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Molecular Orbital
In chemistry, a molecular orbital is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The terms ''atomic orbital'' and ''molecular orbital'' were introduced by Robert S. Mulliken in 1932 to mean ''one-electron orbital wave functions''. At an elementary level, they are used to describe the ''region'' of space in which a function has a significant amplitude. In an isolated atom, the orbital electrons' location is determined by functions called atomic orbitals. When multiple atoms combine chemically into a molecule by forming a valence chemical bond, the electrons' locations are determined by the molecule as a whole, so the atomic orbitals combine to form molecular orbitals. The electrons from the constituent atoms occupy the molecular orbitals. Mathematically, molecular orbitals are an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecular Orbital Theory
In chemistry, molecular orbital theory (MO theory or MOT) is a method for describing the electronic structure of molecules using quantum mechanics. It was proposed early in the 20th century. The MOT explains the paramagnetic nature of O2, which valence bond theory cannot explain. In molecular orbital theory, electrons in a molecule are not assigned to individual chemical bonds between atoms, but are treated as moving under the influence of the atomic nuclei in the whole molecule. Quantum mechanics describes the spatial and energetic properties of electrons as molecular orbitals that surround two or more atoms in a molecule and contain valence electrons between atoms. Molecular orbital theory revolutionized the study of chemical bonding by approximating the states of bonded electrons – the molecular orbitals – as linear combinations of atomic orbitals (LCAO). These approximations are made by applying the density functional theory (DFT) or Hartree–Fock (HF) models to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbitals Acetylene
Orbital may refer to: Sciences Chemistry and physics * Atomic orbital * Molecular orbital * Hybrid orbital Astronomy and space flight * Orbit ** Earth orbit Medicine and physiology * Orbit (anatomy), also known as the ''orbital bone'' * Orbitofrontal cortex, a part of the brain used for decision making Business * Orbital Corporation, an Australian engine technology company * Orbital Sciences Corporation, a U.S. satellite launch and defense systems corporation * Orbital ATK, American aerospace manufacturer formed from the merger of Orbital Sciences Corporation and parts of Alliant Techsystems Transportation * Ring road (or ''orbital road'' in some regions) * Orbital (metro), a rapid transit line usually encircling a city centre * Orbital engine Other uses * ''Orbital'' (novel), a 2023 novel by Samantha Harvey * Orbital (The Culture), artificial worlds from Iain M. Banks's series of science fiction novels, the Culture * Orbital (band), an English electronic dance music duo, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hybrid Orbital
Hybrid may refer to: Science * Hybrid (biology), an offspring resulting from cross-breeding ** Hybrid grape, grape varieties produced by cross-breeding two ''Vitis'' species ** Hybridity, the property of a hybrid plant which is a union of two different genetic parent strains * Hybrid (particle physics), a valence quark-antiquark pair and one or more gluons * Hybrid solar eclipse, a rare solar eclipse type * Hybrid star (other), with properties normally found in different types of stars Technology Transportation * Hybrid vehicle (other), various types of vehicles referred to as hybrids * Hybrid rail, an urban rail service for passengers using lightweight trains * Hybrid rocket, a rocket motor using propellants from two different states of matter * Hybrid shipping container, a container using phase change material in combination with the ability to recharge itself * Hybrid train, a locomotive, railcar, or train that uses an onboard rechargeable energy storage ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pi Bond
In chemistry, pi bonds (π bonds) are covalent chemical bonds, in each of which two lobes of an orbital on one atom overlap with two lobes of an orbital on another atom, and in which this overlap occurs laterally. Each of these atomic orbitals has an electron density of zero at a shared nodal plane that passes through the two bonded nuclei. This plane also is a nodal plane for the molecular orbital of the pi bond. Pi bonds can form in double and triple bonds but do not form in single bonds in most cases. The Greek letter π in their name refers to p orbitals, since the orbital symmetry of the pi bond is the same as that of the p orbital when seen down the bond axis. One common form of this sort of bonding involves p orbitals themselves, though d orbitals also engage in pi bonding. This latter mode forms part of the basis for metal-metal multiple bonding. Properties Pi bonds are usually weaker than sigma bonds. The C–C double bond, composed of one sigma and o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sigma Bond
In chemistry, sigma bonds (σ bonds) or sigma overlap are the strongest type of covalent chemical bond. They are formed by head-on overlapping between atomic orbitals along the internuclear axis. Sigma bonding is most simply defined for diatomic molecules using the language and tools of symmetry groups. In this formal approach, a σ-bond is symmetrical with respect to rotation about the bond axis. By this definition, common forms of sigma bonds are s+s, pz+pz, s+pz and dz2+dz2 (where z is defined as the axis of the bond or the internuclear axis). Quantum theory also indicates that molecular orbitals (MO) of identical symmetry actually mix or ''hybridize''. As a practical consequence of this mixing of diatomic molecules, the wavefunctions s+s and pz+pz molecular orbitals become blended. The extent of this mixing (or hybridization or blending) depends on the relative energies of the MOs of like symmetry. For homodiatomics ( homonuclear diatomic molecules), bonding σ orbit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Configuration Interaction
