Volume 125, Issue 9, 07 September 2006
 ARTICLES

 Theoretical Methods and Algorithms

Microsolvation effects on the electronic transitions in simple aromatic chromophores: The role of the Slatertype Gaussian orbitals in the complete active space selfconsistent field approach
View Description Hide DescriptionOne of the most studied feature of aromatic molecular clusters in the gas phase is the shift of the electronic transitions between the bare aromatic chromophore and its clusters. In the present ab initio complete active space selfconsistent field study the coupling of the basis set superposition error and counterpoise procedure and a combination of Pople and Slatertype Gaussian basis sets has been proven to reproduce quantitatively the gasphase experimental shifts. The quantal results are here analyzed with respect to the electrostatic and polarization forces and electron density differences, and connected with the sign of the shifts of the electronic transitions.

matrix analysis of the RennerTeller effect: An accurate threestate diabatization for
View Description Hide DescriptionSome time ago we published our first article on the RennerTeller (RT) model to treat the electronic interaction for a triatomic molecule [J. Chem. Phys.124, 081106 (2006)]. The main purpose of that Communication was to suggest considering the RT phenomenon as a topological effect, just like the JahnTeller phenomenon. However, whereas in the first publication we just summarized a few basic features to support that idea, here in the present article, we extend the topological approach and show that all the expected features that characterize a three (multi) state RTtype'3 system of a triatomic molecule can be studied and analyzed within the framework of that approach. This, among other things, enables us to employ the topological matrix [Phys. Rev. A62, 032506 (2000)] to determine, a priori, under what conditions a threestate system can be diabatized. The theoretical presentation is accompanied by a detailed numerical study as carried out for the HNH system. The matrix analysis shows that the two original electronic states and (evolving from the collinear degenerate doublet), frequently used to study this RennerTellertype system, are insufficient for diabatization. This is true, in particular, for the stable groundstate configurations of the HNH molecule. However, by including just one additional electronic state—a state (originating from a collinear state)—it is found that a rigorous, meaningful threestate diabatization can be carried out for large regions of configuration space, particularly for those, near the stable configuration of . This opens the way for an accurate study of this important molecule even where the electronic angular momentum deviates significantly from an integer value.

Calculation of twophoton absorption spectra of donoracceptor compounds in solution using quadratic response timedependent density functional theory
View Description Hide DescriptionLinear and quadratic response timedependent density functional theories have been applied to calculate the photophysical properties of donoracceptor molecules which are known to have large nonlinear absorption. The linear absorption and twophoton absorption spectra predicted using hybrid functionals, including the Coulombattenuated model, with continuum solvation models are reported and compared to experiment and to previous theoretical predictions. While the quadratic response with these functionals overestimated the TPA cross sections relative to experiment when a Gaussian linewidth function was used, a fairly good agreement was obtained when a Lorentzian linewidth function was applied. In addition, the comparison of the TPA cross sections calculated by the sum over states with those calculated by the twostate approximation indicates the importance of the higher energy states in TPA, particularly in nondegenerate experiments.

Simple method to obtain symmetry harmonics of point groups
View Description Hide DescriptionWe propose a simple, selfconsistent method to obtain basis functions of irreducible representations of a finite point group. Our method is based on eigenproblem formulation of a projection operator represented as a nonhomogeneous polynomial of angular momentum. The method is shown to be more efficient than the usual numerical methods when applied to the analysis of highorder symmetry harmonics in cubic and icosahedral groups. For loworder symmetry harmonics the method provides rational coefficients of expansion in the basis.

Search for suitable approximation methods for fullerene structure and relative stability studies: Case study with
View Description Hide DescriptionLocal density approximation (LDA), several popular general gradient approximation (GGA), hybrid module based density functionaltheoretical methods: SVWN, BLYP, PBE, HCTH, B3LYP, PBE1PBE, B1LYP, and BHandHLYP, and some nonstandard hybrid methods are applied in geometry prediction for and . HCTH with 321G basis set is found to be one of the best methods for fullerene structural prediction. In the predictions of relative stability of isomers, PM3 is an efficient method in the first step for sorting out the most stable isomers. HCTH with 321G predicts very good geometries for , similar to the performance of . The gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital from the predictions of all the density functional theory methods has the following descending order: .

