Gábor Czakó

Dynamics of the Reaction of Methane with Chlorine Atom on an Accurate Potential Energy Surface

Theory helps explain the counterintuitive impacts of vibrational excitation in a widely studied reaction. The reaction of the chlorine atom with methane has been the focus of numerous studies that aim to test, extend, and/or modify our understanding of mode-selective reactivity in polyatomic systems. To this point, theory has largely been unable to provide accurate results in comparison with experiments. Here, we report an accurate global potential energy surface for this reaction. Quasi-classical trajectory calculations using this surface achieve excellent agreement with experiment on the rotational distributions of the hydrogen chloride (HCl) product. For the Cl + CHD3 → HCl + CD3 reaction at low collision energies, we confirm the unexpected experimental finding that CH-stretch excitation is no more effective in activating this late-barrier reaction than is the translational energy, which is in contradiction to expectations based on results for many atom-diatom reactions.

Toward black-box-type full- and reduced-dimensional variational (ro)vibrational computations

A black-box-type algorithm is presented for the variational computation of energy levels and wave functions using a (ro)vibrational Hamiltonian expressed in an arbitrarily chosen body-fixed frame and in any set of internal coordinates of full or reduced vibrational dimensionality. To make the required numerical work feasible, matrix representation of the operators is constructed using a discrete variable representation (DVR). The favorable properties of DVR are exploited in the straightforward and numerically exact inclusion of any representation of the potential and the kinetic energy including the G matrix and the extrapotential term. In this algorithm there is no need for an a priori analytic derivation of the kinetic energy operator, as all of its matrix elements at each grid point are computed numerically either in a full- or a reduced-dimensional model. Due to the simple and straightforward definition of reduced-dimensional models within this approach, a fully anharmonic variational treatment of large, otherwise intractable molecular systems becomes available. In the computer code based on the above algorithm, there is no inherent limitation for the maximally coupled number of vibrational degrees of freedom. However, in practice current personal computers allow the treatment of about nine fully coupled vibrational dimensions. Computation of vibrational band origins of full and reduced dimensions showing the advantages and limitations of the algorithm and the related computer code are presented for the water, ammonia, and methane molecules.

Accurate ab initio potential energy surface, dynamics, and thermochemistry of the F+CH4→HF+CH3 reaction

An accurate full-dimensional global potential energy surface (PES) for the F+CH(4)-->HF+CH(3) reaction has been developed based on 19 384 UCCSD(T)/aug-cc-pVTZ quality ab initio energy points obtained by an efficient composite method employing explicit UCCSD(T)/aug-cc-pVDZ and UMP2/aug-cc-pVXZ [X=D,T] computations. The PES contains a first-order saddle point, (CH(4)- -F)(SP), separating reactants from products, and also minima describing the van der Waals complexes, (CH(4)- - -F)(vdW) and (CH(3)- - -HF)(vdW), in the entrance and exit channels, respectively. The structures of these stationary points, as well as those of the reactants and products have been computed and the corresponding energies have been determined using basis set extrapolation techniques considering (a) electron correlation beyond the CCSD(T) level, (b) effects of the scalar relativity and the spin-orbit couplings, (c) diagonal Born-Oppenheimer corrections (DBOC), and (d) zero-point vibrational energies and thermal correction to the enthalpy at 298 K. The resulting saddle point barrier and ground state vibrationally adiabatic barrier heights (V(SP) and V(VAGS)), dissociation energy of (CH(3)- - -HF)(vdW) (D(e) and D(0)), and the reaction enthalpy (DeltaH(e) ( degrees ), DeltaH(0) ( degrees ), and DeltaH(298) ( degrees )) are (240+/-40 and 245+/-200 cm(-1)), (1070+/-10 and 460+/-50 cm(-1)), and (-10000+/-50, -11200+/-80, and -11000+/-80 cm(-1)), respectively. Variational vibrational calculations have been carried out for (CH(3)- - -HF)(vdW) in full (12) dimensions. Quasiclassical trajectory calculations of the reaction using the new PES are reported. The computed HF vibrational and rotational distributions are in excellent agreement with experiment.

CH stretching excitation steers the F atom to the CD bond in the F + CHD3 reaction.

Quasiclassical trajectories on an ab initio potential energy surface show that a stereodynamical effect steers the F atom away from the stretching-excited CH bond, thereby promoting the DF + CHD(2) product channel of the F + CHD(3)(nu(1) = 1) reaction at low collision energies. This explains the unexpected results of a recent crossed molecular beam experiment.

Vibrational energy levels with arbitrary potentials using the Eckart-Watson Hamiltonians and the discrete variable representation

An effective and general algorithm is suggested for variational vibrational calculations of N-atomic molecules using orthogonal, rectilinear internal coordinates. The protocol has three essential parts. First, it advocates the use of the Eckart-Watson Hamiltonians of nonlinear or linear reference configuration. Second, with the help of an exact expression of curvilinear internal coordinates (e.g., valence coordinates) in terms of orthogonal, rectilinear internal coordinates (e.g., normal coordinates), any high-accuracy potential or force field expressed in curvilinear internal coordinates can be used in the calculations. Third, the matrix representation of the appropriate Eckart-Watson Hamiltonian is constructed in a discrete variable representation, in which the matrix of the potential energy operator is always diagonal, whatever complicated form the potential function assumes, and the matrix of the kinetic energy operator is a sparse matrix of special structure. Details of the suggested algorithm as well as results obtained for linear and nonlinear test cases including H(2)O, H(3) (+), CO(2), HCNHNC, and CH(4) are presented.

