Curve Crossings Research Articles

Chemiluminescence from the Ba(P3)+N2O→BaO(A Σ1+)+N2 reaction: Collision energy effects on the product rotational alignment and energy release

Both fully dispersed unpolarized and polarized chemiluminescence spectra from the Ba((3)P)+N(2)O reaction have been recorded under hyperthermal laser-ablated atomic beam-Maxwellian gas conditions at three specific average collision energies E(c) in the range of 4.82-7.47 eV. A comprehensive analysis of the whole data series suggests that the A (1)Sigma(+)-->X (1)Sigma(+) band system dominates the chemiluminescence. The polarization results revealed that the BaO(A (1)Sigma(+)) product rotational alignment is insensitive to its vibrational state upsilon(') at E(c)=4.82 eV but develops into an strong negative correlation between product rotational alignment and upsilon(') at 7.47 eV. The results are interpreted in terms of a direct mechanism involving a short-range, partial electron transfer from Ba((3)P) to N(2)O which is constrained by the duration of the collision, so that the reaction has a larger probability to occur when the collision time is larger than the time needed for N(2)O bending. The latter in turn determines that, at any given E(c), collinear reactive intermediates are preferentially involved when the highest velocity components of the corresponding collision energy distributions are sampled. Moreover, the data at 4.82 eV suggest that a potential barrier to reaction which favors charge transfer to bent N(2)O at chiefly coplanar geometries is operative for most of the reactive trajectories that sample the lowest velocity components. Such a barrier would arise from the relevant ionic-covalent curve crossings occurring in the repulsive region of the covalent potential Ba((3)P)cdots, three dots, centeredN(2)O((1)Sigma(+)); from this crossing the BaO(A (1)Sigma(+)) product may be reached through mixings in the exit channel with potential energy surfaces leading most likely to the spin-allowed b (3)Pi and a (3)Sigma(+) products. The variation with increasing E(c) of both the magnitude of the average BaO(A (1)Sigma(+)) rotational alignment and the BaO(A (1)Sigma(+)) rovibrational excitation, as obtained from spectral simulations of the unpolarized chemiluminescence spectra, consistently points to additional dynamic factors, most likely the development of induced repulsive energy release as the major responsible for the angular momentum and energy disposal at the two higher E(c) studied. The results of a simplified version of the direct interaction with product repulsion-distributed as in photodissociation model do not agree with the observed average product rotational alignments, showing that a more realistic potential energy surface model will be necessary to explain the present results.

DFT Study of N2O Activation with La+, Hf+, Ta+ and W+ in the Gas Phase

AbstractThe spin‐forbidden reaction N2O(X1Δ)+M+→N2 (X1Σ+g)+MO+(M+=La+, Hf+, Ta+, W+) was discussed using density functional theory. The reaction mechanism between M+ transition metal ions and N2O is an insertion‐elimination one. All products are formed in exothermic processes. The potential energy curve crossings, which dramatically affect reaction mechanisms, were discussed in detail. In comparison with the previous work, an essential conclusion could be drawn that the reaction N2O(X1Δ)+CO(1Δ+)→N2(X1Σ+g)+CO2(1Σ+g) catalyzed by M+ was endothermic by 358.89 kJ·mol−1 which is in accord with the experiment finding.

Nonadiabatic transitions between adiabatic surfaces: Phase diffusion in superconducting atomic point contacts

Motivated by experiments with current-biased superconducting atomic point contacts the general problem of nonadiabatic transitions between adiabatic surfaces in presence of strong dissipation is studied. For a single-channel device the supercurrent is determined by the diffusive motion of the superconducting phase difference on two Andreev levels. These surfaces are uncoupled only in the adiabatic limit of low to moderate transmissions while for high transmissions curve crossings are important. Starting from a general master equation of the full density matrix an approximate time evolution equation for the populations on the adiabatic surfaces in the overdamped limit is derived from which the relevant observables can be obtained. Specific results for the case of atomic point contacts are in agreement with experimental observations that cannot be explained by conventional theory.

