VSEPR theory molecular geometry
The electron pairs around an atom are all negative, so they push each other away. They try to spread as far apart as they can, and that arrangement is the 3 dimensional shape of the molecule. Lone pairs occupy a place and push, not only the pairs used in bonds. Count the electron domains and the frame is fixed, linear or trigonal planar or tetrahedral, and if lone pairs are present the angle is pressed into a bent or trigonal pyramidal shape. Add the bond polarities as vectors and you also learn whether the whole molecule is polar or nonpolar. The pushing fixes the shape.
Electron domains repel and try to stand as far apart as they can. 2 of them spread opposite into a line at 180°. 3 make a trigonal plane at 120°. 4 make a tetrahedron at 109.5°. 5 are a trigonal bipyramid, and 6 are an octahedron. Change the count and the arrangement shows how it sets itself. The drive to stand far apart chooses the frame of the molecule.
A bonding pair is tied between two atoms and stays narrow, while a lone pair is tied to only one atom and swells wider. So it presses the neighboring bond pairs harder. Water has 4 electron domains, so ideally it should be 109.5°, but 2 lone pairs push and the H-O-H angle narrows to 104.5° and the molecule bends. Turn the lone pairs on and off and the angle shrinking shows itself. The swollen pair presses the angle.
When you name a molecular shape you have to separate the arrangement of electron pairs from the positions of the atoms. 4 electron domains always mean a tetrahedral arrangement, but if some of them are lone pairs the shape judged from the visible atoms alone changes. AX₄ stays tetrahedral, AX₃E with 1 lone pair is trigonal pyramidal, and AX₂E₂ with 2 lone pairs is bent. Move between the whole set of domains and the atoms-only view and the difference shows. The hidden pairs change the name.
Why do the electron domains settle in that arrangement? Because that is where the sum of the repulsion energies, each pair pushing the others, is smallest. Drag one domain off its best place and, the closer it comes to a neighbor, the higher the sum of the repulsion energy climbs. Let go and it returns to the minimum-energy arrangement, spread as far as it can. That minimum is exactly the molecular shape we observe. The lowest sum is the shape.
Each bond is a small dipole, with electrons pulled to one side by a difference in electronegativity. The polarity of the whole molecule is the vector sum of these bond dipoles. In carbon dioxide the two C=O dipoles stand opposite and cancel, so the net is 0 and the molecule is nonpolar. Water is bent, so the two O-H dipoles do not cancel. They add to one side and a net dipole remains, and the molecule is polar. Move between the bond dipoles and the net dipole and the sum of the directions is confirmed. The sum of the directions speaks the polarity.