Non-Born-Oppenheimer molecular dynamics of Na...FH photodissociation

The accuracy of non-Born-Oppenheimer (electronically nonadiabatic) semiclassical trajectory methods for simulations of "deep quantum" systems is reevaluated in light of recent quantum mechanical calculations of the photodissociation of the Na...FH van der Waals complex. In contrast to the conclusion arrived at in an earlier study, semiclassical trajectory methods are shown to be qualitatively accurate for this system, thus further validating their use for systems with large electronic energy gaps. Product branching in semiclassical surface hopping and decay-of-mixing calculations is affected by a region of coupling where the excited state is energetically forbidden. Frustrated hops in this region may be attributed to a failure of the treatment of decoherence, and a stochastic model for decoherence is introduced into the surface hopping method and is shown to improve the agreement with the quantum mechanical results. A modification of the decay-of-mixing method resulting in faster decoherence in this region is shown to give similarly improved results.     

Coherent switching with decay of mixing: an improved treatment of electronic coherence for non-Born-Oppenheimer trajectories

The self-consistent decay-of-mixing (SCDM) semiclassical trajectory method for electronically nonadiabatic dynamics is improved by modifying the switching probability that determines the instantaneous electronic state toward which the system decoheres. This method is called coherent switching with decay of mixing (CSDM), and it differs from the previously presented SCDM method in that the electronic amplitudes controlling the switching of the decoherent state are treated fully coherently in the electronic equations of motion for each complete passage through a strong interaction region. It is tested against accurate quantum mechanical calculations for 12 atom-diatom scattering test cases. Also tested are the SCDM method and the trajectory surface hopping method of Parlant and Gislason that requires coherent passages through each strong interaction region, and which we call the "exact complete passage" trajectory surface hopping (ECP-TSH) method. The results are compared with previously presented results for the fewest switches with time uncertainty and Tully's fewest switches (TFS) surface hopping methods and the semiclassical Ehrenfest method. We find that the CSDM method is the most accurate of the semiclassical trajectory methods tested. Including coherent passages improves the accuracy of the SCDM method (i.e., the CSDM method is more accurate than the SCDM method) but not of the trajectory surface hopping method (i.e., the ECP-TSH method is not more accurate on average than the TFS method).     

\pi -Electron Long-Range Spin–Spin Coupling in the Full Configuration Interaction Method

A technique for calculating spin perturbation effects in the framework of the previously developed matrix version of the full configuration interaction method is presented. The method is adapted to calculations of -electron atom–atomic spin polarizability defined as the -contribution to the indirect spin–spin nuclear coupling constant. Particular calculations show that pronounced long-range spin–spin coupling is actually possible in some characteristic conjugated systems such as polymethine dye carbocations or some nonalternant hydrocarbons. At the same time, spin–spin correlators appearing in McKonnel's theory are inapplicable in describing such long-range effects.     

NeI2 Photofragmentation Dynamics Through Quasiclassical and Semiclassical Studies

The triatomic system NeI₂ is studied under the consideration that the diatom is found in an excited electronic state (B). The vibrational levels (v=13, …, 23) are considered within two well-known theoretical procedures: quasi-classical trajectories (QCT), where the classical equations of motion for nuclei are solved on a single potential energy surface (PES), and the trajectory surface hopping (TSH) method, where the same are solved in a bunch of crossed vibrational PES (diabatic representation). The trajectory surface hopping fewest switches (TSHFS) is implemented to minimize the number of hoppings, thus allowing the calculations of hopping probability between the different PES's, and the kinetic mechanism to track the dissociation path. From these calculations, several observables such as, the lifetimes, vibrational and rotational energies (I₂), dissociation channels, are obtained. Our results are compared with previous experimental and theoretical work.     

