Volume 120, Issue 11, 15 March 2004
 ARTICLES

 Theoretical Methods and Algorithms

Multireference spinadapted variant of density functional theory
View Description Hide DescriptionA new Kohn–Sham formalism is developed for studying the lowest molecular electronic states of given space and spin symmetry whose densities are represented by weighted sums of several reference configurations. Unlike standard spindensity functionaltheory, the new formalism uses total spin conserving spindensity operators and spininvariant density matrices so that the method is fully spinadapted and solves the socalled spinsymmetry dilemma. The formalism permits the use of an arbitrary set of reference (noninteracting) configurations with any number of open shells. It is shown that the requirement of degeneracy of the total noninteracting energies of the reference configurations (or configuration state functions) is equivalent to the stationary condition of the exact energy relative to the weights of the configurations (or configuration state functions). Consequently, at any molecular geometry, the weights can be determined by minimization of the energy, and, for given reference weights, the Kohn–Sham orbitals can be determined. From this viewpoint, the developed theory can be interpreted as an analog of the multiconfiguration selfconsistent field approach within density functional theory.

Blockcorrelated coupled cluster theory: The general formulation and its application to the antiferromagnetic Heisenberg model
View Description Hide DescriptionThe general formalism of the blockcorrelated coupled cluster (BCCC) method, an alternative multireference coupled cluster method for calculating the groundstateelectronic structures of molecular systems, has been presented. The BCCC theory is constructed in terms of a complete set of manyelectron states of individual blocks, assumed that the whole system could be partitioned into a set of blocks. The reference state in the BCCC is selected as a tensor product of the most important manyelectron state of each system block. By truncating the cluster operator to a certain nblock correlation level, an approximate but sizeextensive BCCC method, denoted as is defined. For reducing the computational effort but without much loss of accuracy, the reduced density matrix is introduced to generate an optimal subset of manyelectron states for each block. I have implemented the methods within the Heisenberg Hamiltonian, and applied them to calculate the groundstate energies of onedimensional spin chains and quasionedimensional twoleg spin ladders. The calculated results show that with the appropriate partition of the studied systems the BCCC3 method can yield quite satisfactory groundstate energies for these spin systems.

Densityfunctional theory calculations of optical rotatory dispersion in the nonresonant and resonant frequency regions
View Description Hide DescriptionThe complex linear response function, which can be employed for calculations of secondorder molecular properties in regions of strong absorption, is here extended to encompass the mixed electricdipole–magneticdipole polarizability. The mixed electricdipole–magneticdipole polarizability determines the optical rotation and, when absorption is taken into account, the full anomalous optical rotatory dispersion (ORD) spectra of chiral molecules can be calculated using firstprinciple quantumchemical methods. Gaugeorigin independence of the results is ensured through the use of London atomic orbitals. To illustrate the importance of taking the absorption process properly into account, we here apply this methodology to the study of the anomalous ORD of hydrogen peroxide, 3Rmethylcyclohexanone, 4R1,1dimethyl[3](1,2)ferrocenophan2on, and the isomer of the fullerene.

Simple and accurate method to evaluate tunneling splitting in polyatomic molecules
View Description Hide DescriptionA practical and accurate semiclassical method for calculating the tunneling splitting of the ground state in polyatomic molecules is presented based on a recent version of the instanton theory [J. Chem. Phys. 115, 6881 (2001)]. The method uses ab initio quantum chemical data for the potential energy surface without any concomitant extrapolation and requires only a small number of ab initio data points to get convergence even for large molecules. This enables one to use an advanced level of electronic structuretheory and achieve a high accuracy of the result. The method is applied to the 9atomic malonaldehyde molecule by making use of the potential energy surface at the level of CCSD(T) with the hybrid basis set of augccpVTZ (for oxygen atoms and the transferred hydrogen atom) and ccpVTZ (for other atoms).

Energy partitioning for “fuzzy” atoms
View Description Hide DescriptionThe total energy of a molecule is presented as a sum of one and twoatomic energy components in terms of “fuzzy” atoms, i.e., such divisions of the threedimensional physical space into atomic regions in which the regions assigned to the individual atoms have no sharp boundaries but exhibit a continuous transition from one to another. By proper definitions the energy components are on the chemical energy scale. The method is realized by using Becke’s integration scheme and weight function permitting very effective numerical integrations.

