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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 autotransporter. The head domain, once assembled, then adheres to an element of the host extracellular matrix, for example, collagen, fibronectin, etc. | https://en.wikipedia.org/wiki/Trimeric_autotransporter_adhesin |
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, thymine is replaced by uracil (U). Alternate hydrogen bonding patterns, such as the wobble base pair and Hoogsteen base pair, also occur—particularly in RNA—giving rise to complex and functional tertiary structures. | https://en.wikipedia.org/wiki/Nucleic_acid_secondary_structure |
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 mechanism that underlies the base-pairing rules described above. | https://en.wikipedia.org/wiki/Nucleic_acid_secondary_structure |
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 stacking interactions.The larger nucleobases, adenine and guanine, are members of a class of doubly ringed chemical structures called purines; the smaller nucleobases, cytosine and thymine (and uracil), are members of a class of singly ringed chemical structures called pyrimidines. Purines are only complementary with pyrimidines: pyrimidine-pyrimidine pairings are energetically unfavorable because the molecules are too far apart for hydrogen bonding to be established; purine-purine pairings are energetically unfavorable because the molecules are too close, leading to overlap repulsion. The only other possible pairings are GT and AC; these pairings are mismatches because the pattern of hydrogen donors and acceptors do not correspond. The GU wobble base pair, with two hydrogen bonds, does occur fairly often in RNA. | https://en.wikipedia.org/wiki/Nucleic_acid_secondary_structure |
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 cycle arrests in Xenopus laevis oocytes, a stage to which the cell or organism would not want to return.Ultrasensitivity is a cellular system which triggers entry into a different cellular state. Ultrasensitivity gives a small response to first input signal, but an increase in the input signal produces higher and higher levels of output. | https://en.wikipedia.org/wiki/Ultrasensitivity |
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 often performed approximately by the Hill equation: Response = S t i m u l u s n ( EC 50 n + S t i m u l u s n ) {\textstyle {\ce {Response}}={Stimulus^{n} \over ({\ce {EC50}}^{n}+Stimulus^{n})}} Where Hill's coefficient (n) may represent quantitative measure of ultrasensitive response. | https://en.wikipedia.org/wiki/Ultrasensitivity |
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 lectins that bind strongly to certain glycoproteins; therefore, it can be used to isolate such proteins. | https://en.wikipedia.org/wiki/Cereal_germ |
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 catalytic activity with sphingomyelin and phosphatidylinositol. Sequence studies have shown the protein to be similar both to alpha toxin from Clostridium perfringens and Clostridium bifermentans, a phospholipase C involved in haemolysis and cell rupture, and to lecithinase from Listeria monocytogenes, which aids cell-to-cell spread by breaking down the 2-membrane vacuoles that surround the bacterium during transfer.Each of these proteins is a zinc-dependent enzyme, binding 3 zinc ions per molecule. | https://en.wikipedia.org/wiki/Zinc-dependent_phospholipase_C |
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 this enzyme contain a C-terminal sequence extension that contains a PLAT domain which is thought to be involved in membrane localisation. == References == | https://en.wikipedia.org/wiki/Zinc-dependent_phospholipase_C |
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) and also often referred to as a guide RNA. | https://en.wikipedia.org/wiki/Small_nucleolar_RNA_snR53 |
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 screen of the Saccharomyces cerevisiae genome. | https://en.wikipedia.org/wiki/Small_nucleolar_RNA_snR53 |
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 for this process is more refined and there is a high degree of shared sequence complexity between mice and humans. The difference between knock-in technology and traditional transgenic techniques is that a knock-in involves a gene inserted into a specific locus, and is thus a "targeted" insertion. It is the opposite of gene knockout. | https://en.wikipedia.org/wiki/Gene_knockin |
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 organism in question. The BACs and YACs are used in this case so that large fragments can be transferred. | https://en.wikipedia.org/wiki/Gene_knockin |
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 vectors are plasmids, viral vectors, cosmids, and artificial chromosomes. Of these, the most commonly used vectors are plasmids. | https://en.wikipedia.org/wiki/Vector_DNA |
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 transfers genetic information to another cell is typically to isolate, multiply, or express the insert in the target cell. | https://en.wikipedia.org/wiki/Vector_DNA |
