Nonadiabatic Transition State Theory Research Articles

An experimental and theoretical investigation of the competition between chemical reaction and relaxation for the reactions of 1CH2 with acetylene and ethene: implications for the chemistry of the giant planets

The temperature dependence of the branching ratios for H atom production from the reactions of the first excited state of methylene (a1A1 1CH2) with acetylene and ethene have been measured at approximately 1 Torr total pressure and temperatures of 195, 250 and 298 K by monitoring the production of H atoms using laser induced fluorescence, comparing the signal to that observed from a calibration reaction. For the reaction with acetylene the yield of H increases from 0.28 (195 K) to 0.53 (250 K) to 0.88 at 298 K. The H atom yield from the reaction of 1CH2 with ethene shows similar behaviour, the yields being 0.35 (195 K), 0.51 (250 K) and 0.71 (298 K). The co-products, propargyl (C3H3) and allyl (C3H5) are formed from the dissociation of chemically activated C3H4 and C3H6 intermediates respectively, and are important species in the formation of higher hydrocarbons, including benzene, in the atmospheres of the outer planets and Titan. H atom production is in competition with electronic relaxation to form ground state methylene (X3B1, 3CH2) and collisional stabilization to form C3H4 and C3H6. Master equation calculations have been carried out to demonstrate that for the reaction of 1CH2 with acetylene, collisional stabilization is insignificant under experimental conditions and hence the balance of reaction is due to electronic relaxation. Non-adiabatic transition state theory has been applied to the reaction of 1CH2 with acetylene. The calculations show reasonable agreement with experiment, generally being within the combined errors, and reproduce the negative temperature dependence for electronic relaxation. The implications of the temperature dependence of the absolute rate coefficients for 1CH2 reactions with inert gases, hydrogen, acetylene and ethene and of the branching ratios between chemical reaction and electronic relaxation are discussed.

A Combined Theoretical and Experimental Study on the Role of Spin States in the Chemistry of Fe(CO)5 Photoproducts

A combined experimental and theoretical study is presented of several ligand addition reactions of the triplet fragments (3)Fe(CO)(4) and (3)Fe(CO)(3) formed upon photolysis of Fe(CO)(5). Experimental data are provided for reactions in liquid n-heptane and in supercritical Xe (scXe) and Ar (scAr). Measurement of the temperature dependence of the rate of decay of (3)Fe(CO)(4) to produce (1)Fe(CO)(4)L (L = heptane or Xe) shows that these reactions have significant activation energies of 5.2 (+/-0.2) and 7.1 (+/-0.5) kcal mol(-1) respectively. Nonadiabatic transition state theory is used to predict rate constants for ligand addition, based on density functional theory calculations of singlet and triplet potential energy surfaces. On the basis of these results a new mechanism (spin-crossover followed by ligand addition) is proposed for these spin forbidden reactions that gives good agreement with the new experimental results as well as with earlier gas-phase measurements of some addition rate constants. The theoretical work accounts for the different reaction order observed in the gas phase and in some condensed phase experiments. The reaction of (3)Fe(CO)(4) with H(2) cannot be easily probed in n-heptane since conversion to (1)Fe(CO)(4)(heptane) dominates. scAr doped with H(2) provides a unique environment to monitor this reaction--Ar cannot be added to form (1)Fe(CO)(4)Ar, and H(2) addition is observed instead. Again theory accounts for the reactivity and also explains the difference between the very small activation energy measured for H(2) addition in the gas phase (Wang, W. et al. J. Am. Chem. Soc. 1996, 118, 8654) and the larger values obtained here for heptane and Xe addition in solution.

Charge transfer rates in organic semiconductors beyond first-order perturbation: From weak to strong coupling regimes

Semiclassical Marcus electron transfer theory is often employed to investigate the charge transport properties of organic semiconductors. However, quite often the electronic couplings vary several orders of magnitude in organic crystals, which goes beyond the application scope of semiclassical Marcus theory with the first-order perturbative nature. In this work, we employ a generalized nonadiabatic transition state theory (GNTST) [Zhao et al., J. Phys. Chem. A 110, 8204 (2004)], which can evaluate the charge transfer rates from weak to strong couplings, to study charge transport properties in prototypical organic semiconductors: quaterthiophene and sexithiophene single crystals. By comparing with GNTST results, we find that the semiclassical Marcus theory is valid for the case of the coupling <10 meV for quaterthiophene and <5 meV for sexithiophene. It is shown that the present approach can be applied to design organic semiconductors with general electronic coupling terms. Taking oligothiophenes as examples, we find that our GNTST-calculated hole mobility is about three times as large as that from the semiclassical Marcus theory. The difference arises from the quantum nuclear tunneling and the nonperturbative effects.