Decoupling quantum dissipation interaction via stochastic fields
View Description Hide DescriptionBased on the Hubbard–Stratonovich transformation, the dissipative interaction between the system of interest and the heat bath is decoupled and the separated system and bath thus evolve in common classical random fields. This manipulation allows us to establish a novel theoretical methodology by which the reduced density matrix is formulated as an ensemble average of its random realizations in the auxiliary white noise fields. Within the stochastic description, the interaction between the system and the bath is reflected in the mutually induced mean fields. The relationship between the bathinduced field and the influence functional in the path integral framework is revealed. As a demonstration of this approach, we derive the exact master equations for two model systems.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Mass analyzed threshold ionization spectroscopy of 5methylindole and 3methylindole cations and the methyl substitution effect
View Description Hide DescriptionThe vibrationally resolved mass analyzed threshold ionizationspectra of jetcooled 5methylindole (5MI) and 3methylindole (3MI) have been recorded by ionizing via various vibronic levels of each species. The adiabatic ionization energies (IEs) of 5MI and 3MI are determined to be 61 696±5 and 60 679±5 cm^{−1}, which are less than that of indole by 895 and 1912 cm^{−1}, respectively. Comparing these data with those of 1methylindole and indole suggests that the methyl substitution on the pyrrole part leads to a greater redshift in the IE than on the benzene part. These experimental findings are well supported by the theoretical calculations. Analysis on these new data shows that many active vibrations of the 5MI cation are related to the torsion and inplane ring bending vibrations. In contrast, the observed vibrational bands of the 3MI cation are very weak due to unfavorable Franck–Condon transition.

Quantum solvation of phthalocyanine in superfluid helium droplets
View Description Hide DescriptionWe have measured quantum states of the solvent–solute system of phthalocyanine in superfluidheliumdroplets in a high resolution pump–probe experiment. This provides evidence for the attribution of a splitting effect in the emission spectra of phthalocyanine in heliumdroplets to the relaxation of the first helium layer upon electronic excitation, measured recently by us. Our experimental results are a strong indication for the first helium layer playing a key roll for the solvation of molecules in heliumdroplets and, thus, for their spectroscopic features.

Photophysics of protoporphyrin ions in vacuo: Tripletstate lifetimes and quantum yields
View Description Hide DescriptionLifetimes of tripletstate molecules and triplet quantum yields are important parameters in photobiology as they determine the generation of singletoxygen upon irradiation with visible light. Here we report lifetimes of protoporphyrin IX (pp) in vacuo measured in an ion storage ring. We find that after 532 nm photon absorption, (free base and negatively charged carboxylate) and (single protonation of ring nitrogen) have tripletstate lifetimes of 12 and 6 ms, respectively. After 415 or 390 nm absorption the lifetime of the anion is shorter (1.5 and 0.6 ms) as expected from the increase in temperature. Triplet quantum yields of and are similar, 0.6–0.7, close to values reported for the free base and monocation in solution. The other channel, direct decay to the electronic ground state and subsequent dissociation of vibrationally excited ions, is much faster than triplet–singlet intersystem crossing. We measured lifetimes of 63 μs, 96 μs, and 0.3 ms after 390, 415, and 532 nm excitation, respectively. A fit of a statistical model to the decay results in an Arrhenius activation energy of 0.5±0.2 eV for loss and a low preexponential factor indicative of an entropic barrier.

An ab initio study of the competing reaction channels in the reaction of HOCO radicals with NO and
View Description Hide DescriptionThe reaction between HOCO and NO, and that between HOCO and have been examined using the quadratic configuration interaction method to locate and optimize the critical points on the potential energy surfaces. Analysis of the critical points provides new insight into new intermediates and pathways by which these reactions occur and help explain recent experimental results. In the reaction, the symmetryallowed products, can be obtained both via direct hydrogen abstraction by on the HCO radicals, as well as through an adduct, which can proceed to give the same products. The lessthanunity yield of observed in the experimental studies of the reaction, as well as the lack of CO, can be explained by the formation of a stable HOC(O)NO adduct.

First principles study of the stability and electronic structure of the icosahedral and clusters
View Description Hide DescriptionThe structural stability and electronicstructure of icosahedral and clusters have been studied by DMOL cluster method based on densityfunctional theory. The ground state of allelectron with relativity results is shown to be a distorted icosahedron by the Jahn–Teller effect. However, the binding energies of and are very close to that of the structure for and clusters. The effective core potential results show that the true ground state is structure. The clusters have small magnetic moments and the symmetry of cluster is an important factor in determining the magnetic moments of the clusters. The effects of interatomic spacing and coordination on atomic magnetic moment are discussed. Further, electrons dominate the hybrid orbitals below the Fermi level in the neutral cluster and contribute the main spin of clusters.

