Reduced Dimensionality Calculations Research Articles

Approaching the "Zundel" Limit: Tuning the Vibrational Coupling in N2H+Ng, Ng = {He, Ne, Ar, Kr, Xe, and Rn}.

The diazenylium ion (N2H+) is a ubiquitous ion in dense molecular clouds. This ion is often used as a dense gas tracer in outer space. Most of the previous works on diazenylium ion have focused on the shared-proton stretch band, νH+. In this work, we have performed reduced-dimensional calculations to investigate the vibrational structure of N2H+Ng, Ng = {He, Ne, Ar, Kr, Xe, and Rn}. We demonstrate a few interesting things about this system. First, the vibrational coupling in N2H+ can be tuned to switch on interesting anharmonic effects such as Fermi resonance or combination bands by tagging it with different noble gases. Second, a comparison of the vibrational spectrum from N2H+He to N2H+Rn shows that the νH+ can be swept from an "Eigen-like" to a "Zundel-like" limiting case. Anharmonic calculations were performed using a multilevel approach, which utilized the MP2 and CCSD(T) levels of theories. Binding energies for the elimination of Ng in N2H+Ng are also reported.

Reduced-dimensional vibrational models of the water dimer.

A model based on the finite-basis representation of a vibrational Hamiltonian expressed in internal coordinates is developed. The model relies on a many-mode, low-order expansion of both the kinetic energy operator and the potential energy surface (PES). Polyad truncations and energy ceilings are used to control the size of the vibrational basis to facilitate accurate computations of the OH stretch and HOH bend intramolecular transitions of the water dimer (H2 16O)2. Advantages and potential pitfalls of the applied approximations are highlighted. The importance of choices related to the treatment of the kinetic energy operator in reduced-dimensional calculations and the accuracy of different water dimer PESs are discussed. A range of different reduced-dimensional computations are performed to investigate the wavenumber shifts in the intramolecular transitions caused by the coupling between the intra- and intermolecular modes. With the use of symmetry, full 12-dimensional vibrational energy levels of the water dimer are calculated, predicting accurately the experimentally observed intramolecular fundamentals. It is found that one can also predict accurate intramolecular transition wavenumbers for the water dimer by combining a set of computationally inexpensive reduced-dimensional calculations, thereby guiding future effective-Hamiltonian treatments.

Full-dimensional and reduced-dimensional calculations of initial state-selected reaction probabilities studying the H + CH4 → H2 + CH3 reaction on a neural network PES.

Initial state-selected reaction probabilities of the H + CH4 → H2 + CH3 reaction are calculated in full and reduced dimensionality on a recent neural network potential [X. Xu, J. Chen, and D. H. Zhang, Chin. J. Chem. Phys. 27, 373 (2014)]. The quantum dynamics calculation employs the quantum transition state concept and the multi-layer multi-configurational time-dependent Hartree approach and rigorously studies the reaction for vanishing total angular momentum (J = 0). The calculations investigate the accuracy of the neutral network potential and study the effect resulting from a reduced-dimensional treatment. Very good agreement is found between the present results obtained on the neural network potential and previous results obtained on a Shepard interpolated potential energy surface. The reduced-dimensional calculations only consider motion in eight degrees of freedom and retain the C3v symmetry of the methyl fragment. Considering reaction starting from the vibrational ground state of methane, the reaction probabilities calculated in reduced dimensionality are moderately shifted in energy compared to the full-dimensional ones but otherwise agree rather well. Similar agreement is also found if reaction probabilities averaged over similar types of vibrational excitation of the methane reactant are considered. In contrast, significant differences between reduced and full-dimensional results are found for reaction probabilities starting specifically from symmetric stretching, asymmetric (f2-symmetric) stretching, or e-symmetric bending excited states of methane.

Full dimensional quantum-mechanical simulations for the vibronic dynamics of difluorobenzene radical cation isomers using the multilayer multiconfiguration time-dependent Hartree method

