Chapter 2
Actual Potentials of Theoretical
Chemistry: What Can Be Obtained
Abstract Theoretical calculations of molecules based on quantum chemistry can
afford the electronic structures of those. The electronic structure of any molecule
or supermolecule based on its wavefunction is the most fundamental and important
one, since that gives us the starting point of further analyses of the electronic properties, optical properties, magnetic properties, and other fundamental properties of
the molecule concerned. In this chapter, several actual examples of those are to be
first described prior to the detailed explanation of complicated calculation methods
exhibited in Chap. 3. This plan would be useful to directly have an idea of what kind
of information on molecules can actually be obtained by theoretical calculations and
how they should be further expanded in each subsection.
Keywords Structural optimization · Electronic structure · Electronic property ·
Mechanical property · Chemical reaction
2.1 Molecular Structure
For investigation of the electronic structure of a molecule, it is usually desirable that
it is acquired from the most energetically stable molecular structure often referred
to as the optimized structure. This is because “stable” electronic structure ought to
normally be derived from the wavefunction defined in the optimized structure. In
this sense, one would normally start from the structural-optimization process for the
concerning molecule. Theoretical calculation is capable of providing the optimized
molecular structures both in the ground state and in rather simple excited state as
illustrated in Fig. 2.1, which is to be mentioned sequentially in this section.
The optimization process is achieved by finding the minimum point on the potential energy surface (PES) of each state, also called potential hypersurface, defined
by the collection of energy points corresponding to all the possible structures of
a molecule, as simply illustrated in Fig. 2.2 by changing all the variables which
determine the molecular structure. This optimization process is somewhat similar to
finding the bottom of a certain basin in actual geography. Essential difference from
the geography, however, is that the optimization process for a molecular structure
is generally performed on the multidimensional PES defined as function of all the
© Springer Nature Singapore Pte Ltd. 2020
K. Tanaka, Theoretical Chemistry for Experimental Chemists,
https://doi.org/10.1007/978-981-15-7195-4_2
3
Actual Potentials of Theoretical
Chemistry: What Can Be Obtained
Abstract Theoretical calculations of molecules based on quantum chemistry can
afford the electronic structures of those. The electronic structure of any molecule
or supermolecule based on its wavefunction is the most fundamental and important
one, since that gives us the starting point of further analyses of the electronic properties, optical properties, magnetic properties, and other fundamental properties of
the molecule concerned. In this chapter, several actual examples of those are to be
first described prior to the detailed explanation of complicated calculation methods
exhibited in Chap. 3. This plan would be useful to directly have an idea of what kind
of information on molecules can actually be obtained by theoretical calculations and
how they should be further expanded in each subsection.
Keywords Structural optimization · Electronic structure · Electronic property ·
Mechanical property · Chemical reaction
2.1 Molecular Structure
For investigation of the electronic structure of a molecule, it is usually desirable that
it is acquired from the most energetically stable molecular structure often referred
to as the optimized structure. This is because “stable” electronic structure ought to
normally be derived from the wavefunction defined in the optimized structure. In
this sense, one would normally start from the structural-optimization process for the
concerning molecule. Theoretical calculation is capable of providing the optimized
molecular structures both in the ground state and in rather simple excited state as
illustrated in Fig. 2.1, which is to be mentioned sequentially in this section.
The optimization process is achieved by finding the minimum point on the potential energy surface (PES) of each state, also called potential hypersurface, defined
by the collection of energy points corresponding to all the possible structures of
a molecule, as simply illustrated in Fig. 2.2 by changing all the variables which
determine the molecular structure. This optimization process is somewhat similar to
finding the bottom of a certain basin in actual geography. Essential difference from
the geography, however, is that the optimization process for a molecular structure
is generally performed on the multidimensional PES defined as function of all the
© Springer Nature Singapore Pte Ltd. 2020
K. Tanaka, Theoretical Chemistry for Experimental Chemists,
https://doi.org/10.1007/978-981-15-7195-4_2
3