Operator (physics)

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Operator_(physics)

In physics, an operator is a function over a space of physical states onto another space of physical states. The simplest example of the utility of operators is the study of symmetry (which makes the concept of a group useful in this context). Because of this, they are useful tools in classical mechanics. Operators are even more important in quantum mechanics, where they form an intrinsic part of the formulation of the theory.

Operators in classical mechanics

In classical mechanics, the movement of a particle (or system of particles) is completely determined by the Lagrangian ${\displaystyle L(q,\dot{q},t)}$ or equivalently the Hamiltonian ${\displaystyle H(q,p,t)}$, a function of the generalized coordinates q, generalized velocities ${\displaystyle \dot{q}=\mathrm{d}q/\mathrm{d}t}$ and its conjugate momenta:

${\displaystyle p=\frac{\mathrm{\partial }L}{\mathrm{\partial }\dot{q}}}$

If either L or H is independent of a generalized coordinate q, meaning the L and H do not change when q is changed, which in turn means the dynamics of the particle are still the same even when q changes, the corresponding momenta conjugate to those coordinates will be conserved (this is part of Noether's theorem, and the invariance of motion with respect to the coordinate q is a symmetry). Operators in classical mechanics are related to these symmetries.

More technically, when H is invariant under the action of a certain group of transformations G:

${\displaystyle S\in G,H(S(q,p))=H(q,p)}$.

The elements of G are physical operators, which map physical states among themselves.

Table of classical mechanics operators

Transformation	Operator	Position	Momentum
Translational symmetry	${\displaystyle X(\mathbf{a})}$	${\displaystyle \mathbf{r}\to \mathbf{r}+\mathbf{a}}$	${\displaystyle \mathbf{p}\to \mathbf{p}}$
Time translation symmetry	${\displaystyle U(t_0)}$	${\displaystyle \mathbf{r}(t)\to \mathbf{r}(t+t_0)}$	${\displaystyle \mathbf{p}(t)\to \mathbf{p}(t+t_0)}$
Rotational invariance	${\displaystyle R(\hat{\mathbf{n}},\theta )}$	${\displaystyle \mathbf{r}\to R(\hat{\mathbf{n}},\theta )\mathbf{r}}$	${\displaystyle \mathbf{p}\to R(\hat{\mathbf{n}},\theta )\mathbf{p}}$
Galilean transformations	${\displaystyle G(\mathbf{v})}$	${\displaystyle \mathbf{r}\to \mathbf{r}+\mathbf{v}t}$	${\displaystyle \mathbf{p}\to \mathbf{p}+m\mathbf{v}}$
Parity	${\displaystyle P}$	${\displaystyle \mathbf{r}\to -\mathbf{r}}$	${\displaystyle \mathbf{p}\to -\mathbf{p}}$
T-symmetry	${\displaystyle T}$	${\displaystyle \mathbf{r}\to \mathbf{r}(-t)}$	${\displaystyle \mathbf{p}\to -\mathbf{p}(-t)}$

where ${\displaystyle R(\hat{\mathit{n}},\theta )}$ is the rotation matrix about an axis defined by the unit vector ${\displaystyle \hat{\mathit{n}}}$ and angle θ.

Generators

If the transformation is infinitesimal, the operator action should be of the form

${\displaystyle I+ϵA,}$

where ${\displaystyle I}$ is the identity operator, ${\displaystyle ϵ}$ is a parameter with a small value, and ${\displaystyle A}$ will depend on the transformation at hand, and is called a generator of the group. Again, as a simple example, we will derive the generator of the space translations on 1D functions.

As it was stated, ${\displaystyle T_{a}f(x)=f(x-a)}$. If ${\displaystyle a=ϵ}$ is infinitesimal, then we may write

${\displaystyle T_{ϵ}f(x)=f(x-ϵ)\approx f(x)-ϵf^{\prime }(x).}$

This formula may be rewritten as

${\displaystyle T_{ϵ}f(x)=(I-ϵD)f(x)}$

where ${\displaystyle D}$ is the generator of the translation group, which in this case happens to be the derivative operator. Thus, it is said that the generator of translations is the derivative.

The exponential map

The whole group may be recovered, under normal circumstances, from the generators, via the exponential map. In the case of the translations the idea works like this.

The translation for a finite value of ${\displaystyle a}$ may be obtained by repeated application of the infinitesimal translation:

${\displaystyle T_{a}f(x)=\underset{N\to \mathrm{\infty }}{lim}{T}_{a/N}\cdots T_{a/N}f(x)}$

with the ${\displaystyle \cdots }$ standing for the application ${\displaystyle N}$ times. If ${\displaystyle N}$ is large, each of the factors may be considered to be infinitesimal:

${\displaystyle T_{a}f(x)=\underset{N\to \mathrm{\infty }}{lim}{\left(I-\frac{a}{N}D\right)}^{N}f(x).}$

But this limit may be rewritten as an exponential:

${\displaystyle T_{a}f(x)=\exp (-aD)f(x).}$

To be convinced of the validity of this formal expression, we may expand the exponential in a power series:

${\displaystyle T_{a}f(x)=\left(I-aD+\frac{a^2{D}^2}{2!}-\frac{a^3{D}^3}{3!}+\cdots \right)f(x).}$

The right-hand side may be rewritten as

${\displaystyle f(x)-a{f}^{\prime }(x)+\frac{a^2}{2!}{f}^{″}(x)-\frac{a^3}{3!}{f}^{(3)}(x)+\cdots }$

which is just the Taylor expansion of ${\displaystyle f(x-a)}$, which was our original value for ${\displaystyle T_{a}f(x)}$.

