title: Density functional theory

text: Despite recent improvements, there are still difficulties in using density functional theory to properly describe: intermolecular interactions (of critical importance to understanding chemical reactions), especially van der Waals forces (dispersion); charge transfer excitations; transition states, global potential energy surfaces, dopant interactions and some strongly correlated systems; and in calculations of the band gap and ferromagnetism in semiconductors. The incomplete treatment of dispersion can adversely affect the accuracy of DFT (at least when used alone and uncorrected) in the treatment of systems which are dominated by dispersion (e.g. interacting noble gas atoms) or where dispersion competes significantly with other effects (e.g. in biomolecules). The development of new DFT methods designed to overcome this problem, by alterations to the functional or by the inclusion of additive terms, is a current research topic. Classical density functional theory uses a similar formalism to calculate properties of non-uniform classical fluids.


title: Density functional theory

text: Despite the current popularity of these alterations or of the inclusion of additional terms, they are reported to stray away from the search for the exact functional. Further, DFT potentials obtained with adjustable parameters are no longer true DFT potentials, given that they are not functional derivatives of the exchange correlation energy with respect to the charge density. Consequently, it is not clear if the second theorem of DFT holds in such conditions.


title: Density functional theory

text: In the context of computational materials science, "ab initio" (from first principles) DFT calculations allow the prediction and calculation of material behavior on the basis of quantum mechanical considerations, without requiring higher-order parameters such as fundamental material properties. In contemporary DFT techniques the electronic structure is evaluated using a potential acting on the system's electrons. This DFT potential is constructed as the sum of external potentials , which is determined solely by the structure and the elemental composition of the system, and an effective potential , which represents interelectronic interactions. Thus, a problem for a representative supercell of a material with electrons can be studied as a set of one-electron Schrödinger-like equations, which are also known as Kohn–Sham equations.


title: Density functional theory

text: Although density functional theory has its roots in the Thomas–Fermi model for the electronic structure of materials, DFT was first put on a firm theoretical footing by Walter Kohn and Pierre Hohenberg in the framework of the two Hohenberg–Kohn theorems (HK). The original HK theorems held only for non-degenerate ground states in the absence of a magnetic field, although they have since been generalized to encompass these.


title: Density functional theory

text: The first HK theorem demonstrates that the ground-state properties of a many-electron system are uniquely determined by an electron density that depends on only three spatial coordinates. It set down the groundwork for reducing the many-body problem of electrons with spatial coordinates to three spatial coordinates, through the use of functionals of the electron density. This theorem has since been extended to the time-dependent domain to develop time-dependent density functional theory (TDDFT), which can be used to describe excited states.


title: Density functional theory

text: The second HK theorem defines an energy functional for the system and proves that the ground-state electron density minimizes this energy functional.


title: Density functional theory

text: In work that later won them the Nobel prize in chemistry, the HK theorem was further developed by Walter Kohn and Lu Jeu Sham to produce Kohn–Sham DFT (KS DFT). Within this framework, the intractable many-body problem of interacting electrons in a static external potential is reduced to a tractable problem of noninteracting electrons moving in an effective potential. The effective potential includes the external potential and the effects of the Coulomb interactions between the electrons, e.g., the exchange and correlation interactions. Modeling the latter two interactions becomes the difficulty within KS DFT. The simplest approximation is the local-density approximation (LDA), which is based upon exact exchange energy for a uniform electron gas, which can be obtained from the Thomas–Fermi model, and from fits to the correlation energy for a uniform electron gas. Non-interacting systems are relatively easy to solve, as the wavefunction can be represented as a Slater determinant of orbitals. Further, the kinetic energy functional of such a system is known exactly. The exchange–correlation part of the total energy functional remains unknown and must be approximated.


title: Density functional theory

text: Another approach, less popular than KS DFT but arguably more closely related to the spirit of the original HK theorems, is orbital-free density functional theory (OFDFT), in which approximate functionals are also used for the kinetic energy of the noninteracting system.


title: Density functional theory

text: As usual in many-body electronic structure calculations, the nuclei of the treated molecules or clusters are seen as fixed (the Born–Oppenheimer approximation), generating a static external potential , in which the electrons are moving. A stationary electronic state is then described by a wavefunction satisfying the many-electron time-independent Schrödinger equation


title: Density functional theory

text: where, for the -electron system, is the Hamiltonian, is the total energy, formula_2 is the kinetic energy, formula_3 is the potential energy from the external field due to positively charged nuclei, and is the electron–electron interaction energy. The operators formula_2 and are called universal operators, as they are the same for any -electron system, while formula_3 is system-dependent. This complicated many-particle equation is not separable into simpler single-particle equations because of the interaction term .


title: Density functional theory

text: There are many sophisticated methods for solving the many-body Schrödinger equation based on the expansion of the wavefunction in Slater determinants. While the simplest one is the Hartree–Fock method, more sophisticated approaches are usually categorized as post-Hartree–Fock methods. However, the problem with these methods is the huge computational effort, which makes it virtually impossible to apply them efficiently to larger, more complex systems.


title: Density functional theory

text: Here DFT provides an appealing alternative, being much more versatile, as it provides a way to systematically map the many-body problem, with , onto a single-body problem without . In DFT the key variable is the electron density , which for a normalized is given by


title: Density functional theory

text: This relation can be reversed, i.e., for a given ground-state density it is possible, in principle, to calculate the corresponding ground-state wavefunction . In other words, is a unique functional of ,


title: Density functional theory

text: where the contribution of the external potential formula_10 can be written explicitly in terms of the ground-state density formula_11:


title: Density functional theory

text: More generally, the contribution of the external potential formula_13 can be written explicitly in terms of the density formula_14:


title: Density functional theory

text: The functionals and are called universal functionals, while is called a non-universal functional, as it depends on the system under study. Having specified a system, i.e., having specified formula_3, one then has to minimize the functional


title: Density functional theory

text: with respect to , assuming one has reliable expressions for and . A successful minimization of the energy functional will yield the ground-state density and thus all other ground-state observables.


title: Density functional theory

text: The variational problems of minimizing the energy functional can be solved by applying the Lagrangian method of undetermined multipliers. First, one considers an energy functional that does not explicitly have an electron–electron interaction energy term,


title: Density functional theory

text: where formula_19 denotes the kinetic-energy operator, and formula_20 is an effective potential in which the particles are moving. Based on formula_21, Kohn–Sham equations of this auxiliary noninteracting system can be derived:


title: Density functional theory

text: where formula_25 is the external potential, the second term is the Hartree term describing the electron–electron Coulomb repulsion, and the last term is the exchange–correlation potential. Here, includes all the many-particle interactions. Since the Hartree term and depend on , which depends on the , which in turn depend on , the problem of solving the Kohn–Sham equation has to be done in a self-consistent (i.e., iterative) way. Usually one starts with an initial guess for , then calculates the corresponding and solves the Kohn–Sham equations for the . From these one calculates a new density and starts again. This procedure is then repeated until convergence is reached. A non-iterative approximate formulation called Harris functional DFT is an alternative approach to this.


title: Density functional theory

text: The same theorems can be proven in the case of relativistic electrons, thereby providing generalization of DFT for the relativistic case. Unlike the nonrelativistic theory, in the relativistic case it is possible to derive a few exact and explicit formulas for the relativistic density functional.


title: Density functional theory

text: Let one consider an electron in a hydrogen-like ion obeying the relativistic Dirac equation. The Hamiltonian for a relativistic electron moving in the Coulomb potential can be chosen in the following form (atomic units are used):


title: Density functional theory

text: where is the Coulomb potential of a pointlike nucleus, is a momentum operator of the electron, and , and are the elementary charge, electron mass and the speed of light respectively, and finally and are a set of Dirac 2 × 2 matrices:


title: Density functional theory

text: where is a four-component wavefunction, and is the associated eigenenergy. It is demonstrated in Brack (1983) that application of the virial theorem to the eigenfunction equation produces the following formula for the eigenenergy of any bound state:


title: Density functional theory

text: and analogously, the virial theorem applied to the eigenfunction equation with the square of the Hamiltonian yields


title: Density functional theory

text: It is easy to see that both of the above formulae represent density functionals. The former formula can be easily generalized for the multi-electron case.


title: Density functional theory

text: One may observe that both of the functionals written above do not have extremals, of course, if a reasonably wide set of functions is allowed for variation. Nevertheless, it is possible to design a density functional with desired extremal properties out of those ones. Let us make it in the following way:


title: Density functional theory

text: where in Kronecker delta symbol of the second term denotes any extremal for the functional represented by the first term of the functional . The second term amounts to zero for any function that is not an extremal for the first term of functional . To proceed further we'd like to find Lagrange equation for this functional. In order to do this, we should allocate a linear part of functional increment when the argument function is altered:


title: Density functional theory

text: Deploying written above equation, it is easy to find the following formula for functional derivative:


title: Density functional theory

text: where , and , and is a value of potential at some point, specified by support of variation function , which is supposed to be infinitesimal. To advance toward Lagrange equation, we equate functional derivative to zero and after simple algebraic manipulations arrive to the following equation:


title: Density functional theory

text: Apparently, this equation could have solution only if . This last condition provides us with Lagrange


title: Density functional theory

text: Solutions of this equation represent extremals for functional . It's easy to see that all real densities,


title: Density functional theory

text: that is, densities corresponding to the bound states of the system in question, are solutions of written above equation, which could be called the Kohn–Sham equation in this particular case. Looking back onto the definition of the functional , we clearly see that the functional produces energy of the system for appropriate density, because the first term amounts to zero for such density and the second one delivers the energy value.


