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Concentration of chemical orbitals on adjacent atoms
chemical bonds, an orbital overlap is the concentration of orbitals on adjacent atoms in the same regions of space. Orbital overlap can lead to bond formation
Orbital_overlap
Type of chemical bond
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
Pi_bond
Visual tool in quantum chemistry
molecular orbital diagram, or MO diagram, is a qualitative descriptive tool explaining chemical bonding in molecules in terms of molecular orbital theory
Molecular_orbital_diagram
Wave-like behavior of an electron in a molecule
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
Molecular_orbital
Topics referred to by the same term
rewriting systems Overlap add, an efficient convolution method using FFT Overlap coefficient, a similarity measure between sets Orbital overlap, important concept
Overlap
Type of chemical bond
involved atomic orbital overlap six lobes of the other involved atomic orbital. This overlap leads to the formation of a bonding molecular orbital with three
Phi_bond
Special type of hyperconjugation
These stabilities occur because of a partial overlap between the C–Si σ orbital and the σ* antibonding orbital at the β position, lowering the SN reaction
Negative hyperconjugation in silicon
Negative_hyperconjugation_in_silicon
Chemical bond involving four bonding electrons; has one sigma plus one pi bond
because p-orbital overlap is maximized. 2 sp2 orbitals (total of 3 such orbitals) approach to form a sp2-sp2 sigma bond Two p-orbitals overlap to form a
Double_bond
Function describing an electron in an atom
electron's energy, its orbital angular momentum, and its orbital angular momentum projected along a chosen axis . The orbitals with a well-defined magnetic
Atomic_orbital
Mixing (superposition) of atomic orbitals
In chemistry, orbital hybridisation (or hybridization) is the concept of mixing atomic orbitals to form new hybrid orbitals (with different energies,
Orbital_hybridisation
Chemical bond by sharing of electron pairs
orbital overlap population), COHP (Crystal orbital Hamilton population), and BCOOP (Balanced crystal orbital overlap population). To overcome this issue, an
Covalent_bond
Set of rules pertaining to pericyclic reactions
through orbital symmetry, but it was unclear how far such a principle might extend. Hence, Woodward and Hoffman began extensive orbital-overlap calculations
Woodward–Hoffmann_rules
System of connected p-orbitals with delocalized electrons in a molecule
single spherical lobe of a hydrogen 1s orbital). Each atomic orbital contributes one electron when the orbitals overlap pairwise to form two-electron σ bonds
Conjugated_system
Concept in organic chemistry
pieces of information suffice to determine geometric constraints on the orbital overlap during the attack: the number of atoms in the newly formed ring the
Baldwin's_rules
Theory of molecular orbitals by Erich Hückel
molecular orbital theory, proposed by Erich Hückel in 1930, is a simple method for calculating molecular orbitals as linear combinations of atomic orbitals. The
Hückel_method
Preferential outcome of a chemical reaction
prediction of reactivity, but more factors such as connectivity, atomic orbital overlap, solvent effects, and the addition of supporting reagents can affect
Chemoselectivity
Intermolecular attraction between a hydrogen donor-and-acceptor pair
well-defined, localized interactions with significant charge transfer and orbital overlap, such as those in DNA base pairing or ice. In contrast, "hydrogen-bonding
Hydrogen_bond
One of two foundational theories of quantum chemistry
an HF molecule the covalent bond is formed by the overlap of the 1s orbital of H and the 2pz orbital of F, each containing an unpaired electron. Mutual
Valence_bond_theory
Organic reaction in which a pi bond and sigma bond are interconverted
symmetry allowed. This is because only in these cases would maximum orbital overlap occur in the transition state. Also, the formed product would be in
Electrocyclic_reaction
mainly because of the relatively poor orbital overlap of the substituent's 3p (or higher) orbital with the 2p orbital of the carbon. Due to a stronger resonance
Electrophilic aromatic directing groups