Theory of chemical bonds in metalloenzymes XIII: Singlet and triplet diradical mechanisms of hydroxylations with iron‐oxo species and P450 are revisited

AbstractElectronic structures of the Compound I (CpdI) in P450 are investigated on the basis of spin coupling forms of iron‐oxo (Fe(IV)O) cores and radical ligand (•L) groups to generalize previous singlet and triplet diradical (TD) mechanisms for oxygenations of alkanes with Fe( IV)O. Orbital interaction schemes for four lower‐lying spin configurations of CpdI with HC bond of substrate are examined to elucidate how magnetic coupling modes correlate with radical reaction pathways for hydroxylation reactions on the basis of the broken symmetry (BS) molecular orbital (MO) model. The configuration correlation diagrams for the four configurations model are depicted on the basis of the isoelectronic analogy among O, O2, and Fe( IV)O, in addition to Coulomb exchange energy on the iron site, which determines its local spin configuration. Important role of ligand spin (•L) of CpdI for regulation of hydroxylation mechanisms is clarified with the aid of the spin coupling forms. Transition states for one quartet and three doublet configurations under the BS MO approximation are examined on the basis of potential curve crossings along reaction pathways. The four transition structures and corresponding radical intermediates for methane and trimethyl methane with CpI are located by the BS hybrid Kohn–Sham density functional theory (DFT) (B3LYP) method to confirm the orbital interaction schemes. Spin density populations obtained by the BS B3LYP calculations are found to be consistent with the theoretical predictions based on the four configurations model. The configuration and state correlation diagrams by BS B3LYP before and after spin projection are also consistent with the BS MO interaction schemes, which provide local SD and TD mechanisms of hydroxylation with CpdI. The present BS MO‐theoretical framework is useful for systematic understanding of a lot of recent BS hybrid DFT computational results for hydroxylation reactions with CpdI and configuration correlation diagrams reported by several groups. Implications of the present theoretical and computational results are discussed in relation to several experimental characteristics of hydroxylation reactions with iron‐oxo species and P450. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Reaction Dynamics of O(1D,3P) + OCS Studied with Time-Resolved Fourier Transform Infrared Spectroscopy and Quantum Chemical Calculations

Time-resolved infrared emission of CO(2) and OCS was observed in reactions O((3)P) + OCS and O((1)D) + OCS with a step-scan Fourier transform spectrometer. The CO(2) emission involves Deltanu(3) = -1 transitions from highly vibrationally excited states, whereas emission of OCS is mainly from the transition (0, 0 degrees , 1) --> (0, 0 degrees , 0); the latter derives its energy via near-resonant V-V energy transfer from highly excited CO(2). Rotationally resolved emission lines of CO (v <or= 4 and J <or= 30) were also observed in the reaction O((1)D) + OCS. For O((3)P) + OCS, weak emission of CO(2) diminishes when Ar is added, indicating that O((3)P) is translationally hot to overcome the barrier for CO(2) formation. The band contour of CO(2) agrees with a band shape simulated on the basis of a Dunham expansion model of CO(2); the average vibrational energy of CO(2) in this channel is 49% of the available energy. This vibrational distribution fits with that estimated through a statistical partitioning of energy E* congruent with 18,000 +/- 500 cm(-1) into all vibrational modes of CO(2). For the reaction of O((1)D) + OCS, approximately 51% of the available energy is converted into vibrational energy of CO(2), and a statistical prediction using E* congruent with 30,000 +/- 500 cm(-1) best fits the data. The mechanisms of these reactions are also investigated with the CCSD(T)/6-311+G(3df)//B3LYP/6-311+G(3df) method. The results indicate that the triplet O((3)P) + OCS(X(1)Sigma(+)) surface proceeds via direct abstraction and substitution channels with barriers of 27.6 and 36.4 kJ mol(-1), respectively, to produce SO(X(3)Sigma(-)) + CO(X(1)Sigma(+)) and S((3)P) + CO(2)(X(1)A(1)), whereas two intermediates, OSCO and SC(O)O, are formed from the singlet O((1)D) + OCS(X(1)Sigma(+)) surface without barrier, followed by decomposition to SO(a(1)Delta) + CO(X(1)Sigma(+)) and S((1)D) + CO(2)(X(1)A(1)), respectively. For the ground-state reaction O((3)P) + OCS(X(1)Sigma(+)), the singlet-triplet curve crossings play important roles in the observed kinetics and chemiluminescence.