Full dimensional multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) calculations of the dynamics of the three difluorobenzene cationic isomers in five lowest-lying doublet electronic states using the ab initio multistate multimode vibronic coupling Hamiltonian (MMVCH) model are carried out using the Heidelberg MCTDH package. The same dynamical problems, but treated with the MCTDH scheme and using a reduced dimensional ab initio MMVCH model, have been previously reported [S. Faraji, H.-D. Meyer, and H. Köppel, "Multistate vibronic interactions in difluorobenzene radical cations. II Quantum dynamical simulations," J. Chem. Phys. 129, 074311 (2008)]. For easy comparison with the reduced dimensional results, 11D or 10D ML-MCTDH calculations are also performed. Extensive ML-MCTDH test calculations are performed to find appropriate ML-MCTDH wavefunction structures (ML-trees), and the convergence of the ML-MCTDH calculations are carefully checked to ensure accurate results. Based on the appropriate ML-trees, the photoelectron (PE) spectrum and the mass analyzed threshold ionization (MATI) spectrum are simulated, analyzed, and compared with corresponding experimental spectra. Because of its efficient simulation capability for large systems, ML-MCTDH calculations save a considerable amount of central processing unit (CPU)-time, even when a reduced dimensional MMVCH is used, i.e., the same reduced model as in the corresponding MCTDH calculations. Simulations of the experimental PE spectra by full dimensional ML-MCTDH calculations reproduced main peaks, which originate from different electronic states. The agreement is improved as compared to the reduced dimensionality calculations. Unfortunately, the experimental PE spectra are not very well resolved. Therefore, we compare our calculations additionally with highly resolved MATI spectra, which, however, are only available for the X̃ state. Based on a series of ML-MCTDH simulations with longer propagation time for X̃, a number of vibrational modes, including fundamentals, their combinations, and overtones are simulated and assigned by comparing with the experimental assignments and the ab initio frequencies. Excellent correlation between the experimental and full dimensional ML-MCTDH results show that ML-MCTDH is accurate and very efficient and that the ab initio MMVCH model is very suitable for ML-MCTDH calculations.

A full-dimensional coupled-surface study of the photodissociation dynamics of ammonia using the multiconfiguration time-dependent Hartree method

Full-dimensional quantum mechanical computations are carried out to investigate the photodissociation dynamics of à state NH(3) and ND(3) using the multiconfiguration time-dependent Hartree (MCTDH) method with recently developed coupled ab initio potential energy surfaces (PESs) [Z. H. Li, R. Valero, and D. G. Truhlar, Theor. Chim. Acc. 118, 9 (2007)]. To use the MCTDH method efficiently the PESs are represented as based on the high-dimensional model representation. The à ← X̃ absorption spectra for both isotopomers were calculated for the zeroth vibrational state of the ground electronic state. With a view to treating larger systems, Jacobi coordinates are used. Computations on the coupled PES are carried out for two-, three-, five-, and six-dimensional model systems to understand the validity of reduced-dimensional calculations. In addition to the fully coupled calculations, the effect of nonadiabatic coupling on absorption spectra is shown by propagating the initial wavepacket only in the à electronic state. The calculated absorption spectra are shown to be in good agreement with available theoretical and experimental observations. Comparisons with calculations using Radau and valence coordinates show the effect of including the symmetry of the system explicitly. Finally, branching ratios for loss of a hydrogen atom via the two available channels are calculated. These predict that the nonadiabatic product increases with the dimension of the calculations and confirm the importance of the full-dimensional calculations.

Quantum instanton calculation of rate constants for the C2H6 + H → C2H5 + H2 reaction: anharmonicity and kinetic isotope effects

Thermal rate constants and kinetic isotope effects for the title reaction are calculated by using the quantum instanton approximation within the full dimensional Cartesian coordinates. The obtained results are in good agreement with experimental measurements at high temperatures. The detailed investigation reveals that the anharmonicity of the hindered internal rotation motion does not influence the rate too much compared to its harmonic oscillator approximation. However, the motion of the nonreactive methyl group in C(2)H(6) significantly enhances the rates compared to its rigid case, which makes conventional reduced-dimensionality calculations a challenge. In addition, the temperature dependence of kinetic isotope effects is also revealed.

Quantum dynamics of dissociative chemisorption of CH4 on Ni(111): Influence of the bending vibration

Two-dimensional, three-dimensional, and four-dimensional quantum dynamic calculations are performed on the dissociative chemisorption of CH(4) on Ni(111) using the multiconfiguration time-dependent Hartree (MCTDH) method. The potential energy surface used for these calculations is 15-dimensional (15D) and was obtained with density functional theory for points which are concentrated in the region that is dynamically relevant to reaction. Many reduced dimensionality calculations were already performed on this system, but the molecule was generally treated as pseudodiatomic. The main improvement of our model is that we try to describe CH(4) as a polyatomic molecule by including a degree of freedom describing a bending vibration in our three-dimensional and four-dimensional models. Using a polyspherical coordinate system, a general expression for the 15D kinetic energy operator is derived, which discards all the singularities in the operator and includes rotational and Coriolis coupling. We use seven rigid constraints to fix the CH(3) umbrella of the molecule to its gas phase equilibrium geometry and to derive two-dimensional, three-dimensional, and four-dimensional Hamiltonians, which were used in the MCTDH method. Only four degrees of freedom evolve strongly along the 15D minimum energy path: the distance of the center of mass of the molecule to the surface, the dissociative C[Single Bond]H bond distance, the polar orientation of the molecule, and the bending angle between the dissociative C[Single Bond]H bond and the umbrella. A selection of these coordinates is included in each of our models. The polar rotation is found to be important in determining the mode selective behavior of the reaction. Furthermore, our calculations are in good agreement with the finding of Xiang et al. [J. Chem. Phys. 117, 7698 (2002)] in their reduced dimensional calculation that the helicopter motion of the umbrella symmetry axis is less efficient than its cartwheel motion for promoting the reaction. The effect of pre-exciting the bend modes is qualitatively incorrect at higher energies, suggesting the necessity of including additional rotational and vibrational degrees of freedom in the model.

