Unimolecular rovibrational bound and resonance states for large angular momentum: J=20 calculations for HO2

We explore the calculation of unimolecular bound states and resonances for deep-well species at large angular momentum using a Chebychev filter diagonalization scheme incorporating doubling of the autocorrelation function as presented recently by Neumaier and Mandelshtam [Phys. Rev. Lett. 86, 5031 (2001)]. The method has been employed to compute the challenging J=20 bound and resonance states for the HO2 system. The methodology has firstly been tested for J=2 in comparison with previous calculations, and then extended to J=20 using a parallel computing strategy. The quantum J-specific unimolecular dissociation rates for HO2-->H+O2 in the energy range from 2.114 to 2.596 eV have been reported for the first time, and comparisons with the results of Troe and co-workers [J. Chem. Phys. 113, 11019 (2000) Phys. Chem. Chem. Phys. 2, 631 (2000)] from statistical adiabatic channel method/classical trajectory calculations have been made. For most of the energies, the reported statistical adiabatic channel method/classical trajectory rate constants agree well with the average of the fluctuating quantum-mechanical rates. Near the dissociation threshold, quantum rates fluctuate more severely, but their average is still in agreement with the statistical adiabatic channel method/classical trajectory results.     

HO2 ro-vibrational bound-state calculations for large angular momentum: J = 30, 40, and 50

The Lanczos homogeneous filter diagonalization method and the real Chebyshev filter diagonalization scheme incorporating doubling of the autocorrelation functions have been employed to compute the HO2 ro-vibrational states for high total angular momenta, J = 30, 40, and 50. For such computationally challenging calculations, we have adopted a parallel computing strategy to perform the matrix-vector multiplications. Low-lying bound states and high-lying bound states close to the dissociation threshold are reported. For low-lying bound states, a spectroscopic assignment has been attempted and the widely used approximate J-shifting method has been tested for this deep-well system. For high-lying bound states, the attempted spectroscopic assignments as well as the J-shifting approximation fail because of very strong Coriolis mixing, indicating that the Coriolis couplings are important for this system.     

Quantum mechanical rate constants for H + O2 <--> O + OH and H + O2 --> HO2 reactions

Canonical rate constants for both the forward and reverse H + O(2) <--> O + OH reactions were calculated using a quantum wave packet-based statistical model on the DMBE IV potential energy surface of Varandas and co-workers. For these bimolecular reactions, the results show reasonably good agreement with available experimental and theoretical data up to 1500 K. In addition, the capture rate for the H + O(2) --> HO(2) addition reaction at the high-pressure limit was obtained on the same potential using a time-independent quantum capture method. Excellent agreement with experimental and quasi-classical trajectory results was obtained except for at very low temperatures, where a reaction threshold was found and attributed to the centrifugal barrier of the orbital motion.     

Four-mode quantum calculations of resonance states in complex-forming bimolecular reactions: C- + CH3Br

The vibrational resonance states of the complexes formed in the nucleophilic bimolecular substitution (S(N)2) reaction Cl(-)+CH(3)Br-->ClCH(3)+Br(-) were calculated by means of the filter diagonalization method employing a coupled-cluster potential-energy surface and a Hamiltonian that incorporates an optical potential and is formulated in Radau coordinates for the carbon-halogen stretching modes. The four-dimensional model also includes the totally symmetric vibrations of the methyl group (C-H stretch and umbrella bend). The vast majority of bound states and many resonance states up to the first overtone of the symmetric stretching vibration in the exit channel complex have been calculated, analyzed, and assigned four quantum numbers. The resonances are classified into entrance channel, exit channel, and delocalized states. The resonance widths fluctuate over six orders of magnitude. In addition to a majority of Feshbach-type resonances there are also exceedingly long-lived shape resonances, which are associated with the entrance channel and can only decay by tunneling. The state-selective decay of the resonances was studied in detail. The linewidths of the resonances, and thus the coupling to the energetic continuum, increase with excitation in any mode. Due to the strong mixing of the many progressions in the intermolecular stretching modes of the intermediate complexes, this increase as a function of the corresponding quantum numbers is not monotonic, but exhibits pronounced fluctuations.     

