Stochastic theory of collisional energy transfer: nature of convergence of master equation transition probabilities and moments as a function of cumulant expansion order

Closed form expressions for collisional energy transfer transition probabilities and moments are determined for the forced oscillator model by solving cumulant expansion master equation in second, fourth, sixth and infinite order. This enables a study of convergence properties of the cumulant expansion.     

Accounting for the dependence of P(E',E) on the maximum impact parameter in classical trajectory calculations: application to the H2O-H2O collisional relaxation

In this work we report a novel methodology that is able to predict how energy transfer transition probability density functions [P(E',E)] change with the maximum impact parameter (bmax) used in trajectory calculations (TC's). The method assumes that P(E',E) can be described by a sum of exponential functions and that all the trajectories with an initial impact parameter beyond a certain critical value will contribute only to the elastic peak [P(E',E) for E'=E]. This approach is applied to H2O-H2O collisions at different initial vibrational energies of the excited molecules and temperatures of bath gas. The results show that it is possible to reproduce with high accuracy the whole P(E',E) obtained from a given bmax, using the results of TC's performed at another bmax. The new methodology also leads us to propose a new criterion to choose the value of bmax.     

Electronic to vibrational energy transfer assisted by interacting transition dipole moments: a quantum model for the nonadiabatic I2(E) + CF4 collisions

We report a theoretical study of nonadiabatic transitions within the first-tier ion-pair states of molecular iodine induced by collisions with CF(4). We propose a model that treats the partner as a spherical particle with internal vibrational structure. Potential energy surfaces and nonadiabatic matrix elements for the I(2)-CF(4) system are evaluated using the diatomics-in-molecule perturbation theory. A special form of the intermolecular perturbation theory for quasi-degenerate electronic states is implemented to evaluate the corrections to the long-range interaction of transition dipole moments of colliding molecules. The collision dynamics is studied by using an approximate quantum scattering approach that takes into account the coupling of electronic and vibrational degrees of freedom. Comparison with available experimental data on the rate constants and product state distributions demonstrates a good performance of the model. The interaction of the transition dipole moments is shown to induce very efficient excitation of the dipole-allowed upsilon(3) and upsilon(4) modes of the CF(4) partner. These transitions proceed predominantly through the near-resonant E-V energy transfer. The resonant character of the partner's excitation and the large mismatch in vibrational frequencies allow one to deduce the partner's vibrational product state distributions from the distributions measured for the molecule. The perspectives of the proposed theoretical model for treating a broad range of molecular collisions involving the spherical top partners are discussed.     

Efficient long-range collisional energy transfer between the E0(g)(+)(3P2) and D0(u)(+)(3P2) ion-pair states of I2, induced by H2O, observed using high-resolution Fourier transform emission spectroscopy

Using high-resolution Fourier transform emission techniques, we have resolved rotational structure in the D0(u)(+)((3)P(2)) → X0(g)(+) emission following collisional transfer from the E0(g)(+)((3)P(2)) state in I(2). The P:R branch ratios in the E0(g)(+)((3)P(2)) → D0(u)(+)((3)P(2)) transfer are found to vary enormously with v(E) and v(D). We show that the observed intensities are all consistent with the transfer being dominated by long-range, near-resonant collisions with residual H(2)O. Unequal P:R branch ratios in the E0(g)(+)((3)P(2)) → A1(u) emission have been shown to result from mixing of the E0(g)(+)((3)P(2)) and β1(g)((3)P(2)) states via Ω-uncoupling.     

An experimental study of collisional transfer of electronic excitation,collisional dissociation of excited molecules and photodissociation in alkali vapour

A single-frequency laser is used to excite Na₂ molecules to the electronic B state. Besides the molecular fluorescence also atomic Na resonance radiation is observed. This is caused by: collisional transfer of electronic excitation from a Na₂(B) molecule to a Na atom, collisional dissociation of Na₂(B) molecules and photodissociation of Na₂ from very high vibration—rotation (v. J) levels of the ground state. We show how the contributions of these processes can be separated experimentally and characterized quantitativily over a wide range of temperatures, using a free-jet expansion. Illustrative results are given for one laser frequency (i.e. one molecular transition). Effective collision cross sections for excitation transfer and for collisional dissociation are given. The probability of photodissociation is compared to the probability of the discrete (B ← X) transition. The relaxation of the number of molecules in high (v. J) levels in a free jet is obtained.     

Converged calculations of vibrational energy transfer probabilities for the collision of two HF(v=1) molecules

We present converged quantum mechanical calculations of state-to-state transition probabilities for the collision of two hydrogen fluoride molecules with zero total angular momentum. The potential energy surface is obtained by adding a vibrational dependence to the interaction potential of Alexander and DePristo. We have calculated converged transition probabilities for vibration-to-vibration and vibration-to-translation-and-rotation energy transfer including full vibration-rotation coupling. The calculations include up to 948 coupled channels. Final production runs were carried out with a highly vectorized code on the Minnesota Supercomputer Institute's Control Data Corporation Cyber 205 computer.     

