Volume 112, Issue 14, 08 April 2000
 THEORETICAL METHODS AND ALGORITHMS


Nonadiabatic dynamics via the classical limit Schrödinger equation
View Description Hide DescriptionThe coupled Schrödinger equations that describe nonadiabaticdynamics are recast using the Bohm formulation of quantum mechanics. The resulting coupled Bohm equations are solved numerically for two scattering models, giving results that are essentially identical to wavepacket solution of the original coupled Schrödinger equations. The classical limit of the set of coupled Bohm equations is then described, producing a mixed quantumclassical theory incorporating classicallike motion on each potential energy surface accompanied by quantum transitions between the quantum states. Numerical tests of the mixed quantumclassical method are in excellent agreement with the accurate fullquantum results for the model problems. The method is contrasted with the related surfacehopping approach. It is shown that computing the dynamics of a distribution of classical particles is more consistent and more accurate than computing the motion of independent point particles as with surface hopping.

Generalized quantum Fokker–Planck theory and its application to laser driven intramolecular hydrogen transfer reactions in condensed phases
View Description Hide DescriptionA generalized quantum Fokker–Planck theory is proposed to treat the correlated dynamics of coherent driving and Markovian dissipation. The resulting formulation is applicable to arbitrary external timedependent driving fields and satisfies the detailed balance condition at arbitrary temperatures. Analyzed are also the formal relations among the Caldeira–Leggett quantum Fokker–Planck equation, the Bloch–Redfield theory, and the present formulation. The approach is numerically implemented to study the intramolecular hydrogen transfer reaction dynamics in a onedimensional model system. Different forms of external pulsed driving fields are exploited and their ability to compete with concurring relaxation processes is investigated. Energy relaxation and pure dephasing are shown to have rather different influences on the reaction yield.

A multiple spawning approach to tunneling dynamics
View Description Hide DescriptionQuantum mechanical tunnelingeffects are investigated using an extension of the full multiple spawning (FMS) method. The FMS method uses a multiconfigurational frozen Gaussian ansatz for the wave function and it allows for dynamical expansion of the basis set during the simulation. Basis set growth is controlled by allowing this expansion only when the dynamics signals impending failure of classical mechanics, e.g., nonadiabatic and/or tunnelingeffects. Previous applications of the FMS method have emphasized the modeling of nonadiabaticeffects. Here, a new computational algorithm that accounts for tunnelingeffects is introduced and tested against exact solution of the Schrödinger equation for two multidimensional model problems. The algorithm first identifies the tunneling events and then determines the initial conditions for the newly spawned basis functions. Quantitative agreement in expectation values, tunneling doublets and tunneling splitting is demonstrated for a wide range of conditions.

Period adding and broken Farey tree sequence of bifurcations for mixedmode oscillations and chaos in the simplest threevariable nonlinear system
View Description Hide DescriptionA detailed study of the simplest threevariable model exhibiting mixedmode oscillations and chaos is presented. We show that mixedmode oscillations appear due to a sequence of bifurcations which is characterized by a combination of the Farey tree that is broken by chaotic windows and period adding. This scenario is supported by a family of onedimensional return maps. The model also exhibits hysteresis between stable steady state and mixed modes.

The performance of densityfunctional theory in challenging cases: Halogen oxides
View Description Hide DescriptionHalogen dioxides (FOO, ClOO, BrOO, OClO, OBrO), their cationic and anionic derivatives and two isomers of have been studied by means of densityfunctional theory(DFT) and the results compared with those from high level ab initio molecular orbital calculations. Three different density functionals (SVWN, B3LYP, and G96LYP) combined with a basis set were used to obtain geometries and vibrational frequencies, which were then compared with MP2 (secondorder Moller–Plesset), QCISD, and CCSD(T) (coupledcluster single double triple) results. The calculations generally give geometries and frequencies in excellent agreement with those calculated from high level ab initio calculations such as CCSD(T). Exceptions, such as ClOO and BrOO, arise when high spin contamination at B3LYP level produces spurious results. Atomisation enthalpies evaluated at level of theory are observed to be in good agreement with the experimental values. In some particular cases this agreement is better than that obtained at level. For ionizationenthalpies the CCSD(T) calculations seem to be superior to the DFT ones. Wave function instabilities [with respect to the UHF (unrestricted Hartree–Fock) transformation in the case of the cations and internal symmetry breaking in the case of the OXO compounds and the isomer of are observed less frequently when DFT methods are used.

