Volume 116, Issue 20, 22 May 2002
 ARTICLES

 Theoretical Methods and Algorithms

Symplectic quaternion scheme for biophysical molecular dynamics
View Description Hide DescriptionMassively parallel biophysical molecular dynamics simulations, coupled with efficient methods, promise to open biologically significant time scales for study. In order to promote efficient finegrained parallel algorithms with low communication overhead, the fast degrees of freedom in these complex systems can be divided into sets of rigid bodies. Here, a novel Hamiltonian form of a minimal, nonsingular representation of rigid body rotations, the unit quaternion, is derived, and a corresponding reversible, symplectic integrator is presented. The novel technique performs very well on both model and biophysical problems in accord with a formal theoreticalanalysis given within, which gives an explicit condition for an integrator to possess a conserved quantity, an explicit expression for the conserved quantity of a symplectic integrator, the latter following and in accord with Calvo and SanzSarna, Numerical Hamiltonian Problems (1994), and extension of the explicit expression to general systems with a flat phase space.

Nonadiabatic unimolecular reaction kinetic theory based on l thorder semiMarkov model
View Description Hide DescriptionWe present a microcanonical kinetic theory, which we refer to as the lthorder semiMarkov phase space theory (SMlPST), for nonadiabatic unimolecular dissociations dominated by standard surface hopping dynamics. In this theory,reactiondynamics is considered as a stochastic transport, which is described as an lthorder Markov chain, among cells produced from partition of the available phase space. Kinetic equations are derived by importing residence time of stay cells as a random variable into the Markov chain. An efficient method to determine the parameters of the kinetic equations is developed, which is made up of Monte Carlo phase space integration and shorttime trajectory calculations. As a test calculation, the SMlPST has been applied to a model system for the predissociation of collinear We show that the SMlPST works well, giving rate coefficients of much better accuracy than conventional statistical theory and of comparable accuracy to standard trajectory calculations with a lower computational effort.

Ensemble representable densities for atoms and molecules. III. Analysis of polarized neutron diffraction experiments when several Zeeman levels are populated
View Description Hide DescriptionPolarized neutron diffractionexperiments conducted at 4.2 K on crystals are analyzed by using a 4dimensional model Hilbert space made of ab initio nelectron wave functions of the molecular ion. The magnetic structure factors given by the best ensemble density operator that is representable in our model space are fitted to the experimental ones by optimizing two spinorbit mixing coefficients of the embedded ions and several configuration interaction coefficients. The optimized density operator can in turn be used to calculate any observable. Here we present density maps of the spin density, and the orbital current density. The method, which is general, gives a goodness of fit, less than 1 with fewer parameters optimized than other methods employed so far. It provides a new way of gaining information about spinorbit coupling and the relative contributions of spin and orbital motion to the magnetic properties of an atomic or molecular system. Another interesting finding is that a less than 1, can be obtained with a spin density of the same sign everywhere in space, leading to the conclusion that spin polarization is within the experimental error. The socalled “collinear approximation” has been avoided in this work although it has been found to be justified for this system. A direct comparison is made between calculated and experimental flipping ratios.

A general framework for discrete variable representation basis sets
View Description Hide DescriptionA framework for discrete variable representation (DVR) basis sets is developed that is suitable for multidimensional generalizations. Those generalizations will be presented in future publications. The new axiomatization of the DVR construction places projection operators in a central role and integrates semiclassical and phase space concepts into the basic framework. Rates of convergence of basis set expansions are emphasized, and it is shown that the DVR method gives exponential convergence, assuming conditions of analyticity and boundary conditions are met. A discussion of nonorthogonal generalizations of DVR functions is presented, in which it is shown that projected δfunctions and interpolating functions form a biorthogonal basis. It is also shown that one of the generalized DVR proposals due to Szalay [J. Chem. Phys. 105, 6940 (1996)] gives exponential convergence.

