Vibrational softening of diatomic molecules

An analysis of a model molecular oscillator is presented: a vibrating diatomic molecule carrying N ₀ electrons. The energy derivatives over the number of electron (N) and the deformation (Q), ∂ ⁿ /∂N ⁿ and ∂ ⁿ /∂Q ⁿ have been analyzed up to second order (n=2), including the appropriate mixed derivatives. The effect of coupling between distortion of the electron density induced by ΔN and the vibrational deformation of the molecule has been studied. Anharmonicity of the oscillator has been shown to be a possible result of that coupling; new relations between the parameters characterizing the anharmonicity of the oscillator and the energy derivatives at density functional theory level have been obtained. Ab initio calculations for a set of diatomic molecules have been performed, yielding values for all the derivatives discussed and demonstrating the effect of coupling with vibrations. Received: 1 June 2000 / Accepted: 20 October 2000 / Published online: 21 March 2001     

The effects of static quartic anharmonicity on the quantum dynamics of a linear oscillator with time-dependent harmonic frequency: Perturbative analysis and numerical calculations

The effects of quartic anharmonicity on the quantum dynamics of a linear oscillator with time-dependent force constant (K) or harmonic frequency (ω) are studied both perturbatively and numerically by the time-dependent Fourier grid Hamiltonian method. In the absence of anharmonicity, the ground-state population decreases and the population of an accessible excited state (k = 2, 4, 6…) increases with time. However, when anharmonicity is introduced, both the ground- and excited-state populations show typical oscillations. For weak coupling, the population of an accessible excited state at a certain instant of time (short) turns out to be a parabolic function of the anharmonic coupling constant (λ), when all other parameters of the system are kept fixed. This parabolic nature of the excited-state population vs. the λ profile is independent of the specific form of the time dependence of the force constant, K_t. However, it depends upon the rate at which K_t relaxes. For small anharmonic coupling strength and short time scales, the numerical results corroborate expectations based on the first-order time-dependent perturbative analysis, using a suitably repartitioned Hamiltonian that makes H₀ time-independent. Some of the possible experimental implications of our observations are analyzed, especially in relation to intensity oscillations observed in some charge-transfer spectra in systems in which the dephasing rates are comparable with the time scale of the electron transfer. © 1995 John Wiley & Sons, Inc.     

Infrared and raman spectroscopy of stressed polyethylene

Polyethylene films were stressed in uniaxial tension at room temperature while the infrared (FTIR) or Raman spectra were simultaneously measured. The purpose of these experiments was to gain an understanding of the molecular origins of the stress-induced vibrational frequency shifts Δν and determine the mechanisms of molecular deformation and fracture of PE molecules with stress σ. The PE samples consisted of ultradrawn, high-density, ultrahigh-molecular-weight, solid-state-extruded films and the stress was applied parallel to the nearly perfectly oriented orthorhombic crystal c-axis direction. The experimental frequency shifting coefficients α = (?ν/?σ)_σ→0 were compared with calculated α values determined from a vibrational analysis of an isolated PE chain using conformational energy minimization methods in which both harmonic and anharmonic (Morse) potential energy functions were used for the C? C stretching modes in the valence force field. The following α values were obtained and are compared with theory (anharmonic case in parentheses, in cm^?1/GPa): C? C symmetric stretch, α(1127) = ?5.9 (?5.3); CC asymmetric stretch, α(1059) = ?11.2 to ?5.7 (?5.8); CH₂ rock, α(730/720) = ?2.0 to ?3.0 (?2.2); CH₂ scissors, α(1472/1462) = ?1.0 to ?1.2 (?1.1); CH₂ twist, α(1295) ? 0(0.8); CH₂ wag, α(1370) undetermined owing to weak bands (?4.6); CH₂ stretch α(3000) ≈ 0. The largest negative frequency shifts were observed for the C? C stretching modes, in agreement with the calculations using the Morse potential. The harmonic potential for C? C stretching resulted in small positive α values for both the CC stretching and CH₂ wagging modes, while the other modes were unaffected by this choice of potential. The relative contribution of C? C bond stretching and C?C valence angle bending to the c-axis strain was about 1:1, in agreement with experiment. The Young's tensile modulus of a PE chain was calculated as E_c = 267 GPa.     

