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Section: Rigorous formulation > Definition of Chirgwin–Coulson weights. Given a wave function Ψ = ∑ i C i Φ i {\displaystyle \Psi =\sum \limits _{i}C_{i}\Phi _{i}} where Φ 1 , Φ 2 , … , Φ N {\displaystyle \Phi _{1},\Phi _{2},\dots ,\Phi _{N}} is a complete, linearly independent set of VB structures and C k {\displaysty... | Wikipedia - Chirgwin–Coulson weights - Rigorous formulation > Definition of Chirgwin–Coulson weights | 328 | 823 | null |
Given a wave function Ψ = ∑ i C i Φ i {\displaystyle \Psi =\sum \limits _{i}C_{i}\Phi _{i}} where Φ 1 , Φ 2 , … , Φ N {\displaystyle \Phi _{1},\Phi _{2},\dots ,\Phi _{N}} is a complete, linearly independent set of VB structures and C k {\displaystyle C_{k}} is the coefficient of each structure, the Chirgwin-Coulson wei... | Wikipedia - Chirgwin–Coulson weights - Rigorous formulation > Definition of Chirgwin–Coulson weights | 586 | 1,319 | null |
Other methods of computing weights of VB structure include Löwdin weights, where W i Lowdin = ∑ j , k S i j 1 / 2 C j S i k 1 / 2 C k {\displaystyle W_{i}^{\text{Lowdin}}=\sum \limits _{j,k}S_{ij}^{1/2}C_{j}S_{ik}^{1/2}C_{k}} , and inverse weights, where W i inverse = 1 N ( C i 2 ( S − 1 ) i i ) {\displaystyle W_{i}^{\... | Wikipedia - Chirgwin–Coulson weights - Rigorous formulation > Definition of Chirgwin–Coulson weights | 301 | 687 | null |
Section: Rigorous formulation > Half determinant decomposition of molecular orbitals. Given a set of molecular orbitals, Ψ 1 , Ψ 2 , … , Ψ m {\displaystyle \Psi _{1},\Psi _{2},\dots ,\Psi _{m}} , for a molecule, consider the determinant of a given orbital population, represented by D MO {\displaystyle D_{\text{MO}}} . ... | Wikipedia - Chirgwin–Coulson weights - Rigorous formulation > Half determinant decomposition of molecular orbitals | 219 | 715 | null |
The determinant can be written as the following Slater determinant: D MO = | Ψ 1 Ψ ¯ 1 Ψ 2 Ψ ¯ 2 … | {\displaystyle D_{\text{MO}}=|\Psi _{1}{\overline {\Psi }}_{1}\Psi _{2}{\overline {\Psi }}_{2}\dots |} Computing the determinant explicitly by multiplying this expression can be a computationally difficult task, given t... | Wikipedia - Chirgwin–Coulson weights - Rigorous formulation > Half determinant decomposition of molecular orbitals | 364 | 1,023 | null |
On the other hand, because the determinant of a product of matrices is equal to the product of determinants, the determinant can be regrouped to half-determinants, one of which contains only electrons with α {\displaystyle \alpha } spin and the only with electrons of β {\displaystyle \beta } spin, that is: D MO = h MO ... | Wikipedia - Chirgwin–Coulson weights - Rigorous formulation > Half determinant decomposition of molecular orbitals | 393 | 1,018 | null |
Note that any given molecular orbital Ψ MO {\displaystyle \Psi _{\text{MO}}} can be written as a linear combination of atomic orbitals ϕ 1 , ϕ 2 , … , ϕ n {\displaystyle \phi _{1},\phi _{2},\dots ,\phi _{n}} , that is for each Ψ i {\displaystyle \Psi _{i}} , there exist C i j {\displaystyle C_{ij}} such that Ψ i = ∑ j ... | Wikipedia - Chirgwin–Coulson weights - Rigorous formulation > Half determinant decomposition of molecular orbitals | 272 | 712 | null |
As such, the half determinant h MO α {\displaystyle h_{\text{MO}}^{\alpha }} can be further decomposed into the half determinants for an ordering of atomic orbitals h r α = | ϕ 1 , ϕ 2 , … , ϕ n | {\displaystyle h_{r}^{\alpha }=|\phi _{1},\phi _{2},\dots ,\phi _{n}|} corresponding to a VB structure r {\displaystyle r} ... | Wikipedia - Chirgwin–Coulson weights - Rigorous formulation > Half determinant decomposition of molecular orbitals | 218 | 582 | null |
As such, the molecular orbital Ψ i {\displaystyle \Psi _{i}} can be represented as a combination of the half determinants of the atomic orbitals, h MO α = ∑ r C r α h r α {\displaystyle h_{\text{MO}}^{\alpha }=\sum \limits _{r}C_{r}^{\alpha }h_{r}^{\alpha }} . The coefficient C r α {\displaystyle C_{r}^{\alpha }} can b... | Wikipedia - Chirgwin–Coulson weights - Rigorous formulation > Half determinant decomposition of molecular orbitals | 325 | 767 | null |
The coefficient C r α {\displaystyle C_{r}^{\alpha }} can be determined by evaluating the following matrix: C r α = | C 11 C 21 … C n 1 C 12 C 22 … C n 2 ⋮ ⋮ ⋱ C 1 n C 2 n … C n n | {\displaystyle C_{r}^{\alpha }={\begin{vmatrix}C_{11}&C_{21}&\dots C_{n1}\\C_{12}&C_{22}&\dots C_{n2}\\\vdots &\vdots &\ddots \\C_{1n}&C_{... | Wikipedia - Chirgwin–Coulson weights - Rigorous formulation > Half determinant decomposition of molecular orbitals | 359 | 808 | null |
Section: Sample computations for simple molecules > Computations for the hydrogen molecule. The hydrogen molecule can be considered to be a linear combination of two H {\displaystyle {\ce {H}}} 1 s {\displaystyle 1s} orbitals, indicated as φ 1 {\displaystyle \varphi _{1}} and φ 2 {\displaystyle \varphi _{2}} . The poss... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for the hydrogen molecule | 318 | 1,030 | null |
Because structures 1 and 2 both represent covalent bonding in the hydrogen molecule and exchanging the electrons of structure 1 yields structure 2, the two covalent structures can be combined into one wave function. As such, the Heitler-London model for bonding in H 2 {\displaystyle {\ce {H_2}}} , Φ H L {\displaystyle ... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for the hydrogen molecule | 336 | 989 | null |