Extension of quantized Hamilton dynamics to higher orders
View Description Hide DescriptionThe quantized Hamilton dynamics (QHD) method, which was introduced and developed in J. Chem. Phys. 113, 6557 (2000) to the second order, is extended to the third and fourth orders. The QHD formalism represents an extension of classical mechanics and allows for the derivation of a hierarchy of equations of motion which converge with the quantummechanical limit. Here, the second, third, and fourth order QHD approximations are applied to two model problems: the decay of a particle in a metastable cubic potential and the intermode energy exchange observed in the Henon–Heiles system. The QHD results exhibit good convergence with the quantum data with increasing order yet preserve the computational efficiency of classical calculations. The second order QHD approximation already does an excellent job in maintaining the zeropoint energy in the Henon–Heiles system and describing moderate tunneling events in the metastable potential. Extensions to higher orders substantially improve the QHD results for deep tunneling and are capable of describing the finer details of energy exchange.

A reaction path Hamiltonian defined on a Newton path
View Description Hide DescriptionA reaction path Hamiltonian is formulated in terms of a Newton reference path. The defining differential equation for the latter is solved by quadratically expanding the original equation, which in turn leads to an improved formulation of the reaction path Hamiltonian. This new reference path is found to deal properly with bifurcation points, a difficulty not solved by intrinsic reaction coordinatefollowing algorithms. The Newton path is found, in addition, to be reliable as for the description of chemical rearrangement processes, as it is illustrated with the application to the HCN↔CHN isomerization as well as the 1,2 hydrogen migration between ethyne oxide and the corresponding carbene.

Systematic corrections to the equivalent core model
View Description Hide DescriptionThe widely used equivalent core model (ECM) describes core hole states in systems with atomic charge by considering corresponding states with fully occupied core in systems with increased charge When calculating energies of core hole states, the valence energy of these states often has been assumed to equal the valence energy of the ground state. This approach misses several points: most importantly, the different spin symmetry of the corresponding states. The behavior of core hole states is governed by an effective matrix Hamiltonian due to the two possible spin states of the core hole. A recently introduced diagonalization gives rise to a scalar core hole Hamiltonian. Both the ECM and the core hole Hamiltonian act in valence space. This allows establishment of a connection between these two approaches. By expressing the core hole Hamiltonian in the orbital basis, we systematically derive corrections to the ECM. Those corrections, including the one arising because of the different spin symmetry of the corresponding states, are presented in second order of Møller–Plesset perturbation theory (MP2). Hence, they can be implemented very easily so that groundstate calculations in a system may directly provide the core hole state energy in the original system.

Variational principles for describing chemical reactions: Condensed reactivity indices
View Description Hide DescriptionTwo recent papers [P. W. Ayers and R. G. Parr, J. Am. Chem. Soc. 122, 2010 (2000); 123, 2007 (2001)] have shown how variational principles for the energy may be used to derive and elucidate the significance of the chemical reactivity indices of densityfunctional theory. Here, similar ideas are applied, yielding a systematic, mathematically rigorous, and physically sound approach to condensed reactivity indices. First, we use the variational principle for the energy to derive an expression for the condensed Fukui function index in terms of the condensed hardness kernel. Next, we address an important open problem pertaining to condensed reactivity indices: when (if ever) is the condensed Fukui function for an atom in a molecule negative? In particular, our analysis confirms the observation, hitherto based only on computational evidence, that the Hirshfeld partitioning is optimal for obtaining nonnegative Fukui functions. We also hypothesize that the strong diagonal dominance of the condensed hardness kernel is sufficient for the nonnegativity of the Fukui function. Errors in the partitioning of molecules into atoms and inadequate treatment of correlation are pinpointed as the most likely causes of negative condensed Fukui functions. We conclude by noting that the condensed Fukui functions are, in some respects, more appropriate indicators of a molecular site’s reactivity than the Fukui function itself.

Densityofstates Monte Carlo method for simulation of fluids
View Description Hide DescriptionA Monte Carlo method based on a densityofstates sampling is proposed for study of arbitrary statistical mechanical ensembles in a continuum. A random walk in the twodimensional space of particle number and energy is used to estimate the density of states of the system; this density of states is continuously updated as the random walk visits individual states. The validity and usefulness of the method are demonstrated by applying it to the simulation of a LennardJones fluid. Results for its thermodynamic properties, including the vapor–liquid phase coexistence curve, are shown to be in good agreement with highaccuracy literature data.

