Chapter 1 - The energy landscape perspective: cutting a Gordian knot

A detailed analysis of experimentally obtained temperature-dependent gas-phase kinetic data for the oxygen and carbon monoxide adsorption on small anionic gold (Au(n)(-), n = 1-3), silver (Ag(n)(-), n = 1-5), and binary silver-gold (Ag(n)Au(m)(-), n + m = 2, 3) clusters is presented. The Lindemann energy transfer model in conjunction with statistical unimolecular reaction rate theory is employed to determine the bond dissociation energies E(0) of the observed metal cluster complexes with O(2) and CO. The accuracy limits of the obtained binding energies are evaluated by applying different transition-state models. The assumptions involved in the data evaluation procedure as well as possible sources of error are discussed. The thus-derived binding energies of O(2) to pure silver and binary silver-gold cluster anions are generally in excellent agreement with previously reported theoretical values. In marked contrast, the binding energies of O(2) and CO to Au(2)(-) and Au(3)(-) determined via temperature-dependent reaction kinetics are consistently lower than the theoretically predicted values.

A variety of topics is reviewed with an emphasis on assessment of models and discussion of their underlying physical assumptions, rather than on an overview of applications. Different treatments of angular momentum in the Rice-Ramsperger-Kassel-Marcus theory are surveyed and compared for tight and flexible transition states. The influence of angular momentum on thermal reaction rates is examined within the framework of variational transition state theory. The vibrational/rotational adiabatic theory of unimolecular decomposition is discussed. Various models for product energy distributions are summarized. The nature of non-thermal distributions of reactant angular momentum, arising from particular experimental techniques, is examined. A brief discussion of theoretical studies of vibrational/rotational coupling in the reactant and at the transition state is provided. The review attempts to unify advances in the fields of neutral and ion unimolecular decomposition.

A general equation is proposed for representing the kinetic functions which govern the expression of an isotope effect on the maximal velocity of an enzyme-catalyzed reaction. The origin and form of the functions are illustrated by examining a series of enzymatic mechanisms of progressively increasing complexity. The number of functions similarly increase, reaching a limit of three, with differing thermodynamic and kinetic properties. Further expansion of mechanisms causes an orderly and predictable algebraic expansion of each function, making it possible to write out, by simple inspection, the kinetic equation describing an isotope effect expressed on the maximal velocity for any enzymatic mechanism in which the isotope perturbs a single reactive step. The functions are interactive and allow for the possibility that an isotope effect on Vmax may be independent of the rate of a second, isotopically insensitive step, be it infinitely fast or slow. This allowance leads to an uncertainty of the ability of an isotope effect to detect a rate-limiting step, and the unequal distribution of kinetic and thermodynamic properties among three functions leads to an inadequacy of the singular concept of a rate-limiting step to serve as a basis for interpreting isotope effects on enzyme-catalyzed reactions. A minimal mechanism for consideration of isotope effects is proposed in order to embrace all three functions. It consists of a single catalytic step which is isotopically sensitive and reversible, two reversible precatalytic steps, and one reversible postcatalytic step, plus steps for binding and release of substrates and products.

Toward accurate and efficient dynamic computational strategy for heterogeneous catalysis: Temperature-dependent thermodynamics and kinetics for the chemisorbed on-surface CO

As a favorable alternative and complement of experimental techniques, computational tools on top of ab initio calculations have played an indispensable role in revealing the molecular details, thermodynamics and kinetics in catalytic reactions. The static computational strategy, which recovers the reaction thermodynamics and kinetics based on the calculations of a few stationary geometries at zero temperature and some ideal statistic mechanics models, is the most popular approach in theoretical catalysis due to its simplicity. In comparison, the ab initio molecular dynamics (AIMD) is a well-tested approach to provide more precise descriptions of catalytic processes, however, experiencing a significantly expensive computational cost in the direct ab initio calculation of potential energy and gradients. Here we proposed a highly efficient dynamic computational strategy for the calculation of thermodynamic and kinetic properties in heterogeneous catalysis on the basis of neural network potential energy surface (NN PES) and MD simulations. Taking CO adsorbate on Ru(0001) surface as the illustrative model catalytic system, we demonstrated that our NN-PES-based MD simulations can efficiently generate the reliable smooth two-dimensional potential-of-mean-force (2-D PMF) surfaces in a wide range of temperatures (from 300 to 900 K), and thus temperature-dependent thermodynamic properties can be obtained in a comprehensive investigation on the whole PMF surface rather than a rough estimation using ideal models based on a few optimized geometries. Moreover, MD simulations offer an effective way to describe the surface kinetics such as the CO adsorbate on-surface movement, which goes beyond the most popular static estimation based on calculated free energy barrier and transition state theory (TST). By comparing the results obtained in the dynamic and static approaches, we further revealed that the dynamic strategy significantly improves the predictions of both thermodynamic and kinetic properties as compared to the popular ideal statistic mechanics approaches such as harmonic analysis and TST. It is expected that this accurate yet efficient dynamic strategy can be a powerful tool in understanding reaction mechanisms and reactivity of a catalytic surface system, and further guides the rational design of heterogeneous catalysts.