Electrophilic_aromatic_directing_groups
Compound with a magnesium to magnesium bond
from the s-orbital overlap of the two metals. The bonding interaction that occurs may be connected to the highest occupied molecular orbital (HOMO), giving
Magnesium(I)_dimer
Method for describing the electronic structure of molecules using quantum mechanics
molecular orbital is best characterized by that type. This method of quantifying orbital contribution as a linear combination of atomic orbitals is used
Molecular_orbital_theory
Molecular-structural phenomenon
C−H σ orbital is a better electron donor than the C−F σ orbital, while the C−F σ* orbital is a better electron acceptor than the C−H σ* orbital. Only
Gauche_effect
Affect on molecular properties due to spatial arrangement of electron orbitals
and/or transition states of molecules that arise from considerations of orbital overlap. Thus, a stereoelectronic effect explains a particular molecular property
Stereoelectronic_effect
Reaction in organic chemistry
occurs due to the orbital overlap between the alkene and the allylic enophile. The electrons in the highest occupied molecular orbital (HOMO) of the ene
Group_transfer_reaction
Function used in quantum chemistry
orbitals (STOs) or Slater-type functions (STFs) are functions used as atomic orbitals in the linear combination of atomic orbitals molecular orbital method
Slater-type_orbital
more stable due to higher pi-pi stacking interactions which induces orbital overlap and mixing between the C atoms of the graphene. This introduces a higher
Graphene boron nitride nanohybrid materials
Graphene_boron_nitride_nanohybrid_materials
Reaction impacting chemical bonds
more electron donating groups. This results in higher orbital energies, and thus more orbital overlap with the LUMO of the diene. Common classes of dieneophiles
Inverse electron-demand Diels–Alder reaction
Inverse_electron-demand_Diels–Alder_reaction
Concept in organic chemistry
orbital (e.g. C–H or C–C) with an adjacent unpopulated non-bonding p or antibonding σ* or π* orbitals to give a pair of extended molecular orbitals.
Hyperconjugation
Type of reaction in organometallic chemistry
force the eliminating groups closer together, which allows for more orbital overlap. Kinetics for reductive elimination are hard to predict, but reactions
Reductive_elimination
within the organic linkers, and building off molecular building blocks. Orbital overlap within the intra- and inter- plane regions of the frameworks allow
Conductive metal−organic frameworks
Conductive_metal−organic_frameworks
Chemical bond involving six bonding electrons; one sigma plus two pi bonds
in terms of orbital hybridization. In the case of acetylene, each carbon atom has two sp-orbitals and two p-orbitals. The two sp-orbitals are linear,
Triple_bond
molecules such as CH4, in which four sp³ hybridised orbitals are overlapped by hydrogen's 1s orbital, yielding four sigma (σ) bonds. The four bonds are
History_of_molecular_theory
Sulfide mineral
A (2002). "Low-temperature crystal structures of stibnite implying orbital overlap of Sb 5s 2 inert pair electrons". Physics and Chemistry of Minerals
Stibnite
Class of organic compounds that are superconductive at low temperatures
properties, including planarity, low ionization potential and good orbital overlap between heteroatoms in neighboring donor molecules. These properties
Bechgaard_salt
The unoccupied σ*(Sb–X) orbital contributes to the Lewis acidity of antimony compounds in two ways: donor–acceptor orbital interaction and electrostatic
Organoantimony-based Lewis acids
Organoantimony-based_Lewis_acids
Method in computational chemistry
the basis functions in the molecular orbital are Cμi for the μ'th basis function in the i'th molecular orbital, the density matrix terms are: D μ ν =
Mulliken_population_analysis
Covalent chemical bond
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
Sigma_bond
Hydrocarbon compound containing a non-aromatic ring with a C=C bond
to be omitted from the names. Cycloalkenes require considerable p-orbital overlap in the form of a bridge between the carbon-carbon double bond; however
Cycloalkene
Chemical property
reducing unfavorable p-orbital overlap. This reduction of symmetry lifts the degeneracy of the two formerly non-bonding molecular orbitals, which by Hund's
