Volume 125, Issue 2, 08 July 2006
 ARTICLES

 Theoretical Methods and Algorithms

Evaluation of alternative sumoverstates expressions for the first hyperpolarizability of pushpull conjugated systems
View Description Hide DescriptionA dipolarfree sumoverstates expression for the diagonal components of the first hyperpolarizability tensor has been proposed by Kuzyk [Phys. Rev. A72, 053819 (2005)] as an alternative to the traditional expression. We examine both alternatives for the longitudinal of four typical pushpull conjugated systems using the ab initio CIS and CIS(D) schemes to approximate the excited state properties. Since they are each evaluated approximately the two SOS expressions yield different values for and it is found that (i) they evolve symmetrically as the number of excited states is increased so that their average is nearly constant; (ii) in the static limit, the two values agree better with one another when their average is close to the “exact” correlated result; and (iii) frequency dispersion can affect the agreement between the alternative expressions. On the basis of (i) and (ii) it appears best for typical pushpull conjugated systems to estimate the static , and the error in the value so obtained, by averaging the Kuzyk and traditional results.

A secondquantization framework for the unified treatment of relativistic and nonrelativistic molecular perturbations by response theory
View Description Hide DescriptionA formalism is presented for the calculation of relativistic corrections to molecular electronic energies and properties. After a discussion of the Dirac and Breit equations and their firstorder FoldyWouthuysen [Phys. Rev.78, 29 (1950)] transformation, we construct a secondquantization electronic Hamiltonian, valid for all values of the finestructure constant . The resulting dependent Hamiltonian is then used to set up a perturbation theory in orders of , using the general framework of timeindependent response theory, in the same manner as for geometrical and magnetic perturbations. Explicit expressions are given to second order in for the HartreeFock model. However, since all relativistic considerations are contained in the dependent Hamiltonian operator rather than in the wave function, the same approach may be used for other wavefunction models, following the general procedure of response theory. In particular, by constructing a variational Lagrangian using the dependent electronic Hamiltonian, relativistic corrections can be calculated for nonvariational methods as well.

Firstprinciples calculations of zerofield splitting parameters
View Description Hide DescriptionIn this work, an implementation of an approach to calculate the zerofield splitting (ZFS) constants in the framework of ab initio methods such as complete active space selfconsistent field, multireference configuration interaction, or spectroscopy oriented configuration interaction is reported. The spinorbit coupling (SOC) contribution to ZFSs is computed using an accurate multicenter meanfield approximation for the BreitPauli Hamiltonian. The SOC parts of ZFS constants are obtained directly after diagonalization of the SOC operator in the basis of a preselected number of roots of the spinfree Hamiltonian. This corresponds to an infinite order treatment of the SOC in terms of perturbation theory. The spinspin (SS) part is presently estimated in a meanfield fashion and appears to yield results close to the more complete treatments available in the literature. Test calculations for the first and secondrow atoms as well as firstrow transition metal atoms and a set of diatomic molecules show accurate results for the SOC part of ZFSs. SS contributions have been found to be relatively small but not negligible (exceeding for oxygen molecule). At least for the systems studied in this work, it is demonstrated that the presented method provides much more accurate estimations for the SOC part of ZFS constants than the emerging density functional theory approaches.

Dynamically screened local correlation method using enveloping localized orbitals
View Description Hide DescriptionIn this paper we present a local coupled cluster approach based on a dynamical screening scheme, in which amplitudes are either calculated at the coupled cluster level (in this case CCSD) or at the level of perturbation theory, employing a threshold driven procedure based on MP2 energy increments. This way, controllable accuracy and smooth convergence towards the exact result are obtained in the framework of an a posteriori approximation scheme. For the representation of the occupied space a new set of local orbitals is presented with the size of a minimal basis set. This set is atom centered, is nonorthogonal, and has shapes which are fairly independent of the details of the molecular system of interest. Two slightly different versions of combined local coupled cluster and perturbation theory equations are considered. In the limit both converge to the untruncated CCSD result. Benchmark calculations for four systems (heptane, serine, water hexamer, and oxadiazole2oxide) are carried out, and decay of the amplitudes, truncation error, and convergence towards the exact CCSD result are analyzed.