DFT assessment of the spectroscopic constants and absorption spectra of neutral and charged diatomic species of group 11 and 14 elements

The spectroscopic constants and absorption spectra of neutral and charged diatomic molecules of group 11 and 14 elements formulated as [M₂]^+/0/? (M = Cu, Ag, Au), and [E₂]^+/0/? (E = C, Si, Ge, Sn, Pb) have been calculated at the PBE0/Def2‐QZVPP level of theory. The electronic and bonding properties of the diatomics have been analyzed by natural bond orbital analysis approach and topology analysis by the atoms in molecules method. Particular emphasis was given on the absorption spectra of the diatomic species, which were simulated by time‐dependent density functional theory calculations employing the hybrid Coulomb‐attenuating CAM‐B3LYP density functional. The simulated absorption spectra of the [M₂]^+/0/? (M = Cu, Ag, Au) and [E₂]^+/0/? (E = C, Si, Ge, Sn, Pb) species are in close resemblance with the experimentally observed spectra whenever available. The neutral M₂ and E₂ diatomics strongly absorb in the ultraviolet region, given rise to UVC, UVA and in a few cases UVB absorptions. In a few cases, weak absorbion bands also occur in the visible region. The absorption bands have thoroughly been analyzed and assignments of the contributing principal electronic transitions associated to individual excitations have been made. © 2014 Wiley Periodicals, Inc.     

Harmoniques des vibrations de valence C?H dans les alcanes et les halogénures de t-butyle

The first and second harmonic C? H and C? D valence vibrations of alkanes and t-butyl halides have been measured. A model is proposed for the methyl and methylene groups, which allows the calculation of the anharmonicity constants of every vibrational mode and of the couplings between the modes. The already known large values (?100 to ?150 cm^?1) for the anharmonicity constants that couple the symmetrical with the asymmetrical modes are confirmed. As compared with lower harmonics combination bands become predominant for the higher ones; they allow the application of a diatomic model to estimate higher harmonics and the energy of dissociation.     

INDO Calculation of Spin Densities in Radical Cations of a Series of Substituted Nitro- and m-Dinitrobenzenes

The spin densities in radical cations of 22 substituted nitro- and m-dinitrobenzenes were calculated by the INDO method. For radical anions of substituted nitrobenzenes, a good linear correlation was obtained between the spin densities s_Ns_N and experimental hyperfine coupling constants with the nitrogen atoms of the NO₂ groups (a ^N): a ^N = K _N s _N s _N, where K _N = 428.58 (R ² = 0.96). For radical anions of substi- tuted m-dinitrobenzenes, no satisfactory agreement between the calculated and experimental a ^N constants was attained.     

OH自由基的高精度量子化学研究

采用内收缩MRCI方法(Internally Contracted Multiconfiguration-Reference Configuration Interaction)研究了OH自由基, 计算得到其基态稳定构型的键长是0.09708 nm, 对应的实验值是0.096966 nm, 第一激发态的键长是0.10137 nm,实验值是0.10121 nm. 同时得到势能曲线PECs (Potential Energy Curve), 再分别由Murrell-Sorbie势能函数拟合计算和POLFIT程序计算得到OH自由基在基态X²Π和第一激发态A²Σ⁺时的光谱数据：平衡振动频率ω_e, 非谐性常数ω_eχ_e以及高阶修正ω_eY_e, 平衡转动常数B_e, 振转耦合系数α_e, 解离能D₀和垂直跃迁能量ν₀₀. 这些理论计算结果与最新的实验值非常吻合, 精确度比前人也有很大提高. 其中我们计算得到基态OH(X²Π)的解离能D₀＝35568.86 cm^－1, 第一激发态OH (A²Σ⁺)的解离能D₀＝18953.93 cm^－1, 从第一激发态A²Σ⁺ (ν＝0)到基态X²Π (v＝0)的垂直跃迁能ν₀₀＝32496.42 cm^－1.     