A restrictedopenshell completebasisset model chemistry
View Description Hide DescriptionA restrictedopenshell model chemistry based on the complete basis setquadratic Becke3 (CBSQB3) model is formulated and denoted ROCBSQB3. As the name implies, this method uses spinrestrictedwave functions, both for the direct calculations of the various components of the electronic energy and for extrapolating the correlation energy to the completebasisset limit. These modifications eliminate the need for empirical corrections that are incorporated in standard CBSQB3 to compensate for spin contamination when spinunrestrictedwave functions are used. We employ an initial test set of 19 severely spincontaminated species including doublet radicals and both singlet and triplet biradicals. The mean absolute deviation (MAD) from experiment for the new ROCBSQB3 model is slightly smaller than that of the standard unrestricted CBSQB3 version and substantially smaller than the MAD for the unrestricted CBSQB3 before inclusion of the spin correction . However, when applied to calculate the heats of formation at for the moderately spincontaminated radicals in the G2/97 test set, ROCBSQB3 does not perform quite as well as the standard unrestricted CBSQB3, with a MAD from experiment of (compared with for standard CBSQB3). ROCBSQB3 performs marginally better than standard CBSQB3 for the G2/97 set of ionizationenergies with a MAD of (compared with ) and electron affinities with a MAD of (compared with ), but the differences in MAD values are comparable to the experimental uncertainties. Our overall conclusion is that ROCBSQB3 eliminates the spin correction in standard CBSQB3 with no loss in accuracy.

Calculation of interatomic decay widths of vacancy states delocalized due to inversion symmetry
View Description Hide DescriptionIn a recent publication [J. Chem. Phys.123, 204107 (2005)], we have introduced a new ab initio approach for the calculation of the widths of interatomic electronic decay of innershell vacancies in clusters. The new technique is based on the configuration interaction formalism first introduced for the description of resonance states by Fano [Phys. Rev.124, 1866 (1961)] and on a Green function method for the description of the manyelectron states involved in the electronic decay. Central to the new method is the selection of the physical excitation operators for the construction of the initial and final states of the interatomic decay. The previously described selection procedure has been formulated for localized vacancy states and runs into difficulties when applied to the decay of vacancy states delocalized due to inversion symmetry, e.g., states of . Here we present a modified computational scheme suitable for interatomic decay of the energysplit gerade and ungerade states and apply it to the interatomic Coulombic decay in two homonuclear diatomic clusters: and .

A generalization of the charge equilibration method for nonmetallic materials
View Description Hide DescriptionAssigning effective atomic charges that properly reproduce the electrostatic fields of molecules is a crucial step in the construction of accurate interatomic potentials. We propose a new approach to calculate these charges, which as previous approaches are, is based on the idea of charge equilibration. However, we only allow charge to flow between covalently bonded neighbors by using the concept of socalled split charges. The semiempirical fit parameters in our approach do not only reflect atomic properties (electronegativity and atomic hardness) but also bonddependent properties. The new method contains two popular but hitherto disjunct approaches as limiting cases. We apply our methodology to a set of molecules containing the elements silicon, carbon, oxygen, and hydrogen. Effective charges derived from electrostatic potential surfaces can be predicted more than twice as accurately as with previous works, at the expense of one additional fit parameter per bond type controlling the polarizability between two bonded atoms. Additional bondtype parameters can be introduced, but barely improve the results. An increase in accuracy of only 30% over existing techniques is achieved when predicting Mulliken charges. However, this could be improved with additional bondtype parameters.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Ab initio study of the potential energy surface for the reaction
View Description Hide DescriptionPotential energy surface for the reaction has been calculated using the complete active space selfconsistentfield and multireference configuration interaction methods with the correlation consistent triple, quadruple, and quintuplezeta basis sets. A specific reactionparameters density functional theory has been suggested, in which the B3LYP functional is reoptimized to give the highly accurate potential energy surface with less computational efforts.

