Quantum chemistry is a branch of theoretical chemistry, which applies quantum mechanics and quantum field theory to address issues and problems in chemistry. The description of the electronic behavior of atoms and molecules as pertaining to their reactivity is one of the applications of quantum chemistry. Quantum chemistry lies on the border between chemistry and physics, and significant contributions have been made by scientists from both fields. It has a strong and active overlap with the field of atomic physics and molecular physics, as well as physical chemistry. Theoretical chemistry is the use of reasoning to explain or predict chemical phenomena. ... Fig. ... Quantum field theory (QFT) is the application of quantum mechanics to fields. ... For other uses, see Chemistry (disambiguation). ... e- redirects here. ... Atomic redirects here. ... In chemistry, a molecule is an aggregate of two or more atoms in a definite arrangement held together by chemical bonds [1] [2] [3] [4] [5]. Chemical substances are not infinitely divisible into smaller fractions of the same substance: a molecule is generally considered the smallest particle of a pure... Reactivity refers to the rate at which a chemical substance tends to undergo a chemical reaction in time. ... For other uses, see Chemistry (disambiguation). ... Physics (Greek: (phúsis), nature and (phusiké), knowledge of nature) is the science concerned with the discovery and understanding of the fundamental laws which govern matter, energy, space, and time and explaining them using mathematics. ... Atomic physics (or atom physics) is the field of physics that studies atoms as isolated systems comprised of electrons and an atomic nucleus. ... Molecular physics is the study of the physical properties of molecules and of the chemical bonds between atoms that bind them into molecules. ... Physical Chemistry is the combined science of physics, chemistry, thermodynamics, and quantum mechanics which functions to provide molecular-level interpretations of observed macroscopic phenomena. ...

History

Main article: History of quantum mechanics

The history of quantum chemistry began essentially with the 1838 discovery of cathode rays by Michael Faraday, the 1859 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’ ε such that each of these energy elements is proportional to the frequency ν with which they each individually radiate energy, as defined by the following formula: Niels Bohr’s 1913 quantum model of the atom, which incorporated an explanation of Johannes Rydbergs 1888 formula, Max Planck’s 1900 quantum hypothesis, i. ... Alternative meanings: There is also an Electric-type Pok mon named Electrode. ... Michael Faraday, FRS (September 22, 1791 – August 25, 1867) was an English chemist and physicist (or natural philosopher, in the terminology of that time) who contributed significantly to the fields of electromagnetism and electrochemistry. ... As the temperature decreases, the peak of the black body radiation curve moves to lower intensities and longer wavelengths. ... Gustav Kirchhoff Gustav Robert Kirchhoff (March 12, 1824 – October 17, 1887), a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects. ... Ludwig Eduard Boltzmann (Vienna, Austrian Empire, February 20, 1844 – Duino near Trieste, September 5, 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics. ... Max Karl Ernst Ludwig Planck (April 23, 1858 – October 4, 1947) was a German physicist. ... FreQuency is a music video game developed by Harmonix and published by SCEI. It was released in November 2001. ...

where h is a numerical value called Planck’s 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 Planck’s quantum hypothesis, that light itself consists of individual quantum particles, which later came to be called photons (1926). In the years to follow, this theoretical basis slowly began to be applied to chemical structure, reactivity, and bonding. A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... The photoelectric effect is the emission of electrons from matter upon the absorption of electromagnetic radiation, such as ultraviolet radiation or x-rays. ... Albert Einstein ( ) (March 14, 1879 – April 18, 1955) was a German-born theoretical physicist who is widely considered to have been one of the greatest physicists of all time. ... Prism splitting light Light is electromagnetic radiation with a wavelength that is visible to the eye (visible light) or, in a technical or scientific context, electromagnetic radiation of any wavelength[1]. The elementary particle that defines light is the photon. ... In physics, the photon (from Greek φως, phōs, meaning light) is the quantum of the electromagnetic field; for instance, light. ...

