical reaction pathway networks and new classes of chemical structures.

We sincerely respect all the scientists for their tremendous efforts towards efficient exploration of PESs. We tried a comprehensive review of their work but could not shed light on all of them due to space limitations. Even so, to our best knowledge, this is the first textbook which specifically focuses on the exploration of QM-PES. We believe that better understanding of the theory and techniques would help to “walk” better on PESs. The various applications could give insights into new chemistry. We hope that this book will be of help to readers in pushing their science forward. You might be the one who could change the world.

Koichi Ohno and Hiroko Satoh

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