Quantum chemistry, also called molecular quantum mechanics, is a branch of
physical chemistry
Physical chemistry is the study of macroscopic and microscopic phenomena in chemical systems in terms of the principles, practices, and concepts of physics such as motion, energy, force, time, thermodynamics, quantum chemistry, statistica ...
focused on the application of
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions to physical and chemical properties of
molecules
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bio ...
,
materials, and solutions at the atomic level. These calculations include systematically applied approximations intended to make calculations computationally feasible while still capturing as much information about important contributions to the computed
wave functions as well as to observable properties such as structures, spectra, and thermodynamic properties. Quantum chemistry is also concerned with the computation of quantum effects on
molecular dynamics
Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of th ...
and
chemical kinetics
Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with chemical thermodynamics, which deals with the direction in ...
.
Chemists rely heavily on
spectroscopy
Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter ...
through which information regarding the
quantization of energy on a molecular scale can be obtained. Common methods are
infra-red (IR) spectroscopy,
nuclear magnetic resonance (NMR) spectroscopy, and
scanning probe microscopy. Quantum chemistry may be applied to the prediction and verification of spectroscopic data as well as other experimental data.
Many quantum chemistry studies are focused on the electronic
ground state and
excited states of individual atoms and molecules as well as the study of reaction pathways and
transition state
In chemistry, the transition state of a chemical reaction is a particular configuration along the reaction coordinate. It is defined as the state corresponding to the highest potential energy along this reaction coordinate. It is often marked ...
s that occur during
chemical reaction
A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking ...
s. Spectroscopic properties may also be predicted. Typically, such studies assume the electronic wave function is adiabatically parameterized by the nuclear positions (i.e., the
Born–Oppenheimer approximation
In quantum chemistry and molecular physics, the Born–Oppenheimer (BO) approximation is the best-known mathematical approximation in molecular dynamics. Specifically, it is the assumption that the wave functions of atomic nuclei and elect ...
). A wide variety of approaches are used, including
semi-empirical
Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and ...
methods,
density functional theory,
Hartree-Fock calculations, quantum
Monte Carlo
Monte Carlo (; ; french: Monte-Carlo , or colloquially ''Monte-Carl'' ; lij, Munte Carlu ; ) is officially an administrative area of the Principality of Monaco, specifically the ward of Monte Carlo/Spélugues, where the Monte Carlo Casino is ...
methods, and
coupled cluster
Coupled cluster (CC) is a numerical technique used for describing many-body systems. Its most common use is as one of several post-Hartree–Fock ab initio quantum chemistry methods in the field of computational chemistry, but it is also used in ...
methods.
Understanding
electronic structure and
molecular dynamics
Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of th ...
through the development of computational solutions to the
Schrödinger equation
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of th ...
is a central goal of quantum chemistry. Progress in the field depends on overcoming several challenges, including the need to increase the accuracy of the results for small molecular systems, and to also increase the size of large molecules that can be realistically subjected to computation, which is limited by scaling considerations — the computation time increases as a power of the number of atoms.
History
Some view the birth of quantum chemistry as starting with the discovery of the
Schrödinger equation
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of th ...
and its application to the hydrogen atom in 1926. However, the 1927 article of
Walter Heitler
Walter Heinrich Heitler (; 2 January 1904 – 15 November 1981) was a German physicist who made contributions to quantum electrodynamics and quantum field theory. He brought chemistry under quantum mechanics through his theory of valence bo ...
(1904–1981) and
Fritz London, is often recognized as the first milestone in the history of quantum chemistry. This is the first application of quantum mechanics to the diatomic hydrogen molecule, and thus to the phenomenon of the chemical bond. In the following years much progress was accomplished by
Robert S. Mulliken,
Max Born
Max Born (; 11 December 1882 – 5 January 1970) was a German physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a ...
,
J. Robert Oppenheimer,
Linus Pauling
Linus Carl Pauling (; February 28, 1901August 19, 1994) was an American chemist, biochemist, chemical engineer, peace activist, author, and educator. He published more than 1,200 papers and books, of which about 850 dealt with scientific topi ...
,
Erich Hückel
Erich Armand Arthur Joseph Hückel (August 9, 1896, Berlin – February 16, 1980, Marburg) was a German physicist and physical chemist. He is known for two major contributions:
*The Debye–Hückel theory of electrolytic solutions
*The Hücke ...
,
Douglas Hartree
Douglas Rayner Hartree (27 March 1897 – 12 February 1958) was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree–Fock equations of atomic physics and the c ...
