Computer chemistry (mathematical chemistry) is a relatively young field of chemistry, based on the application of computer methods and discrete mathematics, primarily graph theory and combinatorics, to chemical problems of a fundamental and applied nature. Based on the general definition of chemistry as the science of substances and their transformations into each other, we can say that substances (molecules) are modeled in computer by molecular graphs, and transformations of substances (chemical reactions) – by formal operations with graphs. In a number of cases, this approach considerably simplifies the algorithmization of chemical problems, reducing them to typical problems of combinatorics and discrete mathematics and allows one to search for solutions using computer programs. In this case, along with special programs in computer chemistry, universal programs can also be used: for working with tables, mathematical programs (for example, Maple or Mathematica), etc.Typical tasksAs an example of typical tasks in computer chemistry, we can name: search for dependencies of the „structure – property" type; generation of sets of chemical structures corresponding to specified parameters (composition, presence of functional groups, etc.); enumeration of all kinds of chemical reactions between given reagents (the so-called „computer synthesis"), etc. Along with general chemical problems in computer chemistry, there is also a large group of highly specialized problems closely related to the problems of chemical informatics, for example, the problem of recognizing chemical structures during handling to chemical and physicochemical databases. This group of problems, in turn, is closely related to the graph isomorphism problem.MethodsIn solving problems of computer chemistry, various computational methods and operations with topological indices (graph invariants) are widely used. In some cases, the formal-logical approach is extended by chemical approaches, for example, in addition to topological indices reflecting the structure of a molecule, electronegativities of atoms in a molecule are used, reflecting the composition of a substance. Methods of computer chemistry are often used in combination with methods of quantum chemistry, molecular mechanics, etc. Methods of mathematical statistics are widely used to process the results of a computational experiment. In some cases, artificial intelligence methods are used to find solutions.The methods of computational chemistry play a special role in organic chemistry, which is explained by the difficult formalizability of the latter, both in comparison with other natural sciences, for example, physics, and in comparison with other fields of chemistry, for example, with inorganic chemistry. Computer chemistry is also of great importance for many important areas of biochemical research, for example, when solving problems of the „structure-pharmacological activity" type, often in such studies the methods of computer chemistry are supplemented by modeling methods specific to molecular biological systems.StoryDuring the period of formation and formation into an independent field, a new scientific direction often receives different names from different authors. This happened with computer chemistry: historically, two names have been fixed – "computer chemistry" and "mathematical chemistry". Thus, one of the scientific journals that had a significant impact on the development of computer chemistry is called the Journal of Mathematical Chemistry. However, the name „mathematical chemistry" seems unfortunate given that many areas of chemistry, formed long before the advent of computer chemistry, were originally based on mathematical foundations, for example, physical chemistry, kinetics and catalysis, . Despite the fact that a number of fundamental works in computer chemistry were carried out during the first generation of computers, the development of computer became possible only with the advent of modern computers. Despite the fact that today computers are used in almost all areas of modern chemistry, both for theoretical and experimental research, it is computer chemistry that much more than many other areas of chemistry depends on the level of development of computer technology. This dependence is primarily associated with the specifics of the most important algorithms of graph theory, many of which have exponential computational complexity – the theoretical estimate of the time spent on the execution of the algorithm is an exponential function of the size of the graph, that is, on the number of its vertices and edges, or speaking in general chemical language – on the number of atoms and chemical bonds in the molecule.On the other hand, many tasks of chemical informatics (Chemoinformatics), solved using the methods of computer chemistry, are already in their formulation impossible without using a computer, for example, the formation and operation of a computer on the properties of chemical compounds. It should be noted that chemoinformatics itself arose long before the advent of computers. There are proven and classic methods of searching for these publications using all kinds of printed indexes (author’s, subject, formula, etc.), organized without the involvement of the apparatus of computer chemistry. Thus, in contrast to computer chemistry, chemical informatics (Chemoinformatics), like the vast majority of traditional fields of chemistry, is based on the use of pre-computer technologies. This is the main methodological difference of computational chemistry. With a certain degree of inaccuracy, it can be argued that if the goal of most chemical research is to establish certain chemical laws, then the purpose of research in computer chemistry is, as a rule, some algorithm and a computer program that implements it, which allows you to search for chemical laws, the operation of such a program can take place outside of the field of computer chemistry.