Search

A new approach for preventing zero-point energy (ZPE) violation in quasi-classical trajectory (QCT) simulations is presented and applied to H2CO “roaming” reactions. Zero-point energy may be problematic in roaming reactions because they occur at or near bond dissociation thresholds and these channels may be incorrectly open or closed depending on if, or how, ZPE has been treated. Here we run QCT simulations on a “ZPE-corrected” potential energy surface defined as the sum of the molecular potential energy surface (PES) and the global harmonic ZPE surface. Five different harmonic ZPE estimates are examined with four, on average, giving values within 4 kJ/mol—chemical accuracy—for H2CO. The local harmonic ZPE, at arbitrary molecular configurations, is subsequently defined in terms of “projected” Cartesian coordinates and a global ZPE “surface” is constructed using Shepard interpolation. This, combined with a second-order modified Shepard interpolated PES, V, allows us to construct a proof-of-concept ZPE-corrected PES for H2CO, Veff, at no additional computational cost to the PES itself. Both V and Veff are used to model product state distributions from the H + HCO ! H2 + CO abstraction reaction, which are shown to reproduce the literature roaming product state distributions. Our ZPE-corrected PES allows all trajectories to be analysed, whereas, in previous simulations, a significant proportion was discarded because of ZPE violation. We find ZPE has little effect on product rotational distributions, validating previous QCT simulations. Running trajectories on V, however, shifts the product kinetic energy release to higher energy than on Veff and classical simulations of kinetic energy release should therefore be viewed with caution.

The dynamics of CO production from photolysis of H2CO have been explored over a 8000 cm−1 energy range (345 nm–266 nm). Two-dimensional ion imaging, which simultaneously measures the speed and angular momentum distribution of a photofragment, was used to characterise the distribution of rotational and translational energy and to quantify the branching fraction of roaming, transition state (TS), and triple fragmentation (3F) pathways. The rotational distribution for the TS channel broadens significantly with increasing energy, while the distribution is relatively constant for the roaming channel. The branching fraction from roaming is also relatively constant at 20% of the observed CO. Above the 3F threshold, roaming decreases in favour of triple fragmentation. Combining the present data with our previous study on the H-atom branching fractions and published quantum yields for radical and molecular channels, absolute quantum yields were determined for all five dissociation channels for the entire S1←S0 abs...

Zhang acknowledges partial support from the Academic Research Grant No. RP3991603, The National University of Singapore.

We present a method for expressing a potential energy surface (PES) for polyatomic molecules as an interpolation of local Taylor expansions in internal coordinates. This approach extends and replaces an earlier method which was only directly applicable to molecules of no more than four atoms. In general, the local Taylor expansions are derived from ab initio quantum calculations. Here, the methodology is evaluated by comparison with an analytic surface for the reactions H+CH4⇌H2+CH3. Approximately 1000–1300 data points are required for an accurate 12-dimensional surface which describes both forward and backward reactions, at the energy studied.

Ab initio calculations have been performed to investigate the structures and infrared spectra of the complexes FH:NH3, ClH:NH3, and BrH:NH3, and the effects of the presence of inert gas atoms on structures and spectra. Two-dimensional MP2/6-31+G(d,p) potential energy surfaces were constructed for the complexes XH:NH3, and model two-dimensional Schrodinger equations were solved for the proton stretching and dimer (heavy-atom) stretching modes. Although all complexes have equilibrium structures characterized by traditional hydrogen bonds, their infrared spectra differ significantly. In FH:NH3 both the ground (v=0) and first excited state for the proton stretching mode (v=1) are confined to the potential well describing the equilibrium structure. In this case the harmonic approximation is appropriate, and matrix effects are unimportant. In ClH:NH3 the v=1 proton stretching vibration accesses the more polar, proton-shared region of the potential surface. Here the harmonic treatment leads to a significant over...

We present a new method for expressing a molecular potential energy surface (PES) as an interpolation of local Taylor expansions. By using only Cartesian coordinates for the atomic positions, this method avoids redundancy problems associated with the use of internal coordinates. The correct translation, rotation, inversion, and permutation invariance are incorporated in the PES via the interpolation method itself. The method is most readily employed for bound molecules or clusters and is demonstrated by application to the vibrational motion of acetylene.

A simple model potential energy surface is constructed and used in both quasiclassical trajectory calculations and quantum vibrational close-coupling, infinite order sudden approximation calculations of collision-induced vibrational energy transfer from four vibrational states of S1 p-difluorobenzene. Classical and quantum state-to-state cross sections are compared for excitation of the two lowest energy vibrational states and collision with He or Ar. Qualitatively, the same trends are seen in both sets of results. Classical cross sections, however, are significantly larger at very low collision energies as a consequence of the binning procedures used to determine classical final states and, in the case of the Ar collider, as a result of the possible breakdown of the sudden approximation. Rotational excitation of the p-difluorobenzene molecule is also investigated and found to have only small effects on the dominant energy transfer channels. The theoretical results are compared with recent experimental results of Mudjijono and Lawrance [J. Chem. Phys. 104, 7444 (1996)]. The classical results, for the He, Ne, Ar, and Kr collision partners, show good agreement with experiment, reproducing the major energy transfer channels and the experimental collision partner dependence. Quantum results agree well with experiment for the He collider and are also used to assign experimentally ambiguous product states and to investigate vibrational energy transfer channels that are not experimentally observable. The propensity toward the transfer of multiple quanta of vibrational energy is analyzed and, in general, found to increase with the intermolecular well depth and with the mass of the collision partner. The He collision partner, however, behaves anomalously. © 1997 American Institute of Physics.

