Volume 122, Issue 3, 15 January 2005
 ARTICLES

 Theoretical Methods and Algorithms

Ground and excitedstate diatomic bond lengths, vibrational levels, and potentialenergy curves from conventional and localized Hartree–Fockbased densityfunctional theory
View Description Hide DescriptionGround and excitedstate diatomic bond lengths, vibrational levels, and potentialenergy curves are determined using conventional and localized Hartree–Fock (LHF)based densityfunctional theory. Exchange only and hybrid functionals (with various fractions of exchange) are considered, together with a standard generalized gradient approximation (GGA). Groundstate bond lengths and vibrational wave numbers are relatively insensitive to whether orbital exchange is treated using the conventional or LHF approach. Excitedstate calculations are much more sensitive. For a standard fraction of orbital exchange, and CO vertical excitation energies at experimental bond lengths are accurately described by both conventional and LHFbased approaches, providing an asymptotic correction is present. Excitedstate bond lengths and vibrational levels are more accurate with the conventional approach. The best quality, however, is obtained with an asymptotically corrected GGA functional. For the ground and lowest four singlet excited states, the GGA mean absolute errors in bond lengths are 0.006 Å (0.5%) and 0.011 Å (0.8%) for and CO, respectively. Mean absolute errors in fundamental vibrational wavenumbers are (2.7%) and (5.0%), respectively. The GGA potentialenergy curves are compared with nearexact Rydberg–Klein–Rees curves. Agreement is very good for the ground and first excited state, but deteriorates for the higher states.

Comparative analysis of local spin definitions
View Description Hide DescriptionThis work provides a survey of the definition of electron spin as a local property and its dependence on several parameters in actual calculations. We analyze onedeterminant wave functions constructed from HartreeFock and, in particular, from KohnSham orbitals within the collinear approach to electron spin. The scalar total spin operators and are partitioned by projection operators, as introduced by Clark and Davidson, in order to obtain local spin operators and respectively. To complement the work of Davidson and coworkers, we analyze some features of local spins which have not yet been discussed in sufficient depth. The dependence of local spin on the choice of basis set, density functional, and projector is studied. We also discuss the results of partitioning and show that values depend less on these parameters than values. Furthermore, we demonstrate that for small organic test molecules, a partitioning of with preorthogonalized Löwdin projectors yields nearly the same results as one obtains using atomsinmolecules projectors. In addition, the physical significance of nonzero values for closedshell molecules is investigated. It is shown that due to this problem, values are useful for calculations of relative spin values, but not for absolute local spins, where values appear to be better suited.

Microscopic and macroscopic polarization within a combined quantum mechanics and molecular mechanics model
View Description Hide DescriptionA polarizable quantum mechanics and molecular mechanics model has been extended to account for the difference between the macroscopic electric field and the actual electric field felt by the solute molecule. This enables the calculation of effective microscopic properties which can be related to macroscopic susceptibilities directly comparable with experimental results. By seperating the discrete local field into two distinct contribution we define two different microscopic properties, the socalled solute and effective properties. The solute properties account for the pure solvent effects, i.e., effects even when the macroscopic electric field is zero, and the effective properties account for both the pure solvent effects and the effect from the induced dipoles in the solvent due to the macroscopic electric field. We present results for the linear and nonlinear polarizabilities of water and acetonitrile both in the gas phase and in the liquid phase. For all the properties we find that the pure solvent effect increases the properties whereas the induced electric field decreases the properties. Furthermore, we present results for the refractive index, thirdharmonic generation (THG), and electric field induced secondharmonic generation (EFISH) for liquid water and acetonitrile. We find in general good agreement between the calculated and experimental results for the refractive index and the THG susceptibility. For the EFISH susceptibility, however, the difference between experiment and theory is larger since the orientational effect arising from the static electric field is not accurately described.

