Volume 116, Issue 15, 15 April 2002
 ARTICLES

 Theoretical Methods and Algorithms

Direct calculation of cumulative reaction probabilities from Chebyshev correlation functions
View Description Hide DescriptionThe transitionstate wave packet method of Zhang and Light [J. Chem. Phys. 104, 6184 (1996)] for the direct calculation of cumulative reaction probabilities is implemented in the Chebyshev order domain to take advantage of exactness and efficiency of the Chebyshev propagator. Numerical testing for threedimensional reactive scattering confirms the accuracy and efficiency of the proposed algorithm. This new implementation is then used to compute the cumulative reaction probability of the reaction up to 0.65 eV. It is found that the latter reaction is dominated in low energy region by numerous narrow resonances.

Explicitly correlated secondorder Møller–Plesset methods with auxiliary basis sets
View Description Hide DescriptionIn explicitly correlated Møller–Plesset (MP2R12) methods, the firstorder wave function is expanded not only in terms of products of oneelectron functions—that is, orbitals—but also in terms of twoelectron functions that depend linearly on the interelectronic coordinates With these functions, three and fourelectron integrals occur, but these integrals can be avoided by inserting a resolution of the identity (RI) in terms of the oneelectron basis. In previous work, only one single basis was used for both the electronic wave function and the RI approximation. In the present work, a new computational approach is developed that uses an auxiliary basis set to represent the RI. This auxiliary basis makes it possible to employ standard basis sets in explicitly correlated MP2R12 calculations.

Intermolecular interaction energies from the total energy bifunctional: A case study of carbazole complexes
View Description Hide DescriptionAn approach in which the total energy of interacting subsystems is expressed as a bifunctional depending explicitly on two functions: electron densities of the two molecules forming a complex and was used to determine the equilibrium geometry and the binding energy of several weak intermolecular complexes involving carbazole and such atoms or molecules as Ne, Ar, CO, and For these complexes, the experimental dissociation energies fall within the range from 0.48 to 2.06 kcal/mol. Since the effect of the intermolecular vibrations on the dissociation energy is rather small, the experimental measurements provide an excellent reference set. The obtained interaction energies are in a good agreement with experiment and are superior to the ones derived from conventional Kohn–Sham calculations. A detailed analysis of relative contribution of the terms which are expressed using approximate functionals (i.e., exchangecorrelation and nonadditive kinetic energy is made. The nonvariational version of the applied formalism is also discussed.

Anomalous dielectric relaxation in the context of the Debye model of noninertial rotational diffusion
View Description Hide DescriptionThe Debye theory of dielectric relaxation of an assembly of polar molecules is reformulated using a fractional noninertial Fokker–Planck equation for the purpose of extending that theory to explain anomalous dielectric relaxation. The fractional Fourier–Planck equation in question is a generalization of the Smoluchowski equation for the dynamics of Brownian particles in configuration space to include anomalous relaxation. It is shown that this model can reproduce nonexponential Cole–Coletype anomalous dielectric relaxation behavior and that it reduces to the classical Debye model of rotational diffusion when the anomalous exponent is unity.

On the resolution of the optical rotatory power of chiral molecules into atomic terms. A study of hydrogen peroxide
View Description Hide DescriptionAn additive scheme for resolving average optical rotatory power of a molecule into atomic contributions, based on the acceleration gauge for the electric dipole, and/or the torque formalism, has been applied to hydrogen peroxide. Extended calculations have been carried out to test the reliability of the partition method. Gross atomic isotropic contributions to the average molecular property from oxygen and hydrogen atoms have been evaluated. The force and torque gauges provide different numerical values for atomic contributions.

