Exponential gap relation and the rotational inelasticity of H2M systems

Previously published values of state-to-state integral inelastic cross sections for the H₂(J_i)—M (M  H, He, Li, Li⁺, H₂, CO₂) systems are fitted to the exponential gap relation for the rotational inelastic process to obtain the C value that reflects the magnitudes of relative cross sections. While the vibration of the rotor seems to have little influence, the C value is shown to decrease dramatically with increase in initial collision energy T_i, ΔC/ΔT_i being larger at lower T_i for all systems analysed, in accord with the prediction of the surprisal synthesis of Procaccia and Levine. For the only case of H₂(J_i)-Li⁺ for which results are available for several J_i, C decreases with increase in J_i or J_i(J_i + 1)). The C value predicted by Procaccia and Levine for H₂M systems falls within the range of C values calculated for the various collision partners. However, there is a noticeable change in C (albeit within a factor of two) with change in M, indicating that dynamical factors do play an important role in rotational inelastic processes.     

Rotational energy transfer (theory). I. Comparison of quasiclassical and quantum mechanical results for elastic and rotationally inelastic HClAr collisions

Integral elastic and rotationally inelastic cross sections for HCl (J_i = 0, 1) + Ar collisions at a collision energy of 1.785 kcal/mole are rep     

Estimation of O-H bond dissociation energies in alcohols and acids from kinetic data

The O-H bond dissociation energies (D _O-H) in five alcohols and six acids have been determined from experimental data (rate constants of radical reactions). The ratio of the rate constants of the reactions R¹O˙+RH→R¹OH+R˙ and R ⁱ O˙+RH→R ⁱ OH+R˙ and the intersecting parabolas method are used in the estimation procedure. The D _O-H values are used to calculate the activation energies and rate constants for hydrogen abstraction from 2-methylbutane, butene-1, and cumene by alkoxyl and carboxyl radicals. The geometric parameters of the transition state are calculated for these reactions.     

Time-dependent close coupling for vibrational excitation in three dimensions: Application to H+ - H2

Impact parameter calculations for the non-reactive H⁺ + H₂ (n_i = 0) → H⁺ + H₂ (n_f) collision are reported for energies 10 eV ? E_cm ? 200 eV describing the rotational motion of the molecule in the sudden limit. The time-dependent Schrödinger equation for the vibrational motion has been solved by close coupling techniques expanding the vibrational wavefunction into both harmonic and numerically exact H₂ bound states. The convergence in vibrational basis sets, where up to six vibrational levels are considered, becomes worse with decreasing energy and increasing inelasticity. Furthermore, the harmonic wavefunctions are not suitable over a large range of energies to calculate proper cross sections. The various integral and differential cross sections have been compared with the classical results of Giese and Gentry.     

Energy distribution among reaction products. H + NOCl,H + ICl

The infrared chemiluminescence technique has been used to obtain k(V′, R′, T′) (V′, R′, Tt? are product vibrational, rotational and translational energies) for the reactions (i) H + ClNO → HCl + NO (energy-release E_tot′ = 68.5 kcal mole^?1) and (ii) H + CII → HCl + I (E_tot′ = 55.8 kcal mole^?1). Reaction (i) exhibits inefficient conversion of energy-release into vibration in the new bond, characteristic of a light attacking atom reacting on a repulsive energy-surface. Reaction (ii) has a bimodal HCl product-energy-distribution suggesting that 18% of the reaction proceeds by direct attack at the Cl end of CII to yield low V′ and R′, and 82% by indirect reaction from the 1 end to give high V′ and R′.     

Ultrasonic velocity study of poly(R,R,4,4-cyclohexylidene diphenylene diphenyl ether-4,4-disulfonate) solutions at 30, 35 and 40 °C

Ultrasonic velocity (2 MHz) and acoustic parameters of poly(R,R^′-4,4^′-cyclohexylidene diphenylene diphenyl ether-4,4^′-disulfonate) (PS-1: RR^′H; PS-2: RCH₃ and R^′H; PS-4: RCH₃ and R^′Cl) solutions (chloroform, 1,2-dichloroethane and tetrahydrofuran (THF)) at 30, 35 and 40 °C have been determined to understand the effect of methyl and chlorine substituents on molecular interactions to support solvophilic or solvophobic nature of the polymers. The linear increase of U, Z, R, b, π, (α/f²)_Cl and τ with C and decrease of K_s, r, L_f and V_f with C suggested the existence of strong molecular interactions and hence solvophilic nature of the polymers, which is supported by positive values of S_n. A rise in temperature resulted in less ordered structure and more spacing between the molecules. The solvophilic nature of the polymers caused nonlinear variation of φ_v2 and φ_Ks with C and T. A powerful solvation exists in THF system. Structural modification is found above 2% for PS-2 and PS-4. The decrease of S_n with C and T indicated the presence of polymer-polymer interactions. The decrease of S_n with T is due to disruption of the structure formed by predominant thermal energy over molecular interaction energy.     