title: Density functional theory

text: The major problem with DFT is that the exact functionals for exchange and correlation are not known, except for the free-electron gas. However, approximations exist which permit the calculation of certain physical quantities quite accurately. One of the simplest approximations is the local-density approximation (LDA), where the functional depends only on the density at the coordinate where the functional is evaluated:


title: Density functional theory

text: The local spin-density approximation (LSDA) is a straightforward generalization of the LDA to include electron spin:


title: Density functional theory

text: In LDA, the exchange–correlation energy is typically separated into the exchange part and the correlation part: . The exchange part is called the Dirac (or sometimes Slater) exchange, which takes the form . There are, however, many mathematical forms for the correlation part. Highly accurate formulae for the correlation energy density have been constructed from quantum Monte Carlo simulations of jellium. A simple first-principles correlation functional has been recently proposed as well. Although unrelated to the Monte Carlo simulation, the two variants provide comparable accuracy.


title: Density functional theory

text: The LDA assumes that the density is the same everywhere. Because of this, the LDA has a tendency to underestimate the exchange energy and over-estimate the correlation energy. The errors due to the exchange and correlation parts tend to compensate each other to a certain degree. To correct for this tendency, it is common to expand in terms of the gradient of the density in order to account for the non-homogeneity of the true electron density. This allows corrections based on the changes in density away from the coordinate. These expansions are referred to as generalized gradient approximations (GGA) and have the following form:


title: Density functional theory

text: Using the latter (GGA), very good results for molecular geometries and ground-state energies have been achieved.


title: Density functional theory

text: Potentially more accurate than the GGA functionals are the meta-GGA functionals, a natural development after the GGA (generalized gradient approximation). Meta-GGA DFT functional in its original form includes the second derivative of the electron density (the Laplacian), whereas GGA includes only the density and its first derivative in the exchange–correlation potential.


title: Density functional theory

text: Functionals of this type are, for example, TPSS and the Minnesota Functionals. These functionals include a further term in the expansion, depending on the density, the gradient of the density and the Laplacian (second derivative) of the density.


title: Density functional theory

text: Difficulties in expressing the exchange part of the energy can be relieved by including a component of the exact exchange energy calculated from Hartree–Fock theory. Functionals of this type are known as hybrid functionals.


title: Density functional theory

text: The DFT formalism described above breaks down, to various degrees, in the presence of a vector potential, i.e. a magnetic field. In such a situation, the one-to-one mapping between the ground-state electron density and wavefunction is lost. Generalizations to include the effects of magnetic fields have led to two different theories: current density functional theory (CDFT) and magnetic field density functional theory (BDFT). In both these theories, the functional used for the exchange and correlation must be generalized to include more than just the electron density. In current density functional theory, developed by Vignale and Rasolt, the functionals become dependent on both the electron density and the paramagnetic current density. In magnetic field density functional theory, developed by Salsbury, Grayce and Harris, the functionals depend on the electron density and the magnetic field, and the functional form can depend on the form of the magnetic field. In both of these theories it has been difficult to develop functionals beyond their equivalent to LDA, which are also readily implementable computationally.


title: Density functional theory

text: In general, density functional theory finds increasingly broad application in chemistry and materials science for the interpretation and prediction of complex system behavior at an atomic scale. Specifically, DFT computational methods are applied for synthesis-related systems and processing parameters. In such systems, experimental studies are often encumbered by inconsistent results and non-equilibrium conditions. Examples of contemporary DFT applications include studying the effects of dopants on phase transformation behavior in oxides, magnetic behavior in dilute magnetic semiconductor materials, and the study of magnetic and electronic behavior in ferroelectrics and dilute magnetic semiconductors. It has also been shown that DFT gives good results in the prediction of sensitivity of some nanostructures to environmental pollutants like sulfur dioxide or acrolein, as well as prediction of mechanical properties.


title: Density functional theory

text: In practice, Kohn–Sham theory can be applied in several distinct ways, depending on what is being investigated. In solid-state calculations, the local density approximations are still commonly used along with plane-wave basis sets, as an electron-gas approach is more appropriate for electrons delocalised through an infinite solid. In molecular calculations, however, more sophisticated functionals are needed, and a huge variety of exchange–correlation functionals have been developed for chemical applications. Some of these are inconsistent with the uniform electron-gas approximation; however, they must reduce to LDA in the electron-gas limit. Among physicists, one of the most widely used functionals is the revised Perdew–Burke–Ernzerhof exchange model (a direct generalized gradient parameterization of the free-electron gas with no free parameters); however, this is not sufficiently calorimetrically accurate for gas-phase molecular calculations. In the chemistry community, one popular functional is known as BLYP (from the name Becke for the exchange part and Lee, Yang and Parr for the correlation part). Even more widely used is B3LYP, which is a hybrid functional in which the exchange energy, in this case from Becke's exchange functional, is combined with the exact energy from Hartree–Fock theory. Along with the component exchange and correlation funсtionals, three parameters define the hybrid functional, specifying how much of the exact exchange is mixed in. The adjustable parameters in hybrid functionals are generally fitted to a "training set" of molecules. Although the results obtained with these functionals are usually sufficiently accurate for most applications, there is no systematic way of improving them (in contrast to some of the traditional wavefunction-based methods like configuration interaction or coupled cluster theory). In the current DFT approach it is not possible to estimate the error of the calculations without comparing them to other methods or experiments.


title: Density functional theory

text: The predecessor to density functional theory was the Thomas–Fermi model, developed independently by both Llewellyn Thomas and Enrico Fermi in 1927. They used a statistical model to approximate the distribution of electrons in an atom. The mathematical basis postulated that electrons are distributed uniformly in phase space with two electrons in every formula_39 of volume. For each element of coordinate space volume formula_40 we can fill out a sphere of momentum space up to the Fermi momentum formula_41


title: Density functional theory

text: Solving for and substituting into the classical kinetic energy formula then leads directly to a kinetic energy represented as a functional of the electron density:


title: Density functional theory

text: As such, they were able to calculate the energy of an atom using this kinetic-energy functional combined with the classical expressions for the nucleus–electron and electron–electron interactions (which can both also be represented in terms of the electron density).


title: Density functional theory

text: Although this was an important first step, the Thomas–Fermi equation's accuracy is limited because the resulting kinetic-energy functional is only approximate, and because the method does not attempt to represent the exchange energy of an atom as a conclusion of the Pauli principle. An exchange-energy functional was added by Paul Dirac in 1928.


title: Density functional theory

text: However, the Thomas–Fermi–Dirac theory remained rather inaccurate for most applications. The largest source of error was in the representation of the kinetic energy, followed by the errors in the exchange energy, and due to the complete neglect of electron correlation.


title: Density functional theory

text: Edward Teller (1962) showed that Thomas–Fermi theory cannot describe molecular bonding. This can be overcome by improving the kinetic-energy functional.


title: Density functional theory

text: The Hohenberg–Kohn theorems relate to any system consisting of electrons moving under the influence of an external potential.


title: Density functional theory

text: Theorem 1. The external potential (and hence the total energy), is a unique functional of the electron density.


title: Density functional theory

text: Theorem 2. The functional that delivers the ground-state energy of the system gives the lowest energy if and only if the input density is the true ground-state density.


title: Density functional theory

text: The many-electron Schrödinger equation can be very much simplified if electrons are divided in two groups: valence electrons and inner core electrons. The electrons in the inner shells are strongly bound and do not play a significant role in the chemical binding of atoms; they also partially screen the nucleus, thus forming with the nucleus an almost inert core. Binding properties are almost completely due to the valence electrons, especially in metals and semiconductors. This separation suggests that inner electrons can be ignored in a large number of cases, thereby reducing the atom to an ionic core that interacts with the valence electrons. The use of an effective interaction, a pseudopotential, that approximates the potential felt by the valence electrons, was first proposed by Fermi in 1934 and Hellmann in 1935. In spite of the simplification pseudo-potentials introduce in calculations, they remained forgotten until the late 1950s.


title: Density functional theory

text: A crucial step toward more realistic pseudo-potentials was given by Topp and Hopfield and more recently Cronin, who suggested that the pseudo-potential should be adjusted such that they describe the valence charge density accurately. Based on that idea, modern pseudo-potentials are obtained inverting the free-atom Schrödinger equation for a given reference electronic configuration and forcing the pseudo-wavefunctions to coincide with the true valence wavefunctions beyond a certain distance . The pseudo-wavefunctions are also forced to have the same norm (i.e., the so-called norm-conserving condition) as the true valence wavefunctions and can be written as


title: Density functional theory

text: where is the radial part of the wavefunction with angular momentum , and PP and AE denote the pseudo-wavefunction and the true (all-electron) wavefunction respectively. The index in the true wavefunctions denotes the valence level. The distance beyond which the true and the pseudo-wavefunctions are equal is also dependent on .


