What is the VSEPR theory? On what physical basis is the VSEPR theory founded?

At its core, molecular geometry is the three-dimensional arrangement of atoms within a molecule. Understanding the specific layout of atoms can be crucial for grasping concepts in molecular biology, materials science, and chemistry, especially when predicting how molecules will interact with each other.
Molecular shapes may include linear, bent, trigonal planar, tetrahedral, and more complex arrangements. These shapes are not random but are dictated by the number and type of bonds (single, double, triple) as well as the lone pairs of electrons on the central atom.
For instance, a molecule with two single bonds and no lone pairs on the central atom adopts a linear shape, whereas one with four single bonds is tetrahedral. An understanding of molecular geometry is not just academic; it has practical applications in drug design, the creation of new materials, and in the understanding of environmental effects on chemical structures.

The concept of electron pair repulsion is at the heart of predicting molecular shape. The fundamental idea is that because electrons have a negative charge, pairs of electrons in the valence shell of an atom will repel each other. This repulsion is minimized when the electron pairs are spaced as far apart as possible.
In simple molecules like water (H2O), the lone pairs of electrons on the oxygen also contribute to the shape, pushing the hydrogen atoms closer together, leading to a bent structure instead of a straight line. It's a balancing act of attractions and repulsions that come to a natural rest in the lowest energy configuration, and this underpins much of the behavior of molecules in both chemical reactions and material states.

The valence shell is the outermost electron shell of an atom that can participate in the forming of chemical bonds with other atoms. It contains the valence electrons which are responsible for the reactivity of the element and its ability to form connections.
It's the actions of these valence electrons that determine the chemical properties of an element, and how it interacts with others. For instance, the noble gases, inert and rarely forming compounds, have a full valence shell; their stability is a result of this electron arrangement.
When using VSEPR theory to predict molecular geometry, it’s important to consider not only the number of valence electrons responsible for bond formation but also those which remain as lone pairs, as they also exert a repulsive force influencing the overall molecular shape.

Molecular shape prediction is a valuable skill in various fields of science, particularly chemistry and biochemistry. Using the VSEPR theory, chemists can predict the 3D arrangement of molecules and thus, infer reactions and properties.
For example, when determining molecular geometry, one should first count the total number of bonds and lone pairs on the central atom, then use a VSEPR chart to find the corresponding molecular shape. Factors such as steric number, which is the sum of the number of atoms bonded to the central atom and the number of lone pair electrons, help determine the fundamental geometry.
While the theory is an excellent guide, it is important to note other factors like the presence of double or triple bonds and subtle electronic interactions that can further refine the exact angles and shapes that molecules assume. Ultimately, the task of predicting molecular shape involves synthesizing both theoretical knowledge and experimental evidence to arrive at the most precise model possible.