The mathematical properties of physical operators are a topic of great importance in itself. For further information, see C*-algebra and Gelfand–Naimark theorem.

Operators in quantum mechanics

The mathematical formulation of quantum mechanics (QM) is built upon the concept of an operator.

Physical pure states in quantum mechanics are represented as unit-norm vectors (probabilities are normalized to one) in a special complex Hilbert space. Time evolution in this vector space is given by the application of the evolution operator.

Any observable, i.e., any quantity which can be measured in a physical experiment, should be associated with a self-adjoint linear operator. The operators must yield real eigenvalues, since they are values which may come up as the result of the experiment. Mathematically this means the operators must be Hermitian. The probability of each eigenvalue is related to the projection of the physical state on the subspace related to that eigenvalue. See below for mathematical details about Hermitian operators.

In the wave mechanics formulation of QM, the wavefunction varies with space and time, or equivalently momentum and time (see position and momentum space for details), so observables are differential operators.

In the matrix mechanics formulation, the norm of the physical state should stay fixed, so the evolution operator should be unitary, and the operators can be represented as matrices. Any other symmetry, mapping a physical state into another, should keep this restriction.

Wavefunction

Main article: wavefunction

The wavefunction must be square-integrable (see L^p spaces), meaning:

${\displaystyle {\iiint }_{{\mathbb{R}}^3}|\psi (\mathbf{r}){|}^2{d}^3\mathbf{r}={\iiint }_{{\mathbb{R}}^3}\psi (\mathbf{r}{)}^{\ast }\psi (\mathbf{r})d^3\mathbf{r}<\mathrm{\infty }}$

and normalizable, so that:

${\displaystyle {\iiint }_{{\mathbb{R}}^3}|\psi (\mathbf{r}){|}^2{d}^3\mathbf{r}=1}$

Two cases of eigenstates (and eigenvalues) are:

• for discrete eigenstates ${\displaystyle |{\psi }_i⟩}$ forming a discrete basis, so any state is a sum
  $${\displaystyle |\psi ⟩=\sum _i{c}_i|{\varphi }_i⟩}$$

  
  where c_i are complex numbers such that |c_i|² = c_i^*c_i is the probability of measuring the state ${\displaystyle |{\varphi }_i⟩}$, and the corresponding set of eigenvalues a_i is also discrete - either finite or countably infinite. In this case, the inner product of two eigenstates is given by ${\displaystyle ⟨{\varphi }_i|{\varphi }_j⟩={\delta }_{ij}}$, where ${\displaystyle {\delta }_{mn}}$ denotes the Kronecker Delta. However,
• for a continuum of eigenstates ${\displaystyle |{\psi }_i⟩}$ forming a continuous basis, any state is an integral
  $${\displaystyle |\psi ⟩=\int c(\varphi )d\varphi |\varphi ⟩}$$

  
  where c(φ) is a complex function such that |c(φ)|² = c(φ)^*c(φ) is the probability of measuring the state ${\displaystyle |\varphi ⟩}$, and there is an uncountably infinite set of eigenvalues a. In this case, the inner product of two eigenstates is defined as ${\displaystyle ⟨{\varphi }^{\prime }|\varphi ⟩=\delta (\varphi -{\varphi }^{\prime })}$, where here ${\displaystyle \delta (x-y)}$ denotes the Dirac Delta.

Linear operators in wave mechanics

Main articles: Wave function and Bra–ket notation

Let ψ be the wavefunction for a quantum system, and ${\displaystyle \hat{A}}$ be any linear operator for some observable A (such as position, momentum, energy, angular momentum etc.). If ψ is an eigenfunction of the operator ${\displaystyle \hat{A}}$, then

${\displaystyle \hat{A}\psi =a\psi ,}$

where a is the eigenvalue of the operator, corresponding to the measured value of the observable, i.e. observable A has a measured value a.

If ψ is an eigenfunction of a given operator ${\displaystyle \hat{A}}$, then a definite quantity (the eigenvalue a) will be observed if a measurement of the observable A is made on the state ψ. Conversely, if ψ is not an eigenfunction of ${\displaystyle \hat{A}}$, then it has no eigenvalue for ${\displaystyle \hat{A}}$, and the observable does not have a single definite value in that case. Instead, measurements of the observable A will yield each eigenvalue with a certain probability (related to the decomposition of ψ relative to the orthonormal eigenbasis of ${\displaystyle \hat{A}}$).

In bra–ket notation the above can be written;

${\displaystyle \begin{array}{rl}\hat{A}\psi & =\hat{A}\psi (\mathbf{r})=\hat{A}⟨\mathbf{r}\mid \psi ⟩=⟨\mathbf{r}\left|\hat{A}\right|\psi ⟩\\ a\psi & =a\psi (\mathbf{r})=a⟨\mathbf{r}\mid \psi ⟩=⟨\mathbf{r}\mid a\mid \psi ⟩\end{array}}$

that are equal if ${\displaystyle |\psi ⟩}$ is an eigenvector, or eigenket of the observable A.

Due to linearity, vectors can be defined in any number of dimensions, as each component of the vector acts on the function separately. One mathematical example is the del operator, which is itself a vector (useful in momentum-related quantum operators, in the table below).

