Adiabatic states derived from a spin-coupled diabatic transformation: semiclassical trajectory study of photodissociation of HBr and the construction of potential curves for LiBr+

The development of spin-coupled diabatic representations for theoretical semiclassical treatments of photodissociation dynamics is an important practical goal, and some of the assumptions required to carry this out may be validated by applications to simple systems. With this objective, we report here a study of the photodissociation dynamics of the prototypical HBr system using semiclassical trajectory methods. The valence (spin-free) potential energy curves and the permanent and transition dipole moments were computed using high-level ab initio methods and were transformed to a spin-coupled diabatic representation. The spin-orbit coupling used in the transformation was taken as that of atomic bromine at all internuclear distances. Adiabatic potential energy curves, nonadiabatic couplings and transition dipole moments were then obtained from the diabatic ones and were used in all the dynamics calculations. Nonadiabatic photodissociation probabilities were computed using three semiclassical trajectory methods, namely, coherent switching with decay of mixing (CSDM), fewest switches with time uncertainty (FSTU), and its recently developed variant with stochastic decoherence (FTSU/SD), each combined with semiclassical sampling of the initial vibrational state. The calculated branching fraction to the higher fine-structure level of the bromine atom is in good agreement with experiment and with more complete theoretical treatments. The present study, by comparing our new calculations to wave packet calculations with distance-dependent ab initio spin-orbit coupling, validates the semiclassical trajectory methods, the semiclassical initial state sample scheme, and the use of a distance-independent spin-orbit coupling for future applications to polyatomic photodissociation. Finally, using LiBr(+) as a model system, it is shown that accurate spin-coupled potential curves can also be constructed for odd-electron systems using the same strategy as for HBr.     

The role of Ti as a catalyst for the dissociation of hydrogen on a Mg(0001) surface

In this paper, the dissociative chemisorption of hydrogen on both pure and Ti-incorporated Mg(0001) surfaces are studied by ab initio density functional theory (DFT) calculations. The calculated dissociation barrier of hydrogen molecule on a pure Mg(0001) surface (1.05 eV) is in good agreement with comparable theoretical studies. For the Ti-incorporated Mg(0001) surface, the activated barrier decreases to 0.103 eV due to the strong interaction between the molecular orbital of hydrogen and the d metal state of Ti. This could explain the experimentally observed improvement in absorption kinetics of hydrogen when transition metals have been introduced into the magnesium materials.     

Semiclassical calculations of collision line broadening in Raman spectra of N2 and CO mixtures

We present a detailed theoretical study of pressure-broadened Raman line shapes in binary mixtures of nitrogen and carbon monoxide. The semiclassical Robert-Bonamy theory was used to calculate self-broadened Q-branch linewidths of N(2) and CO, and Lennard-Jones (LJ) potential energy surface parameters were fixed by comparing our results with extensive experimental linewidth data. For the case of N(2), the ab initio PES8 potential energy surface was investigated, however, the anisotropic repulsive part had to be reduced to ensure a good agreement with experimental linewidths. The agreement between calculations and experiments was remarkably good, both for self-broadened N(2) and CO Q-branch linewidths. Yet, our calculations were not able to predict the experimentally observed difference between Q- and S-branch linewidths of self-broadened N(2). The central results of this work are the Q-branch linewidths of N(2)-CO and CO-N(2), which have been calculated through an extrapolation of the parameters of the potential energy surfaces used for self-broadened linewidths by common combination rules.     

The effect of spin-orbit coupling on the surface dynamical properties and electron-phonon interaction of Tl(0001)

We present an ab initio study of the effect of spin-orbit coupling on the dynamical properties of the Tl(0001) surface as well as on the electron-phonon interaction at the surface. The calculations based on density-functional theory were carried out using a linear response approach and a mixed-basis pseudopotential method. It is shown that the spin-orbit effects on the phonon spectrum and the electron-phonon interaction at the Fermi level of the surface are weak but conspire to a reduction in the electron-phonon coupling strength by 16%.     

Hydrogen spillover mechanism on a Pd-doped Mg surface as revealed by ab initio density functional calculation

The hydrogenation kinetics of Mg is slow, impeding its application for mobile hydrogen storage. We demonstrate by ab initio density functional theory (DFT) calculations that the reaction path can be greatly modified by adding transition metal catalysts. Contrasting with Ti doping, a Pd dopant will result in a very small activation barrier for both dissociation of molecular hydrogen and diffusion of atomic H on the Mg surface. This new computational finding supports-for the first time by ab initio simulation-the proposed hydrogen spillover mechanism for rationalizing experimentally observed fast hydrogenation kinetics for Pd-capped Mg materials.     

