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c_1lcvx4boj92a
They all appear to have a head-stalk-anchor structure. Each TAA is made up of three identical proteins, hence the name trimeric. Once the membrane anchor has been inserted into the outer membrane, the passenger domain passes through it into the host extracellular environment autonomously, hence the description of autot...
Trimeric autotransporter adhesin
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In molecular biology, two nucleotides on opposite complementary DNA or RNA strands that are connected via hydrogen bonds are called a base pair (often abbreviated bp). In the canonical Watson-Crick base pairing, adenine (A) forms a base pair with thymine (T) and guanine (G) forms one with cytosine (C) in DNA. In RNA, t...
Nucleic acid secondary structure
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Importantly, pairing is the mechanism by which codons on messenger RNA molecules are recognized by anticodons on transfer RNA during protein translation. Some DNA- or RNA-binding enzymes can recognize specific base pairing patterns that identify particular regulatory regions of genes. Hydrogen bonding is the chemical m...
Nucleic acid secondary structure
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Appropriate geometrical correspondence of hydrogen bond donors and acceptors allows only the "right" pairs to form stably. DNA with high GC-content is more stable than DNA with low GC-content, but contrary to popular belief, the hydrogen bonds do not stabilize the DNA significantly and stabilization is mainly due to st...
Nucleic acid secondary structure
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In molecular biology, ultrasensitivity describes an output response that is more sensitive to stimulus change than the hyperbolic Michaelis-Menten response. Ultrasensitivity is one of the biochemical switches in the cell cycle and has been implicated in a number of important cellular events, including exiting G2 cell c...
Ultrasensitivity
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This acts to filter out noise, as small stimuli and threshold concentrations of the stimulus (input signal) is necessary for the trigger which allows the system to get activated quickly. Ultrasensitive responses are represented by sigmoidal graphs, which resemble cooperativity. The quantification of ultrasensitivity is...
Ultrasensitivity
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In molecular biology, wheat germ extract is used to carry out cell-free in vitro translation experiments since the plant embryo contains all the macromolecular components necessary for translating mRNA into proteins but relatively low levels of its own mRNA.Wheat germ is also useful in biochemistry since it contains le...
Cereal germ
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In molecular biology, zinc-dependent phospholipases C is a family of bacterial phospholipases C enzymes, some of which are also known as alpha toxins. Bacillus cereus contains a monomeric phospholipase C EC 3.1.4.3 (PLC) of 245 amino-acid residues. Although PLC prefers to act on phosphatidylcholine, it also shows weak ...
Zinc-dependent phospholipase C
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The enzymes catalyse the conversion of phosphatidylcholine and water to 1,2-diacylglycerol and choline phosphate.In Bacillus cereus, there are nine residues known to be involved in binding the zinc ions: 5 His, 2 Asp, 1 Glu and 1 Trp. These residues are all conserved in the Clostridium alpha-toxin. Some examples of thi...
Zinc-dependent phospholipase C
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In molecular biology,snoRNA snR53 is a non-coding RNA (ncRNA) molecule which functions in the modification of other small nuclear RNAs (snRNAs). This type of modifying RNA is usually located in the nucleolus of the eukaryotic cell which is a major site of snRNA biogenesis. It is known as a small nucleolar RNA (snoRNA) ...
Small nucleolar RNA snR53
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snoRNA snR53 belongs to the C/D box class of snoRNAs which contain the conserved sequence motifs known as the C box (UGAUGA) and the D box (CUGA). Most of the members of the box C/D family function in directing site-specific 2'-O-methylation of substrate RNAs. snoRNA snR53 was initially discovered using a computational...
Small nucleolar RNA snR53
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In molecular cloning and biology, a gene knock-in (abbreviation: KI) refers to a genetic engineering method that involves the one-for-one substitution of DNA sequence information in a genetic locus or the insertion of sequence information not found within the locus. Typically, this is done in mice since the technology ...
Gene knockin
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A common use of knock-in technology is for the creation of disease models. It is a technique by which scientific investigators may study the function of the regulatory machinery (e.g. promoters) that governs the expression of the natural gene being replaced. This is accomplished by observing the new phenotype of the or...