A quasiclassical trajectory study of collisional energy transfer and dissociation in He + H2(v,j) using a new potential energy surface

Quasiclassical trajectories for He + H2 were carried out using the recent ab initio potential of Boothroyd, Martin, and Peterson (J. Chem. Phys. 2003, 119, 3187) and results for the 348 (v, j) states of H2 are compared to those of earlier calculations that used the potential of Wilson, Kapral, and Burns (Chem. Phys. Lett. 1974, 24, 4884). Examined are the cross sections for energy transfer and dissociation, the extent of threshold elevation, and the interconversion of vibrational and rotational energy. Implications for modeling the interstellar medium are discussed.     

Iodination of cyclo‐E5‐Complexes (E=P,As)

In a high‐yield one‐pot synthesis, the reactions of [Cp*M(η⁵‐P₅)] (M=Fe ( 1 ), Ru ( 2 )) with I₂ resulted in the selective formation of [Cp*MP₆I₆]⁺ salts ( 3 , 4 ). The products comprise unprecedented all‐cis tripodal triphosphino‐cyclotriphosphine ligands. The iodination of [Cp*Fe(η⁵‐As₅)] ( 6 ) gave, in addition to [Fe(CH₃CN)₆]²⁺ salts of the rare [As₆I₈]^2? (in 7 ) and [As₄I₁₄]^2? (in 8 ) anions, the first di‐cationic Fe‐As triple decker complex [(Cp*Fe)₂(μ,η^5:5‐As₅)][As₆I₈] ( 9 ). In contrast, the iodination of [Cp*Ru(η⁵‐As₅)] ( 10 ) did not result in the full cleavage of the M?As bonds. Instead, a number of dinuclear complexes were obtained: [(Cp*Ru)₂(μ,η^5:5‐As₅)][As₆I₈]_0.5 ( 11 ) represents the first Ru‐As₅ triple decker complex, thus completing the series of monocationic complexes [(Cp^RM)₂(μ,η^5:5‐E₅)]⁺ (M=Fe, Ru; E=P, As). [(Cp*Ru)₂As₈I₆] ( 12 ) crystallizes as a racemic mixture of both enantiomers, while [(Cp*Ru)₂As₄I₄] ( 13 ) crystallizes as a symmetric and an asymmetric isomer and features a unique tetramer of {AsI} arsinidene units as a middle deck.     

Infrared fluorescence and collisional energy transfer parameters for vibrationally excited azulene*(So): dependence on internal energy (Evib)

Infrared fluorescence (IRF) from the CH stretch modes of vibrationally excited gas-phase azulene^* was observed to depend on E_vib according to a simple model. The IRF time/pressure behavior shows that the average energy transferred per collision depends strongly on E_vib for azulene^* + azulene and azulene^* + argon collisions.     

Franck-Condon effects in collision-induced electronic energy transfer: I2(E; v = 1,2) + He, Ar

Collisions of I2 in the E electronic state with rare gas atoms result in electronic energy transfer to the D, beta, and D' ion-pair electronic states. Rate constants for each of these channels have been measured when I2 is initially prepared in the J = 55, nu = 1 and 2 levels in the E state. The rate constants and effective hard sphere collision cross sections confirm the trends observed when nu = 0 in the E state is initially prepared: He collisions favor population of the D state, while Ar collisions favor population of the beta state. Final state vibrational level distributions are determined by spectral simulation and are found to be qualitatively consistent with the trends in the Franck-Condon factors. The experimental distributions are also compared to the recent quantum scattering calculations of Tscherbul and Buchachenko.     

The first (<Superscript>31</Superscript>P, <Superscript>17</Superscript>O,and <Superscript>103</Superscript>Rh) NMR observation complex formation of rhodium(III) with phosphoric acid

³¹P, ¹⁷O, and ¹⁰³Rh NMR spectroscopy shows that rhodium(III) reacts with phosphoric acid to generate polynuclear aquaphosphate complexes in which phosphate ions mostly have a bridging function. Assignment of ¹⁰³Rh NMR signals in dominant rhodium complexes is suggested.     

A theoretical and experimental study on the Lewis acid-base adducts (P(4)E(3)).(BX(3)) (E = S, Se; X = Br, I) and (P(4)Se(3)).(NbCl(5))

The Lewis acid-base adducts (P(4)E(3)).(BX(3)) (E = S, Se; X = Br, I) and (P(4)Se(3)).(NbCl(5)) have been prepared and characterized by Raman, IR, and solid-state (31)P MAS NMR spectroscopy. Hybrid density functional calculations (B3LYP) have been carried out for both the apical and the basal (P(4)E(3)).(BX(3)) (E = S, Se; X = Br, I) adducts. The thermodynamics of all considered species has been discussed. In accordance with solid-state (31)P MAS NMR and vibrational data, the X-ray powder diffraction structures of (P(4)S(3)).(BBr(3)) [monoclinic, space group P2(1)/m (No. 11), a = 8.8854(1) A, b = 10.6164(2) A, c = 6.3682(1) A, beta = 108.912(1) degrees, V = 568.29(2) A(3), Z = 2] and (P(4)S(3)).(BI(3)) [orthorhombic, space group Pnma (No. 62), a = 12.5039(5) A, b = 11.3388(5) A, c = 8.9298(4) A, V = 1266.09(9) A(3), Z = 4] indicate the formation of an apical P(4)S(3) complex in the reaction of P(4)S(3) with BX(3) (X = Br, I). Basal adducts are formed when P(4)Se(3) is used as the donor species. Vibrational assignment for the normal modes of these adducts has been made on the basis of comparison between theoretically obtained and experimentally observed vibrational data.     

