Adiabatic Ground State Research Articles

Role of projectile-motion-induced electronic transitions in the dissociation of fast H 2 at a Cu(111) surface

We report measurements of the final molecular axis orientation, released kinetic energy and incident beam translational energy dependence of dissociative scattering of 500–6000 eV H 2 and H + 2 from Cu(111) under glancing angles of incidence (normal energies 0.7−4 eV). We find some evidence that the scattering dynamics of those molecules initially in the ground X 1 Σ g + state may be influenced by the topography of the continuum manifold of PES correlating with the adiabatic ground state. However, we suggest that electronic transitions from the ground state manifold to a dissociative upper state manifold are ultimately responsible for the dissociative scattering events we detect.

Twisted boundary conditions and the adiabatic ground state for the attractive XXZ Luttinger liquid.

The one-dimensional attractive lattice fermion gas equivalent to the Heisenberg-Ising spin-1/2 chain is studied for a ring geometry threaded by magnetic flux. We find that for charged fermions having interaction strength \ensuremath{\Delta}=cos(\ensuremath{\pi}/p) with p noninteger, the adiabatic ground state is periodic in the magnetic flux threading the chain, with period two flux quanta, as found by Shastry and Sutherland for the repulsive case. We find that, at particular values of the threading field, a sequence of initially zero-energy bound states form at the Fermi surface during the adiabatic process, the largest containing [p] (the integer part of p) fermions. This largest bound state moves rapidly around to the other Fermi point where it sequentially unbinds. We find Berry's phase for the whole process to be [p]\ensuremath{\pi}. For p integer, as \ensuremath{\Phi} increases, eventually all the particles in the system go into bound states of size [p]. The period in this case is of order the size of the system. The charge-carrying mass of the fermions is calculated by finding the energy of the adiabatic ground state with twisted boundary conditions.

Towards a macroscopic generator coordinate method

Collective quantities are defined as macroscopic statistical averages over many level crossing points where microscopic densities are redistributed. Accordingly, the generator coordinate method (GCM) is reconsidered. It is concluded that, contrary to earlier arguments, the macroscopically defined inertia parameter which appears in the GCM Hamiltonian has a finite value close to that obtained using traditional theories assuming the existence of the adiabatic BCS ground state.

Ultrafast non-linear optical properties and photoinduced relaxation dynamics of poly(2,5-thienylenevinylene)

The transient absorption spectra of a thin film of poly(2,5-thienylenevinylene) at photon energies between 1.15 and 2.55 eV are measured by femtosecond pump-probe spectroscopy, where the pump pulse (≈ 100 fs) is resonant with the π ∗ → π transition. Several ultrafast non-linear optical processes are observed during the temporal overlap of the pump and probe beams, including bleaching, Raman gain and induced phase modulation. The photoinduced absorbance change signals are found to shift spectrally to higher photon energies with an estimated time constant of 100–200 fs in the spectral region from 1.15 to 1.90 eV, indicating the geometrical relaxation to a self-trapped state. The transient decay curves are not described well by single exponential decays but can be fitted to a biexponential decay function. The fast and slow decay time constants are both found to increase from 0.16 to 0.86 ps and 4 to 14 ps, respectively, with higher probe photon energies from 1.44 to 1.82 eV. The fast decay component included both the relaxation of the hot self-trapped exciton to the adiabatic ground-state potential-energy surface and a phonon emission process. The slow decay component corresponds to both the decay of a thermalized self-trapped state via tunnelling to the ground state and a thermalization process. The observed spectral shift and decay kinetics are similar to photoexcitation dynamics previously observed in polydiacetylenes and polythiophenes.

Keynote article

In most cases the interaction of a molecule with a metallic surface is well represented by an adiabatic ground-state interaction potential. Nonetheless, recent work has demonstrated the viability of non-adiabatic electronic pathways in some processes, such as surface photochemistry and exoelectron emission upon adsorption. The evidence for both types of processes will be discussed referring to two recently studied systems—photodissociation of adsorbed N2O4, and exoelectron emission during the oxidation of a caesium surface.