Aromaticity
Rule in geometry of individual molecules
an atomic orbital and the electrons in the orbital overlap form a covalent bond. Atoms do not usually contribute a pure hydrogen-like orbital to bonds
Bent's_rule
Pericyclic chemical reaction
frontier molecular orbitals (FMO) of the 1,3-dipole and the dipolarophile overlap in the symmetry-allowed π4s + π2s manner. Such orbital overlap can be achieved
1,3-Dipolar_cycloaddition
Ion with a positively charged carbon atom
have a tendency to "lean" towards the carbocationic center to improve orbital overlap. There is, in fact, an entire spectrum of bonding scenarios between
Carbocation
Organic molecular structure
such compounds. This formal discontinuity is apparently bridged by p-orbital overlap, maintaining a contiguous cycle of π electrons that is responsible
Homoaromaticity
Describes the range of energies of an electron within the solid
isolated atom occupy atomic orbitals with discrete energy levels. If two atoms come close enough so that their atomic orbitals overlap, the electrons can tunnel
Electronic_band_structure
Organic chemistry reaction
only when the occupied lone pair orbital of the nucleophile donates electrons to the unfilled σ* antibonding orbital between the central carbon and the
SN2_reaction
Molecular orbital which weakens chemical bonding
In theoretical chemistry, an antibonding orbital is a type of molecular orbital that weakens the chemical bond between two atoms and helps to raise the
Antibonding_orbital
Chemical reaction featuring a sigmatropic rearrangement
with high efficiency even in systems that do not permit efficient orbital overlap, as illustrated by a key step in the synthesis periplanone B: The corresponding
Cope_rearrangement
Type of chemical bond
atomic orbital on one atom overlap four lobes of an atomic orbital on another atom. This overlap leads to the formation of a bonding molecular orbital with
Delta_bond
Chemical reaction of an alkene with mercuric acetate to form an alcohol
in mercury's dxz (or dyz) orbital are donated into the lowest unoccupied molecular orbital of the double bond, the π* orbital, through backbonding. However
Oxymercuration_reaction
Chemical polarity due to interactions between pi bonds or lone pairs
also by the inductive effect. The mesomeric effect as a result of p-orbital overlap (resonance) has absolutely no effect on this inductive effect, as the
Mesomeric_effect
Chemical compound
(2002). "Low-temperature crystal structures of stibnite implying orbital overlap of Sb 5s 2 inert pair electrons". Physics and Chemistry of Minerals
Antimony_trisulfide
Semiempirical quantum chemistry method
band structures, total and projected density of states, and crystal orbital overlap/Hamilton populations (COOPs/COHPs). Erich Hückel Roald Hoffmann Hoffmann
Extended_Hückel_method
Compound containing rings with delocalized pi electrons
pi interactions between the pi bonds of aromatic rings, because of orbital overlap. According to some authors direct stacking of aromatic rings (the "sandwich
Aromatic_compound
Process that leads to chemical changes
depends on the electronic orbitals of the participating species, as only orbitals with the same sign of wave function will overlap and interact constructively
Chemical_reaction
independent, orthogonal set of basis orbitals, the weight of a constituent orbital Ψi would be Ci2 since the overlap integral, Sij , between two wave functions
Chirgwin–Coulson_weights
Covalent bond between carbon and fluorine atoms
the carbon–hydrogen σ orbital is a better electron donor than the carbon–fluorine σ orbital, while the carbon–fluorine σ* orbital is a better electron
Carbon–fluorine_bond
Tendency of some substituents on a cyclohexane ring to prefer axial orientation
into the σ* orbital, hyperconjugation occurs, stabilizing the molecule. This forms a "no bond" resonance form. For this orbital overlap to occur, the
Anomeric_effect
Type of lepton that orbits an atom on its own
occupies a valence p orbital or an sp, sp2 or sp3 hybrid orbital. These orbitals are strongly directional and therefore overlap to form strong covalent
Unpaired_electron
degree of steric congestion, while the endo product is favoured by orbital overlap in the transition state. An outstanding and very rare example of the