Catalytic effects of subsurface carbon in the chemisorption of hydrogen on a Mg(0001) surface: an ab-initio study

Ab initio density functional theory (DFT) calculations are performed to explore possible catalytic effects on the dissociative chemisorption of hydrogen on a Mg(0001) surface when carbon is incorporated into Mg materials. The computational results imply that a C atom located initially on a Mg(0001) surface can migrate into the subsurface and occupy an fcc interstitial site, with charge transfer to the C atom from neighboring Mg atoms. The effect of subsurface C on the dissociation of H2 on the Mg(0001) surface is found to be relatively marginal: a perfect sublayer of interstitial C is calculated to lower the barrier by 0.16 eV compared with that on a pure Mg(0001) surface. Further calculations reveal, however, that sublayer C may have a significant effect in enhancing the diffusion of atomic hydrogen into the sublayers through fcc channels. This contributes new physical understanding toward rationalizing the experimentally observed improvement in absorption kinetics of H2 when graphite or single walled carbon nanotubes (SWCNT) are introduced into the Mg powder during ball milling.     

Matching-pursuit split-operator Fourier-transform simulations of excited-state intramolecular proton transfer in 2-(2'-hydroxyphenyl)-oxazole

The excited-state intramolecular proton-transfer dynamics associated with the keto-enolic tautomerization reaction in 2-(2(')-hydroxyphenyl)-oxazole is simulated according to a numerically exact quantum-dynamics propagation method and a full-dimensional excited-state potential energy surface, based on an ab initio reaction surface Hamiltonian. The reported simulations involve the propagation of 35-dimensional wave packets according to the recently developed matching-pursuit/split-operator-Fourier-transform (MP/SOFT) method by Wu and Batista. The underlying propagation scheme recursively applies the time-evolution operator as defined by the Trotter expansion to second order accuracy in dynamically adaptive coherent-state expansions. Computations of time-dependent survival amplitudes, photoabsorption cross sections, and time-dependent reactant(product) populations are compared to the corresponding calculations based on semiclassical approaches, including the Herman-Kluk semiclassical initial value representation method. The reported results demonstrate the capabilities of the MP/SOFT method as a valuble computational tool to study ultrafast reaction dynamics in polyatomic systems as well as to validate semiclassical simulations of complex (nonintegrable) quantum dynamics in multidimensional model systems.     

Spin-orbit coupled potential energy surfaces and properties using effective relativistic coupling by asymptotic representation

A new method has been reported recently [H. Ndome, R. Welsch, and W. Eisfeld, J. Chem. Phys. 136, 034103 (2012)] that allows the efficient generation of fully coupled potential energy surfaces (PESs) including derivative and spin-orbit (SO) coupling. The method is based on the diabatic asymptotic representation of the molecular fine structure states and an effective relativistic coupling operator and therefore is called effective relativistic coupling by asymptotic representation (ERCAR). The resulting diabatic spin-orbit coupling matrix is constant and the geometry dependence of the coupling between the eigenstates is accounted for by the diabatization. This approach allows to generate an analytical model for the fully coupled PESs without performing any ab initio SO calculations (except perhaps for the atoms) and thus is very efficient. In the present work, we study the performance of this new method for the example of hydrogen iodide as a well-established test case. Details of the diabatization and the accuracy of the results are investigated in comparison to reference ab initio calculations. The energies of the adiabatic fine structure states are reproduced in excellent agreement with reference ab initio data. It is shown that the accuracy of the ERCAR approach mainly depends on the quality of the underlying ab initio data. This is also the case for dissociation and vibrational level energies, which are influenced by the SO coupling. A method is presented how one-electron operators and the corresponding properties can be evaluated in the framework of the ERCAR approach. This allows the computation of dipole and transition moments of the fine structure states in good agreement with ab initio data. The new method is shown to be very promising for the construction of fully coupled PESs for more complex polyatomic systems to be used in quantum dynamics studies.     