Shielding polarizabilities via continuous transformation of the origin of the current density in the set of small molecules: HCN, and HNC
View Description Hide DescriptionA procedure, based on a continuous transformation of the origin of the (quantum mechanical) current density that sets the diamagnetic contribution to zero (CTOCDDZ ) all over the molecular domain, is applied to determine shielding polarizabilities to first order in a perturbing electric field. In any calculations relying on the algebraic approximation, irrespective of size and quality of the (gaugeless) basis set employed, all the components of the CTOCDDZ magnetic shieldingpolarizability are origin independent, and the constraints for charge and current conservation are exactly satisfied. The effects of a static uniform electric field on the nuclear magnetic resonance(NMR) shielding of HCN, and HNC molecules have been investigated within the CTOCDDZ method, and compared with the conventional results evaluated via the same basis sets, and with theoretical results taken from the literature.

Ewald summation and reaction field methods for potentials with atomic charges, dipoles, and polarizabilities
View Description Hide DescriptionThe Ewald summation technique and the reaction field method have been generalized to potentials with atomic charges, dipole moments, and anisotropicpolarizabilities. These are two common methods to treat longrange interactions in molecular simulations. Expressions for the potential energy, the electrostatic potential, the electrostatic field, the electrostatic field gradient, the force, and the virial are given, allowing for the calculation of longrange contributions to these properties within the Ewald summation or reaction field methods. We have compared numerical results using the Ewald summation under vacuum conditions with those from direct summations for a number of simple systems and found a complete agreement within the numerical precision with the exception of trivial shifts of the potential. The expressions given will facilitate the use of polarizable models in molecular simulations and hence improving our understanding of condensed matter.

Distributed first and second order hyperpolarizabilities: An improved calculation of nonlinear optical susceptibilities of molecular crystals
View Description Hide DescriptionThe method of calculating distributed polarizabilities is extended to the first and second dipole hyperpolarizabilities, in order to describe more accurately the molecular response to strong and inhomogeneous external timedependent electric fields. The dipolar response is expressed in terms of both potential related chargedensity response functions and electric field related dipoledensity response functions. The macroscopic linear, quadratic, and cubic optical dipole susceptibilities of molecular crystals are expressed in terms of the distributed (hyper) polarizabilities. This formulation differs from previous theories using distributed dipoles in that it allows for a rigorous treatment of both local induced dipoles and charge flow between different regions of the molecule. As an example, the distributed polarizabilities and first hyperpolarizabilities of urea at the selfconsistentfield level are used to calculate the linear and quadratic susceptibilities of the urea crystal. The linear susceptibility does not differ substantially from that calculated with previous less rigorous models for distributed response, but the quadratic susceptibility is about 50% of that calculated with previous models. This indicates that the present treatment of distributed response should give a quadratic susceptibility in good agreement with experimental data, once the effects of electronic correlation, frequency dispersion, and the permanent crystal field are taken into account.
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 GAS PHASE DYNAMICS AND STRUCTURE: SPECTROSCOPY, MOLECULAR INTERACTIONS, SCATTERING, AND PHOTOCHEMISTRY


Competitive charge transfer reactions in small clusters
View Description Hide DescriptionProduction of stable hydrated magnesium complexes of the general form (where has been possible using the pickup technique. Observations of ion intensities as a function of N together with data from collision induced dissociation processes (for ions in the range indicates the existence of a closed solvation shell for to which additional water molecules are strongly bound. Collisioninduced charge transfer in ions of all sizes yields solvated magnesium hydroxide ions accompanied by the loss of a hydronium ion, and M water molecules. For 4, and 5, the above process is seen to be in competition with charge transfer to unprotonated water, and clusters of the general form are detected, where M now represents the total number of water molecules lost. These two separate loss channels are interpreted as being due to the presence of different structural (or transient) forms of those cluster ions where One structure corresponds to a highly symmetrical arrangement of the water molecules bonded directly to the magnesium dication, and is responsible for the formation of ions by charge transfer. In the second type of structure, at least one water molecule moves to an outer solvation shell, but remains hydrogen bonded to a molecule in the first shell. In this latter configuration, it is suggested that the formation of a saltbridge structure may lower the barrier to proton transfer and lead to the loss of a hydronium ion.

