The objective of this textbook is to provide readers with a comprehensive understanding of the theoretical foundations of quantum chemical calculation programs by manually solving the working equations employed in these programs, utilizing a 'paper-and-pencil' approach. Due to the disparity between the methodologies utilized in quantum chemical calculation programs and the analytical formulations commonly described in regular quantum chemistry textbooks, this endeavor has proven particularly challenging. This volume is followed by 'Practical Guide to Quantum Chemical Computations II: Electron Correlation Methods and Density Functional Theory'.
Volume I begins by examining the fundamental principles of quantum mechanics before delving into numerical calculations using the Hartree-Fock method, accompanied by an array of exercises and 'paper-and-pencil' homework assignments. Additionally, the book includes a comprehensive appendix at its conclusion, which provides in-depth explanations of the exercises and homework assignments and summarizes the essential mathematical concepts necessary for comprehension.
This volume distills the author's extensive experience in graduate-level education, providing readers with a valuable resource for gaining a deeper understanding of quantum chemical calculation programs and their underlying theoretical foundations.
The basis of English translation of this book, originally in Japanese, was facilitated by artificial intelligence. The content was later revised by the author for accuracy.

Dr. Hiromi Nakai completed his doctoral course at the Graduate School of Engineering, Kyoto University in 1992, earning a Doctorate in Engineering. Subsequently, he served as an assistant at Kyoto University (1992), a full-time lecturer (1996), associate professor (1998), and professor (2004) at the Faculty of Science and Engineering, Waseda University, before assuming his current position in 2006. He has been a Fellow of the Royal Society of Chemistry (FRSC) since 2014 and a member of the International Academy of Quantum Molecular Science (IAQMS) since 2023. His research interests involve physical chemistry, theoretical chemistry, quantum chemistry, and electronic state theory.