Configuration interaction (CI) is a post-Hartree–Fock linear variational method for solving the nonrelativistic Schrödinger equation within the Born–Oppenheimer approximation for a quantum chemical multi-electron system. Mathematically, ''configuration'' simply describes the linear combination of Slater determinants used for the wave function. In terms of a specification of orbital occupation (for instance, (1s)2(2s)2(2p)1...), ''interaction'' means the mixing (interaction) of different electronic configurations (states). Due to the long CPU time and large memory required for CI calculations, the method is limited to relatively small systems. In contrast to the Hartree–Fock method, in order to account for electron correlation, CI uses a variational wave function that is a linear combination of configuration state functions (CSFs) built from spin orbitals (denoted by the superscript ''SO''), : \Psi = \sum_ c_ \Phi_^ = c_0\Phi_0^ + c_1\Phi_1^ + where � ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pauli Principle
In quantum mechanics, the Pauli exclusion principle (German: Pauli-Ausschlussprinzip) states that two or more identical particles with half-integer spins (i.e. fermions) cannot simultaneously occupy the same quantum state within a system that obeys the laws of quantum mechanics. This principle was formulated by Austrian physicist Wolfgang Pauli in 1925 for electrons, and later extended to all fermions with his spin–statistics theorem of 1940. In the case of electrons in atoms, the exclusion principle can be stated as follows: in a poly-electron atom it is impossible for any two electrons to have the same two values of ''all'' four of their quantum numbers, which are: ''n'', the principal quantum number; ', the azimuthal quantum number; ''m'', the magnetic quantum number; and ''ms'', the spin quantum number. For example, if two electrons reside in the same orbital, then their values of ''n'', ', and ''m'' are equal. In that case, the two values of ''m''s (spin) pair must be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Chemistry
Computational chemistry is a branch of chemistry that uses computer simulations to assist in solving chemical problems. It uses methods of theoretical chemistry incorporated into computer programs to calculate the structures and properties of molecules, groups of molecules, and solids. The importance of this subject stems from the fact that, with the exception of some relatively recent findings related to the hydrogen molecular ion (dihydrogen cation), achieving an accurate quantum mechanical depiction of chemical systems analytically, or in a closed form, is not feasible. The complexity inherent in the many-body problem exacerbates the challenge of providing detailed descriptions of quantum mechanical systems. While computational results normally complement information obtained by chemical experiments, it can occasionally predict unobserved chemical phenomena. Overview Computational chemistry differs from theoretical chemistry, which involves a mathematical description of chem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Combination Of Atomic Orbitals Molecular Orbital Method
A linear combination of atomic orbitals or LCAO is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum chemistry. In quantum mechanics, electron configurations of atoms are described as wavefunctions. In a mathematical sense, these wave functions are the basis set of functions, the basis functions, which describe the electrons of a given atom. In chemical reactions, orbital wavefunctions are modified, i.e. the electron cloud shape is changed, according to the type of atoms participating in the chemical bond. It was introduced in 1929 by Sir John Lennard-Jones with the description of bonding in the diatomic molecules of the first main row of the periodic table, but had been used earlier by Linus Pauling for H2+. Mathematical description An initial assumption is that the number of molecular orbitals is equal to the number of atomic orbitals included in the linear expansion. In a sense, ''n'' atomic orbitals combine to form ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron Configuration
In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals. For example, the electron configuration of the neon atom is , meaning that the 1s, 2s, and 2p subshells are occupied by two, two, and six electrons, respectively. Electronic configurations describe each electron as moving independently in an orbital, in an average field created by the nuclei and all the other electrons. Mathematically, configurations are described by Slater determinants or configuration state functions. According to the laws of quantum mechanics, a level of energy is associated with each electron configuration. In certain conditions, electrons are able to move from one configuration to another by the emission or absorption of a quantum of energy, in the form of a photon. Knowledge of the electron configuration of different atoms is useful in understanding the structu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomic Nuclei
The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford at the University of Manchester based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron in 1932, models for a nucleus composed of protons and neutrons were quickly developed by Dmitri Ivanenko and Werner Heisenberg. An atom is composed of a positively charged nucleus, with a cloud of negatively charged electrons surrounding it, bound together by electrostatic force. Almost all of the mass of an atom is located in the nucleus, with a very small contribution from the electron cloud. Protons and neutrons are bound together to form a nucleus by the nuclear force. The diameter of the nucleus is in the range of () for hydrogen (the diameter of a single proton) to about for uranium. These dimensions are much smaller than the diameter of the atom itself (nucleus + electron cloud), by a factor of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-bonding Orbital
A non-bonding orbital, also known as ''non-bonding molecular orbital'' (NBMO), is a molecular orbital whose occupation by electrons neither increases nor decreases the bond order between the involved atoms. Non-bonding orbitals are often designated by the letter n in molecular orbital diagrams and electron transition notations. Non-bonding orbitals are the equivalent in molecular orbital theory of the lone pairs in Lewis structures. The energy level of a non-bonding orbital is typically in between the lower energy of a valence shell bonding orbital and the higher energy of a corresponding antibonding orbital. As such, a non-bonding orbital with electrons would commonly be a HOMO ( highest occupied molecular orbital). According to molecular orbital theory, molecular orbitals are often modeled by the linear combination of atomic orbitals. In a simple diatomic molecule such as hydrogen fluoride (chemical formula: HF), one atom may have many more electrons than the other. A sigm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