A comparison of linear and nonlinear correlation factors for basis set limit MøllerPlesset second order binding energies and structures of , , and
View Description Hide DescriptionThe basis set limit MøllerPlesset secondorder equilibrium bond lengths of , , and , accurate to , are computed to be , , and . The corresponding binding energies are , , and , respectively. An accuracy of 95% in the binding energy requires an augccpV6Z basis or larger for conventional MøllerPlesset theory. This accuracy is obtained using an augccpV5Z basis if geminal basis functions with a linear correlation factor are included and with an augccpVQZ basis if the linear correlation factor is replaced by with . The correlation factor does not perform as well, describing the atom more efficiently than the dimer. The geminal functions supplement the orbital basis in the description of both the shortrange correlation, at electron coalescence, and the longrange dispersion correlation and the values of that give the best binding energies are smaller than those that are optimum for the atom or the dimer. It is important to sufficiently reduce the error due to the resolution of the identity approximation for the three and fourelectron integrals and we recommend the complementary auxiliary basis set method. The effect of both orbital and geminal basis set superposition error must be considered to obtain accurate binding energies with small orbital basis sets. In this respect, we recommend using with localized orbitals and the original orbitalvariant formalism.

Multireference configuration interaction studies on the ground and excited states of : The potential energy curves of along N–N distance
View Description Hide DescriptionIn this paper, the ground and excited states of were studied at the multireference configuration interaction (MRCI) level of theory with Dunning's [J. Chem. Phys.90, 1007 (1985); 96, 6796 (1992)] correlation consistent basis sets augoccpVDZ and augccpVTZ. The geometry optimizations were performed for the ground state of . The vertical excitation energies and transition moments were calculated for the lowlying singlet states of including the lowest three states, two states, one state, and two states at the MRCI level of theory with Dunning’s correlation consistent basis sets augccpVDZ, augccpVTZ, and augccpVQZ. Furthermore, for the first time, the potential energy curves were calculated at the complete active space selfconsistentfield and MRCI levels of theory for as many as 12 singlet electronic states along the N–N distance. The dissociation asymptotes of these 12 singlet electronic states were discussed.

Isotope effects in the CO dimer: Millimeter wave spectrum and rovibrational calculations of
View Description Hide DescriptionThe millimeter wavespectrum of the isotopically substituted CO dimer, , was studied with the Orotron jet spectrometer, confirming and extending a previous infrared study [A. R. W. McKellar, J. Mol. Spectrosc.226, 190 (2004)]. A very dilute gas mixture of CO in Ne was used, which resulted in small consumption of sample gas and produced cold and simple spectra. Using the technique of combination differences together with the data from the infrared work, six transitions in the region have been assigned. They belong to two branches, which connect four low levels of symmetry to three previously unknown levels of symmetry. The discovery of the lowest state of symmetry, which corresponds to the projection of the total angular momentum onto the intermolecular axis, identifies the geared bending mode of the dimer at . Accompanying rovibrational calculations using a recently developed hybrid potential from ab initio coupled cluster [CCSD(T)] and symmetryadapted perturbation theory calculations [G. W. M. Vissers et al., J. Chem. Phys.122, 054306 (2005)] gave very good agreement with experiment. The isotopic dependence of the energy splitting, the intermolecular separation , and the energy difference of two ground state isomers, which change significantly when or are substituted into the normal isotopolog [L. A. Surin et al., J. Mol. Spectrosc.223, 132 (2004)], was explained by these calculations. It turns out that the change in anisotropy of the intermolecular potential with respect to the shifted monomer centers of mass is particularly significant.

Electronic spectroscopy of the system of CDBr
View Description Hide DescriptionWe report fluorescence excitation and single vibronic level emission spectra of jetcooled CDBr in the region. A total of 32 cold bands involving the pure bending levels with and combination bands , , , and in the system of this carbene were observed; most of these are reported and/or rotationally analyzed here for the first time. Rotational analysis yielded band origins and effective rotational constants for both bromine isotopomers ( and ). The derived vibrational intervals are combined with results of Yu et al. [J. Chem. Phys.115, 5433 (2001)] to derive barriers to linearity for the , , and progressions. The state C–D stretching frequency is determined for the first time, in excellent agreement with theory, as are the isotope splittings in the excited state. Our emission spectra probe the vibrational structure of the and states up to above the vibrationless level of the state; the total number of levels observed is around twice that previously reported. Unlike CHBr, where even the lowest bending levels are perturbed by spinorbit interaction with the triplet origin, the term energy of every level save one below in CDBr is reproduced by a Dunham expansion to within a standard deviation of , and a spinorbit coupling matrix element of is derived from a deperturbation analysis of the triplet origin. The multireference configuration interaction (MRCI) calculations of Yu et al. [J. Chem. Phys.115, 5433 (2001)] well reproduce triplet perturbations in the pure bending manifold, and globally, the vibrational frequencies of , , and are in excellent agreement with theoretical predictions.

