Substituent effects on acidity of aryl‐substituted fluoroalkanes: a computational study

The gas‐phase acidities (GA) of various aryl‐substituted fluoroalkanes, XC₆H₄CH(R¹)R², were calculated at the B3LYP/6‐311 + G(d,p)//B3LYP/6‐311 + G(d,p). The acidity values of alkanes having a common substituent X varied significantly with the change of R¹ and R². Their changes in acidity of 1 and 2 having two strong electron‐withdrawing groups (CF₃ or C₂F₅) at the deprotonation site and 8 , 9 , 10 , 11 having no fluorine atom at β‐position were linearly correlated with the corrected number of fluorine atoms contained in the fluorinated alkyl group (R² > 0.999). On the other hand, the GA values of β‐fluorine substituted alkanes ( 3 , 4 , 5 , 6 , 7 ) deviated in a stronger acid direction from the line. The enhanced acidity was attributed to the additional stabilization of the conjugate anion caused by the β‐fluorine negative hyperconjugation. The magnitude of β‐fluorine negative hyperconjugation of the fluorinated alkyl group (ΔG^o_β‐F) given by the deviations from the line decreased with increasing electron‐withdrawing ability of substituent X on the benzene ring, indicating that β‐fluorine negative hyperconjugation competes with the electronic effect of the substituent X. The GA_el values obtained by subtraction ΔG^o_β‐F from the apparent GA value were successfully correlated in terms of the Yukawa–Tsuno equation. The obtained ρ_el and r^?_el values were linearly related to the GA_el value of the respective phenyl‐substituted fluoroalkanes, supporting our previous conclusion that the ρ and r^? values for the substituent effect caused by the electronic effects of the substituent on the acidity are determined by the thermodynamic stability of the parent ion (ring substituent = H). Copyright © 2015 John Wiley & Sons, Ltd.     

Berezinskii-Kosterlitz-Thouless phase transition in systems with exotic symmetries

A Berezinksii-Kosterlitz-Thouless phase transition in systems with the exceptional symmetry groups G=E _6,7,8, G ₂, and F ₂ is studied. The critical exponents and the exponents of the logarithmic corrections to the correlation functions at the transition point are found by the renormalization-group method. It is shown that for G=A, D, and E the critical exponents can be expressed in terms of the Coxeter numbers h _G (or the values of the Casimir operator in the adjoint representation K ₂ ^G ). Pis’ma Zh. éksp. Teor. Fiz. 63, No. 9, 743–747 (10 May 1996)     

Unitary equivalence between a spin 1/2 charged particle in a two-dimensional magnetic field and a spin 1/2 neutral particle with an anomalous magnetic moment in a two-dimensional electric field

We prove the unitary equivalence between the Dirac HamiltonianH _D for a relativistic spin 1/2 neutral particle with an anomalous magnetic moment in a two-dimensional electrostatic fieldE = (E ₁,E ₂) and the direct sum of the Dirac-Weyl operatorsD(±A) for a spin 1/2 charged particle in two-dimensional magnetic fields ±dA with the vector potentialA =E ₂ dx ¹ -E ₁ dx ², (x ¹,x ²) ². As applications, we investigate the ground state and the spectra ofH _D.     

Computational study of linear and nonlinear optical properties of substituted thiophene imino dyes using long-range corrected hybrid DFT methods

The molecular structures, linear and nonlinear optical properties of a series constituted by four R-substituted thiophene imino dyes, namely A(R?=?SO₂Me), B(R?=?SO₂Ph), C(R?=?NO₂), and D(R?=?C₂(CN)₃) were analysed using CAM-B3LYP, ωB97XD and LC-ωPBE hybrid DFT functionals in combination of the 6-311++G(d,p) standard basis set. The dipole moments, polarisabilities, HOMO-LUMO energy gaps, maximum absorption wavelengths and first hyperpolarisabilities were calculated in the gas phase and the obtained results are in good agreement with experimental NLO activity order A?<?B?<?C. Compared to synthesised dyes A-C, the designed dye D presents a longer maximum absorption wavelength and a lower HOMO-LUMO gap because of the appreciable stabilisation of its LUMO energy. These results were confirmed by the calculation of the total second-order stabilisation energy E⁽²⁾ defined in the context of the NBO population analysis. Consequently, dye D is predicted to exhibit a higher first hyperpolarisability in comparison with dyes A-C. This result can be justified by the enhanced intramolecular charge transfer in dye D due to the stronger electron-withdrawing ability and the cumulative action of the long π-conjugation of the tricyanovinyl moiety. The very high total hyperpolarisability (27 times greater than that of para-nitroaniline) of the designed dye D suggests its promising use in organic NLO devices.     