Gene knockin
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In molecular cloning, a vector is any particle (e.g., plasmids, cosmids, Lambda phages) used as a vehicle to artificially carry a foreign nucleic sequence – usually DNA – into another cell, where it can be replicated and/or expressed. A vector containing foreign DNA is termed recombinant DNA. The four major types of ve...
Vector DNA
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Common to all engineered vectors are an origin of replication, a multicloning site, and a selectable marker. The vector itself generally carries a DNA sequence that consists of an insert (in this case the transgene) and a larger sequence that serves as the "backbone" of the vector. The purpose of a vector which transfe...
Vector DNA
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All vectors may be used for cloning and are therefore cloning vectors, but there are also vectors designed specially for cloning, while others may be designed specifically for other purposes, such as transcription and protein expression. Vectors designed specifically for the expression of the transgene in the target ce...
Vector DNA
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Transcription vectors are used to amplify their insert. The manipulation of DNA is normally conducted on E. coli vectors, which contain elements necessary for their maintenance in E. coli. However, vectors may also have elements that allow them to be maintained in another organism such as yeast, plant or mammalian cell...
Vector DNA
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In molecular clouds, simple carbon molecules are formed, including carbon monoxide and dicarbon. Reactions with the trihydrogen cation of the simple carbon molecules yield carbon containing ions that readily react to form larger organic molecules. Carbon compounds that exist as ions, or isolated gas molecules in the in...
Geochemistry of carbon
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In molecular crystals the energetic separation between the top of the valence band and the bottom conduction band, i.e. the band gap, is typically 2.5–4 eV, while in inorganic semiconductors the band gaps are typically 1–2 eV. This implies that they are, in fact, insulators rather than semiconductors in the conventiona...
Organic semiconductors
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It is important to realize, however, that the primary optical excitations are neutral excitons with a Coulomb-binding energy of typically 0.5–1.0 eV. The reason is that in organic semiconductors their dielectric constants are as low as 3–4.
Organic semiconductors
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This impedes efficient photogeneration of charge carriers in neat systems in the bulk. Efficient photogeneration can only occur in binary systems due to charge transfer between donor and acceptor moieties. Otherwise neutral excitons decay radiatively to the ground state – thereby emitting photoluminescence – or non-rad...
Organic semiconductors
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In molecular dynamics (MD) simulations, the flying ice cube effect is an artifact in which the energy of high-frequency fundamental modes is drained into low-frequency modes, particularly into zero-frequency motions such as overall translation and rotation of the system. The artifact derives its name from a particularl...
Flying ice cube
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In molecular dynamics (MD) simulations, there are errors due to inadequate sampling of the phase space or infrequently occurring events, these lead to the statistical error due to random fluctuation in the measurements. For a series of M measurements of a fluctuating property A, the mean value is: When these M measurem...
Error analysis (mathematics)
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In molecular dynamics, coarse graining consists of replacing an atomistic description of a biological molecule with a lower-resolution coarse-grained model that averages or smooths away fine details. Coarse-grained models have been developed for investigating the longer time- and length-scale dynamics that are critical...
Coarse graining
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Coarse graining may remove certain degrees of freedom, such as the vibrational modes between two atoms, or represent the two atoms as a single particle. The ends to which systems may be coarse-grained is simply bound by the accuracy in the dynamics and structural properties one wishes to replicate. This modern area of ...
Coarse graining
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In molecular genetics, a DNA adduct is a segment of DNA bound to a cancer-causing chemical. This process could lead to the development of cancerous cells, or carcinogenesis. DNA adducts in scientific experiments are used as biomarkers of exposure. They are especially useful in quantifying an organism's exposure to a ca...
DNA adducts
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The presence of such an adduct indicates prior exposure to a potential carcinogen, but it does not necessarily indicate the presence of cancer in the subject animal. DNA adducts are researched in laboratory settings. A typical experimental design for studying DNA adducts is to induce them with known carcinogens. A scie...
DNA adducts
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In molecular genetics, a regulon is a group of genes that are regulated as a unit, generally controlled by the same regulatory gene that expresses a protein acting as a repressor or activator. This terminology is generally, although not exclusively, used in reference to prokaryotes, whose genomes are often organized in...