As such, the wave function for the H 2 {\displaystyle {\ce {H_2}}} molecule, Ψ H 2 {\displaystyle \Psi _{{\text{H}}_{2}}} , can be considered to be a linear combination of the Heitler-London structure and the two ionic valence bond structures. Ψ H 2 = C 1 Φ H L + C 2 | φ 1 φ 1 ¯ | + C 3 | φ 2 φ 2 ¯ | {\displaystyle \Ps... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for the hydrogen molecule | 311 | 778 | null |
A sample output is given below: S = | S 11 S 21 S 22 S 31 S 32 S 33 | = | 1 0.77890423 1 0.77890423 0.43543258 1 | {\displaystyle S={\begin{vmatrix}S_{11}\\S_{21}&S_{22}\\S_{31}&S_{32}&S_{33}\\\end{vmatrix}}={\begin{vmatrix}1\\0.77890423&1\\0.77890423&0.43543258&1\\\end{vmatrix}}} Finding the eigenvectors of the matrix... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for the hydrogen molecule | 349 | 733 | null |
_{2}{\overline {\varphi _{2}}}|\}=C_{1}\Phi _{HL}+C_{2}|\varphi _{1}{\overline {\varphi _{1}}}|+C_{3}|\varphi _{2}{\overline {\varphi _{2}}}|} Solving for the VB-vector c → {\displaystyle {\vec {c}}} using density functional theory yields the coefficients C 1 = 0.787469 {\displaystyle C_{1}=0.787469} and C 2 = C 3 = 0.... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for the hydrogen molecule | 183 | 365 | null |
Thus, the Coulson-Chrigwin weights can be computed: W 1 = C 1 2 S 11 + C 1 C 2 S 12 + C 1 C 3 S 13 = 0.784 {\displaystyle W_{1}=C_{1}^{2}S_{11}+C_{1}C_{2}S_{12}+C_{1}C_{3}S_{13}=0.784} W 2 = W 3 = 0.108 {\displaystyle W_{2}=W_{3}=0.108} To check for consistency, the inverse weights can be computed by first determining ... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for the hydrogen molecule | 350 | 730 | null |
W 1 = 1 N ( C 1 2 ( S − 1 ) 11 ) = 0.803 {\displaystyle W_{1}={\frac {1}{N}}{\bigg (}{\frac {C_{1}^{2}}{(S^{-1})_{11}}}{\bigg )}=0.803} , and W 2 = W 3 = 0.098 {\displaystyle W_{2}=W_{3}=0.098} . Informally, the computed weights indicate that the wave function for the H 2 {\displaystyle {\ce {H_2}}} molecule has a mino... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for the hydrogen molecule | 171 | 408 | null |
Assuming no atomic orbital overlap, the k th {\displaystyle k^{\text{th}}} structure can be represented by the determinants Φ k {\displaystyle \Phi _{k}} : Φ 1 = 1 2 ( | ϕ 2 ϕ 2 ¯ ϕ 1 ϕ 3 ¯ | + | ϕ 2 ϕ 2 ¯ ϕ 3 ϕ 1 ¯ | ) {\displaystyle \Phi _{1}={\frac {1}{\sqrt {2}}}(|\phi _{2}{\overline {\phi _{2}}}\phi _{1}{\overline... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for ozone | 350 | 687 | null |
+ | ϕ 2 ϕ 1 ¯ ϕ 3 ϕ 3 ¯ | ) {\displaystyle \Phi _{3}={\frac {1}{\sqrt {2}}}(|\phi _{1}{\overline {\phi _{2}}}\phi _{3}{\overline {\phi _{3}}}|+|\phi _{2}{\overline {\phi _{1}}}\phi _{3}{\overline {\phi _{3}}}|)} Φ 4 = | ϕ 1 ϕ 1 ¯ ϕ 2 ϕ 2 ¯ | {\displaystyle \Phi _{4}=|\phi _{1}{\overline {\phi _{1}}}\phi _{2}{\overline ... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for ozone | 350 | 656 | null |
one where all of the oxygen p {\displaystyle p} orbitals are in phase, one where there is a node on the central oxygen, and one where all of the oxygen p {\displaystyle p} orbitals are out of phase, shown below: The wave functions for each of the molecular orbitals π i {\displaystyle \pi _{i}} can be written as a linea... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for ozone | 326 | 770 | null |
_{3}\\\end{vmatrix}}={\begin{vmatrix}0.368&0.764&0.368\\0.710&0&-0.710\\0.614&-0.671&0.614\\\end{vmatrix}}{\begin{vmatrix}\phi _{1}\\\phi _{2}\\\phi _{3}\\\end{vmatrix}}} Where C i j {\displaystyle C_{ij}} indicates the coefficient of ϕ j {\displaystyle \phi _{j}} in a molecular orbital π i {\displaystyle \pi _{i}} . C... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for ozone | 253 | 512 | null |
Using the methods of half determinants, the half determinants for the ground state are: | ϕ 1 ϕ 2 | g = ‖ C 11 C 12 C 21 C 22 ‖ = − 0.542 {\displaystyle |\phi _{1}\phi _{2}|_{g}={\begin{Vmatrix}C_{11}&C_{12}\\C_{21}&C_{22}\\\end{Vmatrix}}=-0.542} | ϕ 2 ϕ 3 | g = ‖ C 12 C 13 C 22 C 23 ‖ = − 0.542 {\displaystyle |\phi _{... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for ozone | 349 | 694 | null |
{\displaystyle |\phi _{i}{\overline {\phi _{j}}}\phi _{k}{\overline {\phi _{l}}}|} is: | ϕ i ϕ j ¯ ϕ k ϕ l ¯ | = | ϕ i ϕ k | | ϕ j ϕ l | {\displaystyle |\phi _{i}{\overline {\phi _{j}}}\phi _{k}{\overline {\phi _{l}}}|=|\phi _{i}\phi _{k}||\phi _{j}\phi _{l}|} Which implies that the ground state has the following coeff... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for ozone | 343 | 705 | null |
{\begin{aligned}\Psi _{g}&=-0.416\Phi _{1}+0.400\Phi _{2}+0.400\Phi _{3}+0.294\Phi _{4}+0.294\Phi _{5}+0.274\Phi _{6}\\&=-0.294(|\phi _{2}{\overline {\phi _{2}}}\phi _{1}{\overline {\phi _{3}}}|+|\phi _{2}{\overline {\phi _{2}}}\phi _{3}{\overline {\phi _{1}}}|)+0.283(|\phi _{1}{\overline {\phi _{1}}}\phi _{2}{\overlin... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for ozone | 348 | 559 | null |
0.294|\phi _{1}{\overline {\phi _{1}}}\phi _{2}{\overline {\phi _{2}}}|+0.294|\phi _{2}{\overline {\phi _{2}}}\phi _{3}{\overline {\phi _{3}}}|+0.274|\phi _{1}{\overline {\phi _{1}}}\phi _{3}{\overline {\phi _{3}}}|\end{aligned}}} Given the following overlap matrix for the half determinants: S = | ⟨ | ϕ 1 ϕ 2 | | | ϕ 1... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for ozone | 347 | 661 | null |