First principles semiclassical calculations of vibrational eigenfunctions

Vibrational eigenfunctions are calculated on-the-fly using semiclassical methods in conjunction with ab initio density functional theory classical trajectories. Various semiclassical approximations based on the time-dependent representation of the eigenfunctions are tested on an analytical potential describing the chemisorption of CO on Cu(100). Then, first principles semiclassical vibrational eigenfunctions are calculated for the CO(2) molecule and its accuracy evaluated. The multiple coherent states initial value representations semiclassical method recently developed by us has shown with only six ab initio trajectories to evaluate eigenvalues and eigenfunctions at the accuracy level of thousands trajectory semiclassical initial value representation simulations.     

Many-body origin of the plasmon resonance in small metal clusters

The origin of the plasmon excitation in small metal clusters is studied within the jellium model through ab initio electronic-structure calculations based on the nuclear shell model. In the limit of infinite size, the plasmon classically represents pure harmonic motion of the center of mass of the valence electrons. It is shown that this limit is already well approximated by clusters of only eight electrons.     

Dynamics of the concerted triple proton transfer in cyclic water trimer using the multiconfiguration molecular mechanics algorithm

Cyclic water clusters are important molecular species to understand the nature of hydrogen bonded networks. Theoretical studies for the dynamics of triple proton transfer in the cyclic water trimer were performed. The potential energy surface (PES) of triple proton transfer is generated by the multiconfiguration molecular mechanics (MCMM) algorithm. We have used the MP2/6-31G(d,p) level for high-level ab initio data (energies, gradients, and Hessians), which are used in the Shepard interpolation. Eight high-level reference points were added step by step, including two points for the critical configurations of the large curvature tunneling paths. The more high-level points are used, the better the potential energy surfaces become. The rate constant and kinetic isotope effect (KIE) for the triple proton transfer at 300 K, which have been calculated by the canonical variational transition-state theory with microcanonical optimized multidimensional semiclassical tunneling approximation, are 1.6 x 10(-3) s(-1) and 230, respectively. Tunneling is very important not only for the triple proton transfer but also for the triple deuterium transfer. The MCMM results show good agreement with those from the direct ab initio dynamics calculations.     

Determination of the orientation of azathioprine adsorbed on a silver electrode by SERS and ab initio calculations

We report the SERS spectrum of azthioprine (AZA) on a silver electrode surface and the results of normal mode calculations using empirical and ab initio calculations of the 6-mercaptopurione (6-MP) component of AZA. The empirical calculations were done with a Urey-Bradley force field (UBFF) and the ab initio calculations with the STO-3G basis set using the UHF, MP2 and BLYP methods. From the difference between the SERS and solid spectra, we determined that AZA attaches edge-on to the surface through the N3 site on the 6-MP component of the molecule. The UBFF calculation on an Ag adatom-molecule model reproduced most of the main observed frequency shifts in the SERS spectrum. With a similar model, the ab initio calculations yielded frequency shifts in the same direction as the one observed for the in-plane normal modes, but they yielded opposite shifts for the out-of-plane normal modes. This phenomenon may be attributed to a face-on interaction of the 6-MP component with a neighboring adatom made possible by an inclination of the molecule on the surface.     

Intermolecular electrostatic energies using density fitting

A method is presented to calculate the electron-electron and nuclear-electron intermolecular Coulomb interaction energy between two molecules by separately fitting the unperturbed molecular electron density of each monomer. This method is based on the variational Coulomb fitting method which relies on the expansion of the ab initio molecular electron density in site-centered auxiliary basis sets. By expanding the electron density of each monomer in this way the integral expressions for the intermolecular electrostatic calculations are simplified, lowering the operation count as well as the memory usage. Furthermore, this method allows the calculation of intermolecular Coulomb interactions with any level of theory from which a one-electron density matrix can be obtained. Our implementation is initially tested by calculating molecular properties with the density fitting method using three different auxiliary basis sets and comparing them to results obtained from ab initio calculations. These properties include dipoles for a series of molecules, as well as the molecular electrostatic potential and electric field for water. Subsequently, the intermolecular electrostatic energy is tested by calculating ten stationary points on the water dimer potential-energy surface. Results are presented for electron densities obtained at four different levels of theory using two different basis sets, fitted with three auxiliary basis sets. Additionally, a one-dimensional electrostatic energy surface scan is performed for four different systems (H2O dimer, Mg2+-H2O, Cu+-H2O, and n-methyl-formamide dimer). Our results show a very good agreement with ab initio calculations for all properties as well as interaction energies.     