An operator in n-dimensional space can be written:

${\displaystyle \hat{\mathbf{A}}=\sum _{j=1}^n{\mathbf{e}}_j{\hat{A}}_j}$

where e_j are basis vectors corresponding to each component operator A_j. Each component will yield a corresponding eigenvalue ${\displaystyle a_j}$. Acting this on the wave function ψ:

${\displaystyle \hat{\mathbf{A}}\psi =\left(\sum _{j=1}^n{\mathbf{e}}_j{\hat{A}}_j\right)\psi =\sum _{j=1}^n\left({\mathbf{e}}_j{\hat{A}}_j\psi \right)=\sum _{j=1}^n\left({\mathbf{e}}_j{a}_j\psi \right)}$

in which we have used ${\displaystyle {\hat{A}}_j\psi =a_j\psi .}$

In bra–ket notation:

${\displaystyle \begin{array}{rl}\hat{\mathbf{A}}\psi =\hat{\mathbf{A}}\psi (\mathbf{r})=\hat{\mathbf{A}}⟨\mathbf{r}\mid \psi ⟩& =⟨\mathbf{r}\left|\hat{\mathbf{A}}\right|\psi ⟩\\ \left(\sum _{j=1}^n{\mathbf{e}}_j{\hat{A}}_j\right)\psi =\left(\sum _{j=1}^n{\mathbf{e}}_j{\hat{A}}_j\right)\psi (\mathbf{r})=\left(\sum _{j=1}^n{\mathbf{e}}_j{\hat{A}}_j\right)⟨\mathbf{r}\mid \psi ⟩& =⟨\mathbf{r}\left|\sum _{j=1}^n{\mathbf{e}}_j{\hat{A}}_j\right|\psi ⟩\end{array}}$

Commutation of operators on Ψ

Main article: Commutator

If two observables A and B have linear operators ${\displaystyle \hat{A}}$ and ${\displaystyle \hat{B}}$, the commutator is defined by,

${\displaystyle \left[\hat{A},\hat{B}\right]=\hat{A}\hat{B}-\hat{B}\hat{A}}$

The commutator is itself a (composite) operator. Acting the commutator on ψ gives:

${\displaystyle \left[\hat{A},\hat{B}\right]\psi =\hat{A}\hat{B}\psi -\hat{B}\hat{A}\psi .}$

If ψ is an eigenfunction with eigenvalues a and b for observables A and B respectively, and if the operators commute:

${\displaystyle \left[\hat{A},\hat{B}\right]\psi =0,}$

then the observables A and B can be measured simultaneously with infinite precision, i.e., uncertainties ${\displaystyle \mathrm{\Delta }A=0}$, ${\displaystyle \mathrm{\Delta }B=0}$ simultaneously. ψ is then said to be the simultaneous eigenfunction of A and B. To illustrate this:

${\displaystyle \begin{array}{rl}\left[\hat{A},\hat{B}\right]\psi & =\hat{A}\hat{B}\psi -\hat{B}\hat{A}\psi \\ & =a(b\psi )-b(a\psi )\\ & =0.\end{array}}$

It shows that measurement of A and B does not cause any shift of state, i.e., initial and final states are same (no disturbance due to measurement). Suppose we measure A to get value a. We then measure B to get the value b. We measure A again. We still get the same value a. Clearly the state (ψ) of the system is not destroyed and so we are able to measure A and B simultaneously with infinite precision.

If the operators do not commute:

${\displaystyle \left[\hat{A},\hat{B}\right]\psi \ne 0,}$

they cannot be prepared simultaneously to arbitrary precision, and there is an uncertainty relation between the observables

${\displaystyle \mathrm{\Delta }A\mathrm{\Delta }B\ge \left|\frac{1}{2}⟨[A,B]⟩\right|}$

even if ψ is an eigenfunction the above relation holds. Notable pairs are position-and-momentum and energy-and-time uncertainty relations, and the angular momenta (spin, orbital and total) about any two orthogonal axes (such as L_x and L_y, or s_y and s_z, etc.).

Expectation values of operators on Ψ

The expectation value (equivalently the average or mean value) is the average measurement of an observable, for particle in region R. The expectation value ${\displaystyle ⟨\hat{A}⟩}$ of the operator ${\displaystyle \hat{A}}$ is calculated from:

${\displaystyle ⟨\hat{A}⟩={\int }_R{\psi }^{\ast }\left(\mathbf{r}\right)\hat{A}\psi \left(\mathbf{r}\right){\mathrm{d}}^3\mathbf{r}=⟨\psi \left|\hat{A}\right|\psi ⟩.}$

This can be generalized to any function F of an operator:

${\displaystyle ⟨F\left(\hat{A}\right)⟩={\int }_R\psi (\mathbf{r}{)}^{\ast }\left[F\left(\hat{A}\right)\psi (\mathbf{r})\right]{\mathrm{d}}^3\mathbf{r}=⟨\psi \left|F\left(\hat{A}\right)\right|\psi ⟩,}$

An example of F is the 2-fold action of A on ψ, i.e. squaring an operator or doing it twice:

${\displaystyle \begin{array}{rl}F\left(\hat{A}\right)& ={\hat{A}}^2\\ \Rightarrow ⟨{\hat{A}}^2⟩& ={\int }_R{\psi }^{\ast }\left(\mathbf{r}\right){\hat{A}}^2\psi \left(\mathbf{r}\right){\mathrm{d}}^3\mathbf{r}=⟨\psi \left|{\hat{A}}^2\right|\psi ⟩\end{array}}$