Structure of the adiabatic ground-state potential surface for the ozone molecule

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The symmetrical octasilasesquioxanes X8Si8O12: electronic structure and reactivity

The electronic structure of the octahedral octasilasesquioxanes X8Si8O12(X = H, Cl or CH3) has been analysed in detail and the Si–X stretching mode investigated. It is amazing that among the many orbitals of H8Si8O12 there is exactly one of A2g symmetry. This pure oxygen lone-pair orbital turns out to be the highest occupied, followed by a number of oxygen lone pairs which interact very slightly with the Si and X atoms. The calculated first ionization energy of 10.7 eV is low but is in good agreement with experimental observations. Analysis of the reaction path of the few experimentally observed substitution reactions, Si–X + Y → Si–Y + X (X = H or Cl; Y = D, Cl, OCH3, or OSiMe3), on X8Si8O12, leads to the result that a five-co-ordinate silicon intermediate is involved, followed by concerted rearrangement of angles and bond distances. The reaction mechanism is dictated by the rigid structure of the Si8O12 framework. This does not allow pseudo-rotation or an attack from the back, thus leading to a new reaction path for four-co-ordinate silicon chemistry. Protonation of a bridging oxygen causes a small weakening of the Si–O bond only, in agreement with the stability of these molecules to acids. It is interesting that no adiabatic ground-state path exists to dissociate (HO)3Si–X into (HO)3Si + X for X = H, while one is expected to exist for X = Cl or CH3. Such a dissociative path is costly in energy in all cases, hence intermediates such as X7Si8O12 can be excluded for reactions of these molecules.

Theoretical studies on CuF+, CuF, CuF?, CuF2, and CuF2 ?

Ab initio SCF studies were performed with Cu and F basis sets of near-Hartree-Fock (HF) limit quality to obtain accurate SCF results for the molecular ground state properties of CuF+, CuF, CuF−, CuF2, and CuF2−, as well as for the first two low-lying excited states of CuF2. A study on the effects of electron correlation was carried out by Moller-Plesset (MP) and configuration interaction (Cl) calculations. The effect of relativity on the63Cu nuclear quadrupole coupling in CuF was determined by use of a coupled HF procedure for a first-order spin-orbital-averaged Pauli operator. At the HF level the63Cu coupling constant was found to be 35.8 MHz (in e2qQ h−1), while allowing for relativity the value was reduced to 29.1 MHz, which is in better agreement with the experimental value of 22.0 MHz. The calculated molecular properties for CuF [re = 1.737 A,De=4.38 eV, ωe = 562 cm−1 (MP4);re= 1.796 A,De = 3.91 eV,ωe=585 cm−1 (CISD)] were in good agreement with experiment (re = 1.745 A,De = 4.43 eV,ωe=623 cm−1). The adiabatic ground-state potential curve of CuF+ avoids crossing near the equilibrium distance between the two ionic potential curves Cu+-F and Cu2+-F−. At the crossing point the Cu and F electric field gradients show a sharp discontinuity.

Fluxionality and stereochemistry of 5-coordinate Cu 2+ complexes. The potential energy surface and spectroscopic implications

Cu 2+ ions in five-coordination (Cl −1, NH 3, NCS −, etc.) generally stabilize an elongated square pyramid, which is slightly preferred to a compressed trigonal bipyramid. This stereochemical behaviour can be understood by considering the vibronic interaction between the A′ 1 ground state and the first excited E′ state via the ε′ vibrations in D 3h symmetry (pseudo-Jahn-Teller coupling), in combination with an E′ ⊗ ε′ interaction (Jahn-Teller coupling in the excited state), leading into the lower C 2v (C 4v) and C s symmetries. The adiabatic ground state potential surface is calculated in a semi-empirical model on the basis of available spectroscopic data. The minima at the points, which characterize the elongated C 2v (C 4v) geometry, are rather flat and can be shifted to any other point of the potential surface by steric ligand and/or geometric packing influences. The CuCl 5 3− square pyramids in [Co (NH 3) 6] CuCl 5 undergo a pseudorotation to (dynamically averaged) trigonal bipyramids at 280 K, with the Cl − ligands along the threefold axis remaining fixed in space. In contrast the nuclear displacements along the ε′ coordinates occur in an unrestricted manner above 285 K in case of the Cu(NH 3) 5 2+ square pyramids in [Cu(NH 3) 5]Br 2 (“Berry rotation”). The wavefunctions, g-tensor components and d-d transition energies have been derived as functions of the ε′ distortion coordinates and were explicitly calculated for the CuCl 5 3− model case.