_{1}\phi _{3}|\rangle &\langle |\phi _{1}\phi _{3}|||\phi _{1}\phi _{3}|\rangle \\\langle |\phi _{1}\phi _{2}|||\phi _{2}\phi _{3}|\rangle &\langle |\phi _{1}\phi _{3}|||\phi _{2}\phi _{3}|\rangle &\langle |\phi _{2}\phi _{3}|||\phi _{2}\phi _{3}|\rangle \end{vmatrix}}={\begin{vmatrix}0.98377\\0.12634&0.99993\\0.00810&... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for ozone | 346 | 641 | null |
_{z}}}|\rangle } can be evaluated by finding the product of the overlap between the two half determinants, that is: ⟨ | ϕ a ϕ b ¯ ϕ c ϕ d ¯ | | | ϕ w ϕ x ¯ ϕ y ϕ z ¯ | ⟩ = ( ⟨ | ϕ a ϕ c | | | ϕ w ϕ y | ⟩ ) ( ⟨ | ϕ b ϕ d | | | ϕ x ϕ z | ⟩ ) {\displaystyle \langle |\phi _{a}{\overline {\phi _{b}}}\phi _{c}{\overline {\ph... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for ozone | 347 | 726 | null |
_{1}{\overline {\phi _{2}}}\phi _{2}{\overline {\phi _{3}}}|} would be: ⟨ | ϕ 1 ϕ 2 ¯ ϕ 3 ϕ 3 ¯ | | | ϕ 1 ϕ 2 ¯ ϕ 2 ϕ 3 ¯ | ⟩ = ( ⟨ | ϕ 1 ϕ 3 | | | ϕ 1 ϕ 2 | ⟩ ) ( ⟨ | ϕ 2 ϕ 3 | | | ϕ 2 ϕ 3 | ⟩ ) = ( 0.12634 ) ( 0.98377 ) = 0.12429 {\displaystyle \langle |\phi _{1}{\overline {\phi _{2}}}\phi _{3}{\overline {\phi _{3}}}... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for ozone | 347 | 665 | null |
The weights can be found by first computing the Chirgwin–Coulson weights for their constituent determinants: W ( | ϕ 1 ϕ 2 ¯ ϕ 3 ϕ 3 ¯ | ) = ∑ k 0.283 C k ⟨ | ϕ 1 ϕ 2 ¯ ϕ 3 ϕ 3 ¯ | | | Φ k | ⟩ = 0.283 [ − 0.294 ( ⟨ | ϕ 1 ϕ 2 ¯ ϕ 3 ϕ 3 ¯ | | | ϕ 2 ϕ 2 ¯ ϕ 1 ϕ 3 ¯ | ⟩ + ⟨ | ϕ 1 ϕ 2 ¯ ϕ 3 ϕ 3 ¯ | | | ϕ 2 ϕ 2 ¯ ϕ 3 ϕ 1 ¯ |... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for ozone | 349 | 758 | null |
0.111 {\displaystyle {\begin{aligned}W(|\phi _{1}{\overline {\phi _{2}}}\phi _{3}{\overline {\phi _{3}}}|)&=\sum \limits _{k}0.283C_{k}\langle |\phi _{1}{\overline {\phi _{2}}}\phi _{3}{\overline {\phi _{3}}}|||\Phi _{k}|\rangle \\&=0.283[-0.294(\langle |\phi _{1}{\overline {\phi _{2}}}\phi _{3}{\overline {\phi _{3}}}|... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for ozone | 348 | 598 | null |
_{3}{\overline {\phi _{3}}}|||\phi _{1}{\overline {\phi _{1}}}\phi _{2}{\overline {\phi _{3}}}|\rangle +\langle |\phi _{1}{\overline {\phi _{2}}}\phi _{3}{\overline {\phi _{3}}}|||\phi _{1}{\overline {\phi _{1}}}\phi _{3}{\overline {\phi _{2}}}|\rangle )\\&\quad \quad +0.283(\langle |\phi _{1}{\overline {\phi _{2}}}\ph... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for ozone | 349 | 595 | null |
_{1}{\overline {\phi _{2}}}\phi _{3}{\overline {\phi _{3}}}|||\phi _{1}{\overline {\phi _{1}}}\phi _{2}{\overline {\phi _{2}}}|\rangle +0.294\langle |\phi _{1}{\overline {\phi _{2}}}\phi _{3}{\overline {\phi _{3}}}|||\phi _{2}{\overline {\phi _{2}}}\phi _{3}{\overline {\phi _{3}}}|\rangle \\&\quad \quad +0.274\langle |... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for ozone | 345 | 610 | null |
_{2}{\overline {\phi _{1}}}\phi _{3}{\overline {\phi _{3}}}|)=W(|\phi _{1}{\overline {\phi _{1}}}\phi _{2}{\overline {\phi _{3}}}|)=W(|\phi _{1}{\overline {\phi _{1}}}\phi _{3}{\overline {\phi _{2}}}|)=0.111} The weights for the standard lewis structures would be the sum of the weights of the constituent determinants. | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for ozone | 152 | 319 | null |
_{2}{\overline {\phi _{1}}}\phi _{3}{\overline {\phi _{3}}}|)=W(|\phi _{1}{\overline {\phi _{1}}}\phi _{2}{\overline {\phi _{3}}}|)=W(|\phi _{1}{\overline {\phi _{1}}}\phi _{3}{\overline {\phi _{2}}}|)=0.111} The weights for the standard lewis structures would be the sum of the weights of the constituent determinants. ... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for ozone | 478 | 972 | null |
For the diradical state, Ψ 1 {\displaystyle \Psi _{1}} , the weight is: W ( | ϕ 2 ϕ 2 ¯ ϕ 1 ϕ 3 ¯ | ) = ∑ k − 0.294 C k | ϕ 2 ϕ 2 ¯ ϕ 1 ϕ 3 ¯ | | Φ k | = 0.106 {\displaystyle W(|\phi _{2}{\overline {\phi _{2}}}\phi _{1}{\overline {\phi _{3}}}|)=\sum \limits _{k}-0.294C_{k}|\phi _{2}{\overline {\phi _{2}}}\phi _{1}{\ove... | Wikipedia - Chirgwin–Coulson weights - Sample computations for simple molecules > Computations for ozone | 345 | 653 | null |
Section: Applications to main group compounds > Borazine. Borazine, (chemical formula B 3 N 3 H 6 {\displaystyle {\ce {B_3N_3H_6}}} ) is a cyclic, planar compound that is isoelectronic with benzene. Given the lone pair in the nitrogen p orbital out of the plane and the empty p orbital of boron, the following resonance ... | Wikipedia - Chirgwin–Coulson weights - Applications to main group compounds > Borazine | 239 | 1,022 | null |
Section: Applications to main group compounds > S2N2. Disulfur dinitride is a square planar compound that contains a 6 electron conjugated π {\displaystyle \pi } system. The primary diradical resonance structures (1 and 2) and a secondary zwitterionic structure (3) are shown below: Valence bond calculations using the D... | Wikipedia - Chirgwin–Coulson weights - Applications to main group compounds > S2N2 | 210 | 920 | null |
Article: Chromogen. In chemistry, the term chromogen refers to a colourless (or faintly coloured) chemical compound that can be converted by chemical reaction into a compound which can be described as "coloured" (a chromophore). There is no universally agreed definition of the term. Various dictionaries give the follow... | Wikipedia - Chromogen - Summary | 198 | 959 | null |
