History of quantum mechanics
The history of quantum mechanics as this interlaces with history of quantum chemistry began essentially with the 1838 discovery of cathode rays by Michael Faraday, during the 1859-1860 winter statement of the black body radiation problem by Gustav Kirchhoff, the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system could be discrete, and the 1900 quantum hypothesis by Max Planck that any energy radiating atomic system can theoretically be divided into a number of discrete energy elements  (epsilon) such that each of these energy elements is proportional to the frequency  with which they each individually radiate energy, as defined by the following formula:
where h is a numerical value called Plancks constant. Then, in 1905, to explain the photoelectric effect (1839), i.e. that shining light on certain materials can function to  eject electrons from the material, Albert Einstein postulated, as based on Plancks quantum hypothesis, that light itself consists of individual quantum particles, which later came to be called photons (1926).  The phrase "quantum mechanics" was first used in Max Born's 1924 paper "Zur Quantenmechanik".  In the years to follow, this theoretical basis slowly began to be applied to chemical structure, reactivity, and bonding.

# Overview
In short, in 1900, German physicist Max Planck introduced the idea that energy is quantized, in order to derive a formula for the observed frequency dependence of the energy emitted by a black body. In 1905, Einstein explained the photoelectric effect by postulating that light, or more specifically all electromagnetic radiation, can be divided into a finite number of "energy quanta" that are localized points in space.  From the introduction section of his March 1905 quantum paper, On a heuristic viewpoint concerning the emission and transformation of light, Einstein states:
This statement has been called the most revolutionary sentence written by a physicist of the twentieth century. These energy quanta later came to be called "photons", a term introduced by Gilbert N. Lewis in 1926. The idea that each photon had to consist of energy in terms of quanta was a remarkable achievement as it effectively removed the possibility of black body radiation attaining infinite energy if it were to be explained in terms of wave forms only. In 1913, Bohr explained the spectral lines of the hydrogen atom, again by using quantization, in his paper of July 1913 On the Constitution of Atoms and Molecules.
These theories, though successful, were strictly phenomenological: during this time, there was no rigorous justification for quantization aside, perhaps, for Henri Poincare's discussion of Planck's theory in his 1912 paper Sur la theorie des quanta. They are collectively known as the old quantum theory.
The phrase "quantum physics" was first used in Johnston's Planck's Universe in Light of Modern Physics (1931).
In 1924, the French physicist Louis de Broglie put forward his theory of matter waves by stating that particles can exhibit wave characteristics and vice versa. This theory was for a single particle and derived from special relativity theory. Building on de Broglie's approach, modern quantum mechanics was born in 1925, when the German physicists Werner Heisenberg and Max Born developed matrix mechanics and the Austrian physicist Erwin Schrodinger invented wave mechanics and the non-relativistic Schrodinger equation as an approximation to the generalised case of de Broglie's theory . Schrodinger subsequently showed that the two approaches were equivalent.
Heisenberg formulated his uncertainty principle in 1927, and the Copenhagen interpretation started to take shape at about the same time. Starting around 1927, Paul Dirac began the process of unifying quantum mechanics with special relativity by proposing the Dirac equation for the electron. The Dirac equation achieves the relativistic description of the wavefunction of an electron that Schrodinger failed to obtain. It predicts electron spin and led Dirac to predict the existence of the positron. He also pioneered the use of operator theory, including the influential bra-ket notation, as described in his famous 1930 textbook. During the same period, Hungarian polymath John von Neumann formulated the rigorous mathematical basis for quantum mechanics as the theory of linear operators on Hilbert spaces, as described in his likewise famous 1932 textbook. These, like many other works from the founding period still stand, and remain widely used.
The field of quantum chemistry was pioneered by physicists Walter Heitler and Fritz London, who published a study of the covalent bond of the hydrogen molecule in 1927. Quantum chemistry was subsequently developed by a large number of workers, including the American theoretical chemist Linus Pauling at Cal Tech, and John C. Slater into various theories such as Molecular Orbital Theory or Valence Theory.
Beginning in 1927, attempts were made to apply quantum mechanics to fields rather than single particles, resulting in what are known as quantum field theories. Early workers in this area included P.A.M. Dirac, W. Pauli, V. Weisskopf, and P. Jordan. This area of research culminated in the formulation of quantum electrodynamics by R.P. Feynman, F. Dyson, J. Schwinger, and S.I. Tomonaga during the 1940s. Quantum electrodynamics is a quantum theory of electrons, positrons, and the electromagnetic field, and served as a role model for subsequent quantum field theories. 
The theory of quantum chromodynamics was formulated beginning in the early 1960s. The theory as we know it today was formulated by Politzer, Gross and Wilczek in 1975.  Building on pioneering work by Schwinger, Higgs, Goldstone, Glashow, Weinberg and Salam independently showed how the weak nuclear force and quantum electrodynamics could be merged into a single electroweak force.

# Timeline
The following timeline shows the key steps and contributors in the precursory development of quantum mechanics and quantum chemistry:

# Founding experiments
- Thomas Young's double-slit experiment demonstrating the wave nature of light (c1805)
- Henri Becquerel discovers radioactivity (1896)
- J. J. Thomson's cathode ray tube experiments (discovers the electron and its negative charge) (1897)
- The study of black body radiation between 1850 and 1900, which could not be explained without quantum concepts.
- The photoelectric effect: Einstein explained this in 1905 (and later received a Nobel prize for it) using the concept of photons, particles of light with quantized energy
- Robert Millikan's oil-drop experiment, which showed that electric charge occurs as quanta (whole units), (1909)
- Ernest Rutherford's gold foil experiment disproved the plum pudding model of the atom which suggested that the mass and positive charge of the atom are almost uniformly distributed.   (1911)
- Otto Stern and Walther Gerlach conduct the Stern-Gerlach experiment, which demonstrates the quantized nature of particle spin (1920)
- Clinton Davisson and Lester Germer demonstrate the wave nature of the electron in the Electron diffraction experiment (1927)
- Clyde L. Cowan and Frederick Reines confirm the existence of the neutrino in the neutrino experiment (1955)
- Claus Jonsson`s double-slit experiment with electrons (1961)
- The Quantum Hall effect, discovered in 1980 by Klaus von Klitzing. The quantized version of the Hall effect has allowed for the definition of a new practical standard for electrical resistance and for an extremely precise independent determination of the fine structure constant.
- The experimental verification of quantum entanglement by Alain Aspect in 1982.