Resonant photodissociation of CoAr+ and CoKr+: Analysis of vibrational structure

The transition-metal rare-gas diatomic ions, CoAr+ and CoKr+, generated and cooled in a supersonic expansion, are studied by visible resonant photodissociation for the first time. Photofragmentation excitation spectra exhibit sharp vibronic features which are members of several excited electronic state vibrational progressions in each molecular ion. Analysis of over 200 vibronic transitions in these spectra reveals details of the potential-energy surfaces characterizing the bonding in these excited states. The adiabatic ground-state dissociation energies of CoAr+ and CoKr+, determined as 4100 cm−1 and 5400 cm−1, respectively, are ca. 37% larger than the diabatic dissociation energy of an excited state which dissociates into 3d8 3P2 Co+1S Ar(Kr) excited atoms and 95% larger than a state dissociating into 3d74s 3F2Co+1S Ar(Kr) atoms. Vibrational frequencies, anharmonicities, electronic origins, and dissociation limits of three electronic states in each molecule have been determined. A simple electrostatic binding model for these transition-metal rare-gas species is discussed.

A comparative study of potential energy surfaces for CH3+H2↔CH4+H

We analyze potential energy surfaces that have been proposed by one of the authors, Bunker, and Chapman and by Raff for the reaction CH3+H2↔CH4+H. The surfaces are modified to remove discontinuities and zero frequencies, where present, and the modified surfaces are compared to each other in terms of reaction-path properties and to ab initio calculations for stationary point properties. They are also used for rate constant calculations which are compared to experiment. The rate constants were calculated by improved canonical variational transition state theory with small-curvature semiclassical adiabatic ground-state transmission coefficients (ICVT/SCSAG) over a wide temperature range, 298–1340 K. Both surfaces yield rate constants in poor agreement with experimental values. The reaction-path analysis leads to a list of potential energy surface features that are important for the rate constants but inaccurate in the existing surfaces and that should be improved in subsequent work.

How adiabatic is quantum tunneling?

We consider the coupling between collective and intrinsic degrees of freedom of a many-dimensional quantum system. We give a criterion for the validity of the adiabatic approximation in tunneling processes and derive an equation for the “lag” of the intrinsic wave function with respect to the adiabatic groundstate. Solutions for several simple cases are presented.

Non-adiabatic electron-phonon coupling in the two-sites two-electrons system

The electronic and ibrational properies of a system of two electrons or excitons at two sites are investgated in a simple model combining the ideas of the Hubbard and Holstein Hamiltonans. We analyse the competition of the interactions which enter this model as parameers for the transfer energyT, the (on-site) Coulomb energyU, the short-range electron-phonon coupling, represented by the stabilization energyS and the vibrational energy (∼ħω). For the whole range of these parameters the spectrum of the 50 lowest eigenstates has been numerically determined. As in the adiabatic approximation (ω=0) the ground state suffers a structural change due to a charge transfer instability, ifS is sufficiently large. In the case of finite ω this transition to a distorted state is no longer sharply defined by a criticalS. With regard to the lowest excited states the electronic system can be described by the adiabatic ground state for smallS as well as for largeS. Correspondingly the eigenfunctions of undisplaced or displaced harmonic oscillators, respectively, yield the lattice dynamics. In the range of intermediateS the situation is more complicated. Here the relation between the eigenfunctions and the adiabatic potentials as well as the appearance of metastable states and their connection to the charge transfer is discussed at some length.

Self-trapping in quasi-one-dimensional solids.

Electronic excitations in highly anisotropic quasi-one-dimensional solids are often regarded as being in a one-dimensional system. Here we determine the degree of anisotropy that is required to justify treating an excess carrier in this manner. In particular, we consider the adiabatic ground-state eigenfunctions for an excess electron in an electronically anisotropic solid in which the electron-lattice interaction is short ranged. In this circumstance an excess carrier in a one-dimensional system always self-traps to form a finite-radius (generally, large) polaron. On the other hand, in a three-dimensional system, an excess carrier will either self-trap to form a severely localized (small) polaron or it will not self-trap at all. We determine that the one-dimensional behavior typically requires the ratio of the electronic transfer integral for the easy direction to that for the transverse directions to be at least two orders of magnitude. Thus, estimated electronic anisotropies in many quasi-one-dimensional systems are not sufficient for these systems to be regarded as one dimensional with regard to self-trapping.

Embedded-cluster model for the effect of phonons on hydrogen surface diffusion on copper

We treat surface diffusion of H on a (100) plane of copper by a model involving 21 degrees of freedom, three for the H and three each for six surface atoms. The six movable surface atoms are embedded on the surface of a bulk crystal. The interaction potential consists of pairwise H–Cu and Cu–Cu interactions, and the dynamics are treated by variational transition state theory with a small-curvature-approximation semiclassical adiabatic ground-state transmission coefficient. The classical barrier height for surface diffusion on the assumed potential energy surface is 11.7 kcal/mol, and we find an Arrhenius activation energy that increases from about 6 kcal/mol, below 160 K, to about 11 kcal/mol, above 400 K. The rate is dominated by tunneling at and below about 200 K. As compared to a treatment with a rigid surface the rate is increased by factors of 16, 3.1, 2.4, 1.6, and 1.3 at 110, 160, 200, 400, and 1000 K, respectively.