Partial differential cross sections for inelastic He++Ne collisions at low energy

We report differential cross section measurements with high angular resolution for different channels of the inelastic processes He⁺+Ne→He⁺+Ne* and He⁺+Ne→He*+Ne⁺, for collision energies between 100 and 200 eV. For the Ne states (2p ⁵3s)^1,3 P ₁, which decay optically, we determined the fraction with the alignment at right angles to the scattering plane. The results are used to discuss the mechanism of the processes and the influence of the spin-orbit interaction upon the collision.     

The low energy collision between metastable Ne*(3 P 0,2) and He(1 S 0): ab initio potentials,differential cross sections and polarization effects

Potential energies for molecular states dissociating into Ne*(¹ P ₁,³ P _0,1,2) + He(¹ S ₀) have been calculated ab initio within the distance range 4–100a ₀. The SCF energy (without spin-orbit interaction) is optimized on the lowest³Σ state. After CI, the four Λ-states (^1,3Σ,^1,3Π)are obtained. They dissociate into Ne*(^1,3 P) + He(¹ S). All of them are repulsive atR ? 8a ₀, they exhibit shallow wells around 12a ₀ and have a correct asymptotic behaviour (～ -R ^?6). The spin-orbit interaction is introduced, using the Cohen-Schneider scheme, and adiabatic Ω-potentials are derived. The collision at low energy (E ≦ 124 meV) is described in the frame of a fragment-state basis. By means of a deflation procedure, it is shown that states dissociating into Ne*(¹ P ₁) + He can be eliminated, which lead to a 9 × 9 interaction matrix dynamically equivalent to the original 12 × 12 matrix, in the subspace of interest. Collision channels are defined by angular momenta,J (total),j (of Ne*) andl (of the relative motion). Scattering radial equations are solved by the algorithm of Gordon and theS matrix is derived. Two sets of physically meaningful scattering amplitudes (and differential cross sections) are constructed, referred to the incident axis or to the initial and final directions of the internuclear axis. Polarization effects are discussed. The case of a quantization axis perpendicular to the collision plane is also mentioned.     

Orientation dependence in collision induced electronic relaxation studied through van der Waals complexes with isomeric structures

Weakly bound molecular complexes with more than one well-defined structures provide us with an unique opportunity to investigate dynamic processes induced by intermolecular interactions with specific orientations. The relative orientation of the two interacting molecules or atoms is defined by the complex structure. The effect of the orientation in the spin changing collisions glyoxal(S₁)+Ar → glyoxal(T₁)+Ar and acetylene (S₁)+Ar → acetylene(T)+Ar have been studied by measuring the intersystem crossing (ISC) rates of the glyoxal(S₁)·Ar and acetylene(S₁)·Ar complexes with different isomeric structures. Results show that there is a strong orientation dependence in the ISC of glyoxal(S₁) induced by interaction with the Ar atom: the Ar atom positioned in the molecular plane is much more effective than in the out-of-plane position in inducing the S₁ → T₁ transition of glyoxal. On the other hand, studies of acetylene(S₁)·Ar complexes indicate that the Ar-induced ISC rates are nearly identical for the in-plane and out-of-plane positions. Orientation dependence in the collision induced vibrational relaxation process C₂H₂(S₁,v _i )+Ar → C₂H₂(S₁,v _f <v _i )+Ar is also studied by measuring the vibrational predissociation rates of the acetylene(S₁)·Ar complex isomers. The results indicate that collisions of C₂H₂(S₁,v ₃=3, 4) with Ar at two orthogonal orientations are equally effective in causing vibrational relaxation of C₂H₂.     