Calculated polar substituent effects on the stability of 4‐substituted(X) ‐ cub‐1‐yl and ‐bicyclo[2.2.2]oct‐1‐yl cations: a DFT study

The effects of substituents on the stability of 4‐substituted(X) cub‐1‐yl cations ( 2 ), as well as the benchmark 4‐substituted(X) bicyclo[2.2.2]oct‐1‐yl cation systems ( 7 ), for a set of substituents (X = H, NO₂, CN, NC, CF₃, COOH , F, Cl, HO, NH₂, CH₃, SiH₃, Si(CH₃)₃, Li, O^?, and NH) covering a wide range of electronic substituent effects were calculated using the DFT theoretical model at the B3LYP/6‐311 + G(2d,p) level of theory. Linear regression analysis was employed to explore the relationship between the calculated relative hydride affinities (ΔE, kcal/mol) of the appropriate isodesmic reactions for 2 / 7 and polar field/group electronegativity substituent constants (σ_F and σ_χ, respectively). The analysis reveals that the ΔE values of both systems are best described by a combination of both substituent constants. This highlights the distinction between through‐space and through‐bond electronic influences characterized by σ_F and σ_χ, respectively. Copyright © 2010 John Wiley & Sons, Ltd.     

Chiral constituent quark model study of the process γp → ηp <Superscript>⋆</Superscript>

A constituent quark model is developed for the reaction γp → ηp , allowing us to investigate all available data for differential cross-sections as well as single polarization asymmetries (beam and target) by including all of the PDG, one to four star, nucleon resonances (S₁₁, P₁₁, P₁₃, D₁₃, D₁₅, F₁₅, F₁₇, G₁₇, G₁₉, H₁₉, I_1,11, and K_1,13). Issues related to the missing resonances are also briefly discussed by examining possible contributions from several new resonances (S₁₁, P₁₁, P₁₃, D₁₃, D₁₅, and H_1,11).     

A DFT‐GIAO and DFT‐NBO study of polar substituent effects on NMR 17O chemical shifts in some rigid polycyclic alkanes

¹⁷O NMR shieldings of 3‐substituted(X)bicyclo[1.1.1]pentan‐1‐ols ( 1 , Y = OH), 4‐substituted(X)bicyclo[2.2.2]octan‐1‐ols ( 2 , Y = OH), 4‐substituted(X)‐bicyclo[2.2.1]heptan‐1‐ols ( 3 , Y = OH), 4‐substituted(X)‐cuban‐1‐ols ( 4 , Y = OH) and exo‐ and endo‐ 6‐substituted(X)exo‐bicyclo[2.2.1]heptan‐2‐ols ( 5 and 6 , Y = OH, respectively), as well as their conjugate bases ( 1 – 6 , Y = O^?), for a set of substituents (X = H, NO₂, CN, NC, CF₃, COOH, F, Cl, OH, NH₂, CH₃, SiMe₃, Li, O^?, and NH) covering a wide range of electronic substituent effects were calculated using the DFT‐GIAO theoretical model at the B3LYP/6‐311 + G(2d, p) level of theory. By means of natural bond orbital (NBO) analysis various molecular parameters were obtained from the optimized geometries. Linear regression analysis was employed to explore the relationship between the calculated ¹⁷O SCS and polar field and group electronegativity substituent constants (σ_F and σ_χ, respectively) and also the NBO derived molecular parameters (oxygen natural charge, Q_n, occupation numbers of the oxygen lone pairs, n_o, and occupancy of the C? O antibonding orbital, σ*_CO(occup)). In the case of the alcohols ( 1 – 6 , Y = OH) the ¹⁷O SCS appear to be governed predominantly by the σ_χ effect of the substituent. Furthermore, the key determining NBO parameters appear to be n_o and σ*_CO(occup). Unlike the alcohols, the calculated ¹⁷O SCS of the conjugate bases ( 1 – 6 , Y = O^?), except for system 1 , do not respond systematically to the electronic effects of the substituents. An analysis of the SCS of 1 (Y = O^?) raises a significant conundrum with respect to their origin. Copyright © 2010 John Wiley & Sons, Ltd.     