Hermitian operators

Main article: Self-adjoint operator

The definition of a Hermitian operator is:

${\displaystyle \hat{A}={\hat{A}}^{†}}$

Following from this, in bra–ket notation:

${\displaystyle ⟨{\varphi }_i\left|\hat{A}\right|{\varphi }_j⟩={⟨{\varphi }_j\left|\hat{A}\right|{\varphi }_i⟩}^{\ast }.}$

Important properties of Hermitian operators include:

• real eigenvalues,
• eigenvectors with different eigenvalues are orthogonal,
• eigenvectors can be chosen to be a complete orthonormal basis,

Operators in matrix mechanics

An operator can be written in matrix form to map one basis vector to another. Since the operators are linear, the matrix is a linear transformation (aka transition matrix) between bases. Each basis element ${\displaystyle {\varphi }_j}$ can be connected to another, by the expression:

${\displaystyle A_{ij}=⟨{\varphi }_i\left|\hat{A}\right|{\varphi }_j⟩,}$

which is a matrix element:

${\displaystyle \hat{A}=\left(\begin{array}{cccc}{A}_{11}& A_{12}& \cdots & A_{1n}\\ A_{21}& A_{22}& \cdots & A_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ A_{n1}& A_{n2}& \cdots & A_{nn}\end{array}\right)}$

A further property of a Hermitian operator is that eigenfunctions corresponding to different eigenvalues are orthogonal. In matrix form, operators allow real eigenvalues to be found, corresponding to measurements. Orthogonality allows a suitable basis set of vectors to represent the state of the quantum system. The eigenvalues of the operator are also evaluated in the same way as for the square matrix, by solving the characteristic polynomial:

${\displaystyle det\left(\hat{A}-a\hat{I}\right)=0,}$

where I is the n × n identity matrix, as an operator it corresponds to the identity operator. For a discrete basis:

${\displaystyle \hat{I}=\sum _i|{\varphi }_i⟩⟨{\varphi }_i|}$

while for a continuous basis:

${\displaystyle \hat{I}=\int |\varphi ⟩⟨\varphi |\mathrm{d}\varphi }$

Inverse of an operator

A non-singular operator ${\displaystyle \hat{A}}$ has an inverse ${\displaystyle {\hat{A}}^{-1}}$ defined by:

${\displaystyle \hat{A}{\hat{A}}^{-1}={\hat{A}}^{-1}\hat{A}=\hat{I}}$

If an operator has no inverse, it is a singular operator. In a finite-dimensional space, an operator is non-singular if and only if its determinant is nonzero:

${\displaystyle det\left(\hat{A}\right)\ne 0}$

and hence the determinant is zero for a singular operator.

Organosilicon chemistry

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Organosilicon_chemistry

 

Polydimethylsiloxane (PDMS) is the principal component of silicones.

Organosilicon chemistry is the study of organometallic compounds containing carbon–silicon bonds, to which they are called organosilicon compounds. Most organosilicon compounds are similar to the ordinary organic compounds, being colourless, flammable, hydrophobic, and stable to air. Silicon carbide is an inorganic compound.

History

See also: Organometallic chemistry

In 1863 Charles Friedel and James Crafts made the first organochlorosilane compound. The same year they also described a «polysilicic acid ether» in the preparation of ethyl- and methyl-o-silicic acid. Extensive research in the field of organosilicon compounds was pioneered in the beginning of 20th century by Frederic S. Kipping. He also had coined the term "silicone" (resembling ketones, this is errorneous though) in relation to these materials in 1904. In recognition of Kipping's achievements the Dow Chemical Company had established an award in 1960s that is given for significant contributions into the silicon chemistry. In his works Kipping was noted for using Grignard reagents to make alkylsilanes and arylsilanes and the preparation of silicone oligomers and polymers for the first time.

In 1945 Eugene G. Rochow has also made a significant contribution into the organosilicon chemistry by first describing Müller-Rochow process.

Occurrence and applications

Organosilicon compounds are widely encountered in commercial products. Most common are antifoamers, caulks (sealant), adhesives, and coatings made from silicones. Other important uses include agricultural and plant control adjuvants commonly used in conjunction with herbicides and fungicides.

Silicone caulk, commercial sealants, are mainly composed of organosilicon compounds mixed with hardener.

Biology and medicine

Carbon–silicon bonds are absent in biology, however enzymes have been used to artificially create carbon-silicon bonds in living microbes. Silicates, on the other hand, have known existence in diatoms. Silafluofen is an organosilicon compound that functions as a pyrethroid insecticide. Several organosilicon compounds have been investigated as pharmaceuticals.

Bonding

In the great majority of organosilicon compounds, Si is tetravalent with tetrahedral molecular geometry. Compared to carbon–carbon bonds, carbon–silicon bonds are longer and weaker. The C–Si bond is somewhat polarised towards carbon due to carbon's greater electronegativity (C 2.55 vs Si 1.90). The strength of the Si-O bond is strikingly high, and this feature is exploited in many reactions such as the Sakurai reaction, the Brook rearrangement, the Fleming–Tamao oxidation, and the Peterson olefination. Another manifestation is the β-silicon effect describes the stabilizing effect of a β-silicon atom on a carbocation with many implications for reactivity.