Phase control in the vibrational qubit
View Description Hide DescriptionIn order to use molecular vibrations for quantum information processing one should be able to shape infrared laser pulses so that they can play the role of accurate quantum gates and drive the required vibrational transitions. In this paper we studied theoretically how the relative phase of the optimized transitions affects accuracy of the quantum gates in such a system. Optimal control theory and numerical propagation of laserdriven vibrational wave packets were employed. The dependencies observed for onequbit gates NOT, rotation, and Hadamard transform are qualitatively similar to each other. The results of the numerical tests agree well with the analytical predictions.

String method in collective variables: Minimum free energy paths and isocommittor surfaces
View Description Hide DescriptionA computational technique is proposed which combines the string method with a sampling technique to determine minimum free energy paths. The technique only requires to compute the mean force and another conditional expectation locally along the string, and therefore can be applied even if the number of collective variables kept in the free energy calculation is large. This is in contrast with other free energy sampling techniques which aim at mapping the full free energy landscape and whose cost increases exponentially with the number of collective variables kept in the free energy. Provided that the number of collective variables is large enough, the new technique captures the mechanism of transition in that it allows to determine the committor function for the reaction and, in particular, the transition state region. The new technique is illustrated on the example of alanine dipeptide, in which we compute the minimum free energy path for the isomerization transition using either two or four dihedral angles as collective variables. It is shown that the mechanism of transition can be captured using the four dihedral angles, but it cannot be captured using only two of them.

An analysis of the accuracy of an initial value representation surface hopping wave function in the interaction and asymptotic regions
View Description Hide DescriptionThe behavior of an initial value representation surface hopping wave function is examined. Since this method is an initial value representation for the semiclassical solution of the time independent Schrödinger equation for nonadiabatic problems, it has computational advantages over the primitive surface hopping wave function. The primitive wave function has been shown to provide transition probabilities that accurately compare with quantum results for model problems. The analysis presented in this work shows that the multistate initial value representation surface hopping wave function should approach the primitive result in asymptotic regions and provide transition probabilities with the same level of accuracy for scattering problems as the primitive method.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Electron localization function at the correlated level
View Description Hide DescriptionThe electron localization function (ELF) has been proven so far a valuable tool to determine the location of electron pairs. Because of that, the ELF has been widely used to understand the nature of the chemical bonding and to discuss the mechanism of chemical reactions. Up to now, most applications of the ELF have been performed with monodeterminantal methods and only few attempts to calculate this function for correlated wave functions have been carried out. Here, a formulation of ELF valid for mono and multiconfigurational wave functions is given and compared with previous recently reported approaches. The method described does not require the use of the homogeneous electron gas to define the ELF, at variance with the ELF definition given by Becke. The effect of the electron correlation in the ELF, introduced by means of configuration interaction with singles and doubles calculations, is discussed in the light of the results derived from a set of atomic and molecular systems.

Semiclassical wave packet study of ozone forming reaction
View Description Hide DescriptionWe have applied the semiclassical wave packet method (SWP) to calculate energies and lifetimes of the metastable states (scattering resonances) in a simplified model of the ozone forming reaction. All values of the total angular momentum up to were analyzed. The results are compared with numerically exact quantum mechanical wave packet propagation and with results of the timeindependent WKB method. The wave functions for the metastable states in the region over the well are reproduced very accurately by the SWP; in the classically forbidden region and outside of the centrifugal barrier, the SWP wave functions are qualitatively correct. Prony’s method was used to extract energies and lifetimes from the autocorrelation functions. Energies of the metastable states obtained using the SWP method are accurate to within 0.1 and for underthebarrier and overthebarrier states, respectively. The SWP lifetimes in the range of are accurate to within 10%. A threelevel model was used to investigate accuracies of different approximations for the reaction rate constant. It was shown that the majority of the metastable states in this system are either long lived (narrow resonances) which can be treated as stable, or short lived (broad resonances) which can be treated without the knowledge of their lifetimes. Only a few metastable states fall into the intermediate range where both energies and lifetimes are needed to model the kinetics. The recombination rate constant calculated with the SWP method at room temperature and pressure is in good agreement with available experimental data.