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 cell are called expression vectors, and generally have a promoter sequence that drives expression of the transgene. Simpler vectors called transcription vectors are only capable of being transcribed but not translated: they can be replicated in a target cell but not expressed, unlike expression vectors. | https://en.wikipedia.org/wiki/Vector_DNA |
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 cells, and these vectors are called shuttle vectors. Such vectors have bacterial or viral elements which may be transferred to the non-bacterial host organism, however other vectors termed intragenic vectors have also been developed to avoid the transfer of any genetic material from an alien species.Insertion of a vector into the target cell is usually called transformation for bacterial cells, transfection for eukaryotic cells, although insertion of a viral vector is often called transduction. | https://en.wikipedia.org/wiki/Vector_DNA |
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 interstellar medium, can condense onto dust grains. Carbonaceous dust grains consist mostly of carbon. Grains can stick together to form larger aggregates. | https://en.wikipedia.org/wiki/Geochemistry_of_carbon |
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 conventional sense. They become semiconducting only when charge carriers are either injected from the electrodes or generated by intentional or unintentional doping. Charge carriers can also be generated in the course of optical excitation. | https://en.wikipedia.org/wiki/Organic_semiconductors |
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. | https://en.wikipedia.org/wiki/Organic_semiconductors |
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-radiatively. The optical absorption edge of organic semiconductors is typically 1.7–3 eV, equivalent to a spectral range from 700 to 400 nm (which corresponds to the visible spectrum). | https://en.wikipedia.org/wiki/Organic_semiconductors |
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 particularly noticeable manifestation that arises in simulations of particles in vacuum, where the system being simulated acquires high linear momentum and experiences extremely damped internal motions, freezing the system into a single conformation reminiscent of an ice cube or other rigid body flying through space. The artifact is entirely a consequence of molecular dynamics algorithms and is wholly unphysical, since it violates the principle of equipartition of energy. | https://en.wikipedia.org/wiki/Flying_ice_cube |
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 measurements are independent, the variance of the mean ⟨A⟩ is: but in most MD simulations, there is correlation between quantity A at different time, so the variance of the mean ⟨A⟩ will be underestimated as the effective number of independent measurements is actually less than M. In such situations we rewrite the variance as: where ϕ μ {\displaystyle \phi _{\mu }} is the autocorrelation function defined by We can then use the auto correlation function to estimate the error bar. Luckily, we have a much simpler method based on block averaging. | https://en.wikipedia.org/wiki/Error_analysis_(mathematics) |
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 to many biological processes, such as lipid membranes and proteins. These concepts not only apply to biological molecules but also inorganic molecules. | https://en.wikipedia.org/wiki/Coarse_graining |
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 research is in its infancy, and although it is commonly used in biological modeling, the analytic theory behind it is poorly understood. | https://en.wikipedia.org/wiki/Coarse_graining |
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 carcinogen. | https://en.wikipedia.org/wiki/DNA_adducts |
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 scientific journal will often incorporate the name of the carcinogen with their experimental design. For example, the term "DMBA-DNA adduct" in a scientific journal refers to a piece of DNA that has DMBA (7,12-dimethylbenz(a)anthracene) attached to it. | https://en.wikipedia.org/wiki/DNA_adducts |
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 into operons; the genes contained within a regulon are usually organized into more than one operon at disparate locations on the chromosome. Applied to eukaryotes, the term refers to any group of non-contiguous genes controlled by the same regulatory gene.A modulon is a set of regulons or operons that are collectively regulated in response to changes in overall conditions or stresses, but may be under the control of different or overlapping regulatory molecules. The term stimulon is sometimes used to refer to the set of genes whose expression responds to specific environmental stimuli. | https://en.wikipedia.org/wiki/Regulon |