Anharmonicities and Isotopic Effects in the Vibrational Spectra of X−·H2O, ·HDO, and ·D2O [X = Cl, Br, and I] Binary Complexes

Vibrational predissociation spectra of the argon-tagged halide monohydrates, X(-) .H(2)O.Ar (X = Cl, Br, or I), are recorded from approximately 800 to 3800 cm(-1) by monitoring the loss of the argon atom. We use this set of spectra to investigate how the spectral signatures of the hydrogen-bonding and large-amplitude hindered rotations of the water molecule are affected by incremental substitution of the hydrogen atoms by deuterium. All six vibrational modes of the X(-).H(2)O complexes are assigned through fundamental transitions, overtones, or combination bands. To complement the experimental study, harmonic and reduced-dimensional calculations of the vibrational spectra are performed based on the MP2/aug-cc-pVTZ level of theory and basis set. Comparison of these results with those from the converged six-dimensional calculations of Rheinecker and Bowman [J. Chem. Phys. 2006, 125, 133206.] show good agreement, with differences smaller than 30 cm(-1). The simpler method has the advantage that it can be readily extended to the heavier halides and was found to accurately recover the wide range of behaviors displayed by this series, including the onset of tunneling between equivalent minima arising from the asymmetrical (single ionic hydrogen-bonded) equilibrium structures of the complexes.

Photodissociation of the water dimer: Three-dimensional quantum dynamics studies on diabatic potential-energy surfaces

The results are presented of three-dimensional model studies of the photodissociation of the water dimer following excitation in the first absorption band. Diabatic potential-energy surfaces are used to investigate the photodissociation following excitation of the hydrogen bond donor molecule and of the hydrogen bond acceptor molecule. In both cases, the degrees of freedom considered are the two OH-stretch modes of the molecule being excited, and the dimer stretch vibration. The diabatic potentials are based on adiabatic potential surfaces computed with the multireference configuration-interaction method, and the dynamics of dissociation was studied using the time-dependent wave-packet method. The dynamics calculations yield a donor spectrum extending over roughly the same range of frequencies as the spectrum of the water monomer computed at the same level of theory. The acceptor spectrum has the same width as the monomer spectrum, but is shifted to the blue by 0.4-0.5 eV. The dimer spectrum obtained by averaging the donor and the acceptor spectrum is broader than the monomer spectrum, with the center of the dimer first absorption band shifted to the blue by about 0.2 eV relative to the monomer band. Our reduced dimensionality calculations do not find the red tail predicted for the dimer first absorption band by Harvey et al. [J. Chem. Phys. 109, 8747 (1998)]. This conclusion also holds if preexcitation of the dimer stretch vibration with one or two quanta is considered.

Quantum mechanical reaction rate constants by vibrational configuration interaction: the OH + H2->H2O + H reaction as a function of temperature.

The thermal rate constant of the 3D OH + H(2)-->H(2)O + H reaction was computed by using the flux autocorrelation function, with a time-independent square-integrable basis set. Two modes that actively participate in bond making and bond breaking were treated by using 2D distributed Gaussian functions, and the remaining (nonreactive) modes were treated by using harmonic oscillator functions. The finite-basis eigenvalues and eigenvectors of the Hamiltonian were obtained by solving the resulting generalized eigenvalue equation, and the flux autocorrelation function for a dividing surface optimized in reduced-dimensionality calculations was represented in the basis formed by the eigenvectors of the Hamiltonian. The rate constant was obtained by integrating the flux autocorrelation function. The choice of the final time to which the integration is carried was determined by a plateau criterion. The potential energy surface was from Wu, Schatz, Lendvay, Fang, and Harding (WSLFH). We also studied the collinear H + H(2) reaction by using the Liu-Siegbahn-Truhlar-Horowitz (LSTH) potential energy surface. The calculated thermal rate constant results were compared with reported values on the same surfaces. The success of these calculations demonstrates that time-independent vibrational configuration interaction can be a very convenient way to calculate converged quantum mechanical rate constants, and it opens the possibility of calculating converged rate constants for much larger reactions than have been treated until now.

