Quantum Chemistry | Research & Encyclopedia Articles

Quantum Chemistry

Quantum chemistry involves the application of the principles of quantum theory to chemistry.

Quantum chemistry helps predict the way atoms combine to form molecules, and the way molecules interact with each other. Applications of quantum chemistry include the calculation of molecular structures, prediction of properties, analysis of spectroscopic data, and the description of chemical reactions in terms of individual molecular events.

Quantum theory states that energy is transferred between systems in discrete amounts. The theory arose from the inability of classical physics to adequately explain certain physical phenomena, such as blackbody radiation and the photoelectric effect. To account for these phenomena, the concept of quantization was introduced in 1901 by the German physicist Max Planck.

Planck devised his quantum hypothesis while studying blackbody radiation. The term perfect blackbody applies to bodies that act as perfect radiators or absorbers of heat. Although there are no known perfect blackbodies, by definition, if a blackbody acted as a perfect absorber, all of the light that hit the blackbody would be absorbed. The blackbody would then return to its normal energy level by emitting thermal radiation, or heat. The spectrum of this emission is called a blackbody emission.

The properties of blackbody radiation depend solely on the temperature used to excite the radiation. Early attempts to account for the distribution of the radiation using classical physics did not match the observed phenomena. Classical physics yielded a distribution that predicted that at a certain temperature, the frequency of the blackbody radiation shoots up to infinity. In 1900, Planck tackled the problem of blackbody radiation with thermodynamics. He assumed that radiation of a certain frequency, v, could be excited only in discrete steps of energy of magnitude hv, where h is Planck's constant (introduced to satisfy observable phenomena). Planck termed the discrete amounts of energy quanta.

Although Planck's formula for the distribution of the blackbody radiation matched the observed distribution of blackbody radiation, the introduction of the quantization of energy and of the constant h was originally thought by Planck to be nothing more than a calculation device. In 1905, however, Albert Einstein showed that Plank's constant was a fundamental constant of nature. Einstein used both the notion of quantization and Planck's constant, h, to explain the photoelectric effect.

Expanding on Planck's theory of blackbody radiation, Einstein assumed that light was transmitted in as a stream of particles termed photons. By treating light as a stream of photons, Einstein was able to explain the photoelectric effect.

The photoelectric effect occurs when photons of light at a certain frequency excite and cause the ejection of electrons from a metal. Regardless of intensity, light with a frequency below the photoelectric threshold--characteristic of the individual metal--will not cause electrons (also, in these circumstances termed photoelectrons) to be emitted from the metal. Above the photoelectric threshold, photoelectrons are emitted in proportion to the intensity of incident light.

When a photon strikes the surface of a metal, it raises the energy level of the metal and causes the ejection of electrons. This ejection of an electron only occurs if the energy overcomes the energy binding the electron to the metal. The energy required to remove an electron from the metal is called the work function, which is written as hv (Planck's constant multiplied by the required frequency of light). If hv is less than the work function, an electron will not be ejected; but if the frequency is large enough to overcome the work function, an electron is ejected, and the photoelectric effect is observed.

As long as the frequency of the light is greater than the work function of the metal, any photon can eject an electron. The intensity of light depends on the number of photons in the light. Accordingly, the more photons, the more intense, or brighter the light. At low intensities of light only a few collisions occur, at higher intensities more collisions and ejections occur. Each photon in a low intensity beam of light, however, carries the same energy as photons in a high intensity beam. Therefore the ejection of electrons again depends only on the frequency of light.

The work of Planck and Einstein regarding the quantization of energy, revolutionized physics and chemistry. The concept of quantization and its application to physical phenomena at the beginning of the twentieth century formed what is now called the old quantum theory.

The old quantum theory was refined by the work of Louis-Victor de Broglie, Erwin Schrödinger,and Werner Heisenberg in the 1920s. De Broglie proposed in his doctoral thesis (published in 1924) that particles, such as electrons, could also be described as waves. This proposal led Schrödinger to publish his wave equation in 1926. The Schrödinger wave equation, applied to a system, gives the wave function of the system. The wave function of a system contains information regarding the properties of the system. In quantum chemistry, the Schrödinger's wave equation is applied to chemical systems, like atoms and molecules, and his system of quantum mechanics is called wave mechanics.