On the definition of molecular structure in quantum mechanics

The usual definition of molecular structure, based on a minimum energy configuration on the Born-Oppenheimer surface, can be generalized to give an energy surface and a structure based on a wavefunction of any level of approximation. It is clear that molecular structure is a concept involving a convention, an agreed upon definition. Alternative definitions are possible; a choice should be based on utility as found by experience. The so-called experimental methods of determining structure require the basic model (usually nuclei plus electrons with Coulomb forces) and the indication of a path from model to predicted spectra (or other observables). This path involves structure at an intermediate step and the structure can be adjusted to yield a fit with experiment, without starting at the beginning and carrying out the ab initio calculations. Stationary states are not necessary or even always desirable provided the change with time is slow. Chemists prepare substances by methods which prepare particular geometries, not particular stationary states, a good example being optical isomers. Various kinds of isomerism, internal motions, etc., create some problems for the concept of structure which can usually be somewhat extended to meet these situations. The most troublesome situations are probably near curve crossings in excited states, particularly when high densities of states are indicated. Other molecular properties are defined and handled in ways similar to structure.

Dissociative recombination of antiprotonic helium ions:e+p¯He2+→p¯+He+

Rearrangement reaction in electron scattering from antiprotonic helium ions $(\overline{p}{\text{He}}^{2+})$ in highly excited states, i.e., $e+\overline{p}{\text{He}}^{2+}\ensuremath{\rightarrow}\overline{p}+{\text{He}}^{+}$, is theoretically investigated by using the $R$-matrix method. This type of reaction can be identified as dissociative recombination (DR) which is well known in molecular physics. If the concept of the adiabatic Born-Oppenheimer separation is applied, the present exotic reaction has a similarity to the DR of ${\text{HeH}}^{+}$ molecules in the sense that the system has no crossings of the adiabatic potential curves. The present exotic DR reaction shows a variety of resonances, which can be described as a Rydberg electron attached to a $\overline{p}{\text{He}}^{2+}$ ion excited to an energetically forbidden state. The cross sections and rate coefficients for the present DR are calculated. As the bound motion of $\overline{p}{\text{-He}}^{2+}$ is closer to a circular orbit, the DR reaction, which leads to the destruction of $\overline{p}{\text{He}}^{2+}$, occurs less frequently. For the antiprotonic ion $\overline{p}{\text{He}}^{2+}$, it turns out that the circular states are the most stable against electron impacts.

Extensive Theoretical Study on Various Low-Lying Electronic States of Silicon Monochloride Cation Including Spin−Orbit Coupling

The potential energy curves of the 23 Omega states generated from the 12 valence Lambda-S states of silicon monochloride cation are calculated for the first time using the internally contracted multireference configuration interaction method with the Davidson correction and entirely uncontracted cc-pV5Z basis set. Spin-orbit coupling is taken into account by the state interaction approach with the full Breit-Pauli Hamiltonian. Very good agreement is achieved between our computed spectroscopic properties and the available experimental data. In particular, the adiabatic excitation energies of the a3Pi(0+) and a3Pi(1) states computed by us are 31,708 and 31,830 cm(-1), respectively, in excellent agreement with the respective experimental values of 31,721 +/- 2 and 31,836 +/- 3 cm(-1). The curve crossings and the predissociation mechanism are investigated. The transition dipole moments are analyzed and the transition properties of the a3Pi(0+)-X1Sigma(0+)+ and a3Pi(1)-X1Sigma(0+)+ transitions are predicted, including the Franck-Condon factors and the radiative lifetimes.

On the Fučík spectrum of the Laplacian on a torus

We study the Fučík spectrum of the Laplacian on a two-dimensional torus T 2 . Exploiting the invariance properties of the domain T 2 with respect to translations we obtain a good description of large parts of the spectrum. In particular, for each eigenvalue of the Laplacian we will find an explicit global curve in the Fučík spectrum which passes through this eigenvalue; these curves are ordered, and we will show that their asymptotic limits are positive. On the other hand, using a topological index based on the mentioned group invariance, we will obtain a variational characterization of global curves in the Fučík spectrum; also these curves emanate from the eigenvalues of the Laplacian, and we will show that they tend asymptotically to zero. Thus, we infer that the variational and the explicit curves cannot coincide globally, and that in fact many curve crossings must occur. We will give a bifurcation result which partially explains these phenomena.