A natural bond orbital analysis of aryl‐substituted polyfluorinated carbanions: negative hyperconjugation

Aryl‐substituted polyfluorinated carbanions, ArCHR_f^? where R_f = CF₃ ( 1 ), C₂F₅ ( 2 ), i‐C₃F₇ ( 3 ), and t‐C₄F₉ ( 4 ), were analyzed by means of the natural bond orbital (NBO) theory at the B3LYP/6‐311+G(d,p) computational level. A lone pair NBO at the formal anionic center carbon (Cα) was not found in the Lewis structure. Instead, significant donor/acceptor NBO interactions between π(Cα‐C1) and σ*(Cβ‐F) or σ*(Cβ‐Cγ) were observed for 1 , 2 , 3a (strong electron‐withdrawing substituent, from p‐CF₃ to p‐NO₂), and 4 . Their second‐order donor/acceptor perturbation interaction energy, E(2), values decreased with the increase of the stability of carbanions. A larger E(2) value corresponds to longer Cβ‐F and Cβ‐Cγ bonds and a shorter Cα‐Cβ bond, indicating that the E(2) values can be associated with the negative hyperconjugation of the Cβ‐F and Cβ‐Cγ bonds. In accordance with this, the E(2) values for π(Cα‐C1) → σ*(Cβ‐F) were linearly correlated with the ΔG^o_β‐F values (an empirical measure of β‐fluorine negative hyperconjugation obtained from an increased acidity). In 3b (weak electron‐withdrawing substituents, from H to m‐NO₂) very large E(2) values for LP(Fβ) → π*(Cα‐Cβ) were obtained. This was attributed to the Cβ‐F bond cleavage and the Cα‐Cβ double bond formation in the Lewis structure that is caused by the extremely strong negative hyperconjugation of the Cβ‐F bond.     

Semi-simple real subal gebras of non-compact semi-simple real lie algebras V

The investigation of the problem of embedding a semi-simple real Lie algebra $\text{L}$ in a non-compact semi-simple real Lie algebra $\text{L}$ is extended to the case when $\text{L}$ and/or $\text{L}$ is exceptional. Matrix representations for all the exceptional Lie algebras are calculated. Detailed procedures are given, which, together with those given in previous papers, allow the construction of all embeddings of $\text{L}$ in $\text{L}$, when their complex extensions are A₁, B₁, C₁, D₁, E₆, E₇, E₈, F₄, G₂ or a direct sum of any two of there. The procedures are illustrated by examples, including all real semi-simple Lie subalgebras of real forms of G₂ and sub-algebras of real forms of F₄ whose complex extensions are B₄ or A₁ (representation (16) + (9)). Because of its physical significance, all embeddings of SL (2, C) in real forms of F₄ and E₆ are given. Many of these are new results.     

Braided m-Lie Algebras

Braided m-Lie algebras induced by multiplication are introduced, which generalize Lie algebras, Lie color algebras and quantum Lie algebras. The necessary and sufficient conditions for the braided m-Lie algebras to be strict Jacobi braided Lie algebras are given. Two classes of braided m-Lie algebras are given, which are generalized matrix braided m-Lie algebras and braided m-Lie subalgebras of End _F M, where M is a Yetter–Drinfeld module over B with dimB < . In particular, generalized classical braided m-Lie algebras sl _{q, f} (GM _G (A), F) and osp _{q, t} (GM _G (A), M, F) of generalized matrix algebra GM _G (A) are constructed and their connection with special generalized matrix Lie superalgebra sl _{s, f} (GM _{Z_2}(A ^s ), F) and orthosymplectic generalized matrix Lie super algebra osp _{s, t} (GM _{Z_2}(A ^s ), M ^s , F) are established. The relationship between representations of braided m-Lie algebras and their associated algebras are established.This revised version was published online in March 2005 with corrections to the cover date.     