Exchange potential from the common energy denominator approximation for the Kohn–Sham Green’s function: Application to (hyper)polarizabilities of molecular chains
View Description Hide DescriptionAn approximate Kohn–Sham (KS) exchange potential is developed, based on the common energy denominator approximation (CEDA) for the static orbital Green’s function, which preserves the essential structure of the density response function. is an explicit functional of the occupied KS orbitals, which has the Slater and response potentials as its components. The latter exhibits the characteristic step structure with “diagonal” contributions from the orbital densities as well as “offdiagonal” ones from the occupied–occupied orbital products Comparison of the results of atomic and molecular groundstate CEDA calculations with those of the Krieger–Li–Iafrate (KLI), exact exchange (EXX), and Hartree–Fock (HF) methods show, that both KLI and CEDA potentials can be considered as very good analytical “closure approximations” to the exact KS exchange potential. The total CEDA and KLI energies nearly coincide with the EXX ones and the corresponding orbital energies are rather close to each other for the light atoms and small molecules considered. The CEDA, KLI, values provide the qualitatively correct order of ionizations and they give an estimate of VIPs comparable to that of the HF Koopmans’ theorem. However, the additional offdiagonal orbital structure of appears to be essential for the calculated response properties of molecular chains. KLI already considerably improves the calculated (hyper)polarizabilities of the prototype hydrogen chains over local density approximation(LDA) and standard generalized gradient approximations (GGAs), while the CEDA results are definitely an improvement over the KLI ones. The reasons of this success are the specific orbital structures of the CEDA and KLI response potentials, which produce in an external field an ultranonlocal fieldcounteracting exchange potential.

A chemical Hamiltonian approach study of the basis set superposition error changes on electron densities and one and twocenter energy components
View Description Hide DescriptionThe basis set superposition errorcorrected firstorder electron densities of several hydrogen bonded complexes of increasing molecular size have been obtained with the Hartree–Fock and densityfunctional theory versions of the chemical Hamiltonian approach (CHA) methodology. A detailed analysis of the local basis set superposition error (BSSE) effects has been carried out by comparing the uncorrected electron densities and energy components with the CHA ones. Topological analysis of the electron density through the atoms in molecules theory is used in order to obtain a quantitative measure of the BSSE effects in terms of the characterization of the critical points of the electron density. Density difference isocontour maps are also depicted in order to show the local electron density redistributions induced by the BSSEcorrection. We show that the effects of the BSSE are common for all the complexes studied, namely water dimer, formic acid dimer and uracil–water complex. The formic acid dimer and uracil–water density difference maps at frozen geometry reveal that the effects of the BSSE do not extend significantly beyond the atoms involved in the interaction and their first neighbors. The main redistribution effects are not strictly localized on the intermolecular region and mostly take place in the valence shells of the heavy atoms directly involved in the intermolecular interaction. These trends are also confirmed by means of an energy decomposition analysis performed at the Hartree–Fock level of theory with the recently proposed chemical energy component analysis (CECA) method. In agreement to previous results, we found that inclusion of diffuse functions is of utmost importance in order to minimize the magnitude of the BSSE. However, both the electron density difference maps and the CECA analysis confirm that the local effects of the BSSE are very different when diffuse functions are present in the calculation.

A new correlation functional based on analysis of the Colle–Salvetti functional
View Description Hide DescriptionThe behavior of the Colle–Salvetti (CS) correlation functional based on the Hartree–Fock (HF) secondorder density matrix is investigated in the case of the He atom. The analysis of the correlation hole and energy contributions show that correlation effects are not taken into account appropriately due to the missing kinetic correlation. The CS final simplified energy expression also has some problems. To address these problems, we have constructed a new correlation functional based on the HF secondorder density matrix including the effects of not only electron–electron interaction but also the kinetic energy by using an adiabatic connection formula. In addition, correlation effects for opposite and parallel spins are treated independently. This functional reproduces accurate correlation energies for H–Ar atoms. Combining it with the Becke 1988 exchange functional, we get reasonable atomization energies for the G2 set.