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-binding repressor binds to the mRNA and prevents translation of the mRNA into protein. This blocking or reducing of expression is called repression. | https://en.wikipedia.org/wiki/Repressor_(genetics) |
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 that carries information from DNA to the ribosome, the site of protein synthesis (translation) within a cell. The mRNA is initially transcribed from the corresponding DNA sequence and then translated into protein. | https://en.wikipedia.org/wiki/Untranslated_region |
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 sequence. Within the 5' UTR is a sequence that is recognized by the ribosome which allows the ribosome to bind and initiate translation. | https://en.wikipedia.org/wiki/Untranslated_region |
The mechanism of translation initiation differs in prokaryotes and eukaryotes. The 3' UTR is found immediately following the translation stop codon. | https://en.wikipedia.org/wiki/Untranslated_region |
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 regulatory aspects of gene expression in eukaryotic organisms. The importance of these non-coding regions is supported by evolutionary reasoning, as natural selection would have otherwise eliminated this unusable RNA. | https://en.wikipedia.org/wiki/Untranslated_region |
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. | https://en.wikipedia.org/wiki/Untranslated_region |
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-coding RNA. | https://en.wikipedia.org/wiki/Untranslated_region |
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. | https://en.wikipedia.org/wiki/Kruppel-like_transcription_factors |
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 transcribed from the DNA sequence and is later translated into a protein. Several regions of the mRNA molecule are not translated into a protein including the 5' cap, 5' untranslated region, 3′ untranslated region and poly(A) tail. | https://en.wikipedia.org/wiki/3′_UTR |
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 of various mRNAs by either inhibiting translation or directly causing degradation of the transcript. | https://en.wikipedia.org/wiki/3′_UTR |
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). | https://en.wikipedia.org/wiki/3′_UTR |
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 protein (PABP) binds to this tail, contributing to regulation of mRNA translation, stability, and export. | https://en.wikipedia.org/wiki/3′_UTR |
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, or perform other types of localization. In addition to sequences within the 3′-UTR, the physical characteristics of the region, including its length and secondary structure, contribute to translation regulation. These diverse mechanisms of gene regulation ensure that the correct genes are expressed in the correct cells at the appropriate times. | https://en.wikipedia.org/wiki/3′_UTR |
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. | https://en.wikipedia.org/wiki/Bond_distance |
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 volume having approximately the velocity v = ( v x , v y , v z ) {\displaystyle \mathbf {v} =(v_{x},v_{y},v_{z})} near the position r = ( x , y , z ) {\displaystyle \mathbf {r} =(x,y,z)} and time t {\displaystyle t} . The usual normalization of the distribution function is n ( x , y , z , t ) = ∫ f d v x d v y d v z , {\displaystyle n(x,y,z,t)=\int f\,dv_{x}\,dv_{y}\,dv_{z},} N ( t ) = ∫ n d x d y d z , {\displaystyle N(t)=\int n\,dx\,dy\,dz,} where N is the total number of particles and n is the number density of particles – the number of particles per unit volume, or the density divided by the mass of individual particles. A distribution function may be specialised with respect to a particular set of dimensions. | https://en.wikipedia.org/wiki/Distribution_function_(physics) |
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 z ) {\displaystyle (p_{x},p_{y},p_{z})} . Particle distribution functions are often used in plasma physics to describe wave–particle interactions and velocity-space instabilities. | https://en.wikipedia.org/wiki/Distribution_function_(physics) |
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 + v y 2 + v z 2 ) 2 k T ) . {\displaystyle f=n\left({\frac {m}{2\pi kT}}\right)^{3/2}\exp \left({-{\frac {m(v_{x}^{2}+v_{y}^{2}+v_{z}^{2})}{2kT}}}\right).} | https://en.wikipedia.org/wiki/Distribution_function_(physics) |
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},u_{y},u_{z})} is the bulk velocity of the fluid. Distribution functions may also feature non-isotropic temperatures, in which each term in the exponent is divided by a different temperature. Plasma theories such as magnetohydrodynamics may assume the particles to be in thermodynamic equilibrium. | https://en.wikipedia.org/wiki/Distribution_function_(physics) |
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 mathematical analogue of a distribution is a measure; the time evolution of a measure on a phase space is the topic of study in dynamical systems. | https://en.wikipedia.org/wiki/Distribution_function_(physics) |