Ab initio nonadiabatic dynamics study of ultrafast radiationless decay over conical intersections illustrated on the cluster
View Description Hide DescriptionWe present a theoretical approach for the ultrafast nonadiabaticdynamics based on the ab initiomolecular dynamics carried out “on the fly” in the framework of the configuration interaction method combined with Tully’s surface hopping algorithm for nonadiabatic transitions. This approach combined with our Wigner distribution approach allows us to perform accurate simulations of femtosecond pumpprobe spectra in the systems where radiationless transitions among electronic states take place. In this paper we illustrate this by theoretical simulation of ultrafast processes and nonradiative relaxation in the cluster, involving three excited states and the ground electronic state. Furthermore, we show that our accurate simulation of the photoionization pumpprobe spectrum is in full agreement with the experimental signal. Based on the nonadiabaticdynamics at high level of accuracy and taking into account all degrees of freedom, the nonradiative lifetime for the excited state of has been determined to be .

Nonstatistical effects in the dissociation of ethyl radical: Finding order in chaos
View Description Hide DescriptionHow does one identify order in complex dynamical systems? A BornOppenheimer molecular dynamics simulation of the dissociation of ethyl radical, , produces an ensemble of classical trajectories which are decomposed in the timefrequency domain using wavelets. A timedependent scalar metric, the normalized instantaneous orbital complexity, is constructed and shown to correlate not only to the more conventional Lyapunov exponents but also to the dissociation time for an individual trajectory. The analysis of the ensemble of trajectories confirms that the longlived trajectories are associated with a low degree of ergodicity. While the analysis of molecular dissociationdynamics is the narrow focus of the present work, the method is more general for discovery and identification of ordered regimes within large sets of chaotic data.

Conformational identification of tryptamine embedded in superfluid helium droplets using electronic polarization spectroscopy
View Description Hide DescriptionWe report electronic polarizationspectroscopy of tryptamine embedded in superfluidheliumdroplets. In a dc electric field, dependence of laser induced fluorescence from tryptamine on the polarization direction of the excitation laser is measured. Among the three observed major conformers A, D, and E, conformers D and E display preference for perpendicular excitation relative to the orientation field, while conformer A is insensitive to the polarization direction of the excitation laser. We attribute the behavior of conformer A to the fact that the angle between the permanent dipole and the transition dipole is close to the magic angle. Using a linear variation method, we can reproduce the polarization preference of the three conformers and determine the angle between the transition dipole and the permanent dipole. Since the side chain exerts small effect on the direction of the transition dipole in the frame of the indole chromophore, all three conformers have a common transition dipole more or less in the indole plane at an angle of relative to the long axis of the chromophore. The orientation of the side chain, on the other hand, determines the size and direction of the permanent dipole, thereby affecting the angle between the permanent dipole and the transition dipole. For conformer D in the droplet, our results agree with the Anti(ph) structure, rather than the Anti(py) structure. Our work demonstrates that polarizationspectroscopy is effective in conformational identification for molecules that contain a known chromophore. Although coupling of the electronic transition with the helium matrix is not negligible, it does not affect the direction of the transition dipole.

Electronic states and potential energy curves of molybdenum carbide and its ions
View Description Hide DescriptionThe potential energy curves and spectroscopic constants of the ground and 29 lowlying excited states of MoC with different spin and spatial symmetries within have been investigated. We have used the complete active space multiconfiguration selfconsistent field methodology, followed by multireference configuration interaction (MRCI) methods. Relativistic effects were considered with the aid of relativistic effective core potentials in conjunction with these methods. The results are in agreement with previous studies that determined the ground state as . At the level, the transition energies to the and states are 3430 and , respectively, in fair agreement with the results obtained by DaBell et al. [J. Chem. Phy.114, 2938 (2001)], namely, 4003 and , respectively. The three band systems located at 18 611, 20 700, and observed by Brugh et al. [J. Chem. Phy.109, 7851 (1998)] were attributed to the excited , , and states respectively. At the MRCISD level, these states are 17 560, 20 836, and above the ground state respectively. We have also identified a state lying above the ground state. The ground states of the molecular ions are predicted to be and for and , respectively.

Ab initio studies on clusters: Existence of surface and interiorbound extra electrons
View Description Hide DescriptionA recent paper by Turi et al.[Science309, 914 (2005)] suggests that the anionic water clusters smaller than (at a low temperature) will only have surfacebound extra electrons and no internally bound electrons. Accordingly, cluster isomers should only have surfacebound extra electrons. The ab initio results presented here, however, suggest that the cluster isomers can have two distinct types of isomers with almost the same energy. The one type of isomer (type 1) has all the nonHbonding H atoms (NHB H) directed outward and surfacebound extra electron while the other type (type 2) has a number of NHB H atoms directed toward cavity and has an interiorbound electron, and thus, contradicts the earlier quantum simulation results of Turi et al.