A new ab initio potential-energy surface of HO2(X2A") and quantum studies of HO2 vibrational spectrum and rate constants for the H + O2 <--> O + OH reactions

A new global potential-energy surface for the ground electronic state of HO(2)(X(2)A(")) has been developed by three-dimensional cubic spline interpolation of more than 15 000 ab initio points, which were calculated at the multireference configuration-interaction level with Davidson correction using the augmented correlation-consistent polarized valence quadruple zeta basis set. Low-lying vibrational states were obtained in this new potential using the Lanczos method and assigned. The calculated vibrational frequencies are in much better agreement with the available experimental band origins than those obtained from a previous potential. In addition, rate constants for the H+O(2) <--> O + OH reactions were obtained using a wave-packet-based statistical model. Reasonably good agreement with experimental data was obtained. These results demonstrate the accuracy of the potential.     

Complex autocorrelation function and energy spectrum by classical trajectory calculations

A quasiclassical method which enables evaluation of complex autocorrelation function from classical trajectory calculations is proposed. The method is applied for two highly excited nonlinearly coupled harmonic oscillators in regimes prevailed either by regular or chaotic classical motions. A good agreement of classical and quantum autocorrelation functions is found within short (Ehrnfest) time limit. Fourier transforms of the autocorrelation functions provide moderate resolved energy spectra, where classical and quantum results nearly coincide. The actual energy levels are obtained from approximate short-time autocorrelation functions with the help of filter diagonalization. This study is a follow up to our previous work [P. Zdanska and N. Moiseyev, J. Chem. Phys. 115, 10608 (2001)], where the complex autocorrelation has been obtained up to overall phase factors of recurrences.     

Rate constant for OH(2 Pi)+O(3P)-->H(2S)+O2(3 Sigma g-) reaction on an improved ab initio potential energy surface and implications for the interstellar oxygen problem

The authors report a global potential energy surface for the ground electronic state of HO(2)(X (2)A(")), which improves upon the XXZLG potential [Xu and et al., J. Chem. Phys. 122, 244305 (2005)] with additional high-level ab initio points for the long-range interaction potential in the O+OH channel. Exact J=0 quantum mechanical reaction probabilities were calculated on the new potential and the rate constant for the title reaction was obtained using a J-shifting method. The calculated rate constant is in good agreement with available experimental values and our results predict a significantly lower rate at temperature range below 30 K, offering a possible explanation for the "interstellar oxygen problem."     

Potential energy surface and quantum dynamics study of rovibrational states for HO(3) (X (2)A')

An analytic potential energy surface has been constructed by fitting to about 28 thousand energy points for the electronic ground-state (X (2)A') of HO(3). The energy points are calculated using a hybrid density functional HCTH and a large basis set aug-cc-pVTZ, i.e., a HCTH/aug-cc-pVTZ density functional theory (DFT) method. The DFT calculations show that the trans-HO(3) isomer is the global minimum with a potential well depth of 9.94 kcal mol(-1) with respect to the OH + O(2) asymptote. The equilibrium geometry of the cis-HO(3) conformer is located 1.08 kcal mol(-1) above that of the trans-HO(3) one with an isomerization barrier of 2.41 kcal mol(-1) from trans- to cis-HO(3). By using this surface, a rigorous quantum dynamics (QD) study has been carried out for computing the rovibrational energy levels of HO(3). The calculated results determine a dissociation energy of 6.15 kcal mol(-1), which is in excellent agreement with the experimental value of Lester et al. [J. Phys. Chem. A, 2007, 111, 4727.].     

High level ab initio study of the structure and vibrational spectra of HO(2)NO(2)

A high-level ab initio study has been performed on the conformational structure and vibrational spectra of HO(2)NO(2). Calculations carried out with coupled-cluster methods using a series of Pople and Dunning basis sets reveal that there is a significant basis set dependence on the predicted ab initio structure. Higher angular momentum basis sets are shown to be necessary in order to bring the calculated structure into agreement with experimental rotational constants. Harmonic vibrational frequencies of HO(2)NO(2) are computed at the CCSD(T)/aug-cc-pVTZ level of theory while the corresponding vibrational anharmonicities are calculated at the MP2/cc-pVTZ level. In addition, the absorption cross sections of OH stretching overtones in HO(2)NO(2) are calculated using a dipole function computed at the QCISD level of theory and found to be in good agreement with the available experimental data.     

Studies of the g factors of the ground 4A2 and the first excited 2E state of Cr3+ ions in emerald

By using complete diagonalization method, the zero-field splitting and g factors of the ground 4A2 and the first excited 2E states of Cr3+ ions in emerald are calculated. The theoretical results are in good agreement with the experimental data. The dependencies of the g factors on the crystal field parameters, including Dq, v, and v', have been studied. It is shown that, the g factors of the ground state varied with the crystal field parameters approximately in a linear way, but the g factors of the first excited state varied nonlinearly with these parameters.     