The folding of an enzyme: I. Theory of protein engineering analysis of stability and pathway of protein folding

Sustainable methods of clean fuel production are needed in all countries in the world in the face of depleting oil reserves and the need to reduce carbon dioxide emissions. The technology on the basis of fuel cells for electricity production or transport sector is already developed. However, a key missing element is a large-scale method of hydrogen production. The Cu-Cl combined thermochemical cycle is a promising thermochemical cycle to produce cheap hydrogen in large amounts. Especially is this process interested in combination with nuclear or thermal power plants. This paper focuses on a copper-chlorine (Cu-Cl) cycle and describes the models how to calculate thermodynamic and transport properties. This paper discusses the mathematical model for computing the thermodynamic properties for pure HCl and CuCl2. The developed mathematical model for solid phase takes into account vibrations of atoms in molecules and intermolecular forces. This mathematical model can be used for the calculation of thermodynamic properties of polyatomic crystals on the basis of the Einstein and Debye equations. We developed the model in the low temperature and high temperature region. All analytical data are compared with some experimental results and show good agreement. For solid phase we have developed model for calculation of thermal conductivity on the basis of electron and phonon contributions. For fluid phase we have calculated viscosity and thermal conductivity on the basis of Chung-Lee-Starling kinetic model. For the fluid phase we have developed expressions for thermodynamic properties obtained on the basis of statistical associating fluid theory (SAFT). All these models are based on the Lennard-Jones intermolecular potential function and the influence of SAFT. On the basis of statistical thermodynamics we have taken into account translation, rotation, internal rotation, vibration energy of molecules and atoms. To calculate the thermodynamic properties of Lennard-Jones chains, I have used the Liu-Li-Lu model.Sustainable methods of clean fuel production are needed in all countries in the world in the face of depleting oil reserves and the need to reduce carbon dioxide emissions. The technology on the basis of fuel cells for electricity production or transport sector is already developed. However, a key missing element is a large-scale method of hydrogen production. The Cu-Cl combined thermochemical cycle is a promising thermochemical cycle to produce cheap hydrogen in large amounts. Especially is this process interested in combination with nuclear or thermal power plants. This paper focuses on a copper-chlorine (Cu-Cl) cycle and describes the models how to calculate thermodynamic and transport properties. This paper discusses the mathematical model for computing the thermodynamic properties for pure HCl and CuCl2. The developed mathematical model for solid phase takes into account vibrations of atoms in molecules and intermolecular forces. This mathematical model can be used for the calculation of thermodynami...

Collisional stabilization of ion-molecule association complexes in He, H2, or N2 buffer gases

Simplified models for anharmonic numbers and densities of vibrational states. II. All the bound states of HO 2

Experimental and theoretical investigations on the ultrafast photoinduced decomposition of three tert-butyl peroxides of general structure R−C(O)O−O−tert-butyl with R = phenyloxy, benzyl, or naphthyloxy in solution are presented. Photoinduced O−O bond scission occurs within the time resolution (200 fs) of the pump−probe experiment. The subsequent dissociation of photochemically excited carbonyloxy radicals, R−CO2, has been monitored on a picosecond time scale by transient absorption at wavelengths between 290 and 1000 nm. The measured decay of R−CO2 is simulated via statistical unimolecular rate theory using molecular energies, geometries, and vibrational frequencies obtained from density functional theory (DFT) calculations. The results are compared with recent data for tert-butyl peroxybenzoate (R = phenyl). While benzoyloxy radicals exhibit nanosecond to microsecond lifetimes at ambient temperature, insertion of an oxygen atom or a methylene group between the phenyl or naphthyl chromophore and the CO2 ...

