A test of RRKM theory against numerical simulation for classical chain molecules. II. Decomposition and vibrational relaxation in uniform chains

Deviations from RRKM predictions for the fragmentation of a one-dimensional chain molecule are here studied in detail by numerical simulation and related to the rate of the vibrational relaxation. A measure of the degree of completion of vibrational relaxation is constructed, and its time development followed and compared with the progress of the reaction. The vibrational relaxation is initially rapid but then slows down as the reaction depletes the ensemble of rapidly relaxing trajectories. The observed decay rate starts from the RRKM value and then typically exceeds it at intermediate times crossing over to fall below the RRKM prediction at long times.     

A test of RRKM theory against numerical simulation for classical chain molecules. I. Method and preliminary results

A systematic investigation of the internal part of the unimolecular reaction dynamics of one-dimensional chain molecules has been undertaken to examine the validity of RRKM theory. The basic aims, means and scope of this program of research are reported here together with results for uniform chains. Classical mechanics is used and the atoms in the chain interact by Morse pair potentials acting between neighbouring particles. The simulation method described here consists of a very efficient Monte Carlo sampling of microcanonical initial states coupled with a predictor-corrector molecular dynamics algorithm. Time-dependent and best fitting time-independent decay rate coefficients can be extracted from the set of lifetimes to dissociation observed in the simulation. These are then compared to the corresponding rate coefficients predicted by the usual form of RRKM theory where anharmonic contributions ot the density of states are neglected or to a more rigorous implementation where the anharmonic contributions are accounted for. Calculations for uniform chains reported here establish a pattern of deviations from RRKM prediction which will be explored and explained in greater detail in this program of research.     

Time-dependent quantum theory III. Model for vibrational relaxation in crystals

A one-dimensional model consisting of a “diatomic” spring attached on one side to a rigid wall and on the other side to a linear array of mass-springs is proposed as a model for the vibrational relaxation of small solute molecules in host lattices. A modification allowing a change in the equilibrium internuclear extension of the diatomic spring is also incorporated. The Hamiltonian divides naturally into pure diatomic, pure linear crystal, and the two mixed perturbation terms, one giving rise to stepwise vibrational cascade damping accompanied by phonon emission, and the other process, lattice relaxation, giving rise to phonon emission without any change of the quantum number of the diatomic spring. The cascade damping rate for a diatomic spring with a frequency less than the the maximum frequency of the linear crystal is calculated to second-order, and it is shown that the perturbation series converges in this range. An upper bound to the cascade damping rate for a diatomic spring with a frequency greater (i.e., 4.5 ×) than the cut-off frequency of the linear crystal is determined to be very small, λ ≦ 10⁴ sec ^?;1. The rate for the lattice relaxation process corresponds to a line-width λ = 6 cm ^?1 at ⁰K. An explanation for the thermal quenching of the low-temperature luminescence of SO₂ is based upon induced cascade-phonon emission.     

Perturbation theory for excited states of molecules. III

The configuration interaction perturbation theory and the single configuration perturbation theory developed in Paper I is applied to the problem of chemical reactivity for conjugated hydrocarbon molecules. Various related hetromolecules are also considered. It is found that the pattern of reactivity for excited states is much the same as for the ground state.I wish to express my appreciation to Dr. A. T. Amos for constant encouragement during the preparation of this paper and to the S.R.C. for the provision of a maintenance grant.     

Coupled‐cluster theory for the polarizable continuum model. III. A response theory for molecules in solution

A coupled‐cluster (CC) response functions theory for molecular solutes described with the framework of the polarizable continuum model (PCM) is presented. The theory is an extension to the dynamical molecular properties of the PCM‐CC analytic derivatives recently proposed for the calculation of static molecular properties (Cammi, Jr Chem Phys 2009, 131, 164104). The theory is presented for linear and quadratic response functions, and the operative expressions of these response functions can accurately account for the nonequilibrium solvation effects. The excitation energies and transition moments of the solvated chromophores have been determined from the linear response functions. Accurate expressions for gradients of excitation energies for the evaluation of the excited state properties have been also discussed. © 2012 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

A second-order perturbation theory route to vibrational averages and transition properties of molecules: general formulation and application to infrared and vibrational circular dichroism spectroscopies

A general formulation to compute anharmonic vibrational averages and transition properties at the second-order of perturbation theory is derived from the Rayleigh-Schro?dinger development. This approach is intended to be applicable to any property expanded as a Taylor series up to the third order with respect to normal coordinates or their associated momenta. The equations are straightforward to implement and can be easily adapted to various properties, as illustrated for the case of electric and magnetic dipole moments. From those, infrared and vibrational circular dichroism spectra can be readily obtained. This fully automatic procedure has been applied to several chiral molecules of small-to-medium sizes and compared to the standard double harmonic approximation and to experimental data.     

