Volume 115, Issue 13, 01 October 2001
 ARTICLES

 Theoretical Methods and Algorithms

Efficient localized Hartree–Fock methods as effective exactexchange Kohn–Sham methods for molecules
View Description Hide DescriptionThe form of the Kohn–Sham (KS) exchange potential, which arises from the approximation that the Hartree–Fock (HF) and the exchangeonly KS determinant are equal, is derived. Two related procedures to determine the KS exchange potential follow from this approximation: a selfconsistent localized HF procedure and a transformation localized HF procedure yielding the local KS exchange potential from HF orbitals. Both procedures can be considered as almost exact exchange KS methods which require only occupied orbitals and are invariant with respect to unitary transformations of the orbitals, i.e., depend only on the first order density matrix. The resulting local KS exchange potentials are free of Coulomb selfinteractions and exhibit the correct longrange behavior. The Krieger, Li, and Iafrate (KLI) procedure to determine the KS exchange potential can be considered as an approximation to the introduced localized HF procedures. Highly efficient methods to carry out the presented localized HF as well as KLI procedures are introduced. An efficient basis set approach to calculate the Slater potential is presented. The methods can easily be implemented in present standard quantum chemistry codes. Applications to small and medium size molecules and clusters are presented. The Hartree–Fock and the exchangeonly KS determinant are found to be surprisingly close. Qualitatively correct, Coulomb selfinteraction free KS orbitals and eigenvalue spectra are obtained.

A theoretical model for molecules interacting with intense laser pulses: The Floquetbased quantumclassical Liouville equation
View Description Hide DescriptionThe Floquetbased quantumclassical Liouville equation (FQCLE) is presented as a novel theoreticalmodel for the interaction of molecules with intense laser pulses. This equation efficiently combines the following two approaches: First, a small but spectroscopically relevant part of the molecule is treated quantummechanically while the remaining degrees of freedom are modeled by means of classical molecular dynamics. The corresponding nonadiabaticdynamics is given by the quantumclassical Liouville equation which is a firstorder approximation to the partial Wigner transform of full quantum dynamics. Second, the dynamics of the quantum subsystem is described in terms of instantaneous Floquet states thus eliminating highly oscillatory terms from the equations of motion. The resulting FQCLE is shown to have a well defined adiabatic limit: For infinitely heavy classical particles and for infinitely slow modulation the dynamics adiabatically follows the Floquet quasienergy surfaces for a strictly timeperiodic field. Otherwise, nonadiabtic effects arise both from the motion of the classical particles and from the modulation of the field which is assumed to be much slower than the carrier frequency. A numerical scheme to solve the FQCLE is based on a Trotter splitting of the time evolution. The simplest implementation can be realized by an ensemble of trajectories stochastically hopping between different Floquet surfaces. As a first application we demonstrate the excellent agreement of quantumclassical and fully quantummechanical dynamics for a twostate model of photodissociation of molecular fluorine. In summary, due to the favorable scaling of the numerical effort the FQCLE provides an efficient tool for the simulation of medium to large molecules interacting with intense fields beyond the perturbative regime.

Fluctuations and asymmetry via local Lyapunov instability in the timereversible doubly thermostated harmonic oscillator
View Description Hide DescriptionForward and backward trajectories from timesymmetric equations of motion can have timeasymmetric stability properties, and exhibit timeasymmetric fluctuations. Away from equilibrium this symmetry breaking is the mechanical equivalent of the second law of thermodynamics. Strange attractor states obeying the second law are timereversed versions of (unobservable) repeller states which violate that law. Here, we consider both the equilibrium and the nonequilibrium cases for a simple deterministically thermostated oscillator.At equilibrium the extended phasespace distribution is a smooth Gaussian function. Away from equilibrium the distribution is instead a fractal strange attractor. In both cases we illustrate local timesymmetry breaking. We also quantify the forward–backward fluctuation asymmetry for the thermostated oscillator.

Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to
View Description Hide DescriptionResonance phenomena associated with the unimolecular dissociation of have been investigated quantummechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation functionbased filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of show strong fluctuations, indicating the dissociation of is essentially irregular.