Variational transition state theory and tunneling calculations of potential energy surface effects on the reaction of O( 3P) with H 2

Rate constants for the important combustion O(3P state) + H/sub 2/ yield OH + H are calculated using variational transition state theory (VTST) with adiabatic and least-action ground-state transmission coefficients (VTST/G). Five different potential energy surfaces were considered and rates were computed for temperatures from 200 to 1400 K. First, collinear VTST/G calculations were compared with accurate quantum-mechanical ones to assess the accuracy of the dynamical and energetic approximations, which include the no-recrossing assumption of generalized transition state theory, semiclassical methods for tunneling calculations, and a Morse approximation for quantizing the generalized-transition state theory, stretching vibrations. For all five surfaces, which show widely different behavior, the calculations with the least-action ground-state transmission coefficients agree with the accurate quantal results within a factor of 2.9 in all cases. Next the three-dimensional VTST/G calculations were compared with experiment in an attempt to assess the validity of the potential energy surfaces. From this work, only one of the five surfaces could be definitively eliminated. The three-dimensional reaction was found to be dominated by tunneling at room temperature and nearby for all five surfaces. For the calculations on the most accurate ab initio potential energy surface, 60% of the ground-state reaction proceeds by tunnelingmore » even at 400 K.« less

Reaction dynamics for O(3P)+H2 and D2. IV. Reduced dimensionality quantum and quasiclassical rate constants with an adiabatic incorporation of the bending motion

Reduced dimensionality exact quantum and quasiclassical reaction probabilities, transmission coefficients, and rate constants are presented for the O(3P)+H2(ν=0,1) and O(3P)+D2(ν=0,1) reactions on an effective potential surface given by the ab initio MOD POLCI potential energy surface reported previously plus the adiabatic ground state bending energy eigenvalue obtained from the two (nondegenerate) nonlinear potential energy surfaces reported here. The new rate constants are compared to experiment. Good agreement is found for thermal rate constants and isotope effects and for vibrationally excited rate constants.

Comparison of variational transition state theory and quantum sudden calculations of three-dimensional rate coefficients for the reactions D(H)+BrH → DBr(HBr)+H

We calculate rate coefficients for the three-dimensional reactions H+BrH → HBr+H and D+BrH → DBr+H using two different dynamical methods but with the same potential energy surface. One method is a three-dimensional quantum mechanical technique in which the energy sudden approximation is used for the entrance reaction channel and the centrifugal sudden approximation is applied to the exit reaction channel. The second method is improved canonical variational transition state theory with small-curvature-tunneling semiclassical adiabatic ground-state transmission coefficients. The potential energy surface is an empirically adjusted diatomics-in-molecules surface which has a very narrow barrier to reaction. The rate coefficients predicted by the two very different dynamical theories are in excellent agreement—they differ by less than 20% over the temperature range from 150 to 500 K.

Kinetic isotope effects in the Mu+H2 and Mu+D2 reactions: Accurate quantum calculations for the collinear reactions and variational transition state theory predictions for one and three dimensions

We consider three reactions: H+H2→H2+H; Mu+H2→MuH+H; Mu+D2 →MuD+D. We calculate accurate quantum mechanical reaction probabilities and thermal rate coefficients for all three reactions in collinear geometry using the Liu–Siegbahn–Truhlar–Horowitz (LSTH) accurate potential energy surface. These rate coefficients are used to test conventional transition state theory and the improved canonical variational theory with Marcus–Coltrin-path semiclassical adiabatic ground-state transmission coefficients (ICVT/MCPSAG). The ICVT/MCPSAG theory is found to be greatly superior and reasonably reliable. These conclusions are tested for sensitivity to variations in the potential energy surface by repeating the calculations for the less accurate Porter–Karplus surface. The conclusions are unaltered by this. The ICVT/MCPSAG theory and LSTH surface are then employed to predict the rate coefficients for all three reactions in three dimensions.

Temperature dependence of the activation energy: D+H2

Rate constants and activation energies are calculated for D+H2→DH+H over the temperature range 444–2400 K by trajectory calculations and over the temperature range 300–2400 K by improved canonical variatonal theory with small-curvature-approximation semiclassical adiabatic ground-state transmission coefficients. Both calculations use the most accurate available potential energy surface. The results are compared to each other results for this system and for H+H2μH2+H.