Puddleskimming: An efficient sampling of multidimensional configuration space
View Description Hide DescriptionWe examine the effectiveness of a simple method for surmounting energy barriers and enhancing the exploration of configuration space in Monte Carlo(MC) and molecular dynamics (MD) simulations. Proposed previously for treatingsurfacediffusion [M. M. Steiner, P.A. Genilloud, and J. W. Wilkins, Phys. Rev. B 57, 10236 (1998)], the method has widespread applicability and is particularly advantageous for systems with potential energy landscapes whose features are not known a priori. The algorithm requires selection of a single parameter, a “boost energy” The MC or MD simulation is carried out on an effective potential energy function that is equal to the true potential energy when it is greater than but is equal to otherwise. Since the effective potential energy is, therefore, never less than deep energy minima are removed analogous to a rough landscape that has been flooded with water. The bias introduced by altering the potential energy function in this way is easily and rigorously removed “onthefly.” We test the method with a MD simulation of the equilibrium populations of conformations of npentane. The method recovers the canonical equilibrium distribution with dramatically increased sampling efficiency and modest additional computational overhead, over a range of temperatures. In cases for which the potential energy function can be written as a sum of terms, the energy boost can be applied to the selected terms rather than to the entire potential energy function. We illustrate this by application to the dihedral angle term only of the empirical npentane potential energy function and show that this further enhances sampling efficiency. The simple nature of this algorithm allows it to be readily scaled to highdimensional systems. We discuss the prognosis for applying this method to more complex systems such as liquids and macromolecules.

Assessment of timedependent densityfunctional theory for the calculation of critical features in the absorption spectra of a series of aromatic donor–acceptor systems
View Description Hide DescriptionSinglet and triplet vertical excitation energies of a series of acceptor parasubstituted dimethyl–anilines named, respectively, 4DMAB–CN, 4AB–CN, 4DMAB–CHO, TMAB–CN, 4DMAB–COMe, and have been calculated with TDDFT. Geometry optimization and excitation energy calculations have been performed, in most cases, with the B3LYP functional using a 631G(d) and a basis set (hereafter referred to as Sm and Bg, respectively). 4DMAB–CN and TMAB–CN have been investigated with particular care since gasphase absorption spectra exist for those two molecules allowing thus a direct comparison with experimental results. The first and second singlet excited states of 4DMAB–CN, commonly named locally excited (LE) state and charge transfer (CT) state, are 0.1 and 0.04 eV higher than the experimental results at the B3LYPBg level, leading to a 0.06 eV underestimation of the gap between the two states. In the case of TMAB–CN, which is twisted in its ground state,B3LYP–(Sm/Bg) results show an error of 0.36 eV for the singlet CT state. Better agreement with experiment is obtained using the MPW1PW91 functional and Bg basis set with an underestimation of 0.17 eV for the singlet CT state and an overestimation of 0.16 eV for the second singlet state. Contrary to DFT/SCI results, the relative order and position of excitation energies of 4AB–CN and 4DMAB–CHO are well reproduced compared to solution spectra results. The singlet CT state using B3LYP and a Bg basis set is calculated 0.1 eV higher in energy than the experimental value obtained in isopentane for while the same excitation energy is predicted 0.08 and 0.28 eV too low compared to the gasphase values for 4DMAB–COMe and respectively. Finally, the CT excitation energy and its relative position to the LE state agrees with the acceptor strength concept.