,
Vladimir Fock, to cite a few. The history of quantum chemistry also goes through the 1838 discovery of
cathode rays by
Michael Faraday
Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic inducti ...
, the 1859 statement of the
black-body radiation
Black-body radiation is the thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body (an idealized opaque, non-reflective body). It has a specific, continuous spe ...
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
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
''ν'' with which they each individually radiate
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of ...
and 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
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theor ...
postulated, based on Planck's quantum hypothesis, that light itself consists of individual quantum particles, which later came to be called
photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they alwa ...
s (1926). In the years to follow, this theoretical basis slowly began to be applied to chemical structure, reactivity, and bonding. Probably the greatest contribution to the field was made by
Linus Pauling
Linus Carl Pauling (; February 28, 1901August 19, 1994) was an American chemist, biochemist, chemical engineer, peace activist, author, and educator. He published more than 1,200 papers and books, of which about 850 dealt with scientific topi ...
.
Electronic structure
The first step in solving a quantum chemical problem is usually solving the
Schrödinger equation
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of th ...
(or
Dirac equation in
relativistic quantum chemistry
Relativistic quantum chemistry combines relativistic mechanics with quantum chemistry to calculate elemental properties and structure, especially for the heavier elements of the periodic table. A prominent example is an explanation for the color of ...
) 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. An exact solution for the Schrödinger equation can only be obtained for the hydrogen atom (though exact solutions for the bound state energies of the
hydrogen molecular ion
The dihydrogen cation or hydrogen molecular ion is a cation (positive ion) with formula . It consists of two hydrogen nuclei (protons) sharing a single electron. It is the simplest molecular ion.
The ion can be formed from the ionization of a ne ...
have been identified in terms of the
generalized Lambert W function). Since all other atomic, or molecular systems, involve the motions of three or more "particles", their Schrödinger equations cannot be solved exactly and so approximate solutions must be sought.
Valence bond
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
Walter Heinrich Heitler (; 2 January 1904 – 15 November 1981) was a German physicist who made contributions to quantum electrodynamics and quantum field theory. He brought chemistry under quantum mechanics through his theory of valence bo ...
and
Fritz London on the hydrogen (H
2) molecule in 1927. Heitler and London's method was extended by the American theoretical physicist
John C. Slater
John Clarke Slater (December 22, 1900 – July 25, 1976) was a noted American physicist who made major contributions to the theory of the electronic structure of atoms, molecules and solids. He also made major contributions to microwave electroni ...
and the American theoretical chemist
Linus Pauling
Linus Carl Pauling (; February 28, 1901August 19, 1994) was an American chemist, biochemist, chemical engineer, peace activist, author, and educator. He published more than 1,200 papers and books, of which about 850 dealt with scientific topi ...
to become the valence-bond (VB)
r 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. It focuses on how the atomic orbitals of an atom combine to give individual chemical bonds when a molecule is formed, incorporating the two key concepts of
orbital hybridization
In chemistry, orbital hybridisation (or hybridization) is the concept of mixing atomic orbitals to form new ''hybrid orbitals'' (with different energies, shapes, etc., than the component atomic orbitals) suitable for the pairing of electrons to ...
and
resonance
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscil ...
.
Molecular orbital
An alternative approach was developed in 1929 by
Friedrich Hund and
Robert S. Mulliken, in which
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have n ...
s are described by mathematical functions delocalized over an entire
molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and b ...
. 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 conceptual basis of the
Hartree–Fock method and further
post Hartree–Fock methods.
Density functional theory
The
Thomas–Fermi model was developed independently by
Thomas
Thomas may refer to:
People
* List of people with given name Thomas
* Thomas (name)
* Thomas (surname)
* Saint Thomas (disambiguation)
* Thomas Aquinas (1225–1274) Italian Dominican friar, philosopher, and Doctor of the Church
* Thomas the A ...
and
Fermi
Enrico Fermi (; 29 September 1901 – 28 November 1954) was an Italian (later naturalized American) physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the nuclear age" and t ...
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 (DFT). Modern day DFT uses the
Kohn–Sham method, where the density functional is split into four terms; the Kohn–Sham kinetic energy, an external potential, exchange and correlation energies. A large part of the focus on developing DFT is on improving the exchange and correlation terms. Though this method is less developed than post Hartree–Fock methods, its significantly lower computational requirements (scaling typically no worse than ''n''
3 with respect to ''n'' basis functions, for the pure functionals) allow it to tackle larger
polyatomic molecules and even
macromolecules. This computational affordability and often comparable accuracy to
MP2 and
CCSD(T) (post-Hartree–Fock methods) has made it one of the most popular methods in
computational chemistry.