Synthesis,Structure, and Optical Properties of New Cadmium Chalcogenide Clusters of the Type [Cd10E4(E'Ph)12(PR3)4], (E,E' = Te,Se, S)

New cadmium chalcogenide cluster molecules [Cd₁₀E₄(E'Ph)₁₂(PⁿPr₃)₄], E = Te, E' = Te ( 1 ) and [Cd₁₀E₄(E'Ph)₁₂ (PⁿPr₂Ph)₄] E = Te, E' = Se ( 2 ); E = Te E' = S ( 3 ); E = Se, E' = S ( 4 ) have been synthesized and structurally characterized by single crystal X‐ray structure analysis. The influence of the variation of the chalcogen atom is investigated by structural means and by optical spectroscopy. All cluster‐molecules have a broad emission in the blue‐visible range at low temperature as indicated by photo luminescence (PL) measurements. A clear classification of the emission peak position can be made based on the E' species suggesting that the emission is assigned to transitions associated with the cluster surface ligands. Photoluminescence excitation and absorption measurements display a systematic shift of the band gap to the higher energies with the variation of E and E' from Te to Se to S, as also occurs in the respective series of the bulk semiconductors.     

CASSCF and CASPT2 studies on the structures, transition energies, and dipole moments of ground and excited states for azulene

The electronic structure of azulene molecule has been studied. We have obtained the optimized structures of ground and singlet excited states by using the complete active space self-consistent-field (CASSCF) method, and calculated vertical and 0-0 transition energies between the ground and excited states with second-order M?ller-Plesset perturbation theory (CASPT2). The CASPT2 calculations indicate that the bond-equalized C(2v) structure is more stable than the bond-alternating C(s) structure in the ground state. For a physical understanding of electronic structure change from C(2v) to C(s), we have performed the CASSCF calculations of Duschinsky matrix describing mixing of the b(2) vibrational mode between the ground (1A(1)) and the first excited (1B(2)) states based on the Kekule-crossing model. The CASPT2 0-0 transition energies are in fairly good agreement with experimental results within 0.1-0.3 eV. The CASSCF oscillator strengths between the ground and excited states are calculated and compared with experimental data. Furthermore, we have calculated the CASPT2 dipole moments of ground and excited states, which show good agreement with experimental values.     

Statistical theory of collisional energy transfer in molecular collisions. trans-stilbene deactivation by argon, carbon dioxide, and n-heptane

Recent advances in experimental techniques have made it possible to measure the full conditional probability density P(E, E') of the energy transfer between two colliding molecules in the gas phase, one of which is highly energized and the other in thermal equilibrium at a given temperature. Data have now become available for trans-stilbene deactivation by the three bath gas molecules Ar, CO2, and n-heptane (C7H16). The initial energies of trans-stilbene are set to 10 000, 20 000, 30 000, and 40 000 cm (-1). The results show that exceptionally large amounts of energy are transferred in each collision. By application of our partially ergodic collision theory (PECT), we find that the energy transfer efficiency betaE ranges from a rather normal value of 0.15 for n-heptane at the highest excitation energy to 0.93-nearly in the ergodic collision limit-for the argon bath gas at high excitation energy. Generally, the PECT produces a good fit of the data except for the nearly elastic peak in the case of n-heptane, where PECT produces a rounded and downshifted peak in contrast to a sharply defined elastic maximum of the monoexponential functional fit produced from the original experimental data obtained by kinetically controlled selective ionization in the work of the group of Luther in G?ttingen. This problem is analyzed and found to be related partly to the lack of treatment of glancing collisions in the theory with a remaining uncertainty due to the weak dependence of energy transfer efficiency on nearly elastic collisions. A summary of the present state of understanding shows that collisional activation and deactivation of reactant molecules is more efficient and more statistical than has been previously realized.     

Fixation and Release of Intact E4 Tetrahedra (E=P,As)

By the reaction of [NacnacCuCH₃CN] with white phosphorus (P₄) and yellow arsenic (As₄), the stabilization and enclosure of the intact E₄ tetrahedra are realized and the disubstituted complexes [(NacnacCu)₂(μ,η^2:2‐E₄)] ( 1 a : E=P, 1 b : E=As) are formed. The mono‐substituted complex [NacnacCu(η²‐P₄)] ( 2 ), was detected by the exchange reaction of 1 a with P₄ and was only isolated using low‐temperature work‐up. All products were comprehensively spectroscopically and crystallographically characterized. The bonding situation in the products as intact E₄ units (E=P, As) was confirmed by theory and was experimentally proven by the pyridine promoted release of the bridging E₄ tetrahedra in 1 .