Internal state distributions of fragment HCO via and pathways of glyoxal after photolysis in the ultraviolet region
View Description Hide DescriptionThe dynamics of photodissociation of glyoxal (HOC–COH) near the dissociation threshold on the triplet manifold are studied through measurement of distributions of nascent fragment HCO in various internal states. Three rotational levels and of vibrational stateU (excitation wavelength ∼394.4 nm, origin at 25 331.865 cm^{−1}) of glyoxal in state and two other vibrational states at excitation wavelengths 390.33 and 382.65 nm are selected to produce fragment HCO. By means of fluorescence in the transition of HCO, we determined the relative populations of internal states of that fragment. Rotational states of product HCO up to and are populated, and bimodal distributions of these rotational states are observed for the photolysis wavelengths used in this work. The high rotational part of the distribution with average energy near values calculated on the basis of the statistical model—phasespace theory is assigned to arise from glyoxal on its surface, and the low rotational part from the surface with an exit barrier. After photolysis near the threshold region on the triplet surface, HCO arising from the state appears to be a major component of products because these rotational levels and of U state selected are gateway states with an enhanced rate of intersystem crossing.

Comparing the dynamical effects of symmetric and antisymmetric stretch excitation of methane in the reaction
View Description Hide DescriptionThe effects of two nearly isoenergetic C–H stretching motions on the gasphase reaction of atomic chlorine with methane are examined. First, a 1:4:9 mixture of and He is coexpanded into a vacuum chamber. Then, either the antisymmetric stretch of is prepared by direct infrared absorption or the infraredinactive symmetric stretch of is prepared by stimulated Raman pumping. Photolysis of at 355 nm generates fast Cl atoms that initiate the reaction with a collision energy of (0.16±0.02 eV). Finally, the nascent HCl or products are detected statespecifically via resonance enhanced multiphoton ionization and separated by mass in a timeofflight spectrometer. We find that the rovibrational distributions and stateselected differential cross sections of the HCl and products from the two vibrationally excited reactions are nearly indistinguishable. Although Yoon et al. [J. Chem. Phys. 119, 9568 (2003)] report that the reactivities of these two different types of vibrational excitation are quite different, the present results indicate that the reactions of symmetricstretch excited or antisymmetricstretch excited methane with atomic chlorine follow closely related product pathways. Approximately 37% of the reaction products are formed in states with little rotational excitation. At low J states these products are sharply forward scattered, but become almost equally forward and backward scattered at higher J states. The remaining reaction products are formed in and have more rotational excitation. The products are predominantly back and side scattered. Measurements of the products indicate production of a nonnegligible amount of umbrella bend excited methyl radicals primarily in coincidence with the products. The data are consistent with a model in which the impact parameter governs the scattering dynamics.

Ground state, growth, and electronic properties of small lanthanum clusters
View Description Hide DescriptionThe DMol cluster method based on densityfunctional theory has been employed to study the structural stability and electronic structure of clusters. The ground states have been found out for lanthanum clusters. The JahnTeller effect plays an important role in this process because there are many isomers near the ground state. The magnetism is not sensitive to interatomic spacing when the change of interatomic spacing is in a small range. Lanthanum clusters grow in an icosahedral pattern. The results of the mean binding energy, of the second derivative of binding energy, and of the formation energy show strong odd–even alternation and that 7 and 13atom clusters are magic. Further, the HOMOLUMO gap, the mean nearest bond lengths, and the mean magnetic moments suggest that the convergence to bulk is slow and it shows an oscillatory behavior for small lanthanum clusters.

Submillimeterwave spectra of hypoiodous acid
View Description Hide DescriptionPure rotational spectra of hypoiodous acid, HOI, and its deuterated species, DOI, were measured in the frequency range of 320–670 GHz. The molecule was efficiently produced by a reaction of atomic oxygen with iodoethane. Rotational constants and centrifugal distortion constants for the molecule were determined accurately. The vibrationally averaged structure for HOI was obtained by taking the isotopic difference of the OH bond length into consideration: and where the errors were estimated from the residual inertial defect. Equilibrium bond lengths for the OH and OI bonds were derived as 0.959(8) Å and 1.9874(3) Å, respectively, by assuming anharmonic constants of the corresponding diatomic molecules. Electricquadrupole interaction constants and nuclearspin–rotation coupling constants for the iodine nucleus were obtained. Nonaxial terms of the electricquadrupole constant for HOI can be determined as well, which enabled us to derive the principal values of the coupling tensor. The values obtained were used to gauge the ionicity of the bond in the molecular system. The nuclearspinrotation coupling constant along the a inertial axis is found to be significantly smaller than others, which may be explained by a contribution from two lowlying singlet excited states.