Electronic structure

Main article: Computational chemistry#Electronic structure

The first step in solving a quantum chemical problem is usually solving the Schrödinger equation (or Dirac equation in relativistic quantum chemistry) with the electronic molecular Hamiltonian. This is called determining the electronic structure of the molecule. It can be said that the electronic structure of a molecule or crystal implies essentially its chemical properties. Computational chemistry is a branch of chemistry that uses the results of theoretical chemistry incorporated into efficient computer programs to calculate the structures and properties of molecules and solids, applying these programs to real chemical problems. ... In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the space- and time-dependence of quantum mechanical systems. ... In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ... Relativistic quantum chemistry is a branch of quantum chemistry that applies relativistic mechanics, and, in particular the Dirac equation or approximation to it (e. ... The electronic Hamiltonian for a multi-electron molecule in atomic units is: where is the vector position of electron with vector components in Bohr radii, is the charge of fixed nucleus a in units of the elementary charge, is the vector position of nucleus with vector components in Bohr radii. ...

Wave model

The foundation of quantum mechanics and quantum chemistry is the wave model, in which the atom is a small, dense, positively charged nucleus surrounded by electrons. Unlike the earlier Bohr model of the atom, however, the wave model describes electrons as "clouds" moving in orbitals, and their positions are represented by probability distributions rather than discrete points. The strength of this model lies in its predictive power. Specifically, it predicts the pattern of chemically similar elements found in the periodic table. The wave model is so named because electrons exhibit properties (such as interference) traditionally associated with waves. See wave-particle duality. A semi-accurate depiction of the helium atom. ... The Bohr model of the hydrogen atom, where negatively charged electrons confined to atomic shells encircle a small positively charged atomic nucleus, and that an electron jump between orbits must be accompanied by an emitted or absorbed amount of electromagnetic energy hν. The orbits that the electrons travel in are... Electron cloud is a term used for introducing the concept of wavefunction in low-level pedagogical introductions to atomic physics, molecular physics, chemistry or quantum chemistry. ... In quantum chemistry, molecular orbitals are the statistical states electrons can have within molecules. ... In quantum mechanics, a probability amplitude is a complex-valued function that describes an uncertain or unknown quantity. ... The New York Times reported on Einsteins confirmed prediction. ... The periodic table of the chemical elements, also called the Mendeleev periodic table, is a tabular display of the known chemical elements. ... In physics, wave-particle duality holds that light and matter exhibit properties of both waves and of particles. ...

Valence bond

Main article: Valence bond theory

Although the mathematical basis of quantum chemistry had been laid by Schrödinger in 1926, it is generally accepted that the first true calculation in quantum chemistry was that of the German physicists Walter Heitler and Fritz London on the hydrogen (H₂) molecule in 1927. Heitler and London's method was extended by the American theoretical physicist John C. Slater and the American theoretical chemist Linus Pauling to become the Valence-Bond (VB) [or Heitler-London-Slater-Pauling (HLSP)] method. In this method, attention is primarily devoted to the pairwise interactions between atoms, and this method therefore correlates closely with classical chemists' drawings of bonds. The valence bond theory is a concept in chemistry that explains the nature of a chemical bond in a molecule [1] . It has its origins with G.N. Lewis who in 1916 first proposed that a chemical bond forms by the interaction of two shared bonding electrons, with the representation... Erwin Rudolf Josef Alexander Schrödinger (August 12, 1887 – January 4, 1961) was an Austrian physicist who achieved fame for his contributions to quantum mechanics, especially the Schrödinger equation, for which he received the Nobel Prize in 1933. ... Year 1926 (MCMXXVI) was a common year starting on Friday (link will display the full calendar). ... Walter Heinrich Heitler (02. ... Fritz Wolfgang London (March 7, 1900–March 30, 1954) was a German-born American physicist for whom the London force is named. ... 1927 (MCMXXVII) was a common year starting on Saturday (link will take you to calendar). ... John Clark Slater (1900-1976) was a major physicist and theoretical chemist. ... Linus Carl Pauling (February 28, 1901 – August 19, 1994) was an American quantum chemist and biochemist. ... A chemical bond is the PHYSICAL process responsible for the ATTRACTIVE INTERACTIONS between atoms and molecules, and that which confers stability to diatomic and polyatomic chemical compounds. ...