Regulon
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In molecular genetics, a repressor is a DNA- or RNA-binding protein that inhibits the expression of one or more genes by binding to the operator or associated silencers. A DNA-binding repressor blocks the attachment of RNA polymerase to the promoter, thus preventing transcription of the genes into messenger RNA. An RNA...
Repressor (genetics)
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In molecular genetics, an untranslated region (or UTR) refers to either of two sections, one on each side of a coding sequence on a strand of mRNA. If it is found on the 5' side, it is called the 5' UTR (or leader sequence), or if it is found on the 3' side, it is called the 3' UTR (or trailer sequence). mRNA is RNA th...
Untranslated region
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However, several regions of the mRNA are usually not translated into protein, including the 5' and 3' UTRs. Although they are called untranslated regions, and do not form the protein-coding region of the gene, uORFs located within the 5' UTR can be translated into peptides.The 5' UTR is upstream from the coding sequenc...
Untranslated region
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The mechanism of translation initiation differs in prokaryotes and eukaryotes. The 3' UTR is found immediately following the translation stop codon.
Untranslated region
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The 3' UTR plays a critical role in translation termination as well as post-transcriptional modification.These often long sequences were once thought to be useless or junk mRNA that has simply accumulated over evolutionary time. However, it is now known that the untranslated region of mRNA is involved in many regulator...
Untranslated region
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It is important to distinguish the 5' and 3' UTRs from other non-protein-coding RNA. Within the coding sequence of pre-mRNA, there can be found sections of RNA that will not be included in the protein product. These sections of RNA are called introns.
Untranslated region
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The RNA that results from RNA splicing is a sequence of exons. The reason why introns are not considered untranslated regions is that the introns are spliced out in the process of RNA splicing. The introns are not included in the mature mRNA molecule that will undergo translation and are thus considered non-protein-cod...
Untranslated region
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In molecular genetics, the Krüppel-like family of transcription factors (KLFs) are a set of eukaryotic C2H2 zinc finger DNA-binding proteins that regulate gene expression. This family has been expanded to also include the Sp transcription factor and related proteins, forming the Sp/KLF family.
Kruppel-like transcription factors
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In molecular genetics, the three prime untranslated region (3′-UTR) is the section of messenger RNA (mRNA) that immediately follows the translation termination codon. The 3′-UTR often contains regulatory regions that post-transcriptionally influence gene expression. During gene expression, an mRNA molecule is transcrib...
3′ UTR
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Regulatory regions within the 3′-untranslated region can influence polyadenylation, translation efficiency, localization, and stability of the mRNA. The 3′-UTR contains binding sites for both regulatory proteins and microRNAs (miRNAs). By binding to specific sites within the 3′-UTR, miRNAs can decrease gene expression ...
3′ UTR
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The 3′-UTR also has silencer regions which bind to repressor proteins and will inhibit the expression of the mRNA. Many 3′-UTRs also contain AU-rich elements (AREs).
3′ UTR
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Proteins bind AREs to affect the stability or decay rate of transcripts in a localized manner or affect translation initiation. Furthermore, the 3′-UTR contains the sequence AAUAAA that directs addition of several hundred adenine residues called the poly(A) tail to the end of the mRNA transcript. Poly(A) binding protei...
3′ UTR
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For example, poly(A) tail bound PABP interacts with proteins associated with the 5' end of the transcript, causing a circularization of the mRNA that promotes translation. The 3′-UTR can also contain sequences that attract proteins to associate the mRNA with the cytoskeleton, transport it to or from the cell nucleus, o...
3′ UTR
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In molecular geometry, bond length or bond distance is defined as the average distance between nuclei of two bonded atoms in a molecule. It is a transferable property of a bond between atoms of fixed types, relatively independent of the rest of the molecule.
Bond distance
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In molecular kinetic theory in physics, a system's distribution function is a function of seven variables, f ( x , y , z , t ; v x , v y , v z ) {\displaystyle f(x,y,z,t;v_{x},v_{y},v_{z})} , which gives the number of particles per unit volume in single-particle phase space. It is the number of particles per unit volum...
Distribution function (physics)
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E.g. take the quantum mechanical six-dimensional phase space, f ( x , y , z ; p x , p y , p z ) {\displaystyle f(x,y,z;p_{x},p_{y},p_{z})} and multiply by the total space volume, to give the momentum distribution, i.e. the number of particles in the momentum phase space having approximately the momentum ( p x , p y , p...