The unimolecular decomposition of chemically activated complexes: Cross sections for the chemi-ionization of Ca,Sr, Ba with NF3 and SF6

Integral reactive cross sections for chemi-ionization have been measured in a crossed-beam experiment for Ba, Sr + SF₆ → BaF⁺, SrF⁺ + SF₅^? and Ca, Sr + NF₃ → CaF⁺, SrF⁺ + NF₂^? at collision energies E_c.m. < 4 eV. The experimental results confirm a collision complex. The applicability of RRKM theory to chemi-ionization of polyatomic molecules is discussed. The presence of competing neutral-product reactions, included in the calculation, is important for the determination of dynamical and statistical properties of the intermediate states formed. The slope of the chemi-ionization cross section as a function of collision energy indicates directly that all vibrational degrees of freedom are activated.     

A quantum algorithm for spin chemistry: a Bayesian exchange coupling parameter calculator with broken-symmetry wave functions

The Heisenberg exchange coupling parameter J (H = −2JS_i · S_j) characterises the isotropic magnetic interaction between unpaired electrons, and it is one of the most important spin Hamiltonian parameters of multi-spin open shell systems. The J value is related to the energy difference between high-spin and low-spin states, and thus computing the energies of individual spin states are necessary to obtain the J values from quantum chemical calculations. Here, we propose a quantum algorithm, B̲ayesian ex̲change coupling parameter calculator with b̲roken-symmetry wave functions (BxB), which is capable of computing the J value directly, without calculating the energies of individual spin states. The BxB algorithm is composed of the quantum simulations of the time evolution of a broken-symmetry wave function under the Hamiltonian with an additional term jS², the wave function overlap estimation with the SWAP test, and Bayesian optimisation of the parameter j. Numerical quantum circuit simulations for H₂ under a covalent bond dissociation, C, O, Si, NH, OH⁺, CH₂, NF, O₂, and triple bond dissociated N₂ molecule revealed that the BxB can compute the J value within 1 kcal mol⁻¹ of errors with less computational costs than conventional quantum phase estimation-based approaches.

A quantum algorithm “Bayesian exchange coupling parameter calculator with broken-symmetry wave function (BxB)” enables us to calculate Heisenberg exchange coupling parameter J without inspecting total energies of individual spin states, within 1 kcal mol⁻¹ of energy tolerance.     

A classical trajectory study of the effect of reaction barrier height on the vibrational energy transfer efficiency in the Cl + HCl system

The effects of reaction barrier height and initial rotational excitation of the reactants on the overall rate of H atom exchange between atomic chlorine and HCl (v = 0) and on the 0 → 1 vibrational excitation of HCl via reactive and nonreactive collisions have been investigated using quasiclassical trajectory techniques. Two empirical LEPS potential energy surfaces were employed in the calculations having reaction barrier heights of 9.84 and 7.05 kcal mol^?1. Trajectory studies of planar collisions were carried out on each surface over a range of relative translational energies with the ground-state HCI collision partner given initial rotational excitation corresponding J = 0, 3, and 7. Initial molecular rotation was found to be relatively inefficient in promoting the H atom exchange; the computed rate coefficient for H atom exchange between Cl + HCl (v = 0, J = 7) was only 4 times larger than that for CI + HCI (v = 0, J = 0). The vibrational excitation rate coefficient exhibited a stronger dependence on initial molecular rotational excitation. The observed increase in the vibrational excitation rate coefficient with increasing initial molecular rotational excitation was due primarily to nonreactive intermolecular R → V energy transfer. The vibrational excitation rate coefficients increase with decreasing reaction barrier height.     

Energy transfer in classical collinear and perpendicular central collisions of a structureless atom with a morse oscillator

The energy transfer in classical collinear (C_∞) and perpendicular (C_2v) central collisions of an atom with a Morse oscillator is compared. These collision geometries contribute in classical collisions to experimentally observed inelastic backward scattering of alkali ions from H₂ molecules. For both collision geometries the equations of motion reduce to a set of only two coupled differential equations which can be easily solved numerically. The calculations show that the C_2v collisions are much more effective than C_∞ collisions at all but the very lowest energies. The calculated ΔE/E versus E curves for C_2v collisions using a Born-Mayer potential for the atom atom-in-molecule interaction could be fitted to the experimental results for Na⁺-D₂ yielding reasonable potential values.     