Section: Psychoactive substances > By precursor chemicals. Prepared substances (as opposed to those that occur naturally in a consumable form, such as cannabis and psilocybin mushrooms) require reagents. Some drugs, like cocaine and morphine, are extracted from plant sources and refined with the aid of chemicals. Semi-... | Wikipedia - Clandestine chemistry - Psychoactive substances > By precursor chemicals | 335 | 1,539 | null |
Section: Psychoactive substances > By precursor chemicals > Suppliers of precursor chemicals. Chemicals critical to the production of cocaine, heroin, and synthetic drugs are produced in many countries throughout the world. Many manufacturers and suppliers exist in Europe, China, India, the United States, and many othe... | Wikipedia - Clandestine chemistry - Psychoactive substances > By precursor chemicals > Suppliers of precursor chemicals | 200 | 1,114 | null |
Section: Psychoactive substances > By precursor chemicals > Enforcement of controls on precursor chemicals > General. The Multilateral Chemical Reporting Initiative encourages governments to exchange information on a voluntary basis in order to monitor international chemical shipments.: 8–9 Over the past decade, key in... | Wikipedia - Clandestine chemistry - Psychoactive substances > By precursor chemicals > Enforcement of controls on precursor chemicals > General | 345 | 1,805 | null |
Beginning in July 2001, the International Narcotics Control Board (INCB) has opted to organize an international conference with the goal of devising a specific action plan to counter the traffic in MDMA precursor chemicals.: 68 They hope to prevent the diversion of chemicals used in the production of amphetamine-type s... | Wikipedia - Clandestine chemistry - Psychoactive substances > By precursor chemicals > Enforcement of controls on precursor chemicals > General | 177 | 912 | null |
Section: Psychoactive substances > By precursor chemicals > Enforcement of controls on precursor chemicals > Cocaine. Operation Purple is a U.S. DEA driven international chemical control initiative designed to reduce the illicit manufacture of cocaine in the Andean Region, identify rogue firms and suspect individuals, ... | Wikipedia - Clandestine chemistry - Psychoactive substances > By precursor chemicals > Enforcement of controls on precursor chemicals > Cocaine | 332 | 1,881 | null |
Section: Psychoactive substances > By precursor chemicals > Enforcement of controls on precursor chemicals > Heroin. Similarly, heroin-producing countries depend on supplies of acetic anhydride (AA) from the international market. This heroin precursor continues to account for the largest volume of internationally seize... | Wikipedia - Clandestine chemistry - Psychoactive substances > By precursor chemicals > Enforcement of controls on precursor chemicals > Heroin | 332 | 1,689 | null |
Section: Psychoactive substances > By precursor chemicals > Enforcement of controls on precursor chemicals > Amphetamines. The practice of clandestine chemistry to synthesize controlled substance analogues and circumvent drug laws was first noticed in the late 1960s, as types of drugs became controlled substances in ma... | Wikipedia - Clandestine chemistry - Psychoactive substances > By precursor chemicals > Enforcement of controls on precursor chemicals > Amphetamines | 246 | 1,176 | null |
Section: Psychoactive substances > By precursor chemicals > Enforcement of controls on precursor chemicals > Methamphetamine. As of the early 1990s, methamphetamine use was concentrated among young white males in California and nearby states. Since then its use has spread both demographically and geographically. Metham... | Wikipedia - Clandestine chemistry - Psychoactive substances > By precursor chemicals > Enforcement of controls on precursor chemicals > Methamphetamine | 342 | 1,733 | null |
This made it somewhat more difficult for underground chemists to produce methamphetamine. In May 1995, the DEA shut down two major suppliers of precursors in the United States, seizing 25 metric tons of ephedrine and pseudoephedrine from Clifton Pharmaceuticals and 500 cases of pseudoephedrine from X-Pressive Looks, In... | Wikipedia - Clandestine chemistry - Psychoactive substances > By precursor chemicals > Enforcement of controls on precursor chemicals > Methamphetamine | 206 | 1,011 | null |
Section: Psychoactive substances > By contamination > Methamphetamine. A common adulterant is dimethyl sulfone, a solvent and cosmetic base without known effect on the nervous system; other adulterants include dimethylamphetamine HCl, ephedrine HCl, sodium thiosulfate, sodium chloride, sodium glutamate, and a mixture o... | Wikipedia - Clandestine chemistry - Psychoactive substances > By contamination > Methamphetamine | 340 | 1,643 | null |
How information is categorized and tracked may also inflate or minimize the apparent results. Missouri has reported some of the highest rates of meth-lab arrests in the country, and has pursued an aggressive and highly publicized policy of policing meth labs. This has resulted in as many as 205 cases per year in one co... | Wikipedia - Clandestine chemistry - Psychoactive substances > By contamination > Methamphetamine | 310 | 1,486 | null |