In this paper we demonstrate, at the UHF/6‐311++G(d,p) level of theory, the practical feasibility of using ab initio quantum chemical calculations to generate a molecular potential energy surface (PES) for the OH+H2→H2O+H reaction using our previously suggested interpolation and iteration schemes. The successful, and almost completely automated, merger of the PES algorithm and quantum chemical calculations involves a number of significant practical problems, the solutions of which are presented in detail. The convergence of the interpolated potential surface was monitored in terms of reaction probability and we find that the surface converges once the energy, gradient and Hessian have been calculated at approximately 350 geometries. We also find that, although the initial geometries used consisted only of points along a reaction path for the OH+H2→H2O+H reaction, the potential energy surface iteration process rapidly adds information about other, energetically accessible, reaction channels.

In this paper we evaluate the use of higher order derivatives in the construction of an interpolated potential energy surface for the OH+H2→H2O+H reaction. The surface construction involves interpolating between local Taylor expansions about a set of known data points. We examine the use of first, second, third, and fourth order Taylor expansions in the interpolation scheme. The convergence of the various interpolated surfaces is evaluated in terms of the probability of reaction. We conclude that first order Taylor expansions (and by implication zeroth order expansions) are not suitable for constructing potential energy surfaces for reactive systems. We also conclude that it is inefficient to use fourth order derivatives. The factors differentiating between second and third order Taylor expansions are less clear. Although third order surfaces require substantially fewer data points to converge than second order surfaces, this faster convergence does not offset the large cost incurred in calculating numeri...

Trajectory data are reported for the reaction CH4+H→CH3+H2, designed to provide information that can be used to test approximate quantitative theories for the dynamics of abstraction reactions. A potential function was devised which properly reflects the nuclear permutation symmetry of the process. Microscopic reaction rate coefficients were obtained as functions of fixed rotational and vibrational energy, and of the angular momentum. The data indicated significant uncoupling between the various modes although, at a minimum, the symmetric stretch is directly coupled to the reaction coordinate at the transition state. The data were used to test the assumption that the total angular momentum, J, may be approximated by the orbital angular momentum, L. L is approximately conserved from the reactant to the saddle point configuration in reactive and nonreactive collisions and may be well approximated by J. The angular momentum about the long axis of the reacting system (equivalent to the K quantum number) is no...

Quantum and anharmonic effects are investigated in (H2)2-Li(+)-benzene, a model for hydrogen adsorption in metal-organic frameworks and carbon-based materials, using rigid-body diffusion Monte Carlo (RBDMC) simulations. The potential-energy surface (PES) is calculated as a modified Shepard interpolation of M05-2X/6-311+G(2df,p) electronic structure data. The RBDMC simulations yield zero-point energies (ZPE) and probability density histograms that describe the ground-state nuclear wavefunction. Binding a second H2 molecule to the H2-Li(+)-benzene complex increases the ZPE of the system by 5.6 kJ mol(-1) to 17.6 kJ mol(-1). This ZPE is 42% of the total electronic binding energy of (H2)2-Li(+)-benzene and cannot be neglected. Our best estimate of the 0 K binding enthalpy of the second H2 to H2-Li(+)-benzene is 7.7 kJ mol(-1), compared to 12.4 kJ mol(-1) for the first H2 molecule. Anharmonicity is found to be even more important when a second (and subsequent) H2 molecule is adsorbed; use of harmonic ZPEs results in significant error in the 0 K binding enthalpy. Probability density histograms reveal that the two H2 molecules are found at larger distance from the Li(+) ion and are more confined in the θ coordinate than in H2-Li(+)-benzene. They also show that both H2 molecules are delocalized in the azimuthal coordinate, ϕ. That is, adding a second H2 molecule is insufficient to localize the wavefunction in ϕ. Two fragment-based (H2)2-Li(+)-benzene PESs are developed. These use a modified Shepard interpolation for the Li(+)-benzene and H2-Li(+)-benzene fragments, and either modified Shepard interpolation or a cubic spline to model the H2-H2 interaction. Because of the neglect of three-body H2, H2, Li(+) terms, both fragment PESs lead to overbinding of the second H2 molecule by 1.5 kJ mol(-1). Probability density histograms, however, indicate that the wavefunctions for the two H2 molecules are effectively identical on the "full" and fragment PESs. This suggests that the 1.5 kJ mol(-1) error is systematic over the regions of configuration space explored by our simulations. Notwithstanding this, modified Shepard interpolation of the weak H2-H2 interaction is problematic and we obtain more accurate results, at considerably lower computational cost, using a cubic spline interpolation. Indeed, the ZPE of the fragment-with-spline PES is identical, within error, to the ZPE of the full PES. This fragmentation scheme therefore provides an accurate and inexpensive method to study higher hydrogen loading in this and similar systems.