Differential Cross Sections of F+HD→DF+H Reaction at Collision Energies from 3.03 meV to 17.97 meV

The prototypical reaction of F+HD→DF+H was investigated at collision energies from 3.03 meV to 17.97 meV using a crossed molecular beam apparatus with multichannel Rydberg tagging time-of-flight detection. Significant contributions from both the Born-Oppenheimer (BO) forbidden reaction F^*(²P_1/2)+HD→DF+H and the BO-allowed reaction F(²P_3/2)+HD→DF+H were observed. In the backward scattering direction, the contribution from the BO-forbidden reaction F^*(²P_1/2)+HD was found to be considerably greater than the BO-allowed reaction F(²P_3/2)+HD, indicating the non-adiabatic effects play an important role in the dynamics of the title reaction at low collision energies. Collision-energy dependence of differential cross sections (DCSs) in the backward scattering direction was found to be monotonously decreased as the collision energy decreases, which does not support the existence of resonance states in this energy range. DCSs of both BO-allowed and BO-forbidden reactions were measured at seven collision energies from 3.03 meV to 17.97 meV. It is quite unexpected that the angular distribution gradually shifts from backward to sideway as the collision energy decreases from 17.97 meV to 3.03 meV, suggesting some unknown mechanisms may exist at low collision energies.     

Measurement of state-to-state rotational transfer rates in collision of I2*(B 0u+, υ = 15, j) with 3He, 4He,Ne, Ar,H2, D2 and I2

The selective laser excitation and induced fluorescence observation technique has been used to study rotationally inelastic collisions of I₂^*(B 0_u⁺, υ = 15,j) with I₂, ³He, ⁴He, Ne, Ar, H₂ and D₂. For each collision partner, several initial rotational levels ranging from j_i = 12 up to j_i = 146 have been excited. For purely rotational transfer within the υ = 15 level, our data are perfectly consistent with energy sudden (eventually corrected) scaling laws. Thus, any thermally averaged rate constant, k(j_i → j_f), can be expressed as a function of the basis rate constants k(l → 0). Furthermore, these k(l → 0) are found to follow simple empirical fitting laws. Consequently any k(j_i → j_f) can be predicted given a set of two or three fitting parameters. Collisions with relatively heavy particles (I₂, Ar and Ne) are well described by using the inverse power fitting law k(l → 0) = b[l(l+1)]^?γ, where b = 1.7, 1.2 and 1.2×10^?10 cm³ s^?1 and γ = 1.08, 1.02 and 1.17 for I₂^*-Ne, I₂^*-Ar and I₂^*-I₂ collisions respectively. For collisions with light particles (³He, ⁴He, H₂ and D₂), k(l → 0) shows a sharp decrease with l which can be accounted for by a hybrid power-exponential fitting law k(l → 0) = b[l(l+1)]^?γ exp[-l(l+1)/l^* (l^*+1)], where b = 0.84, 0.71, 2.77 and 2.78×10^?10 cm³ s^?1l⁺ = 20.6, 23.1, 18.8 and 31.4, and γ = 0.66, 0.66, 0.78 and 0.91 for I₂^*-³He, I₂^*-He, I₂^*-H₂ and I₂^*-D₂ collisions, respectively. We confirm that the rotational transfer dynamics in heavy molecules is mainly governed by angular momentum exchange.     

Collision cross sections for excitation energy transfer in Na* (3P 1/2)+K(4S 1/2)⇔Na*(3P 3/2)+K(4S 1/2) processes

The cross sections for the excitation energy transfer between the 3² P _J states of sodium atoms by collisions with ground-state potassium atoms have been measured by resonant Doppler-free two-photon spectroscopy, where the population densities of directly pumped and collisionally excited Na(3P _J )(J=1/2, 3/2) levels were probed by counter-propagating Na(3P _J ) → Na(4D _{3/2, 5/2}) excitation and detected with the thermionic diode. Cross sections of σ(3P _1/2 → 3P _3/2)=190 Ų±20% and σ(3P _3/2 → 3P _1/2)=100 Ų±20% were found. The theoretical calculations taking into account the long-range interaction termsR ^?6,R ^?8 andR ^?10 yield a value σ(3P _1/2 → 3P _3/2)=165 Ų. On the basis of these long-range interaction potentials the differential cross section has been calculated and compared with recently published experimental data. Very good agreement between the theoretical and experimental data was found.     

