Quantum chemistry - Citizendia

Quantum chemistry is a branch of theoretical chemistry, which applies quantum mechanics and quantum field theory to address issues and problems in chemistry. Theoretical chemistry involves the use of physics to explain or predict chemical phenomena Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons In quantum field theory (QFT the forces between particles are mediated by other particles Chemistry (from Egyptian kēme (chem meaning "earth") is the Science concerned with the composition structure and properties The description of the electronic behavior of atoms and molecules as pertaining to their reactivity is one of the applications of quantum chemistry. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by Quantum chemistry lies on the border between chemistry and physics, and significant contributions have been made by scientists from both fields. Chemistry (from Egyptian kēme (chem meaning "earth") is the Science concerned with the composition structure and properties Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. It has a strong and active overlap with the field of atomic physics and molecular physics, as well as physical chemistry. Atomic physics (or atom physics) is the field of Physics that studies atoms as an isolated system 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 Physical chemistry, is the application of Physics to macroscopic microscopic atomic subatomic and particulate phenomena in chemical systems It is mostly defined as a large

Quantum chemistry mathematically describes the fundamental behavior of matter at the molecular scale. Matter is commonly defined as being anything that has mass and that takes up space. In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by ^[1] It is, in principle, possible to describe all chemical systems using this theory. In practice, only the simplest chemical systems may realistically be investigated in purely quantum mechanical terms, and approximations must be made for most practical purposes (e. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons g. , Hartree-Fock, post Hartree-Fock or Density functional theory, see computational chemistry for more details). In Computational physics and Computational chemistry, the Hartree-Fock ( HF) method is an approximate method for the determination of the ground-state 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 (DFT is a quantum mechanical theory used in Physics and Chemistry to investigate the Electronic structure (principally Computational chemistry is a branch of Chemistry that uses computers to assist in solving chemical problems Hence a detailed understanding of quantum mechanics is not necessary for most chemistry, as the important implications of the theory (principally the orbital approximation) can be understood and applied in simpler terms. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons An atomic orbital is a Mathematical function that describes the wave-like behavior of an electron in an atom

In quantum mechanics (several applications in computational chemistry and quantum chemistry), the Hamiltonian, or the physical state, of a particle can be expressed as the sum of two operators, one corresponding to kinetic energy and the other to potential energy. In Quantum mechanics, the Hamiltonian H is the Observable corresponding to the Total energy of the system The kinetic energy of an object is the extra Energy which it possesses due to its motion Potential energy can be thought of as Energy stored within a physical system The Hamiltonian in the Schrödinger wave equation used in quantum chemistry does not contain terms for the spin of the electron. In Physics, especially Quantum mechanics, the Schrödinger equation is an equation that describes how the Quantum state of a Physical system In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin

Solutions of the Schrödinger equation for the hydrogen atom gives the form of the wave function for atomic orbitals, and the relative energy of the various orbitals. An atomic orbital is a Mathematical function that describes the wave-like behavior of an electron in an atom The orbital approximation can be used to understand the other atoms e. g. helium, lithium and carbon. Helium ( He) is a colorless odorless tasteless non-toxic Inert Monatomic Chemical Lithium (ˈlɪθiəm is a Chemical element with the symbol Li and Atomic number 3 Carbon (kɑɹbən is a Chemical element with the symbol C and its Atomic number is 6

1 History
2 Electronic structure
3 Chemical dynamics
- 3.1 Adiabatic chemical dynamics
- 3.2 Non-adiabatic chemical dynamics
4 Quantum chemistry and quantum field theory
5 See also
6 Further reading
7 External links
- 7.1 Nobel lectures by quantum chemists
8 References

History

Main article: History of quantum mechanics

The history of quantum chemistry essentially began 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:

$\epsilon = h \nu \,$

where h is a numerical value called Planck’s Constant. The history of Quantum mechanics as this interlaces with history of Quantum chemistry began essentially with the 1838 discovery of Cathode rays Cathode rays (also called an electron beam or e-beam) are streams of Electrons observed in Vacuum tubes i Michael Faraday, FRS ( September 22 1791 – August 25 1867) was an English The Electromagnetic radiation emitted by a Black body. You may also be looking for Incandescence, the radiation from a body Gustav Robert Kirchhoff ( March 12, 1824 &ndash October 17, 1887) was a German Physicist who contributed to the fundamental Ludwig Eduard Boltzmann ( February 20, 1844 &ndash September 5, 1906) was an Austrian Physicist famous for his founding Frequency is a measure of the number of occurrences of a repeating event per unit Time. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta. Then, in 1905, to explain the photoelectric effect (1839), i. Introduction When a Metallic surface is exposed to Electromagnetic radiation above a certain threshold Frequency, the light is absorbed and Electrons e. , that shining light on certain materials can function to eject electrons from the material, Albert Einstein postulated, based on Planck’s quantum hypothesis, that light itself consists of individual quantum particles, which later came to be called photons (1926). Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena In the years to follow, this theoretical basis slowly began to be applied to chemical structure, reactivity, and bonding.