The exchangecorrelation potential in ab initio density functional theory
View Description Hide DescriptionFrom coupledcluster theory and manybody perturbationtheory we derive the local exchangecorrelation potential of density functional theory in an orbital dependent form. We show the relationship between the coupledcluster approach and density functional theory, and connections and comparisons with our previous secondorder correlation potential [OEPMBPT(2) (OEP—optimized effective potential)] [I. Grabowski, S. Hirata, S. Ivanov, and R. J. Bartlett, J. Chem. Phys. 116, 4415 (2002)]. Starting from a general theoretical framework based on the density condition in Kohn–Sham theory, we define a rigorous exchangecorrelation functional, potential and orbitals. Specifying initially to secondorder terms, we show that our ab initio correlation potential provides the correct shape compared to those from reference quantum Monte Carlo calculations, and we demonstrate the superiority of using Fock matrix elements or more general infiniteorder semicanonical transformations. This enables us to introduce a method that is guaranteed to converge to the right answer in the correlation and basis set limit, just as does ab initiowave functiontheory. We also demonstrate that the energies obtained from this generalized secondorder method [OEPMBPT(2)f] and [OEPMBPT(2)sc] are often of coupledcluster accuracy and substantially better than ordinary Hartree–Fock based secondorder

Calculation of nonadiabatic couplings in densityfunctional theory
View Description Hide DescriptionThis paper proposes methods for calculating the derivative couplings between adiabatic states in densityfunctional theory(DFT) and compares them with each other and with multiconfigurational selfconsistent field calculations. They are shown to be accurate and, as expected, the costs of their calculation scale more favorably with system size than postHartreeFock calculations. The proposed methods are based on singleparticle excitations and the associated Slater transitionstate densities to overcome the problem of the unavailability of multielectron states in DFT which precludes a straightforward calculation of the matrix elements of the nuclear gradient operator. An iterative scheme employing linearresponse theory was found to offer the best tradeoff between accuracy and efficiency. The algorithms presented here have been implemented for doubletdoublet excitations within a planewavebasis and pseudopotential framework but are easily generalizable to other excitations and basis sets. Owing to their fundamental importance in cases where the BornOppenheimer separation of motions is not valid, these derivative couplings can facilitate, for example, the treatment of nonadiabaticcharge transfers, of electronphonon couplings, and of radiationless electronic transitions in DFT.

Calculating intensities using effective Hamiltonians in terms of Coriolisadapted normal modes
View Description Hide DescriptionThe calculation of rovibrational transition energies and intensities is often hampered by the fact that vibrational states are strongly coupled by Coriolis terms. Because it invalidates the use of perturbation theory for the purpose of decoupling these states, the coupling makes it difficult to analyze spectra and to extract information from them. One either ignores the problem and hopes that the effect of the coupling is minimal or one is forced to diagonalize effective rovibrational matrices (rather than diagonalizing effective rotational matrices). In this paper we apply a procedure, based on a quantum mechanical canonical transformation for deriving decoupled effective rotational Hamiltonians. In previous papers we have used this technique to compute energy levels. In this paper we show that it can also be applied to determine intensities. The ideas are applied to the ethylene molecule.

Efficient and accurate approximations to the molecular spinorbit coupling operator and their use in molecular tensor calculations
View Description Hide DescriptionApproximations to the BreitPauli form of the spinorbit coupling(SOC) operator are examined. The focus is on approximations that lead to an effective quasioneelectron operator which leads to efficient property evaluations. In particular, the accurate spinorbit meanfield (SOMF) method developed by Hess, Marian, Wahlgren, and Gropen is examined in detail. It is compared in detail with the “effective potential” spinorbit operator commonly used in density functional theory(DFT) and which has been criticized for not including the spinother orbit (SOO) contribution. Both operators contain identical oneelectron and Coulomb terms since the SOO contribution to the Coulomb term vanishes exactly in the SOMF treatment. Since the DFTcorrelation functional only contributes negligibly to the SOC the only difference between the two operators is in the exchange part. In the SOMF approximation, the SOO part is equal to two times the spinsame orbit contribution. The DFT exchange contribution is of the wrong sign and numerically shown to be in error by a factor of 2–2.5 in magnitude. The simplest possible improvement in the DFTSOC treatment is to multiply the exchange contribution to the operator by This is verified numerically in calculations of molecular tensors and oneelectron SOC constants of atoms and ions. Four different ways of handling the computationally critical Coulomb part of the SOMF and operators are discussed and implemented. The resolution of the identity approximation is virtually exact for the SOC with standard auxiliary basis sets which need to be slightly augmented by steep functions for heavier elements. An almost as efficient seminumerical approximation is equally accurate. The effective nuclear charge model gives results within (on average) of the SOMF treatment. The onecenter approximation to the Coulomb and oneelectron SOC terms leads to errors on the order of Small absolute errors are obtained for the onecenter approximation to the exchange term which is consequently the method of choice for large molecules.