Thermodynamic and kinetic reaction control
Thermodynamic_and_kinetic_reaction_control
Property of substances to change colour due to a change in temperature
when cold, and the intermolecular spacing is sufficiently short for orbital overlap. The energy levels of the resulting bands then depend on the intermolecular
Thermochromism
Chemistry rule of thumb
elements, when they exist, are often weak due to poor orbital overlap between the n>2 orbitals of the two atoms. Although such compounds are not intrinsically
Double_bond_rule
Any cation that has a pentavalent carbon atom
p-orbital parallel to the cyclopropyl ring system: In terms of bent-bond theory, this preference is explained by assuming favorable orbital overlap between
Carbonium_ion
Hydrocarbon compound (HC≡CH)
in each carbon atom the 2s orbital hybridizes with one 2p orbital thus forming an sp hybrid. The other two 2p orbitals remain unhybridized. The two
Acetylene
Effect in chemistry
on the nucleophilic center and (2) small HOMO-LUMO orbital energy gap that ensures orbital overlap with the substrate. It was proposed that both of these
Alpha_effect
Chemical reaction
selectivity. The secondary orbital overlap explanation was first proposed by Woodward and Hoffmann. In this explanation, the orbitals associated with the group
Diels–Alder_reaction
Class of semiconductor nanocrystals
orthorhombic structure at room temperature. This results in reduced orbital overlap between the halide and lead atoms and blue shifts the absorption and
Perovskite_nanocrystal
Instability in molecules with bonds at unnatural angles
are expected. The intense angle strain leads to nonlinear orbital overlap of its sp3 orbitals. Because of the bond's instability, cyclopropane is more
Ring_strain
Chemical reaction in which two ligands of a metal complex combine
(i) orbital overlap of the alkyl group initially attached to the metal and (ii) the strength of the metal-alkyl bond. With greater orbital overlap between
Migratory_insertion
Predictive model in organic chemistry
and the lowest unoccupied molecular orbital (LUMO) of another system have comparable energies and spatial overlap, the electrons can delocalize and sink
Cieplak_effect
Model of electronic band structures of solids
ionization energy corresponding to the chosen atomic orbital and U is the energy shift of the orbital as a result of the potential of neighboring atoms.
Tight_binding
A triangle showing varying degrees of ionic, metallic and covalent bonding
delocalized bonding and the other are covalent bonds in which the orbitals overlap in a particular direction. The left side (from ionic to metallic) is
Van_Arkel–Ketelaar_triangle
Compound with a metal center bound to ligands
that shape are the locations of the ligands), where orbital overlap (between ligand and metal orbitals) and ligand-ligand repulsions tend to lead to certain
Coordination_complex
Pollution around Earth by defunct artificial objects
trash, space garbage, orbital space debris or cosmic debris) are defunct human-made objects in space – principally in Earth orbit – which no longer serve
Space_debris
Class of ions
donation of electron density from a β C-H or C-C bond into the unoccupied p orbital of the carbocation (a σCH/CC → p interaction) allows the positive charge
Carbenium_ion
Aspect of quantum chemistry
orbitals, while the corresponding "nonbonding" orbitals of carbenes are generally treated as a filled σ(out) orbital and an unfilled pure p orbital,
Localized_molecular_orbitals
Nucleophilic-addition system
is not based on random collision, and so the relationship between orbital overlap principles and reactivity is more complex. For instance, while a simple
Flippin–Lodge_angle
Angle in physical organic chemistry
to maximize overlap between the highest occupied molecular orbital (HOMO) of the nucleophile, and the lowest unoccupied molecular orbital (LUMO) of the
Bürgi–Dunitz_angle
Chemical compound
proposed to arise from the overlap of four d-orbitals on each metal with the same orbitals on the other metal: the dz2 orbitals overlap to give a sigma bonding
Chromium(II)_acetate
material. By careful selection of organic building units, long range π-orbital overlap parallel to the stacking direction of certain organic frameworks can