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. Computational chemistry is a branch of Chemistry that uses computers to assist in solving chemical problems In Physics, especially Quantum mechanics, the Schrödinger equation is an equation that describes how the Quantum state of a Physical system In Physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides Relativistic quantum chemistry is a branch of Quantum chemistry that applies relativistic mechanics, and in particular the Dirac equation or an approximation In Atomic molecular and optical physics as well as in Quantum chemistry, molecular Hamiltonian is the name given to the Hamiltonian representing the 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.

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. The nucleus of an Atom is the very dense region consisting of Nucleons ( Protons and Neutrons, at the center of an atom 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. In Atomic physics, the Bohr model created by Niels Bohr depicts the Atom as a small positively charged nucleus surrounded by Electrons Electron cloud is a term used if not originally coined by the Nobel Prize laureate and acclaimed educator Richard Feynman in The Feynman Lectures on Physics In Chemistry, a molecular orbital (or MO) is a region in which an Electron may be found in a Molecule. In Quantum mechanics, a probability amplitude is a complex -valued function that describes an uncertain or unknown quantity The strength of this model lies in its predictive power. The predictive power of a Scientific theory refers to its ability to generate testable predictions Specifically, it predicts the pattern of chemically similar elements found in the periodic table. The periodic table of the chemical elements is a tabular method of displaying the Chemical elements Although precursors to this table exist its invention is The wave model is so named because electrons exhibit properties (such as interference) traditionally associated with waves. See wave-particle duality. In Physics and Chemistry, wave–particle duality is the concept that all Matter and Energy exhibits both Wave -like and

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. In Chemistry, valence bond theory explains the nature of a Chemical bond in a Molecule in terms of atomic valencies. Year 1926 ( MCMXXVI) was a Common year starting on Friday (link will display the full calendar of the Gregorian calendar. Walter Heinrich Heitler ( 2 January 1904 &ndash 15 November 1981) was a German physicist who made contributions to Quantum electrodynamics Fritz Wolfgang London ( March 7, 1900 &ndash March 30, 1954) was a German -born American theoretical Physicist. Year 1927 ( MCMXXVII) was a Common year starting on Saturday (link will display full calendar of the Gregorian calendar. 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. John Clarke Slater (1900-1976 was a noted American physicist and theoretical chemist. Linus Carl Pauling (February 28 1901 – August 19 1994 was an American Scientist, Peace activist, Author and educator. 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. A chemical bond is the physical process responsible for the attractive interactions between Atoms and Molecules and which confers stability to diatomic and polyatomic

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. In Chemistry, molecular orbital theory ( MO theory) is a method for determining molecular structure in which Electrons are not assigned to individual Year 1929 ( MCMXXIX) was a Common year starting on Tuesday (link will display the full calendar of the Gregorian calendar. Friedrich Hund (4 February 1896 - 31 March 1997 was a German Physicist from Karlsruhe known for his work on atoms and molecules Robert Sanderson Mulliken ( June 7, 1896 &ndash October 31, 1986) was an American physicist and chemist The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by 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. Spectroscopy was originally the study of the interaction between Radiation and Matter as a function of Wavelength (λ This approach is the conceptional basis of the Hartree-Fock method and further post Hartree-Fock methods. In Computational physics and Computational chemistry, the Hartree-Fock ( HF) method is an approximate method for the determination of the ground-state 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. Density functional theory (DFT is a quantum mechanical theory used in Physics and Chemistry to investigate the Electronic structure (principally In Quantum mechanics, 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 Llewellyn Hilleth Thomas ( 31 October 1903 - 20 April 1992) was a British Physicist and applied mathematician. Year 1927 ( MCMXXVII) was a Common year starting on Saturday (link will display full calendar of the Gregorian calendar. 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. In Quantum mechanics, and in particular Quantum chemistry, the electronic density is a probabilistic measure of the number of Electrons occupying A wave function or wavefunction is a mathematical tool used in Quantum mechanics to describe any physical system 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. In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by The term macromolecule by definition implies "large Molecule " Computational chemistry is a branch of Chemistry that uses computers to assist in solving 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. In Physics, especially Quantum mechanics, the Schrödinger equation is an equation that describes how the Quantum state of a Physical system In Atomic molecular and optical physics as well as in Quantum chemistry, molecular Hamiltonian is the name given to the Hamiltonian representing the 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). In Physics, the adjective semiclassical has different precise meanings depending on the context Classical mechanics is used for describing the motion of Macroscopic objects from Projectiles to parts of Machinery, as well as Astronomical objects Molecular dynamics ( MD) is a form of Computer simulation in which atoms and molecules are allowed to interact for a period of time by approximations of Statistical approaches, using for example Monte Carlo methods, are also possible. Monte Carlo methods are a class of Computational Algorithms that rely on repeated Random sampling to compute their results

