Simulatedelectron localization function (ELF) map of afuran (C₄H₄O)molecule. Colour indicates the magnitude of the ELF field, which reflects the degree of electron localisation at each point in the molecular plane.
Quantum chemistry, also calledmolecular quantum mechanics, is a branch ofphysical chemistry focused on the application ofquantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions to physical and chemical properties ofmolecules,materials, and solutions at the atomic level.[1] These calculations include systematically applied approximations intended to make calculations computationally feasible while still capturing as much information about important contributions to the computedwave functions as well as to observable properties such as structures, spectra, andthermodynamic properties. Quantum chemistry is also concerned with the computation of quantum effects onmolecular dynamics andchemical kinetics.
Understandingelectronic structure andmolecular dynamics through the development of computational solutions to theSchrödinger equation 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.[2]
Some view the birth of quantum chemistry as starting with the discovery of theSchrödinger equation and its application to the hydrogen atom. However, a 1927 article ofWalter Heitler (1904–1981),Fritz London and Vincent Raphael Kwok, is often recognized as the first milestone in the history of quantum chemistry.[3] This was the first application of quantum mechanics to the diatomichydrogen molecule, and thus to the phenomenon of the chemical bond.[4] However, prior to this a critical conceptual framework was provided byGilbert N. Lewis in his 1916 paperThe Atom and the Molecule,[5] wherein Lewis developed the first working model ofvalence electrons. Important contributions were also made by Yoshikatsu Sugiura[6][7] and S.C. Wang.[8] A series of articles byLinus Pauling, written throughout the 1930s, integrated the work of Heitler, London, Sugiura, Wang, Lewis, andJohn C. Slater on the concept of valence and its quantum-mechanical basis into a new theoretical framework.[9] Many chemists were introduced to the field of quantum chemistry by Pauling's 1939 textThe Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry, wherein he summarized this work (referred to widely now asvalence bond theory) and explained quantum mechanics in a way which could be followed by chemists.[10] The text soon became a standard text at many universities.[11] In 1937,Hans Hellmann appears to have been the first to publish a book on quantum chemistry, in the Russian[12] and German languages.[13]
Theelectronic structure of an atom or molecule is thequantum state of its electrons.[14] The first step in solving a quantum chemical problem is usually solving theSchrödinger equation (orDirac equation inrelativistic quantum chemistry) with theelectronic molecular Hamiltonian, usually making use of the Born–Oppenheimer (B–O) approximation. This is called determining the electronic structure of the molecule.[15] An exact solution for the non-relativistic Schrödinger equation can only be obtained for the hydrogen atom (though exact solutions for the bound state energies of thehydrogen molecular ion within the B-O approximation have been identified in terms of thegeneralized Lambert W function). Since all other atomic and molecular systems involve the motions of three or more "particles", their Schrödinger equations cannot be solved analytically and so approximate and/or computational solutions must be sought. The process of seeking computational solutions to these problems is part of the field known ascomputational chemistry.[2]
As mentioned above, Heitler and London's method was extended by Slater and Pauling to become the valence-bond (VB) method. In this method, attention is primarily devoted to the pairwise interactions between atoms, and this method therefore correlates closely with classical chemists' drawings ofbonds. 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 oforbital hybridization andresonance.[16]
A covalent bond is formed when there is an overlap of half-filled atomic orbitals from two atoms, which together form an electron pair. The strength and energy of the system is dependent on the amount of overlap. As the atoms move together, they begin to overlap their orbitals and the electrons begin to feel the attraction of the other's nucleus. There is also a repulsion that begins to occur, which becomes too strong when the atoms are two close together. The ideal and most stable length between the two atoms is the bond distance, which is the combined repulsive and attractive forces resulting in the lowest energy configuration.