Section: Psychoactive substances > By contamination > Methamphetamine > Cleanup. Clean up processes were regulated by the EPA as of 2007. The Methamphetamine Remediation Research Act of 2007 required EPA to develop guidelines for remediation of former methamphetamine labs. This creates guidelines for States and local a... | Wikipedia - Clandestine chemistry - Psychoactive substances > By contamination > Methamphetamine > Cleanup | 302 | 1,630 | null |
Article: Clay chemistry. Clay chemistry is an applied subdiscipline of chemistry which studies the chemical structures, properties and reactions of or involving clays and clay minerals. It is a multidisciplinary field, involving concepts and knowledge from inorganic and structural chemistry, physical chemistry, materia... | Wikipedia - Clay chemistry - Summary | 332 | 1,661 | null |
It also plays an important role in the fate of most Ca2+ arriving from land (river water) into the seas. The ability to change and control the CEC of clay minerals offers a valuable tool in the development of selective adsorbents with applications as varied as chemical sensors or pollution cleaning substances for conta... | Wikipedia - Clay chemistry - Summary | 333 | 1,730 | null |
Article: Colloidal probe technique. The colloidal probe technique is commonly used to measure interaction forces acting between colloidal particles and/or planar surfaces in air or in solution. This technique relies on the use of an atomic force microscope (AFM). However, instead of a cantilever with a sharp AFM tip, o... | Wikipedia - Colloidal probe technique - Summary | 230 | 1,127 | null |
Section: Purpose. The possibility to measure forces involving particles and surfaces directly is essential since such forces are relevant in a variety of processes involving colloidal and polymeric systems. Examples include particle aggregation, suspension rheology, particle deposition, and adhesion processes. One can ... | Wikipedia - Colloidal probe technique - Purpose | 209 | 1,158 | null |
Section: Principle. The colloidal probe technique uses a standard AFM for the force measurements. But instead the AFM cantilever with an attached sharp tip one uses the colloidal probe. This colloidal probe is normally obtained by attaching a colloidal particle to a cantilever. By recording the deflection of the cantil... | Wikipedia - Colloidal probe technique - Principle | 339 | 1,645 | null |
The lever signal is therefore proportional to the deflection ξ. During an approach-retraction cycle, one records the lever signal S as a function of the vertical displacement D of the scanner. Suppose for the moment that the probe and the substrate are hard and non-deformable objects and that no forces are acting betwe... | Wikipedia - Colloidal probe technique - Principle | 340 | 1,568 | null |
Depending on the substrate, the precision in determining this contact point is between 0.5–2 nm. In the constant compliance region, the lever deformation is given by ξ = (S − S0)/a In this fashion, one can detect deflections of the cantilever with typical resolution of better than 0.1 nm. Let us now consider the releva... | Wikipedia - Colloidal probe technique - Principle | 346 | 1,566 | null |
From stability considerations one finds that the cantilever will be unstable provided dF/dh > k This instability is illustrated in the right panel of the figure on the right. As the cantilever approaches, the slope of the force curve increases. When the slope becomes larger than the spring constant of the cantilever, t... | Wikipedia - Colloidal probe technique - Principle | 174 | 813 | null |
Section: Extensions. The colloidal probes are normally fabricated by gluing a colloidal particle to a tip-less cantilever with a micromanipulator in air. The subsequent rewetting of the probe may lead to the formation of nanosized bubbles on the probe surface. This problem can be avoided by attaching the colloidal part... | Wikipedia - Colloidal probe technique - Extensions | 343 | 1,675 | null |
The frictional force method relies on measurement of the approach and retract curves of the cantilever through a viscous fluid. Since the hydrodynamic drag of a sphere close to a planar substrate is known theoretically, the spring constant of the cantilever can be deduced. The geometrical method exploits relations betw... | Wikipedia - Colloidal probe technique - Extensions | 320 | 1,680 | null |
Section: History. Hitherto, recent publications that broke the wall of putative chemical understanding and presented detection/isolation of novel compounds with intriguing bonding characters can still be provocative at times. The stir in such discoveries arose partly from the lack of a universally accepted bond descrip... | Wikipedia - Compliance constants - History | 325 | 1,661 | null |
Section: Theory > Force constants. By Taylor series expansion, the potential energy, V {\displaystyle V} , of any molecule can be expressed as: V = V 0 + G T Z + 1 2 Z T H Z + . . . {\displaystyle V=V_{0}+G^{T}Z+{1 \over 2}Z^{T}HZ+...} (eq. 1) where Z {\displaystyle Z} is a column vector of arbitrary and fully determin... | Wikipedia - Compliance constants - Theory > Force constants | 275 | 959 | null |