Relativistic correction to the and electronic states of the molecular ion and the moleculelike states of the antiprotonic helium
View Description Hide DescriptionEffective potentials of the relativistic BreitPauli corrections for the and electron states of the molecular ion and the , , and states of the antiprotonic helium atom are calculated within the BornOppenheimer approximation. The variational expansion with randomly chosen exponents has been used for numerical studies. The results obtained for the BreitPauli effective potentials are accurate up to ten significant digits for the molecular ion and eight digits for the atom.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Hostassisted intramolecular vibrational relaxation at low temperatures: OH in an argon cage
View Description Hide DescriptionThe vibrational relaxation of hydroxyl radicals in the state has been studied using the semiclassical perturbation treatment at cryogenic temperatures. The radical is considered to be trapped in a closest packed cage composed of the 12 nearest argon atoms and undergoes local translation and hindered rotation around the cage center. The primary relaxation pathway is towards local translation, followed by energy transfer to rotation through hinderedtofree rotational transitions. Freetofree rotational transitions are found to be unimportant. All pathways are accompanied by the propagation of energy to argon phonon modes. The deexcitation probability of is and the rate constant is between 4 and . The negligible temperature dependence is attributed to the presence of intermolecular attraction in the guesthost encounter, which counteracts the dependence resulting from local translation. Calculated relaxation time scales are much shorter than those of homonuclear molecules, suggesting the importance of the hindered and free motions of OH and strong guesthost interactions.

Dynamic light scattering in mixed alkali metaphosphate glass forming liquids
View Description Hide DescriptionWe report the first ever photon correlation spectroscopy performed on single alkali and mixed alkali metaphosphate glasses at refractory temperatures above the glass transition. We find not only a significant decrease in the glass transition temperature but also a decrease in fragility for the mixed alkali composition as compared with the single akali glasses. We argue that structural relaxation in these polymeric oxide glasses is largely controlled by the cross linking cations and that the changes in fragility that we observed are a reflection of changes in the cooperativity of structural relaxation wrought by the substantial decrease in the ion mobility that accompanies the mixing of alkali ions.

Symmetrized correlation function for liquid parahydrogen using complextime pairproduct propagators
View Description Hide DescriptionWe present a simple and efficient method for calculating symmetrized time correlation functions of neat quantum fluids. Using the pairproduct approximation to each complextime quantum mechanical propagator, symmetrized correlation functions are written in terms of a double integral for each degree of freedom with a purely positive integrand. At moderate temperatures and densities, where the pairproduct approximation to the Boltzmann operator is sufficiently accurate, the method leads to quantitative results for the early time part of the correlation function. The method is tested extensively on liquid parahydrogen at and used to obtain accurate quantum mechanical results for the initial segment of the symmetrized velocity autocorrelation function of this system, as well as the incoherent dynamic structure factor at certain momentum transfer values.

Solvent response and dielectric relaxation in supercooled butyronitrile
View Description Hide DescriptionWe have measured the dynamics of solvation of a triplet state probe, quinoxaline, in the glassforming dipolar liquid butyronitrile near its glass transition temperature . The Stokes shift correlation function displays a relaxation time dispersion of considerable magnitude and the optical linewidth changes along the solvation coordinate in a nonmonotonic fashion. These features are characteristic of solvation in viscoussolvents and clearly indicate heterogeneous dynamics, i.e., spatially distinct solvent response times. Using the dielectric relaxation data of viscous butyronitrile as input, a microscopic model of dipolar solvation captures the relaxation time, the relaxation dispersion, and the amplitude of the dynamical Stokes shift remarkably well.

Global phase diagram for the honeycomb potential
View Description Hide DescriptionWe calculate the global phase diagram using classical statistical mechanics for an isotropic pair potential that has been previously [Rechtsman et al., Phys. Rev. Lett.95, 228301 (2005)] shown to produce the lowcoordinated twodimensional honeycomb crystal as the groundstate structure. Lowcoordinated crystals are of practical interest because they have desirable photonic bandgap properties. The phase diagram is obtained from Helmholtz free energies calculated using thermodynamic integration and Monte Carlo simulations. Our results show that the honeycomb crystal remains stable in the global phase diagram even after temperature effects are taken fully into account. Other stable phases in the phase diagram are high and low density triangular phases and a fluid phase. We find no evidence of gasliquid or liquidliquid phase coexistence.