Working at about the same time, Heisenberg formulated matrix mechanics, which was the first complete and self-consistent theory of quantum mechanics. Matrix mathematics was well-established by the 1920s, and Heisenberg applied this tool to quantum mechanics. In 1926, Heisenberg put forward his uncertainty principle that states that two complementary properties of a system, such as position and momentum, can never both be known exactly. This proposition helped cement the dual nature of particles (e.g., light can be described as having both wave and a particle characteristics).

Schrödinger's wave mechanics and Heisenberg's matrix mechanics initially looked quite different from each other, but they are actually mathematically equivalent. When these two systems were put together they forced a complete revision of classical physics. De Broglie, Schrödinger, and Heisenberg's development of Planck's quantum theory form what is now called the new quantum theory.

Quantum theory was firmly applied to chemistry in the late 1920s and early 1930s by Linus Pauling. In 1931, Pauling published a paper that used quantum mechanics to explain how two electrons, from two different atoms, are shared to make a covalent bond between the two atoms. Pauling's work provided the connection needed in order to fully apply the new quantum theory to chemistry.

One of the main points in quantum chemistry, proposed by Heisenberg, is that, because an electron is not a classical particle located at a definite point in space (as classical physics dictated), even a single electron can surround the nucleus of an atom. The region the electron occupies is called an orbital. Each atom can contain many orbitals, which are also called shells. These shells are all interpenetrating like ripples on a puddle and are spread around the nucleus of the atom. Some of the shells are concentrated further from the nucleus than others. Because the binding energy between the negative electrons and the positive nucleus decreases with distance, the further electrons are from the nucleus, the less energy is required to remove them from the atom.

This first orbital forms a shell around the nucleus and is assigned a principal quantum number (n) of n. Additional orbital shells are assigned values n, n, n, etc. The orbital shells are not spaced at equal distances from the nucleus and the radius of each shell increases rapidly as the square of n. Increasing numbers of electrons can fit into these orbital shells according to the formula 2n². Accordingly, the first shell can hold up to two electrons, the second shell (n) up to eight electrons, the third shell (n) up to 18 electrons, Subshells or suborbitals (designated s,p,d, and f) with differing shapes and orientations allow each element a unique electron configuration.

Atoms tend to be more stable with either empty or full outer shells (some also seek half-filled shells) and will lose or gain electrons to gain those configurations. For example, helium has two electrons (first orbital full) and neon has 10 electrons (first and second orbitals full). Both of these elements are stable and relatively unreactive. Hydrogen, in contrast, has one electron; so its first orbital is not full. Because it needs another electron to fill its first orbital, hydrogen is highly reactive.

This is the basis of quantum chemistry. When Pauling used quantum mechanics to explain how two electrons from two different atoms shared their electrons to form a bond, quantum chemistry became a field unto its own. Quantum chemistry can detail the structure of all the electrons, and the way that electrons are arranged around the nucleus. Using quantum chemistry, each electron can be characterized by a set of four quantum numbers. Each quantum number describes the value of a property of the electron.

The four quantum numbers that characterize an electron are the principal quantum number, the orbital quantum number, the magnetic quantum number, and the spin quantum number. The principal quantum number, n, gives the main energy level, or the distance of the electron from the nucleus. The orbital quantum number, l, gives the angular momentum of the electron. The possible values of l range from (n - 1) to 0. Therefore electrons in the first shell (n = 1) can only have angular momentum of zero. The magnetic quantum number, m, gives the energies of electrons in an external magnetic fields. Finally, the spin quantum number, m_s, gives the spin of the individual electrons and has values of +1/2 or -1/2. All of these quantum numbers define the quantum state of the electron.

Quantum chemistry is an exciting field of research. There are two types of quantum chemistry, computational and non-computational. Computational quantum chemistry is concerned with the numerical computation of molecular structures. Typical activities in computational quantum chemistry include calculating the electron distributions in molecules, predicting molecular geometries, and screening molecules for pharmacological activity. Noncomputational quantum chemistry is concerned with formulating expressions for the properties of molecules and their reactions. Typical problems in non-computational quantum chemistry include analyzing features of potential energy surfaces for rate constants and other aspects of molecular collisions, analyzing the symmetry properties of molecules, and manipulating the functions that represent interactions in molecules.

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