Frontiers in Surface Scattering Simulations

Theorists have recently made substantial progress in simulating reactive molecule-metal surface scattering but still face major challenges. The grand challenge is to develop an approach that enables accurate predictive calculations of reactions involving electronically excited states with potential curve crossings. This challenge is all the more daunting because collisions involving molecules heavier than H2 may be accompanied by substantial energy exchange with the surface vibrations (phonons), and because an electronic structure approach that allows molecule-surface interaction energies to be computed with chemical accuracy (1 kilocalorie per mole) is not yet available even for the electronic ground state of molecule-metal surface systems.

Hydrogen Tunneling in an Enzyme Active Site: A Quantum Wavepacket Dynamical Perspective

We study the hydrogen tunneling problem in a model system that represents the active site of the biological enzyme, soybean lipoxygenase-1. Toward this, we utilize quantum wavepacket dynamics performed on potential surfaces obtained by using hybrid density functional theory under the influence of a dynamical active site. The kinetic isotope effect is computed by using the transmission amplitude of the wavepacket, and the experimental value is reproduced. By computing the hydrogen nuclear orbitals (eigenstates) along the reaction coordinate, we note that tunneling for both hydrogen and deuterium occurs through the existence of distorted, spherical s-type proton wave functions and p-type polarized proton wave functions for transfer along the donor-acceptor axis. In addition, there is also a significant population transfer through distorted p-type proton wave functions directed perpendicular to the donor-acceptor axis (via intervening pi-type proton eigenstate interactions) which underlines the three-dimensional nature of the tunneling process. The quantum dynamical evolution indicates a significant contribution from tunneling processes both along the donor-acceptor axis and along directions perpendicular to the donor-acceptor axis. Furthermore, the tunneling process is facilitated by the occurrence of curve crossings and avoided crossings along the proton eigenstate adiabats.

Assessment of quantum chemical methods and basis sets for excitation energy transfer

The validity of several standard quantum chemical approaches and other models for the prediction of exciton energy transfer is investigated using the HOMO–LUMO excited states of benzene dimer as an example. The configuration interaction singles (CIS), time-dependent Hartree-Fock (TD-HF), time dependent density functional theroy (TD-DFT), and complete-active-space self-consistent-field (CASSCF) methods are applied with a supermolecule approach and compared to the previously established monomer transition density method and the ideal dipole approximation. Strong and physically incorrect admixture of charge-transfer states makes TD-DFT inappropriate for investigations of potential energy surfaces in such dimer systems. CIS, TD-HF and CASSCF perform qualitatively correct. TD-HF seems to be a particularly appropriate method due to its general applicability and overall good performance for the excited state and for transition properties. Double-zeta basis sets with polarisation functions are found to be sufficient to predict transfer rates of dipole allowed excitations. Efficient excitation energy transfer is predicted between degenerate excited states while avoided curve crossings of nearly spaced π-aggregates are identified as a possible trapping mechanism.

X-ray absorption and resonant Auger spectroscopy of O2 in the vicinity of the O 1s→σ* resonance: Experiment and theory

We report on an experimental and theoretical investigation of x-ray absorption and resonant Auger electron spectra of gas phase O(2) recorded in the vicinity of the O 1s-->sigma(*) excitation region. Our investigation shows that core excitation takes place in a region with multiple crossings of potential energy curves of the excited states. We find a complete breakdown of the diabatic picture for this part of the x-ray absorption spectrum, which allows us to assign an hitherto unexplained fine structure in this spectral region. The experimental Auger data reveal an extended vibrational progression, for the outermost singly ionized X (2)Pi(g) final state, which exhibits strong changes in spectral shape within a short range of photon energy detuning (0 eV>Omega>-0.7 eV). To explain the experimental resonant Auger electron spectra, we use a mixed adiabatic/diabatic picture selecting crossing points according to the strength of the electronic coupling. Reasonable agreement is found between experiment and theory even though the nonadiabatic couplings are neglected. The resonant Auger electron scattering, which is essentially due to decay from dissociative core-excited states, is accompanied by strong lifetime-vibrational and intermediate electronic state interferences as well as an interference with the direct photoionization channel. The overall agreement between the experimental Auger spectra and the calculated spectra supports the mixed diabatic/adiabatic picture.