Application of density functional theory for studies of excited states and phosphorescence of platinum(II) acetylides
View Description Hide DescriptionThe electronic states of different conformations of platinum acetylides and (PE1 and PE2) were calculated with density functional theory(DFT) using effective core potential basis sets. Time dependent DFT calculations of UV absorption spectra showed strong dependence of the intense absorption band maxima on mutual orientation of the phenyl rings with respect to the P–Pt–P axis. Geometry optimization of the first excited triplet state indicates broken symmetry structure with the excitation being localized in one ligand. This splits the two substitution ligands into a nondistorted aromatic ring with the bonds for one side and into a quinoid structure with a cumulenic link on the other side. Quadratic response (QR) calculations of spinorbit coupling and phosphorescence radiative lifetime indicated a good agreement with experimental values reported for solid PE1 and PE2 and PE2 capped with dendrimers in tetrahydrofuran solutions. The QR calculations reproduced an increase of upon prolongation of chain of ligands and concommittant redshift of the phosphorescence. Moreover, it is shown how the phosphorescence borrows intensity from transitions localized at the fragments and that there is no intensity borrowing from delocalized transitions.

Infrared spectra of and clusters
View Description Hide DescriptionWe study the solvation of and with acetylene ligands by means of midinfrared photodissociation spectroscopy in the CH stretching region, monitoring evaporation upon infrared photon absorption by the parent cluster ions. Our findings are interpreted with the help of density functional theory. The infrared spectra indicate that while the binding generally occurs through ionic H bonds, there are two different classes of ligands which differ in their binding strength. This holds true for both core ions, even though their electronic structures and charge distributions are very different.

Gas phase electronic spectra of the carbon chains , , , and
View Description Hide DescriptionThree electronic absorption systems for at 511, 445, and and one for , , and centered at 228, 259, and have been observed in the gas phase. The chain was produced in both discharge and ablation sources and detected using resonant twocolor twophoton ionization spectroscopy involving photons. The decay of the excited singlet electronic states indicates fast intramolecular processes on a subpicosecond time scale. The internal energy is assumed to be trapped in a triplet state for at least . Holeburning experiments on the transition of , , and of confirm the predissociative nature of the excited electronic states.

Photodissociation of (, Cl, Br, and I) complexes. I. Electronic spectra and dissociation pathways
View Description Hide DescriptionPhotodissociationspectra of (, Cl, Br, and I) complexes have been measured in the ultraviolet region . Several fragment ions with and without charge transfer(CT),, , , , , and , were formed by evaporation (intermolecular bonddissociation) and intracluster reaction (intramolecular bonddissociation) via excited electronic states. Branching ratios of these ions were found to depend both on absorption bands and on halogen atoms. The ground states of the complexes were calculated to have geometries in which the Mg atom lies next to atom of methyl halide molecules. Positive charges of the complexes are confirmed to be almost localized on Mg. Observed absorption bands were assigned to the transitions of the atomic line perturbed by interactions with methyl halide molecules. Branching ratios of fragment ions can be partly explained by the stability of fragment ions and neutral counterparts. From the excited state potential energy curves along the bond distance, dissociationreaction after CT was concluded to proceed predissociatively; potential curve crossings between the initially excited states and repulsive CT states may have a crucial role in the formation of , , and . In particular, ions were formed via repulsive CT states having a character of electron excitation from to .

