# Theoretical Background

• Anne-Marie Sapse
Chapter

## Abstract

Inadequate descriptions of atoms and molecules by the methods of classical physics led researchers to propose new ways to describe physical reality, giving birth to a totally new science, quantum mechanics. The methods of quantum mechanics are based on the introduction of a wave function, whose physical meaning is related to the probability of finding a certain particle, at a certain time in a volume element, positioned between x and x + dx in the x = direction, between y and y + dy in the y = direction, and between z and z + dz in the z = direction at certain time t. This wave function Ψ satisfies the Schrödinger equation,
$$\left( { - \frac{{{\hbar ^2}}}{{2m}}{\nabla ^2} + v} \right)\Psi = {\rm E}\Psi,\hbar = \frac{h}{{2\pi }},$$
or for short, HΨ = EΨ, where H, the Hamiltonian operator, is defined by the expression
$$H = - \frac{{{\hbar ^2}}}{{2m}}{\nabla ^2} + V;$$
h is Planck’s constant; ∇2 is the sum of the partial second derivatives with respect to x, y, and z; m is the mass of the particle; and V is the potential energy of the system. The Hamiltonian H represents the quantum equivalent of the sum of the kinetic energy and potential energy, with V being the potential energy operator and $$\frac{{ - {\hbar ^2}}}{{2m}}{\nabla ^2}$$ the kinetic energy operator. Finally, E is the total energy of the system and is a number, not an operator.

## Keywords

Correlation Energy Schrodinger Equation Gaussian Program Kinetic Energy Operator Mulliken Population Analysis
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

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Moller, C., and Plesset, M.S. Phys. Rev. 46, 618, 1934.

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