Rotationally inelastic scattering of OH(2Π) by HCl(1Σ). Comparison of experiment and theory

State-to-state integral cross sections were calculated using quantum open-shell and closed shell close coupling scattering calculations and quasi-classical trajectory calculations. Reduced dimensionality calculations for the OH–HCl system are compared to those for the OH–Ar system. We have explored the sensitivity of the cross section to the nature of the PES, using either a two-dimensional or a four-dimensional PES. Only the diagonal diabatic Vsum potential was used in the calculations and therefore the electronic fine structure, i.e. the spin–orbit and Λ-doublet structure, could not be accounted for. All the calculations were performed for the same collision energy of 920 cm−1 and assuming that initially all OH molecules are in the lowest rotational state, J = 3/2, Ω = 3/2. The theoretical results are discussed in comparison with the experimental data measured under similar conditions. The agreement of experimental results with the theoretical model based on four-dimensional close coupling calculations and treating the OH molecule as a closed-shell species is good. The validity of different proposed correspondence schemes for the transitions in OH considered as a closed-shell and as an open-shell molecule is examined by comparing the cross sections obtained for the OH + Ar system and the two-dimensional model for the OH + HCl system.

Optimal reduced dimensional representation of classical molecular dynamics

An optimal reduced space method for capturing the low-frequency motion in classical molecular dynamics calculations is presented. This technique provides a systematic means for carrying out reduced-dimensional calculations in an effective set of reduced coordinates. The method prescribes an optimal reduced subspace linear transformation for the low frequency motion. The method is illustrated with a dynamics calculation for a model potential, where the original six-dimensional space is reduced to two (three) dimensions, depending on the desired frequency cutoff value.

A reduced dimensionality, six-degree-of-freedom, quantum calculation of the H+CH4→H2+CH3 reaction

A reduced dimensionality, time-dependent wave-packet calculation is reported for the H+CH4→H2+CH3 reaction in six degrees of freedom and for zero total angular momentum, employing the Jordan–Gilbert potential energy surface. Reaction probabilities for seven initial vibrational states of nonrotating “CH4,” and for the three lowest energy vibrational states and numerous initial rotational states are presented. Excitation of the C–H stretch, and the bending of H–CH3, enhances the reaction probability more than excitation of the umbrella mode. The six-degree-of-freedom cumulative reaction probability (CRP) for zero total angular momentum is obtained by direct summation over initial state-resolved reaction probabilities. An approximate full-dimensional CRP for zero total angular momentum is obtained using the energy-shift approximation to account for the contribution of degrees of freedom missing in the reduced dimensionality calculations. Then J–K shifting is applied to this CRP to obtain the thermal rate constant which is compared with previous calculations.

Improving reduced dimensionality quantum reaction dynamics with a generalized transition state. Application to CH4+O(3P)

We present a new procedure to calculate rate constants from reduced dimensionality reaction probabilities. The method combines an energy-shifting correction, as used in reduced dimensionality calculations of three and four-atom reactions, with a generalized transition state. The procedure, in combination with a recently developed reduced dimensionality model, is used to calculate rate constants for CH4+O(3P)→CH3+OH and its fully deuterated counterpart. These rate constants are compared with the ones obtained using the standard technique and with experimental values. Also, we study the effect on reactivity of exciting selected modes of methane. Similarities and differences between the deuterated and undeuterated reactions are discussed.

Quasi-classical rate constants for the inelastic process O2(υi≫ 1) + O2 → O2(υf) + O2

Rate constants have been calculated using quasi-classical trajectories (QCT) for the vibrational relaxation of highly excited O2:O2(X3Σḡ,vi) + O2(X3Σḡ,0) → O2(X3Σḡ,vf) + O2(X3Σḡ) with 22 ≤vi≤28. The present full-dimensional QCT results agree very well with recent quantum reduced dimensionality calculations, giving further support to the hypothesis that the observed experimental jump in depletion rates would be due partially to enhanced vibrational relaxation.

Quantum calculations of thermal rate constants and reaction probabilities: H 2+CN→H+HCN

Five-dimensional quantum calculations on the thermal rate constant and the cumulative reaction probability of the H 2+CN→H+HCN reaction are presented. Employing a flux correlation function, these quantities are computed directly without resorting to a scattering calculation. In an analysis of the cumulative reaction probability, the contributions of the different vibrational states of the activated complex are identified and the corresponding vibrational frequencies are obtained. The calculated rate constants are compared to experiment and to results of reduced dimensionality calculations of Takayanagi, ter Horst and Schatz.