Monte Carlo simulation of RRKM unimolecular decomposition in molecular beam experiments. III. Application to angular distributions and branching fractions for the system K + CsF

The experiments on the reactive systems K + CsF and K + RbF by Stolte et al. are unique in that product angular distributions and branching fractions with variation of both translational and rotational energies have been obtained. The results for the reaction K + CsF with translational energy variation have now been re-evaluated using an algorithm recently published by us. A satisfactory fit to the experimental data is found by a long-lived collision complex model including strict angular momentum conservation in both the reactive and the non-reactive channels. No “osculating” behaviour has to be added to the model. Angular momentum limits have to be included in the model to reach agreement with the measured branching fractions and cross sections. This indicates that the internal dynamics of the complexes is important. The calculation shows that the reactants giving reactive complexes have large rotational and vibrational energies, while their translational energy is nearly average. The internal energy of reactive pairs of molecules decreases with increasing translational energy. The question how rapidly the branching fraction varies with translational energy is thus more complicated to answer than believed previously.     

A new method to calculate overlap integrals of vibrational wave functions in the theory of vibronic spectra of polyatomic molecules

An approximate method to calculate overlap integrals of vibrational wave functions of combined electron states is proposed. It uses reducibility of the general transformation of normal coordinates and quasiorthogonality of the Dushinsky matrix. Simple analytical expressions and convenient recurrent relations for the desired integrals of Franck-Condon and Herzberg-Teller types are found. The errors of calculation are of the same order as those of the existing “accurate” methods (≤5%), and the speed of calculation is higher by more than two orders. The study was carried out under financial support of the Russian Fundamental Research Fund (93-02-3405). K. A. Timiryazev Moscow Agricultural Academy. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 2, pp. 16–23, March–April, 1994. Translated by L. Chernomorskaya     

Optical activity of oriented molecules III. The absorption process and the vibrational coupling effects for the tensor of rotation

Equations for the rotation and the ellipticity of samples exhibiting linear and circular birefringence and dichroism (i.e. for small elliptical birefringence and dichroism) are given. By this a second presentation of the frequency dependence for linear and circular birefringence of anisotropic solutions is developed. The absorption coefficients of anisotropic solutions for linearly polarized light are calculated from the H-matrix of Gō. For a special type of orientational distribution function the absorption behaviour is analysed. Within the adiabatic approximation and by neglecting the variation of the electronic transition moments with the nuclear distances, the structure of a circular dichroism band is independent of the orientational distribution function. Empirically, this is not the case for α, β-unsaturated keto steroids. By including this variation in the adiabatic approximation the coordinates of the tensor of rotation R^NnKk_ij are altered by different amounts due to the coupling by vibrations of the involved states with other electronic states of the system (Herzberg-Teller method). As a consequence of this coupling electric dipole and magnetic dipole/electric quadrupole transition moments not belonging to the observed transition |K⁰> ← |N⁰> are added to the zeroth order tensor of rotation R^NK_ij. Le., first order tensor of rotation R^LM/PR_ij = $\text{1}\text{4}$ <μ_k>_LM|ε_kli <C_tj>_PR + ε_klj<C_lj>_PR}, multiplied by a mixing parameter depending on the type of vibration have to be added to R^NK_ij. As a consequence, the structure of the CD band will depend on the orientational distribution function. The model developed is demonstrated for molecules with symmetry D₂.     

Methanol in its own gravy. A PCM study for simulation of vibrational spectra

For studying both hydrogen bond and dipole-dipole interactions between methanol molecules (self-association) the geometry of clusters of increasing numbers of methanol molecules (n = 1,2,3) were optimized and also their vibrational frequencies were calculated with quantum chemical methods. Beside these B3LYP/6-311G** calculations, PCM calculations were also done for all systems with PCM at the same quantum chemical method and basis set, for considering the effect of the liquid continuum on the cluster properties. Comparing the results, the measured and calculated infrared spectra are in good accordance.     

A self-consistent molecular field theory for aggregates of neutral molecules. I

A self-consistent theory is presented for aggregates of neutral molecules. According to the LCAO Hartree-Fock formalism a set of effective Hartree-Fock equations for molecules in the aggregate is derived. The molecular orbitals of each molecule are to be determined from the effective H-F equation for the molecule in which the interactions between the molecule and the surrounding ones are included as an intermolecular interaction field (molecular field). A self-consistent treatment leads to the molecular orbitals which are self-consistent with the molecular field. By this method, then-molecule problem becomesn times of one-molecule problem.     

A study of molecular vibrational relaxation mechanism in condensed phase based upon mixed quantum-classical molecular dynamics. I. A test of IBC model for the relaxation of a nonpolar solute in nonpolar solvent at high density

