# Development of Molecular Theory in Quantum Chemistry

Quantum computational chemistry has evolved dramatically and it can now treat real systems with predictable accuracy. Quantum computational chemistry has opened a world of new possibilities and is becoming an integral part of chemistry research. Theory can now make very significant contribution to chemistry. Professor Kimihiko Hirao did a wide range of original contributions to theoretical chemistry by developing new methods and by applying them to wide fields of chemistry. He has published more than 250 papers, various review papers and books. His research contributions fall roughly into the following four categories:

**1. Development of ab initio Molecular Orbital Theory**

One of the goals of computational quantum chemistry is to offer a computational method for electronic structure applicable to chemical systems containing elements across the whole periodic table with accuracy that can be increased to meet the purpose of individual calculations. Historically Hartree-Fock (HF) theory has played a very important role in qualitative theoretical chemistry. However, HF approximation is not accurate enough to predict the molecular properties. The HF error is called the correlation energy. The accurate description of the electron correlation has long been recognized as one of the central problems in quantum chemistry. Professor Hirao has developed Multireference Møller-Plesset (MRMP) theory. MRMP has been established as an efficient theory for treating both dynamical and nondynamical correlation effects. MRMP has opened much potentiality in the field of theoretical chemistry. His contribution to the development and establishment of the multireference approach is worthy of special mention. MRMP can handle any state, regardless of charge, spin, or symmetry, and has surprisingly high and consistent accuracy. MRMP has been successfully applied to a number of chemical and spectroscopic problems. CAS valence bond (CASVB) theory has also been proposed as an interpretive tool of underlying chemistry. His early contribution to the development of open shell orbital theory is worthy of notice. He formulated correct variational conditions for general SCF orbitals and proposed a general SCF operator. His work is proved to be of much insight on the nature of the orbital theory.

**2. Development of Density Functional Theory (DFT) Functional**

DFT has advanced to one of the most popular theoretical approaches to calculate molecular properties. The first-order molecular properties (energies, geometries, frequencies, dipole moments, etc) are well predicted by local GGA functionals. However, DFT fails to describe induced or response properties. This failure has been attributed to the wrong long-range behavior of the standard exchange-correlation functionals. Professor Hirao has claimed that the DFT functional should satisfy the correct physical conditions of the exact functional and be parameter-free or parameter-less. He has developed the one-parameter progressive (OP) functional. OP contains only one parameter and satisfies physical requirements. He has also proposed a parameter-free exchange functional. These functionals yield the chemical accuracy almost equivalent to B3LYP for G1 and G2 sets of molecules with the maximum error being much smaller than that of hybrid B3LYP. Recently he has derived a new exchange functional which includes the long-range interaction. New functional makes it possible to calculate the Rydberg excited states and van der Waals interactions accurately, that the conventional functionals fail to describe.

**3. Development of Relativistic Molecular Theory**

Before recent years the relativistic effect had ever been thought less important for chemical properties because the relativity appears primarily in the core electrons, which had been believed to be unlikely to affect chemically active valence regions dramatically. Recent studies, however, have revealed not only quantitatively but also qualitatively that the relativistic effect plays essential and comprehensive roles in total natures of molecular electronic structures for heavy-element systems. We are nowadays convinced that a general theory of atomic and molecular electronic structure, applicable uniformly to all elements of the periodic table, must be based on the Dirac equation rather than the Schrödinger. Professor Hirao's relativistic theory is also noteworthy. He has proposed 2-component RESC and the higher-order Douglas-Kroll (DK) Hamiltonians. RESC and third-order DK (DK3) methods can easily be incorporated into any *ab initio* and DFT theory, and proved to be efficient, numerically stable, and reliable. Using generally contracted spherical harmonic Gaussian-type spinors, he has developed a highly efficient computational scheme for solving 4-component Dirac-Hartree-Fock and Dirac-Kohn-Sham equations. Owing to his theory the entire field of heavy-element chemistry is now open for an accurate theoretical treatment.

**4. Development of UTChem**

Software forms a basis for computational chemistry. However, it is not an easy task for an individual/group to develop a comprehensive new program package in *ab initio* quantum chemistry from scratch since modern molecular quantum theory is highly sophisticated, and has evolved dramatically. Professor Hirao and his group at the University of Tokyo decided to accept this challenge and developed a quantum chemistry program called UTChem. UTChem is high-performance program software for * ab initio* quantum chemistry to calculate electronic wavefuntions, energies, and several chemical properties for polyatomic molecules. UTChem contains a large number of improvements and some interesting new features, which other programs cannot match. UTChem has been released on the web.

Professor Hirao has distinguished himself by the value of his scientific work, his role of pioneer and international leader of theoretical chemistry. He has most contributed to the advancement of theoretical/computational chemistry. Thus it is recognized that Profess Hirao deserves The Chemical Society Award of The Chemical Society of Japan.