Combined nonadiabatic transition-state theory and ab initio molecular dynamics study on selectivity of the α and β bond fissions in photodissociation of bromoacetyl chloride

The selectivity of the alpha C-Cl and beta C-Br bond fissions upon n-->pi(*) excitation of bromoacetyl chloride has been investigated with combined nonadiabatic Rice-Ramsperger-Kassel-Marcus theory and ab initio molecular dynamics calculations, which are based on the potential energy profiles calculated with the complete active space self-consistent field and multireference configuration interaction methods. The Zhu-Nakamura [J. Chem. Phys. 101, 10630 (1994); 102, 7448 (1995)] theory is chosen to calculate the nonadiabatic hopping probability. It is found that nonadiabatic effect plays an important role in determining selective dissociations of the C-Cl and C-Br bonds. The calculated rate constants are close to those from experimentally inferred values, but the branching ratio of the alpha C-Cl and beta C-Br bond fissions is different from the experimental findings. The direct molecular dynamics calculations predict that fission of the C-Cl bond occurs on a time scale of picoseconds and cleavage of the beta C-Br bond proceeds with less probability within the same period. This reveals that the initial relaxation dynamics is probably another important factor that influences the selectivity of the C-Cl and C-Br bond fissions in photodissociation of BrCH(2)COCl at 248 nm.

Dynamics of Nonadiabatic Chemical Reactions

New methods are proposed to treat nonadiabatic chemical dynamics in realistic large molecular systems by using the Zhu-Nakamura (ZN) theory of curve-crossing problems. They include the incorporation of the ZN formulas into the Herman-Kluk type semiclassical wave packet propagation method and the trajectory surface hopping (TSH) method, formulation of the nonadiabatic transition state theory, and its application to the electron transfer problem. Because the nonadiabatic coupling is a vector in multidimensional space, the one-dimensional ZN theory works all right. Even the classically forbidden transitions can be correctly treated by the ZN formulas. In the case of electron transfer, a new formula that can improve the celebrated Marcus theory in the case of normal regime is obtained so that it can work nicely in the intermediate and strong electronic coupling regimes. All these formulations mentioned above are demonstrated to work well in comparison with the exact quantum mechanical numerical solutions and are expected to be applicable to large systems that cannot be treated quantum mechanically numerically exactly. To take into account another quantum mechanical effect, namely, the tunneling effect, an efficient method to detect caustics from which tunneling trajectories emanate is proposed. All the works reported here are the results of recent activities carried out in the author's research group. Finally, the whole set of ZN formulas is presented in Appendix.

Semiclassical Treatment of Thermally Activated Electron Transfer in the Intermediate to Strong Electronic Coupling Regime under the Fast Dielectric Relaxation

The generalized nonadiabatic transition-state theory (NA-TST) (Zhao, Y.; et al. J. Chem. Phys. 2004, 121, 8854) is used to study electron transfer with use of the Zhu-Nakamura (ZN) formulas of nonadiabatic transition in the case of fast dielectric relaxation. The rate constant is expressed as a product of the well-known Marcus formula and a coefficient which represents the correction due to the strong electronic coupling. In the case of general multidimensional systems, the Monte Carlo approach is utilized to evaluate the rate by taking into account the multidimensionality of the crossing seam surface. Numerical demonstration is made by using a model system of a collection of harmonic oscillators in the Marcus normal region. The results are naturally coincident with the perturbation theory in the weak electronic coupling limit; while in the intermediate to strong electronic coupling regime where the perturbation theory breaks down the present results are in good agreement with those from the quantum mechanical flux-flux correlation function within the model of effective one-dimensional mode.

Semiclassical calculation of nonadiabatic thermal rate constants: Application to condensed phase reactions

The nonadiabatic transition state theory proposed recently by Zhao et al. [J. Chem. Phys. 121, 8854 (2004)] is extended to calculate rate constants of complex systems by using the Monte Carlo and umbrella sampling methods. Surface hopping molecular dynamics technique is incorporated to take into account the dynamic recrossing effect. A nontrivial benchmark model of the nonadiabatic reaction in the condensed phase is used for the numerical test. It is found that our semiclassical results agree well with those produced by the rigorous quantum mechanical method. Comparing with available analytical approaches, we find that the simple statistical theory proposed by Straub and Berne [J. Chem. Phys. 87, 6111 (1987)] is applicable for a wide friction region although their formula is obtained using Landau-Zener [Phys. Z. Sowjetunion 2, 46 (1932); Proc. R. Soc. London, Ser. A 137, 696 (1932)] nonadiabatic transition probability along a one-dimensional diffusive coordinate. We also investigate how the nuclear tunneling events affect the dependence of the rate constant on the friction.

ELECTRON TRANSFER RATE UNIFORMLY VALID FROM NONADIABATIC TO ADIABATIC REGIME BASED ON THE ZHU–NAKAMURA THEORY

On the basis of the generalized nonadiabatic transition state theory recently introduced to remedy the crucial deficiencies of the conventional transition state theory, we have presented a new formula for electron transfer rate, which can cover the whole range from adiabatic to nonadiabatic regime in the absence of solvent dynamics control. The rate is expressed as a product of the well-known Marcus theory and a new coefficient that represents the effects of nonadiabatic transition at the crossing seam surface. The numerical comparisons are performed with different approaches and the present approach shows an excellent agreement with the quantum mechanical numerical solutions from weak to strong electronic coupling. The explanation of the experimental data of Nelsen et al. manifests the potential applicability of the present theory.

