Volume 120, Issue 18, 08 May 2004
 ARTICLES

 Theoretical Methods and Algorithms

Excitation energies for a benchmark set of molecules obtained within timedependent currentdensity functional theory using the Vignale–Kohn functional
View Description Hide DescriptionIn this article we explain how the existing linear response theory of timedependent densityfunctional theory can be extended to obtain excitation energies in the framework of timedependent currentdensityfunctional theory. We use the Vignale–Kohn currentfunctional [G. Vignale and W. Kohn, Phys. Rev. Lett. 77, 2037 (1996)] which has proven to be successful for describing ultranonlocal exchangecorrelation effects in the case of the axial polarizability of molecular chains [M. van Faassen, P. L. de Boeij, R. van Leeuwen, J. A. Berger, and J. G. Snijders, Phys. Rev. Lett. 88, 186401 (2002); J. Chem. Phys. 118, 1044 (2003)]. We study a variety of singlet excitations for a benchmark set of molecules. The π^{*}←π transitions obtained with the Vignale–Kohn functional are in good agreement with experiment and other theoretical results and they are in general an improvement upon the adiabatic local density approximation. In case of the transitions the Vignale–Kohn functional fails, giving results that strongly overestimate the experimental and other theoretical results. The benchmark set also contains some other types of excitations for which no clear failures or improvements are observed.

The spinunrestricted molecular Kohn–Sham solution and the analogue of Koopmans’s theorem for openshell molecules
View Description Hide DescriptionSpinunrestricted Kohn–Sham (KS) solutions are constructed from accurate ab initio spin densities for the prototype doublet molecules and with the iterative local updating procedure of van Leeuwen and Baerends (LB). A qualitative justification of the LB procedure is given with a “strong” form of the Hohenberg–Kohn theorem. The calculated energies of the occupied KS spin orbitals provide numerical support to the analogue of Koopmans’ theorem in spindensity functionaltheory. In particular, the energies of the minor spin (β) valence orbitals of the considered doublet molecules correspond fairly well to the experimental vertical ionization potentials (VIPs) to the triplet cationic states. The energy of the highest occupied (spinunpaired) α orbital is equal to the first VIP to the singlet cationic state. In turn, the energies of the major spin (α) valence orbitals of the closed subshells correspond to a fiftyfifty average of the experimental VIPs and to the triplet and singlet states. For the Li atom we find that the exact spin densities are represented by a spinpolarized Kohn–Sham system which is not in its ground state, i.e., the orbital energy of the lowest unoccupied β spin orbital is lower than that of the highest occupied α spin orbital (“a hole below the Fermi level”). The addition of a magnetic field in the direction will shift the β levels up so as to restore the Aufbau principle. This is an example of the nonuniqueness of the mapping of the spin density on the KS spindependent potentials discussed recently in the literature. The KS potentials may no longer go to zero at infinity, and it is in general the differences that can be interpreted as (averages of) ionization energies. In total, the present results suggest the spinunrestricted KS theory as a natural oneelectron independentparticle model for interpretation and assignment of the experimental photoelectron spectra of openshell molecules.

Disentangling multidimensional femtosecond spectra of excitons by pulse shaping with coherent control
View Description Hide DescriptionSequences of carefully timed and shaped optical pulses provide femtosecond snapshots of molecular structure as well as electronic and vibrational dynamical processes, in analogy with multidimensional NMR. We apply a genetic learning algorithm towards the design of pulse sequences which simplify the multidimensional signals by controlling the relative intensities of various peaks. Numerical simulations demonstrate how poorly resolved weak features may be amplified and observed by using optimized optical pulses, specifically shaped to achieve a desired spectroscopic target.

