The beginning of the twentieth century brought surprising nonclas- sical phenomena. Max Planck’s explanation of black-body radiation [1], the work of Albert Einstein on the photoelectric effect [2], and Niels Bohr’s model to account for the electron orbits around the nuclei [3] established what is now known as the old quantum theory. To describe and explain these effects, phenomenological models and theories were first developed, without any rigorous and global justification. In order to provide a complete explanation for the underlying physics of such new nonclassical phenomena, physicists were forced to abandon classical mechanics to develop novel, abstract, and imaginative formalisms.
The beginning of the twentieth century brought surprising nonclas- sical phenomena. Max Planck’s explanation of black-body radiation [1], the work of Albert Einstein on the photoelectric effect [2], and Niels Bohr’s model to account for the electron orbits around the nuclei [3] established what is now known as the old quantum theory. To describe and explain these effects, phenomenological models and theories were first developed, without any rigorous and global justification. In order to provide a complete explanation for the underlying physics of such new nonclassical phenomena, physicists were forced to abandon classical mechanics to develop novel, abstract, and imaginative formalisms.
Toward the end of the nineteenth century, it became clear that some experiments cannot be explained on the basis of known physics, now referred to as classical physics. In 1900, Max Planck was able to correctly describe the distribution of blackbody radiation energy as a function of wavelength λ or frequency ν = c/λ. He had to accept the existence of energy packets (quanta) with energy E = hν. A few years later, Albert Einstein found that this unexpected relation between energy and frequency is also necessary in order to understand photoemission from metallic surfaces. A decade later, Niels Bohr arrived at the correct equation for the electronic spectrum of the hydrogen atom by applying “quantum conditions” on the motion of the electron around the nucleus and the Planck’s relation E = hν on the energy difference between the energy levels (1916). A decade later, Heisenberg, Born, and Jordan introduced “quantum mechanics” and de Broglie and Schrödinger (1925-1926) introduced “wave mechanics.”
Abstract Chemistry is about the atom and molecule, motion of which follows quantum mechanics established 100 years ago by Werner Heisenberg, inspired by a number of milestone findings including Max Planck’s first quanta concept for black body radiation, Albert Einstein’s photon concept for photoelectric effect and oscillator quanta for heat capacity of solid, and Niels Bohr’s quantum model for atomic structure. Independently, inspired by Louis de Broglie’s particle-wave duality, Erwin Schrödinger established wave mechanics, which is shown to be equivalent to Heisenberg’s mechanics by Paul Dirac. The latter further established the relativistic quantum mechanics, and then claimed that the underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws lead to equations much too complicated to be soluble. In the occasion of celebrating The International Year of Quantum Science and Technology (IYQ 2025, quantum2025.org), we will present a heuristic review of the development of quantum theory and its application to chemistry, namely, quantum chemistry (QC). Then, we will discuss some of the current challenges and the future developments, especially on the quantum computing for quantum chemistry (QCQC).
Abstract In the first quarter of this century physicists were slowly and somewhat reluctantly forced to realize that the view of the physical world, so painstakingly built up over the preceding four centuries, was in serious need of revision. In particular, the laws that governed the motion of particles on the atomic scale were not those of classical mechanics. Physics found itself catapulted into the strange new world of quantum theory in which the very notion of position or velocity of a particle became blurred and statistical laws dominated everything.
The new physics just described was still based largely on Newtonian ideas. Indeed, in its theoretical aspects, it might not unfairly be described as a final attempt to explain the world in materialistic terms—as particles being pushed and pulled about in space and time. Nevertheless, the new physics had found it necessary to abolish most of the forces of pushing and pulling, replacing the gradual changes of motion of the particles under these forces by sudden and unpredictable jumps. These appeared to involve violations of the law of causality, both in the disintegration of radioactive atoms and also in the internal changes of ordinary atoms. We seemed to see Fate defying this law as she picked out certain atoms for disintegration or collapse and, by her apparently capricious acts, sent the universe along one path or another according to her whim. On such lines the new physics had explained many phenomena which had hitherto seemed inexplicable, but it had by no means met with complete success. For instance, while it gave a perfect interpretation of the simplest spectrum of all, namely that of the hydrogen atom, it failed with more complex spectra. This was not necessarily a fatal objection; a few emendations and possibly a few new ad hoc assumptions might have effected a complete reconciliation, although this seems improbable.