Distribution function (physics)
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Distribution functions are also used in fluid mechanics, statistical mechanics and nuclear physics. The basic distribution function uses the Boltzmann constant k {\displaystyle k} and temperature T {\displaystyle T} with the number density to modify the normal distribution: f = n ( m 2 π k T ) 3 / 2 exp ⁡ ( − m ( v x 2...
Distribution function (physics)
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Related distribution functions may allow bulk fluid flow, in which case the velocity origin is shifted, so that the exponent's numerator is m ( ( v x − u x ) 2 + ( v y − u y ) 2 + ( v z − u z ) 2 ) {\displaystyle m((v_{x}-u_{x})^{2}+(v_{y}-u_{y})^{2}+(v_{z}-u_{z})^{2})} , where ( u x , u y , u z ) {\displaystyle (u_{x}...
Distribution function (physics)
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In this case, the distribution function is Maxwellian. This distribution function allows fluid flow and different temperatures in the directions parallel to, and perpendicular to, the local magnetic field. More complex distribution functions may also be used, since plasmas are rarely in thermal equilibrium. The mathema...
Distribution function (physics)
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In molecular mechanics, VALBOND is a method for computing the angle bending energy that is based on valence bond theory. It is based on orbital strength functions, which are maximized when the hybrid orbitals on the atom are orthogonal. The hybridization of the bonding orbitals are obtained from empirical formulas base...
VALBOND
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The VALBOND functions are suitable for describing the energy of bond angle distortion not only around the equilibrium angles, but also at very large distortions. This represents an advantage over the simpler harmonic oscillator approximation used by many force fields, and allows the VALBOND method to handle hypervalent...
VALBOND
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In molecular mechanics, several ways exist to define the environment surrounding a molecule or molecules of interest. A system can be simulated in vacuum (termed a gas-phase simulation) with no surrounding environment, but this is usually undesirable because it introduces artifacts in the molecular geometry, especially...
Molecular mechanics
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The most accurate way to solvate a system is to place explicit water molecules in the simulation box with the molecules of interest and treat the water molecules as interacting particles like those in the other molecule(s). A variety of water models exist with increasing levels of complexity, representing water as a si...
Molecular mechanics
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In molecular modelling, docking is a method which predicts the preferred orientation of one molecule to another when bound together in a stable complex. In the case of protein docking, the search space consists of all possible orientations of the protein with respect to the ligand. Flexible docking in addition consider...
Searching the conformational space for docking
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In molecular nanotechnology, chemosynthesis is any chemical synthesis where reactions occur due to random thermal motion, a class which encompasses almost all of modern synthetic chemistry. The human-authored processes of chemical engineering are accordingly represented as biomimicry of the natural phenomena above, and...
Chemosynthesis (nanotechnology)
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In this case synthesis is most efficiently performed through the use of molecular building blocks with a small amount of linkages. Unstrained molecules are also preferred, which is when molecules undergo minimal external stress, which leads to the molecule having a low internal energy. There are two main types of synth...
Chemosynthesis (nanotechnology)
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In additive synthesis the structure starts with nothing, and then gradually molecular building blocks are added until the structure that is needed is created. In subtractive synthesis they start with a large molecule and remove building blocks one by one until the structure is achieved.This form of engineering is then ...
Chemosynthesis (nanotechnology)
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For instance, sheet diamond or carbon nanotubes could be produced by a chain of non-biological reactions that have been designed using the basic model of biology. Use of the term chemosynthesis reinforces the view that this is feasible by pointing out that several alternate means of creating complex proteins, mineral s...
Chemosynthesis (nanotechnology)
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In molecular orbital theory, bond order is defined as half the difference between the number of bonding electrons and the number of antibonding electrons as per the equation below. This often but not always yields similar results for bonds near their equilibrium lengths, but it does not work for stretched bonds. Bond o...
Bond Order
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bond order = number of bonding electrons - number of antibonding electrons/2Generally, the higher the bond order, the stronger the bond. Bond orders of one-half may be stable, as shown by the stability of H+2 (bond length 106 pm, bond energy 269 kJ/mol) and He+2 (bond length 108 pm, bond energy 251 kJ/mol).Hückel molec...