Reduced dimensionality calculations of quantum reactive scattering for the H+CH4→H2+CH3 reaction

The dynamics for the H+CH4→H2+CH3 reaction has been studied using reduced dimensionality quantum-mechanical theory. The system is treated as a linear four-atom chemical reaction, reducing the system to a three-dimensional scattering problem. The vibrational modes of ν1 and ν4 of CH4, the stretching vibration of H2, and the umbrella ν2 mode of CH3 are taken into consideration in the reaction dynamics based on the vibrational analysis along the reaction path. The semiempirical potential energy surface which has recently been developed by Jordan and Gilbert [J. Chem. Phys. 102, 5669 (1995)] is employed. Rotationally averaged cross sections and thermal rate constants are calculated using an energy-shifting approximation in order to take into account the effect of all the degrees of freedom. It is shown that excitation of the ν1 mode of CH4 significantly enhances the reactivity, indicating that there is a strong coupling between the ν1 mode of CH4 and the reaction coordinate. The vibrational state distributions for the products H2 and CH3 have also been studied. In the energy range considered here, the population of vibrationally excited H2 is found to be very small, while the umbrella ν2 mode of CH3 is found to be excited.

Quantum Dynamics Study for D2 + OH Reaction

A PA5D (potential averaged 5D) TD (time-dependent) quantum wave-packet calculation is reported for the reaction D{sub 2} + OH {yields} D + DOH on the Schatz-Elgersma potential energy surface. The dynamics calculation is carried out on a workstation with a modest memory, which is made possible by using a normalized angular quadrature scheme to minimize the requirement for computer memory during wave-packet propagation. Reaction probabilities, cross sections, and rate constants are presented for the title reaction, and the comparison of the present result with those of the isotopic reactions, H{sub 2} + OH and HD + OH, is given. Consistent with its isotopic reactions, the rotational orientation of D{sub 2} has a stronger effect than that of OH and, in particular, the D{sub 2} (j=1) reactant produces the largest reaction probability, which is attributed to a general steric effect. The comparison of all three isotopic reactions shows that the reactivity (reaction probability and cross section) of the HH(D) + OH system is in the order of P{sub H(2)} > P{sub HD} > P{sub D(2)}. This trend is in good agreement with reduced dimensionality calculations. 27 refs., 8 figs., 4 tabs.

Quantum calculations of reaction probabilities for HO + CO→ H + CO2 and bound states of HOCO

A time-dependent (TD) quantum wavepacket calculation of reaction probabilities is reported for the reaction HO + CO → H + CO2 for total angular momentum J=0. The dynamics calculation employs the potential-averaged five-dimensional model (PA5D) and is made possible by using a normalized angular quadrature scheme to minimize the requirement for computer memory. Reaction probabilities are obtained from the ground state as well as rotationally excited state in either one of the reactant diatoms. Strong resonances are found in the present study and calculated reaction probabilities are dominated by many narrow and overlapping resonances. These features are in qualitative agreement with several lower dimensional quantum dynamics studies. However, quantitative comparison of the present result with previously reported quantum calculations, including a recent planar four-dimensional (4D) calculation of Goldfield et al., shows that our calculated reaction probabilities are much smaller than those found in reduced dimensionality calculations. We also found reaction probability to be more sensitive to the rotational motion of CO than of HO. In addition to reaction probabilities, the bound state calculation for the stable intermediate complex HOCO has also been carried out and energies of several low-lying vibrational states are obtained. The potential energy surface (PES) of Schatz–Fitzcharles–Harding (SFH) is used in all the calculates presented in this paper.

Quantum mechanical calculations of the rate constant for the H2+OH→H+H2O reaction: Full-dimensional results and comparison to reduced dimensionality models

The cumulative reaction probability is calculated for the H2+OH→H+H2O reaction in its full (six) dimensionality for total angular momentum J=0. The calculation, which should give the (numerically) exact result for the assumed potential energy surface, yields the cumulative reaction probability directly, without having to solve the complete state-to-state reactive scattering problem. Higher angular momenta (J≳0) were taken into account approximately to obtain the thermal rate constant k(T) over the range 300°<T<700°. The result deviates significantly from the experimental rate constant, suggesting that the potential energy surface needs to be improved. A systematic series of reduced dimensionality calculations is carried out in order to characterize the behavior and reliability of these more approximate treatments; a comparison of the full dimensional results with previous reduced dimensionality calculations is also made.