Experimental and theoretical differential cross sections for the N(2D) + H2 reaction

In this paper, we report a combined experimental and theoretical study on the dynamics of the N(2D) + H2 insertion reaction at a collision energy of 15.9 kJ mol(-1). Product angular and velocity distributions have been obtained in crossed beam experiments and simulated by using the results of quantum mechanical (QM) scattering calculations on the accurate ab initio potential energy surface (PES) of Pederson et al. (J. Chem. Phys. 1999, 110, 9091). Since the QM calculations indicate that there is a significant coupling between the product angular and translational energy distributions, such a coupling has been explicitly included in the simulation of the experimental results. The very good agreement between experiment and QM calculations sustains the accuracy of the NH2 ab initio ground state PES. We also take the opportunity to compare the accurate QM differential cross sections with those obtained by two approximate methods, namely, the widely used quasiclassical trajectory calculations and a rigorous statistical method based on the coupled-channel theory.     

Vibrational spectroscopy of protonated imidazole and its complexes with water molecules: ab initio anharmonic calculations and experiments

The results of anharmonic frequency calculations on neutral imidazole (C3N2H4, Im), protonated imidazole (ImH+), and its complexes with water (ImH+)(H2O)n, are presented and compared to gas phase infrared photodissociation spectroscopy (IRPD) data. Anharmonic frequencies are obtained via ab initio vibrational self-consistent field (VSCF) calculations taking into account pairwise interactions between the normal modes. The key results are: (1) Prediction of anharmonic vibrational frequencies on an MP2 ab initio potential energy surface show excellent agreement with experiment and outstanding improvement over the harmonic frequencies. For example, the ab initio calculated anharmonic frequency for (ImH+)(H2O)N2 exhibits an overall average percentage error of 0.6% from experiment. (2) Anharmonic vibrational frequencies calculated on a semiempirical potential energy surface fitted to ab initio harmonic data represents spectroscopy well, particularly for water complexes. As an example, anharmonic frequencies for (ImH+)H2O and (ImH+)(H2O)2 show an overall average deviation of 1.02% and 1.05% from experiment, respectively. This agreement between theory and experiment also supports the validity and use of the pairwise approximation used in the calculations. (3) Anharmonic coupling due to hydration effects is found to significantly reduce the vibrational frequencies for the NH stretch modes. The frequency of the NH stretch is observed to increase with the removal of a water molecule or replacement of water with N2. This result also indicates the ability of the VSCF method to predict accurate frequencies in a matrix environment. The calculation provides insights into the nature of anharmonic effects in the potential surface. Analysis of percentage anharmoncity in neutral Im and ImH+ shows a higher percentage anharmonicity in the NH and CH stretch modes of neutral Im. Also, we observe that anharmonicity in the NH stretch modes of ImH+ have some contribution from coupling effects, while that of neutral Im has no contribution whatsoever from mode-mode coupling. It is concluded that the incorporation of anharmonic effects in the calculation brings theory and experiment into much closer agreement for these systems.     

Resonances in three-dimensional H + HLi scattering: a time-dependent wave packet dynamical study

This paper examines the resonances in H + HLi scattering. The signature of these resonances is obtained from the oscillations in its reaction probability versus energy curves. They are identified here from a set of pseudospectra calculated for different initial locations of a stationary Gaussian wave packet on the ab initio potential energy surface (PES) reported by Dunne, Murrel, and Jemmer. The nuclear motion on this PES is monitored with the aid of a time-dependent wave packet method and the pseudospectrum are calculated by Fourier transforming the time autocorrelation function of the initial wave packet. The resonances are further examined and assigned by computing their eigenfunctions through spectral quantization algorithm. Both the linewidth as well as decay lifetimes of the resonances are reported.     

Determination of sugar structures in solution from residual dipolar coupling constants: methodology and application to methyl beta-D-xylopyranoside