Nonadiabatic transition-state theory: A Monte Carlo study of competing bond fission processes in bromoacetyl chloride

Nonadiabatic Monte Carlo transition-state theory is used to explore competing C–Cl and C–Br bond fission processes in a simple model of [n,π1*(CO)] photoexcited bromoacetyl chloride. Morse potentials are used to represent bond stretching coordinates, and the positions and magnitudes of nonadiabatic coupling between excited state potentials are modeled using ab initio data. The main effect of nonadiabaticity is to favor C–Cl fission over C–Br, despite a larger barrier to C–Cl dissociation. The absolute values of the rate constants are smaller than observed experimentally, but the calculated branching ratios are close to the experimental value. For C–Cl fission, it is shown that the minimum energy crossing point is not sufficient to describe the rate constant, suggesting that care must be taken when using alternative models which make this assumption.

The spin-forbidden reaction CH( 2 ∏) + N 2 → HCN + N( 4 S) revisited I. Ab initio study of the potential energy surfaces

High-level ab initio electronic structure theories have been applied to investigate the detailed reaction mechanism of the spin-forbidden reaction CH(2∏) + N2 → HCN + N(4S). The G2M(RCC) calculations provide accurate energies for the intermediates and transition states involved in the reaction, whereas the B3LYP/6-311G(d,p) method overestimates the stability of some intermediates by as much as about 10 kcal/mol. A few new structures have been found for both the doublet and quartet electronic states, which are mainly involved in the dative pathways. However, due to the higher energies of these structures, the dominant mechanism remains the one involving the C2 intersystem-crossing step. The C2 minima on the seam of crossing (MSX) structures and the spin-orbit coupling between the doublet and quartet electronic states are rather close to those found in previous studies. Vibrational frequencies orthogonal to the normal of the seam which have been applied in a separate publication to calculate the rate of the CH(2∏) + N2 → HCN + N(4S) reaction with a newly proposed nonadiabatic transition-state theory for spin-forbidden reactions have been calculated at the MSX from first principles.

Potential-energy surfaces and their dynamic implications

Accurate density functional and abinitio calculations have been performed to study the potential-energy surfaces (PESs) and their implications for kinetics and dynamics of: (1) the spin-forbidden reaction CH(2Π) +N2→HCN+N(4S); PES characteristics are calculated and used to evaluate the overall rate using non-adiabatic transition-state theory. (2) Gas-phase ion–molecule reactions: C2H2++NH3; PESs are calculated and the mechanism of efficient charge transfer and proton transfer competing with stable complex formation is discussed. C2H2++CH4; the mode-enhancement effect has been elucidated in terms of the new transition state and by direct trajectory calculations.

Nonadiabatic transition state theory and multiple potential energy surface molecular dynamics of infrequent events

Classical transition state theory (TST) provides the rigorous basis for the application of molecular dynamics (MD) to infrequent events, i.e., reactions that are slow due to a high energy barrier. The TST rate is simply the equilibrium flux through a surface that divides reactants from products. In order to apply MD to infrequent events, corrections to the TST rate that account for recrossings of the dividing surface are computed by starting trajectories at the dividing surface and integrating them backward and forward in time. Both classical TST and conventional MD invoke the adiabatic approximation, i.e., the assumption that nuclear motion evolves on a single potential energy surface. Many chemical rate processes involve multiple potential energy surfaces, however, and a number of ‘‘surface-hopping’’ MD methods have been developed in order to incorporate nonadiabatic transitions among the potential energy surfaces. In this paper we generalize TST to processes involving multiple potential energy surfaces. This provides the framework for a new method for MD simulation of infrequent events for reactions that evolve on multiple potential energy surfaces. We show how this method can be applied rigorously even in conjunction with phase-coherent surface-hopping methods, where the probability of switching potential energy surfaces depends on the history of the trajectory, so integrating trajectories backward to calculate the recrossing correction is problematic. We illustrate this new method by applying it in conjunction with the ‘‘molecular dynamics with quantum transitions’’ (MDQT) surface-hopping method to a one-dimensional two-state barrier crossing problem.

On nonadiabatic transition state theory

A nonseparable semiclassical transition state approximation for reactions involving more than one electronic surface is suggested. The single surface formulation in terms of quasiprobability distributions used by Miller is discussed along with a separable semiclassical approximation for the nonadiabatic rate suggested in the Soviet literature. A thermally averaged nonadiabatic rate is defined, and a semiclassical approximation is presented, wherein the surface through which flux is calculated in the transition state approach is determined by the intersection of adiabatic electronic surfaces viewed as functions of imaginary (or complex) time.