Inhomogeneous multiscale dynamics in harmonic lattices
View Description Hide DescriptionWe use projection operators to address the coarsegrained multiscale problem in harmonic systems. Stochastic equations of motion for the coarsegrained variables, with an inhomogeneous level of coarse graining in both time and space, are presented. In contrast to previous approaches that typically start with thermodynamic averages, the key element of our approach is the use of a projection matrix chosen both for its physical appeal in analogy to mechanical stability theory and for its algebraic properties. We show that thermodynamic equilibrium can be recovered and obtain the fluctuation dissipation theorema posteriori. All systemspecific information can be computed from a series of feasible molecular dynamics simulations. We recover previous results in the literature and show how this approach can be used to extend the quasicontinuum approach and comment on implications for dissipative particle dynamics type of methods. Contrary to what is assumed in the latter models, the stochastic process of all coarsegrained variables is not necessarily Markovian, even though the variables are slow. Our approach is applicable to any system in which the coarsegrained regions are linear. As an example, we apply it to the dynamics of a single mesoscopic particle in the infinite onedimensional harmonic chain.

A localized basis that allows fast and accurate secondorder MøllerPlesset calculations
View Description Hide DescriptionWe present a method for computing a basis of localized orthonormal orbitals (both occupied and virtual), in whose representation the Fock matrix is extremely diagonal dominant. The existence of these orbitals is shown empirically to be sufficient for achieving highly accurate secondorder MøllerPlesset (MP2) energies, calculated according to Kapuy’s method. This method (which we abbreviate KMP2) involves a different partitioning of the electron Hamiltonian and scales at most quadratically, with potential for linearity, in the number of electrons. As such, we believe the KMP2 algorithm presented here could be the basis of a viable approach to localcorrelation calculations.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Vibrations in the rhombic structure
View Description Hide DescriptionA double minimum sixdimensional potential energy surface (PES) is determined in symmetry coordinates for the most stable rhombic isomer in its electronic ground state by fitting to energies calculated ab initio. The PES exhibits a barrier to the square structure of 255 cm^{−1}. The vibrational levels are calculated variationally using an approach which involves the Watson kinetic energy operator expressed in normal coordinates. The pattern of about 65 vibrational levels up to 1600 cm^{−1} for all stable isotopomers is analyzed. Analogous to the inversion in ammonialike molecules, the rhombus rearrangements lead to splittings of the vibrational levels. In it is the mode which distorts the square molecule to its planar rhombic form. The anharmonic fundamental vibrational transitions of are calculated to be (splittings in parentheses): and notation). Their variations in all stable isotopomers were investigated. Due to the presence of strong anharmonic resonances between the inplane distortion and the outofplane bending modes, the higher overtones and combination levels are difficult to assign unequivocally.

Heterodyned fifthorder 2DIR spectroscopy of the azide ion in an ionic glass
View Description Hide DescriptionA heterodyned fifthorder infrared pulse sequence has been used to measure a twodimensional infrared (2DIR) spectrum of azide in the ionic glass By rephasing a twoquantum coherence, a process not possible with thirdorder spectroscopy, the 2DIR spectra are line narrowed, allowing the frequencies, anharmonicities, and their correlations to be measured for the first four antisymmetric stretch vibrational levels. In this glass, the vibrational levels are extremely inhomogeneously broadened. Furthermore, the glass shifts the energy of the state more than the others, causing an inhomogeneous distribution in the anharmonic constants that are partially correlated to the inhomogeneous distribution of the fundamental frequency. These effects are discussed in light of the strong interactions that exist between the charged solute and solvent. Since this is the first example of a heterodyned fifthorder infrared pulse sequence, possible cascaded contributions to the signal are investigated. No evidence of cascaded signals is found. Compared to thirdorder spectroscopies, fifthorder pulse sequences provide advanced control over vibrational coherence and population times that promise to extend the capabilities of ultrafast infrared spectroscopy.