In order to investigate vibrational relaxation mechanism in condensed phase, a series of mixed quantum-classical molecular dynamics calculations have been executed for nonpolar solute in nonpolar solvent and polar solute in polar solvent. In the first paper (Paper I), relaxation mechanism of I2 in Ar, where Lennard-Jones force is predominant in the interaction, is investigated as a function of density and temperature, focusing our attention on the isolated binary collision (IBC) model. The model was originally established for the relaxation in gas phase. A key question, here, is "can we apply the IBC model to the relaxation in the high-density fluid?" Analyzing the trajectory of solvent molecule as well as its interaction with the solute, we found that collisions between them may be defined clearly even in the high-density fluid. Change of the survival probability of the vibrationally first excited state on collision was traced. The change caused by collisions with a particular solvent molecule was also traced together with the interaction between them. Each collision makes a contribution to the relaxation by a stepwise change in the probability. The analysis clearly shows that the relaxation is caused by collisions even in the high-density fluid. The difference between stepwise relaxation and the continuous one found for the total relaxation in the low-density fluid and in the high-density one, respectively, was clarified to come from just the difference in frequency of the collision. The stronger the intensity of the collision is, the greater the relaxation caused by the collision is. Further, the shorter the collision time is, the greater the resultant relaxation is. The discussion is followed by the succeeding paper (Paper II), where we report that molecular mechanism of the relaxation of a polar molecule in supercritical water is significantly different from that assumed in the IBC model despite that the density dependence of the relaxation rate showed a linear correlation with the local density of water around the solute, the linear correlation being apparently in good accordance with the IBC model. The puzzle will be solved in Paper II.     

Applications of molecular orbital theory to the interpretation of mass spectra. Prediction of primary fragmentation sites in organic molecules

Semi-empirical molecular orbital calculations have been carried out on the steroidal hormone estrone, both as a neutral molecule and the corresponding positively charge molecular ion. These calculations provide estimates of bond densities and net atomic charges, factors deemed important in past correlations of observed mass spectra with molecular structure. Calculated net charges appear to be unrelated to fragmentation processes. Calculated bond densities of the ground state molecular ion of estrone allow prediction of gross features of fragmentation. Bond densities of excited electronic states of the molecular ion may provide a basis for finer distinction among sites of initial bond cleavage, which is information crucial to rationalization of subsequent fragmentation of the molecular ion.     

Equation of state for square-well chain molecules with variable range II. Extension to mixtures

An equation of state (EOS) developed in our previous work for square-well chain molecules with variable range is further extended to the mixtures of non-associating fluids. The volumetric properties of binary mixtures for small molecules as well as polymer blends can well be predicted without using adjustable parameter. With one temperature-independent binary interaction parameter, satisfactory correlations for experimental vapor–liquid equilibria (VLE) data of binary normal fluid mixtures at low and elevated pressures are obtained. In addition, VLE of n-alkane mixtures and nitrogen + n-alkane mixtures at high pressures are well predicted using this EOS. The phase behavior calculations on polymer mixture solutions are also investigated using one-fluid mixing rule. The equilibrium pressure and solubility of gas in polymer are evaluated with a single adjustable parameter and good results are obtained. The calculated results for gas + polymer systems are compared with those from other equations of state.     

A theory of molecules in molecules IV. Application to the Hydrogen Bonding Interaction in NH3 · H2O

The theory of molecules in molecules introduced in previous articles is applied to study the hydrogen bonding interaction between an ammonia molecule as proton acceptor and a water molecule as proton donor. The localized orbitals which are assumed to be least affected by the formation of the hydrogen bond are transferred unaltered from calculations on the fragments NH₃ and H₂O, the remaining orbitals are recalculated. A projection operator is used to obtain orthogonality to the transferred orbitals. Additional approximations have been introduced in order to be able to save computational time. These approximations can be justified and are seen to lead to binding energies and bond lengths which are in satisfactory agreement with the SCF values. The point charge approximation for the calculation of the interaction energy between the two sets of transferred localized orbitals is, however, not applicable in this case. An energy analysis of the effect of the hydrogen bond on the localized orbitals of the two fragments is given.     

The relaxation of the double layer around colloidal particles and the low-frequency dielectric dispersion: Part III. Application of theory to experiments

A theory for the dielectric relaxation of homodisperse colloids, derived in Part I of this series, has been applied to the experimental results reported in Part II. The main prediction of the theory, namely that double-layer polarization is dominated by that of the diffuse part of the double layer over that of the bound ions, has been confirmed both with respect to the relaxation time and the low-frequency dispersion. Quantitative agreement is obtained for the relaxation time but not for the dielectric increment. The reason for the discrepancy is probably a slight aggregation of the latex particles in addition to some peculiarities in the ion binding mechanisms.     

A compact time-of-flight mass spectrometer for the structural analysis of biological molecules using laser desorption.

A compact laser-desorption time-of-flight mass spectrometer using a 600 ps nitrogen laser and 1 Gsample/s transient recorder is described. The instrument incorporates two electrically-isolatable, reflecting flight tubes designed for subsequent configuration of the mass spectrometer as a tandem instrument. In this first report, we compare mass resolution in the laser-desorption mass spectra of an organic dye, sinapinic and caffeic acid matrices, and several small peptides. For directly desorbed ions, peak widths are generally of the order of 11 to 13 ns, so that mass resolution increases with increasing mass. For peptide ions in the range of 500 to 1000 u, formed by matrix-assisted desorption, peak widths range from 9.5 to 17.6 ns and increase with mass. However, better than unit mass resolution (1600 to 2400) is maintained throughout this mass range. Mass measurement accuracy is better than 0.1 u using a single calibration peak and a prompt start trigger pulse. Prospects for extending mass range and resolution are discussed.