We have developed a multi-agent quantum Monte Carlo model to describe the spatial dynamics of multiple majority charge carriers during conduction of electric current in the channel of organic field-effect transistors. The charge carriers are treated by a neglect of diatomic differential overlap Hamiltonian using a lattice of hydrogen-like basis functions. The local ionization energy and local electron affinity defined previously map the bulk structure of the transistor channel to external potentials for the simulations of electron- and hole-conduction, respectively. The model is designed without a specific charge-transport mechanism like hopping- or band-transport in mind and does not arbitrarily localize charge. An electrode model allows dynamic injection and depletion of charge carriers according to source-drain voltage. The field-effect is modeled by using the source-gate voltage in a Metropolis-like acceptance criterion. Although the current cannot be calculated because the simulations have no time axis, using the number of Monte Carlo moves as pseudo-time gives results that resemble experimental I/V curves.

We outline an approach for building molecular dipole moment surfaces using modified Shepard interpolation. Our approach is highly automated, requires minimal parameterization, and is iteratively improvable. Using the water molecule as a test case, we investigate how different aspects of the interpolation scheme affect the rate of convergence of calculated IR spectral line intensities. It is found that the interpolation scheme is sensitive to coordinate singularities present at linear geometries. Due to the generally monotonic nature of the dipole moment surface, the one-part weight function is found to be more effective than the more complicated two-part variant, with first-order interpolation also giving better-than-expected results. Almost all sensible schemes for choosing interpolation reference data points are found to exhibit acceptable convergence behavior.

The response of a molecule to an electric field E, often a model of environment, can be expressed in terms of a sum of power series expansions. We investigate the accuracy and limits of applicability of this expression using one-, two-, and three-dimensional models of the hydrogen-bonded complex, ClH:NH(3). Energetic, structural, and vibrational spectroscopic characteristics are determined at first- and second-order in E and [nabla]E and compared with ab initio values for a range of uniform and non-uniform electric fields chosen to simulate molecular environments. It is found that even at field strengths large enough to cause dramatic structural change in the complex, energetic, structural, and vibrational spectroscopic characteristics are accurately calculated using only terms linear in E and [nabla]E. These results suggest that knowledge of the zero-field molecular potential energy, dipole, and quadrupole moment surfaces may be sufficient to accurately model the interaction of a molecule with a wide range of chemical environments.

One of the largest remaining errors in thermochemical calculations is the determination of the zero-point energy (ZPE). The fully coupled, anharmonic ZPE and ground state nuclear wave function of the SSSH radical are calculated using quantum diffusion Monte Carlo on interpolated potential energy surfaces (PESs) constructed using a variety of method and basis set combinations. The ZPE of SSSH, which is approximately 29 kJ mol(-1) at the CCSD(T)/6-31G* level of theory, has a 4 kJ mol(-1) dependence on the treatment of electron correlation. The anharmonic ZPEs are consistently 0.3 kJ mol(-1) lower in energy than the harmonic ZPEs calculated at the Hartree-Fock and MP2 levels of theory, and 0.7 kJ mol(-1) lower in energy at the CCSD(T)/6-31G* level of theory. Ideally, for sub-kJ mol(-1) thermochemical accuracy, ZPEs should be calculated using correlated methods with as big a basis set as practicable. The ground state nuclear wave function of SSSH also has significant method and basis set dependence. The analysis of the nuclear wave function indicates that SSSH is localized to a single symmetry equivalent global minimum, despite having sufficient ZPE to be delocalized over both minima. As part of this work, modifications to the interpolated PES construction scheme of Collins and co-workers are presented.

A global potential energy surface for the water dimer is constructed using the modified Shepard interpolation scheme of Collins et al. According to this interpolation scheme, the energy at an arbitrary geometry is expressed as a weighted sum of Taylor series expansions from neighboring data points, where the energy and derivative data required are obtained from ab initio calculations. For some ab initio methods, errors are introduced into the second derivative matrix, either by numerical differencing of ab initio energies or numerical integration during the ab initio calculation. Therefore, we test the accuracy required of the second derivative data by truncation of the exact second derivatives to a series of approximate second derivatives, and assess the effect on the results of a quantum diffusion Monte Carlo (QDMC) simulation. Our results show that the calculated zero-point energy and wave function histograms converge to within the numerical uncertainty of the QDMC simulation by inclusion of either three significant figures or three decimal places in the second derivatives.