title: Density functional theory

text: The electrons of a system will occupy the lowest Kohn–Sham eigenstates up to a given energy level according to the Aufbau principle. This corresponds to the steplike Fermi–Dirac distribution at absolute zero. If there are several degenerate or close to degenerate eigenstates at the Fermi level, it is possible to get convergence problems, since very small perturbations may change the electron occupation. One way of damping these oscillations is to "smear" the electrons, i.e. allowing fractional occupancies. One approach of doing this is to assign a finite temperature to the electron Fermi–Dirac distribution. Other ways is to assign a cumulative Gaussian distribution of the electrons or using a Methfessel–Paxton method.


title: Density functional theory

text: Classical density functional theory is a classical statistical method to investigate the properties of many-body systems consisting of interacting molecules, macromolecules, nanoparticles or microparticles. The classical non-relativistic method is correct for classical fluids with particle velocities less than the speed of light and thermal de Broglie wavelength smaller than the distance between particles. The theory is based on the calculus of variations of a thermodynamic functional, which is a function of the spatially dependent density function of particles, thus the name. The same name is used for quantum DFT, which is the theory to calculate the electronic structure of electrons based on spatially dependent electron density with quantum and relativistic effects. Classical DFT is a popular and useful method to study fluid phase transitions, ordering in complex liquids, physical characteristics of interfaces and nanomaterials. Since the 1970s it has been applied to the fields of materials science, biophysics, chemical engineering and civil engineering. Computational costs are much lower than for molecular dynamics simulations, which provide similar data and a more detailed description but are limited to small systems and short time scales. Classical DFT is valuable to interpret and test numerical results and to define trends although details of the precise motion of the particles are lost due to averaging over all possible particle trajectories. As in electronic systems, there are fundamental and numerical difficulties in using DFT to quantitatively describe the effect of intermolecular interaction on structure, correlations and thermodynamic properties.


title: Density functional theory

text: Classical DFT addresses the difficulty of describing thermodynamic equilibrium states of many-particle systems with nonuniform density. Classical DFT has its roots in theories such as the van der Waals theory for the equation of state and the virial expansion method for the pressure. In order to account for correlation in the positions of particles the direct correlation function was introduced as the effective interaction between two particles in the presence of a number of surrounding particles by Leonard Ornstein and Frits Zernike in 1914. The connection to the density pair distribution function was given by the Ornstein–Zernike equation. The importance of correlation for thermodynamic properties was explored through density distribution functions. The functional derivative was introduced to define the distribution functions of classical mechanical systems. Theories were developed for simple and complex liquids using the ideal gas as a basis for the free energy and adding molecular forces as a second-order perturbation. A term in the gradient of the density was added to account for non-uniformity in density in the presence of external fields or surfaces. These theories can be considered precursors of DFT.


title: Density functional theory

text: To develop a formalism for the statistical thermodynamics of non-uniform fluids functional differentiation was used extensively by Percus and Lebowitz (1961), which led to the Percus–Yevick equation linking the density distribution function and the direct correlation. Other closure relations were also proposed;the Classical-map hypernetted-chain method, the BBGKY hierarchy. In the late 1970s classical DFT was applied to the liquid–vapor interface and the calculation of surface tension. Other applications followed: the freezing of simple fluids, formation of the glass phase, the crystal–melt interface and dislocation in crystals, properties of polymer systems, and liquid crystal ordering. Classical DFT was applied to colloid dispersions, which were discovered to be good models for atomic systems. By assuming local chemical equilibrium and using the local chemical potential of the fluid from DFT as the driving force in fluid transport equations, equilibrium DFT is extended to describe non-equilibrium phenomena and fluid dynamics on small scales.


title: Density functional theory

text: Classical DFT allows the calculation of the equilibrium particle density and prediction of thermodynamic properties and behavior of a many-body system on the basis of model interactions between particles. The spatially dependent density determines the local structure and composition of the material. It is determined as a function that optimizes the thermodynamic potential of the grand canonical ensemble. The grand potential is evaluated as the sum of the ideal-gas term with the contribution from external fields and an excess thermodynamic free energy arising from interparticle interactions. In the simplest approach the excess free-energy term is expanded on a system of uniform density using a functional Taylor expansion. The excess free energy is then a sum of the contributions from "s"-body interactions with density-dependent effective potentials representing the interactions between "s" particles. In most calculations the terms in the interactions of three or more particles are neglected (second-order DFT). When the structure of the system to be studied is not well approximated by a low-order perturbation expansion with a uniform phase as the zero-order term, non-perturbative free-energy functionals have also been developed. The minimization of the grand potential functional in arbitrary local density functions for fixed chemical potential, volume and temperature provides self-consistent thermodynamic equilibrium conditions, in particular, for the local chemical potential. The functional is not in general a convex functional of the density; solutions may not be local minima. Limiting to low-order corrections in the local density is a well-known problem, although the results agree (reasonably) well on comparison to experiment.


title: Density functional theory

text: A variational principle is used to determine the equilibrium density. It can be shown that for constant temperature and volume the correct equilibrium density minimizes the grand potential functional formula_60 of the grand canonical ensemble over density functions formula_49. In the language of functional differentiation (Mermin theorem):


title: Density functional theory

text: The functional derivative in the density function determines the local chemical potential: formula_65.


title: Density functional theory

text: In classical statistical mechanics the partition function is a sum over probability for a given microstate of classical particles as measured by the Boltzmann factor in the Hamiltonian of the system. The Hamiltonian splits into kinetic and potential energy, which includes interactions between particles, as well as external potentials. The partition function of the grand canonical ensemble defines the grand potential. A correlation function is introduced to describe the effective interaction between particles.


title: Density functional theory

text: The "s"-body density distribution function is defined as the statistical ensemble average formula_66 of particle positions. It measures the probability to find "s" particles at points in space formula_67:


title: Density functional theory

text: From the definition of the grand potential, the functional derivative with respect to the local chemical potential is the density; higher-order density correlations for two, three, four or more particles are found from higher-order derivatives:


title: Density functional theory

text: The radial distribution function with "s" = 2 measures the change in the density at a given point for a change of the local chemical interaction at a distant point.


title: Density functional theory

text: In a fluid the free energy is a sum of the ideal free energy and the excess free-energy contribution formula_70 from interactions between particles. In the grand ensemble the functional derivatives in the density yield the direct correlation functions formula_71:


title: Density functional theory

text: The one-body direct correlation function plays the role of an effective mean field. The functional derivative in density of the one-body direct correlation results in the direct correlation function between two particles formula_73. The direct correlation function is the correlation contribution to the change of local chemical potential at a point formula_74 for a density change at formula_75 and is related to the work of creating density changes at different positions. In dilute gases the direct correlation function is simply the pair-wise interaction between particles (Debye–Huckel equation). The Ornstein–Zernike equation between the pair and the direct correlation functions is derived from the equation


title: Density functional theory

text: Various assumptions and approximations adapted to the system under study lead to expressions for the free energy. Correlation functions are used to calculate the free-energy functional as an expansion on a known reference system. If the non-uniform fluid can be described by a density distribution that is not far from uniform density a functional Taylor expansion of the free energy in density increments leads to an expression for the thermodynamic potential using known correlation functions of the uniform system. In the square gradient approximation a strong non-uniform density contributes a term in the gradient of the density. In a perturbation theory approach the direct correlation function is given by the sum of the direct correlation in a known system such as hard spheres and a term in a weak interaction such as the long range London dispersion force. In a local density approximation the local excess free energy is calculated from the effective interactions with particles distributed at uniform density of the fluid in a cell surrounding a particle. Other improvements have been suggested such as the weighted density approximation for a direct correlation function of a uniform system which distributes the neighboring particles with an effective weighted density calculated from a self-consistent condition on the direct correlation function.


title: Density functional theory

text: The variational Mermin principle leads to an equation for the equilibrium density and system properties are calculated from the solution for the density. The equation is a non-linear integro-differential equation and finding a solution is not trivial, requiring numerical methods, except for the simplest models. Classical DFT is supported by standard software packages, and specific software is currently under development. Assumptions can be made to propose trial functions as solutions, and the free energy is expressed in the trial functions and optimized with respect to parameters of the trial functions. Examples are a localized Gaussian function centered on crystal lattice points for the density in a solid, the hyperbolic function formula_77 for interfacial density profiles.


title: Density functional theory

text: The extension of classical DFT towards nonequilibrium systems is known as dynamical density functional theory (DDFT). DDFT allows to describe the time evolution of the one-body density formula_78 of a colloidal system, which is governed by the equation


title: Density functional theory

text: with the mobility formula_80 and the free energy formula_81. DDFT can be derived from the microscopic equations of motion for a colloidal system (Langevin equations or Smoluchowski equation) based on the adiabatic approximation, which corresponds to the assumption that the two-body distribution in a nonequilibrium system is identical to that in an equilibrium system with the same one-body density. For a system of noninteracting particles, DDFT reduces to the standard diffusion equation.


title: Ed Begley

text: Edward James Begley Sr. (March 25, 1901 – April 28, 1970) was an American actor of theatre, radio, film, and television. He won an Academy Award for Best Supporting Actor for his performance in the film "Sweet Bird of Youth" (1962) and appeared in such classics as "12 Angry Men" (1957) and "The Unsinkable Molly Brown" (1964). He was nominated for an Emmy Award for his portrayal of Matthew Harrison Brady in a television adaptation of "Inherit the Wind". He is the father of actor and environmental activist Ed Begley Jr.


