Density functional theoryDensity-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function. In the case of DFT, these are functionals of the spatially dependent electron density.
Metal–organic frameworkMetal–organic frameworks (MOFs) are a class of compounds consisting of metal clusters (also known as SBUs) coordinated to organic ligands to form one-, two-, or three-dimensional structures. The organic ligands included are sometimes referred to as "struts" or "linkers", one example being 1,4-benzenedicarboxylic acid (BDC). More formally, a metal–organic framework is an organic-inorganic porous extended structure. An extended structure is a structure whose sub-units occur in a constant ratio and are arranged in a repeating pattern.
Functional analysisFunctional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, inner product, norm, or topology) and the linear functions defined on these spaces and suitably respecting these structures. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining, for example, continuous or unitary operators between function spaces.
Functional (mathematics)In mathematics, a functional (as a noun) is a certain type of function. The exact definition of the term varies depending on the subfield (and sometimes even the author). In linear algebra, it is synonymous with linear forms, which are linear mappings from a vector space into its field of scalars (that is, they are elements of the dual space ) In functional analysis and related fields, it refers more generally to a mapping from a space into the field of real or complex numbers.
Linear formIn mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars (often, the real numbers or the complex numbers). If V is a vector space over a field k, the set of all linear functionals from V to k is itself a vector space over k with addition and scalar multiplication defined pointwise. This space is called the dual space of V, or sometimes the algebraic dual space, when a topological dual space is also considered.
Binding energyIn physics and chemistry, binding energy is the smallest amount of energy required to remove a particle from a system of particles or to disassemble a system of particles into individual parts. In the former meaning the term is predominantly used in condensed matter physics, atomic physics, and chemistry, whereas in nuclear physics the term separation energy is used. A bound system is typically at a lower energy level than its unbound constituents.
Ab initio quantum chemistry methodsAb initio quantum chemistry methods are computational chemistry methods based on quantum chemistry. The term ab initio was first used in quantum chemistry by Robert Parr and coworkers, including David Craig in a semiempirical study on the excited states of benzene. The background is described by Parr. Ab initio means "from first principles" or "from the beginning", implying that the only inputs into an ab initio calculation are physical constants.
Molecular mechanicsMolecular mechanics uses classical mechanics to model molecular systems. The Born–Oppenheimer approximation is assumed valid and the potential energy of all systems is calculated as a function of the nuclear coordinates using force fields. Molecular mechanics can be used to study molecule systems ranging in size and complexity from small to large biological systems or material assemblies with many thousands to millions of atoms.
Minkowski functionalIn mathematics, in the field of functional analysis, a Minkowski functional (after Hermann Minkowski) or gauge function is a function that recovers a notion of distance on a linear space. If is a subset of a real or complex vector space then the or of is defined to be the function valued in the extended real numbers, defined by where the infimum of the empty set is defined to be positive infinity (which is a real number so that would then be real-valued).
Nuclear binding energyNuclear binding energy in experimental physics is the minimum energy that is required to disassemble the nucleus of an atom into its constituent protons and neutrons, known collectively as nucleons. The binding energy for stable nuclei is always a positive number, as the nucleus must gain energy for the nucleons to move apart from each other. Nucleons are attracted to each other by the strong nuclear force. In theoretical nuclear physics, the nuclear binding energy is considered a negative number.