Molecular orbital

Main article: Molecular orbital theory

An alternative approach was developed in 1929 by Friedrich Hund and Robert S. Mulliken, in which electrons are described by mathematical functions delocalized over an entire molecule. The Hund-Mulliken approach or molecular orbital (MO) method is less intuitive to chemists, but has turned out capable of predicting spectroscopic properties better than the VB method. This approach is the conceptional basis of the Hartree-Fock method and further post Hartree-Fock methods. In quantum chemistry, molecular orbitals are the statistical states electrons can have within molecules. ... 1929 (MCMXXIX) was a common year starting on Tuesday (link will take you to calendar). ... Carl von Weizacker & Friedrich Hund, Goettingen DPI Friedrich Hund (February 4, 1896 - March 31, 1997) : German physicist known for his work on atoms and molecules. ... Robert Sanderson Mulliken (June 7, 1896 – October 31, 1986) was an American physicist and chemist, primarily responsible for the elaboration of the molecular orbital method of computing the structure of molecules. ... e- redirects here. ... In chemistry, a molecule is an aggregate of two or more atoms in a definite arrangement held together by chemical bonds [1] [2] [3] [4] [5]. Chemical substances are not infinitely divisible into smaller fractions of the same substance: a molecule is generally considered the smallest particle of a pure... Extremely high resolution spectrum of the Sun showing thousands of elemental absorption lines (fraunhofer lines) Spectroscopy is the study of matter and its properties by investigating light, sound, or particles that are emitted, absorbed or scattered by the matter under investigation. ... In computational physics and computational chemistry, the Hartree-Fock (HF) or self-consistent field (SCF) calculation scheme is a self-consistent iterative variational procedure to calculate the Slater determinant (or the molecular orbitals which it is made of) for which the expectation value of the electronic molecular Hamiltonian is minimum. ... In computational chemistry, Post-Hartree-Fock methods are the set of methods developed to improve on the Hartree-Fock (HF), or self-consistent field (SCF) method. ...

Density functional theory

Main article: Density functional theory

The Thomas-Fermi model was developed independently by Thomas and Fermi in 1927. This was the first attempt to describe many-electron systems on the basis of electronic density instead of wave functions, although it was not very successful in the treatment of entire molecules. The method did provide the basis for what is now known as density functional theory. Though this method is less developed than post Hartree-Fock methods, its lower computational requirements allow it to tackle larger polyatomic molecules and even macromolecules, which has made it the most used method in computational chemistry at present. Density functional theory (DFT) is a quantum mechanical method used in physics and chemistry to investigate the electronic structure of many-body systems, in particular molecules and the condensed phases. ... The results of the quantum particle in a box can be used to look at the equilibrium situation for a quantum ideal gas in a box which is a box containing a large number particles which do not interact with each other except for instantaneous thermalizing collisions. ... Llewellyn Hilleth Thomas born in 1903 died in 1992. ... Enrico Fermi (September 29, 1901 – November 28, 1954) was an Italian physicist most noted for his work on the development of the first nuclear reactor, and for his contributions to the development of quantum theory, particle physics and statistical mechanics. ... 1927 (MCMXXVII) was a common year starting on Saturday (link will take you to calendar). ... In quantum mechanics, and in particular in quantum chemistry, the electronic density corresponding to an N-electron wavefunction is the one-electron function given by In the case is a Slater determinant made of N spin orbitals : The two-electron electronic density is given by Those quantities are particulary important... In the most restricted usage in quantum mechanics, the wavefunction associated with a particle such as an electron, is a complex-valued square integrable function ψ defined over a portion of space normalized in such a way that In Max Borns probabilistic interpretation of the wavefunction, the amplitude squared... In chemistry a polyatomic molecule is a molecule that consists only of atoms of a single element. ... A macromolecule is a large molecule with a large molecular mass bonded covalently, but generally the use of the term is restricted to polymers and molecules which structurally include polymers. ... Computational chemistry is a branch of chemistry that uses the results of theoretical chemistry incorporated into efficient computer programs to calculate the structures and properties of molecules and solids, applying these programs to real chemical problems. ...

Chemical dynamics

A further step can consist of solving the Schrödinger equation with the total molecular Hamiltonian in order to study the motion of molecules. Direct solution of the Schrödinger equation is called quantum molecular dynamics, within the semiclassical approximation semiclassical molecular dynamics, and within the classical mechanics framework molecular dynamics (MD). Statistical approaches, using for example Monte Carlo methods, are also possible. In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the space- and time-dependence of quantum mechanical systems. ... The molecular Hamiltonian is an operator in quantum chemistry and atomic, molecular, and optical physics which describes the motions of electrons and nuclei in a polyatomic molecule. ... In physics, the adjective semiclassical has different precise meanings depending on the context. ... Classical mechanics is a branch of physics which studies the deterministic motion of objects. ... Molecular dynamics (MD) is a form of computer simulation where atoms and molecules are allowed to interact for a period of time under known laws of physics. ... Monte Carlo methods are a widely used class of computational algorithms for simulating the behavior of various physical and mathematical systems, and for other computations. ...