title: Ed Begley

text: Begley was born in Hartford, Connecticut to two Irish immigrants, Hannah (née Clifford) and Michael Joseph Begley. After he dropped out of school as a fifth-grader, Begley ran away from home several times, going to work for "carnivals, fairs, and small circuses". Later he sold brushes, delivered milk, and served four years in the United States Navy during World War I.


title: Ed Begley

text: Begley began his career as a Broadway and radio actor while in his teens. He appeared in the hit musical "Going Up" on Broadway in 1917 and in London the next year. He later acted in roles as Sgt. O'Hara in the radio show "The Fat Man". His radio work included "Stroke of Fate" and a period as Charlie Chan, among other roles. He also starred in the 1950s radio program "Richard Diamond, Private Detective", playing Lieutenant Walter Levinson, head of homicide at the 5th Precinct, Manhattan. He was elected a member of The Lambs in 1943. In the late 1940s, he began appearing regularly in supporting film roles.


title: Ed Begley

text: In the 1952–1953 television season, Begley co-starred with Eddie Albert in the CBS sitcom "Leave It to Larry". In 1954 Begley starred in the NBC Television show "Robert Montgomery Presents" in "Big Boy", an episode sponsored by Lucky Strike, as Joe Grant, an engineer for the Union Pacific Railroad living in Cheyenne, Wyoming, who worked on the famous Union Pacific Big Boy steam locomotives. The show is about how Begley's character copes with the transition from steam locomotives to diesel locomotives in the 1950s.


title: Ed Begley

text: He won the Academy Award for Best Supporting Actor for his role in "Sweet Bird of Youth" (1962). Some of his other notable films include "Deadline – U.S.A." (1952), "12 Angry Men" (1957) as juror #10, "The Unsinkable Molly Brown" (1964), and "Wild in the Streets" (1968). One notable role Begley played both on television (twice in 1955) and in the theatrical film (1956) is William (Bill) Briggs, one of the three primary characters in Rod Serling's "Patterns".


title: Ed Begley

text: In 1956, he appeared in the Broadway production of "Inherit the Wind", in the role of Matthew Harrison Brady. For this performance, he won the Tony Award for Best Featured Actor in a Play. In 1968 he appeared with Clint Eastwood in the classic western "Hang 'Em High".


title: Ed Begley

text: His other television work included appearances on the 1954 TV series "Justice", "Empire", "The Virginian", "Bonanza", "The Fugitive", "The Dick Van Dyke Show", "", " The Invaders", "The Wild Wild West", "My Three Sons", "Wagon Train" and "Going My Way", with Gene Kelly. Among his many Broadway credits were "All My Sons" and "Our Town".


title: Ed Begley

text: Begley married his first wife, Amanda Huff, in 1922; they had two children. Huff died in 1957. His second marriage ended in divorce and his third wife, Helen, survived him. Begley is father of actor Ed Begley Jr, from his relationship with Allene Jeanne Sanders.


title: Ed Begley

text: Begley died of a heart attack while attending a party at the home of Jay Bernstein in Hollywood, California on April 28, 1970. He is buried at the San Fernando Mission Cemetery in Mission Hills, California.


title: Greenwashing

text: Greenwashing (a compound word modeled on "whitewash"), also called "green sheen", is a form of advertising or marketing spin in which green PR and green marketing are deceptively used to persuade the public that an organization's products, aims and policies are environmentally friendly. Companies that intentionally take up greenwashing communication strategies often do so in order to distance themselves from the environmental lapses of themselves or their suppliers.


title: Greenwashing

text: An example of greenwashing is when an organization spends significantly more resources on advertising being "green" than on environmentally sound practices. Greenwashing can range from changing the name or label of a product to evoke the natural environment (for example on a product containing harmful chemicals) to multimillion-dollar campaigns that portray highly-polluting energy companies as eco-friendly. Greenwashing covers up unsustainable corporate agendas and policies. Highly public accusations of greenwashing have contributed to the term's increasing use.


title: Greenwashing

text: Many corporations use greenwashing to improve public perception of their brands. Complex corporate structures can further obscure the big picture. Critics of the practice suggest the rise of greenwashing, paired with ineffective regulation, contributes to consumer skepticism of all green claims and diminishes the power of the consumer to drive companies toward greener manufacturing processes and business operations.


title: Greenwashing

text: Greenwashing has increased in recent years to meet consumer demand for environmentally-friendly goods and services. New regulations, laws, and guidelines by organizations such as the Committee of Advertising Practice mean to discourage companies from using greenwashing to deceive consumers.


title: Greenwashing

text: TerraChoice, an environmental consulting division of UL, described "seven sins of greenwashing" in 2007 to quantify the growth of greenwashing:


title: Greenwashing

text: The organization noted that by 2010 approximately 95% of consumer products in the U.S. claiming to be green were discovered to commit at least one of these sins.


title: Greenwashing

text: Keep America Beautiful was a campaign founded by beverage manufacturers and others in 1953. The campaign focused on recycling and littering, diverting attention away from corporate responsibility to protect the environment. The objective was to forestall the regulation of disposable containers such as the one established by Vermont.


title: Greenwashing

text: In the mid-1960s, the environmental movement gained momentum. This prompted many companies to create a new green image through advertising. Jerry Mander, a former Madison Avenue advertising executive, called this new form of advertising "ecopornography".


title: Greenwashing

text: The first Earth Day was held on April 22, 1970. This encouraged many industries to advertise themselves as being friendly to the environment. Public utilities spent $300 million advertising themselves as clean green companies. This was eight times more than the money they spent on pollution reduction research.


title: Greenwashing

text: The term "greenwashing" was coined by New York environmentalist Jay Westerveld in a 1986 essay about the hotel industry's practice of placing notices in bedrooms promoting reuse of towels to "save the environment". He noted that often little or no effort toward reducing energy waste was made by these institutions, although towel reuse saved them laundry costs. He concluded that often the real objective was increased profit, and labeled this and other profitable-but-ineffective "environmentally-conscientious" acts as "greenwashing".


title: Greenwashing

text: In 1991, a study published in the "Journal of Public Policy and Marketing" (American Marketing Association) found that 58% of environmental ads had at least one deceptive claim. Another study found that 77% of people said the environmental reputation of a company affected whether they would buy its products. One-fourth of all household products marketed around Earth Day advertised themselves as being green and environmentally friendly. In 1998 the Federal Trade Commission created the "Green Guidelines", which defined terms used in environmental marketing. The following year the FTC found that the Nuclear Energy Institute's claims of being environmentally clean were not true. The FTC did nothing about the ads because they were out of the agency's jurisdiction. This caused the FTC to realize they needed new, clear, enforceable standards. In 1999 the word "greenwashing" was added to the "Oxford English Dictionary".


title: Greenwashing

text: Days before the 1992 Earth Summit in Rio de Janeiro, Greenpeace released the Greenpeace Book on Greenwash, which described the corporate takeover of the UN conference and provided case studies of the contrast between corporate polluters and their rhetoric. An expanded version of that report was published by Third World Network as "Greenwash: The Reality Behind Corporate Environmentalism."


title: Greenwashing

text: In 2002, during the World Summit on Sustainable Development in Johannesburg, the Greenwashing Academy hosted the Greenwash Academy Awards. The ceremony awarded companies like BP, ExxonMobil, and even the U.S. Government for their elaborate greenwashing ads and support for greenwashing.


title: Greenwashing

text: Greenwashing is a relatively new area of research within psychology and there is little consensus among studies on how greenwashing affects consumers and stakeholders. Because of the variance in country and geography in recently published studies, the discrepancy between consumer behavior in studies could be attributed to cultural or geographic differences.


title: Greenwashing

text: Researchers found that products that are truly environmentally friendly are significantly more favored by consumers than their greenwashed counterparts. A survey by Lending Tree found that 55% of Americans are willing to spend more money on products they perceive to be more sustainable and eco-friendly.


title: Greenwashing

text: Consumer perceptions of greenwashing are also found to be mediated by the level of greenwashing they are exposed to. Other research suggests that few consumers actually notice greenwashing, particularly when they perceive the company or brand as reputable. When consumers perceive green advertising as credible, they develop more positive attitudes towards the brand, even when the advertising is greenwashed.


title: Greenwashing

text: Other research suggests that consumers with more green concern are more able to tell the difference between honest green marketing and greenwashed advertising; the more green concern, the stronger the intention not to purchase from companies from which they perceive greenwashing advertising behavior. When consumers use word-of-mouth to communicate about a product, green concern strengthens the negative relationship between the consumer's intent to purchase and the perception of greenwashing.


title: Greenwashing

text: Research suggests that consumers distrust companies who greenwash because they view the act as deceptive. If consumers perceive that a company would realistically benefit from a green marketing claim being true, then it is more likely that the claim and the company will be seen as genuine.


title: Greenwashing

text: Consumers’ willingness to purchase green decreases when they perceive the green attributes compromise the product quality, making greenwashing potentially risky, even when the consumer or stakeholder is not skeptical of the green messaging. Words and phrases often used in green messaging and greenwashing, such as "gentle", can lead consumers to believe the green product is less effective than a non-green option.