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. In Atomic molecular and optical physics as well as in Quantum chemistry, molecular Hamiltonian is the name given to the Hamiltonian representing the In Physics, a scalar is a simple Physical quantity that is not changed by Coordinate system rotations or translations (in Newtonian mechanics or The Mathematical study of potentials is known as Potential theory; it is the study of Harmonic functions on Manifolds This mathematical A potential energy surface is generally used within the adiabatic or Born–Oppenheimer approximation in Quantum mechanics and Statistical mechanics This is the Born-Oppenheimer approximation introduced by Born and Oppenheimer in 1927. In Quantum chemistry, the computation of the energy and Wavefunction of an average-size Molecule is a formidable task that is alleviated by the Born-Oppenheimer Max Born (11 December 1882 &ndash 5 January 1970 was a German Physicist and Mathematician who was instrumental in the development of Quantum Year 1927 ( MCMXXVII) was a Common year starting on Saturday (link will display full calendar of the Gregorian calendar. 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. Year 1928 ( MCMXXVIII) was a Leap year starting on Sunday (link will display full calendar of the Gregorian calendar. This theory of chemical Reactivity was developed by Rice and Ramsperger in 1927 and Kassel in 1928 (the RRK theory Year 1952 ( MCMLII) was a Leap year starting on Tuesday (link will display full calendar of the Gregorian calendar. Rudolph "Rudy" Arthur Marcus (born July 21 1923 is an American chemist who 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 in – December 26, 1981 in Salt Lake City Utah) was a Mexican -born American Year 1935 ( MCMXXXV) was a Common year starting on Tuesday (link will display full calendar of the Gregorian calendar. These methods enable simple estimates of unimolecular reaction rates from a few characteristics of the potential surface. The reaction rate or rate of reaction for a Reactant or product in a particular reaction is intuitively defined as how fast a reaction takes

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). In Theoretical chemistry, the vibronic coupling terms (which are neglected within the Born-Oppenheimer approximation) are proportional to the interaction between In Quantum physics, a quantum state is a mathematical object that fully describes a quantum system. 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. This article is about the physicist for his grandfather the Swiss artist see Ernst Alfred Stueckelberg Ernst Carl Gerlach Stueckelberg ( Lev Davidovich Landau ( Russian language: Ле́в Дави́дович Ланда́у ( January 22, 1908 &ndash April 1, 1968 Clarence Melvin Zener ( December 1, 1905 – July 15, 1993) was the American Physicist who first described the electrical Year 1930 ( MCMXXX) was a Common year starting on Wednesday (link will display 1930 calendar of the Gregorian calendar. The Landau–Zener formula is an analytic solution to the equations of motion governing the transition dynamics of a 2- level quantum mechanical system with a time-dependent Their formula allows the transition probability between two diabatic potential curves in the neighborhood of an avoided crossing to be calculated. See also Adiabatic process, a concept in Thermodynamics In Quantum chemistry, the Potential energy surfaces are obtained Avoided crossing (sometimes misleadingly called intended crossing)

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. In quantum field theory (QFT the forces between particles are mediated by other particles One of the first and most fundamentally explicit appearances of this is seen in the theory of the photomagneton. The photomagneton is a theoretical treatment of the Unitary group in Quantum field theory and Quantum chemistry that effectively describes the experimentally 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. In Physics and Chemistry, plasma is an Ionized Gas, in which a certain proportion of Electrons are free rather than being bound In Physics, quantization is a procedure for constructing a Quantum field theory starting from a classical field theory. In Particle physics, bosons are particles which obey Bose-Einstein statistics; they are named after Satyendra Nath Bose and Albert Einstein However, quantum field theory is of interest in many fields of chemistry, including: nuclear chemistry, astrochemistry, sonochemistry, and quantum hydrodynamics. Nuclear chemistry is a subfield of Chemistry dealing with Radioactivity, nuclear processes and nuclear properties Astrochemistry is the study of the Chemical elements found in outer space generally on larger scales than the Solar System, particularly in molecular gas clouds 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. Field theoretic methods have also been critical in developing the ab initio Effective Hamiltonian theory of semi-empirical pi-electron methods.

External links

Nobel lectures by quantum chemists

References

^ Quantum Chemistry. The NIH Guide to Molecular Modeling. National Institutes of Health. "NIH" redirects here For other meanings of NIH see NIH (disambiguation. Retrieved on 2007-09-08. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 70 - Roman forces under Titus sack Jerusalem. 1264 - The Statute of Kalisz

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