Energy versus amplitude corrected coupledcluster approaches. I
View Description Hide DescriptionIn the spirit of recently proposed renormalized CCSD(T) and CCSD(TQ) methods [K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 5644 (2000), and references therein], we explore the additive, noniterative energy corrections for both the standard and reduced multireference (RMR) CCSD approaches. Our study is based on a simple asymmetric energy expression of the standard single reference (SR) coupled cluster theory and casts a new light on the RMR CCSD method and its relationship with the corresponding MR CISD and SR reference CCSD methods, thus interrelating the amplitude and energy corrected schemes. These developments are illustrated on two exactly solvable model systems, namely, on the DZP models of the H4 system and of the HF molecule. We find that appropriately projected CCSD provides an almost identical energies as does the RMR CCSD method.

Energy versus amplitude corrected coupledcluster approaches. II. Breaking the triple bond
View Description Hide DescriptionWe examine the effectiveness of various energy corrections to the standard CCSD and to the reduced multireference (RMR) CCSD methods. These corrections are based on the asymmetric energy formula, but instead of projecting onto the reference configuration, as in the standard CCSD method, we employ for this purpose either the MR CISD wave function that is based on a suitable model space of the kind used in RMR CCSD, or simply the zeroorder wave function in that model space. Both full completeactivespace and severelytruncated model spaces are employed. The method is applied to the prototypical case of the triplebond dissociation, namely, to the exactly solvable doublezeta model of the molecule. It is shown that in this way we can eliminate the breakdown of the standard CCSD method in the region of highly stretched geometries and obtain reliable potential energy curves. The comparison with the recently proposed renormalized CCSD(T) and variational CCD methods is also briefly addressed.

Response properties and stability conditions in density matrix functional theory
View Description Hide DescriptionExpressions for the secondorder energy variations in the density matrix functionaltheory (DMFT) are derived, resulting in a formalism for timeindependent response properties (including absolute electronegativity and hardness) and stability conditions. A quadratically convergent scheme for a direct determination of natural spinorbitals and their occupancy numbers is developed and tested with the Goedecker–Umrigar and the exact twoelectron functionals. The derivatives of the electronic energy with respect to the number of electrons are found to be very sensitive to the DMFT description of the exchangecorrelation energy, providing a sensitive measure of accuracy that can be readily employed in testing and development of approximate functionals.

Reconstruction of frozencore allelectron orbitals from pseudoorbitals
View Description Hide DescriptionWe investigate the numerical feasibility of reconstructing frozencore allelectron molecular orbitals from corresponding pseudoorbitals. We perform densityfunctional calculations on simple atomic and molecular model systems using ultrasoft pseudopotentials to represent the atomic cores. We apply a transformation due to Blöchl [Phys. Rev. B 50, 17953 (1994)] to each calculated pseudoorbital to obtain a corresponding frozencore allelectron molecular orbital. Our model systems include the reconstruction of the orbital of a gold atom, and the occupied valence states of the molecule. Comparison of the resulting allelectron orbitals to corresponding ones that were obtained from calculations in which the core electrons were explicitly included indicates that allelectron molecular orbital reconstruction is a feasible and useful operation in reproducing the correct behavior of molecular orbitals in the nuclear core regions.

Can ordinary singlereference coupledcluster methods describe potential energy surfaces with nearly spectroscopic accuracy? The renormalized coupledcluster study of the vibrational spectrum of HF
View Description Hide DescriptionThe recently proposed renormalized (R) and completely renormalized (CR) CCSD(T) and CCSD(TQ) methods, which remove the failing of the standard CCSD(T) and approaches at large internuclear separations, have been used to obtain the potential energy function and the vibrational spectrum of the HF molecule. The vibrational term values obtained in the renormalized and completely renormalized CCSD(T) and CCSD(TQ) calculations have been found to be in a better agreement with the experimental [Rydberg–Klein–Rees (RKR)] data than than the results of the expensive full CCSDT calculations. The simple RCCSD(T) method gives errors for the vibrational energies up to The CRCCSD(T) and CRCCSD(TQ) methods reduce the errors in the full CCSDT results for the highlying states near dissociation to 100–200