Adiabatic chemical dynamics

Main article: Adiabatic formalism or Born-Oppenheimer approximation

In adiabatic dynamics, interatomic interactions are represented by single scalar potentials called potential energy surfaces. This is the Born-Oppenheimer approximation introduced by Born and Oppenheimer in 1927. Pioneering applications of this in chemistry were performed by Rice and Ramsperger in 1927 and Kassel in 1928, and generalized into the RRKM theory in 1952 by Marcus who took the transition state theory developed by Eyring in 1935 into account. These methods enable simple estimates of unimolecular reaction rates from a few characteristics of the potential surface. The molecular Hamiltonian is an operator in quantum chemistry and atomic, molecular, and optical physics which describes the motions of electrons and nuclei in a polyatomic molecule. ... In physics, a scalar is a simple physical quantity that does not depend on direction, and therefore does not depend on the choice of a coordinate system. ... It has been suggested that this article or section be merged with Scalar potential. ... A potential energy surface is generally used within the adiabatic or Born–Oppenheimer approximation in quantum mechanics and statistical mechanics to model chemical reactions and interactions in simple chemical and physical systems. ... The Born-Oppenheimer approximation, also known as the adiabatic approximation, is a technique used in quantum chemistry and condensed matter physics in order to de-couple the motion of nuclei and electrons (i. ... Max Born (December 11, 1882 in Breslau – January 5, 1970 in Göttingen) was a mathematician and physicist. ... J. Robert Oppenheimer, the father of the atomic bomb served as the first director of Los Alamos National Laboratory, beginning in 1943. ... 1927 (MCMXXVII) was a common year starting on Saturday (link will take you to calendar). ... Year 1928 (MCMXXVIII) was a leap year starting on Sunday (link will display full calendar). ... This theory of chemical reactivity was developed by Rice and Ramsperger in 1927 and Kassel in 1928 (the RRK theory). ... 1952 (MCMLII) was a Leap year starting on Tuesday (link will take you to calendar). ... Rudolph Rudy Arthur Marcus (born July 21, 1923) received the 1992 Nobel Prize in Chemistry for his theory of Electron transfer. ... The transition state of a chemical reaction is a particular configuration along the reaction coordinate. ... Henry Eyring (February 20, 1901 - December 26, 1981) was a Mexican-American theoretical chemist whose primary contribution was in the study of chemical reaction rates and intermediates. ... 1935 (MCMXXXV) was a common year starting on Tuesday (link will take you to calendar). ... The reaction rate of a chemical reaction is the speed of production of products from reactants. ...

Non-adiabatic chemical dynamics

Main article: Vibronic coupling

Non-adiabatic dynamics consists of taking the interaction between several coupled potential energy surface (corresponding to different electronic quantum states of the molecule). The coupling terms are called vibronic couplings. The pioneering work in this field was done by Stueckelberg, Landau, and Zener in the 1930s, in their work on what is now known as the Landau-Zener transition. Their formula allows the transition probability between two diabatic potential curves in the neighborhood of an avoided crossing to be calculated. In theoretical chemistry, the vibronic coupling terms (which are neglected within the Born-Oppenheimer approximation) are proportional to the interaction between electronic and nuclear motions of molecules. ... A quantum state is any possible state in which a quantum mechanical system can be. ... Ernst Carl Gerlach Stueckelberg (February 1, 1905, Basel - September 4, 1984, Basel) was a Swiss mathematician and physicist. ... Lev Davidovich Landau (Ле́в Дави́дович Ланда́у) (January 22, 1908 – April 1, 1968) was a prominent Soviet physicist and winner of the Nobel Prize for Physics whose broad field of work included the theory of superconductivity and superfluidity, quantum electrodynamics, nuclear physics and particle physics. ... Clarence Melvin Zener (December 1, 1905 _ July 15, 1993) was the American physicist who first described the electrical property exploited by the Zener diode, which Bell Labs then named after him. ... Year 1930 (MCMXXX) was a common year starting on Wednesday (link is to a full 1930 calendar). ... The phrase Landau-Zener transition refers to the following general problem in quantum dynamics, which was first solved by Landau and Zener in 1932. ... In quantum chemistry, the potential energy surfaces are obtained within the adiabatic or Born-Oppenheimer approximation. ... The eigenvalues of a Hermitian matrix depending on N continuous real parameters cannot cross except at a manifold of N-1 dimensions. ...