Loworder scaling local electron correlation methods. V. Connected triples beyond (T): Linear scaling local CCSDT1b
View Description Hide DescriptionA new method for the iterative treatment of connected triple substitutions in the framework of local coupled cluster theory is introduced here, which is the local equivalent of the canonical CCSDT1b method. The effect of the triple substitutions is treated in a selfconsistent manner in each coupled cluster iteration. As for the local (T) method presented earlier in this series the computational cost of the method scales asymptotically linear with molecular size. The additional computational burden due to the involvement of triples in each coupled cluster iteration hence is not nearly as dramatic as for the parental canonical method, where it implies an increase in the computational complexity of the coupled cluster iteration from to The method has certain advantages in comparison to the perturbative a posteriori treatment of connected triples (T) for cases where static correlation effects start to play a role. It is demonstrated that molecules with about 100 atoms and 1000 basis functions can be treated with the local CCSDT1b method, i.e., at a level beyond local CCSD(T). The new local coupled cluster methods introduced here and in previous papers of this series are applied in a study on the energetics of the Bergman autocyclization and retroBergman ring opening of an azaenediyne derivate, which was recently proposed as a promising candidate for anticancer drug development.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Translational dynamics of a cold water cluster in the presence of an external uniform electric field
View Description Hide DescriptionMolecular dynamics simulations for a TIP4P water cluster consisting of 32 molecules at under the influence of a broad range of constant electric fields are presented. This work focuses on the evolution of the single particle translational dynamics, mainly along the field axis as the field is progressively increased, by means of meansquaredisplacement curves, the selfpart of the van Hove distribution functions and the intermediate scattering functions. Two critical fields have been identified, the one, assigned to the onset of the dipole alignment and the second one to the onset of crystallization. These transitions are marked by an abrupt increase of the corresponding structurerelaxation times, which remain nearly constant for electric fields between and Structure relaxation has been found to obey stretched exponential dynamics, whereas the Q dependence of the relaxation times, for all fields, followed a power law. Fields weaker than have been found to induce a weakening of the molecular interactions. In this case, the system develops a dynamic behavior similar to that met in the liquid.

Quantum control of molecular handedness in a randomly oriented racemic mixture using three polarization components of electric fields
View Description Hide DescriptionA new laser control scenario is presented for obtaining substantial amounts of enantiomeric enrichment from a randomly oriented racemic mixture. This is carried out by using three polarization components of electric fields; one is used for orientation, the other two for controlling the chirality. The effectiveness is demonstrated by numerical simulations on the enantiomeric enrichment of the axial chiral molecule.

Vacuum ultraviolet laser pulsed field ionization photoelectron study of cis2butene
View Description Hide DescriptionThe vacuum ultraviolet pulsed field ionizationphotoelectron spectra of supersonically cooled cis2butene have been measured in the photon energy range of 73 560–75 460 cm^{−1}. Using the ab initiotheoreticalrotational constants of and its cation and a semiempirical simulation scheme, we have obtained a good fit of the origin vibrational band with partially resolved contours of rotational branches. After taking into account the Stark shift, the ionization energy of is determined to be Guided by ab initio vibrational frequency calculations, we have also assigned the vibrational bands observed for in its ground state.

Conformationselective photoionization of covalentlylinked diaryl compounds: Excimermediated onecolor twophoton ionization in seeded beams of 1,3diphenylpropane
View Description Hide DescriptionHoleburning spectroscopy and ionization threshold measurement were combined with fluorescence excitation (FE) and resonant twophotonionization (R2PI) spectroscopies to probe conformation dependence of photoionization for jetcooled 1,3diphenylpropane (DPP). The excitation energy dependence of excimer fluorescence and that of onecolor R2PI indicate formation of an intramolecular excimer and an efficient photoionization of the excimer that occur at higher energies. The energy threshold for the enhanced photoionization, which concurs with that for the excimer formation, is considerably lower for the trans–gauche conformer than for the trans–trans or the gauche–gauche conformer. These results demonstrate the occurrence of conformation selective excimermediated photoionization in DPP. The important precursor role of the singlet excimer in the photoionization is attributed to the conformational similarity between the intramolecular singlet excimer and the most stable groundstate cation of DPP, which leads to a very favorable Franck–Condon factor for the photoionization of the excimer. Even for excitation energies far below the energy threshold for excimer formation, the efficiency of onecolor R2PI is substantially greater for tg than for tt or gg for photoionization with a high intensity laser. Comparison of the ionization threshold measured with high photon flux with that obtained with low photon flux suggests that the greater ionization efficiency of the tg conformer at high photon flux may be related to direct photoionization of the tg to the ionic state of DPP with Tshaped arrangement of the phenyl moieties.

