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Koopmans' Theorem
Koopmans' theorem states that in closed-shell Hartree–Fock theory (HF), the first ionization energy of a molecular system is equal to the negative of the orbital energy of the highest occupied molecular orbital (HOMO). This theorem is named after Tjalling Koopmans, who published this result in 1934. Koopmans' theorem is exact in the context of restricted Hartree–Fock theory if it is assumed that the orbitals of the ion are identical to those of the neutral molecule (the ''frozen orbital'' approximation). Ionization energies calculated this way are in qualitative agreement with experiment – the first ionization energy of small molecules is often calculated with an error of less than two electron volts. Therefore, the validity of Koopmans' theorem is intimately tied to the accuracy of the underlying Hartree–Fock wavefunction. The two main sources of error are orbital relaxation, which refers to the changes in the Fock operator and Hartree–Fock orbitals when chan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ionization Energy
Ionization, or Ionisation is the process by which an atom or a molecule acquires a negative or positive Electric charge, charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule is called an ion. Ionization can result from the loss of an electron after collisions with subatomic particles, collisions with other atoms, molecules and ions, or through the interaction with electromagnetic radiation. Heterolytic bond cleavage and heterolytic substitution reactions can result in the formation of ion pairs. Ionization can occur through radioactive decay by the internal conversion process, in which an excited nucleus transfers its energy to one of the inner-shell electrons causing it to be ejected. Uses Everyday examples of gas ionization are such as within a fluorescent lamp or other electrical discharge lamps. It is also used in radiation detectors such as the Geiger-Müller counter or the ionization cham ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Chemistry
Quantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions to physical and chemical properties of molecules, materials, and solutions at the atomic level. These calculations include systematically applied approximations intended to make calculations computationally feasible while still capturing as much information about important contributions to the computed wave functions as well as to observable properties such as structures, spectra, and thermodynamic properties. Quantum chemistry is also concerned with the computation of quantum effects on molecular dynamics and chemical kinetics. Chemists rely heavily on spectroscopy through which information regarding the quantization of energy on a molecular scale can be obtained. Common methods are infra-red (IR) spectroscopy, nuclear magnetic r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fock Matrix
In the Hartree–Fock method of quantum mechanics, the Fock matrix is a matrix approximating the single-electron energy operator of a given quantum system in a given set of basis vectors. It is most often formed in computational chemistry when attempting to solve the Roothaan equations for an atomic or molecular system. The Fock matrix is actually an approximation to the true Hamiltonian operator of the quantum system. It includes the effects of electron-electron repulsion only in an average way. Because the Fock operator is a one-electron operator, it does not include the electron correlation energy. The Fock matrix is defined by the Fock operator. For the restricted case which assumes closed-shell orbitals and single- determinantal wavefunctions, the Fock operator for the ''i''-th electron is given by:Levine, I.N. (1991) ''Quantum Chemistry'' (4th ed., Prentice-Hall), p.403 :\hat F(i) = \hat h(i)+\sum_^ \hat J_j(i)-\hat K_j(i)/math> where: :\hat F(i) is the Fock opera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LUMO
In chemistry, HOMO and LUMO are types of molecular orbitals. The acronyms stand for ''highest occupied molecular orbital'' and ''lowest unoccupied molecular orbital'', respectively. HOMO and LUMO are sometimes collectively called the ''frontier orbitals'', such as in the frontier molecular orbital theory. Gap The energy difference between the HOMO and LUMO is ''the HOMO–LUMO gap''. Its size can be used to predict the strength and stability of transition metal complexes, as well as the colors they produce in solution.Griffith, J. S. and L. E. Orgel"Ligand Field Theory" ''Q. Rev. Chem. Soc.'' 1957, 11, 381–383. As a rule of thumb, the larger a compound's HOMO-LUMO gap, the more stable the compound. Semiconductors The HOMO level is to organic semiconductors roughly what the maximum valence band is to inorganic semiconductors and quantum dots. The same analogy can be made between the LUMO level and the conduction band minimum.Bredas, J,-L"Mind the gap!" ''Mater. Horiz.'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron Affinity
The electron affinity (''E''ea) of an atom or molecule is defined as the amount of energy released when an electron attaches to a neutral atom or molecule in the gaseous state to form an anion. ::X(g) + e− → X−(g) + energy Note that this is not the same as the enthalpy change of electron capture ionization, which is defined as negative when energy is released. In other words, the enthalpy change and the electron affinity differ by a negative sign. In solid state physics, the electron affinity for a surface is defined somewhat differently ( see below). Measurement and use of electron affinity This property is used to measure atoms and molecules in the gaseous state only, since in a solid or liquid state their energy levels would be changed by contact with other atoms or molecules. A list of the electron affinities was used by Robert S. Mulliken to develop an electronegativity scale for atoms, equal to the average of the electrons affinity and ionization potential. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basis Set (chemistry)