Statistical mechanics of quantumclassical systems
View Description Hide DescriptionThe statistical mechanics of systems whose evolution is governed by mixed quantumclassical dynamics is investigated. The algebraic properties of the quantumclassical time evolution of operators and of the density matrix are examined and compared to those of full quantum mechanics. The equilibrium density matrix that appears in this formulation is stationary under the dynamics and a method for its calculation is presented. The response of a quantumclassical system to an external force which is applied from the distant past when the system is in equilibrium is determined. The structure of the resulting equilibrium time correlation function is examined and the quantumclassical limits of equivalent quantum time correlation functions are derived. The results provide a framework for the computation of equilibrium time correlation functions for mixed quantumclassical systems.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Simulation of single vibronic level emissions: Including anharmonic and Duschinsky effects
View Description Hide DescriptionCASSCF/MRCI/augccpVQZ(no g) and RCCSD(T)/augccpVQZ potential energy functions were reported for the and states of respectively. Vibrational wave functions of the symmetric stretching and bending modes of the two states of were obtained in variational calculations, employing Watson’s Hamiltonian for a nonlinear molecule and anharmonic vibrational wave functions expressed as linear combinations of harmonic basis functions. Franck–Condon factors (FCFs) were computed for single vibronic level (SVL) emissions and the SVL emission spectra were simulated with the computed FCFs. When compared with the observed spectra, the simulated spectra obtained in the present investigation, which include allowance for anharmonicity and the Duschinsky effect, were found to be significantly superior to those reported previously, based on the harmonic oscillator model. Using the iterative Franck–Condon analysis procedure, with the geometry of the state fixed at the recently determined experimental equilibrium geometry, the geometry of the state of which gave the best match between simulated and observed spectra, was found to be and

Photodissociation spectroscopy of
View Description Hide DescriptionWe have investigated the spectroscopy and photochemistry of in an angular reflectron timeofflightmass spectrometer. We identify four absorption bands in the spectral range 220–550 nm. These bands are assigned to radiative transitions in the bimolecular complex correlating with Zncentered and ethylenecentered absorptions, and with Zn–ethylene photoinduced charge transfer processes. The lowest energy band, assigned as is a weak continuum consistent with a large geometry change and fast predissociation. The higher energy band shows a long progression in the intermolecular stretch with a mode frequency of The spectroscopic results, including partially resolved rotational structure, are consistent with a weakly bound, πbonded complex in symmetry. A Birge–Sponer analysis gave an estimate for the dissociation energies of the excited state as and the ground state as A second structured band at still higher energies is tentatively assigned as and shows activation of higher frequency intramolecular ethylene modes. and fragment ions are observed over most of the spectral range. At higher energies we also see a significant branching to reactive products and that result from charge transfer accompanied by C–H bond cleavage. We propose a reaction mechanism that involves coupling through an excited chargetransfer state followed by C–H bond insertion.

Coalescence of fullerenes
View Description Hide DescriptionCoalescence of fullerenes with was studied by laser desorption and ionization in a timeofflightmass spectrometer (337 nm excimer laser). The fullerenes were produced by elimination of bromine from extensively brominated dodecahedranes (mixture, mean composition and mixtures with somewhat higher hydrogen content accessible by photobromination of the cage hydrocarbon. For Y probes at 80 mJ/cm^{2} laser fluence, coalescence of the generated fullerenes was identified as the dominant process providing a series of oligomers there is evidence for the formation of from At lower fluences (30 mJ/cm^{2}) in the mass spectrameasured near the desorption threshold or in the low ion velocity regime, the bromine substituents were not (totally) eliminated, the original degree of bromination has even been raised. High laser fluences (1500 mJ/cm^{2}) primarily effect the bromine content, generating ions with m ranging from 0 to 18, fullerene coalescence is suppressed. For X probes the only slightly higher hydrogen content inhibits coalescence; a ion is interpreted as fullerene.

and reversal: The dissociationlimit region of the state of
View Description Hide DescriptionUsing narrowbandwidth vacuumultraviolet radiation generated by differencefrequency fourwave mixing in Xe, the photoabsorption cross section in the Schumann–Runge system near the dissociation limit of the B state, is measured with a resolution of fullwidth at halfmaximum. The rotational structure of is assigned for the first time, and evidence is found for transitions into the levels of Experimental values for the tripletsplitting constants and for are found to be inconsistent with the rising trend observed for due to a change in the sense of the perturbation of the Bstate levels by the levels near A new value for the dissociation energy of the B state, determined from an analysis of the observed and missing lines near the dissociation limit, is in excellent agreement with previous values arising from the observation of rotational thresholds in the Schumann–Runge continuum. © 2001 American Institute of Physics.