Technique for incorporating the density functional Hessian into the geometry optimization of biomolecules, solvated molecules, and large floppy molecules
View Description Hide DescriptionTraditional geometry optimization methods require the gradient of the potential surface, together with a Hessian which is often approximated. Approximation of the Hessian causes difficulties for large, floppy molecules, increasing the number of steps required to reach the minimum. In this article, the costly evaluation of the exact Hessian is avoided by expanding the density functional to second order in both the nuclear and electronic variables, and then searching for the minimum of the quadratic functional. The quadratic search involves the simultaneous determination of both the geometry step and the associated change in the electron density matrix. Trial calculations on indicate that the cost of the quadratic search is comparable to the cost of the density functional energy plus gradient. While this procedure circumvents the bottleneck coupledperturbed step in the evaluation of the full Hessian, the second derivatives of the electronrepulsion integrals are still required for atomicorbitalbased calculations, and they are presently more expensive than the energy plus gradient. Hence, we anticipate that the quadratic optimizer will initially find application in fields in which existing optimizers breakdown or are inefficient, particularly biochemistry and solvation chemistry.

Complex dynamics in a periodically perturbed electrochemical system
View Description Hide DescriptionDynamical response of a passivationmodel subjected to parametric periodic and stochastic perturbations is studied numerically. In response to weak periodic modulation, the system exhibits a rich variety of resonance behavior and induced dynamics, including periodically induced oscillation, birhythmicity, switching between two bistable states, selection of one of the bistable states, mixedmode and chaotic oscillations. These phenomena are discussed in terms of the stability of saddle focus and an incomplete homoclinic connection. Our numerical results are relevant for a wide class of electrochemical oscillatory systems, where the reinjection of unstable trajectory on the neighborhood of a saddle focus is a typical feature in the phase space.

Independent particle theory with electron correlation
View Description Hide DescriptionWe formulate an effective independent particle model where the effective Hamiltonian is composed of the Fock operator and a correlation potential. Within the model the kinetic energy and the exchange energy can be expressed exactly leaving the correlation energy functional as the remaining unknown. Our efforts concentrate on finding a correlation potential such that exact ionization potentials and electron affinities can be reproduced as orbital energies. The equationofmotion coupledcluster approach enables us to define an effective Hamiltonian from which a correlation potential can be extracted. We also make the connection to electron propagator theory. The disadvantage of the latter is the inherit energy dependence of the potential resulting in a different Hamiltonian for each orbital. Alternatively, the Fock space coupledcluster approach employs an effective Hamiltonian which is energy independent and universal for all orbitals. A correlation potential is extracted which yields the exact ionization potentials and electron affinities and a set of associated molecular orbitals. We also describe the close relationship to Brueckner theory.

Full configuration interaction calculation of
View Description Hide DescriptionThe full configuration interaction (FCI) study of the ground state of the neutral beryllium trimer has been performed using an atomic natural orbitals basis set. Both triangular and linear structures have been considered for the cluster. The optimal geometry for the equilateral triangle has been calculated. The potential energy cut sections along the normal mode and one of the components of the mode have then been studied. The FCI symmetric atomization potential of the linear cluster is also reported. It shows a secondary van der Waals minimum at a long bond distance. All singular points in the potential energy curves are characterized. Other properties, like dissociation energies and vibrational frequencies, have been estimated from a fourthorder fitting of a large range of points around the minima. The calculated FCI wave number values for the and normal modes are (467.33±0.43) cm^{−1} and (390.77±0.56) cm^{−1}.

Finitesize scaling for critical conditions for stable quadrupolebound anions
View Description Hide DescriptionWe present finitesize scaling calculations of the critical parameters for binding an electron to a finite linear quadrupole field. This approach gives very accurate results for the critical parameters by using a systematic expansion in a finite basis set. The model Hamiltonian consists of a charge located at the origin of the coordinates and charges located at distances After proper scaling of distances and energies, the rescaled Hamiltonian depends only on one free parameter Two different linear charge configurations with and are studied using basis sets in both spherical and prolate spheroidal coordinates. For the case with the finite size scaling calculations give an extrapolated critical value of by using a basis set with prolate spheroidal coordinates. For the quadrupole case with we obtained an extrapolated critical value of for stable quadrupole bound anions. The corresponding critical exponent for the ground state energy with

Derivation of the electronic nonadiabatic coupling field in molecular systems: An algebraicvectorial approach
View Description Hide DescriptionIn this Communication it is suggested that various elements of the nonadiabatic coupling matrix, are created by the singularnonadiabatic coupling terms of the system. Moreover, given the spatial distribution of these coupling terms in the close vicinity of their singularity points yields, according to this approach, the integrated intensity of the field at every point in the region of interest. To support these statements we consider the conical intersections of the three lower states of the system: From an ab initio treatment we obtain the nonadiabatic coupling terms around each conical intersection separately (at its close vicinity) and having those, create the field at every desired point employing vectoralgebra. This approach is also used to calculate the intensity of the Curl of those matrix elements that lack their own sources in the present case]. The final results are compared with relevant ab initio calculations.