An SCF-MS-Xα study of the bonding and nuclear quadrupole coupling in diatomic halogens and interhalogens in the ground X Σ and B Π 0 excited states

SCF-MS-Xα calculations of the electronic structure of diatomic halogens and interhalogens XY (X = I, Br, Cl; Y = I, Br, Cl, F) have been used to investigate the bonding and nuclear quadrupole coupling in these molecules. Calculations have been carried out for the ground X ¹ Σ electronic state, and for the excited B ³ Π₀ state in the case of I₂, Br₂, ICl and IBr. Good agreement (to within 10% in most cases) is obtained between the calculated and observed nuclear quadrupole coupling constants for the molecules in the ground state. For the excited state the agreement is not as good, but the calculation does reproduce the observed decrease in the coupling constants to less than one quarter of their ground state values, and analysis of the contributions to the field gradients clearly shows the reasons for this. The electric dipole moments and electric quadrupole moments of the molecules have also been calculated. However, these prove to be much more strongly dependent on the variables used in the calculation (atomic sphere radii, inclusion of d orbitals). The results of the calculations have also been used to test some of the assumptions made in the Townes and Dailey method of analysis of nuclear quadrupole coupling data.     

Substitution of ligands in dichloro-2-(arylazo)heterocyclepalladium(II) by 8-quinolinol: kinetics and mechanistic studies

Nucleophilic substitutions of Pd(N,N)Cl₂[(N,N = 1-methyl-2-(arylazo)imidazole (RaaiMe), p-RC₆H₄N=NC₃H₂NN-1-Me; 2-(arylazo)pyridine (Raap), p-RC₆H₄N=NC₅H₄N; 2-(arylazo)pyrimidine (Raapm), p-RC₆H₄N=NC₄H₃N₂ where R = H (a), Me (b), Cl (c)] with 8-quinolinol (HQ) have been examined by spectrophotometry at 298 K in MeCN solution. The product, Pd(Q)₂, has also been confirmed by independent synthesis from Na₂[PdCl₄] and HQ in EtOH. The kinetics of the reaction have been studied under pseudo-first-order conditions and the analyses support a nucleophilic association path. A single phase reaction has been observed and follows the rate law, rate = a + k [Pd(N,N)Cl₂] [HQ]². Thus, the reaction is first order in [Pd(N,N)Cl₂] and second order in [HQ]. External addition of Cl^–(LiCl) suppresses the rate. The rate increases as follows: Pd(RaaiMe)Cl₂ < Pd(Raap)Cl₂ < Pd(Raapm)Cl₂.     

Quantum-chemical investigation of the influence of the vacant orbitals of the heteroatom on the shaping of the electronically excited states and luminescence-spectroscopic properties of triphenylgallium

The electronic structure of the triphenylgallium molecule in the ground and electronically excited states has been calculated in the framework of the CNDO/S-CI method in sp and spd bases. The electron density in the AO's and atoms, the first ionization potential the energies and matrices of the changes in the electron density of the S_n and T_n states, the matrix elements of the spin-orbit coupling operator $$ " align="middle" border="0"> and $$ " align="middle" border="0"> , the intensities and directions of polarization of the S_n S_o and T₂ T_n transitions, and the phosphorescence lifetimes have been calculated. The following spectroscopic parametrization has been proposed for the Ga atom in the sp and spd bases: 1/2(I_s + a_s) = 10.075 eV, 1/2(I_p + A_p) = 4.265 eV, 1/2(I_d + A_d)=0, _Ga ^p =5 eV, _Ga ^d =O, _Ga ^sp =–7 eV, _Ga ^spd =–10 eV, and _s,p,d=1.433. The influence of the d AO's on the shaping of the orbital nature of the S₁ and T₂ states has been analyzed.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 21, No. 5, pp. 584–590, September–October, 1985.     

Vibronic transitions in the collision of Na with N2

Quenching, by collision, of an alkali atom A with a diatomic molecule X₂ is considered, on the assumption that the reaction occurs via formation of the intermediate complex A ⁺X ₂ ^– . The Landau-Zener approximation is used to calculate the partial rate constants of Na(²P)+N₂(v=0) Na(²S)+N₂(v>0) corresponding to transitions to different vibrational states in the diatomic molecule.I am indebted to A. I. Voronin, E. I. Dinaburg, E. E. Nikitin, and M. Ya. Ovchinnikova for assistance in this work and for valuable discussions.     