A multireference perturbation theory study on the vertical electronic spectrum of thiophene

The vertical electronic spectrum of the thiophene molecule is investigated by means of second and third order multireference perturbation theory (NEVPT). Single-state and quasi-degenerate NEVPT calculations of more than 25 singlet excited states have been performed. The study is addressed to the theoretical characterization of the four lowest-energy valence states, as well as the 3s, 3p and 3d Rydberg states. In addition, the excitation energies of two and valence states are also reported. For almost all the excited states, coupled cluster calculations (CCSD and CCSDR(3)) have been also carried out, using the same geometry and basis set used for the NEVPT ones, in order to make the comparison between the results of the two methods meaningful. A remarkable accordance between the NEVPT and CC excitation energies is found. The present results, over all, confirm the experimental assignments but, above all, represent an important contribution to the assignments of some low-energy states, valence and Rydberg, for which a firm interpretation is not available in the literature.     

The three-dimensional nonadiabatic dynamics calculation of DH(2)(+) and HD(2)(+) systems by using the trajectory surface hopping method based on the Zhu-Nakamura theory

A theoretical investigation on the nonadiabatic processes of the full three-dimensional D(+)+H(2) and H(+)+D(2) reaction systems has been performed by using trajectory surface hopping (TSH) method based on the Zhu-Nakamura (ZN) theory. This ZN-TSH method refers to not only classically allowed hops but also classically forbidden hops. The potential energy surface constructed by Kamisaka et al. is employed in the calculation. A new iterative method is proposed to yield the two-dimensional seam surface from the topography of the adiabatic potential surfaces, in which the inconvenience of directly solving the first-order partial differential equation is avoided. The cross sections of these two systems are calculated for three competing channels of the reactive charge transfer, the nonreactive charge transfer, and the reactive noncharge transfer, for ground rovibrational state of H(2) or D(2). Also, this study provides reaction probabilities of these three processes for the total angular momentum J=0 and ground initial vibrational state of H(2) or D(2). The calculated results from ZN-TSH method are in good agreement with the exact quantum calculations and the experimental measurements.     

Generalized trajectory surface hopping method based on the Zhu-Nakamura theory

We present a generalized formulation of the trajectory surface hopping method applicable to a general multidimensional system. The method is based on the Zhu-Nakamura theory of a nonadiabatic transition and therefore includes the treatment of classically forbidden hops. The method uses a generalized recipe for the conservation of angular momentum after forbidden hops and an approximation for determining a nonadiabatic transition direction which is crucial when the coupling vector is unavailable. This method also eliminates the need for a rigorous location of the seam surface, thereby ensuring its applicability to a wide class of chemical systems. In a test calculation, we implement the method for the DH(2) (+) system, and it shows a remarkable agreement with the previous results of C. Zhu, H. Kamisaka, and H. Nakamura, [J. Chem. Phys. 116, 3234 (2002)]. We then apply it to a diatomic-in-molecule model system with a conical intersection, and the results compare well with exact quantum calculations. The successful application to the conical intersection system confirms the possibility of directly extending the present method to an arbitrary potential of general topology.     

Direct evaluation of one-electron properties in coupled cluster methods

Summary An analysis of a method for approximate calculations of expectation values for one-electron operators from available coupled cluster amplitudes is presented and illustrated numerically for the polarizability of the Be atom. The one-particle density matrix resulting from the present approach is accurate through the fourth order in the electron correlation perturbation. It has been found that, in order to obtain quantitative agreement between the energy derivative results and the approximate expectation value formalism, the third orderT ₁ T ₂⁽⁰⁾ wave function term must be included into the calculation of the one-particle density matrix. The present method is also considered as a promising tool for calculations of higher-order atomic and molecular properties from high level correlated wave functions.     