Competition between adiabatic and nonadiabatic fragmentation pathways in the unimolecular decay of the van der Waals complex
View Description Hide DescriptionThe competition between vibrational and electronic predissociations of the van der Waals complex has been studied using several dynamical computational methods: exact quantum wavepacket propagation, timedependent golden rule, and quasiclassical trajectory with quantum jumpsmodel. Five electronic states are considered using recent threedimensional coupled surfaces obtained with a perturbative diatomsinmolecules method. Final vibrational and electronic populations, predissociation rates, and absorption spectra have been computed for excitations within the complex. The contribution of vibrational predissociation into the total decay oscillates as a function of vibrational excitation due to intramolecular vibrational relaxation in a sparseintermediate regime, which induces irregular variations of the total decay rate. Franck–Condon oscillations control the branching ratios of the individual electronic predissociation channels. However, since these oscillations are out of phase as a function of vibrational excitation, they have limited effect on the oscillatory behavior of the total predissociation rate. Comparison between exact quantum and perturbative golden rule calculations shows that vibrational predissociation has some impact on the electronic predissociation process and affects the final electronic distributions. On the contrary, vibrational product distributions are not significantly affected by the electronic predissociation. A classical description of the dynamics provides an averaged picture of the competing predissociation processes, being better adapted for treating intermolecular vibrational relaxation in the statistical limit.

Laser induced fluorescence and resonant twophoton ionization spectroscopy of jetcooled 1hydroxy9,10anthraquinone
View Description Hide DescriptionWe carried out laser induced fluorescence and resonance enhanced twocolor twophotonionization spectroscopy of jetcooled 1hydroxy9,10anthraquinone (1HAQ). The 00 band transition to the lowest electronically excited state was found to be at 461.98 nm (21 646 cm^{−1}). A wellresolved vibronic structure was observed up to 1100 cm^{−1} above the 00 band, followed by a rather broad absorption band in the higher frequency region. Dispersed fluorescence spectra were also obtained. Single vibronic level emissions from the 00 band showed Stokesshifted emission spectra. The peak at 2940 cm^{−1} to the red of the origin in the emission spectra was assigned as the OH stretching vibration in the ground state, whose combination bands with the C=O bending and stretching vibrations were also seen in the emission spectra. In contrast to the excitation spectrum, no significant vibronic activity was found for low frequency fundamental vibrations of the ground state in the emission spectrum. The spectral features of the fluorescence excitation and emission spectra indicate that a significant change takes place in the intramolecular hydrogen bonding structure upon transition to the excited state, such as often seen in the excited state proton (or hydrogen) transfer. We suggest that the electronically excited state of interest has a double minimum potential of the 9,10quinone and the 1,10quinone forms, the latter of which, the protontransferred form of 1HAQ, is lower in energy. On the other hand, ab initio calculations at the level predicted that the electronic ground state has a single minimum potential distorted along the reaction coordinate of tautomerization. The 9,10quinone form of 1HAQ is the lowest energy structure in the ground state, with the 1,10quinone form lying ∼5000 cm^{−1} above it. The intramolecular hydrogen bond of the 9,10quinone was found to be unusually strong, with an estimated bond energy of ∼13 kcal/mol (∼4500 cm^{−1}), probably due to the resonanceassisted nature of the hydrogen bonding involved.

Infraredvisible and visiblevisible double resonance spectroscopy of complexes
View Description Hide DescriptionThe structures of hydrated 1hydroxyanthraquinone complexes (1HAQ), with intramolecular and intermolecular hydrogen bonding interactions were studied using laser spectroscopic methods such as laser induced fluorescence, fluorescencedetected infrared, infraredvisible hole burning, and visiblevisible hole burning spectroscopy. In the 1:1 complex the water binds to the free carbonyl group of 1HAQ not associated with intramolecular hydrogen bond. The second water in the 1:2 complex, binds to the first water of the 1:1 complex rather than other hydrogen bonding sites of 1HAQ. A pair of two geometric isomers was produced in a supersonic jet for each of the 1:1 and 1:2 complexes. Both isomers of each complex have the same vibrational spectra in the region of the OH stretching vibration of water, but have different energies for the 00 band of vibronic transition due to the asymmetry of the two phenyl rings in 1HAQ. The 00 bands for all four species of were unambiguously assigned by comparing with the results of ab initio calculations, which yielded the structures, vibrational frequencies, and relative energies of the frontier molecular orbitals.

Structural and electronic properties of Sdoped fullerene Where is the S atom situated?
View Description Hide DescriptionStructural and electronic properties of Sdoped fullerene were calculated systematically via Hartree–Fock selfconsistent field (SCF) and density functional B3LYP levels of theory with basis set. The most stable represents an open cage structure with a ninemember ring orifice, which provides a large hole for large atoms or small molecules to pass through into the cage. The most stable endohedral has the S atom seated near the center of the cage. The calculated highest occupied molecular orbital–lowest unoccupied molecular orbital energy gaps of the isomers lie in the range of 1.42–2.50 eV. The electron affinity and the ionization potential were also presented as an indicator of the kinetic stability. Our results may aid in the design of experimental methods for controlling the nature of fullerene cages (for example, doping, opening, and reclosing them).