Timedependent density functional theory employing optimized effective potentials
View Description Hide DescriptionExchangeonly ab initio (parameterfree) timedependent density functional calculations for the vertical excitation energies of atoms and polyatomic molecules are performed by employing optimized effective potentials (OEP’s) and their corresponding adiabatic exchange kernels for the first time. Accurate OEP’s are obtained by a novel linearcombinationofatomicorbital (LCAO) algorithm [R. Colle and R. K. Nesbet, J. Phys. B 34, 2475 (2001)] in which a potential is represented as a sum of a seed potential having the correct asymptotic behavior and a small and rapidly decaying correction, the latter being approximated accurately by a linear combination of Gaussian functions. The timedependent OEP (TDOEP) methods with and without the Tamm–Dancoff approximation are implemented by using a trialvector algorithm, which allows us to avoid the storage or manipulation of transformed twoelectron integrals or the diagonalization of large matrices. No approximation is made to TDOEP, besides the adiabatic approximation to the exchange kernel, the LCAO expansion of the orbitals and potentials, and occasionally the Tamm–Dancoff approximation. The vertical excitation energies of the beryllium atom and the nitrogen and water molecules calculated by TDOEP are compared with those obtained from timedependent density functional theory (TDDFT) employing conventional local or gradientcorrected functionals, configuration interaction singles (CIS), timedependent Hartree–Fock (TDHF) theory, similaritytransformed equationofmotion coupledcluster with single and double substitutions, and experiments. TDOEP, which neglects electron correlation while treating the exchange contribution rigorously within the Kohn–Sham DFT framework, performs equally well as, or even appreciably better than, CIS or TDHF. The slightly better performance of TDOEP might be attributed to the local nature of the exchange potentials that allows the bare orbital energy differences to approximate excitation energies well. Nevertheless, TDDFT employing local or gradientcorrected functionals outperforms TDOEP for lowlying valence excited states, implying that the former somehow accounts for electron correlation effectively, whereas for highlying and Rydbergexcited states, the latter performs better than the former. By combining the desirable features of OEP and local or gradientcorrected exchangecorrelation potentials, we arrive at a simple asymptotic correction scheme to the latter. TDDFT with the asymptotic correction yields uniformly accurate excitation energies for both valence and Rydberg excited states.

Molecular equilibrium structures from experimental rotational constants and calculated vibration–rotation interaction constants
View Description Hide DescriptionA detailed study is carried out of the accuracy of molecular equilibrium geometries obtained from leastsquares fits involving experimental rotational constants and sums of ab initio vibration–rotation interaction constants The vibration–rotation interaction constants have been calculated for 18 singleconfiguration dominated molecules containing hydrogen and firstrow atoms at various standard levels of ab initio theory. Comparisons with the experimental data and tests for the internal consistency of the calculations show that the equilibrium structures generated using Hartree–Fock vibration–rotation interaction constants have an accuracy similar to that obtained by a direct minimization of the CCSD(T) energy. The most accurate vibration–rotation interaction constants are those calculated at the CCSD(T)/ccpVQZ level. The equilibrium bond distances determined from these interaction constants have relative errors of 0.02%–0.06%, surpassing the accuracy obtainable either by purely experimental techniques (except for the smallest systems such as diatomics) or by ab initio methods.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Stereodynamics and rovibrational effect for reaction
View Description Hide DescriptionIn this work, we employ the semirigid vibrating rotor target (SVRT) model to study the influence of rotational and vibrational excitation of the reagent on reactivity for the benchmark reaction The excitation of the pseudo stretching vibration of the SVRT model gives significant enhancement of reaction probability, consistent with the later position of the reaction barrier on the potential energy surface. The vibrationally thermalaveraged rate constant is much larger than the rate constant of the ground vibrational state. Detailed study of the influence of initial rotational states on reaction probability shows strong steric effect. The reaction probability is directly correlated with the angular distribution of the initial wave function determined by different angular momentum relationships among three vectors j, R, and r. The steric effect of polyatomic reactions, treated by the SVRT model, is more complex and richer than theoretical calculations involving linear molecular models.

Highresolution infrared spectra of jetcooled allyl radical and C–H stretch vibrations
View Description Hide DescriptionThe highresolution infrared spectrum of jetcooled allyl radical in the region 3010–3045 cm^{−1} has been recorded in pulsed slit jet expansions using both modulated discharge and excimer laser flash photolysis methods to produce the radicals. Over 400 transitions are observed and assigned to the and C–H stretch vibrations. The band origins have been determined to be 3033.8745(6), 3023.4605(6), and 3020.32(1) cm^{−1}, respectively. Spectral analysis indicates that all three upper states are perturbed, with the perturbations in the upper state so pervasive as to make leastsquares analysis difficult. The gas phase frequencies reveal a somewhat unusual, in comparison with the other bands, matrix shift to the blue for of 18 cm^{−1}.

