Computational Chemistry

Quantum chemical calculations

What can we learn from theoretical calculations?

　Various analyses are possible, including stable molecular structures (bond length and three-dimensional structure), heat of formation, transition state structure, activation energy, molecular orbitals and their energy levels, ionization potential, electron affinity, electron density, electrostatic potential, dipole moment, and various spectra (UV-visible absorption, IR, NMR).

Electrostatic potential map

HOMO/LUMO analysis

　When organic chemists deal with “molecules,” they often target aggregated states such as solutions and crystals. Theoretical calculations generally provide information on isolated single-molecule states. Since there are often differences in the stable structure of molecules between aggregated and single-molecule states, some calculation methods take the solvent into account. However, the effect of the solvent can affect the reaction substrate, making it difficult to see the true nature of the reaction site. Therefore, the starting point for calculations is to first look at an isolated system in a vacuum.

　Generally, the calculation method and basis set are collectively referred to as the “calculation level”. For example, when the calculation level is B3LYP/6-31G**, this means that the calculation method uses the B3LYP parameters of the density functional method, and the basis set is 6-31G**. Below, we will briefly explain the types of calculation methods and basis sets.

Calculation method types

　The calculations we handle are broadly divided into three categories: semi-empirical molecular orbital methods, non-empirical molecular orbital (ab initio) methods, and density functional methods.

　Semi-empirical molecular orbital methods, such as PM3 and PM6, are methods that replace complex integral calculations with　experimental parameters to speed up the calculations. Therefore, depending on the system being handled, there are strengths and weaknesses, so precautions must be taken.

　On the other hand, ab initio molecular orbital methods include the Hartree Fock method, the MP perturbation method, and the CI method, which use mathematical approximation to solve integral calculations. These methods have a wide range of applications, but the calculation time tends to increase exponentially as the systems become larger. With improvements in computer performance, calculation times are becoming faster every year, and the range of applicable molecular systems is also expanding.

　The basic idea of ​​the aforementioned ab initio molecular orbital method is that all the electrons in the system and the forces acting on them (external potential) determine the electronic properties of the system, so the number of variables used in the calculation increases in proportion to the number of electrons. This means that the calculation time increases exponentially depending on the number of electrons. On the contrary, in the method called density functional theory, the number of variables does not change even when the number of electrons increases. This method has the characteristic of being applicable to crystalline systems containing an infinite number of electrons. Density functional theory also has several parameters, and B3LYP and PW91 are often used for practical application calculations.

What are basis functions?

　When performing calculations, we use what are called “basis functions” in combination with the above calculation method. There are several types of basis functions, so it is necessary to choose an appropriate one based on the system and calculation time. Basis functions are mathematical expressions of orbitals that accommodate electrons. For example, in organic chemistry, a hydrogen atom is only considered to have one electron in the 1s orbital, but in reality, there is a possibility that the electron exists outside the 1s orbital, or that the electron is spread out in the 2s or 2p orbitals. Therefore, when performing calculations, we must consider “what size, shape, and orbital the electron should be accommodated in.” There are several types of basis functions depending on “how much consideration is given to the size and spread of the orbital.” Of course, the accuracy of calculations tends to improve when more flexible basis functions (higher level basis functions) are used. However, if the level of the basis functions is raised too high, the calculation will take an enormous amount of time.

　Basis functions are broadly divided into three types: minimal basis sets, split valence basis sets, and polarizable basis sets. 　Minimal basis sets are basis functions that consider only the minimum number of orbitals. It is considered that electrons are accommodated only in the 1s orbital for hydrogen atoms, and only in the 1s, 2s, and 2p orbitals for carbon atoms. A representative basis function is called STO-3G, which represents the behavior of electrons using three Gaussian functions (3G). STO-3G shows good agreement with experimental values ​​for atoms with few valence electrons located on the left side of the periodic table, such as hydrogen, lithium, boron, and carbon, but it is empirically known that the error becomes large for molecules with atoms with more valence electrons located to the right side of the periodic table, such as oxygen and fluorine.

　A split valence basis set is a basis set that has two or more functions of different sizes in one orbital. Compared to a minimal basis set, even when expressing the same 1s orbital, having multiple 1s orbitals of different sizes allows for a more flexible (spread) orbital to be depicted, which is expected to improve the accuracy of calculations. In actual calculations, basis functions called 3-21G and 6-31G are often used.

　Polarized basis sets are basis functions that take into account orbitals of different shapes. In the case of hydrogen atoms, they are considered to have 2p orbitals in addition to 1s orbitals. Also, in the case of carbon, they are considered to have 3d orbitals in addition to 1s, 2s, and 2p orbitals. This means that places where electrons can exist can be described more widely, and the flexibility of the basis functions is further increased. In actual calculations, 6-31G(d) and 6-31G(d,p) are often used. These are sometimes written as 6-31G* and 6-31G**, respectively, but either way they have the same meaning. 6-31G(d) is the basis set of 6-31G, which is a split valence basis set, with the d orbital function added to elements other than hydrogen. 6-31G(d,p) means that the p orbital function is added to the hydrogen atom in the 6-31G(d) basis set.

　In addition to the three types of basis functions mentioned above, there are dispersion functions (swelling functions). By incorporating dispersion functions into the above basis set, the flexibility of the basis set can be further expanded. However, the calculation time increases dramatically. For example, when a dispersion function is incorporated into 6-31G(d), it is called 6-31+G(d). This is a system that takes into account the dispersion function for elements other than hydrogen. When a dispersion function is also incorporated into hydrogen atoms, it is called 6-31++G(d). In fact, it is known that incorporating a dispersion function into hydrogen atoms does not have much effect on the calculation accuracy, but it is important to include hydrogen atoms when calculating polarizability.