A longrangecorrected timedependent density functional theory
View Description Hide DescriptionWe apply the longrange correction (LC) scheme for exchange functionals of density functional theory to timedependent density functional theory (TDDFT) and examine its efficiency in dealing with the serious problems of TDDFT, i.e., the underestimations of Rydbergexcitation energies,oscillator strengths, and chargetransferexcitation energies. By calculating vertical excitation energies of typical molecules, it was found that LCTDDFT gives accurate excitation energies, within an error of 0.5 eV, and reasonable oscillator strengths, while TDDFT employing a pure functional provides 1.5 eV lower excitation energies and two orders of magnitude lower oscillator strengths for the Rydberg excitations. It was also found that LCTDDFT clearly reproduces the correct asymptotic behavior of the chargetransferexcitation energy of ethylene–tetrafluoroethylene dimer for the long intramolecular distance, unlike a conventional farnucleus asymptotic correction scheme. It is, therefore, presumed that poor TDDFT results for pure functionals may be due to their lack of a longrange orbital–orbital interaction.

Spectrally resolved femtosecond twocolor threepulse photon echoes: Study of ground and excited state dynamics in molecules
View Description Hide DescriptionWe report the use of spectrally resolved femtosecond twocolor threepulse photon echoes as a potentially powerful multidimensional technique for studying vibrational and electronic dynamics in complex molecules. The wavelengths of the pump and probe laser pulses are found to have a dramatic effect on the spectrum of the photon echo signal and can be chosen to select different sets of energy levels in the vibrational manifold, allowing a study of the dynamics and vibrational splitting in either the ground or the excited state. The technique is applied to studies of the dynamics of vibrational electronic states in the dye molecule Rhodamine 101 in methanol.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Intracluster stereochemistry in van der Waals complexes: Steric effects in ultraviolet photodissociation of stateselected
View Description Hide DescriptionHighresolution IRUV multiple resonance methods are employed to elucidate the photodissociationdynamics of quantum stateselected Ar–HOD and van der Waals clusters. A single mode pulsed OPO operating in the region of the OH second overtone is used to prepare individual rovibrational states that are selectively photodissociated at specific excimer wavelengths. Subsequent fluorescence excitation of the resulting OH (OD) fragments yields dynamical information on the photofragmentation event and any resulting intracluster collisions. This technique is used to characterize spectroscopically the overtone band of the Ar–HOD complex with an origin at 10648.27 cm^{−1}. The effects of Ar complexation on the dissociationdynamics are inferred by comparison of the OD photofragment quantum state distributions resulting from dissociation of single rovibrational states of the complex with those from isolated HOD photodissociation. The important role played by the initial internal state of the complex is demonstrated by comparison of the current Ar–HOD data with previously published results for the state. We interpret the dramatic differences in the dynamics of the two systems as manifestations of the nodal structure of the vibrational state in the parent complex and the way in which it governs the collision probability between the Ar atom and the escaping photofragments.