Orientation of the orbitals can have a great affect on which bond is formed if any is formed. When there is a direct overlap of one atomic orbital from each atom, a sigma (σ) bond is formed. This can be created from two s-orbitals, an s-orbital and a p-orbital, or two p-orbitals. A pi (π) bond is formed from a side-to-side overlap of two p-orbitals. The pi bond only forms if the phases of the overlapping p-orbitals are the same.[17]
An alternative approach to valence bond theory was developed in 1929 byFriedrich Hund andRobert S. Mulliken, in whichelectrons are described by mathematical functions delocalized over an entiremolecule. The Hund–Mulliken approach or molecular orbital (MO) method is less intuitive to chemists but predictsspectroscopic properties better than the VB method. As opposed to VB theory, MO theory does not focus just the overlap of electron density in one area causing a bond but instead describes the whole molecule as one system. This leads to a more complex understanding of the system. This approach is the conceptual basis of theHartree–Fock method and furtherpost-Hartree–Fock methods.[2]
MO calculations result in orbitals or wavefunctions and energies for a molecule, which can be filled with electrons from two different atomic orbitals. These atomic orbitals come from separate atoms resulting in molecular orbitals being linear combinations of atomic orbitals.
TheThomas–Fermi model was developed independently byThomas andFermi in 1927. This was the first attempt to describe many-electron systems on the basis ofelectronic density instead ofwave 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 theKohn–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 thann3 with respect ton basis functions, for the pure functionals) allow it to tackle largerpolyatomic molecules and evenmacromolecules. This computational affordability and often comparable accuracy toMP2 andCCSD(T) (post-Hartree–Fock methods) has made it one of the most popular methods incomputational chemistry.[18]
A further step can consist of solving theSchrödinger equation with the totalmolecular Hamiltonian in order to study the motion of molecules. Direct solution of the Schrödinger equation is calledquantum dynamics, whereas its solution within thesemiclassical approximation is calledsemiclassical dynamics. Purelyclassical simulations of molecular motion are referred to asmolecular dynamics (MD). Another approach to dynamics is a hybrid framework known asmixed quantum-classical dynamics; yet another hybrid framework uses theFeynman path integral formulation to add quantum corrections to molecular dynamics, which is calledpath integral molecular dynamics. Statistical approaches, using for example classical and quantumMonte Carlo methods, are also possible and are particularly useful for describing equilibrium distributions of states.[2]
In adiabatic dynamics, interatomic interactions are represented by singlescalarpotentials calledpotential energy surfaces. This is theBorn–Oppenheimer approximation introduced byBorn andOppenheimer in 1927. Pioneering applications of this in chemistry were performed by Rice and Ramsperger in 1927 and Kassel in 1928, and generalized into theRRKM theory in 1952 byMarcus who took thetransition state theory developed byEyring in 1935 into account. These methods enable simple estimates of unimolecularreaction rates from a few characteristics of the potential surface.[2]
Non-adiabatic dynamics consists of taking the interaction between several coupled potential energy surfaces (corresponding to different electronicquantum states of the molecule). The coupling terms are called vibronic couplings. The pioneering work in this field was done byStueckelberg,Landau, andZener in the 1930s, in their work on what is now known as theLandau–Zener transition. Their formula allows the transition probability between twoadiabatic potential curves in the neighborhood of anavoided crossing to be calculated.Spin-forbidden reactions are one type of non-adiabatic reactions where at least one change inspin state occurs when progressing fromreactant toproduct.[2]
^McQuarrie, Donald A. (2007).Quantum Chemistry (2nd ed.). University Science Books.ISBN978-1891389504.
^abcdefMcQuarrie, Donald A.; Simon, John D. (200).Physical chemistry: a molecular approach. Sausalito, Calif: Univ. Science Books.ISBN978-0-935702-99-6.{{cite book}}:ISBN / Date incompatibility (help)
^Pauling, Linus (1939).The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry (1st ed.). Cornell University Press.
^Martin, Richard M. (2008-10-27).Electronic Structure: Basic Theory and Practical Methods. Cambridge: Cambridge University Press.ISBN978-0-521-53440-6.
^Shaik, S.S.; Hiberty, P.C. (2007).A Chemist's Guide to Valence Bond Theory. Wiley-Interscience.ISBN978-0470037355.
Gavroglu, Kostas; Simões, Ana (2011).Neither Physics nor Chemistry: A History of Quantum Chemistry. MIT Press.ISBN978-0-262-01618-6.
Karplus, M.; Porter, R. N. (1971).Atoms and Molecules: An Introduction for Students of Physical Chemistry. Benjamin–Cummings Publishing Company.ISBN978-0-8053-5218-4.
Pauling, L.; Wilson, E. B. (1963) [1935].Introduction to Quantum Mechanics with Applications to Chemistry. Dover Publications.ISBN0-486-64871-0.{{cite book}}:ISBN / Date incompatibility (help)