Gas‐phase Acidities of 2‐Aryl‐2‐chloro‐1,1,1‐trifluoroethanes and Related Compounds. Experimental and Computational Studies

The gas‐phase acidities (GA) of 2‐aryl‐2‐chloro‐1,1,1‐trifluoroethanes ( 1a ), 2‐aryl‐2‐fluoro‐1,1,1‐trifluoroethanes ( 2a ), and related compounds, XC₆H₄CH(Z)R where Z = Cl ( 1 ) or F ( 2 ) and R = C₂F₅ ( b ), t‐C₄F₉ ( c ), C(CF₃)₂C₂F₅ ( d ), C(CF₃)₂Me ( e ), Me ( f ), H ( g ), were investigated experimentally and computationally. On the basis of an excellent linear correlation (R² > 0.99) of acidities of 1c , 1d , 1e , 1f and 2c , 2d , 2e , 2f where there is no fluorine atom at β‐position to the deprotonation site with the corrected number of fluorine atoms contained in the fluorinated alkyl group, the extent of β‐fluorine negative hyperconjugation of the CF₃ and C₂F₅ groups (ΔG^o_β‐F) was evaluated. The GA_el values given by subtraction ΔG^o_β‐F from the apparent GA value were considered to represent the electronic effect of the substituent X. The substituent effects on the GA_el values and GA values for 1c , 1d , 1e , 1f and 2c , 2d , 2e , 2f were successfully analyzed in terms of the Yukawa–Tsuno equation. The variation of resonance demand parameter r^? with the R group observed for various XC₆H₄CH(Z)R was linearly related to the GA (GA_el) value of the respective phenyl‐substituted fluorinated alkanes. On the other hand, the corresponding correlation for the ρ values provided three lines for ArCH(Cl)R, ArCH(F)R and ArCH₂R, respectively. These results supported our previous conclusion that the r^? and ρ values are governed by the thermodynamic stability of the parent ion (ring substituent = H). Other factors arising from an atom bonded to the acidic center also influence the ρ value. Copyright © 2016 John Wiley & Sons, Ltd.     

The quest for a better system for evaluating pi‐electron substituent constant: a comparison of benzoic,acrylic and tria‐, penta‐, heptafulvene‐based carboxylic acids. A computational study

Carboxylic acids based on exo‐substituted tria‐, penta‐, heptafulvenes and ethylene (acrylic acids) were examined in order to determine if they are more sensitive to the substituent effect than benzoic acid – the system originally employed by Hammett. In order to accomplish this task, all possible structural isomers of benzoic acid, tria‐, penta‐ and heptafulvene‐based carboxylic acids, acrylic and methacrylic acids substituted by 13 substiuents (BH₂, CHO, CN, COCN, NO₂, CF₃, Me, Cl, F, OH, OMe, NH₂ and NMe₂) were optimized at the B3LYP/6‐311++G(d,p) level of theory, and Gibbs free energies of carboxylic group dissociation (ΔG_dis) were calculated. These energies were subsequently intercorrelated, and from the slopes of linear regressions, it was estimated which system is associated with greatest changes of ΔG_dis due to substitution and thus is most sensitive to the substituent effect. It was found that all fulvene‐based carboxylic acids have greater range of ΔG_dis change than benzoic acid, but the largest range of change was observed in the case of acrylic and methacrylic acids. The acrylic acid as the most sensitive system to substitution could replace benzoic acid for an improved version of substituent constant used to measure pi‐electron substituent effect. Copyright © 2013 John Wiley & Sons, Ltd.     