The SiP molecule: The first observation and spectroscopic characterization
View Description Hide DescriptionSiP molecules have been produced in a molecular free jet apparatus by laser vaporizing a silicon rod in the presence of He doped with phosphine gas. Excitation spectra have been observed in the range by monitoring laser induced fluorescence. Dispersed fluorescence spectra have been recorded out of the upper states of the excitation bands. The ground electronic state is with the spin–orbit splitting the harmonic wavenumber and the equilibrium internuclear distance Two excited electronic states, and are observed at and respectively. The harmonic wavenumbers, and the equilibrium internuclear distances, are and 1.9658(13) Å, respectively, for the state and and 2.1278(8) Å, respectively, for the state. For the and electronic states, RKR potentials have been generated. Franck–Condon factors for the and systems have been calculated. perturbations have been observed. A deperturbation procedure has yielded the offdiagonal spin–orbit electronic matrix element equal to This work represents the first spectroscopic investigation of the SiP molecule.

Anion photoelectron spectroscopy of
View Description Hide DescriptionThe anion photoelectron (PE) spectra of small massselected vanadium oxide clusters are measured at a fixed photonenergy of 4.66 eV with the aid of a magnetic bottle photoelectron spectrometer. Cluster anions are generated in a pulsed laservaporization cluster source. The electronic structure of clusters is investigated as a function of size n and composition m with special regard to the increasing oxidation state. The addition of one or two oxygen atoms to the vanadium cluster core induces a change of the electronic structure in the nearthreshold binding energy region below 2 eV. Main spectral features are contributed from the transition metal dderived orbitals, whereas the oxygen 2p contribution induces a hybridization between vanadium and oxygen frontier orbitals in the entire series of the investigated clusters Generally, electron affinities and vertical detachment energies increase with increasing cluster size revealing sizedependent discontinuities. Furthermore, relative dissociation energies for different oxygenloss channels from the parent clusters are determined from thermochemical cycles, and first insights into the stability patterns of neutral and negatively charged vanadium oxide clusters are provided.

An accurate description of the ground and excited states of SiH
View Description Hide DescriptionThe astrophysical importance of the SiH radical has motivated significant experimental and theoretical work. However, only the and states of SiH have been extensively investigated experimentally, while the study of higher excited states is rather limited. From a theoretical point of view, most of the studies have been focused on spectroscopic and thermochemical quantities of the ground state. The lack of accurate spectroscopic parameters pertaining to higher excited states was the driving force of the present work, in line with our previous study of the isovalent CH molecule [A. Kalemos, A. Mavridis, and A. Metropoulos, J. Chem. Phys. 111, 9536 (1999)]. Using the multireference configuration interaction approach coupled with very large correlationconsistent basis sets, we have constructed potential energy curves for 18 molecular states correlating to At the same level, the potential energy curve of the ground state has also been constructed. We report total energies, dissociation energies, and the usual spectroscopic constants for and for all states studied. Most of our results are in excellent agreement with existing experimental values. In particular, we believe that our dissociation energy for the X state, is the most reliable reported so far in the literature.

Strong coupling of the single excitations in the Qlike bands of phenylenelinked freebase and zinc bacteriochlorin dimers: A timedependent density functional theory study
View Description Hide DescriptionTimedependent densityfunctional theory (TDDFT) calculations were carried out to predict the Qlike bands of the two structural isomers of the phenylenelinked freebase (FBBC) and zinc (ZnBC) bacteriochlorin dimers. The calculated singlet excitation energies and oscillator strengths for the lowlying excited states of the reference monomers, FBBC and ZnBC, are quite consistent with recent ab initio calculations. The 1,3 and 1,4phenylenelinked dimers have monomerlike Q bands and new bands comprised of the crosslinked (i.e., charge transfer) excitations from the FBBC (ZnBC) ring to the ZnBC (FBBC) ring, whose excitation energies are slightly and considerably redshifted by about 0.03 eV and 0.5–0.7 eV compared to the monomers, respectively. The monomerlike bands are of the mixed highest occupied molecular orbital (HOMO)→lowest unoccupied molecular orbital (LUMO) excitations in the bands from the different bacteriochlorin rings, whose origin is the coupling of the transition dipole moments through the π–π interaction between the unreduced pyrroles situated across the phenylene group. This mixing character is still maintained in the monomers separated by the same distance in the dimer, which is quite different from previous TDDFT calculations for the phenylenelinked freebase and zincporphyrin dimers. The present dimers may show a more efficient excitation energy transfer between the bacteriochlorins via each’s throughspace overlapped LUMOs than the conventional porphyrin dimers.