By assuming harmonic potential and regarding the third derivative term and forth as negligible, the potential energy formula then simply becomes: V = 1 2 Z T H Z {\displaystyle V={1 \over 2}Z^{T}HZ} (eq. 2) Transitioning from cartesian coordinates Z {\displaystyle Z} to internal coordinates Q {\displaystyle Q} , which ... | Wikipedia - Compliance constants - Theory > Force constants | 320 | 1,103 | null |
Section: Theory > Compliance constants. Rather than internal displacement coordinates, an alternative approach to write the potential energy of a molecule as explained by Decius is to write it as a quadratic form in terms of generalized displacement forces (negative gradient) G q {\displaystyle G_{q}} . V = 1 2 G q T C... | Wikipedia - Compliance constants - Theory > Compliance constants | 331 | 1,010 | null |
Section: Archetype of compliance constants calculation > Cyclobutane: force constants calculations. To illustrate how choices of coordinate systems for calculations of chemical bonds can immensely affect the results and consequently engender ill-defined descriptors of the bonds, sample calculations for n-butane and cyc... | Wikipedia - Compliance constants - Archetype of compliance constants calculation > Cyclobutane: force constants calculations | 342 | 1,539 | null |
Section: Archetype of compliance constants calculation > Cyclobutane: compliance constants calculations. A more accurate approach as claimed by Grunenberg is to exploit compliance constants as means for describing chemical bonds as shown below. All the calculated compliance constants above are given in N−1 unit. For bo... | Wikipedia - Compliance constants - Archetype of compliance constants calculation > Cyclobutane: compliance constants calculations | 219 | 1,083 | null |
Section: Applications to main group compounds > Diboryne. Diboryne or a compound with boron-boron triple bond was first isolated as a N-heterocyclic carbene supported complex (NHC-BB-NHC) in the Braunschweig group, and its unique, peculiar bonding structure thereupon catalyzed new research to computationally assess the... | Wikipedia - Compliance constants - Applications to main group compounds > Diboryne | 206 | 900 | null |
Section: Applications to main group compounds > Watson-Crick base pairs. Besides chemical bonds, compliance constants are also useful for determining non-covalent bonds, such as H-bonds in Watson-Crick base pairs. Grunenberg calculated the compliance constant for each of the donor-H⋯acceptor linkages in AT and CG base ... | Wikipedia - Compliance constants - Applications to main group compounds > Watson-Crick base pairs | 153 | 693 | null |
Section: Common origin and structure. Any significant quantity of a polyhalogenated compound is by default a blend of multiple molecule types because each molecule forms independently, and chlorine and bromine do not strongly select which site(s) they bond to. Polychlorinated biphenyls (PCBs) are a family of 209 congen... | Wikipedia - Congener (chemistry) - Common origin and structure | 207 | 734 | null |
Article: Cononsolvency. Cononsolvency is a phenomenon where two solvents that can typically readily dissolve a polymer, when mixed, at certain ratios of these two solvents, are no longer able to dissolve the polymer. This phenomenon is in contrast to cosolvency where two solvents that are both poor at dissolving a mate... | Wikipedia - Cononsolvency - Summary | 345 | 1,525 | null |
After 45 years of research, the origin of the molecular mechanism behind the cononsolvency effect in a mixture of solvents remains not fully resolved yet. To date, researchers have considered various interactions between polymer and solvent/cosolvent as possible factors leading to the cononsolvency effect, such as comp... | Wikipedia - Cononsolvency - Summary | 240 | 1,063 | null |
Article: Core–shell semiconductor nanocrystal. Core–shell semiconducting nanocrystals (CSSNCs) are a class of materials which have properties intermediate between those of small, individual molecules and those of bulk, crystalline semiconductors. They are unique because of their easily modular properties, which are a r... | Wikipedia - Core–shell semiconductor nanocrystal - Summary | 287 | 1,333 | null |
Section: Background. Colloidal semiconductor nanocrystals, which are also called quantum dots (QDs), consist of ~1–10 nm diameter semiconductor nanoparticles that have organic ligands bound to their surface. These nanomaterials have found applications in nanoscale photonic, photovoltaic, and light-emitting diode (LED) ... | Wikipedia - Core–shell semiconductor nanocrystal - Background | 330 | 1,635 | null |
At the surface of the crystal, the periodicity abruptly stops, resulting in surface atoms having a lower coordination number than the interior atoms. This incomplete bonding (relative to the interior crystal structure) results in atomic orbitals that point away from the surface called "dangling orbitals" or unpassivate... | Wikipedia - Core–shell semiconductor nanocrystal - Background | 325 | 1,589 | null |
Alkylamines have been incorporated into the TOP/TOPO synthetic method to increase the quantum yields to ~50%. The main challenge in using organic ligands for quantum dot surface trap passivation is the difficulty in simultaneously passivating both anionic and cationic surface traps. Steric hindrance between bulky organ... | Wikipedia - Core–shell semiconductor nanocrystal - Background | 201 | 989 | null |