Dynamic 1H NMR investigation along with a theoretical study around the C–C and C = C bonds in a particular phosphorus ylide

In the present work, the dynamic ¹H NMR effects were investigated at variable temperatures within a particular phosphorus ylide involving a 2‐benzoxazolinone around the carbon–carbon single bond and also partial carbon–carbon double bond in two Z‐ and E‐rotational isomers. Activation and kinetic parameters including ΔH^≠, ΔG^≠, ΔS^≠ and E_a were determined in accord with the dynamic ¹H NMR data for three rotational processes. In addition, theoretical studies based upon rotation around the same bonds were investigated using ab initio and DFT methods at the HF/6‐31G(d,p) and B3LYP/6‐31G(d,p) levels of theory. Theoretical activation and kinetic parameters including ΔH^≠, ΔG^≠, ΔS^≠ and E_a were calculated at 298 K and experimental temperatures for five rotational processes. These results (experimental and theoretical), taken together, indicate that the rotational energy barrier around the C = C double bond was considerably high and the observation of the two rotational isomers was impossible (seen as a single isomer) at the high temperatures, in this case rotation around the C = C bond was too fast on the NMR time scale. When the temperature was relatively low, the rate of rotation was sufficiently slow; therefore, observation of the two Z‐ and E‐isomers was possible. In addition, calculations at the HF/6‐31G(d,p) level of theory showed very favorable results in agreement with the experimental data on rotation around the C = C bond. While, B3LYP level using the 6‐31G(d,p) basis set was provided the reasonable data for the restricted rotations around the C–C and C–N single bond. Copyright © 2012 John Wiley & Sons, Ltd.     

Sequential Product and Jordan Product of Quantum Effects

The quantum effects for a physical system can be described by the set E(H)\mathcal{E(H)} of positive operators on a complex Hilbert space H\mathcal{H} that are bounded above by the identity operator I. We denote the set of sharp effects by P(H){\mathcal{P(H) }}. For A,B ? E(H)A,B\in\mathcal{E(H)}, the operation of sequential product A°B=A^\frac12BA^\frac12A\circ B=A^{\frac{1}{2}}BA^{\frac{1}{2}} was proposed as a model for sequential quantum measurements. Denote by A*B=\fracAB+BA2A\ast B=\frac{AB+BA}{2} the Jordan product of A,B ? E(H)A,B\in\mathcal{E(H)}. The main purpose of this note is to study some of the algebraic properties of the Jordan product of effects. Many of our results show that algebraic conditions on A∗B imply that A and B commute for the usual operator product. And there are many common properties between Jordan product and sequential product of effects. For example, if A∗B satisfies certain associative laws, then AB=BA. Moreover, A*B ? P(H)A\ast B\in{\mathcal{P(H) }} if and only if A°B ? P(H)A\circ B\in{\mathcal{P(H)}}.     

A Way To Discover Maxwell's Equations Theoretically

The Coulomb force, established in the rest frame of a source-charge Q, when transformed to a new frame moving with a velocity V has a form F = q E + q v × B, where E = E′_∥ + γE′_⊥ and B = (1/c ²)v × E and E′ is the electric field in the rest frame of the source. The quantities E and B are then manifestly interdependent. We prove that they are determined by Maxwell's equations, so they represent the electric and magnetic fields in the new frame and the force F is the well known from experiments Lorentz force. In this way Maxwell's equations may be discovered theoretically for this particular situation of uniformly moving sources. The general solutions of the discovered Maxwell's equations lead us to fields produced by accelerating sources.     

水分子F态超快动力学：时间分辨光电子能谱研究

本文利用双光子激发和时间分辨的光电子成像技术研究了水分子■态的超快动力学.这是首次对水分子■态进行时间分辨的实验研究.水(重水)分子■和■态的寿命分别为1.0±0.3(1.9±0.4)和10±3(30±10)皮秒.我们提出■态主要通过非绝热耦合内转换到■态,而■态通过科里奥利相互作用耦合到■态.     