We have developed methodology for the determination of solution structures of small molecules from residual dipolar coupling constants measured in dilute liquid crystals. The power of the new technique is demonstrated by the determination of the structure of methyl beta-d-xylopyranoside (I) in solution. An oriented sample of I was prepared using a mixture of C(12)E(5) and hexanol in D(2)O. Thirty residual dipolar coupling constants, ranging from -6.44 to 4.99 Hz, were measured using intensity-based J-modulated NMR techniques. These include 15 D(HH), 4 (1)D(CH), and 11 (n)D(CH) coupling constants. The accuracy of the dipolar coupling constants is estimated to be < +/- 0.02 Hz. New constant-time HMBC NMR experiments were developed for the measurement of (n)D(CH) coupling constants, the use of which was crucial for the successful structure determination of I, as they allowed us to increase the number of fitted parameters. The structure of I was refined using a model in which the directly bonded interatom distances were fixed at their ab initio values, while 16 geometrical and 5 order parameters were optimized. These included 2 CCC and 6 CCH angles, and 2 CCCC and 6 CCCH dihedral angles. Vibrationally averaged dipolar coupling constants were used during the refinement. The refined solution structure of I is very similar to that obtained by ab initio calculations, with 11 bond and dihedral angles differing by 0.8 degrees or less and the remaining 5 parameters differing by up to 3.3 degrees . Comparison with the neutron diffraction structure showed larger differences attributable to crystal packing effects. Reducing the degree of order by using dilute liquid crystalline media in combination with precise measurement of small residual dipolar coupling constants, as shown here, is a way of overcoming the limitation of strongly orienting liquid crystals associated with the complexity of (1)H NMR spectra for molecules with more than 12 protons.     

The tetracycline: Mg2+ complex: a molecular mechanics force field

Tetracycline (Tc) is an important antibiotic, which binds specifically to the ribosome and several proteins, in the form of a Tc-:Mg2+ complex. To model Tc:protein and Tc:RNA interactions, we have developed a molecular mechanics force field model of Tc, which is consistent with the CHARMM force field for proteins and nucleic acids. We used structures from the Cambridge Crystallographic Data Base to identify the main Tc conformations that are likely to be present in solution and in biomolecular complexes. A conformational search was also done, using the MM3 force field to perform simulated annealing of Tc. Several resulting, low-energy structures were optimized with an ab initio model and used in developing the new Tc force field. Atomic charges and Lennard-Jones parameters were derived from a supermolecule ab initio approach. We considered the ab initio energies and geometries of a probe water molecule interacting with Tc at 36 different positions. We considered both a neutral and a zwitterionic Tc form, with and without bound Mg2+. The final rms deviation between the ab initio and force field energies, averaged over all forms, was just 0.35 kcal/mol. The model also reproduces the ab initio geometry and flexibility of Tc. As further tests, we did simulations of a Tc crystal, of Tc:Mg2+ and Tc:Ca2+ complexes in aqueous solution, and of a solvated complex between Tc:Mg2+ and the Tet repressor protein (TetR). With slight, ad hoc adjustments, the model can reproduce the experimental, relative, Tc binding affinities of Mg2+ and Ca2+. It performs well for the structure and fluctuations of the Tc:Mg2+:TetR complex. The model should therefore be suitable to investigate the interactions of Tc with proteins and RNA. It provides a starting point to parameterize other compounds in the large Tc family.     

Ab initio molecular dynamics of hydrogen dissociation on metal surfaces using neural networks and novelty sampling

We outline a hybrid multiscale approach for the construction of ab initio potential energy surfaces (PESs) useful for performing six-dimensional (6D) classical or quantum mechanical molecular dynamics (MD) simulations of diatomic molecules reacting at single crystal surfaces. The algorithm implements concepts from the corrugation reduction procedure, which reduces energetic variation in the PES, and uses neural networks for interpolation of smoothed ab initio data. A novelty sampling scheme is implemented and used to identify configurations that are most likely to be predicted inaccurately by the neural network. This hybrid multiscale approach, which couples PES construction at the electronic structure level to MD simulations at the atomistic scale, reduces the number of density functional theory (DFT) calculations needed to specify an accurate PES. Due to the iterative nature of the novelty sampling algorithm, it is possible to obtain a quantitative measure of the convergence of the PES with respect to the number of ab initio calculations used to train the neural network. We demonstrate the algorithm by first applying it to two analytic potentials, which model the H2/Pt(111) and H2/Cu(111) systems. These potentials are of the corrugated London-Eyring-Polanyi-Sato form, which are based on DFT calculations, but are not globally accurate. After demonstrating the convergence of the PES using these simple potentials, we use DFT calculations directly and obtain converged semiclassical trajectories for the H2/Pt(111) system at the PW91/generalized gradient approximation level. We obtain a converged PES for a 6D hydrogen-surface dissociation reaction using novelty sampling coupled directly to DFT. These results, in excellent agreement with experiments and previous theoretical work, are compared to previous simulations in order to explore the sensitivity of the PES (and therefore MD) to the choice of exchange and correlation functional. Despite having a lower energetic corrugation in our PES, we obtain a broader reaction probability curve than previous simulations, which is attributed to increased geometric corrugation in the PES and the effect of nonparallel dissociation pathways.