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 based on Bent's rule, which relates the preference towards p character with electronegativity. | https://en.wikipedia.org/wiki/VALBOND |
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 molecules and transition metal complexes. The VALBOND energy term has been combined with force fields such as CHARMM and UFF to provide a complete functional form that includes also bond stretching, torsions, and non-bonded interactions. | https://en.wikipedia.org/wiki/VALBOND |
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 in charged molecules. Surface charges that would ordinarily interact with solvent molecules instead interact with each other, producing molecular conformations that are unlikely to be present in any other environment. | https://en.wikipedia.org/wiki/Molecular_mechanics |
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 simple hard sphere (a united-atom model), as three separate particles with fixed bond angle, or even as four or five separate interaction centers to account for unpaired electrons on the oxygen atom. As water models grow more complex, related simulations grow more computationally intensive. A compromise method has been found in implicit solvation, which replaces the explicitly represented water molecules with a mathematical expression that reproduces the average behavior of water molecules (or other solvents such as lipids). This method is useful to prevent artifacts that arise from vacuum simulations and reproduces bulk solvent properties well, but cannot reproduce situations in which individual water molecules create specific interactions with a solute that are not well captured by the solvent model, such as water molecules that are part of the hydrogen bond network within a protein. | https://en.wikipedia.org/wiki/Molecular_mechanics |
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 considers all possible conformations of the protein paired with all possible conformations of the ligand.With present computing resources, it is impossible to exhaustively explore these search spaces; instead, there are many strategies which attempt to sample the search space with optimal efficiency. Most docking programs in use account for a flexible ligand, and several attempt to model a flexible protein receptor. Each "snapshot" of the pair is referred to as a pose. | https://en.wikipedia.org/wiki/Searching_the_conformational_space_for_docking |
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 the entire class of non-photosynthetic chains by which complex molecules are constructed is described as chemo-. Chemosynthesis can be applied in many different areas of research, including in positional assembly of molecules. This is where molecules are assembled in certain positions in order to perform specific types of chemosynthesis using molecular building blocks. | https://en.wikipedia.org/wiki/Chemosynthesis_(nanotechnology) |
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 synthesis: additive and subtractive. | https://en.wikipedia.org/wiki/Chemosynthesis_(nanotechnology) |
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 contrasted with mechanosynthesis, a hypothetical process where individual molecules are mechanically manipulated to control reactions to human specification. Since photosynthesis and other natural processes create extremely complex molecules to the specifications contained in RNA and stored long-term in DNA form, advocates of molecular engineering claim that an artificial process can likewise exploit a chain of long-term storage, short-term storage, enzyme-like copying mechanisms similar to those in the cell, and ultimately produce complex molecules which need not be proteins. | https://en.wikipedia.org/wiki/Chemosynthesis_(nanotechnology) |
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 shells of mollusks and crustaceans, etc., evolved naturally, not all of them dependent on photosynthesis and a food chain from the sun via chlorophyll. Since more than one such pathway exists to creating complex molecules, even extremely specific ones such as proteins edible to fish, the likelihood of humans being able to design an entirely new one is considered (by these advocates) to be near certainty in the long run, and possible within a generation. | https://en.wikipedia.org/wiki/Chemosynthesis_(nanotechnology) |
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 order is also an index of bond strength and is also used extensively in valence bond theory. | https://en.wikipedia.org/wiki/Bond_Order |
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 molecular orbital theory offers another approach for defining bond orders based on molecular orbital coefficients, for planar molecules with delocalized π bonding. The theory divides bonding into a sigma framework and a pi system. | https://en.wikipedia.org/wiki/Bond_Order |