Vibrational and collision energy effects on the reaction of with methanol
View Description Hide DescriptionIntegral cross sections and product velocity distributions were measured for reaction of acetaldehyde cation with methanol over a centerofmass collision energy range from 0.1 to 2.2 eV. Reactivity is dominated by exoergic proton transfer (PT), which is strongly suppressed by collision energy, and mildly suppressed by vibrational excitation. PT is complexmediated at low energies, switching to a direct stripping mechanism at high energies. Of the two possible PT channels, it appears that transfer of the aldehyde proton dominates. Hydrogen abstraction (HA) is a minor channel at low collision energies, also complexmediated. Abstraction is observed from both hydroxyl and methyl sites on methanol, and the two channels have different, and counterintuitive collision energy dependence. Despite being exoergic, with no barriers, the HA channel shows apparent threshold behavior, attributed to competition with the dominant PT channel. The competition indicates that different intermediate complexes must interconvert efficiently, at least for low collision energies. At low energies, HA is strongly enhanced by collision energy, while vibrational excitation has no effect. Finally, there is a minor product channel corresponding to methyl elimination (ME) from a complex. Despite a relatively complicated reaction coordinate, the ME channel shows substantial recoil energy release and an asymmetric velocity distribution. A series of ab initio and RRKM calculations were performed to help interpret the results.

Valence oneelectron and shakeup ionization bands of polycyclic aromatic hydrocarbons. I. Benzene, naphthalene, anthracene, naphthacene, and pentacene
View Description Hide DescriptionThe valence ionization bands of benzene and of polyacenes ranging from naphthalene to pentacene have been entirely assigned by means of oneparticle Green’s function calculations, performed using the thirdorder algebraicdiagrammatic construction [ADC(3)] scheme and series of basis sets of improving quality. For the sake of consistency, the computations are based on correlated (DFT/B3LYP) rather than uncorrelated geometries. Ionization bands pertaining to πorbitals are subject to a severe shakeup contamination at already quite low binding energies (e.g., down to 8.0 eV in the case of pentacene). In sharp contrast, the orbital picture of ionization holds to a much greater extent within the σband system (e.g., for pentacene, up to binding energies of 14.6 eV). Despite the intricacy of ionization bands, and, possibly, vibrational complications, ADC(3) spectra consistently match photoionizationmeasurements up to the innervalence region, where the orbital picture completely breaks down.

The complex of and A theoretical study
View Description Hide DescriptionThe complex of and is studied using B3LYP, MP2, and QCISD methods. Energetics, geometries, and vibrational frequencies of the equilibrium structure and two transition states are calculated using and basis sets. For the equilibrium structure there is a hydrogen bond between one of the F atoms of and one of the H atoms of The two transition states are only about 0.5 kcal/mol higher. The equilibrium structure is planar and, at the level, the F–H–O bond angle is nearly linear at 174.4° and the F–O distance is 2.59 Å. With zero point energy and counterpoise correction, the binding energy is 14.9 kcal/mol and the strong hydrogen bond of is weakened by 11.3 kcal/mol (25%). In the experimental F–F distance is 2.28 Å and the F–H–F bond angle is 180°. The most intense IR vibration is the F–H–F asymmetric stretch at 1331 cm^{−1}. In the calculated F–F distance is 2.30 Å and in the equilibrium structure the F–H distance for the hydrogen bonded F atom is longer by 0.13 Å but the F–H distance for the free F atom is shorter by 0.10 Å and the F–F distance is only 0.03 Å longer. The F–H–F bond angle is very close to linear at 179.4°. The most intense IR vibration remains the F–H–F asymmetric stretch, blueshifted by 648 cm^{−1}. The F–H–O asymmetric stretch is also an intense IR vibration, redshifted by 729 cm^{−1} from the O–H local mode stretch for