Section: Classification > Type I. Description In a Type I CSSNC, the bandgap of the core is smaller than that of the shell. Both the conduction and valence band edges of the core lie within the bandgap of the shell, which confines both electrons and holes in the core. This can be seen in figure X, where the electron an... | Wikipedia - Core–shell semiconductor nanocrystal - Classification > Type I | 180 | 693 | null |
Section: Classification > Type II. Description In the type II configuration, the valence and conduction band edge of the core are both lower or higher than the band edges of the shell. An example of a type II is shown in figure X, ZnTe (bandgap:2.26) /CdSe (bandgap:1.74). The lowest energy separation of the electron an... | Wikipedia - Core–shell semiconductor nanocrystal - Classification > Type II | 184 | 791 | null |
Section: Synthesis. In synthesizing core shell nanoparticles, scientists have studied and found several wet chemical methods, such as chemical precipitation, sol-gel, microemulsion and inverse micelle formation. Those methods have been used to grow core shell chalcogenide nanoparticles with an emphasis on better contro... | Wikipedia - Core–shell semiconductor nanocrystal - Synthesis | 333 | 1,523 | null |
Core–shell semiconductor nanocrystals can be grown by using colloidal chemistry methods with an appropriate control of the reaction kinetics. Using this method which results in a relatively high control of size and shape, semiconductor nanostructures could be synthesized in the form of dots, tubes, wires and other form... | Wikipedia - Core–shell semiconductor nanocrystal - Synthesis | 225 | 1,148 | null |
Section: Synthesis > Characterization. An increase in either the core size or shell length results in longer emission wavelengths. The interface between the core and shell can be tailored to passivate relaxation pathways and form radiative states. The size dependence of the band gap in these nanoparticles due to the qu... | Wikipedia - Core–shell semiconductor nanocrystal - Synthesis > Characterization | 200 | 946 | null |
Section: Purification techniques. As synthesized core-shell nanocrystals contains impurities, such as unreacted precursors, reaction by products, high b.p. solvents, and necessary ligands that were used during the synthesis of NCs to control growth. Such impurities often perturb the surface chemistry of the NCs and it ... | Wikipedia - Core–shell semiconductor nanocrystal - Purification techniques | 169 | 822 | null |
Section: Purification techniques > Purification techniques based on polarity > Precipitation and re-dissolution. Generally, high boiling non-polar solvents are frequently used during the synthesis of CSNCs. By introducing an antisolvent (a solvent in which the desired product is insoluble) to the solvent mixture, a flo... | Wikipedia - Core–shell semiconductor nanocrystal - Purification techniques > Purification techniques based on polarity > Precipitation and re-dissolution | 329 | 1,471 | null |
Section: Purification techniques > Purification techniques based on polarity > Extraction. A liquid-liquid extraction process can be exploited as a purification technique for the CSNCs. When an extracting solvent is introduced to the as-synthesized CSNC solution, due to the partition coefficient, CSNCs and impurities a... | Wikipedia - Core–shell semiconductor nanocrystal - Purification techniques > Purification techniques based on polarity > Extraction | 226 | 1,127 | null |
Section: Purification techniques > Purification based on electrophoresis. Electrophoresis techniques are common as a purification technique for primarily proteins, DNA and RNA. Electrophoresis techniques exploit the mobility of two or more different species – different by their size, charge or binding affinity – under ... | Wikipedia - Core–shell semiconductor nanocrystal - Purification techniques > Purification based on electrophoresis | 164 | 782 | null |
Section: Applications > Biomedical applications. The properties desired of CSSNCs when using them for biological applications include high quantum yield, narrow fluorescence emission, broad absorption profile, stability against photobleaching, 20 second fluorescent lifetime, and high brightness. High quantum yields mea... | Wikipedia - Core–shell semiconductor nanocrystal - Applications > Biomedical applications | 342 | 1,615 | null |
Section: Applications > Biomedical applications > In vitro cell labeling. Because multiple colors can be imaged, CSSNCs’ ability to be used in cell labeling is of growing importance. However, it can be difficult to get CSSNCs across the cell membrane. This has been achieved via endocytosis (the most common method), dir... | Wikipedia - Core–shell semiconductor nanocrystal - Applications > Biomedical applications > In vitro cell labeling | 350 | 1,581 | null |
Section: Applications > Biomedical applications > In vivo and deep tissue imaging. Because CSSNCs emit in the near-infrared region (700–900 nm) of the electromagnetic spectrum, imaging them is not complicated by autofluorescence of tissue, which occurs at higher frequencies (400–600 nm), and scattering effects. This ha... | Wikipedia - Core–shell semiconductor nanocrystal - Applications > Biomedical applications > In vivo and deep tissue imaging | 336 | 1,562 | null |