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 occupying orbital i with coefficients cri and csi on atoms r and s respectively. Assuming a bond order contribution of 1 from the sigma component this gives a total bond order (σ + π) of 5/3 = 1.67 for benzene, rather than the commonly cited bond order of 1.5, showing some degree of ambiguity in how the concept of bond order is defined. For more elaborate forms of molecular orbital theory involving larger basis sets, still other definitions have been proposed. A standard quantum mechanical definition for bond order has been debated for a long time. A comprehensive method to compute bond orders from quantum chemistry calculations was published in 2017. | https://en.wikipedia.org/wiki/Bond_Order |
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, in benzene, the MO model gives us 6 π MOs which are combinations of the 2pz AOs on each of the 6 C atoms. Thus, each π MO is delocalized over the whole benzene molecule and any electron occupying an MO will be delocalized over the whole molecule. | https://en.wikipedia.org/wiki/Resonance_energy |
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 particularly useful in predicting the effect of substituents on π systems such as benzene. | https://en.wikipedia.org/wiki/Resonance_energy |
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. | https://en.wikipedia.org/wiki/Resonance_energy |
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 atoms and qi > 1 for an electron-releasing group. | https://en.wikipedia.org/wiki/Resonance_energy |
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 gene expression. In eukaryotes, making phylogenetic inferences using RNA is complicated by alternative splicing, which produces multiple transcripts from a single gene. As such, a variety of approaches may be used to improve phylogenetic inference using transcriptomic data obtained from RNA-Seq and processed using computational phylogenetics. | https://en.wikipedia.org/wiki/Phylogenetic_inference_using_transcriptomic_data |
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 coordination complexes, in particular optical spectra (colors). CFT successfully accounts for some magnetic properties, colors, hydration enthalpies, and spinel structures of transition metal complexes, but it does not attempt to describe bonding. CFT was developed by physicists Hans Bethe and John Hasbrouck van Vleck in the 1930s. CFT was subsequently combined with molecular orbital theory to form the more realistic and complex ligand field theory (LFT), which delivers insight into the process of chemical bonding in transition metal complexes. CFT can be complicated further by breaking assumptions made of relative metal and ligand orbital energies, requiring the use of inverted ligand field theory (ILFT) to better describe bonding. | https://en.wikipedia.org/wiki/Crystal_field_stabilization_energy |
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, and C is the London coefficient in the particle–particle pair interaction. The magnitude of this constant reflects the strength of the vdW-force between two particles, or between a particle and a substrate.The Hamaker constant provides the means to determine the interaction parameter C from the vdW-pair potential, w ( r ) = − C r 6 . {\displaystyle w(r)={\frac {-C}{r^{6}}}.} | https://en.wikipedia.org/wiki/Hamaker_constant |
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 Waals forces are effective only up to several hundred angstroms. When the interactions are too far apart, the dispersion potential decays faster than 1 / r 6 ; {\displaystyle 1/r^{6};} this is called the retarded regime, and the result is a Casimir–Polder force. | https://en.wikipedia.org/wiki/Hamaker_constant |
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 limited in their scope, application and complexity, as is the Extended Hückel method. This approach was developed in the 1950s by Rudolph Pariser with Robert Parr and co-developed by John Pople. It is essentially a more efficient method of finding reasonable approximations of molecular orbitals, useful in predicting physical and chemical nature of the molecule under study since molecular orbital characteristics have implications with regards to both the basic structure and reactivity of a molecule. | https://en.wikipedia.org/wiki/Pariser–Parr–Pople_method |
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 using this method was to predict the characteristics of complex organic dyes, but this was never realized. The method has wide applicability in precise prediction of electronic transitions, particularly lower singlet transitions, and found wide application in theoretical and applied quantum chemistry. | https://en.wikipedia.org/wiki/Pariser–Parr–Pople_method |
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 strong ab initio basis. The PPP formulation is actually an approximate pi-electron effective operator, and the empirical parameters, in fact, include effective electron correlation effects. | https://en.wikipedia.org/wiki/Pariser–Parr–Pople_method |
