Molecular volume means the volume of the space inside the molecular surface. Since there is no unique definition of molecular surface on which the molecular volume depends, different definitions of molecular volume can be obtained. The common molecular volume is Van der Waals volume (*V*w), related to the Van der Waals radius (*r*w) and Van der Waals surface. The *r*w isn't fixed and varies with the particular chemical environment of the atom. Since crystal molecules are held together through Van der Waals forces, the sum of two atoms' *r*w is the closest distance between these two atoms from the distinct molecules in principle.

### Small Molecular Volume Calculation

The volume of the crystal is a crucial characteristic for material function, high-performance detection efficiency, and crystal structure. Accurate calculation of molecular volume can accelerate the development of crystal structure and materials. As for small molecules, there are two steps for volume calculation.

1. Optimize conformation.

2. Calculate molecular volume (use the optimized molecule as the initial structure, and apply a larger method basis set to calculate the molecular volume).

3. Read the calculation results.

Figure 1. Molecular volume prediction (Bier, I. and Marom, N. 2020)

### Large Molecular Volume Calculation

Experimental calculation of large molecules (for example, proteins) exists obvious problems such as complex operation, low efficiency, big errors. With experienced quantum chemistry calculation, Alfa Chemistry provides molecular volume calculation services to simplify the process, increase efficiency, and reduce calculation errors. The steps for volume calculation of large molecules are as follows.

1. Describe all atoms' structures.

2. Calculate molecular superficial area.

3. Calculate molecular volume.

### Computational Methods

- Additive models

Estimation on an additive model is actually very simple and only relies on univariate smoothing. Additive models tend to balance the strengths of the fully nonparametric and parametricestimates, for example, additive models have a lower variance than fully nonparametric ones. We can develop additive models created by fitting to data for hundreds of molecules for the calculation of molecular volumes. We also conduct tests on data for thousands of organic molecules in the database, and the results show that the best models have satisfying median absolute errors for the volume.

- Machine learning model for molecular volume calculation

Nowadays, machine learning technology is gradually supplementing or replacing traditional quantum mechanics (QM) calculations. Combining machine learning and quantum chemistry, scientists have completed accurate predictions of molecular structure using various learning algorithms and molecular descriptors. At Alfa Chemistry, we use a data-driven model derived from machine learning methods to establish a mapping between features and target attributes, thereby obtaining the calculated molecular volume.

- Marching tetrahedra (MT) methods.

The marching tetrahedron algorithm is a technique of constructing real-space function isosurfaces based on grid data. We use MT methods to quantitatively analyze the molecular surface, and the molecular surface involved in this calculation process is generated by electron density grid data based on the MT algorithm. Our teams use the electron density isosurface to define the molecular surface, and the final output volume is the Van der Waals volume defined by Bader.

- Monte Carlo calculation

One of the commonly used methods for calculating van der Waals volume is the Monte Carlo method. Both Bader's definition and high random point density are applied in the Monte Carlo calculations. Alfa Chemistry supports a variety of volume definition methods: When the volume is defined by van der Waals sphere superposition method, any file containing atomic coordinate information can be used as the input file; We can also use the electronic wave function information of the system to calculate the Van der Waals volume when the volume is defined by the electron density isosurface.

### Key Advantages

High efficiency

Accurate volume calculation of complex molecules

Professional personnel

Updated algorithms for diverse cases

### Service Specification

- Specific requirements of molecular volume calculation services
- Analysis cycle

### Analysis Service

- Calculation algorithms and methods
- Raw data
- Analysis report

Alfa Chemistry provides personalized molecular volume calculation services to facilitate your innovative scientific study. Volume calculations of small and large molecules with accurate results are available to satisfy the development demands of chemistry and biomedicine. Our clients have direct access to our staff and prompt feedback to their inquiries. If you have any questions, please feel free to contact us.

Reference

- Bier, I. and Marom, N. Machine learned model for solid form volume estimation based on packing-accessible surface and molecular topological fragments.
*J. Phys. Chem. A*2020, 124: 10330-10345.