Chemical dynamics
A further step can consist of solving the
Schrödinger equation
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of th ...
with the total
molecular Hamiltonian
In atomic, molecular, and optical physics and quantum chemistry, the molecular Hamiltonian is the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule. This operator and the associated Schrödinger equation pl ...
in order to study the motion of molecules. Direct solution of the Schrödinger equation is called ''
quantum dynamics'', whereas its solution within the
semiclassical approximation is called ''semiclassical dynamics.'' Purely
classical simulations of molecular motion are referred to as ''
molecular dynamics
Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of th ...
(MD)''. Another approach to dynamics is a hybrid framework known as ''
mixed quantum-classical dynamics;'' yet another hybrid framework uses the
Feynman path integral
The path integral formulation is a description in quantum mechanics that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional ...
formulation to add quantum corrections to molecular dynamics, which is called
path integral molecular dynamics. Statistical approaches, using for example classical and quantum
Monte Carlo method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deter ...
s, are also possible and are particularly useful for describing equilibrium distributions of states.
Adiabatic chemical dynamics
In adiabatic dynamics, interatomic interactions are represented by single
scalar potentials called
potential energy surfaces. This is the
Born–Oppenheimer approximation
In quantum chemistry and molecular physics, the Born–Oppenheimer (BO) approximation is the best-known mathematical approximation in molecular dynamics. Specifically, it is the assumption that the wave functions of atomic nuclei and elect ...
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
In chemistry, the transition state of a chemical reaction is a particular configuration along the reaction coordinate. It is defined as the state corresponding to the highest potential energy along this reaction coordinate. It is often marked ...
theory developed by
Eyring in 1935 into account. These methods enable simple estimates of unimolecular
reaction rates
The reaction rate or rate of reaction is the speed at which a chemical reaction takes place, defined as proportional to the increase in the concentration of a product per unit time and to the decrease in the concentration of a reactant per unit ...
from a few characteristics of the potential surface.
Non-adiabatic chemical dynamics
Non-adiabatic dynamics consists of taking the interaction between several coupled potential energy surface (corresponding to different electronic
quantum state
In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution i ...
s of the molecule). The coupling terms are called vibronic couplings. The pioneering work in this field was done by
Stueckelberg,
Landau
Landau ( pfl, Landach), officially Landau in der Pfalz, is an autonomous (''kreisfrei'') town surrounded by the Südliche Weinstraße ("Southern Wine Route") district of southern Rhineland-Palatinate, Germany. It is a university town (since 1990 ...
, 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.
Spin-forbidden reactions are one type of non-adiabatic reactions where at least one change in
spin state occurs when progressing from
reactant to
product.
See also
*
Atomic physics
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned wit ...
*
Computational chemistry
*
Condensed matter physics
*
Car–Parrinello molecular dynamics
*
Electron localization function
*
International Academy of Quantum Molecular Science
*
Molecular modelling
*
Physical chemistry
Physical chemistry is the study of macroscopic and microscopic phenomena in chemical systems in terms of the principles, practices, and concepts of physics such as motion, energy, force, time, thermodynamics, quantum chemistry, statistica ...
*
List of quantum chemistry and solid-state physics software
*
QMC@Home
* ''
Quantum Aspects of Life''
*
Quantum electrochemistry
The scientific school of Quantum electrochemistry began to form in the 1960s under Revaz Dogonadze. Generally speaking, the field comprises the notions arising in electrodynamics, quantum mechanics, and electrochemistry; and so is studied by a ve ...
*
Relativistic quantum chemistry
Relativistic quantum chemistry combines relativistic mechanics with quantum chemistry to calculate elemental properties and structure, especially for the heavier elements of the periodic table. A prominent example is an explanation for the color of ...
*
Theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...
*
Spin forbidden reactions
References
*
*
*
*
* Gavroglu, Kostas; Ana Simões: ''Neither Physics nor Chemistry: A History of Quantum Chemistry'', MIT Press, 2011,
* Karplus M., Porter R.N. (1971). ''Atoms and Molecules. An introduction for students of physical chemistry'', Benjamin–Cummings Publishing Company,
*
*
*
*
*
*
* Considers the extent to which chemistry and especially the periodic system has been reduced to quantum mechanics.
*
*
External links
The Sherrill Group – NotesChemViz Curriculum Support ResourcesEarly ideas in the history of quantum chemistry
{{DEFAULTSORT:Quantum Chemistry