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, etc.) have confirmed many of the approximations of the PPP model and explain why the PPP-like models work so well with such a simple formulation. == References == | https://en.wikipedia.org/wiki/Pariser–Parr–Pople_method |
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 case. However, the following presentation is restricted to the case of homonuclear diatomic molecules, or other symmetric molecules with an inversion centre. | https://en.wikipedia.org/wiki/Molecular_term_symbol |
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 form: where S {\displaystyle S} is the total spin quantum number Λ {\displaystyle \Lambda } (Lambda) is the projection of the orbital angular momentum along the internuclear axis Ω {\displaystyle \Omega } (Omega) is the projection of the total angular momentum along the internuclear axis g / u {\displaystyle g/u} indicates the symmetry or parity with respect to inversion ( i ^ {\displaystyle {\hat {i}}} ) through a centre of symmetry + / − {\displaystyle +/-} is the reflection symmetry along an arbitrary plane containing the internuclear axis | https://en.wikipedia.org/wiki/Molecular_term_symbol |
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 vanishes at longer distances between interacting molecules. | https://en.wikipedia.org/wiki/Van_der_Waals_forces |
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 molecular solids, including their solubility in polar and non-polar media. If no other force is present, the distance between atoms at which the force becomes repulsive rather than attractive as the atoms approach one another is called the van der Waals contact distance; this phenomenon results from the mutual repulsion between the atoms' electron clouds.The van der Waals forces are usually described as a combination of the London dispersion forces between "instantaneously induced dipoles", Debye forces between permanent dipoles and induced dipoles, and the Keesom force between permanent molecular dipoles whose rotational orientations are dynamically averaged over time. | https://en.wikipedia.org/wiki/Van_der_Waals_forces |
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 at one of its ends). In nanomaterials, carbon nanotubes (CNTs) are typical ones for electrostatic deflections. | https://en.wikipedia.org/wiki/Electrostatic_deflection_(structural_element) |
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 shows a beam-like structure/element in an electric field. | https://en.wikipedia.org/wiki/Electrostatic_deflection_(structural_element) |
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. | https://en.wikipedia.org/wiki/Electrostatic_deflection_(structural_element) |
Meanwhile, the electrically induced torque and stiffness of the CNT compete against each other. This deformation has been observed in experiments. | https://en.wikipedia.org/wiki/Electrostatic_deflection_(structural_element) |
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 and feedback device which are designed for memory, sensing or actuation uses. Furthermore, theoretical studies have been carried out to try to get a full understanding of the electric deflection of carbon nanotubes. == References == | https://en.wikipedia.org/wiki/Electrostatic_deflection_(structural_element) |
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 its ends). In nanomaterials, carbon nanotubes (CNTs) are typical ones for electrostatic deflections. | https://en.wikipedia.org/wiki/Electrostatic_deflection_(molecular_physics/nanotechnology) |
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 structure/element in an electric field. | https://en.wikipedia.org/wiki/Electrostatic_deflection_(molecular_physics/nanotechnology) |
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. | https://en.wikipedia.org/wiki/Electrostatic_deflection_(molecular_physics/nanotechnology) |
Meanwhile the electrically induced torque and stiffness of the CNT compete against each other. This deformation has been observed in experiments. | https://en.wikipedia.org/wiki/Electrostatic_deflection_(molecular_physics/nanotechnology) |
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 and feedback device which are designed for memory, sensing or actuation uses. Furthermore, theoretical studies have been carried out to try to get a full understanding of the electric deflection of carbon nanotubes, == References == | https://en.wikipedia.org/wiki/Electrostatic_deflection_(molecular_physics/nanotechnology) |
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 squiggly arrows and radiative transitions by straight arrows. The vibrational ground states of each electronic state are indicated with thick lines, the higher vibrational states with thinner lines. The diagram is named after the Polish physicist Aleksander Jabłoński who first proposed it in 1933. | https://en.wikipedia.org/wiki/Jablonski_diagram |