In theoretical and computational chemistry, a basis set is a set of functions (called basis functions) that is used to represent the electronic wave function in the Hartree–Fock method or density-functional theory in order to turn the partial differential equations of the model into algebraic equations suitable for efficient implementation on a computer. The use of basis sets is equivalent to the use of an approximate resolution of the identity: the orbitals , \psi_i\rangle are expanded within the basis set as a linear combination of the basis functions , \psi_i\rangle \approx \sum_\mu c_ , \mu\rangle, where the expansion coefficients c_ are given by c_ = \sum_\nu \langle \mu, \nu \rangle^ \langle \nu , \psi_i \rangle. The basis set can either be composed of atomic orbitals (yielding the linear combination of atomic orbitals approach), which is the usual choice within the quantum chemistry community; plane waves which are typically used within the solid state community, or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronvolt
In physics, an electronvolt (symbol eV, also written electron-volt and electron volt) is the measure of an amount of kinetic energy gained by a single electron accelerating from rest through an electric potential difference of one volt in vacuum. When used as a unit of energy, the numerical value of 1 eV in joules (symbol J) is equivalent to the numerical value of the charge of an electron in coulombs (symbol C). Under the 2019 redefinition of the SI base units, this sets 1 eV equal to the exact value Historically, the electronvolt was devised as a standard unit of measure through its usefulness in electrostatic particle accelerator sciences, because a particle with electric charge ''q'' gains an energy after passing through a voltage of ''V.'' Since ''q'' must be an integer multiple of the elementary charge ''e'' for any isolated particle, the gained energy in units of electronvolts conveniently equals that integer times the voltage. It is a common unit of ene ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ultraviolet Photoelectron Spectroscopy
Ultraviolet photoelectron spectroscopy (UPS) refers to the measurement of kinetic energy spectroscopy, spectra of photoelectric effect, photoelectrons emitted by molecules which have absorbed ultraviolet photons, in order to determine molecular orbital energies in the valence region. Basic theory If Albert Einstein's photoelectric law is applied to a free molecule, the kinetic energy ( E_K) of an emitted Photoelectric effect, photoelectron is given by : E_K = h\nu - I\,, where ''h'' is Planck's constant, ν is the frequency of the ionizing light, and I is an ionization energy for the formation of a singly charged ion in either the ground state or an excited state. According to Koopmans' theorem, each such ionization energy may be identified with the energy of an occupied molecular orbital. The ground-state ion is formed by removal of an electron from the highest occupied molecular orbital, while excited ions are formed by removal of an electron from a lower occupied orbital. Hist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecular Symmetry
Molecular symmetry in chemistry describes the symmetry present in molecules and the classification of these molecules according to their symmetry. Molecular symmetry is a fundamental concept in chemistry, as it can be used to predict or explain many of a molecule's chemical properties, such as whether or not it has a dipole moment, as well as its allowed spectroscopic transitions. To do this it is necessary to use group theory. This involves classifying the states of the molecule using the irreducible representations from the character table of the symmetry group of the molecule. Symmetry is useful in the study of molecular orbitals, with applications to the Hückel method, to ligand field theory, and to the Woodward-Hoffmann rules. Many university level textbooks on physical chemistry, quantum chemistry, spectroscopy and inorganic chemistry discuss symmetry. Another framework on a larger scale is the use of crystal systems to describe crystallographic symmetry in bulk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HOMO/LUMO
In chemistry, HOMO and LUMO are types of molecular orbitals. The acronyms stand for ''highest occupied molecular orbital'' and ''lowest unoccupied molecular orbital'', respectively. HOMO and LUMO are sometimes collectively called the ''frontier orbitals'', such as in the frontier molecular orbital theory. Gap The energy difference between the HOMO and LUMO is ''the HOMO–LUMO gap''. Its size can be used to predict the strength and stability of transition metal complexes, as well as the colors they produce in solution.Griffith, J. S. and L. E. Orgel"Ligand Field Theory" ''Q. Rev. Chem. Soc.'' 1957, 11, 381–383. As a rule of thumb, the larger a compound's HOMO-LUMO gap, the more stable the compound. Semiconductors The HOMO level is to organic semiconductors roughly what the maximum valence band is to inorganic semiconductors and quantum dots. The same analogy can be made between the LUMO level and the conduction band minimum.Bredas, J,-L"Mind the gap!" ''Mater. Horiz.' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density Functional Theory
Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function. In the case of DFT, these are functionals of the spatially dependent electron density. DFT is among the most popular and versatile methods available in condensed-matter physics, computational physics, and computational chemistry. DFT has been very popular for calculations in solid-state physics since the 1970s. However, DFT was not considered accurate enough for calculations in quantum chemistry until the 1990s, when the approximations used in the theory were greatly refined to better model the exchange and correlation interactio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