A first principles study of the acetylene–water interaction
View Description Hide DescriptionWe present an extensive study of the stationary points on the acetylene–water (AW) groundstatepotential energy surface (PES) aimed in establishing accurate energetics for the two different bonding scenarios that are considered. Those include arrangements in which water acts either as a proton acceptor from one of the acetylene hydrogen atoms or a proton donor to the triple bond. We used a hierarchy of theoretical methods to account for electron correlation [MP2 (secondorder Moller–Plesset), MP4 (fourthorder Moller–Plesset), and CCSD(T) (coupledcluster single double triple)] coupled with a series of increasing size augmented correlation consistent basis sets We furthermore examined the effect of corrections due to basis set superposition error (BSSE). We found that those have a large effect in altering the qualitative features of the PES of the complex. They are responsible for producing a structure of higher symmetry for the global minimum. Zeropoint energy (ZPE) corrections were found to increase the stability of the arrangement. For the global (water acceptor) minimum of symmetry our best estimates are and a van der Waals distance of The water donor arrangement lies 0.3 kcal/mol (0.5 kcal/mol including ZPE corrections) above the global minimum. The barrier for its isomerization to the global minimum is however, inclusion of BSSE and ZPEcorrections destabilize the water donor arrangement suggesting that it can readily convert to the global minimum. We therefore conclude that there exists only one minimum on the PES in accordance with previous experimental observations. To this end, vibrational averaging and to a lesser extend proper description of intermolecular interactions (BSSE) were found to have a large effect in altering the qualitative features of the groundstate PES of the acetylene–water complex.

Determination of μvj vector correlations in photodissociation experiments using resonanceenhanced multiphoton ionization with timeofflight mass spectrometer detection
View Description Hide DescriptionA practical method is described for resonanceenhanced multiphotonionization probing of photofragment μvjcorrelations arising in molecular photodissociation on a linearly polarized singlephoton electricdipole transition. The scheme uses polarized spectroscopy on the twophoton resonant transition with velocity detection by timeofflight mass spectrometry. The technique is based on the theory of Kummel, Sitz, and Zare for polarized twophoton detection of angular momentum alignment and orientation and Dixon’s bipolar moment description of vector correlations. Optimal experimental and polarization geometries are described for selective measurement of targeted bipolar moments. The utility of the technique is demonstrated in experiments using REMPI to probe methyl radical vector correlations in the 266 nm photodissociation of methyl iodide.

The use of locally dense basis sets in the calculation of indirect nuclear spin–spin coupling constants: The vicinal coupling constants in F, Cl, Br, I)
View Description Hide DescriptionWe have calculated the vicinal indirect nuclear spinspin coupling constants in the series of molecules with X=H, F, Cl, Br, and I at the selfconsistent field level and using the second order polarization propagator approximation (SOPPA). We have studied the effect of electron correlation and of the substituents (X=F, Cl, Br, and I) on all four contributions to the coupling constants. But in particular we have investigated the possibility of using locally dense basis sets, i.e., we have carried out calculations with basis sets, where the basis functions on the hydrogen atoms were optimized for the calculation of spin–spin coupling constants whereas on the other atoms smaller, contracted sets of basis functions were used. This changes the results for the couplings by ∼0.3 Hz or 3%. However, the change is almost entirely due to the orbital paramagnetic term and is independent of electron correlation, which enables one to estimate the SOPPA results in the full basis sets. Furthermore we find that the Fermi contact term is the dominant contribution to the vicinal coupling constants, because it is about an order of magnitude larger than the other contributions and because the two orbital angular moment terms almost cancel each other completely. Also the changes in the calculated couplings due to electron correlation are solely due to the Fermi contact term. However, the shifts in the coupling constants caused by the different substituents arise in equal amounts from the Fermi contact and the orbital diamagnetic term, whereas the changes in the orbital paramagnetic term are smaller and are in the opposite direction. In comparison with the experimental data we find very good agreement for and However, the agreement becomes less good with increasing nuclear charge of the substituent X.