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 + 1 2 = G ( v + 1 ) − G ( v ) {\displaystyle \Delta G_{v+{\frac {1}{2}}}=G(v+1)-G(v)} can be calculated. This sum will have a maximum at v m a x {\displaystyle v_{max}} , representing the point of bond dissociation; summing over all the differences up to this point gives the total energy required to dissociate the molecule, i.e. to promote it from the ground state to an unbound state. This can be written: D 0 = ∑ v = 0 v m a x Δ G v + 1 2 {\displaystyle D_{0}=\sum _{v=0}^{v_{max}}\Delta G_{v+{\frac {1}{2}}}} where D 0 {\displaystyle D_{0}} is the dissociation energy. | https://en.wikipedia.org/wiki/Birge-Sponer_method |
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 unaccounted anharmonicity in the potential; furthermore, the low population of the higher states (or the Franck–Condon principle) makes it difficult to experimentally obtain data at high values of v {\displaystyle v} . | https://en.wikipedia.org/wiki/Birge-Sponer_method |
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. | https://en.wikipedia.org/wiki/Birge-Sponer_method |
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 state containing thermal population of another vibrational mode. For example, for a molecule with 3 normal modes, ν 1 {\displaystyle \nu _{1}} , ν 2 {\displaystyle \nu _{2}} and ν 3 {\displaystyle \nu _{3}} , the transition 101 {\displaystyle 101} ← 001 {\displaystyle 001} , would be a hot band, since the initial state has one quantum of excitation in the ν 3 {\displaystyle \nu _{3}} mode. Hot bands are distinct from combination bands, which involve simultaneous excitation of multiple normal modes with a single photon, and overtones, which are transitions that involve changing the vibrational quantum number for a normal mode by more than 1. | https://en.wikipedia.org/wiki/Hot_transition |
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 and a half bond). Furthermore, bond orders of 1.1 (eleven tenths bond), 4/3 (or 1.333333..., four thirds bond) or 0.5 (half bond), for example, can occur in some molecules and essentially refer to bond strength relative to bonds with order 1. In the nitrate anion (NO−3), the bond order for each bond between nitrogen and oxygen is 4/3 (or 1.333333...). Bonding in dihydrogen cation H+2 can be described as a covalent one-electron bond, thus the bonding between the two hydrogen atoms has bond order of 0.5. | https://en.wikipedia.org/wiki/Bond_Order |
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 energy than PCl5. Despite their identical trigonal bipyramidal molecular geometry, the higher electron count of chlorine as compared to fluorine causes a potential energy spike as the molecule enters its intermediate in the mechanism and the substituents draw nearer to each other. | https://en.wikipedia.org/wiki/Steric_strain |
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. | https://en.wikipedia.org/wiki/Double_bonds |
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. | https://en.wikipedia.org/wiki/Double_bonds |
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 bonding, whereas, if the antibonding interactions outnumber the bonding interactions, the molecular orbital is said to be antibonding. For example, butadiene has pi orbitals which are delocalized over all four carbon atoms. | https://en.wikipedia.org/wiki/Antibonding_orbitals |
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 are vacant in the ground state, but may be occupied in excited states. Similarly benzene with six carbon atoms has three bonding pi orbitals and three antibonding pi orbitals. | https://en.wikipedia.org/wiki/Antibonding_orbitals |
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 Kenichi Fukui shared the 1981 Nobel Prize in Chemistry for their work and further development of qualitative molecular orbital explanations for chemical reactions. | https://en.wikipedia.org/wiki/Antibonding_orbitals |
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 planar ring. This is sometimes shown diagrammatically as a series of alternating single and double bonds. In the case of phenol and benzene, a circle inside a hexagon shows the delocalised nature of the compound. | https://en.wikipedia.org/wiki/Electronic_density |
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 is higher next to the single bonds. Conjugated systems can sometimes represent regions where electromagnetic radiation is absorbed at different wavelengths resulting in compounds appearing coloured. | https://en.wikipedia.org/wiki/Electronic_density |
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 sum of products of basis functions, φ: ρ ( r ) = ∑ μ ∑ ν P μ ν ϕ μ ( r ) ϕ ν ( r ) {\displaystyle \rho (\mathbf {r} )=\sum _{\mu }\sum _{\nu }P_{\mu \nu }\phi _{\mu }(\mathbf {r} )\phi _{\nu }(\mathbf {r} )} where P is the density matrix. Electron densities are often rendered in terms of an isosurface (an isodensity surface) with the size and shape of the surface determined by the value of the density chosen, or in terms of a percentage of total electrons enclosed. | https://en.wikipedia.org/wiki/Electronic_density |
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