Unraveling the highly overlapping photoelectron bands of Nonadiabatic effects due to conical intersection
View Description Hide DescriptionThe highly overlapping photoelectron bands of molecule are studied theoretically with the aid of ab initio quantum dynamical methods. The theoretical results are compared with the highresolution 58.4 nm He I recording of MotteTollet et al. [Chem. Phys. 284, 452 (1998)]. The theoretical findings reveal the existence of a conical intersection in the electronic manifold of the radical cation and the highly overlapping photoelectron bands originate from the associated nonadiabatic interactions. A diabatic vibronic Hamiltonian for the interactingmanifold of is constructed in terms of the dimensionless normal coordinates of the neutral employing a linear vibronic coupling scheme. The coupling parameters of the Hamiltonian are derived from ab initioelectronic structure results. The photoelectron bands are then calculated with this Hamiltonian by solving the eigenvalue equation using a quantum dynamical method and the Lanczos algorithm. The photoelectron bands reveal a prominent progression of the bend vibrational mode and a weak progression of the symmetric stretch vibrational mode of the cation. The vibronic fine structures of the photoelectron bands are carefully examined and an adiabatic ionization energy value of 12.171 eV is estimated for the band. The impact of nonadiabatic coupling between the and electronic states of on the photoelectron dynamics is also explicitly discussed.

interactions in organic light emitting devices: The different roles of Mg, Al, and Li atoms
View Description Hide DescriptionThe geometrical and electronic structures of tris(8hydroxyquinoline)aluminum molecule interacting with low work function metals of Mg, Al, and Li used in organic light emitting devices have been studied by firstprinciple calculations using density functional theory. We found that energetically the most favorable complexation for the interacting systems is the metal atom inserting into the core of the molecule with the metal atom bridging two oxygen atoms and being coplanar with one of the quinoline ligands. The related various core level and energy shifts and the characteristic vibrational modes determined consequently are in reasonable agreements with the available experimental data. The cohesion energies of the metal complexes increase in the order of among which the is considerably smaller, indicating the distinctive feature of interaction from those of Al and Li. The calculated electronic structures show that there are only slight changes in the frontier orbitals for and complexations, while for the Al insertion into considerable electronic localizations are induced, indicating the significantly different roles they may play in metal–organic interface and thus in the device performance.

On the electronic structure of by allelectron Dirac–Hartree–Fock calculations
View Description Hide DescriptionDirac–Hartree–Fock (DHF) calculations were performed to investigate the hydration of the trivalent Cm ion with a configuration on the models of The curium–oxygen distances and stabilization energies were evaluated. The DHF wave functions were analyzed by the Mulliken populations and spinor projections. Hydration was found to be characterized by the coordinate bond. An increase in the number of water molecules caused an increase in the curium–oxygen distance and a reduction of the stabilization energy per water molecule. The fluorescence transition energy was also estimated using the complete openshell configuration interaction (COSCI) method. Redshifts due to hydration were obtained and were in accord with observations of the nephelauxetic effect. The isovalent gadolinium ion was also studied for comparison.

Visible emission from the vibrationally hot radical following vacuumultraviolet photolysis of acetylene: Experiment and theory
View Description Hide DescriptionPhotolysis of acetylene has been performed by vacuumultraviolet excitation with the synchrotron radiation via the Rydberg states converging to the first ionization potential (IP) at 11.4 eV. Only the visible fluorescence of the ethynyl radical was observed in the system. Excitation of several Rydberg states of acetylene over a large energy range between 9 and 11.4 eV allowed us to observe for the first time the evolution of this continuum with increasing Rydberg excitation. Intensity calculations based on accurate ab initiopotential energy surfaces of were performed by using a onedimensional model accounting for the largeamplitude motion of the H atom around the C–C bond and for the overall rotation of the radical. These calculations successfully reproduce the observed visible continuum (maximum at 500 nm and blue side cutoff at 400 nm) and bring new information on the distribution of the internal energy deposited in the fragment. For most excited Rydberg states,predissociation occurs in a rather low time scale, leaving the fragment in the state, vibrationally hot, mostly with significant excitation in the bending mode around the isomerization barrier.