Properties Relevant to OrganoSi Chemistry

Bond	Bond length (pm)	Approx. bond strength (kJ/mol)
C-C	154	334
Si-Si	234	196
C-Si	186	314
C-H	110	414
Si-H	146	314
C-O	145	355
Si-O	159	460

Electronegativities 

Relevant to OrganoSi Chemistry

C	Si	H	O
2.5	1.8	2.1	3.4

Preparation

The first organosilicon compound, tetraethylsilane, was prepared by Charles Friedel and James Crafts in 1863 by reaction of tetrachlorosilane with diethylzinc.

The bulk of organosilicon compounds derive from organosilicon chlorides (CH
₃)
_4-xSiCl
_x. These chlorides are produced by the "Direct process", which entails the reaction of methyl chloride with a silicon-copper alloy. The main and most sought-after product is dimethyldichlorosilane:

2 CH
₃Cl + Si → (CH
₃)
₂SiCl
₂

A variety of other products are obtained, including trimethylsilyl chloride and methyltrichlorosilane. About 1 million tons of organosilicon compounds are prepared annually by this route. The method can also be used for phenyl chlorosilanes.

Hydrosilylation

Main article: Hydrosilylation

Another major method for the formation of Si-C bonds is hydrosilylation (also called hydrosilation). In this process, compounds with Si-H bonds (hydrosilanes) add to unsaturated substrates. Commercially, the main substrates are alkenes. Other unsaturated functional groups — alkynes, imines, ketones, and aldehydes — also participate, but these reactions are of little economic value.

Idealized mechanism for metal-catalysed hydrosilylation of an alkene

Hydrosilylation requires metal catalysts, especially those based on platinum group metals.

In the related silylmetalation, a metal replaces the hydrogen atom.

Cleavage of Si-Si bonds

Hexamethyldisilane reacts with methyl lithium to give trimethylsilyl lithium:

(CH₃)₆Si₂ + CH₃Li → (CH₃)₃SiLi + (CH₃)₄Si

Similarly, tris(trimethylsilyl)silyl lithium is derived from tetrakis(trimethylsilyl)silane:

((CH₃)₃Si)₄Si + CH₃Li → ((CH₃)₃Si)₃SiLi + (CH₃)₄Si

Functional groups

Silicon is a component of many functional groups. Most of these are analogous to organic compounds. The overarching exception is the rarity of multiple bonds to silicon, as reflected in the double bond rule.

Silanols, siloxides, and siloxanes

Silanols are analogues of alcohols. They are generally prepared by hydrolysis of silyl chlorides:

R
₃SiCl + H₂O → R
₃SiOH + HCl

Less frequently silanols are prepared by oxidation of silyl hydrides, a reaction that uses a metal catalyst:

2 R
₃SiH + O
₂ → 2 R
₃SiOH

Many silanols have been isolated including (CH
₃)
₃SiOH and (C
₆H
₅)
₃SiOH. They are about 500x more acidic than the corresponding alcohols. Siloxides are the deprotonated derivatives of silanols:

R
₃SiOH + NaOH → R
₃SiONa + H₂O

Silanols tend to dehydrate to give siloxanes:

2 R
₃SiOH → R
₃Si-O-SiR
₃ + H₂O

Polymers with repeating siloxane linkages are called silicones. Compounds with an Si=O double bond called silanones are extremely unstable.

Silyl ethers

Silyl ethers have the connectivity Si-O-C. They are typically prepared by the reaction of alcohols with silyl chlorides:

(CH
₃)
₃SiCl + ROH → (CH
₃)
₃Si-O-R + HCl

Silyl ethers are extensively used as protective groups for alcohols.

Exploiting the strength of the Si-F bond, fluoride sources such as tetra-n-butylammonium fluoride (TBAF) are used in deprotection of silyl ethers:

(CH
₃)
₃Si-O-R + F⁻
+ H₂O → (CH
₃)
₃Si-F + H-O-R + OH⁻

Silyl chlorides

Main article: Chlorosilane

Organosilyl chlorides are important commodity chemicals. They are mainly used to produce silicone polymers as described above. Especially important silyl chlorides are dimethyldichlorosilane (Me
₂SiCl
₂), methyltrichlorosilane (MeSiCl
₃), and trimethylsilyl chloride (Me
₃SiCl) are all produced by direct process. More specialized derivatives that find commercial applications include dichloromethylphenylsilane, trichloro(chloromethyl)silane, trichloro(dichlorophenyl)silane, trichloroethylsilane, and phenyltrichlorosilane.

Although proportionately a minor outlet, organosilicon compounds are widely used in organic synthesis. Notably trimethylsilyl chloride Me
₃SiCl is the main silylating agent. One classic method called the Flood reaction for the synthesis of this compound class is by heating hexaalkyldisiloxanes R
₃SiOSiR
₃ with concentrated sulfuric acid and a sodium halide.

Silyl hydrides

Main article: Hydrosilane

 

Tris(trimethylsilyl)silane is a well-investigated hydrosilane.

The silicon to hydrogen bond is longer than the C–H bond (148 compared to 105 pm) and weaker (299 compared to 338 kJ/mol). Hydrogen is more electronegative than silicon hence the naming convention of silyl hydrides. Commonly the presence of the hydride is not mentioned in the name of the compound. Triethylsilane has the formula Et
₃SiH. Phenylsilane is PhSiH
₃. The parent compound SiH
₄ is called silane.