Two-dimensional_polymer
Greek letter
Sometimes profit in microeconomics. A type of chemical bond in which the p orbitals overlap, called a pi bond. The natural projection on the tangent bundle on
Pi_(letter)
Chinese modular space station (since 2021)
mission. Tiangong is the first crewed spacecraft to use ion thrusters, for orbital station-keeping, while communications are relayed through the Tianlian
Tiangong_space_station
Mechanism of spontaneous symmetry breaking
the excited state wavefunction belongs (mainly) to the other, the orbital overlap resulting from the distortion adds covalency to the bond between them
Pseudo_Jahn–Teller_effect
Heat-activated light emission
moieties showing small orbital overlap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). As a consequence
Thermally activated delayed fluorescence
Thermally_activated_delayed_fluorescence
Solid consisting of discrete molecules
conductivity, such as TTF-TCNQ with ρ = 5 × 102 Ω−1 cm−1 but in such cases orbital overlap is evident in the crystal structure. Fullerenes, which are insulating
Molecular_solid
Chemistry based on quantum physics
from two s-orbitals, an s-orbital and a p-orbital, or two p-orbitals. A pi (π) bond is formed from a side-to-side overlap of two p-orbitals. The pi bond
Quantum_chemistry
Chemical compound
in d orbitals, its LUMO is the lowest-energy d-orbital dz2. dz2 is stabilized by σ-donation from the nitrogen lone pair (with sp-hybridized orbital) of
Molybdenum imido alkylidene complex
Molybdenum_imido_alkylidene_complex
Chemical compound
this model the carbon-carbon bonds are bent outwards so that the inter-orbital angle is 104°. The unusual structural properties of cyclopropane have spawned
Cyclopropane
American scientist and activist (1901–1994)
by the molecular orbital theory of Robert Mulliken, valence bond theory still competes, in its modern form, with molecular orbital theory and density
Linus_Pauling
Class of aluminium compounds
worse at forming multiple bonds than carbon because of the weaker orbital overlap. Unlike alkenes and alkynes, which typically form rigid planar or linear
Dialumene
Electrically neutral group of two or more atoms
molecules such as CH4, in which four sp³ hybridised orbitals are overlapped by hydrogen's 1s orbital, yielding four sigma (σ) bonds. The four bonds are
Molecule
Molecular orbital
A non-bonding orbital, also known as non-bonding molecular orbital (NBMO), is a molecular orbital whose occupation by electrons neither increases nor
Non-bonding_orbital
Chemical reaction
shortening of the C1-C6 bond. In the case of electron donating groups, orbital overlap is again possible now in the LUMO, resulting in an increase in antibonding
Buchner_ring_expansion
Charged species in chemistry
be shown through a molecular orbital diagram. Because of the additional overlap between the orbitals, the bonding orbital for the "closed" type is pushed
Hydrogen-bridged_cations
Chemical element with atomic number 113 (Nh)
significant pi bonding character (side-on orbital overlap), unlike the almost pure sigma bonding (head-on orbital overlap) in thallium monohydride (TlH). The
Nihonium
Enzymes that break down DNA
dsDNA, the bases are no longer stacked as they are in dsDNA, so that orbital overlap is minimized and UV absorbance increases. This increase in absorbance
Deoxyribonuclease
Special type of aromaticity
molecular orbital theory these compounds have in common a monocyclic array of molecular orbitals in which there is an odd number of out-of-phase overlaps, the
Möbius_aromaticity
Hypotheses about Triton's origin
debris and thus orbit prograde. As a result, astronomers have proposed various hypotheses on how Triton acquired its unusual orbital configuration, with
Capture_of_Triton
Equations in quantum chemistry
coefficients, S is the overlap matrix of the basis functions, and ϵ {\displaystyle \epsilon } is the (diagonal, by convention) matrix of orbital energies. In the
Roothaan_equations
Elements with atomic numbers 57-70
little or no covalent character and are not influenced by orbital geometries. The lack of orbital interaction also means that varying the metal typically
Lanthanide
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