How to choose basis functions?

　In actual calculations, the best strategy is to combine the calculation method and basis set according to the purpose. So, which calculation method and basis set should be used when actually performing calculations? This is the biggest concern for customers. In the case of organic substances, when the molecular weight is about 200 to 300, the calculation method is often B3LYP or MP2 combined with 6-31+G(d,p). For molecular weights above that, it is appropriate to combine 6-31G(d,p) with B3LYP and 6-31G(d) with MP2 in terms of both accuracy and calculation time. Also, it is important to incorporate dispersion functions when calculating negatively charged chemical species or excited states. This is because the probability that electrons exist far away from the nucleus increases for these chemical species, making it necessary to apply spread basis functions.

Reaction analysis

　Reaction analysis is about observing the transition state (TS). By observing the TS, we can obtain a lot of information about the reaction. However, this TS cannot be monitored experimentally. Theoretical calculations using CASS technology make it possible to observe the TS along with the energy and three-dimensional structure.

The energy information obtained from the TS corresponds to activation energy = reaction temperature, pressure, and rate, and stabilization energy = product stability, selectivity, and yield. In addition, structural information clarifies the three-dimensional shape and bulkiness of molecules, and is useful for molecular design, reaction design, catalyst design, etc..

Application examples of reaction analysis

Development of synthetic route narrowing down and reaction control methods

The results of CASS analysis of the Mitsunobu reaction pathway for the synthesis of antibacterial agents are shown below. The main and by-products were clarified, and good agreement was obtained with the experimental results.

Target compound (antibacterial agent) Pharmacological activity: Treatment of diarrhea and dysentery, tonic

Isolated from Leontopodium alpinum (Edelweiss) by John Walsh et al. (1997)

Synthesis route via Mitsunobu reaction.

By comparing the potential energies, we can determine that path 8 will proceed.

Due to the difference in activation energy, we can determine that path 21 will proceed.

It was estimated that 1 (major) + 4 (minor) would be obtained, which is in good agreement with the experimental results.

CASS Technology

　CASS (Computer Aided Synthesis) is a technology system proposed by our company. This technology uses computers to assist chemical synthesis and can be described as the chemical version of CAD/CAM/CAE. By using the power of computers in the world of chemical synthesis, it is possible to solve problems that were previously impossible to solve and to carry out efficient research and development backed by theoretical data. Using high-speed parallel computers, we perform huge quantum chemical calculations to derive solutions.

New drug and compound development process (Wet)

Innovative, knowledge-based and experience-based
(Limited route search, plenty of trial and error)

A compass to quickly guide chemists to innovative and optimal synthetic methods!!

Scope of CASS technology

Improving the efficiency of the drug discovery process
Synthesis of molecular imaging materials
Functional analysis of proteins (reaction centers)

Development of alternative materials for rare metals
Development of alternative solvents for halogens
Development of organic materials

Development of innovative reaction processes such as supercritical reactions
Dynamic analysis and control of chemical reactions
Pursuit of optimized processes

Reducing environmental impact
Achieving high reliability and safety

Potential customers and benefits

Applicable fields

Molecular dynamics calculations

What can we learn from molecular dynamics calculations?

　Molecular dynamics (MD) calculations can be applied to a wide range of fields, including biology, materials science, medicine, and environmental science.
Using MD simulation, we can analyze the dynamic behavior and interactions of atoms and molecules, which can lead to the design of new materials and the creation of guidelines for improving existing materials.
For example, in the materials field, we can analyze the following properties of various types of materials, including polymers, metals, and composites:

• Transport coefficients, thermodynamic properties
  It is possible to evaluate density, specific heat, surface tension, saturation pressure, viscosity, dielectric constant, thermal conductivity, entropy, glass transition, boiling point, melting point, diffusion, solubility, etc..
• Mechanical strength
  Mechanical properties such as tensile strength, compressive strength, and ductility can be evaluated and visualized at the molecular level.
• Electronic properties
  In the fields of electronic materials and semiconductors, it is possible to evaluate surface energy and adsorption energy by analyzing the electronic and atomic structures of various material states such as crystals and surface systems.

Applicable scale of MD simulation

1. First-principles MD simulation
   First-principles MD simulation is a method of solving Schrödinger’s wave equation for groups of particles that interact with each other, such as electrons and atomic nuclei, as they evolve over time. It can be applied to systems involving the movement of electrons and allows for highly accurate calculations, but due to limitations imposed by the enormous amount of calculations, it can only be used on a scale of a few to a few hundred atoms.

2. All-atom MD simulation
   The motion of atoms and molecules is calculated according to the equations of Newtonian mechanics, and interactions are expressed in a simple functional form called a force field, making it possible to obtain the time evolution of motion without solving wave equations. As the value of the atomic point charge for each atom is determined in advance, it is not possible to express the movement of electrons, but it is possible to evaluate transport coefficients, thermodynamic properties, physical adsorption and adhesion energies, etc. as macroscopic physical properties. It can be applied to scales ranging from several thousand atoms to several hundred thousand atoms, and the properties of polymers of a certain size can also be evaluated.

3. Coarse-grained MD simulation
   Coarse-grained MD simulation treats multiple atoms as a single large particle. This allows MD simulations to be performed on much larger time and space scales than all-atom models, making it suitable for evaluating, for example, cell membrane dynamics and phase-separated structures.

Thus, due to its wide range of applications and abundant analytical methods, MD simulation can be a powerful tool in the industrial use of computational chemistry.

For each of the above MD simulation methods, there are various approximation methods and force field parameters, and it is important to set the calculation method and simulation conditions according to the purpose. Our contract research service will propose the optimal calculation model according to the customer’s needs.