# Overlap integrals: What are they and how do we arrive at the formula?

• Mazzur
In summary, overlap integrals are a measure of the interaction between a nucleus and electron density centered on another nucleus. They are calculated by considering the combination of atomic orbitals and can provide information about molecular orbitals.
Mazzur
Hey I've been looking all over the web and I can't find any comprehensible information on overlap integrals. What does the overlap integral of two functions give us? And why?

hint: change of basis

ansgar said:
hint: change of basis

lol sorry - I don't have a clue what the basis even refers to...

Mazzur said:
lol sorry - I don't have a clue what the basis even refers to...

Basis(basis set) = atomic orbitals from which the MO is built.
So overlap integrals is a measure of the interracton between a nucleus and electron density centred on the other nucleus . Note that this is just partial example of what overlap integral is.
I guess we arrive at the formula by considering the fact that atomic orbitals can be combined linearly.

## 1. What are overlap integrals?

Overlap integrals are mathematical calculations used in quantum mechanics to determine the extent to which two quantum wavefunctions overlap. They provide a measure of the probability that two particles will occupy the same space at the same time.

## 2. How do we calculate overlap integrals?

The formula for overlap integrals involves taking the product of the two wavefunctions, multiplying by a factor that accounts for the distance between the two particles, and then integrating over all space. This calculation can be done analytically or numerically using computer software.

## 3. Why are overlap integrals important?

Overlap integrals are essential for understanding the behavior of particles in quantum systems. They help us determine the likelihood of particle interactions and the stability of molecular structures. They also play a crucial role in predicting the physical and chemical properties of materials.

## 4. What factors affect the value of overlap integrals?

The value of overlap integrals depends on the nature and shape of the two wavefunctions involved, as well as the distance between the two particles. It is also affected by the orientation of the particles and the presence of any barriers or potential energy barriers between them.

## 5. How are overlap integrals used in real-world applications?

Overlap integrals have numerous applications in fields such as chemistry, physics, and materials science. They are used to predict molecular properties, study chemical reactions, and design new materials with specific properties. They are also essential in fields such as quantum computing and quantum cryptography.

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