First excitations in two- and three-dimensional random-field Ising systems

We present results on the first excited states for the random-field Ising model. These arebased on an exact algorithm, with which we study the excitation energies and theexcitation sizes for two- and three-dimensional random-field Ising systems with a Gaussiandistribution of the random fields. Our algorithm is based on an approach of Frontera andVives which, in some cases, does not yield the true first excited states. Using the correctedalgorithm, we find that the order–disorder phase transition for three dimensions isvisible via crossings of the excitation energy curves for different system sizes,while in two dimensions these crossings converge to zero disorder. Furthermore,we obtain in three dimensions a fractal dimension of the excitation cluster ofds = 2.42(2). We also provide analytical droplet arguments to understand the behavior of theexcitation energies for small and large disorder as well as close to the criticalpoint.

Singlet and Triplet Excited States and Intersystem Crossing in Free‐Base Porphyrin: TDDFT and DFT/MRCI Study

Extensive time-dependent DFT (TDDFT) and DFT/multireference configuration interaction (MRCI) calculations are performed on the singlet and triplet excited states of free-base porphyrin, with emphasis on intersystem crossing processes. The equilibrium geometries, as well as the vertical and adiabatic excitation energies of the lowest singlet and triplet excited states are determined. Single and double proton-transfer reactions in the first excited singlet state are explored. Harmonic vibrational frequencies are calculated at the equilibrium geometries of the ground state and of the lowest singlet and triplet excited states. Furthermore, spin-orbit coupling matrix elements of the lowest singlet and triplet states and their numerical derivatives with respect to nuclear displacements are computed. It is shown that opening of an unprotonated pyrrole ring as well as excited-state single and double proton transfer inside the porphyrin cavity lead to crossings of the potential energy curves of the lowest singlet and triplet excited states. It is also found that displacements along out-of-plane normal modes of the first excited singlet state cause a significant increase of the <T2|Hso|S1>, <T1|Hso|S1>, and <T1|Hso|S0> spin-orbit coupling matrix elements. These phenomena lead to efficient radiationless deactivation of the lowest excited states of free-base porphyrin via intercombination conversion. In particular, the S1-->T1 population transfer is found to proceed at a rate of approximately 10(7) s(-1) in the isolated molecule.

The infrared-driven cis– trans isomerization of nitrous acid HONO III: A mixed quantum–classical simulation

A mixed quantum–classical simulation of the IR-driven cis– trans isomerization of HONO in a Kr matrix at 30 K is presented, treating the hydrogen atom as quantum particle and the Kr matrix as well as intermolecular degrees of freedom of the ONO-body as classical. A new method is presented to time-propagate the coupled set of equations in a DVR basis in internal spherical coordinates, rather than in laboratory frame fixed cartesian coordinates. In spherical coordinates, a much more precise computation of the weak vibrational couplings is possible using a still manageable basis size. Good qualitative agreement between simulation and experiment is obtained, underestimating relaxation and isomerization rates by a modest factor ≈5. Upon matrix fluctuations, frequent curve crossings occur between the initially excited OH-stretch vibration and a closely lying combination mode of torsional and bending coordinate that lead to a transfer of population. The subsequent pathway of energy flow is deduced and discussed within a tier model, where trans-states, that belong to the second tier, are populated through a first tier of states that is composed of combinations of bending and torsional excitations. No specific energy pathway is revealed that would funnel the hydrogen atom directly towards the trans-side, hence the experimentally observed high cis → trans quantum yield of close to one probably has to be explained in a statistical scenario on a timescale much longer than that of the present simulation.