A justification for a nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation of the time evolution operator

A justification is given for the validity of a nonadiabatic surface hopping Herman-Kluk (HK) semiclassical initial value representation (SC-IVR) method. The method is based on a propagator that combines the single surface HK SC-IVR method [J. Chem. Phys. 84, 326 (1986)] and Herman's nonadiabatic semiclassical surface hopping theory [J. Chem. Phys. 103, 8081 (1995)], which was originally developed using the primitive semiclassical Van Vleck propagator. We show that the nonadiabatic HK SC-IVR propagator satisfies the time-dependent Schrodinger equation to the first order of variant Planck's over 2pi and the error is O(variant Planck's over 2pi(2)). As a required lemma, we show that the stationary phase approximation, under current assumptions, has an error term variant Planck's over 2pi(1) order higher than the leading term. Our derivation suggests some changes to the previous development, and it is shown that the numerical accuracy in applications to Tully's three model systems in low energies is improved.     

The classification of tensor surface harmonic functions for clusters and coordination compounds

A simple method for enumerating theL and functions for polyhedral cluster and coordination molecules, within Stone's tensor surface harmonic methodology, is described. The nature of theL orbitals which are generated depends on the polyhedral topology and in particular the number of layers of vertices and the number of vertices within each layer. The functions are enumerated from theL 's by a number of spherical harmonic multiplication rules.     

Functional and protective hole hopping in metalloenzymes

Electrons can tunnel through proteins in microseconds with a modest release of free energy over distances in the 15 to 20 Å range. To span greater distances, or to move faster, multiple charge transfers (hops) are required. When one of the reactants is a strong oxidant, it is convenient to consider the movement of a positively charged “hole” in a direction opposite to that of the electron. Hole hopping along chains of tryptophan (Trp) and tyrosine (Tyr) residues is a critical function in several metalloenzymes that generate high-potential intermediates by reactions with O₂ or H₂O₂, or by activation with visible light. Examination of the protein structural database revealed that Tyr/Trp chains are common protein structural elements, particularly among enzymes that react with O₂ and H₂O₂. In many cases these chains may serve a protective role in metalloenzymes by deactivating high-potential reactive intermediates formed in uncoupled catalytic turnover.

Hole hopping through tryptophan and tyrosine residues in metalloenzymes facilitates catalysis and prolongs survival.     

Investigations on electric properties of polymers—V: On the a.c. conductivity of polyphenylacetylenes

The electric conductivity of polyphenylacetylene with various physical and isomeric structures (cis-cisoidal, cis-transoidal and trans-cisoidal) was investigated over the frequency and temperature ranges of 10-10⁵ Hz and 273–347 K, respectively. The transient currents from polyphenylacetylene having cis-cisoidal structure were also studied at 293 K. It was found that a.c. conductivity of cis-cisoidal polymer can be explained in terms of a hopping mechanism. The type of mechanism (classical or quantum) depends both on frequency and temperature. At temperatures <284 K and high frequencies, the quantum mechanism (predominantly by single hops) is involved. As frequency decreases and temperature increases, there is a gradual passing to the classical mechanism (many multiple hops) and then to the Maxwell-Wagner conduction. The electric properties of cis-transoidal polymer are similar to those of trans-cisoidal one, but are different from those for the cis-cisoidal structure. The quantum hopping mechanism, almost entirely involving single hops, seems to predominate in these two polymers. Adsorption of oxygen decreases both conductivity and dielectric constant, as compared with those in nitrogen, only in the case of cis-cisoidal polymer.     

A vectorizable potential energy functional for reactive scattering

Critical steps in trajectory programs for vector restructuring are analysed. The crucial effect of potential energy routine design on the efficiency of trajectory calculations performed on supercomputers have been investigated using a test program for which time consumptions when different algorithms are implemented are compared. Comparisons have been extended to more realistic computational situations by inserting related routines in a trajectory program and calculating reactive properties of some systems of chemical interest.This paper was presented at the International Conference on The Impact of Supercomputers on Chemistry, held at the University of London, London, UK, 13–16 April 1987     

Glass capillary gas chromatography of hop bitter acids. II. Desoxy-α-acids in hop extracts

Summary The presence of about 0.5 to 1% desoxy--acids in hops and hop extracts is confirmed. Desoxy--acids are supposed to be biogenetic precursors and these compounds could be present in the hops as a surplus to this activity, but it is more likely that they have been formed from -and -acids. A gas chromatographic method for analysing the desoxy--acids amount in hops and in hop extracts is described.     