Crystal Structures and Properties of New Mixed-Ligand Complexes of Nickel(II) Diisobutyldithiophosphinate with Imidazole and 3,5-Dimethylpyrazole

The reaction of Ni{(i-C₄H₉)₂PS₂}₂ with imidazole and 3,5-dimethylpyrazole in ethanol gave paramagnetic (_ef = 3.02 and 3.11 BM) mixed-ligand complex compounds [Ni(Im)₂{(i-C₄H₉)₂PS₂}₂] (I) and [Ni(Pyr){(i-C₄H₉)₂PS₂}₂] (II). Single crystals were grown and the crystal structures of I and II were determined from X-ray diffraction data (CAD-4 diffractometer, Mo radiation, 1483 , R = 0.0344 for I and 2630 , R = 0.0486 for II). The crystals are monoclinic with cell dimensions a = 12.845(2), b = 10.250(1), c = 13.431(1) , = 115.89(1)°, V = 1591(1) ³, Z = 2, d _calc = 1.281 g/cm³, space group (for I); a = 11.152(3), b = 12.483(2), c = 23.389(4) , = 100.78(1)°, V = 3199(2) ³, Z = 4, d _calc = 1.191 g/cm³, space group (for II). The structures consist of discrete monomer molecules. The coordination polyhedron of the Ni atom is a compressed octahedron NiN₂S₄ (in I) and a tetragonal pyramid NiNS₄ (in II) formed by four S atoms of the two cyclic bidentate ligands i-Bu₂ and the N atoms of two monodentate ligands (Im molecules in trans-positions) or the N atom of the monodentate Pyr ligand in complexes I and II, respectively. The character of interaction between molecules I and II and molecular packing modes are considered. The electronic spectra of the complexes are consistent with the symmetry of chromophores found from X-ray data.     

Improved interaction potential for alkali halide molecules

An improved interaction potential has been devised for diatomic alkali halide molecules. This potential, in addition to similar attraction terms as in the Rittner potential, includes a new exponential for the short-range repulsion. The constant m in the exponential is seen to be well expressible in terms of the parameters of the Rittner potential. The new potential is also correlated with different properties, as for example, effective charges, effective radii, effective principal quantum numbers, etc., of the combining ions. Various spectroscopic constants, viz., the ionic dissociation energy D_i, the vibrational–rotational coupling constant α_e, the vibrational anharmonicity constant ω_ex_e, as well as two second-order spectroscopic constants γ_e and β_e have been calculated for this and for the Rittner potential. From comparisons between these two potentials, the new one has been observed better than the other.     

Synthesis of flexible ligands for assembling two metals in close proximity. Magnetic,electrochemical and spectral properties of binuclear copper (II) complexes with different exogenous bridging motifs

Binuclear Cu^II complexes having new flexible heptadentate ligands 2,6-bis{[bis(3,3-N,N-dimethylaminopropyl)amino]methyl}-4-bromophenol [HL¹], 2,6-bis(3,3-N,N-dimethylaminopropyl)amino]methyl}-4-methylphenol [HL²], and 2,6-bis{[bis(3,3-N,N-dimethylaminopropyl)amino]methyl}-4-methoxyphenol [HL³], capable of assembling two copper ions in close proximity have been synthesized. Comparisons of the charge-transfer (CT) features, observed in electronic spectra of these complexes, are correlated with the electronic effect on the aromatic ring of the ligand systems. Cyclic voltammetry has revealed the existence of two reduction couples,

Cyanogen pyrolysis and the CN + NO reaction behind incident shock waves

The reaction chemistry of C₂N₂? Ar and C₂N₂? NO? Ar mixtures has been investigated behind incident shock waves. Progress of the reaction was monitored by observing the cyano radical (CN) in absorption at 388.3 nm. A quantitative spectroscopic model was used to determine concentration histories of CN. From initial slopes of CN concentration during cyanogen pyrolysis, the rate constant for C₂N₂ + M → 2CN + M (1) was determined to be k₁ = (4.11 ± 1.8) × 10¹⁶ exp(?47,070 ± 1400/T) cm³/mol · s. A reaction sequence for the C₂N₂? NO system was developed, and CN profiles were computed. By comparison with experimental CN profiles the rate constant for the reaction CN + NO → NCO + N (3) was determined to be k₃ = 10^{(14.0 ± 0.3)} exp(?21,190 ± 1500/T) cm³/mol · s. In addition, the rate of the four-centered reaction CN + NO → N₂ + CO (2) was estimated to be approximately three orders of magnitude below collision frequency.     