Bond Order
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The π-bond order between atoms r and s derived from Hückel theory was defined by Charles Coulson by using the orbital coefficients of the Hückel MOs: p r s = ∑ i n i c r i c s i {\displaystyle p_{rs}=\sum _{i}n_{i}c_{ri}c_{si}} ,Here the sum extends over π molecular orbitals only, and ni is the number of electrons occu...
Bond Order
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In molecular orbital theory, the main alternative to valence bond theory, the molecular orbitals (MOs) are approximated as sums of all the atomic orbitals (AOs) on all the atoms; there are as many MOs as AOs. Each AOi has a weighting coefficient ci that indicates the AO's contribution to a particular MO. For example, i...
Resonance energy
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This MO interpretation has inspired the picture of the benzene ring as a hexagon with a circle inside. When describing benzene, the VB concept of localized σ bonds and the MO concept of delocalized π orbitals are frequently combined in elementary chemistry courses. The contributing structures in the VB model are partic...
Resonance energy
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They lead to the models of contributing structures for an electron-withdrawing group and electron-releasing group on benzene. The utility of MO theory is that a quantitative indication of the charge from the π system on an atom can be obtained from the squares of the weighting coefficient ci on atom Ci. Charge qi ≈ c2i...
Resonance energy
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The reason for squaring the coefficient is that if an electron is described by an AO, then the square of the AO gives the electron density. The AOs are adjusted (normalized) so that AO2 = 1, and qi ≈ (ciAOi)2 ≈ c2i. In benzene, qi = 1 on each C atom. With an electron-withdrawing group qi < 1 on the ortho and para C ato...
Resonance energy
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In molecular phylogenetics, relationships among individuals are determined using character traits, such as DNA, RNA or protein, which may be obtained using a variety of sequencing technologies. High-throughput next-generation sequencing has become a popular technique in transcriptomics, which represent a snapshot of ge...
Phylogenetic inference using transcriptomic data
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In molecular physics, crystal field theory (CFT) describes the breaking of degeneracies of electron orbital states, usually d or f orbitals, due to a static electric field produced by a surrounding charge distribution (anion neighbors). This theory has been used to describe various spectroscopies of transition metal co...
Crystal field stabilization energy
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In molecular physics, the Hamaker constant (denoted A; named for H. C. Hamaker) is a physical constant that can be defined for a van der Waals (vdW) body–body interaction: A = π 2 C ρ 1 ρ 2 , {\displaystyle A=\pi ^{2}C\rho _{1}\rho _{2},} where ρ1, ρ2 are the number densities of the two interacting kinds of particles, ...
Hamaker constant
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Hamaker's method and the associated Hamaker constant ignores the influence of an intervening medium between the two particles of interaction. In 1956 Lifshitz developed a description of the vdW energy but with consideration of the dielectric properties of this intervening medium (often a continuous phase).The Van der W...
Hamaker constant
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In molecular physics, the Pariser–Parr–Pople method applies semi-empirical quantum mechanical methods to the quantitative prediction of electronic structures and spectra, in molecules of interest in the field of organic chemistry. Previous methods existed—such as the Hückel method which led to Hückel's rule—but were li...
Pariser–Parr–Pople method
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This method used the zero-differential overlap (ZDO) approximation to reduce the problem to reasonable size and complexity but still required modern solid state computers (as opposed to punched card or vacuum tube systems) before becoming fully useful for molecules larger than benzene. Originally, Pariser's goal of usi...
Pariser–Parr–Pople method
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The two basic papers on this subject were among the top five chemistry and physics citations reported in ISI, Current Contents 1977 for the period of 1961–1977 with a total of 2450 references. In contrast to the Hartree–Fock-based semiempirical method counterparts (i.e.: MOPAC), the pi-electron theories have a very str...
Pariser–Parr–Pople method
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A rigorous, ab initio theory of the PPP method is provided by diagrammatic, multi-reference, high order perturbation theory (Freed, Brandow, Lindgren, etc.). (The exact formulation is non-trivial, and requires some field theory) Large scale ab initio calculations (Martin and Birge, Martin and Freed, Sheppard and Freed,...