Selective photochemistry via adiabatic passage: Degenerate product states with different lifetimes
View Description Hide DescriptionTwopulse selective photochemistry that exploits population transfer via adiabatic passage is considered for the case that there are degenerate product states with different lifetimes. As an example, a fourlevel model system with a complex symmetric Hamiltonian is constructed. Analytical and numerical studies of this model system demonstrate that extensive control over the product branching ratio can be achieved by detuning either the pump pulse or the Stokes pulse while maintaining negligible population in the intermediate state. This control approach represents a significant simplification of both the Kobrak–Rice extended stimulated Raman adiabatic passage scheme and the Chen–Shapiro–Brumer strongfield control scheme.

Stability and structure of molecules Experimental and density functional study
View Description Hide DescriptionThe molecules and have been identified in massspectrometric measurements over solutions of hydrogen in liquid Li, and the gaseous equilibria of the reactions: and have been measured.Density functional calculations of molecules provide structures, vibrational frequencies, ionization energies, and free energy functions of these molecules, and these are used to estimate the enthalpies of these reactions and the atomization energies of (119.4 kcal/mol) and (151.8 kcal/mol).

Excitations, optical absorption spectra, and optical excitonic gaps of heterofullerenes. I. and Theory and experiment
View Description Hide DescriptionLowenergy excitations and optical absorptionspectrum of are computed by using timedependent (TD) Hartree–Fock, TDdensity functional theory (TDDFT), TD DFTbased tightbinding (TDDFTTB), and a semiempirical Zerner intermediate neglect of diatomic differential overlap method. A detailed comparison of experiment and theory for the excitation energies, optical gap, and absorptionspectrum of is presented. It is found that electron correlations and correlation of excitations play important roles in accurately assigning the spectral features of and that the TDDFT method with nonhybrid functionals or a local spin density approximation leads to more accurate excitation energies than with hybrid functionals. The level of agreement between theory and experiment for justifies similar calculations of the excitations and optical absorptionspectrum of a monomeric azafullerene cation to serve as a spectroscopy reference for the characterization of carborane anion salts. Although it is an isoelectronic analogue to exhibits distinguishing spectral features different from (1) the first singlet is dipoleallowed and the optical gap is redshifted by 1.44 eV; (2) several weaker absorption maxima occur in the visible region; (3) the transient triplet–triplet absorption at 1.60 eV (775 nm) is much broader and the decay of the triplet state is much faster. The calculated spectra of characterize and explain well the measured ultraviolet–visible (UV–vis) and transient absorption spectra of the carborane anion salt [Kim et al., J. Am. Chem. Soc. 125, 4024 (2003)]. For the most stable isomer of we predict that the first singlet is dipoleallowed, the optical gap is redshifted by 1.22 eV relative to that of and optical absorption maxima occur at 585, 528, 443, 363, 340, 314, and 303 nm. We point out that the characterization of the UV–vis and transient absorption spectra of isomers is helpful in distinguishing the isomer structures required for applications in molecular electronics. For and as well as TDDFTTB yields reasonable agreement with TDDFT calculations at a highly reduced cost. Our study suggests that and which differ in their optical gaps, have potential applications in polymer science, biology, and medicine as singlemolecule fluorescent probes, in photovoltaics as the ntype emitter and/or ptype base of a junction solar cell, and in nanoelectronics as fluorescencebased sensors and switches.

Effects of solvation and core switching on the photoelectron angular distributions from and
View Description Hide DescriptionPhotoelectron images are recorded in the photodetachment of two series of cluster anions, and with linearly polarized 400 nm light. The energetics of the observed photodetachment bands compare well with previous studies, showing evidence for switching between two anionic core structures: The monomer and covalent dimer anions. The systematic study of photoelectron angular distributions (PADs) sheds light on the electronic structure of the different core anions and indicates that solvation by several molecules and/or one water molecule has only moderate effect on the excesselectron orbitals. The observed PAD character is reconciled with the symmetry properties of the parent molecular orbitals. The most intriguing result concerns the PADs showing remarkable similarities between the monomer and dimer anion clustercore types. This observation is explained by treating the highestoccupied molecular orbital of the covalent dimer anion as a linear combination of two spatially separated monomeric orbitals.

Electronic spectroscopy and ionization potential of in the gas phase
View Description Hide DescriptionThe electronic spectroscopy of has been examined using multiphoton ionization with massselected detection of the ions. Supersonic jet cooling was used to reduce the spectral congestion. Twentytwo vibronic bands of neutral were observed in the range from 17 400 to 32 000 cm^{−1}. These bands originated from the and states. The stronger band systems are attributed to metalcentered transitions. Threshold ionization measurements were used to determine the ionization potentials of UO and These were found to be higher than the values obtained previously from electron impact measurements but in agreement with the results of recent theoretical calculations.