Silenes

Organosilicon compounds, unlike their carbon counterparts, do not have a rich double bond chemistry. Compounds with silene Si=C bonds (also known as alkylidenesilanes) are laboratory curiosities such as the silicon benzene analogue silabenzene. In 1967, Gusel'nikov and Flowers provided the first evidence for silenes from pyrolysis of dimethylsilacyclobutane. The first stable (kinetically shielded) silene was reported in 1981 by Brook.

Disilenes have Si=Si double bonds and disilynes are silicon analogues of an alkyne. The first Silyne (with a silicon to carbon triple bond) was reported in 2010.

Siloles

Chemical structure of silole

Siloles, also called silacyclopentadienes, are members of a larger class of compounds called metalloles. They are the silicon analogs of cyclopentadienes and are of current academic interest due to their electroluminescence and other electronic properties. Siloles are efficient in electron transport. They owe their low lying LUMO to a favorable interaction between the antibonding sigma silicon orbital with an antibonding pi orbital of the butadiene fragment.

Pentacoordinated silicon

See also: Hypervalent molecule § Pentacoordinated silicon

Unlike carbon, silicon compounds can be coordinated to five atoms as well in a group of compounds ranging from so-called silatranes, such as phenylsilatrane, to a uniquely stable pentaorganosilicate:

The stability of hypervalent silicon is the basis of the Hiyama coupling, a coupling reaction used in certain specialized organic synthetic applications. The reaction begins with the activation of Si-C bond by fluoride:

R-SiR'
₃ + R"-X + F⁻
→ R-R" + R'
₃SiF + X⁻

Various reactions

Certain allyl silanes can be prepared from allylic esters such as 1 and monosilylcopper compounds, which are formed in situ by the reaction of the disilylzinc compound 2, with Copper Iodide, in:

In this reaction type, silicon polarity is reversed in a chemical bond with zinc and a formal allylic substitution on the benzoyloxy group takes place.

Environmental effects

Organosilicon compounds affect bee (and other insect) immune expression, making them more susceptible to viral infection.

Judeo-Christian ethics

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Judeo-Christian_ethics

 

This article is about the 20th-century American concept of common values shared between the two religions. For the term "Judeo-Christian", grouping Judaism and Christianity, see Judeo-Christian. For the intersection in general of Judaism with Christianity, see Christianity and Judaism.

 

A monument at the Texas State Capitol depicting the Ten Commandments. The U.S. Supreme Court let it stand in Van Orden v. Perry (2005).

The idea that a common Judaeo-Christian ethics or Judeo-Christian values underpins American politics, law and morals has been part of the "American civil religion" since the 1940s. In recent years, the phrase has been associated with American conservatism, but the concept—though not always the exact phrase—has frequently featured in the rhetoric of leaders across the political spectrum, including that of Franklin D. Roosevelt and Lyndon B. Johnson.

Ethical value system

See also: Christian ethics and Jewish ethics

The current American use of "Judeo-Christian" — to refer to a value system common to Jews and Christians — first appeared in print in a book review by the English writer George Orwell in 1939, with the phrase "the Judaeo-Christian scheme of morals." Orwell's usage of the term followed at least a decade of efforts by Jewish and Christian leaders, through such groups as the U.S. National Conference of Christians and Jews (founded in 1927), to emphasize common ground. The term continued to gain currency in the 1940s. In part, it was a way of countering antisemitism with the idea that the foundation of morals and law in the United States was a shared one between Jews and Christians.

Franklin D. Roosevelt

The first inaugural address of Franklin D. Roosevelt (FDR), in 1933, the famous speech in which FDR declared that "the only thing we have to fear is fear itself", had numerous religious references, which was widely commented upon at the time. Although it did not use the term "Judeo-Christian", it has come to be seen by scholars as in tune with the emerging view of a Judeo-Christian tradition. Historian Mary Stuckey emphasizes "Roosevelt's use of the shared values grounded in the Judeo-Christian tradition" as a way to unify the American nation, and justify his own role as its chief policymaker.

In the speech, FDR attacked the bankers and promised a reform in an echo of the gospels: "The money changers have fled from their high seats in the temple of our civilization. We may now restore that temple to the ancient truths. The measure of the restoration lies in the extent to which we apply social values more noble than mere monetary profit." Houck and Nocasian, examining the flood of responses to the First Inaugural, and commenting on this passage, argue:

The nation's overwhelmingly Judeo-Christian response to the address thus had both textual and extratextual warrants. For those inclined to see the Divine Hand of Providence at work, Roosevelt's miraculous escape [from assassination] in Miami was a sign—perhaps The Sign—that God had sent another Washington or Lincoln at the appointed hour. ... Many others could not resist the subject position that Roosevelt ... had cultivated throughout the address—that of savior. After all, it was Christ who had expelled the moneychangers from the Temple. ... [Many listeners saw] a composite sign that their new president had a godly mandate to lead.

Gary Scott Smith stresses that Roosevelt believed his welfare programs were "wholly in accord with the social teachings of Christianity." He saw the achievement of social justice through government action as morally superior to the old laissez-faire approach. He proclaimed, "The thing we are seeking is justice," as guided by the precept of "Do unto your neighbor as you would be done by." Roosevelt saw the moral issue as religiosity versus anti-religion. According to Smith, "He pleaded with Protestants, Catholics, and Jews to transcend their sectarian creeds and 'unite in good works' whenever they could 'find common cause.'"