Section: Applications > Optics > LEDs. Currently, CSSNC LED efficiency is less than that of organic LEDs. However, studies show that they have potential to accomplish what organic LEDs cannot. CSSNC LEDs constructed using multiple layers of CSSNCs resulted in poor conduction, charge imbalance, low luminescence efficien... | Wikipedia - Core–shell semiconductor nanocrystal - Applications > Optics > LEDs | 290 | 1,281 | null |
Section: Applications > Optics > Lasers. In CSSNCs with only one exciton, absorption and stimulated emission occur equally and in CSSNCs with more than one exciton, non-radiative Auger recombination occurs, which decays optical gain, an important quality in lasers. However, type II CSSNCs, CdS/ZnSe, were used in optica... | Wikipedia - Core–shell semiconductor nanocrystal - Applications > Optics > Lasers | 168 | 718 | null |
Article: Corrosion inhibitors for the petroleum industry. Corrosion inhibitors are substances used in the oil industry to protect equipment and pipes against corrosion. Corrosion is a common problem in the oil industry due to the presence of water, gases, and other corrosive contaminants in the production environment. ... | Wikipedia - Corrosion inhibitors for the petroleum industry - Summary | 190 | 1,039 | null |
Section: Corrosion Inhibitor Families. There are different chemical families of corrosion inhibitors used in the oil industry, among them are the following: Fatty Imidazolines: These are imidazole-based compounds, usually with a long unsaturated chain length, derived mainly from oleic acid. They are very effective in p... | Wikipedia - Corrosion inhibitors for the petroleum industry - Corrosion Inhibitor Families | 322 | 1,549 | null |
Pyridines: Some studies have shown that certain pyridines can inhibit corrosion caused by the presence of acid gases, such as carbon dioxide and hydrogen sulfide, which are common in the oil industry. Pyridine and its derivatives have been shown to be effective inhibitors for a wide range of metals, such as carbon stee... | Wikipedia - Corrosion inhibitors for the petroleum industry - Corrosion Inhibitor Families | 345 | 1,616 | null |
They are effective against corrosion caused by the presence of hydrochloric acid (HCl) in drilling fluids. Maleate polymers: These polymers are used as corrosion inhibitors in the industry due to their good adsorption capacity on metal surfaces and their high solubility in oil and drilling fluids. They offer protection... | Wikipedia - Corrosion inhibitors for the petroleum industry - Corrosion Inhibitor Families | 252 | 1,196 | null |
Article: Crossover experiment (chemistry). In chemistry, a crossover experiment is a method used to study the mechanism of a chemical reaction. In a crossover experiment, two similar but distinguishable reactants simultaneously undergo a reaction as part of the same reaction mixture. The products formed will either cor... | Wikipedia - Crossover experiment (chemistry) - Summary | 274 | 1,552 | null |
Section: Purpose. Crossover experiments allow for experimental study of a reaction mechanism. Mechanistic studies are of interest to theoretical and experimental chemists for a variety of reasons including prediction of stereochemical outcomes, optimization of reaction conditions for rate and selectivity, and design of... | Wikipedia - Crossover experiment (chemistry) - Purpose | 175 | 1,026 | null |
Section: Theory. The concept underlying the crossover experiment is a basic one: provided that the labeling method chosen does not affect the way a reaction proceeds, a shift in the labeling as observed in the products can be attributed to the reaction mechanism. The most important limitation in crossover experiment de... | Wikipedia - Crossover experiment (chemistry) - Theory | 339 | 1,875 | null |
Section: Design. In designing a crossover experiment the first task is to propose possible mechanisms for the reaction being studied. Based on these possible mechanisms, the goal is to determine either a traditional crossover experiment or an isotope scrambling experiment that will enable the researcher to distinguish ... | Wikipedia - Crossover experiment (chemistry) - Design | 345 | 1,906 | null |
It is possible that labeling at one position could distinguish between only two of several possible mechanisms, while placing the isotopic label at a different position could distinguish between three potential mechanisms or provide insight into transition states or intermediates, etc. After the interpretational value ... | Wikipedia - Crossover experiment (chemistry) - Design | 349 | 1,872 | null |
Section: Isotopic labeling experiment. An isotopic labeling experiment is an experiment used in mechanistic study that employs isotopes as labels and traces these labels in the products. Isotopic labeling experiments are commonly considered to be a type of crossover experiment. However, there are far more possibilities... | Wikipedia - Crossover experiment (chemistry) - Isotopic labeling experiment | 348 | 1,851 | null |
Section: Characterization. A major advantage of the crossover experiment is that the results of the experiment are obtained by direct characterization of the product. The techniques involved are therefore those already familiar to the experimental chemist. Mass spectrometry and NMR spectroscopy are the two most common ... | Wikipedia - Crossover experiment (chemistry) - Characterization | 164 | 880 | null |
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