Hydrogen bonds in 1,4dioxane/ammonia binary clusters
View Description Hide DescriptionWith synchrotron radiation, we have studied the photoionization and dissociation of 1,4dioxane/ammonia clusters in a supersonic expansion. The observed major product ions are the 1,4dioxane cation and protonated cluster ions (where M=1,4dioxane), and the intensities of the unprotonated cluster ions are much lower. Fully optimized geometries and energies of the neutral cluster and related cluster ions have been obtained using the ab initio molecular orbital method and density functional theory. The potential energy surface of the excited state of was also calculated. With these results, the mechanisms of different photoionization–dissociation channels have been suggested. The most probable channel is electron ejection from the highest occupied molecular orbital, followed by the dissociation into and For another main channel, after removing an electron from the second highest occupied molecular orbital, the intracluster proton transfer process takes place to form the stable unprotonated cluster ion which usually leads to the dissociated protonated cluster ion and a radical

Firstprinciples study of the electronic structures of icosahedral clusters
View Description Hide DescriptionWe have studied the electronic structures of icosahedral clusters 19, 43, and 55) by using a realspace firstprinciples cluster method with generalized gradient approximation for exchangecorrelation potential. The hexagonal closepacked and fcc closepacked clusters have been studied additionally for comparisons. It is found that the icosahedral structures are the most stable ones except for where fcc closepacked structure is favorable in energy. We present and discuss the variation of bond length, the features of the highest occupied molecular orbitals and the lowest unoccupied molecular orbital, the evolution of density of states, and the magnetic moment in detail. The results are in good agreement with the predictions from the collisioninduced dissociation and sizeselected anion photoelectron spectroscopy experiments.

Heuristic overlapexchange model of noble gas chemical shifts
View Description Hide DescriptionIt is now generally recognized that overlapexchange interactions are the primary cause of the mediumdependent magnetic shielding(chemical shift) in all noble gases except helium, although the attractive electrostaticdispersion (van der Waals) interactions play an indirect role in determining the penetration of the interacting species into the repulsive overlapexchange region. The shortrange nature of these overlapexchange interactions, combined with the fact that they often can be approximated by simple functions of the overlap of the wave functions of the interacting species, suggests a useful semiempiricalmodel of these chemical shifts. In it the total shielding is the sum of shieldings due to pairwise interactions of the noble gas atom with the individual atoms of the medium, with the “atomic” shielding terms either estimated by simple functions of the atomic overlap integrals averaged over their Boltzmannweighted separations, or determined by fits to experimental data in systems whose complexity makes the former procedure impractical. Results for chemical shifts in the noble gases and in a variety of molecular and condensed systems, including families of nalkanes, straightchain alcohols, and the endohedral compounds and are encouraging for the applicability of the model to systems of technical and biomedical interest.

Vacuum ultraviolet pulsed field ionization study of Accurate thermochemistry for the and system
View Description Hide DescriptionThe dissociation of energyselected to form near its threshold has been investigated using the pulsed field ionizationphotoelectron (PFIPE)photoion coincidence method. The breakdown curves for and give a value of for the 0 K dissociation threshold or appearance energy (AE) for from We have also measured the PFIPE vibrational bands for 1, 2, and 3), revealing partially resolved rotational structures. The simulation of these bands yields precise ionization energies (IEs) for Using the 0 K AE and determined in the present study, together with the known 0 K bonddissociation energy for we have determined the and 0 K heat of formation for to be and respectively. The PFIPE spectrum is found to exhibit a steplike feature near the indicating that the dissociation of excited at energies slightly above the dissociation threshold is prompt, occurring in the time scale as observed for the system. The available energetic data for the and system are found to be in excellent accord with those for the and system after taking into account the zeropoint vibrational energy corrections. This finding indicates that the thermochemical data for these two systems are reliable with wellfounded error limits.

Angleenergy distributions of Penning ions in crossed molecular beams. IV.
View Description Hide DescriptionRelative doubly differential cross sections for the Penning ionization of by spinstateselected metastable He are reported at centerofmass collision energies E of 3.1 and 4.2 kcal/mol in a crossed supersonic beam experiment employing a rotatable mass spectrometerdetector. The measurements are sufficiently dense in velocity space as to avoid having to functionalize the differential cross sections in order to transform the intensities into the c.m. The product is scattered sharply forward, c.m. halfwidth at halfmaximum, with respect to the incident direction of at both energies for both spin states. On the average the products have lost energy upon recoil, mean recoil energy and coupling is significant and increasing with E. Extensive comparison is made with infiniteordersudden quantum scattering calculations based on previous experimental optical potential surfaces and a recent ab initio exit channel surface. Aside from predicted even sharper forward scattering, agreement is fair to good for both spin states. The calculations allow an assessment of the possibility of observing quantum effects in the differential reactive scattering in these systems.