Atalia Omer and Jason A. Springs point to Roosevelt's 1939 State of the Union address, which called upon Americans to "defend, not their homes alone, but the tenets of faith and humanity on with which their churches, their governments and their very civilization are founded." They state that, "This familiar rhetoric invoked a conception of the sanctity of the United States' Judeo-Christian values as a basis for war."

Timothy Wyatt notes that in the coming of World War II Roosevelt's isolationist opponents said he was calling for a "holy war." Wyatt says:

Often in his Fireside Chats or speeches to the houses of Congress, FDR argued for the entrance of America into the war by using both blatant and subtle religious rhetoric. Roosevelt portrayed the conflict in the light of good versus evil, the religious against the irreligious. In doing so, he pitted the Christian ideals of democracy against the atheism of National Socialism.

Lyndon Johnson

Biographer Randall B. Woods has argued that President Lyndon B. Johnson effectively used appeals to the Judeo-Christian ethical tradition to garner support for the civil rights law of 1965. Woods writes that Johnson undermined the Southern filibuster against the bill:

LBJ wrapped white America in a moral straight jacket. How could individuals who fervently, continuously, and overwhelmingly identified themselves with a merciful and just God continue to condone racial discrimination, police brutality, and segregation? Where in the Judeo-Christian ethic was there justification for killing young girls in a church in Alabama, denying an equal education to black children, barring fathers and mothers from competing for jobs that would feed and clothe their families? Was Jim Crow to be America's response to "Godless Communism"?

Woods went on to assess the role of Judeo-Christian ethics among the nation's political elite:

Johnson's decision to define civil rights as a moral issue, and to wield the nation's self-professed Judeo-Christian ethic as a sword in its behalf, constituted something of a watershed in twentieth-century political history. All presidents were fond of invoking the deity, and some conservatives like Dwight Eisenhower had flirted with employing Judeo-Christian teachings to justify their actions, but modern-day liberals, both politicians and the intellectuals who challenged and nourished them, had shunned spiritual witness. Most liberal intellectuals were secular humanists. Academics in particular had historically been deeply distrustful of organized religion, which they identified with small-mindedness, bigotry, and anti-intellectualism. Like his role model, FDR, Johnson equated liberal values with religious values, insisting freedom and social justice served the ends of both god and man. And he was not loath to say so.

Woods notes that Johnson's religiosity ran deep: "At 15 he joined the Disciples of Christ, or Christian, church and would forever believe that it was the duty of the rich to care for the poor, the strong to assist the weak, and the educated to speak for the inarticulate."

History

1930s and 1940s

Promoting the concept of the United States as a Judeo-Christian nation first became a political program in the 1940s, in response to the growth of anti-Semitism in America. The rise of Nazi anti-semitism in the 1930s led concerned Protestants, Catholics, and Jews to take steps to increase understanding and tolerance.

In this effort, precursors of the National Conference of Christians and Jews created teams consisting of a priest, a rabbi, and a minister, to run programs across the country, and fashion a more pluralistic America, no longer defined as a Christian land, but "one nurtured by three ennobling traditions: Protestantism, Catholicism and Judaism. ... The phrase 'Judeo-Christian' entered the contemporary lexicon as the standard liberal term for the idea that Western values rest on a religious consensus that included Jews."

In the 1930s, "In the face of worldwide antisemitic efforts to stigmatize and destroy Judaism, influential Christians and Jews in America labored to uphold it, pushing Judaism from the margins of American religious life towards its very center." During World War II, Jewish chaplains worked with Catholic priests and Protestant ministers to promote goodwill, addressing servicemen who, "in many cases had never seen, much less heard a Rabbi speak before." At funerals for the unknown soldier, rabbis stood alongside the other chaplains and recited prayers in Hebrew. In a much publicized wartime tragedy, the sinking of the Dorchester, the ship's multi-faith chaplains gave up their lifebelts to evacuating seamen and stood together "arm in arm in prayer" as the ship went down. A 1948 postage stamp commemorated their heroism with the words: "interfaith in action."

1950s, 1960s, and 1970s

In December 1952 President Dwight Eisenhower, speaking extemporaneously a month before his inauguration, said, in what may be the first direct public reference by a U.S. president to the Judeo-Christian concept:

[The Founding Fathers said] 'we hold that all men are endowed by their Creator ... ' In other words, our form of government has no sense unless it is founded in a deeply felt religious faith, and I don't care what it is. With us of course it is the Judeo-Christian concept, but it must be a religion with all men created equal.

By the 1950s, many conservatives emphasized the Judeo-Christian roots of their values. In 1958, economist Elgin Groseclose claimed that it was ideas "drawn from Judeo-Christian Scriptures that have made possible the economic strength and industrial power of this country."

Senator Barry Goldwater noted that conservatives "believed the communist projection of man as a producing, consuming animal to be used and discarded was antithetical to all the Judeo-Christian understandings which are the foundations upon which the Republic stands."

Belief in the superiority of Western Judeo-Christian traditions led conservatives to downplay the aspirations of the Third World to free themselves from colonial rule.

The emergence of the "Christian right" as a political force and part of the conservative coalition dates from the 1970s. According to Cambridge University historian Andrew Preston, the emergence of "conservative ecumenism." bringing together Catholics, Mormons, and conservative Protestants into the religious right coalition, was facilitated "by the rise of a Judeo-Christian ethic." These groups "began to mobilize together on cultural-political issues such as abortion and the proposed Equal Rights Amendment for women." As Wilcox and Robinson conclude:

The Christian Right is an attempt to restore Judeo-Christian values to a country that is in deep moral decline. ... [They] believe that society suffers from the lack of a firm basis of Judeo-Christian values and they seek to write laws that embody those values.