Ab initio study of the isomerization of retinal chromophore and its derivatives
View Description Hide DescriptionThe structures, vibrational frequencies, electronic properties, and cistrans photoisomerization process of retinal chromophore and its derivatives (i.e., Schiff base and protonated Schiff base) are studied using the densityfunctional theory with Becke’s threeparameter exchange functional together with the correlation functionals of Lee–Yang–Parr (B3LYP) and the second order Møller–Plesset perturbation theory (MP2). The optical transition energies for photoisomerization are reported at the configuration interaction (CI) level with single excitations (CIS) as well as at the B3LYP/631G^{*} level using the randomphaseapproximation (RPA). For slightly simplified model systems of retinal chromophore and its derivatives, the RPA values are very close to those of the complete activespace selfconsistentfield (CASSCF) method and the multireference CI (MRCI) method, and are also in reasonable agreement with the experiments. We have also tried to investigate the solvent effect of the vertical transition energies in the presence of one or two water molecules. The present study deals with the mechanism of the cistrans (or transcis) photoisomerization based on the molecular orbital (MO) analysis.

Collisioninduced dissociation and photodetachment of singly and doubly charged anionic polynuclear transition metal carbonyl clusters: and
View Description Hide DescriptionThree polynuclear transition metal carbonyl cluster anions, and have been studied using energydependent electrospray ionizationmass spectrometry (EDESI–MS) and photodetachmentphotoelectron spectroscopy (PES). EDESI–MS maps show a simple collisioninduced dissociation (CID) process for by stripping CO down to the metal core. For the doubly charged species, two competing CID channels were observed, viz. loss of neutral CO and loss of It was found that the parent dianions first lose neutral CO down to producing a series of dianions, and For the dianions become electronically unstable against autodetachment, and singly charged anions, and were observed. The PES spectra of the dianions show the electron binding energies decrease monotonically as n decreases and become ∼0.0 eV for in exact agreement with the CID patterns that reflect the electronic instability of the doubly charged metal complexes with All of the PES spectra show congested features, indicating very high density of lowlying electronic states for the transition metal carbonyl clusters. The electron binding energies of are similar for but decrease sharply from to 0. The intramolecular Coulomb repulsion in the dianions was observed to increase with loss of CO, ranging from ∼1.8 eV for to ∼2.4 eV for

Revival structures in picosecond laserinduced alignment of molecules. I. Experimental results
View Description Hide DescriptionWe report experiments on the formation of wave packets consisting of coherently excited ground electronic state rotational levels of using excitation with an intense nonresonant picosecond laser. As measured in a velocitymapimaging experiment using Coulomb explosion for the determination of the angular distribution of the molecules, these wave packets display alignment of the internuclear axis along the laser polarization axis, both during the laser interaction and at welldefined time delays following the laser interaction, which correspond to rotational revival times of the molecule. The alignment is studied as a function of the intensity and the pulse duration of the pump laser, the rotational temperature of the molecular beam, the polarization geometry of the pump and probe lasers, and the fragmentioncharge state used to probe the alignment. We observe experimentally that the alignment at revival times is maximal for intermediate pulse durations of a few picoseconds, where the laser–molecule interaction is neither diabatic nor adiabatic. The alignment increases with intensity, but reaches saturation once the intensity is raised sufficiently high. At this point the degree of alignment is limited by the initial rotational temperature of the molecular beam. Our conclusions are corroborated by model calculations, which are presented in detail in the following paper.

Revival structures in picosecond laserinduced alignment of molecules. II. Numerical modeling
View Description Hide DescriptionWe report quantummechanical calculations on the formation of aligned rotational wave packets in the ground state of following the excitation of a rotationally cold sample of molecules with an intense picosecond laser pulse. Using these calculations, we have studied (1) the dynamic alignment during or shortly after the intense pump pulse, (2) the alignment at characteristic revival times following the laser excitation, and (3) the alignment between the revivals, as a function of the laserpulse duration and peak intensity and the initial rotational temperature of the molecular beam. We conclude that the alignment at a revival is maximum for intermediate pulse durations (∼3 ps for that are long enough to get efficient population transfer out of the initially populated state, yet short enough for the interaction to remain partially diabatic and partially adiabatic. The alignment at the revivals increases with laser intensity, although the timedependent structure of the revivals becomes increasingly complicated as the laser intensity is increased, and the maximum degree of alignment that is obtained is eventually limited by the initial rotational temperature of the molecular beam. The findings in this paper qualitatively agree with experimental results on shortpulse laserinduced alignment that were presented in our experimental article (preceding paper).