Theoretical study of intramolecular vibrational relaxation of acetylenic CH vibration for v=1 and 2 in large polyatomic molecules (CX3)3YCCH, where X=H or D and Y=C or Si

Quantum calculations are reported for the intramolecular vibrational energy redistribution and absorption spectra of the first two excited states of the acetylenic CH stretch vibration in the polyatomic molecules (CX3)3YCCH, where X=H or D and Y=C or Si. Using approximate potential energy surfaces, comparison is made with the corresponding recent experimental spectra. It is found that a model of intramolecular vibrational relaxation based on the assumption of sequential off-resonance transitions via third and fourth order vibrational couplings (as opposed to direct high order couplings) is in agreement with experimental results on spectral linewidths. In a semiclassical limit this type of relaxation corresponds to a dynamic tunneling in phase space. It is shown that the local density of resonances of third and fourth order, rather than the total density of states, plays a central role for the relaxation. It is found that in the Si molecule an accidental absence of appropriate resonances results in a bottleneck in the initial stages of relaxation. As a result, an almost complete localization of the initially prepared excitation occurs. It is shown that an increase of the mass alone of the central atom from C to Si cannot explain the observed difference in the C and Si molecules. The spectral linewidths were calculated with the Golden Rule formula after prediagonalization of the relevant vibrational states which are coupled in the molecule to the CH vibration, directly or indirectly. For the spectral calculations, in addition to the direct diagonalization, a modified recursive residue generation method was used, allowing one to avoid diagonalization of the transformed Lanczos Hamiltonian. With this method up to 30 000 coupled states could be analyzed on a computer with relatively small memory. The efficiency of C programming language for the problem is discussed

On the Analytical Mechanics of Chemical Reactions. Quantum Mechanics of Linear Collisions

The analytical quantum mechanics of chemically reactive linear collisions is treated in the vibrationally near‐adiabatic approximation. The "reaction coordinate" in this approximation is found to be the curve on which the classical local vibrational and internal centrifugal forces balance. Expressions are obtained for the calculation of transmission coefficients for these nonseparable systems. Some implications for tunneling calculations in the literature are noted. Expressions for nonadiabatic corrections are derived, the latter being associated with vibrational transitions undergone by the transmitted and reflected waves. When the system does not have enough energy to react, the last results refer to the vibration—translation energy‐transfer problem in linear collisions. Two novel features are the introduction of an actual coordinate system which passes smoothly from one suited to reactants to one suited to products and the introduction of an adiabatic‐separable method, a method which includes curvilinear effects. Extensions to collisions in higher dimensions are given in later papers

Photochemical Studies in Flash Photolysis. III. Photolysis of Acetone in Different Wavelength Regions

The flash photolysis of acetone was studied at wavelength regions centered around 260, 280, and 300 mμ, using absorbed intensities of the order of 10^(19) quanta/cc/sec for each wavelength region. The light source was an exploding wire, and the maximum temperature increase per flash was calculated to be not more than 5°C. The products, analyzed by gas chromatography using a sensitive electric discharge detector, consisted of C_2H_6, CO, biacetyl, and, in smaller amounts, CH_4. A search was made for other products as well, and detection limits are given. The C_2H_6/CO ratio decreased with increasing acetone pressure at all wavelength regions and was independent of light intensity in the range investigated. The R_(CO)/p_(acet) ratio, measured over a wide pressure range, was pressure‐independent at 260 and 300 mμ but increased appreciably with pressure at 280 mμ. At low pressures, where the C_2H_6/CO ratio approached a limiting value, the ratio decreased with wavelength according to the order 280>260>300 mμ. The lifetime of the excited acetone molecules at the respective wavelengths was estimated, from a steady‐state treatment, to be 0.6×10^(—9), 1×10^(—9), and 4×10^(—9) sec at 260, 280, and 300 mμ, assuming a collision deactivation efficiency of unity. At 300 mμ there was a marked difference in value of C_2H_6/CO at flash and low intensities: certain second‐order reactions involving excited states appear to occur completely at the relatively high concentrations prevailing under flash conditions. The transition region of intensity effects is described in subsequent papers of this series

Free Energy of Non equilibrium Polarization Systems. III. Statistical Mechanics of Homogeneous and Electrode Systems

A statistical mechanical treatment is given for homogeneous and electrochemical systems having nonequilibrium dielectric polarization. A relation between the free energy of these systems and those of related equilibrium ones is deduced, having first been derived in Part II by a dielectric continuum treatment. The results can be applied to calculating polar contributions in the theory of electron transfers and in that of shifts of electronic spectra in condensed media. The effect of differences in polarizability (of a light emitting or absorbing molecule in its initial and final electronic states) on the polar term in the shift is included by a detailed statistical analysis, thereby extending Part II. Throughout, the "particle" description of the entities contributing to these phenomena is employed, so as to derive the results for rather general potential energy functions

Enzymatic catalysis and transfers in solution. I. Theory and computations, a unified view

The transfer of hydride, proton, or H atom between substrate and cofactor in enzymes has been extensively studied for many systems, both experimentally and computationally. A simple equation for the reaction rate, an analog of an equation obtained earlier for electron transfer rates, is obtained, but now containing an approximate analytic expression for the bond rupture-bond forming feature of these H transfers. A "symmetrization," of the potential energy surfaces is again introduced [R. A. Marcus, J. Chem. Phys. 43, 679 (1965); J. Phys. Chem. 72, 891 (1968)], together with Gaussian fluctuations of the remaining coordinates of the enzyme and solution needed for reaching the transition state. Combining the two expressions for the changes in the difference of the two bond lengths of the substrate-cofactor subsystem and in the fluctuation coordinates of the protein leading to the transition state, an expression is obtained for the free energy barrier. To this end a two-dimensional reaction space (m,n) is used that contains the relative coordinates of the H in the reactants, the heavy atoms to which it is bonded, and the protein/solution reorganization coordinate, all leading to the transition state. The resulting expression may serve to characterize in terms of specific parameters (two "reorganization" terms, thermodynamics, and work terms), experimental and computational data for different enzymes, and different cofactor-substrate systems. A related characterization was used for electron transfers. To isolate these factors from nuclear tunneling, when the H-tunneling effect is large, use of deuterium and tritium transfers is of course helpful, although tunneling has frequently and understandably dominated the discussions. A functional form is suggested for the dependence of the deuterium kinetic isotope effect (KIE) on DeltaG° and a different form for the 13C KIE. Pressure effects on deuterium and 13C KIEs are also discussed. Although formulated for a one-step transfer of a light particle in an enzyme, the results would also apply to single-step transfers of other atoms and groups in enzymes and in solution

Semiclassical S-matrix theory. VI. Integral expression and transformation of conventional coordinates

Sometimes, as in reactive systems, action‐angle variables are not conveniently defined at all points of the trajectory and recourse must be made to conventional coordinates. A simple canonical transformation converts the latter to coordinates of which one is time and the remainder are constant along the trajectory. The transformation serves to remove the singularities of the semiclassical wavefunction at the turning points of the trajectory. It yields, thereby, an integral expression for the S matrix by having produced wavefunctions which can be integrated over all space. The result supplements that of Paper III [R. A. Marcus, J. Chem. Phys. 56, 311 (1972)], which was derived for systems for which action‐angle variables could be defined throughout the collision