1980s and 1990s

By the 1980s and 1990s, favorable references to "Judeo-Christian values" were common, and the term was used by conservative Christians.

President Ronald Reagan frequently emphasized Judeo-Christian values as necessary ingredients in the fight against Communism. He argued that the Bible contains "all the answers to the problems that face us." Reagan disapproved of the growth of secularism and emphasized the need to take the idea of sin seriously. Tom Freiling, a Christian publisher and head of a conservative PAC, stated in his 2003 book, Reagan's God and Country, that "Reagan's core religious beliefs were always steeped in traditional Judeo-Christian heritage." Religion—and the Judeo-Christian concept—was a major theme in Reagan's rhetoric by 1980.

President Bill Clinton during his 1992 presidential campaign, likewise emphasized the role of religion in society, and in his personal life, having made references to the Judeo-Christian tradition.

The term became especially significant in American politics, and, promoting "Judeo-Christian values" in the culture wars, usage surged in the 1990s.

James Dobson, a prominent evangelical Christian, said the Judeo-Christian tradition includes the right to display numerous historical documents in Kentucky schools, after they were banned by a federal judge in May 2000 because they were "conveying a very specific governmental endorsement of religion".

Since 9/11

According to Hartmann et al., usage shifted between 2001 and 2005, with the mainstream media using the term less, in order to characterize America as multicultural. The study finds the term is now most likely to be used by liberals in connection with discussions of Muslim and Islamic inclusion in America, and renewed debate about the separation of church and state.

In 2012, the book Kosher Jesus by Orthodox rabbi Shmuley Boteach was published. In it, Boteach concludes by writing, as to Judeo-Christian values, that "the hyphen between Jewish and Christian values is Jesus himself."

In U.S. law

In the case of Marsh v. Chambers, 463 U.S. 783 (1983), the Supreme Court of the United States held that a state legislature could constitutionally have a paid chaplain to conduct legislative prayers "in the Judeo-Christian tradition." In Simpson v. Chesterfield County Board of Supervisors, the Fourth Circuit Court of Appeals held that the Supreme Court's holding in the Marsh case meant that the "Chesterfield County could constitutionally exclude Cynthia Simpson, a Wiccan priestess, from leading its legislative prayers, because her faith was not 'in the Judeo-Christian tradition.'" Chesterfield County's board included Jewish, Christian, and Muslim clergy in its invited list.

Several legal disputes, especially in Alabama, have challenged the public display of the Ten Commandments. See:

• Glassroth v. Moore for Alabama
• Green v. Haskell County Board of Commissioners, for Oklahoma
• McCreary County v. American Civil Liberties Union, for Kentucky
• Pleasant Grove City v. Summum, for Utah
• Stone v. Graham for Kentucky
• Van Orden v. Perry for Texas

Responses

Some theologians warn against the uncritical use of "Judeo-Christian" entirely, arguing that it can license mischief, such as opposition to secular humanism with scant regard to modern Jewish, Catholic, or Christian traditions, including the liberal strains of different faiths, such as Reform Judaism and liberal Protestant Christianity.

Two notable books addressed the relations between contemporary Judaism and Christianity. Abba Hillel Silver's Where Judaism Differs and Leo Baeck's Judaism and Christianity were both motivated by an impulse to clarify Judaism's distinctiveness "in a world where the term Judeo-Christian had obscured critical differences between the two faiths."

Reacting against the blurring of theological distinctions, Rabbi Eliezer Berkovits wrote that "Judaism is Judaism because it rejects Christianity, and Christianity is Christianity because it rejects Judaism."

Theologian and author Arthur A. Cohen, in The Myth of the Judeo-Christian Tradition, questioned the theological validity of the Judeo-Christian concept and suggested that it was essentially an invention of American politics, while Jacob Neusner, in Jews and Christians: The Myth of a Common Tradition, writes, "The two faiths stand for different people talking about different things to different people."

Law professor Stephen M. Feldman, looking at the period before 1950, chiefly in Europe, sees the concept of a Judeo-Christian tradition as supersessionism, which he characterizes as "dangerous Christian dogma (at least from a Jewish perspective)", and as a "myth" which "insidiously obscures the real and significant differences between Judaism and Christianity."

Abrahamic religion

Advocates of the term "Abrahamic religion" since the second half of the 20th century have proposed an inclusivism that widens the "Judeo-Christian" concept to include Islam as well. The rationale for the term "Abrahamic" is that Islam, like Judaism and Christianity, traces its origins to the figure of Abraham, whom Islam regards as a prophet. Advocates of this umbrella term consider it the "exploration of something positive" in the sense of a "spiritual bond" between Jews, Christians, and Muslims.

Australia

Australian historian Tony Taylor points out that Australia has borrowed the "Judeo-Christian" theme from American conservative discourse.

Jim Berryman, another Australian historian, argues that from the 1890s to the present, rhetoric upholding Australia's traditional attachment to Western civilisation emphasizes three themes: the core British heritage; Australia's Judeo-Christian belief system; and the rational principles of the Enlightenment. These themes have been expressed mostly on the Australian center-right political spectrum, and most prominently among conservative-leaning commentators.