Quantum chemistry and quantum field theory

The application of quantum field theory (QFT) to chemical systems and theories has become increasingly common in the modern physical sciences. One of the first and most fundamentally explicit appearances of this is seen in the theory of the photomagneton. In this system, plasmas, which are ubiquitous in both physics and chemistry, are studied in order to determine the basic quantization of the underlying bosonic field. However, quantum field theory is of interest in many fields of chemistry, including: nuclear chemistry, astrochemistry, sonochemistry, and quantum hydrodynamics. Field theoretic methods have also been critical in developing the ab initio Effective Hamiltonian theory of semi-empirical pi-electron methods. Quantum field theory (QFT) is the application of quantum mechanics to fields. ... The photomagneton is a theoretical treatment of the unitary group in quantum field theory and quantum chemistry that effectively describes the experimentally observed inverse Faraday effect. ... A plasma lamp, illustrating some of the more complex phenomena of a plasma, including filamentation. ... In physics, quantization is a procedure for constructing a quantum field theory starting from a classical field theory. ... In particle physics, bosons, named after Satyendra Nath Bose, are particles having integer spin. ... Nuclear chemistry is a subfield of chemistry dealing with radioactivity, nuclear processes and nuclear properties. ... Astrochemistry is the study of the chemicals found in outer space, usually in molecular gas clouds, and their formation, interaction and destruction. ... In chemistry, the study of sonochemistry is concerned with understanding the effect of sonic waves and wave properties on chemical systems. ... Quantum hydrodynamics is more than the study of superfluidity. ...

See also

• Computational chemistry
• Theoretical chemistry
• Physical chemistry
• Atomic physics
• Theoretical physics
• Condensed matter physics
• International Academy of Quantum Molecular Science
• Quantum electrochemistry

Computational chemistry is a branch of chemistry that uses the results of theoretical chemistry incorporated into efficient computer programs to calculate the structures and properties of molecules and solids, applying these programs to real chemical problems. ... Theoretical chemistry is the use of reasoning to explain or predict chemical phenomena. ... Physical Chemistry is the combined science of physics, chemistry, thermodynamics, and quantum mechanics which functions to provide molecular-level interpretations of observed macroscopic phenomena. ... Atomic physics (or atom physics) is the field of physics that studies atoms as isolated systems comprised of electrons and an atomic nucleus. ... Theoretical physics employs mathematical models and abstractions of physics, as opposed to experimental processes, in an attempt to understand nature. ... Condensed matter physics is the field of physics that deals with the macroscopic physical properties of matter. ... The International Academy of Quantum Molecular Science was created in Menton in 1967, with Professors Raymond Daudel (France), Per-Olov Löwdin (Sweden), Robert G. Parr (USA), John A. Pople (USA) and Bernard Pullman (France) as its founding members, under the inspiration and with the support of Professor Louis de... The scientific school of Quantum electrochemistry began to form in 1960s under ruling of Revaz Dogonadze. ...

Further reading

• Pauling, L. (1954). General Chemistry. Dover Publications. ISBN 0-486-65622-5. 
• Pauling, L., and Wilson, E. B. Introduction to Quantum Mechanics with Applications to Chemistry (Dover Publications) ISBN 0-486-64871-0
• Atkins, P.W. Physical Chemistry (Oxford University Press) ISBN 0-19-879285-9
• McWeeny, R. Coulson's Valence (Oxford Science Publications) ISBN 0-19-855144-4
• Landau, L.D. and Lifshitz, E.M. Quantum Mechanics:Non-relativistic Theory(Course of Theoretical Physics vol.3) (Pergamon Press)
• Eric R. Scerri, The Periodic Table: Its Story and Its Significance, Oxford University Press, 2006. Considers the extent to which chemistry and especially the periodic system has been reduced to quantum mechanics. ISBN 0-19-530573-6

External links

• The Sherrill Group - Notes
• ChemViz Curriculum Support Resources
• Early ideas in the history of quantum chemistry

Nobel lectures by quantum chemists

• Walter Kohn's Nobel lecture
• Rudolph Marcus' Nobel lecture
• Robert Mulliken's Nobel lecture
• Linus Pauling's Nobel lecture
• John Pople's Nobel lecture