title: Greenwashing

text: Eco-labels can be given to a product both from an external organization and by the company itself, which has raised concerns because companies can label a product green or environmentally friendly by selectively disclosing positive attributes of the product while not disclosing environmental harms. Consumers expect to see eco-labels from both internal and external sources but perceive labels from external sources to be more trustworthy. Researchers from the University of Twente found that uncertified or greenwashed internal eco-labels may still contribute to consumer perceptions of a responsible company, with consumers attributing internal motivation to a company's internal eco-labeling. Other research connecting attribution theory and greenwashing found that consumers often perceive green advertising as greenwashing when companies use green advertisements, attributing the green messaging to corporate self-interest. Green advertising can backfire, particularly when the advertised environmental claim does not match a company's actual environmental engagement.


title: Greenwashing

text: Researchers working with consumer perception, psychology, and greenwashing note that in order for companies to avoid the negative connotations and perceptions of greenwashing, companies should "walk the walk" when it comes to green advertising and green behavior. Green marketing, labeling, and advertising are found to be most effective when it matches a company's actual environmental engagement. This is also mediated by the visibility of those environmental engagements, meaning that if consumers are unaware of a company's commitment to sustainability or environmentally-conscious ethos, they cannot factor greenness in their assessment of the company or product.


title: Greenwashing

text: Significant exposure to greenwashing can make a consumer indifferent to or generate negative feelings toward green marketing. Genuinely green businesses then have to work harder to differentiate themselves from those who use false claims. Consumers may also react negatively to true sustainability claims because of negative experiences with greenwashing.


title: Greenwashing

text: Companies may pursue environmental certification to avoid greenwashing through independent verification of their green claims. For example, the Carbon Trust Standard launched in 2007 with the stated aim "to end 'greenwash' and highlight firms that are genuine about their commitment to the environment".


title: Greenwashing

text: There have been attempts to reduce the impact of greenwashing by exposing it to the public. The Greenwashing Index, created by the University of Oregon in partnership with EnviroMedia Social Marketing, allowed the public to upload and rate examples of greenwashing, but it was last updated in 2012.


title: Greenwashing

text: Research published in the Journal of Business Ethics in 2011 shows that Sustainability Ratings might deter greenwashing. Results concluded that higher sustainability ratings lead to significantly higher brand reputation compared to lower sustainability ratings. This same trend was found regardless of the company’s level of corporate social responsibility (CSR) communications. This finding establishes that consumers pay more attention to sustainability ratings than CSR communications or greenwashing claims.


title: Greenwashing

text: The World Federation of Advertisers released six new guidelines for advertisers in 2022 that aim to prevent greenwashing. These approaches encourage credible environmental claims and more sustainable outcomes.


title: Greenwashing

text: Worldwide regulations on misleading environmental claims vary from criminal liability to fines or just voluntary guidelines.


title: Greenwashing

text: The Australian Trade Practices Act punishes companies that provide misleading environmental claims. Any organization found guilty of such could face up in fines. In addition, the guilty party must pay for all expenses incurred while setting the record straight about their product or company's actual environmental impact.


title: Greenwashing

text: Canada's Competition Bureau along with the Canadian Standards Association discourage companies from making "vague claims" about their products' environmental impact. Any claims must be backed up by "readily available data".


title: Greenwashing

text: The European Anti-Fraud Office (OLAF) handles investigations that have an environmental or sustainability element, such as misspending of EU funds intended for green products and the counterfeiting and smuggling of products with the potential to harm the environment and health. It also handles illegal logging and smuggling of precious wood and timber into the EU (wood laundering).


title: Greenwashing

text: The European Union has also struck a provisional agreement to mandate new reporting rules for companies with over 250 staff and a turnover of 40 million euros. They will need to disclose environmental, social, and governance (ESG) information, which will help combat greenwashing. These requirements go into effect in 2024.


title: Greenwashing

text: Norway's consumer ombudsman has targeted automakers who claim their cars are "green", "clean", or "environmentally friendly" with some of the world's strictest advertising guidelines. Consumer Ombudsman official Bente Øverli said: "Cars cannot do anything good for the environment except less damage than others." Manufacturers risk fines if they fail to drop misleading advertisements. Øverli said she did not know of other countries going so far in cracking down on cars and the environment.


title: Greenwashing

text: The Green Leaf Certification is an evaluation method created by the Association of Southeast Asian Nations (ASEAN) as a metric that rates the hotels' environmental efficiency of environmental protection. In Thailand, this certification is believed to help regulate greenwashing phenomena associated with green hotels. Eco hotel or "green hotel" are hotels that have adopted sustainable environmentally-friendly practices in hospitality business operations. Since the development of the tourism industry in the ASEAN, Thailand superseded its neighboring countries in inbound tourism, with 9 percent of Thailand's direct GDP contributions coming from the travel and tourism industry in 2015. Because of the growth and reliance on tourism as an economic pillar, Thailand developed "responsible tourism" in the 1990s to promote the well-being of local communities and the environment affected by the industry. However, studies show the green hotel companies' principles and environmental perceptions contradict the basis of corporate social responsibilities in responsible tourism. Against this context, the issuance of the Green Leaf Certification aims at keeping the hotel industry and supply chains accountable for corporate social responsibilities in regard to sustainability by having an independent international organization evaluate a hotel and rate it one through five leaves.


title: Greenwashing

text: The Competition and Markets Authority is the UK's primary competition and consumer authority. In September 2021, it published a Green Claims Code intended to protect consumers from misleading environmental claims and to protect businesses from unfair competition.


title: Greenwashing

text: The Federal Trade Commission (FTC) provides voluntary guidelines for environmental marketing claims. These guidelines give the FTC the right to prosecute false and misleading claims. These guidelines are not enforceable but instead were intended to be followed voluntarily:


title: Greenwashing

text: The FTC said in 2010 that it will update its guidelines for environmental marketing claims in an attempt to reduce greenwashing. The revision to the FTC's Green Guides covers a wide range of public input, including hundreds of consumer and industry comments on previously proposed revisions. The updates and revisions to the existing Guides include a new section about carbon offsets, "green" certifications as well as . According to FTC Chairman Jon Leibowitz, "The introduction of environmentally-friendly products into the marketplace is a win for consumers who want to purchase greener products and producers who want to sell them." Leibowitz also says such a win-win can only operate if marketers' claims are straightforward and proven.


title: Greenwashing

text: In 2013 the FTC began enforcing these revisions. It cracked down on six different companies; five of the cases concerned false or misleading advertising surrounding the biodegradability of plastics. The FTC charged ECM Biofilms, American Plastic Manufacturing, CHAMP, Clear Choice Housewares, and Carnie Cap, for misrepresenting the biodegradability of their plastics treated with additives.


title: Greenwashing

text: The FTC charged a sixth company, AJM Packaging Corporation, with violating a commission consent order put in place that prohibits companies from using advertising claims based on the product or packaging being "degradable, biodegradable, or photodegradable" without reliable scientific information. The FTC now requires companies to disclose and provide the information that qualifies their environmental claims, to ensure transparency.


title: Greenwashing

text: Bluewashing is a term that describes deceptive marketing that overstates a company's commitment to responsible social practices. It focuses mainly on economic and community factors.


title: Greenwashing

text: Carbon emission trading can be similar to greenwashing in that it gives an environmentally-friendly impression, but can be counterproductive if carbon is priced too low, or if large emitters are given "free credits". For example, Bank of America subsidiary MBNA offers "Eco-Logique" MasterCards that reward Canadian customers with carbon offsets when they use them. Customers may feel that they are nullifying their carbon footprint by purchasing goods with these, but only 0.5% of the purchase price goes to buy carbon offsets; the rest of the interchange fee still goes to the bank.


title: Greenwashing

text: Greenscamming is when an organization or product takes on a name that falsely implies environmental friendliness. It is related to both greenwashing and greenspeak. This is analogous to aggressive mimicry in biology.


title: Greenwashing

text: Greenscamming is used in particular by industrial companies and associations that deploy astroturfing organisations to try to dispute scientific findings that they consider threatening to their business model. One example is the denial of man-made global warming by companies in the fossil energy sector, also driven by specially-founded greenscamming organizations.


title: Greenwashing

text: One reason to establish greenscamming organizations is that it is difficult to openly communicate the benefits of activities that damage the environment. Sociologist Charles Harper stresses that it would be difficult to market a group called "Coalition to Trash the Environment for Profit". Anti-environment initiatives therefore must give their front organizations deliberately deceptive names if they want to be successful, as surveys show that environmental protection has a social consensus. However, there is a danger of being exposed as an anti-environmental initiative, which entails a considerable risk that the greenscamming activities backfire and are counterproductive for the initiators.


title: Greenwashing

text: Greenscamming organizations are active in organized climate denial. An important financier of greenscamming organizations was the oil company ExxonMobil, which financially supported more than 100 climate denial organizations and spent about 20 million U.S. dollars on greenscamming groups. James Lawrence Powell identified the "admirable" designations of many of these organizations as the most striking common feature, which for the most part sounded very rational. He quotes a list of climate denial organizations drawn up by the Union of Concerned Scientists, which includes 43 organizations funded by Exxon. None had a name that would lead one to infer that climate change denial was their "raison d’être". The list is headed by Africa Fighting Malaria, whose website features articles and commentaries opposing ambitious climate mitigation concepts, even though the dangers of malaria could be exacerbated by global warming.