Photodissociation of (, Cl, Br, and I) complexes. II. Fragment angular and energy distributions
View Description Hide DescriptionAngular and energy distributions of photofragments from (, Cl, Br, and I) were deduced from timeofflight (TOF) profiles measured by rotating the polarization direction of the dissociation laser with respect to ion beam direction. The TOF profiles of and fragment ions produced from complex with 266 and photons showed clear but opposite recoil anisotropy to each other. In addition, formed by a dissociation of the complex at a photolysis wavelength of also showed an anisotropic distribution in the TOF profile which had the same behavior as the profile of . For complex, and formed with a photon had also spatial anisotropy, in which the TOF profile of was almost opposite to that of . These anisotropic distributions were explained by (1) local excitation on the ion, (2) rapid dissociation compared with a rotational period of the parent complex, and (3) geometrical structures of the parent complexes. Anisotropy parameter values were determined to be , , , and and ). This dependence on the halogen atom observed in values was qualitatively explained by both the geometrical parameters and classical rotational periods of parent complexes. In the product energy distribution, 46%, 40%, 21%, 16%, and 16% of available energies were found to be transferred into translational energies of , , , , and , respectively. These values were compared with energy distributions estimated by a statistical prior distribution and a nonstatistical impulsive model. For and , the translational energies determined from the measurement had values between those estimated from statistical and nonstatistical models. On the other hand, the energy partitioning for the product ions of , , and was found to be almost statistical. From these considerations, we concluded that nonstatistical processes were more important in the dissociation of than in other systems.

Calculating vibrational energies and wave functions of vinylidene using a contracted basis with a locally reorthogonalized coupled twoterm Lanczos eigensolver
View Description Hide DescriptionWe use a contracted eigensolver approach to compute vinylidenelike vibrational states of the acetylenevinylidene system. To overcome problems caused by loss of orthogonality of the Lanczos vectors we reorthogonalize Lanczos vector and use a coupled twoterm approach. The calculations are done in CC–HH diatomdiatom Jacobi coordinates which make it easy to compute states one irreducible representation at a time. The most costly parts of the calculation are parallelized and scale well. We estimate that the vinylidene energies we compute are converged to .

Intermolecular potentials of the methane dimer calculated with MøllerPlesset perturbation theory and density functional theory
View Description Hide DescriptionWe have calculated the intermolecular interaction potentials of the methane dimer at the minimumenergy conformation using the HartreeFock (HF) selfconsistent theory, the correlationcorrected secondorder MøllerPlesset (MP2) perturbation theory, and the density functional theory(DFT) with the PerdewWang (PW91) functional as the exchange or the correlation part. The HF calculations yield unbound potentials largely due to the exchangerepulsion interaction. In the MP2 calculations, the basis set effects on the repulsion exponent, the equilibrium bond length, the binding energy, and the asymptotic behavior of the calculated intermolecular potentials have been thoroughly studied. We have employed basis sets from the Slatertype orbitals fitted with Gaussian functions [Quantum Theory of Molecular and Solids: The SelfConsistent Field for Molecular and Solids (McGrawHill, New York, 1974), Vol. 4], Pople’s medium size basis sets of Krishnan et al. [J. Chem. Phys.72, 650 (1980)] [up to ] to Dunning’s correlation consistent basis sets [J. Chem. Phys.90, 1007 (1989)] ( and ) (, T, and Q). With increasing basis size, the repulsion exponent and the equilibrium bond length converge at the basis set and the basis set, respectively, while a large basis set (augccpVTZ) is required to converge the binding energy at a chemical accuracy . Up to the largest basis set used, the asymptotic dispersion coefficient has not converged to the destined value from molecular polarizability calculations. The slow convergence could indicate the inefficacy of using the MP2 calculations with Gaussiantype functions to model the asymptotic behavior. Both the basis set superposition error (BSSE) corrected and uncorrected results are presented to emphasize the importance of including such corrections. Only the BSSE corrected results systematically converge to the destined potential curve with increasing basis size. The DFT calculations generate a wide range of interaction patterns, from purely unbound to strongly bound, underestimating or overestimating the binding energy. The binding energy calculated using the PW91PW91 functional and the equilibrium bond length calculated using the PW91VP86 functional are close to the MP2 results at the basis set limit.