ALBERT

Notes: A new method for simulating the effect of outgoing-wave boundary conditions in the calculation of quantum resonances is presented. The Hermitian Hamiltonian operator H is multiplied on each side by a damping operator D, consisting of a real function d(R), which is unity in the resonance region and falls gradually to zero in the asymptotic region. The spectrum of the symmetrically damped Hamiltonian operator, DHD is shown to provide an excellent approximation to the resonance energies of the Hamiltonian with outgoing-wave boundary conditions. Applications to the calculation of resonance energies for collinear H+H2 scattering and for HO2 dissociation are presented. In addition, we explore the feasibility of extracting resonance widths by using the DHD operator within a filter diagonalization (FD) scheme. Application of the FD scheme to HO2 yields encouraging results. © 1997 American Institute of Physics.

Notes: Transition state theory (TST) approximates the reactive flux in an elementary chemical reaction by the instantaneous flux passing through a hypersurface (the "transition state") which completely divides the reactant and product regions of phase space. The rigorous classical evaluation of this instantaneous flux is carried out as a trace in phase space: effectively a multidimensional integral. We present an analysis of the momentum-space component of this flux integral for the case of a generalized reaction coordinate. The classic analysis of the canonical flux by Marcus [J. Chem. Phys. 41, 2624 (1964)] is refined by reducing the determinant which appears in the transition state partition function to a very simple form, facilitating the ensuing integration over coordinate space. We then extend the analysis to provide analytic expressions for the momentum flux integrals in both the energy-resolved, and the energy+angular-momentum-resolved microcanonical ensembles. These latter expressions allow substantial gains in the efficiency of microcanonical variational implementations of Transition State Theory with generalized reaction coordinates. © 1999 American Institute of Physics.

Notes: It has been shown that an approximately band-limited function can be reconstructed by using the function's values taken at appropriate equidistant grid points and a generalized Hermite-contracted-continuous-distributed-approximating-function (Hermite-CCDAF) as the reconstruction function. A sampling theorem prescribing the possible choices of grid spacing and DAF parameters has been derived and discussed, and discretized-Hermite-contracted DAFs have been introduced. At certain values of its parameters the generalized Hermite-CCDAF is identical to the Shannon–Gabor-wavelet-DAF (SGWDAF). Simple expressions for constructing the matrix of a vibrational Hamiltonian in the discretized-Hermite-contracted DAF approximation have been given. As a special case the matrix elements corresponding to sinc-DVR (discrete variational representation) are recovered. The usefulness and properties of sinc-DVR and discretized-Hermite-contracted-DAF (or SGWDAF) in bound state calculations have been compared by solving the eigenvalue problem of a number of one- and two-dimensional Hamiltonians. It has been found that if one requires that the same number of energy levels be computed with an error less than or equal to a given value, the SGWDAF method with thresholding is faster than the standard sinc-DVR method. The results obtained with the Barbanis Hamiltonian are described and discussed in detail. © 1999 American Institute of Physics.

Notes: The potential energy surface of the NH2+NO reaction, which involves nine intermediates (1–9) as well as twenty-three possible transition states (a–w), has been fully characterized at the B3LYP/cc-pVQZ//B3LYP/6-311G(d,p)+ZPE[B3LYP/6-311G(d,p)] and modified Gaussian-2 (G2M) levels of theory. The reaction is shown to have three different groups of products (HN2+OH, N2O+H2, and N2+H2O denoted as A, B, and C, respectively) and a very complicated reaction mechanism. The first reaction path is initiated by the N–N bond association of the reactants to form an intermediate H2NNO, 1, which then undergoes a 1,3-H migration to yield an isomer pair HNNOH (2,3) (separated by a low energy torsional barrier) which can then proceed along three different paths. Because of the essential role it would play kinetically, the enthalpy of the NH2+NO→HN2+OH reaction has been further investigated using various levels of theory. The best theoretical results of this study predicted it to be 0.9 and 2.4 kcal mol−1 at the B3LYP and CCSD(T) levels, respectively, using a relatively large basis set (AUG-cc-pVQZ) based on the geometry optimized at the B3LYP/6-311G(d,p) level of theory. It has been found that TS g(4→B) is expected to be the rate-determining transition state responsible for the NH2+NO→N2O+H2 reaction. TS g lies above the reactants by only 2.6 kcal mol−1 according to the G2M prediction. On the other hand, TS h(3→7) is a new transition state discovered in this work which may allow some kinetic contribution from the NH2+NO→N2+H2O reaction under high temperature conditions due to its relatively low energy as well as its loose transition state property. A modified G2 additivity scheme based on the G2(DD) approach has been shown to be necessary for better predicting the energetics for TS h, which gives a value of 2.3 kcal mol−1 in energy with respect to the reactants. Generally, the cost-effective B3LYP method is found to give very good predictions for the optimized geometries and vibrational frequencies of various species in the system if compare them with those optimized at the QCISD/6-311G(d,p) and 12-in-11 CASSCF/cc-pVDZ levels of theory. Furthermore, it is noticeable in this study that most of the relative energies calculated via the B3LYP method are more close to the G2M results than those predicted at the PMP4 and CCSD(T) levels using the same 6-311G(d,p) basis set. © 1997 American Institute of Physics.