Experimental Characterization of Secular Frequency Scanning in Ion Trap Mass Spectrometers

Secular frequency scanning is implemented and characterized using both a benchtop linear ion trap and a miniature rectilinear ion trap mass spectrometer. Separation of tetraalkylammonium ions and those from a mass calibration mixture and from a pesticide mixture is demonstrated with peak widths approaching unit resolution for optimized conditions using the benchtop ion trap. The effects on the spectra of ion trap operating parameters, including waveform amplitude, scan direction, scan rate, and pressure are explored, and peaks at black holes corresponding to nonlinear (higher-order field) resonance points are investigated. Reverse frequency sweeps (increasing mass) on the Mini 12 are shown to result in significantly higher ion ejection efficiency and superior resolution than forward frequency sweeps that decrement mass. This result is accounted for by the asymmetry in ion energy absorption profiles as a function of AC frequency and the shift in ion secular frequency at higher amplitudes in the trap due to higher order fields. We also found that use of higher AC amplitudes in forward frequency sweeps biases ions toward ejection at points of higher order parametric resonance, despite using only dipolar excitation. Higher AC amplitudes also increase peak width and decrease sensitivity in both forward and reverse frequency sweeps. Higher sensitivity and resolution were obtained at higher trap pressures in the secular frequency scan, in contrast to conventional resonance ejection scans, which showed the opposite trend in resolution on the Mini 12. Mass range is shown to be naturally extended in secular frequency scanning when ejecting ions by sweeping the AC waveform through low frequencies, a method which is similar, but arguably superior, to the more usual method of mass range extension using low q resonance ejection.

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Surface hopping simulation of vibrational predissociation of methanol dimer

The mixed quantum-classical surface hopping method is applied to the vibrational predissociation of methanol dimer, and the results are compared to more exact quantum calculations. Utilizing the vibrational SCF basis, the predissociation problem is cast into a curve crossing problem between dissociative and quasibound surfaces with different vibrational character. The varied features of the dissociative surfaces, arising from the large amplitude OH torsion, generate rich predissociation dynamics. The fewest switches surface hopping algorithm of Tully [J. Chem. Phys. 93, 1061 (1990)] is applied to both diabatic and adiabatic representations. The comparison affords new insight into the criterion for selecting the suitable representation. The adiabatic method's difficulty with low energy trajectories is highlighted. In the normal crossing case, the diabatic calculations yield good results, albeit showing its limitation in situations where tunneling is important. The quadratic scaling of the rates on coupling strength is confirmed. An interesting resonance behavior is identified and is dealt with using a simple decoherence scheme. For low lying dissociative surfaces that do not cross the quasibound surface, the diabatic method tends to overestimate the predissociation rate whereas the adiabatic method is qualitatively correct. Analysis reveals the major culprits involve Rabi-like oscillation, treatment of classically forbidden hops, and overcoherence. Improvements of the surface hopping results are achieved by adopting a few changes to the original surface hopping algorithms.     

Die Wechselwirkung zwischen Walsh- und π-Orbitalen im 7-Cyclopropyliden-norbornadien

The qualitative analysis of the PE.-spectrum of 7-cyclopropylidene-norbornadiene ( 3 ) shows that the ‘through-space’ interaction of the e _A-Walsh orbital with the antisymmetric linear combination \documentclass{article}\pagestyle{empty}\begin{document}$ {{\pi _ - = (\pi _a - \pi _b)} \mathord{\left/ {\vphantom {{\pi _ - = (\pi _a - \pi _b)} {\sqrt 2}}} \right. \kern-\nulldelimiterspace} {\sqrt 2}} $\end{document} of the two π-orbitals in 3 is of the same order as the analogous interaction between π- and the π-orbital of the exocyclic double bond in 7-isopropylidene-norbornadiene ( 2 ).