On the Nitroxide Quasi‐Equilibrium in the Alkoxyamine‐Mediated Radical Polymerization of Styrene

Summary: The range of validity of two popular versions of the nitroxide quasi‐equilibrium (NQE) approximation used in the theory of kinetics of alkoxyamine mediated styrene polymerization, are systematically tested by simulation comparing the approximate and exact solutions of the equations describing the system. The validity of the different versions of the NQE approximation is analyzed in terms of the relative magnitude of (dN/dt)/(dP/dt). The approximation with a rigorous NQE, k_c[P][N] = k_d[P N], where P, N and P N are living, nitroxide radicals and dormant species respectively, with kinetic constants k_c and k_d, is found valid only for small values of the equilibrium constant K (10⁻¹¹–10⁻¹² mol · L⁻¹) and its validity is found to depend strongly of the value of K. On the other hand, the relaxed NQE approximation of Fischer and Fukuda, k_c[P][N] = k_d[P N]₀ was found to be remarkably good up to values of K around 10⁻⁸ mol · L⁻¹. This upper bound is numerically found to be 2–3 orders of magnitude smaller than the theoretical one given by Fischer. The relaxed NQE is a better one due to the fact that it never completely neglects dN/dt. It is found that the difference between these approximations lies essentially in the number of significant figures taken for the approximation; still this subtle difference results in dramatic changes in the predicted course of the reaction. Some results confirm previous findings, but a deeper understanding of the physico‐chemical phenomena and their mathematical representation and another viewpoint of the theory is offered. Additionally, experiments and simulations indicate that polymerization rate data alone are not reliable to estimate the value of K, as recently suggested.

Validity of the rigorous nitroxide quasi‐equilibrium assumption as a function of the nitroxide equilibrium constant.     

Analysis of the unimolecular reaction N2O5 + M ⇌ NO2 + NO3 + M

Recent experimental results on the thermal decomposition of N₂O₅ in N₂ are evaluated in terms of unimolecular rate theory. A theoretically consistent set of fall-off curves is constructed which allows to identify experimental errors or misinterpretations. Limiting rate constants k₀ = [N₂] 2.2 × 10^?3 (T/300)^?4.4 exp(?11,080/T) cm³/molec·s over the range of 220–300 K, k_∞ = 9.7 × 10¹⁴ (T/300)^+0.1 exp(?11,080/T) s^?1 over the range of 220–300 K, and broadening factors of the fall-off curve F_cent = exp(-T/250) + exp(?1050/T) over the range of 220–520 K have been derived. NO₂ + NO₃ recombination rate constants over the range of 200–300 K are k_rec,0 = [N₂] 3.7 × 10^?30 (T/300)^?4.1 cm⁶/molec²·s and k_rec,∞ = 1.6 × 10^?12 (T/300)^+0.2 cm³/molec·s.     

New unsymmetrical μ-phenoxo bridged binuclear copper(II) complexes

A series of binuclear Cu^II complexes [Cu₂XL] ⁿ⁺ having two copper(II) ions bridged by different motifs (X = OH^–, MeCO₂ ^–, or Cl^–) have been prepared using the ligands: H₂L¹ = 4-methyl-2-[N-(2-{dimethylamino}ethyl-N-methyl)aminomethyl]-6-[(prolin-1-yl)methyl]phenol, H₂L² = 4-nitro-2-[N-(2-{dimethylamino}ethyl-N-methyl)aminomethyl]-6-[(prolin-1-yl)methyl]phenol, H₂L³ = 4-methyl-2-[N-(2-{diethylamino}ethyl-N-ethyl)aminomethyl]-6-[(prolin-1-yl)methyl]phenol and H₂L⁴ = 4-nitro-2-[N-(2-{diethylamino}ethyl-N-ethyl)aminomethyl]-6-[(prolin-1-yl)methyl]phenol. The complexes have been characterized by spectroscopic, analytical, magnetic and electrochemical measurements. Cryomagnetic investigations (80–300 K) revealed anti-ferromagnetic exchange between the Cu^II ions (–2J in the range –50 to –182 cm^–1). The strength of anti-ferromagnetic coupling lies in the order: OAc > OH > Cl. Cyclic voltammetry revealed the presence of two redox couples, assigned to Cu^II/Cu^II/Cu^II/Cu^I/Cu^I/Cu^I. The first reduction potential is sensitive to electronic effects from the aromatic ring substituents and steric effect on the donor nitrogens (side arm) of the ligand systems.     