Curve crossing and negative refraction in simulations of near-field coupled metallic nanoparticle arrays

We extend our previous results [R. Baer et al., J. Chem. Phys. 126, 014705 (2007).] to develop a simple theory of localized surface plasmon-polariton (LSPP) dispersion on regular arrays of metal nanoparticles in the weak-field and weak-damping limits. This theory describes the energy-momentum as well as the polarization-momentum properties of LSPP waves, both of which are crucial to plasmonic device design. We then explicitly compute the dispersion relation for isotropic and anisotropic two-dimensional square lattices, and show curve crossings between all three levels as well as negative refraction where the phase and group velocities (refractive indices), or at least their projection along the main axis, have different signs. The curve crossing implies that scattering between the different polarizations, and therefore different velocities, is easy at the curve crossing momenta, so that a quick change in wave packet direction can be achieved. Time-resolved wave packet dynamics simulations demonstrate negative refraction and the easy scattering over nanometer length scales. This paper also gives some computational schemes for future applications, such as a way to include source terms and how to efficiently treat dissipative effects.

Extensive theoretical study on the low‐lying electronic states of silicon monofluoride cation including spin‐orbit coupling

Ab initio calculations on the low-lying electronic states of SiF+ are performed using the internally contracted multireference configuration interaction method with the Davidson correction and entirely uncontracted aug-cc-pV5Z basis set. The effects of spin-orbit coupling are accounted for by the state interaction approach with the full Breit-Pauli Hamiltonian. The entire 23 Omega states generated from the 12 valence Lambda-S states, which correlate with the first dissociation channel are studied for the first time. Good agreement is found between the calculated results and the available experimental data. The spin-orbit coupling effects on the potential energy curves and spectroscopic properties are studied. Various curve crossings are revealed, which could lead to the predissociation of the a3Pi, A1Pi, and (2)3Sigma+ states and the predissociation pathways are analyzed based upon the calculated spin-orbit matrix elements. The calculated ionization potentials of the ground-state SiF to a few states of SiF+ are in good agreement with the available experimental measurements. Moreover, the transition dipole moments of the dipole-allowed transitions and the transition properties for the A3Pi0+ -X1Sigma+ 0+ and B3Pi1-X1Sigma+ 0+ transitions are predicted, including the Franck-Condon factors and the radiative lifetimes.

Femtosecond Dynamics of the tert-Butyl Radical, t-C4H9

The excited-state dynamics of the tert-butyl radical, t-C4H9, was investigated by femtosecond time-resolved photoionization and photoelectron spectroscopy. The experiments were supported by ab initio calculations. tert-Butyl radicals, generated by flash pyrolysis of azo-tert-butane, were excited into the A 2A1 (3s) state between 347 and 307 nm and the 3p band at 274 and 268 nm and ionized by 810-nm radiation, in a [1 + 2'] or [1 + 3'] process. Electronic structure calculations confirm that the two states are of s and p Rydberg characters, respectively. The carbon framework becomes planar and thus ion-like in both states. The photoelectron spectra are broad and seem to be mediated by accidental intermediate resonances in the probe step. All time-resolved photoelectron spectra can be described by a single decay time. For the A 2A1 state, lifetimes between 180 and 69 fs were measured. Surprisingly, a much longer lifetime of around 2 ps was found for the 3p state. To understand the decay dynamics, the potential energy was computed as a function of several important nuclear coordinates. A [1,2] H-atom shift to the isobutyl radical seems not to be important for the excited-state dynamics. Qualitative considerations indicate curve crossings between the ground state, the 3s state, and a valence state along the asymmetric C-C stretch coordinate that correlates to the dimethylcarbene + methyl product channel. The implications of the present study for earlier work on the nanosecond time scale are discussed.

Detecting Level Crossings without Looking at the Spectrum

In many physical systems it is important to be aware of the crossings and avoided crossings which occur when eigenvalues of a physical observable are varied using an external parameter. We have discovered a powerful algebraic method of finding such crossings via a mapping to the problem of locating the roots of a polynomial in that parameter. We demonstrate our method on atoms and molecules in a magnetic field, where it has implications in the search for Feshbach resonances. In the atomic case our method allows us to point out a new class of invariants of the Breit-Rabi Hamiltonian of magnetic resonance. In the case of molecules, it enables us to find curve crossings with practically no knowledge of the corresponding Born-Oppenheimer potentials.