Theoretical Study of the Validity of the Polanyi Rules for the Late-Barrier Cl + CHD3 Reaction

The Polanyi rules, which state that vibrational energy is more efficient in promoting a late-barrier reaction than translational energy, were questioned recently by an experimental unexpected finding that the CH stretch excitation is no more effective in promoting the late-barrier Cl + CHD3 reaction than the translational energy. However, the present quantum dynamics study on the best-available potential energy surface for the title reaction reveals that the CH stretch excitation does promote the reaction significantly, except at low collision energies. Further studies should be carried out to solve the disagreements between theory and experiment on the reaction.

Accurate ab initio potential energy surface, thermochemistry, and dynamics of the Cl(2P, 2P3/2) + CH4 → HCl + CH3 and H + CH3Cl reactions

We report a high-quality, ab initio, full-dimensional global potential energy surface (PES) for the Cl((2)P, (2)P(3/2)) + CH(4) reaction, which describes both the abstraction (HCl + CH(3)) and substitution (H + CH(3)Cl) channels. The analytical PES is a least-squares fit, using a basis of permutationally invariant polynomials, to roughly 16,000 ab initio energy points, obtained by an efficient composite method, including counterpoise and spin-orbit corrections for the entrance channel. This composite method is shown to provide accuracy almost equal to all-electron CCSD(T)/aug-cc-pCVQZ results, but at much lower computational cost. Details of the PES, as well as additional high-level benchmark characterization of structures and energetics are reported. The PES has classical barrier heights of 2650 and 15,060 cm(-1) (relative to Cl((2)P(3/2)) + CH(4)(eq)), respectively, for the abstraction and substitution reactions, in good agreement with the corresponding new computed benchmark values, 2670 and 14,720 cm(-1). The PES also accurately describes the potential wells in the entrance and exit channels for the abstraction reaction. Quasiclassical trajectory calculations using the PES show that (a) the inclusion of the spin-orbit corrections in the PES decreases the cross sections by a factor of 1.5-2.5 at low collision energies (E(coll)); (b) at E(coll) ≈ 13,000 cm(-1) the substitution channel opens and the H/HCl ratio increases rapidly with E(coll); (c) the maximum impact parameter (b(max)) for the abstraction reaction is ~6 bohr; whereas b(max) is only ~2 bohr for the substitution; (d) the HCl and CH(3) products are mainly in the vibrational ground state even at very high E(coll); and (e) the HCl rotational distributions are cold, in excellent agreement with experiment at E(coll) = 1280 cm(-1).

Mode Selectivity for a "Central" Barrier Reaction: Eight-Dimensional Quantum Studies of the O(3P) + CH4 --> OH + CH3 Reaction on an Ab Initio Potential Energy Surface

The dynamics of a combustion reaction, namely, O((3)P) + CH4 → OH + CH3, is investigated with an eight-dimensional quantum model that includes representatives of all vibrational modes of CH4 and with a full-dimensional quasi-classical trajectory (QCT) method. The calculated excitation functions for the ground vibrational state CH4 agree well with experiment. Both quantum and QCT results suggest that excitation of the stretching modes of CH4 enhances the reaction, while the bending and umbrella modes have a smaller impact on reactivity, again consistent with experimental findings. However, none of the vibrational excitations has comparable efficiency in promoting the reaction as translational energy.

Dynamics of the O(3P) + CHD3(vCH = 0,1) reactions on an accurate ab initio potential energy surface

Recent experimental and theoretical studies on the dynamics of the reactions of methane with F and Cl atoms have modified our understanding of mode-selective chemical reactivity. The O + methane reaction is also an important candidate to extend our knowledge on the rules of reactivity. Here, we report a unique full-dimensional ab initio potential energy surface for the O(3P) + methane reaction, which opens the door for accurate dynamics calculations using this surface. Quasiclassical trajectory calculations of the angular and vibrational distributions for the ground state and CH stretching excited O + CHD3(v1 = 0,1) → OH + CD3 reactions are in excellent agreement with the experiment. Our theory confirms what was proposed experimentally: The mechanistic origin of the vibrational enhancement is that the CH-stretching excitation enlarges the reactive cone of acceptance.

Revealing a double-inversion mechanism for the F−+CH3Cl SN2 reaction

Stereo-specific reaction mechanisms play a fundamental role in chemistry. The back-side attack inversion and front-side attack retention pathways of the bimolecular nucleophilic substitution (SN2) reactions are the textbook examples for stereo-specific chemical processes. Here, we report an accurate global analytic potential energy surface (PES) for the F(-)+CH₃Cl SN2 reaction, which describes both the back-side and front-side attack substitution pathways as well as the proton-abstraction channel. Moreover, reaction dynamics simulations on this surface reveal a novel double-inversion mechanism, in which an abstraction-induced inversion via a FH···CH₂Cl(-) transition state is followed by a second inversion via the usual [F···CH₃···Cl](-) saddle point, thereby opening a lower energy reaction path for retention than the front-side attack. Quasi-classical trajectory computations for the F(-)+CH₃Cl(ν1=0, 1) reactions show that the front-side attack is a fast direct, whereas the double inversion is a slow indirect process.