Global analytical potential energy surfaces for HO2(X2A") based on high-level ab initio calculations

Two global analytical potential energy surfaces for the HO2(X2A") system have been developed by fitting approximately 15,000 ab initio points at the icMRCI+Qaug-cc-pVQZ level of theory, using the reproducing kernel Hilbert space method. One analytical potential is designed to give a very accurate representation of the low energy range that determines the vibrational spectrum, while the other attempts to provide a fast and uniformly accurate potential function for reaction dynamics. The quality of the fitted potential functions is confirmed by good agreement of the (J=0) HO2 vibrational spectrum and (J=0) quantum reaction probability for the H+O2(ji=0,nui=0) reaction with those obtained using the spline fitted potential. Quasiclassical trajectory calculations carried out on the new potential energy surface provided the reaction probability with a zero impact parameter (b=0), which is in reasonably good agreement with the J=0 quantum results.     

Calculation of avoided crossings for highly excited Stark states of Rb

Using the method of diagonalization, in which zero-field wavefunctions from a potential model are chosen as a basis, we calculate positions and widths of anticrossings for highly excited Stark states of Rb with principal quantum number n up to 49. We obtain the theoretical positions and widths in good agreement with available experimental values, and we present scaling laws of the field positions and widths of anticrossings that can be used to provide information for future experiments.     

Calculation of the rate constant for state-selected recombination of H+O2(nu) as a function of temperature and pressure

Classical trajectory calculations using the MERCURY/VENUS code have been carried out on the H+O(2) reactive system using the DMBE-IV potential energy surface. The vibrational quantum number and the temperature were selected over the ranges nu=0 to 15, and T=300 to 10 000 K, respectively. All other variables were averaged. Rate constants were determined for the energy transfer process, H+O(2)(nu)-->H+O(2)(nu(")), for the bimolecular exchange process, H+O(2)(nu)-->OH(nu('))+O, and for the dissociative process, H+O(2)(nu)-->H+O+O. The dissociative process appears to be a mere extension of the process of transferring large amounts of energy. State-to-state rate constants are given for the exchange reaction, and they are in reasonable agreement with previous results, while the energy transfer and dissociative rate constants have never been reported previously. The lifetime distributions of the HO(2) complex, calculated as a function of v and temperature, were used as a basis for determining the relative contributions of various vibrational states of O(2) to the thermal rate coefficients for recombination at various pressures. This novel approach, based on the complex's ability to survive until it collides in a secondary process with an inert gas, is used here for the first time. Complete falloff curves for the recombination of H+O(2) are also calculated over a wide range of temperatures and pressures. The combination of the two separate studies results in pressure- and temperature-dependent rate constants for H+O(2)(nu)(+Ar) right arrow over left arrow HO(2)(+Ar). It is found that, unlike the exchange reaction, vibrational and rotational-translational energy are liabilities in promoting recombination.     

Cross sections and rate coefficients for electronic excitation of the triplet states of the hydrogen molecule in different vibrational levels

Cross sections for the excitation of the triplet state of H₂ from different vibrational levels of the ground electronic state have been calculated by using the Gryzinski approximation. The results for the ground vibrational level are in satisfactory agreement with the corresponding values obtained by the quantum mechanical close coupling method. The calculated cross sections have been used to generate rate coefficients for the excitation of the triplet states by using a self-consistent electron energy distribution function, obtained by numerical integration of the Boltzmann equation. The results show a strong increase of the different rate coefficients with increasing the vibrational quantum number.     

Mechanism of cysteine oxidation by a hydroxyl radical: a theoretical study.