聚合型硼氢化物(BH3)n(n=1-3)的几何结构与光谱的研究

采用不同方法B3P86,B3LYP,MP2和LSDA,结合Dunning的相关一致基组cc-PVTZ,对聚合型硼氢化物(BH₃)_n(n=1-3)分子的可能几何构型进行优化计算,得出最稳定构型的几何参数、电子结构、振动频率和光谱等性质参数,并给出了最稳定结构的总能量(E_T),结合能(E_BT),平均结合能(E_av),电离势(E_IP),能隙(E_g),费米能级(E_F)等.结果表明:采用密度泛函DFT中的方法B3P86计算的能量最低,结构参数更接近文献值;三种硼氢化物分子基态都为1重态,电子态分别为¹A',¹A和¹A; BH₃分子的最稳定几何构型为平面三角形结构;B₂H₆为对称性乙烯式D_2h立体结构,H-B之间生成氢桥式三中心双电子键;B₃H₉为C_3ν立体结构,也生成氢桥式三中心双电子键,但三个氢桥三中心双电子键彼此隔离.最后分析了三种氢化物的红外和拉曼光谱、平均结合能、电离势、能隙和费米能级等特性,说明(BH₃)_n(n=1-3)三分子中B₂H₆最稳定,H-B桥键键长比端键更长,最强峰红外光谱强度最大. 关键词： 聚合型硼氢化物 几何构型 光谱     

Are deformed modes still Raman active for single-wall carbon nanotubes?

Using group theory calculations combined with the force-constant model and molecular-dynamics simulations, whether the deformed modes are Raman active or not for (10,10) and (10,0) single-wall carbon nanotubes under hydrostatic pressure is discussed. With increasing pressure, the tube symmetry lowers from D_20h to D_2h then to C_2h point group. For D_20h, A_1g is changed to A_g, while E_1g and E_2g are split: E_1g→B_2g+B_3g→2B_g and E_2g→A_g+B_1g→2A_g. On the basis of the correlation between D_20h, D_2h, and C_2h point groups, the deformed modes should be still Raman active. The result can help us clarify the essence of the experimental observations.     

Theory of Gravitational-Inertial Field of Universe. IV. The Universe and the Microcosm

On basis of principle of discreteness of the space and time the following relations are obtained Λ_oM_oc = 2π?, τ_oE_o = 2π? and c² = 2GM_o/Λ_o giving the values of fundamental elements of length Λ_o ≈ (?G/c³)^1/2, mass M_o ≈ (?c/G)^1/2, time τ_o ≈ (?G/c⁵)^1/2 and energy E_o ≈ (?c⁵/G)^1/2. The geon crown of any critical system and the crown of the Universe must have a thickness equal to the fundamental length Λ_o = 2(π?G/c³)^1/2 = 5.74. 10^?33 cm. Each critical system has its specific (most probable) quantum with an average invariant mass which in the case of the Universe is equal to (2π²?H_u/Gc)^1/3 ≈ 300 m_e where H_u is Hubble's constant. There are all reasons to consider the universal virtual quanta of an invariant mass m_u ≈ 300 m_e as carriers of gravitational, electromagnetic and nuclear fields in the Universe.     

Reactivity of sodium arenesulfinates in the substitution reaction to γ‐functionalized allyl bromides

The kinetics of nucleophilic bimolecular substitution reactions of γ‐functionalized allyl bromides with non‐substituted and p‐substituted sodium arenesulfinates has been studied. Both the structure of allyl bromides and nucleophilicity of arenesulfinate ions exerted a significant effect on the values of the kinetic parameters such as the second‐order rate constants k, activation energy E_A, and changes in the entropy ΔS^≠, enthalpy ΔH^≠, and free energy ΔG^≠ of the formation of the activated complex from reactants. Based on the evaluation of kinetic parameters, the reactants could be arranged, according to their decreasing reactivity in the S_N2‐reactions as follows: p‐toluenesulfinate ion > benzenesulfinate ion > p‐chlorobenzenesulfinate ion and 4‐bromo‐2‐butenenitrile > 1,3‐ dibromopropene, respectively. Comparison was also made between the kinetic data obtained and some delocalization reactivity indexes for both the substrates and nucleophiles. The enthalpy–entropy compensation effect was observed for the reactions of sodium arenesulfinates with γ‐functionalized allyl bromides. Copyright © 2009 John Wiley & Sons, Ltd.