Quantitative analysis of photoisomerization rates in trans-stilbene and 4-methyl-trans-stilbene

Specific rate constants k(E) of the photoisomerization of four isotopomers of trans-stilbene, of 4-chloro-(4CS) and 4-methyl-trans-stilbene (4MS), of all-trans-1,4-diphenyl-1,3-butadiene (DPB), and of 4-(dimethylamino)-4‘-cyanostilbene (DCS) are represented by conventional RRKM theory, using new ab initio calculations of excited state frequencies. Data from supersonic beam experiments are reproduced quantitatively when the barrier heights are fitted to the experiments and activated complex frequencies are taken unchanged from the parent molecules. The main difference to earlier work lies in the smaller frequencies now calculated for the reaction coordinates. The results of this work clearly support an adiabatic mechanism of the reaction which can very well be quantified by statistical unimolecular rate theory.

Rate coefficients of β-scission reactions in tertiary alkoxy radicals, R(CH3)2CO (R = methyl, ethyl, tert-butyl and neo-pentyl) have been estimated via density functional theory (DFT) calculations in conjunction with statistical unimolecular rate theory. For tert-butoxy, results obtained by employing different basis sets are compared with experimental values, indicating that UB3LYP/6-31G(d,p) excellently predicts kinetic data. Rate coefficients for inter- and intramolecular hydrogen abstraction are also reported. Depending on R, the β-scission rate may vary by orders of magnitude. The predicted temperature dependence of the alcohol-to-ketone product ratios for alkoxy radical decomposition in a hydrocarbon environment is in remarkably close agreement with the corresponding ratios measured on the product mixtures from decomposition of tert-butyl and tert-amyl peroxyacetates in solution of n-heptane.

Rate constants for the dissociation/recombination reaction N2H4 (+ M) ⇄ NH2 + NH2 (+ M) are determined by a combination of quantum-chemical calculations and statistical unimolecular rate theory. Between 1100 and 2500 K, limiting low-pressure rate constants for hydrazine dissociation in the bath gas Ar of k0 = [Ar] 6.1 × 1020 (T/1000 K)−7.3 exp (-34490 K/T) cm3 mol−1 s−1, limiting high-pressure rate constants of k∞ = 7.6 × 1016 (T/1000 K)−1.0 exp(-33600 K/T) s − 1, and center broadening factors of the falloff curves (between 1100 and 1600 K in Ar) of Fcent = 0.71 exp(- T/1460 K) + 0.29 exp(- T/21 K) + exp(-13400 K/T) were calculated. Using equilibrium constants KC = 1.7 × 103 (T/1000 K)−1.5 exp(-33,460 K/T) mol cm−3, between 300 and 600 K limiting low-pressure rate constants for the reverse recombination of NH2 radicals in the bath gas N2 of krec,0 = [N2] 4.4 × 1020(T/400 K)−6.9 exp (-1630 K/T) cm6 mol−2 s−1, limiting high-pressure rate constants of krec,∞ = 4.4 × 1013 (T/1000 K)0.44 exp(-140 K/T) cm3 mol-1 s−1, and center broadening factors (between 300 and 600 K in N2) of Fcent = exp(- T/1130 K) + exp (-10340 K/T) were obtained. A comparison with experimental results for hydrazine dissociation from the literature suggests incomplete falloff extrapolations toward k∞ and experimental problems in the determination of k0 at temperatures above about 1600 K. Implications of the present re-evaluated rate constants for the modeling of high temperature ammonia oxidation kinetics are discussed, showing an only small influence of their precise values on the overall properties of the process.

Time-resolved infrared diode laser absorption spectroscopy has been used to probe CO internal excitation following 193 nm photolysis of 300 K H2S/CO2 samples. Vibrations and rotations are colder than statistical, i.e., Eint(CO) is only ∼1500 cm−1 even though ∼10 000 cm−1 is available for product excitations, assuming modest collisional deactivation of the hot H atoms that undergo reaction. A [v=1]/[v=0] ratio of ∼0.4 is obtained and there is essentially no population at v≥2. Both the v=0 and 1 rotational distributions are cold, peaking at Jmax∼11 and 13, respectively. The vibrational distribution is nascent while the rotational distributions may be partially relaxed, but not enough to alter the main conclusions. Combined with earlier results for OH internal excitations and center-of-mass (CM) kinetic energies, we conclude that at high collision energies there is a propensity toward product CM kinetic energy. In this regime, the reaction cross section rises rapidly with energy and statistical unimolecular rate theory is not applicable, even with a HOCO° intermediate.