Cysteine oxidation by HO(.) was studied at a high level of ab initio theory in both gas phase and aqueous solution. Potential energy surface scans in the gas phase performed for the model system methanethiol+HO(.) indicate that the reactants can form two intermediate states: a sulfur-oxygen adduct and a hydrogen bound reactant complex. However these states appear to play a minor role in the reaction mechanism as long as they are fast dissociating states. Thus the main reaction channel predicted at the QCISD(T)/6-311+G(2df,2pd) level of theory is the direct hydrogen atom abstraction. The reaction mechanism is not perturbed by solvation which was found to induce only small variations in the Gibbs free energy of different reactant configurations. The larger size reactant system cysteine+HO* was treated by the integrated molecular orbital+molecular orbital (IMOMO) hybrid method mixing the QCISD(T)/6-311+G(2df,2pd) and the UMP2/6-311+G(d,p) levels of theory. The calculated potential energy, enthalpy, and Gibbs free energy barriers are slightly different from those of methanethiol. The method gave a rate constant for cysteine oxidation in aqueous solution, k=2.4 x 10(9) mol(-1) dm(3) s(-1), which is in good agreement with the experimental rate constant. Further analysis showed that the reaction is not very sensitive to hydrogen bonding and electrical polarity of the molecular environment.     

HOCl Ro-vibrational bound-state calculations for nonzero total angular momentum

The Lanczos homogeneous filter diagonalization method has been employed to compute the HOCl ro-vibrational states for a range of total angular momenta (J = 0, 1, 5, 10, 11, 20, 30) on a newly developed ab initio potential energy surface by Nanbu et al. (J. Theor. Comput. Chem. 2002, 1, 263). For such computationally challenging calculations, a parallel computing strategy has been incorporated into our method to perform the matrix-vector multiplications. For the computed low bound states, a spectroscopic assignment has been made and the widely used approximate adiabatic rotation method has been tested for the broad range of total angular momenta for this deep-well system. Comparison of experimental results with exact quantum mechanical calculations for the selected far-infrared transitions involving the range of total angular momenta has been made possible for the first time.     

A rigorous full-dimensional quantum dynamics calculation of the vibrational energies of H3O-2

The vibrational energy levels of the H(3)O-(2) anion have been calculated using a rigorous quantum dynamics method based on an accurate ab initio potential energy surface. The eigenvalue problem is solved using the two-layer Lanczos iterative diagonalization algorithm in a mixed grid/nondirect product basis set, where the system Hamiltonian is expressed in a set of orthogonal polyspherical coordinates. The lowest 312 vibrational energy levels in each inversion symmetry, together with a comparison of fundamental frequencies with previous quantum dynamics calculations, are reported. Finally, a statistical analysis of nearest level spacing distribution is carried out, revealing a strongly chaotic nature.     

Accurate and highly efficient calculation of the highly excited pure OH stretching resonances of O(1D)HCl, using a combination of methods

Accurate calculation of the energies and widths of the resonances of HOCl--an important intermediate in the O(1D)HCl reactive system--poses a challenging benchmark for computational methods. The need for very large direct product basis sets, combined with an extremely high density of states, results in difficult convergence for iterative methods. A recent calculation of the highly excited OH stretch mode resonances using the filter diagonalization method, for example, required 462,000 basis functions, and 180,000 iterations. In contrast, using a combination of new methods, we are able to compute the same resonance states to higher accuracy with a basis less than half the size, using only a few hundred iterations-although the CPU cost per iteration is substantially greater. Similar performance enhancements are observed for calculations of the high-lying bound states, as reported in a previous paper [J. Theo. Comput. Chem. 2, 583 (2003)].     

A quantum wave packet dynamics study of the N(2D) + H2 reaction

We report a dynamics study of the reaction N((2)D) + H(2) (v=0, j=0-5) --> NH + H using the time-dependent quantum wave packet method and a recently reported single-sheeted double many-body expansion potential energy surface for NH(2)(1(2)A' ') which has been modeled from accurate ab initio multireference configuration-interaction calculations. The calculated probabilities for (v=0, j=0-5) are shown to display resonance structures, a feature also visible to some extent in the calculated total cross sections for (v=0, j=0). A comparison between the calculated centrifugal-sudden and coupled-channel reaction probabilities validate the former approximation for the title system. Rate constants calculated using a uniform J-shifting scheme and averaged over a Boltzmann distribution of rotational states are shown to be in good agreement with the available experimental values. Comparisons with other theoretical results are also made.     

Semiclassical initial value calculations of the collinear helium atom

Semiclassical calculations using the Herman-Kluk initial value treatment are performed to determine energy eigenvalues of bound and resonance states of the collinear helium atom. Both the eZe configuration (where the classical motion is fully chaotic) and the Zee configuration (where the classical dynamics is nearly integrable) are treated. The classical motion is regularized to remove singularities that occur when the electrons collide with the nucleus. Very good agreement is obtained with quantum energies for bound and resonance states calculated by the complex rotation method.