Mediated Electrocatalysis at the Electrodes Covered with [MIII(bpy)3](ClO4)3 (M=Co and Fe) in the Presence of Electroactive Solutes

Electron transfer processes for selected redox systems (ferrocene^0/+, decamethylferrocene^0/+, N,N,N′,N′‐tetramethyl‐1,4‐phenylenediamine^0/+, 7,7,8,8‐tetracyano‐quinonedimethane^0/?/2?, cobaltocene^0/+, C₆₀^0/?, and benzoquinone^0/?) at electrodes modified by precipitation of electrochemically inactive [M^III(bpy)₃](ClO₄)₃ (M=Co and Fe, bpy=2,2′‐bipyridine) layers have been investigated by cyclic voltammetry and electrochemical quartz crystal microbalance studies. The mediation of heterogeneous electron transfer is observed for these systems. For an electrode modified with [M^III(bpy)₃](ClO₄)₃, the rate of the electrocatalytic mediation process depends on the formal potential of the redox system. If the formal potential of the redox system is close to the potential of [Co^II(bpy)₃]²⁺ oxidation (as is the case with the decamethylferrocene^0/+, N,N,N′,N′‐tetramethyl‐1,4‐phenylenediamine^0/+ and 7,7,8,8‐tetracyanoquinonedimethane^0/? systems), the rate of the electrode reaction is limited by the rate of the chemical reduction of the [Co^III(bpy)₃](ClO₄)₃ solid phase by the reduced form of redox couple. For C₆₀ and benzoquinone, which have more negative formal potentials for reduction, the rate of diffusion of the electroactive reactant to the electrode surface limits the rate of electrode process. The kinetics of mediated electrocatalysis are also affected by the solvent. In the case of the Fe(III)‐based layer, the diffusion of the electroactive reactant in the solution is the rate determining step for the catalytic process at the modified electrode for all studied systems. Electrodes modified with [Fe^III(bpy)₃](ClO₄)₃ have been used for the quantitative determination of electroactive compounds. For ferrocene and decamethylferrocene, a linear relationship between the catalytic reduction current and the concentration of reactant in the solution has been observed over the concentration range from 1 to 50 mM.     

Palladium(II) iminophosphine complexes

New complexes of general formula [PdCl₂(NP)] (NP = o-Ph₂PC₆H₄-CH=N-R; R = Me, ⁱ Pr, ^t Bu, NH-Me) and [Pd(NP)₂](ClO₄)₂ (NP = o-Ph₂PC₆H₄-CH=N-R; R = Me, ⁱ Pr) have been prepared by directly reacting the precursor PdCl₂(PhCN)₂ with iminophosphines (NP) in 1:1 and 1:2 molar ratios respectively. When the chloro-complex [PdCl₂(o-Ph₂PC₆H₄-CH=N ⁱ -Pr)] was treated with CF₃SO₃Ag in MeCN, the labile complex [Pd(o-Ph₂PC₆H₄-CH=N ⁱ -Pr)(MeCN)₂](CF₃SO₃)₂ was obtained in good yield. The reactivity of the new precursor towards a variety of neutral N- and P-donor ligands (py, PMe₂Ph, PMePh₂, PEt₃, bipy, dppe, 2-thpy) has been studied. The new complexes were characterized by partial elemental analyses and by spectroscopy (i.r., ¹H- and ³¹P-n.m.r.). The molecular structure of the aquo-complex [Pd(NP)(2-thpy)(H₂O)](CF₃SO₃)₂ has been determined by a single-crystal diffraction study, showing that the iminophosphine acts as a chelating ligand with coordination around the palladium atom slightly distorted from square-planar geometry.