Structural diversity in imidazolidinone organocatalysts: a synchrotron and computational study

(S)‐1‐(Methylaminocarbonyl)‐3‐phenylpropanaminium chloride (S2·HCl), C₁₀H₁₅N₂O⁺·Cl⁻, crystallizes in the orthorhombic space group P2₁2₁2₁ with a single formula unit per asymmetric unit. (5R/S)‐5‐Benzyl‐2,2,3‐trimethyl‐4‐oxoimidazolidin‐1‐ium chloride (R3 and S3), C₁₃H₁₉N₂O⁺·Cl⁻, crystallize in the same space group as S2·HCl but contain three symmetry‐independent formula units. (R/S)‐5‐Benzyl‐2,2,3‐trimethyl‐4‐oxoimidazolidin‐1‐ium chloride monohydrate (R4 and S4), C₁₃H₁₉N₂O⁺·Cl⁻·H₂O, crystallize in the space group P2₁ with a single formula unit per asymmetric unit. Calculations at the B3LYP/6–31G(d,p) and B3LYP/6–311G(d,p) levels of the conformational energies of the cation in R3, S3, R4 and S4 indicate that the ideal gas‐phase global energy minimum conformation is not observed in the solid state. Rather, the effects of hydrogen‐bonding and van der Waals interactions in the crystal structure cause the molecules to adopt higher‐energy conformations, which correspond to local minima in the molecular potential energy surface.     

Tandem mass spectrometry of peptides: Mechanistic aspects and structural information based on neutral losses. II—Tri- and larger peptides

The neutral products arising during the collisionally activated dissociation of protonated oligopeptides (MH⁺) are post-ionized by collision and detected in neutral fragment-reionization (⁺N_fR⁺) mass spectra. For the isomeric tripeptides Ala-Gly-Gly, Gly-Ala-Gly and Gly-Gly-Ala, the amino acid and dipeptide losses from the C-terminus and the diketopiperazine losses from the N-terminus allow for differentiation. These neutral fragments are identified in the corresponding ⁺N_fR⁺ spectra by comparison to reference collision-induced dissociative ionization (CIDI) mass spectra of individual amino acids, dipeptides and diketopiperazines. Peptides with distinct C-termini but otherwise identical sequences are found to yield ⁺N_fR⁺ products that are characteristic of the respective C-terminal amino acid. This is demonstrated for several peptide pairs, including leucine- and methionine-enkephalin. In general, ⁺N_fR⁺ spectra are dominated by the heavier neutral losses; further, ⁺N_fR⁺ and CIDI cause extensive dissociation, indicating that the collisional ionization process imparts high average internal energies.     

Electronic energy transfer from the S2 state of rhodamine 6G

In this paper we present the results of an experimental study of intermolecular electronic energy transfer (EET) from the short-lived Second excited singlet state of rhodamine 6G (R6G) to the ground state of 2,5-bis [5′-tert-butyl-2-benzoxazolyl] thiophene (BBOT). The S₂ state of the donor was excited by sequential, time-delayed, two-photon excitation (STDTPE) utilizing the second harmonic and the first harmonic of a mode-locked Nd³⁺: glass laser, while the EET process was interrogated by monitoring the enhancement of the S₁ → S₀ fluorescence of BBOT. The enhancement of the fluorescence intensity of BBOT was found to be linear in the energies of the two exciting pulses, and linear in the concentration of the energy acceptor (over the BBOT concentration range of (0.3–7) × 10^?5 M), which is in accord with the predictions of the Forster—Dexter mechanism for resonant EET from an ultrashort-lived donor state at low acceptor concentrations. Quantitative measurements of the S₂ → S₀ fluorescence yield in R6G solution directly excited by STDTPE and of the S₁ → S₀ fluorescence of BBOT from R6G + BBOT solutions resulting from EET led to the values of Y_D(S₂ → S₀) = (2.1 ± 0.5) × 10^?6 for the emission quantum yield of the S₂ state of R6G and τr_D(S₂) ≈ 3 × 10^?14 s for the lifetime of the metastable S₂ state of this molecule.     

Two-photon induced fluorescence and resonance-enhanced ionization of sulfur atoms

Two-photon induced fluorescence and resonance-enhanced photoionization have been observed in atomic sulfur originating from both the ³P_2,1,0 and the ¹D₂ states. Sulfur atoms are generated by the sequential multiphoton dissociation of CS₂ at probing wavelengths. The two-photon absorption process involves the 3 ³P_2,1,0 → 4 ³P_2,0,1 or the 3 ¹D₂ → 4 ¹F₃ transitions with resolution of the individual J″ → J′ transitions in most cases. Intensities of the 3³P_J″ → 4 ³P_J′ transitions have been compared with Hartree-Fock calculated transition probabilities from the analogous transitions in atomic oxygen. Photoionization is observed in a three-photon (two to resonance) ionization originating from the ³P_2,1,0 and the ¹D₂ states. Induced fluorescence is observed at 167 and 180 nm which is dipole-allowed radiation from the intermediate ³S⁰₁ and ¹D⁰₂ states, respectively.