The development of quantum mechanics in the early twentieth century marked one of the most profound conceptual revolutions in physics. Beginning with Planck's quantization of radiation and Einstein's interpretation of the photoelectric effect, followed by Bohr's atomic model, and later formalized by Heisenberg and Schrödinger, the theory provided a new description of nature—one in which probability amplitudes replaced deterministic trajectories. Within this framework, microscopic systems such as atoms, electrons, and photons are characterized by wavefunctions and operators rather than by points in phase space.
Quantum Mechanics and its Interpretations Peter E. Hodgson (bio) Quantum Mechanics is an elegant and indeed beautiful formalism, and enables the results of many physical measurements to be calculated with great accuracy. But from the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything, it is becoming more intense over the years. It should therefore be evident that the most that can be done here is to try to show where the real difficul-ties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. The Discovery of the Quantum The quantum nature of the physical world was discovered by Max Planck in the early years of the twentieth century. He was studying thermodynamics and his attention was drawn to the frequency distribution of black-body radiation. This radiation is emitted from a small hole in a heated enclosure with rough walls, which ensures [End Page 62] that the radiation reaches statistical equilibrium before emission. The frequency distribution is found to be independent of the material lining the walls of the oven, so Planck realized that it must be a fundamental characteristic of all matter. This frequency distribution had been measured by several experimentalists, and Planck resolved to try to see how it can be derived theoretically. Already Rayleigh and Jeans had used classical radiation theory to derive an expression that fitted the data well at low frequencies but tended to infinity at high energies, which was of course unacceptable. The physicist Wien had derived a formula that fitted the data at high frequencies but failed at low frequencies. Planck used an ingenious argument based on entropy to interpolate between these two formulae and obtained a formula, now known as the Planck distribution, that fitted the data perfectly. His next task was to understand the physics behind his formula. He used the familiar technique of assuming that the energy is emitted in small finite amounts, and then let their size tend to zero, so as to represent a continuous distribution. To his great surprise, the intermediate formula with discrete amounts of energy, called quanta, gave the Planck distribution, but the final result, with infinitely small quanta, did not. All his instincts as a physicist rebelled against this conclusion. Surely energy must be emitted continuously. He tried hard to find a way to avoid this unwelcome conclusion, but without success. He had to admit that it is a feature of the world. Soon it was confirmed by Einstein’s interpretation of the photoelectric effect. This story shows clearly that physicists do not impose their ideas on the world, but recognize and accept what they find, whether or not it agrees with their original ideas. The world is made by God in ways that often we cannot imagine. [End Page 63] The Old Quantum Theory A few years later Rutherford discovered that the atom has a small central nucleus containing most of its mass surrounded by a number of electrons. Bohr used the idea of the quantum to build his model of the atom. He assumed that the electrons go around the nucleus in discrete orbits, and that radiation is emitted when an electron falls from one orbit to a lower one. With this model, he was able to calculate to high accuracy the frequencies of the radiation emitted from an excited hydrogen atom. This was a great achievement, but to get his result he had to assume that the electrons stayed in their orbits, whereas classical theory predicted that they would continuously lose energy and rapidly spiral into the nucleus. Quantum Mechanics and its Interpretations These problems were solved by the development of quantum mechanics in the 1920s by Heisenberg, Schrodinger, Dirac, and others. This enabled what is called the wave function to be calculated for any physical system, and from the wave function the probabilities of occurrence of measurable quantities can be found. It is a beautiful theory, and is the indispensable means of calculation for atomic, nuclear...