Pariser–Parr–Pople method
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In molecular physics, the molecular term symbol is a shorthand expression of the group representation and angular momenta that characterize the state of a molecule, i.e. its electronic quantum state which is an eigenstate of the electronic molecular Hamiltonian. It is the equivalent of the term symbol for the atomic ca...
Molecular term symbol
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For heteronuclear diatomic molecules, the u/g symbol does not correspond to any exact symmetry of the electronic molecular Hamiltonian. In the case of less symmetric molecules the molecular term symbol contains the symbol of the group representation to which the molecular electronic state belongs. It has the general fo...
Molecular term symbol
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In molecular physics, the van der Waals force is a distance-dependent interaction between atoms or molecules. Unlike ionic or covalent bonds, these attractions do not result from a chemical electronic bond; they are comparatively weak and therefore more susceptible to disturbance. The van der Waals force quickly vanish...
Van der Waals forces
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Named after Dutch physicist Johannes Diderik van der Waals, the van der Waals force plays a fundamental role in fields as diverse as supramolecular chemistry, structural biology, polymer science, nanotechnology, surface science, and condensed matter physics. It also underlies many properties of organic compounds and mo...
Van der Waals forces
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In molecular physics/nanotechnology, electrostatic deflection is the deformation of a beam-like structure/element bent by an electric field (Fig. 1). It can be due to interaction between electrostatic fields and net charge or electric polarization effects. The beam-like structure/element is generally cantilevered (fix ...
Electrostatic deflection (structural element)
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Mechanisms of electric deflection due to electric polarization can be understood as follows: As shown in Fig.2, when a material is brought into an electric field (E), the field tends to shift the positive charge (in red) and the negative charge (in blue) in opposite directions. Thus, induced dipoles are created. Fig. 3...
Electrostatic deflection (structural element)
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The interaction between the molecular dipole moment and the electric field results an induced torque (T). Then this torque tends to align the beam toward the direction of field. In case of a cantilevered CNT (Fig. 1), it would be bent to the field direction.
Electrostatic deflection (structural element)
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Meanwhile, the electrically induced torque and stiffness of the CNT compete against each other. This deformation has been observed in experiments.
Electrostatic deflection (structural element)
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This property is an important characteristic for CNTs promising nanoelectromechanical systems applications, as well as for their fabrication, separation and electromanipulation. Recently, several nanoelectromechanical systems based on cantilevered CNTs have been reported such as: nanorelays, nanoswitches, nanotweezers ...
Electrostatic deflection (structural element)
c_wzi9onhlfzy1
In molecular physics/nanotechnology, electrostatic deflection is the deformation of a beam-like structure/element bent by an electric field. It can be due to interaction between electrostatic fields and net charge or electric polarization effects. The beam-like structure/element is generally cantilevered (fix at one of...
Electrostatic deflection (molecular physics/nanotechnology)
c_ytl4bgh5pl5q
Mechanisms of electric deflection due to electric polarization can be understood as follows: When a material is brought into an electric field (E), the field tends to shift the positive charge (in red) and the negative charge (in blue) in opposite directions. Thus, induced dipoles are created. Fig. 3 shows a beam-like ...
Electrostatic deflection (molecular physics/nanotechnology)
c_xp6vbz8xz2py
The interaction between the molecular dipole moment and the electric field results an induced torque (T). Then this torque tends to align the beam toward the direction of field. In case of a cantilevered CNT, it would be bent to the field direction.
Electrostatic deflection (molecular physics/nanotechnology)
c_740rcfp8zdf2
Meanwhile the electrically induced torque and stiffness of the CNT compete against each other. This deformation has been observed in experiments.
Electrostatic deflection (molecular physics/nanotechnology)
c_f72zbobh88oi
This property is an important characteristic for CNTs promising nanoelectromechanical systems applications, as well as for their fabrication, separation and electromanipulation. Recently, several nanoelectromechanical systems based on cantilevered CNTs have been reported such as: nanorelays, nanoswitches, nanotweezers ...
Electrostatic deflection (molecular physics/nanotechnology)
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In molecular spectroscopy, a Jablonski diagram is a diagram that illustrates the electronic states and often the vibrational levels of a molecule, and also the transitions between them. The states are arranged vertically by energy and grouped horizontally by spin multiplicity. Nonradiative transitions are indicated by ...