title: Greenwashing

text: Examples of greenscamming organizations include the National Wetlands Coalition, Friends of Eagle Mountain, The Sahara Club, The Alliance for Environment and Resources, The Abundant Wildlife Society of North America, the Global Climate Coalition, the National Wilderness Institute, the Environmental Policy Alliance of the Center for Organizational Research and Education, and the American Council on Science and Health. Behind these ostensible environmental protection organizations lie the interests of business sectors. For example, the National Wetlands Coalition is backed by oil drilling companies and real estate developers, while the Friends of Eagle Mountain is backed by a mining company that wants to convert open-cast mines into landfills. The Global Climate Coalition was backed by commercial enterprises that fought against government-imposed climate protection measures. Other Greenscam organizations include the U.S. Council for Energy Awareness, backed by the nuclear industry; the Wilderness Impact Research Foundation, representing the interests of lumberjacks and ranchers; and the American Environmental Foundation, representing the interests of landowners.


title: Greenwashing

text: Another Greenscam organization is the Northwesterners for More Fish, which had a budget of $2.6 million in 1998. This group opposed conservation measures for endangered fish that restricted the interests of energy companies, aluminum companies, and the timber industry in the region, as well as tried to discredit environmentalists who promoted fish habitats. The Center for the Study of Carbon Dioxide and Global Change, the National Environmental Policy Institute, and the Information Council on the Environment funded by the coal industry are also greenscamming organizations.


title: Greenwashing

text: In Germany, this form of mimicry or deception is used by the "European Institute for Climate and Energy" (EIKE), which suggests by its name that it is an important scientific research institution. In fact, EIKE is not a scientific institution at all, but a lobby organization that neither has an office nor employs climate scientists, but instead disseminates fake news on climate issues on its website.


title: Water conservation

text: Water conservation includes all the policies, strategies and activities to sustainably manage the natural resource of fresh water, to protect the hydrosphere, and to meet the current and future human demand (thus avoiding water scarcity). Population, household size and growth and affluence all affect how much water is used. Factors such as climate change have increased pressures on natural water resources especially in manufacturing and agricultural irrigation. Many countries have already implemented policies aimed at water conservation, with much success. The key activities to conserve water are as follows: any beneficial reduction in water loss, use and waste of resources, avoiding any damage to water quality; and improving water management practices that reduce the use or enhance the beneficial use of water. Technology solutions exist for households, commercial and agricultural applications. Water conservation programs involved in social solutions are typically initiated at the local level, by either municipal water utilities or regional governments. Common strategies include public outreach campaigns, tiered water rates (charging progressively higher prices as water use increases), or restrictions on outdoor water use such as lawn watering and car washing.


title: Water conservation

text: One of the strategies in water conservation is rain water harvesting. Digging ponds, lakes, canals, expanding the water reservoir, and installing rain water catching ducts and filtration systems on homes are different methods of harvesting rain water. Many people in many countries keep clean containers so they can boil it and drink it, which is useful to supply water to the needy. Harvested and filtered rain water can be used for toilets, home gardening, lawn irrigation, and small scale agriculture.


title: Water conservation

text: Another strategy in water conservation is protecting groundwater resources. When precipitation occurs, some infiltrates the soil and goes underground. Water in this saturation zone is called groundwater. Contamination of groundwater causes the groundwater water supply to not be able to be used as a resource of fresh drinking water and the natural regeneration of contaminated groundwater can take years to replenish. Some examples of potential sources of groundwater contamination include storage tanks, septic systems, uncontrolled hazardous waste, landfills, atmospheric contaminants, chemicals, and road salts. Contamination of groundwater decreases the replenishment of available freshwater so taking preventative measures by protecting groundwater resources from contamination is an important aspect of water conservation.


title: Water conservation

text: An additional strategy to water conservation is practicing sustainable methods of utilizing groundwater resources. Groundwater flows due to gravity and eventually discharges into streams. Excess pumping of groundwater leads to a decrease in groundwater levels and if continued it can exhaust the resource. Ground and surface waters are connected and overuse of groundwater can reduce and, in extreme examples, diminish the water supply of lakes, rivers, and streams. In coastal regions, over pumping groundwater can increase saltwater intrusion which results in the contamination of groundwater water supply. Sustainable use of groundwater is essential in water conservation.


title: Water conservation

text: A fundamental component to water conservation strategy is communication and education outreach of different water programs. Developing communication that educates science to land managers, policy makers, farmers, and the general public is another important strategy utilized in water conservation. Communication of the science of how water systems work is an important aspect when creating a management plan to conserve that system and is often used for ensuring the right management plan to be put into action.


title: Water conservation

text: The conservation of water is extremely important in order to preserve wildlife habitats. There are many organisms in temperate regions who are affected by shortages in water. Additionally, many freshwater organisms are increasingly feeling the impacts of water pollution as it disrupts the ecosystem.


title: Water conservation

text: Water conservation programs involved in social solutions are typically initiated at the local level, by either municipal water utilities or regional governments. Common strategies include public outreach campaigns, tiered water rates (charging progressively higher prices as water use increases), or restrictions on outdoor water use such as lawn watering and car washing. Cities in dry climates often require or encourage the installation of xeriscaping or natural landscaping in new homes to reduce outdoor water usage. Most urban outdoor water use in California is residential, illustrating a reason for outreach to households as well as businesses.


title: Water conservation

text: One fundamental conservation goal is universal water metering. The prevalence of residential water metering varies significantly worldwide. Recent studies have estimated that water supplies are metered in less than 30% of UK households. Although individual water meters have often been considered impractical in homes with private wells or in multifamily buildings, the US Environmental Protection Agency estimates that metering alone can reduce consumption by 20 to 40 percent. In addition to raising consumer awareness of their water use, metering is also an important way to identify and localize water leakage. Water metering might benefit society by providing a financial incentive to avoid waste in water use.


title: Water conservation

text: Some researchers have suggested that water conservation efforts should be primarily directed at farmers, in light of the fact that crop irrigation accounts for 70% of the world's fresh water use. The agricultural sector of most countries is important both economically and politically, and water subsidies are common. Conservation advocates have urged removal of all subsidies to force farmers to grow more water-efficient crops and adopt less wasteful irrigation techniques.


title: Water conservation

text: New technology poses a few new options for consumers, features such as full flush and half flush when using a toilet are trying to make a difference in water consumption and waste. It is also possible to use/"pollute" the water in stages (keeping use in flush toilets for last), hereby allowing more use of the water for various tasks within a same cycle (before it needs to be purified again, which can also be done in-situ). Earthships often use such a setup.


title: Water conservation

text: Also available are modern shower heads that help reduce wasting water: Old shower heads are said to use 5-10 gallons per minute, while new fixtures available use 2.5 gallons per minute and offer equal water coverage.


title: Water conservation

text: Another method is to recycle the water of the shower directly, by means a semi-closed system which features a pump and filter. Such a setup (called a "water recycling shower") has also been employed at the VIRTUe LINQ house. Besides recycling water, it also reuses the heat of the water (which would otherwise be lost).


title: Water conservation

text: Contrary to the popular view that the most effective way to save water is to curtail water-using behavior (e.g., by taking shorter showers), experts suggest the most efficient way is replacing toilets and retrofitting washers; as demonstrated by two household end use logging studies in the US.


title: Water conservation

text: Smart water meters are also a promising technology for reducing household water usage. A study conducted in Valencia, Spain, shows the potential that smart meter-based water consumption feedback has for conserving water in households. The findings showed that households that were equipped with smart water meters increased their water savings. This technology works to show people how much water they were using in their household, suggest ways they can reduce water usage, and incentivize water savings with physical rewards.


title: Water conservation

text: Many water-saving devices (such as low-flush toilets) that are useful in homes can also be useful for business water saving. Other water-saving technology for businesses includes:


title: Water conservation

text: It is important to consider implementing water-conserving changes to industrial and commercial application use. It was found that high-income countries use roughly 59% of their water for industrial usage while low-income countries use 8% for industrial usage. One big change that industrial and commercial companies can implement are to improve the assessment and maintenance of water systems. It is easy to add water-efficient applications but it is the proper maintenance and inspection of it which will lead to long-term changes. A water conservation plan can be created, including adding various goals and benchmarks for both the employees and the company. Another change that industrial and commercial companies can make are to check water-consuming systems at regular intervals for any leaks or problems. By doing this, it will ensure that water is not unnecessarily being lost and there is no excess money being spent on utility bills. A third change that industrial and commercial companies can implement is installing a rain sensor. This sensor should be able to detect when precipitation is occurring and stop the program which would normally irrigate the land. After the rain ends, the sensor should turn the program back on and resume to its normal watering cycle.


title: Water conservation

text: Water is a very important part in irrigation. Plants always take a lot of ground water thus ground water should be replenished. For crop irrigation, optimal water efficiency means minimizing losses due to evaporation, runoff or subsurface drainage while maximizing production. An evaporation pan in combination with specific crop correction factors can be used to determine how much water is needed to satisfy plant requirements. Flood irrigation, the oldest and most common type, is often very uneven in distribution, as parts of a field may receive excess water in order to deliver sufficient quantities to other parts. Overhead irrigation, using center-pivot or lateral-moving sprinklers, has the potential for a much more equal and controlled distribution pattern. Drip irrigation is the most expensive and least-used type, but offers the ability to deliver water to plant roots with minimal losses. However, drip irrigation is increasingly affordable, especially for the home gardener and in light of rising water rates. Using drip irrigation methods can save up to 30,000 gallons of water per year when replacing irrigation systems that spray in all directions. There are also cheap effective methods similar to drip irrigation such as the use of soaking hoses that can even be submerged in the growing medium to eliminate evaporation.