Photodissociation spectroscopy and dynamics of the radical
View Description Hide DescriptionThe photodissociation spectroscopy and dynamics resulting from excitation of the transition of have been examined using fast beam photofragment translational spectroscopy. The photofragment yield spectrum reveals vibrationally resolved structure between 29 870 and 38 800 cm^{−1}, extending ∼6000 cm^{−1} higher in energy than previously reported in a laserinduced fluorescence excitation spectrum. At all photonenergies investigated, only the and HCCO+HF fragment channels are observed. Both product channels yield photofragment translational energy distributions that are characteristic of a decay mechanism with a barrier to dissociation. Using the barrier impulsive model, it is shown that fragmentation to products occurs on the ground statepotential energy surface with the isomerization barrier between and governing the observed translational energy distributions.

Inelastic electron interaction (attachment/ionization) with deoxyribose
View Description Hide DescriptionWe have investigated experimentally the formation of anions and cations of deoxyribose sugar via inelastic electron interaction (attachment/ionization) using a monochromatic electron beam in combination with a quadrupole mass spectrometer. The ion yields were measured as a function of the incident electron energy between about 0 and 20 eV. As in the case of other biomolecules (nucleobases and amino acids), low energy electron attachment leads to destruction of the molecule via dissociative electron attachment reactions. In contrast to the previously investigated biomolecules dehydrogenation is not the predominant reaction channel for deoxyribose; the anion with the highest dissociative electron attachment (DEA) cross section of deoxyribose is formed by the release of neutral particles equal to two water molecules. Moreover, several of the DEA reactions proceed already with “zero energy” incident electrons. In addition, the fragmentation pattern of positively charged ions of deoxyribose also indicates strong decomposition of the molecule by incident electrons. For sugar the relative amount of fragment ions compared to that of the parent cation is about an order of magnitude larger than in the case of nucleobases. We determined an ionization energy value for of 10.51±0.11 eV, which is in good agreement with ab initio calculations. For the fragment ion we obtained a threshold energy lower than the ionization energy of the parent molecular ion. All of these results have important bearing for the question of what happens in exposure of living tissue to ionizing radiation. Energy deposition into irradiated cells produces electrons as the dominant secondary species. At an early time after irradiation these electrons exist as ballistic electrons with an initial energy distribution up to several tens of electron volts. It is just this energy regime for which we find in the present study rather characteristic differences in the outcome of electron interaction with the deoxyribose molecule compared to other nucleobases (studied earlier). Therefore, damage induced by these electrons to the DNA or RNA strands may start preferentially at the ribose backbone. In turn, damaged deoxyribose is known as a key intermediate in producing strand breaks, which are the most severe form of lesion in radiation damage to DNA and lead subsequently to cell death.

A stable nitrogencontaining radical with cyclic ground state
View Description Hide DescriptionThe structures and isomerization of species are explored at density functional theory and ab initio levels. Fourteen minimum isomers are located connected by 23 interconversion transition states. At the coupledcluster single double +zeropoint vibrational energies level, the thermodynamically most stable isomer is a fourmembered ring form cSiSiCN 1 with Si–C cross bonding. Isomer 1 has very strong C–N multiple bonding characters, formally suggestive of a radical adduct between and CN. Such a highly πelectron localization can effectively stabilize isomer 1 to be the ground state. The second lowlying isomer is a linear form SiCNSi 5 (9.8 kcal/mol above 1) with resonating structure among Si=C⋅–N=Si, ⋅Si=C=N=Si, and Si=C=N–Si⋅ with the former two bearing more weight. The species 1 and 5 have very high kinetic stability stabilized by the barriers of at least 25 kcal/mol. Both isomers should be experimentally or astrophysically observable. In light of the fact that no cyclic nitrogencontaining species have been detected in space, the cyclic species 1 could be a very promising candidate. The calculated results are compared to those of the analogous molecules and Implications of in interstellar and Ndoped SiC vaporization processes are also discussed.