Rotational spectra of four of the five conformers of 1pentene
View Description Hide DescriptionThe rotational spectra of four of the five expected conformers of 1pentene, together with their monosubstituted isotopic forms, have been measured in a molecular beam using a pulsednozzle Fouriertransform microwave spectrometer. One of the conformers has pointgroup symmetry while the other three conformers have pointgroup symmetry. The measurements are compared to results from molecular modeling calculations using the MM3 molecularmechanics force field of Allinger et al. and to ab initio electronic structure calculations (MP2/631G^{*}, MP2/6311G^{*}, MP4/631G^{*}, MP4/6311G^{*}). Both types of calculations suggest the existence of five distinct conformers of 1pentene, four of symmetry and one of symmetry. Both the MM3 and ab initiorotational constants deviate from the measured values by ⩽5%. The relatively high barriers between the four conformers limit the conformational cooling in the expansion, allowing all four conformers to be observed at the <2 K rotational temperature of the molecular beam. Efforts to identify the fifth conformer were unsuccessful, presumably due to its reduced intensity, which makes it difficult to identify its spectral pattern from among the plethora of weak unassigned lines due to impurities, complexes, and possible vibrationally excited conformers. The fifth conformer is predicted to have the highest energy of the five conformers of 1pentene, as well as a lowenergy barrier (109 cm^{−1} at MP2/6311G^{*} level) for conformational isomerization.

Reproducing kernel technique for extracting accurate potentials from spectral data: Potential curves of the two lowest states and of the sodium dimer
View Description Hide DescriptionThis work describes an extension of the Reproducing Kernel Hilbert Space (RKHS) method, in conjunction with the Tikhonov regularization, for constructing potential energy surfaces, with correct asymptotic forms, from high quality experimental measurements. The method is applied to the construction of new, global potential energy curves of the two lowest states and of the sodium dimer using rovibrational spectral measurements. The exchange interaction of at intermediate and long ranges is accordingly derived and adopted for determining the ionization energy of the corresponding valence electron. It is found that the resulting groundstatedissociation energy of agrees within the experimental errors with the most recent experimental value Jones et al., Phys. Rev. A 54, R1006 (1996)]. The well depth of the state is determined to be compared to the Rydberg–Klein–Rees (RKR) value of [Li et al., J. Chem. Phys. 82, 1178 (1985)]. Moreover, the equilibrium positions of both RKHS potential curves, for the state and for the state, are in excellent agreement with previously determined RKR results of [Babaky and Hussein, Can. J. Phys. 67, 912 (1989)] and 5.0911 Å (Li et al.), respectively. The experimentally determined values of the equilibrium position and well depth for the state differ from recent theoretical values of 5.192 Å and obtained by highly accurate ab initio calculations [Gutowski, J. Chem. Phys. 110, 4695 (1999)]. Finally, both RKHS potential curves at large distances reproduce very recent theoretical dispersion coefficients within percentage errors.

Electronic properties of mixed barium–oxygen clusters
View Description Hide DescriptionIonization potentials of clusters have been measured by one photonionization. These measurements, combined with relative abundances observed in mass spectra recorded under low (direct ionization) and high (dissociativeionization) laser intensity, allow to derive general trends in the evolution of the structure and stability of barium–oxide clusters. Stoichiometric clusters exhibit a very fast transition toward the ionic bulk barium–oxide structure while suboxides exhibit a completely different behavior. In the small size range the evolution of the electronic properties does not show any regular behavior. In particular, present very low ionization potentials while, on the opposite, the ionization potentials of clusters are relatively high. On the other hand, beyond the evolution of the electronic properties is rather smooth and a specific structural transition is observed when the oxygen/barium ratio increases.

Structural information on the and state of fluorophenol by hole burning and high resolution ultraviolet spectroscopy
View Description Hide DescriptionThe electronic transitions of fluorophenol situated at 36 799.382 and 36 906.710 denoted the A and B bands, respectively, have been investigated by high resolution fluorescence excitation spectroscopy.Hole burning studies together with the high resolution spectroscopy results show that both bands originate in the same ground state and can be fitted to the rotational constants of the cis isomer. The rotational constants for the excited states are found to be MHz, MHz and MHz for the A band and MHz, MHz and MHz for the B band. The planarity of the ground state is lost upon electronic excitation, which enhances the activity of an outofplane vibration. The A and B band transitions arise from excitations to respectively the zero and first overtone levels in the doubleminimum potential of this outofplane vibration, which shows similarities to the socalled butterfly mode observed in other benzene derivatives.