title: Water conservation

text: As changing irrigation systems can be a costly undertaking, conservation efforts often concentrate on maximizing the efficiency of the existing system. This may include chiselling compacted soils, creating furrow dikes to prevent runoff, and using soil moisture and rainfall sensors to optimize irrigation schedules. Usually large gains in efficiency are possible through measurement and more effective management of the existing irrigation system. The 2011 UNEP Green Economy Report notes that "[i]mproved soil organic matter from the use of green manures, mulching, and recycling of crop residues and animal manure increases the water holding capacity of soils and their ability to absorb water during torrential rains", which is a way to optimize the use of rainfall and irrigation during dry periods in the season.


title: Water conservation

text: As seen in China, plastic mulch also has the potential to conserve water in agricultural practices. The "mulch" is really a thin sheet of plastic that is placed over the soil. There are holes in the plastic for the plants to grow through. Some studies have shown that plastic mulch conserves water by reducing the evaporation of soil moisture, however, there haven't been enough applied studies to determine the total water savings that this practice may bring about.


title: Water conservation

text: Water shortage has become an increasingly difficult problem to manage. More than 40% of the world's population live in a region where the demand for water exceeds its supply. The imbalance between supply and demand, along with persisting issues such as climate change and population growth, has made water reuse a necessary method for conserving water. There are a variety of methods used in the treatment of waste water to ensure that it is safe to use for irrigation of food crops and/or drinking water.


title: Water conservation

text: Seawater desalination requires more energy than the desalination of fresh water. Despite this, many seawater desalination plants have been built in response to water shortages around the world. This makes it necessary to evaluate the impacts of seawater desalination and to find ways to improve desalination technology. Current research involves the use of experiments to determine the most effective and least energy intensive methods of desalination.


title: Water conservation

text: Sand filtration is another method used to treat water. Recent studies show that sand filtration needs further improvements, but it is approaching optimization with its effectiveness at removing pathogens from water. Sand filtration is very effective at removing protozoa and bacteria, but struggles with removing viruses. Large-scale sand filtration facilities also require large surface areas to accommodate them.


title: Water conservation

text: The removal of pathogens from recycled water is of high priority because wastewater always contains pathogens capable of infecting humans. The levels of pathogenic viruses have to be reduced to a certain level in order for recycled water to not pose a threat to human populations. Further research is necessary to determine more accurate methods of assessing the level of pathogenic viruses in treated wastewater.


title: Water conservation

text: Wasting of water is the flip side of water conservation and, in household applications, it means causing or permitting discharge of water without any practical purpose. Inefficient water use is also considered wasteful. By EPA estimate, household leaks in the US can waste approximately 900 billion gallons (3.4 billion cubic meters) of water annually nationwide. Generally, water management agencies are reluctant or unwilling to give a concrete definition to a relatively vague concept of water waste.


title: Water conservation

text: However, definition of water waste is often given in local drought emergency ordinances. One example refers to any acts or omissions, whether willful or negligent, that are "causing or permitting water to leak, discharge, flow or run to waste into any gutter, sanitary sewer, watercourse or public or private storm drain, or to any adjacent property, from any tap, hose, faucet, pipe, sprinkler, pond, pool, waterway, fountain or nozzle." In this example, the city code also clarifies that "in the case of washing, "discharge," "flow" or "run to waste" means that water in excess of that necessary to wash, wet or clean the dirty or dusty object, such as an automobile, sidewalk, or parking area, flows to waste.


title: Water conservation

text: Water utilities (and other media sources) often provide listings of wasteful water-use practices and prohibitions of wasteful uses. Examples include utilities in San Antonio, Texas. Las Vegas, Nevada, California Water Service company in California, and City of San Diego, California. The City of Palo Alto in California enforces permanent water use restrictions on wasteful practices such as leaks, runoff, irrigating during and immediately after rainfall, and use of potable water when non-potable water is available. Similar restrictions are in effect in the State of Victoria, Australia. Temporary water use bans (also known as "hosepipe bans") are used in England, Scotland, Wales and Northern Ireland.


title: Water conservation

text: Strictly speaking, water that is discharged into the sewer, or directly to the environment is not wasted or lost. It remains within the hydrologic cycle and returns to the land surface and surface water bodies as precipitation. However, in many cases, the source of the water is at a significant distance from the return point and may be in a different catchment. The separation between extraction point and return point can represent significant environmental degradation in the watercourse and riparian strip. What is "wasted" is the community's supply of water that was captured, stored, transported and treated to drinking quality standards. Efficient use of water saves the expense of water supply provision and leaves more fresh water in lakes, rivers and aquifers for other users and also for supporting ecosystems. For example, we should not treat toilet as a trash can. If we flush cigarette butts or tissues in it, we are wasting gallons of water. Because the process of recycling water cannot be accomplished.


title: Water conservation

text: A concept that is closely related to water wasting is "water-use efficiency". Water use is considered inefficient if the same purpose of its use can be accomplished with less water. Technical efficiency derives from engineering practice where it is typically used to describe the ratio of output to input and is useful in comparing various products and processes. For example, one showerhead would be considered more efficient than another if it could accomplish the same purpose (i.e., of showering) by using less water or other inputs (e.g., lower water pressure). The technical efficiency concept is not useful in making decisions of investing money (or resources) in water conservation measures unless the inputs and outputs are measured in value terms. This expression of efficiency is referred to as economic efficiency and is incorporated into the concept of water conservation.


title: Spanish American wars of independence

text: The Spanish American wars of independence (25 September 1808 – 29 September 1833; ) were numerous wars in Spanish America with the aim of political independence from Spanish rule during the early 19th century. These began shortly after the start of the French invasion of Spain during the Napoleonic Wars. Thus, the strict period of military campaigns would go from the battle of Chacaltaya (1809), in present-day Bolivia, to the battle of Tampico (1829), in Mexico.


title: Spanish American wars of independence

text: In 1808, the sequestration of the Spanish royal family by Napoleon Bonaparte, the Abdications of Bayonne, gave rise to an emergence of liberalism and desire for liberties throughout the Spanish Empire. The violent conflicts started in 1809, with short-lived governing juntas established in Chuquisaca, La Paz and Quito opposing the government of the Supreme Central Junta of Seville. At the beginning of 1810, numerous new juntas appeared across the Spanish domains in the Americas when the Central Junta fell to the French invasion. Although various regions of Spanish America objected to many crown policies, "there was little interest in outright independence; indeed there was widespread support for the Spanish Central Junta formed to lead the resistance against the French." While some Spanish Americans believed that independence was necessary, most who initially supported the creation of the new governments saw them as a means to preserve the region's autonomy from the French. Although there had been research on the idea of a separate Spanish American ("creole") identity separate from that of Iberia, political independence was not initially the aim of most Spanish Americans, nor was it necessarily inevitable. But the conflict began as a dispute between Liberalism movements in both hemispheres between those who wanted a unitary monarchy in Spain rather than a plural monarchy in Spanish America.


title: Spanish American wars of independence

text: At the end of 1810, Ferdinand VII of Spain, captive, was recognized by the Cortes of Cádiz and by the governing juntas in the Americas as a subordinate king to popular sovereignty. In agreement on this, a military conflict arose between Royalists and Patriots over the unity or independence of the empire. However, in 1814, with the defeat of Napoleon after the treaty of Valençay, Ferdinand VII returned, and with a coup d'état, reimposed absolutism. Ferdinand was able to defeat and repress the peninsular liberals, and abolished the liberal Constitution of Cadiz, although he could not defeat the revolutionaries, who resisted and formed their own national congresses. The Spanish navy had collapsed in the war against Napoleon, so therefore, in practice, was supporting the expeditionary forces who arrived in small groups. In 1820 the Spanish army, led by Rafael Riego, revolted against absolutism, restored the so-called Trienio Liberal, and ended the threat of invasion against the Río de la Plata and Venezuela, but did not change the position of Spain against separatism, resulting in the defenders of the King collapsing in Americas. Over the course of the next decade, the Patriots’ armies won major victories and obtained independence in their respective countries. The political instability in Spain, without a navy, army or treasury, convinced many Spanish Americans of the need to formally establish independence from the mother country. In Spain, a French army of the Holy Alliance invaded and supported the absolutists, restored Ferdinand VII, and occupied Spain until 1828.


title: Spanish American wars of independence

text: These conflicts were fought both as irregular warfare and conventional warfare. These wars began as localized civil wars, that later spread and expanded as secessionist civil wars to promote general independence from Spanish rule. This independence led to the development of new national boundaries based on the colonial provinces, which would form the future independent countries that constituted contemporary Latin America during the early 19th century. Cuba and Puerto Rico remained under Spanish rule until the Spanish–American War in 1898. The independence of Spanish America did not constitute an anticolonial movement. The conflict resulted in the dissolution of the Spanish Monarchy and the creation of new States. Slavery was not abolished, but the new republics immediately left the formal system of racial classification and hierarchy, the caste system, the Inquisition, and noble titles. Criollos (those of Spanish descent born in the New World) and mestizos (those of mixed American Indigenous and Spanish blood or culture) replaced Spanish-born appointees in most political governments. Criollos remained at the top of a social structure that retained some of its traditional features culturally, if not legally. Slavery finally ended in all of the new nations. For almost a century thereafter, conservatives and liberals fought to reverse or to deepen the social and political changes unleashed by those rebellions.