Notes: The ion–molecule association system (CH+3/CH3CN) has been reexamined by the ion cyclotron double resonance technique. An experimental distribution of lifetimes has been measured for the collision complex (CH3CNCH+3)* formed in the association reaction between CH+3 and CH3CN. The experimental mean lifetime of the association complex formed within the ICR cell was 140 μs. A theoretical examination of the distribution of complex lifetimes using an RRKM model was also undertaken. The matrix of lifetimes for the various values of the total energy of the system (E) and the total angular momentum of the system (J) was obtained. This information was used to visualize the canonical ensemble of collision complexes in the ICR experiment in terms of their lifetimes. Once the distribution of lifetimes predicted by the model was modified to conform to experimental constraints, it was found to give a good approximation of the lifetime distribution determined experimentally. As a result of the new measurements of the complex lifetimes, we report absolute values of the collisional stabilization efficiencies. We also report rate coefficients for unimolecular dissociation and radiative relaxation.

Notes: An efficient Lanczos subspace method has been devised for calculating state-to-state reaction probabilities. The method recasts the time-independent wave packet Lippmann–Schwinger equation [Kouri et al., Chem. Phys. Lett. 203, 166 (1993)] inside a tridiagonal (Lanczos) representation in which action of the causal Green's operator is affected easily with a QR algorithm. The method is designed to yield all state-to-state reaction probabilities from a given reactant-channel wave packet using a single Lanczos subspace; the spectral properties of the tridiagonal Hamiltonian allow calculations to be undertaken at arbitrary energies within the spectral range of the initial wave packet. The method is applied to a H+O2 system (J=0), and the results indicate the approach is accurate and stable. © 2002 American Institute of Physics.

Notes: Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O2 show strong fluctuations, indicating the dissociation of HO2 is essentially irregular. © 2001 American Institute of Physics.

Notes: A new solution to the master equation relating the rate coefficients for unimolecular, recombination (association) and chemical activation reactions, incorporating weak collision effects, is presented. The solution establishes conditions for the validity of the commonly used procedure of relating the recombination rate coefficient, throughout the falloff regime, to the reverse single-channel unimolecular rate coefficient via the equilibrium constant. In addition, a relationship between the rate coefficient for stabilization in a chemical activation reaction and the reverse multichannel unimolecular dissociation rate coefficient is derived. This result, in conjunction with recently developed methods for fully incorporating angular momentum conservation into the solution of the master equation for unimolecular dissociation, enables both angular momentum and weak collision effects to be accurately incorporated into the solution of the master equation for chemical activation reactions in the falloff regime. Application of this method to a typical ion/molecule chemical activation reaction, that of CH+3 with NH3, illustrates the importance of weak collision and angular momentum effects in this system.

Notes: The classical evaluation of the angular-momentum-resolved sum of states for the loosely hindered rotational degrees of freedom, i.e., the transitional modes, in loose transition states occurring in unimolecular dissociation, radical–radical recombination, ion–molecule, and other collision-complex-forming bimolecular reactions is considered. Exact analytic expressions are derived for the momentum-space volume available to the transitional modes at a given configuration q with energy E and total angular momentum vector J. The results are completely general with respect to the type of fragment rotors involved and their relative orientation within the loose transition state, and constitute a dramatically simplified technique for J-resolved classical state counting. The utility of the expressions lies in the fact that they obviate the necessity of numerical integration over the system's momentum space, thus reducing substantially the computational effort involved in the exact evaluation of the transitional-mode sum of states. The present results verify expressions which were postulated to apply to arbitrary configurations in our earlier work.