Coupledcluster studies of the hyperfine splitting constants of the thioformyl radical
View Description Hide DescriptionHyperfine splitting constants (hfs) of the electronic ground state of the thioformyl radical (HCS) have been determined at the coupledcluster level with single, double, and perturbatively applied connected triple excitations [CCSD(T)] using 39 basis sets. Variation of the CCSD(T) hyperfine splittings with basis set was ascertained using a fixed geometry, optimized at the CCSD(T) level with Dunning’s correlationconsistent polarized valence quadrupleζ basis set (ccpVQZ). Pople basis sets, and give isotropic coupling constants in good agreement with the experimental vibrationally averaged value of 127.4 MHz, deviating by 5.5 and 9.3 MHz, respectively. Dunning’s valence correlationconsistent basis sets (ccpVDZ, augccpVDZ, ccpVTZ, augccpVTZ, ccpVQZ, augccpVQZ) deviate 6.4 MHz (augccpVQZ) to 14.9 MHz (ccpVDZ) from the experimental value. The correlationconsistent core valence analogues of these sets give very similar values with deviations from experiment of 7.4 MHz (ccpCVQZ) to 14.2 MHz (ccpCVDZ). A direct comparison with the vibrationally averaged experimental value is not precisely possible since the hyperfine splittings are strongly geometry dependent and all theoretical predictions refer to the equilibrium geometry. Small Pople basis sets (312G, 631G, and 6311G) give the worst results, deviating by 49.5, 34.1, and 31.8 MHz, respectively. All CCSD(T) values fall below the experimental value. The and hyperfine splittings are not known experimentally, but the equilibrium values are predicted here to be 274.7 MHz and 21.7 MHz at the ccpCVQZ CCSD(T) level of theory. Significantly different values are predicted by density functional theory(DFT) for the and hyperfine splittings.

Scheme for stateselective formation of highly rotationally excited diatomic molecules
View Description Hide DescriptionA scheme is proposed for making highly rotationally excited diatomic molecules (“super rotors”) in their ground vibrational and electronic state, e.g., where the rotational energy exceeds the bond strength Such levels, while strictly speaking quasibound, have very long tunneling lifetimes for and should have very interesting and unique collisional properties, especially at low temperature. The rotation of the molecules is “spun up” by sequential irradiation by R branch photons in the bands starting with cold molecules at low J. Spontaneous emission to other vibrational levels is overcome by using a pump laser and its multiple Raman sidebands as in previous work on “spinning down” diatomics.

A study of the BrO and radicals with vacuum ultraviolet photoelectron spectroscopy
View Description Hide DescriptionThe BrO radical, prepared by the reaction, has been investigated by ultraviolet photoelectron spectroscopy. Two vibrationally resolved bands were observed corresponding to the ionizations and These assignments are supported by the results of complete active space selfconsistent field/multireference configuration interaction (CASSCF/MRCI) calculations performed as part of this work. The adiabatic ionization energies of these bands were measured as and respectively. Measurement of the vibrational separations in these bands led to estimates of the vibrational constants in the ionic states of and and Franck–Condon simulations of the vibrational envelopes gave values of the ionic state bond lengths of and for the and states of respectively. The reaction was found to give a band at associated with a reaction product. Comparison of the results obtained for the reaction showed that it could not be assigned to ionization of BrO. Calculations of the first adiabatic ionization energies and Franck–Condon simulations of the vibrational envelopes of the first photoelectron bands of and and their isomers demonstrated that this band corresponds to the first ionization of OBrO, the ionization. Franck–Condon simulations were performed with the experimental geometry of but with different cationic state geometries. The simulated envelope which most closely matched the experimental envelope gave geometrical parameters of and for the ionic state.

Infrared spectroscopy of CH stretching vibrations of jetcooled alkylbenzene cations by using the “messenger” technique
View Description Hide DescriptionThe CH stretching vibrations of the benzene–Ar, toluene–Ar, and ethylbenzene–Ar clusters prepared in jet expansion were observed in both the neutral and cationic ground states by using infrared–ultraviolet double resonance and infrared photodissociationspectroscopy, respectively. Vibrational frequencies for the inplane modes of the clusters have been found to be practically the same as those of the corresponding bare molecules. The aromatic CH stretching vibrations showed high frequency shifts upon ionization, and their infrared absorption intensities remarkably decreased. The alkyl CH stretching vibrations were also significantly changed in both frequency and intensity upon ionization.Density functional calculations well reproduced the observed infrared spectra of the neutral and cationic states, and enhancement of hyperconjugation in the cationic state was pointed out.