title: Spanish American wars of independence

text: The events in Spanish America were related to the wars of independence in the former French colony of St. Domingue, Haiti, and the transition to independence in Brazil. Brazil's independence, in particular, shared a common starting point with that of Spanish America, since both conflicts were triggered by Napoleon's invasion of the Iberian Peninsula, which forced the Portuguese royal family to flee to Brazil in 1807. The process of Latin American independence took place in the general political and intellectual climate of Popular sovereignty that emerged from the Age of Enlightenment that influenced all of the Atlantic Revolutions, including the earlier revolutions in the United States and France. A more direct cause of the Spanish American wars of independence were the unique developments occurring within the Kingdom of Spain and its monarchy triggered by the Cortes of Cadiz, concluding with the emergence of the new Spanish American republics in the post-Napoleonic world.


title: Spanish American wars of independence

text: Political independence was not necessarily the foreordained outcome of the political turmoil in Spanish America. "There was little interest in outright independence." As historians R.A. Humphreys and John Lynch note, "it is all too easy to equate the forces of discontent or even the forces of change with the forces of revolution." Since "by definition, there was no history of independence until it happened," when Spanish American independence did occur, explanations for why it came about have been sought. The Latin American Wars of Independence were essentially led by European diaspora against European empires.


title: Spanish American wars of independence

text: There are a number of factors that have been identified to have provoked the independent movements. First, increasing control by the Crown of its overseas empire via the Bourbon Reforms of the mid-eighteenth century introduced changes to the relationship of Spanish Americans to the Crown. The language used to describe the overseas empire shifted from "kingdoms" with independent standing with the crown to "colonies" subordinate to Spain. In an effort to better control the administration and economy of the overseas possessions the Crown reintroduced the practice of appointing outsiders, almost all "peninsulars", to the royal offices throughout the empire. This meant that Spanish American elites were thwarted in their expectations and ambitions by the crown's upending of long-standing practices of creole access to office holding.


title: Spanish American wars of independence

text: The regalist and secularizing policies of the Bourbon monarchy were aimed at decreasing the power of the Roman Catholic Church. The crown had already expelled the Jesuits in 1767, which saw many creole members of the Society of Jesus go into permanent exile. By limiting the power of the Church, the crown attempted to centralize itself within the institutions of colonial Latin America. Because of the physical and ideological proximity that the clergy had, they could directly influence and dictate the interactions between populations of colonial Latin America, either as legal counsel or an advisor; a directness which the crown would need to attempt to create the centralized, colonial state which it wanted to implement.


title: Spanish American wars of independence

text: Later in the eighteenth century the crown sought to decrease the privileges ("fueros") of the clergy, restricting clerical authority to spiritual matters and undermining the power of parish priests, who often acted as agents of the crown in rural parishes. By desacralizing power and frontal attacks on the clergy, the crown, according to William B. Taylor, undermined its own legitimacy, since parish priests had been traditionally the "natural local representatives of their Catholic king."


title: Spanish American wars of independence

text: In the economic sphere, the crown sought to gain control over church revenues. The Church functioned as one of the largest economic institutions within colonial Latin America. It owned and retained jurisdiction over large amounts of land, which the crown wanted for itself because of the economic value which could be derived from the land. Moreover, by taking that land for itself, the Crown had the opportunity to cut down the physical presence of the Church to further weaken its ideological and social role within local colonial communities.


title: Spanish American wars of independence

text: In a financial crisis of 1804, the crown attempted to call in debts owed the church, mainly in the form of mortgages for haciendas owned by the elites. The Act of Consolidation simultaneously threatened the wealth of the church, whose capital was mainly lent for mortgages, as well as threatening the financial well-being of elites, who depended on mortgages for acquiring and keeping their estates. Shortening the repayment period meant many elites were faced with bankruptcy. The crown also sought to gain access to benefices elite families set aside to support a priest, often their own family members, by eliminating these endowed funds ("capellanías") that the lower clergy depended on disproportionately. Prominently in Mexico, lower clergy participated in the insurgency for independence with priests Miguel Hidalgo and José María Morelos.


title: Spanish American wars of independence

text: The reforms had mixed results. In some areas—such as Cuba, Río de la Plata and New Spain—the reforms had positive effects, improving the local economy and the efficiency of the government. In other areas, the changes in the crown's economic and administrative policies led to tensions with locals, which at times erupted into open revolts, such as the Revolt of the Comuneros in New Granada and the Rebellion of Túpac Amaru II in Peru.


title: Spanish American wars of independence

text: The loss of high offices to Peninsulars and the eighteenth-century revolts in Spanish South America were some of the direct causes of the wars of independence, which took place decades later, but they have been considered important elements of the political background in which the wars took place. Many Creoles, particularly the wealthy Creoles, were negatively impacted by the Bourbon Reforms. This resulted in their taking action by using their wealth and positions within society, often as leaders within their communities, to spur resistance to convey their displeasure with Spanish reforms because of the negative economic impact which they had. However, because of how quickly their revolts would further radicalize the lower classes, the Creoles quickly stopped supporting general violent insurrection because they benefitted from social change that occurred through the systems of the Spanish crown. Institutional change ensured stability by supporting the political institutions that allowed for the creation of a wealthy Creole class and further adapting those institutions to meet demands, rather than propose a radical shift in the complete make-up of socioeconomic life and traditions. However, institutional change did not come as anticipated and further spurred on the radicalization of Spanish-American social classes towards independence.


title: Spanish American wars of independence

text: Spain's international wars in the second half of the 18th century evidenced the empire's difficulties in reinforcing its colonial possessions and provide them with economic aid. This led to an increased local participation in the financing of the defense and an increased participation in the militias by the Chilean-born. Such development was at odds with the ideals of the centralized absolute monarchy. The Spanish did also formal concessions to strengthen the defense: In Chiloé Archipelago Spanish authorities promised freedom from the encomienda those indigenous locals who settled near the new stronghold of Ancud (founded in 1768) and contributed to its defense. The increased local organization of the defenses would ultimately undermine metropolitan authority and bolster the independence movement.


title: Spanish American wars of independence

text: Other factors may include Enlightenment thinking and the examples of the Atlantic Revolutions. The Enlightenment spurred the desire for social and economic reform to spread throughout Spanish America and the Iberian Peninsula. Ideas about free trade and physiocratic economics were raised by the Enlightenment in Spain and spread to the overseas empire and a homegrown Spanish American Enlightenment. The political reforms implemented and the many constitutions written both in Spain and throughout the Spanish world during the wars of independence were influenced by these factors.


title: Spanish American wars of independence

text: The Peninsular War was the trigger for conflicts in Spanish America in the absence of a legitimate monarch. The Peninsular War began an extended period of instability in the worldwide Spanish monarchy that lasted until 1823. Napoleon's capture of the Bourbon monarchs precipitated a political crisis in Spain and Spanish America. Although the Spanish world almost uniformly rejected Napoleon's plan to place his brother, Joseph, on the throne, there was no clear solution to the lack of a king. Following traditional Spanish political theories on the contractual nature of the monarchy (see Philosophy of Law of Francisco Suárez), the peninsular provinces responded to the crisis by establishing juntas. The move, however, led to more confusion, since there was no central authority and most juntas did not recognize the claim of some juntas to represent the monarchy as a whole. The Junta of Seville, in particular, claimed authority over the overseas empire, because of the province's historic role as the exclusive entrepôt of the empire.


title: Spanish American wars of independence

text: This impasse was resolved through negotiations between the several juntas in Spain counted with the participation of the Council of Castile, which led to the creation of a main government: the "Supreme Central and Governmental Junta of Spain and the Indies" on 25 September 1808. It was agreed that the kingdoms of the peninsula would send two representatives to this Supreme Central Junta, and that the overseas kingdoms would send one representative each. These kingdoms were defined as "the viceroyalties of New Spain (Mexico), Peru, New Granada, and Buenos Aires, and the independent captaincies general of the island of Cuba, Puerto Rico, Guatemala, Chile, Province of Venezuela, and the Philippines." This plan was criticized for providing unequal representation to Spanish America; nevertheless, throughout the end of 1808 and early 1809, the regional capitals elected candidates, whose names were forwarded to the capitals of the viceroyalties or captaincies general. Several important and large cities were left without direct representation in the Supreme Junta. In particular Quito and Chuquisaca, which saw themselves as the capitals of kingdoms, resented being subsumed in the larger Viceroyalty of Peru and Viceroyalty of the Río de la Plata respectively. This unrest led to the establishment of juntas in these cities in 1809, which were eventually quashed by the authorities within the year. An unsuccessful attempt at establishing a junta in New Spain was also stopped.


title: Spanish American wars of independence

text: The escape to Cádiz and the dissolution of the Supreme Central Junta on 29 January 1810, because of the reverses suffered after the Battle of Ocaña by the Spanish forces paid with Spanish American money, set off another wave of juntas being established in the Americas. French forces had taken over southern Spain and forced the Supreme Junta to seek refuge in the island-city of Cádiz.