Jablonski diagram
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In molecular spectroscopy, the Birge–Sponer method or Birge–Sponer plot is a way to calculate the dissociation energy of a molecule. By observing transitions between as many vibrational energy levels as possible, for example through electronic or infrared spectroscopy, the difference between the energy levels, Δ G v + ...
Birge-Sponer method
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If a Morse potential is assumed, plotting Δ G v + 1 2 {\displaystyle \Delta G_{v+{\frac {1}{2}}}} against v + 1 / 2 {\displaystyle v+1/2} should give a straight line, from which it is easy to extract v m a x {\displaystyle v_{max}} from the intercept with the x-axis. In practice, such plots often give curves because of...
Birge-Sponer method
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Thus the extrapolation can be inaccurate and only an upper limit for the value of the dissociation energy can be obtained. This method takes its name from Raymond Thayer Birge and Hertha Sponer, the two physical chemists that developed it. A detailed example may be found here.
Birge-Sponer method
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In molecular vibrational spectroscopy, a hot band is a band centred on a hot transition, which is a transition between two excited vibrational states, i.e. neither is the overall ground state. In infrared or Raman spectroscopy, hot bands refer to those transitions for a particular vibrational mode which arise from a st...
Hot transition
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In molecules which have resonance or nonclassical bonding, bond order may not be an integer. In benzene, the delocalized molecular orbitals contain 6 pi electrons over six carbons, essentially yielding half a pi bond together with the sigma bond for each pair of carbon atoms, giving a calculated bond order of 1.5 (one ...
Bond Order
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In molecules whose vibrational mode involves a rotational or pseudorotational mechanism (such as the Berry mechanism or the Bartell mechanism), Van der Waals strain can cause significant differences in potential energy, even between molecules with identical geometry. PF5, for example, has significantly lower potential ...
Steric strain
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In molecules with alternating double bonds and single bonds, p-orbital overlap can exist over multiple atoms in a chain, giving rise to a conjugated system. Conjugation can be found in systems such as dienes and enones. In cyclic molecules, conjugation can lead to aromaticity.
Double bonds
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In cumulenes, two double bonds are adjacent. Double bonds are common for period 2 elements carbon, nitrogen, and oxygen, and less common with elements of higher periods. Metals, too, can engage in multiple bonding in a metal ligand multiple bond.
Double bonds
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In molecules with several atoms, some orbitals may be delocalized over more than two atoms. A particular molecular orbital may be bonding with respect to some adjacent pairs of atoms and antibonding with respect to other pairs. If the bonding interactions outnumber the antibonding interactions, the MO is said to be bon...
Antibonding orbitals
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There are two bonding pi orbitals which are occupied in the ground state: π1 is bonding between all carbons, while π2 is bonding between C1 and C2 and between C3 and C4, and antibonding between C2 and C3. There are also antibonding pi orbitals with two and three antibonding interactions as shown in the diagram; these a...
Antibonding orbitals
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Since each carbon atom contributes one electron to the π-system of benzene, there are six pi electrons which fill the three lowest-energy pi molecular orbitals (the bonding pi orbitals). Antibonding orbitals are also important for explaining chemical reactions in terms of molecular orbital theory. Roald Hoffmann and Ke...
Antibonding orbitals
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In molecules, regions of large electron density are usually found around the atom, and its bonds. In de-localised or conjugated systems, such as phenol, benzene and compounds such as hemoglobin and chlorophyll, the electron density is significant in an entire region, i.e., in benzene they are found above and below the ...
Electronic density
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This is shown below: In compounds with multiple ring systems which are interconnected, this is no longer accurate, so alternating single and double bonds are used. In compounds such as chlorophyll and phenol, some diagrams show a dotted or dashed line to represent the delocalization of areas where the electron density ...
Electronic density
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In polymers, these areas are known as chromophores. In quantum chemical calculations, the electron density, ρ(r), is a function of the coordinates r, defined so ρ(r)dr is the number of electrons in a small volume dr. For closed-shell molecules, ρ ( r ) {\displaystyle \rho (\mathbf {r} )} can be written in terms of a su...
Electronic density