Reaction mechanism and isotope effects derived from centroid transition state theory in intramolecular proton transfer reactions
View Description Hide DescriptionIn this article the tautomerization reaction of the enol form of malonaldehyde is used to investigate the magnitude and origin of changes in centroid transition state theoryproton transferreaction rate predictions caused by the quantum dispersion of heavy nuclei. Using an empirical valence bond method to construct the potential energy surface, it is found that quantization of the nuclear degrees of freedom of the carbon atoms significantly influences the centroid potential of mean force used to describe the proton transferreaction. In contrast, an ab initio simulation carried out using a recently developed molecular mechanics based importance sampling method [J. Chem. Phys. 114, 6763 (2001)] in combination with an accurate density functional theory evaluation of the electronic energies shows a substantially smaller influence of the quantum nuclear degrees of freedom of the secondary atoms on the centroid potential of mean force. A detailed analysis of the different influence of quantization of the nuclear degrees of freedom of secondary atoms observed in the ab initio and empirical valence bond centroid potential of mean force was carried out. It is shown that for the empirical valence bond potential, a significant decrease of the centroid potential of mean force arises through the quantum tunneling of carbon atoms in the molecular backbone. Furthermore, it is demonstrated that in molecular mechanics potentials aimed to describe intramolecular proton transferreactions, the functional form of the potential energy terms coupling the primary and secondary atom motions as the reaction proceeds as well as the mass of the primary particle can significantly influence the centroid transition state theory predictions of secondary kinetic isotope effects. Finally, the dependence of the reaction rate predictions and isotope effects on the choice of reaction coordinate is investigated and the validity of calculating kinetic isotope effects using the centroid transition state theory formalism is discussed.

Successive mechanism of doubleproton transfer in formic acid dimer: A classical study
View Description Hide DescriptionThe dynamics of doubleproton transfer reaction in formic acid dimer is investigated by performing ab initiomolecular dynamics simulations. From the viewpoint of optimized energetics alone, the synchronous (simultaneous) proton transfer is more favorable than the successive one. However, a fulldimensional classical dynamics shows that there is a certain time lag, about 8 fs in average, between two proton transfers. When a proton undergoes the first transfer, it moves from an oxygen with higher electron density to the counterpart having the lower one. The proton thus needs an energy sufficient enough to break the chemical bond, resulting in a clime of a potential barrier. On the other hand, the second proton moves from the lower electrondensity oxygen atom to the higher one. Hence, the second proton is shifted predominantly by the thusformed electronic field. Not only due to the time lag observed but mainly because of the difference in the mechanism of transfer, therefore, the present doubleproton transfer is identified as successive. A detailed study on dynamics shows that the vibrational modes of the O–C–O skeletons dominate the second proton transfer.

Comparison of ab initio and density functional calculations of electric field gradients: The nuclear quadrupole moment from Mössbauer data
View Description Hide DescriptionThe difficulty in accurate determination of the nuclear quadrupole moment of the first excited nuclear state of from electronic structure calculations of the ironelectric field gradient combined with Mössbauer measurements of the nuclear quadrupole splitting in the isomer shift is addressed by comparing ab initio with density functional calculations for iron pentacarbonyl, ferrocene, and the electronic ground states of and While the ligand field gradient tensor components change relatively little with the method applied, the ironelectric field gradient is sensitive to the specific density functional used. Single reference manybody perturbation theory for electron correlation also performs poorly for the ironelectric field gradient and shows extreme oscillatory behavior with a change in the order of the perturbation series. Even with larger basis sets and coupled cluster techniques a precise value for the ironelectric field gradient could not be determined from electronic structure calculations due to limitations in the theoretical procedures. In order to avoid uncertainties in the measured isomer shift which enters into the nuclear quadrupole coupling constant we determined the Mössbauer spectrum of between temperatures of 4.2 and 295 K. In this range two phase transitions are observed, but the quadrupole splitting is not very dependent on the solid state structure in each phase. Solid state effects for the are determined by comparing the ironelectric field gradient of the isolated molecule with the value obtained from first principle solid state calculations at various levels of theory. These calculations show that the influence of near neighboring effects to the ironelectric field gradient is small. Fully relativistic Dirac–Hartree–Fock calculations for reveal that relativistic effects for the ironelectric field gradient are small as well. is therefore an ideal test molecule for the determination of an accurate nuclear quadrupole moment from electronic structure calculations if combined with an experimental nuclear quadrupole coupling constant. Our best estimate for the nuclear quadropole moment is 0.14(2) barn in reasonable agreement with recent nuclear structure calculations.