Vibrationrotation interactions between overtone and combination levels of asymmetrictop molecules: Application to the infrared spectroscopy of formaldehyde and ketene
View Description Hide DescriptionThe conventional vibrationrotation Hamiltonian for an asymmetrictop molecule is rewritten by expanding the elements of the inverse inertial tensor about the equilibrium molecular geometry. The approach allows the identification of terms in the Hamiltonian that couple states differing by two, three, or four vibrational quanta and hence the calculation of dimensioned Coriolis ξ coupling coefficients for interacting fundamental, overtone, and combination levels. The matrix elements that result from the application of the expanded Hamiltonian depend upon the harmonic vibrational wave numbers, equilibrium moments of inertia, Coriolis ζ parameters, and the derivatives of the elements of the inertial tensor matrix with respect to each of the normal coordinates. The Coriolis coupling coefficients may be calculated through evaluation of the summations that result from the appropriate terms. The validity of the approach is demonstrated through the calculation of coupling coefficients for interacting levels in formaldehyde and ketene. The uncertainty in the calculated values of the coupling coefficients is typically better than ±6%, although the values calculated for interactions that involve lowfrequency vibrational modes are less reliable. Comparisons are made between the calculated values and experimental results.

The dynamics of formation in the photodissociation of vinyl and perfluorovinyl bromides
View Description Hide DescriptionThe photodissociationdynamics of vinyl bromide and perfluorovinyl bromide have been investigated at 234 nm using a photofragment ion imaging technique coupled with a stateselective [2+1] resonanceenhanced multiphoton ionization scheme. The nascent Br atoms stem from the primary C–Br bonddissociation leading to the formation of and The obtained translational energy distributions have been well fitted by a single Boltzmann and three Gaussian functions. Boltzmann component has not been observed in the perfluorovinyl bromide. The repulsive state has been considered as the origin of the highest Gaussian components. Middle translational energy components with Gaussian shapes are produced from the and/or which are very close in energy. Lowenergy Gaussian components are produced via predissociation from the state. The assignments have also been supported by the recoil anisotropy corresponding to the individual components. It is suggested that intersystem crossing from the triplet states to the ground state has been attributed to the Boltzmann component and the fluorination reduces the probability of this electronic relaxation process.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Distantdipole field in liquids and diffusion: A perturbative approach
View Description Hide DescriptionA perturbative approach is employed to solve the BlochTorrey equations in the presence of distantdipole fields in nuclear magnetic resonance. The procedure, although only carried out to first order in the perturbation parameter could, in principle, be generalized to higher orders. Here D is the diffusivity, the dipolar demagnetization time, and k is the wave vector of the spatial modulation of magnetization produced by the magnetic field gradient. The results are especially interesting for dilute binary mixtures consisting of molecular species with different diffusivities. In this case the calculated twodimensional correlation spectroscopy revamped by asymmetric Zgradient echo detection spectra are shown to be free from some inadequacies resulting from a simplistic application of standard approximations.

Quantum modecoupling theory for binary mixtures
View Description Hide DescriptionWe extend the quantum modecoupling theory of neat liquids to the case of binary mixtures, in order to study supercooled liquids where quantum fluctuations may compete with thermal fluctuations. We apply the theory to a generic model of a binary mixture of LennardJones particles. Our treatment may be used to study quantum aging and exotic glass melting scenarios in structural supercooled quantum liquids.

Highresolution electron spin resonance spectroscopy of in solid argon. The hyperfine structure constants as a probe of relativistic effects in the chemical bonding properties of a heavy noble gas atom
View Description Hide DescriptionXenon fluoride radicals were generated by solidstate chemical reactions of mobile fluorine atoms with xenon atoms trapped in Ar matrix. Highly resolved electron spin resonance spectra of were obtained in the temperature range of 5–25 K and the anisotropichyperfine parameters were determined for magnetic nuclei and using naturally occurring and isotopically enriched xenon. Signs of parallel and perpendicular hyperfine components were established from analysis of temperature changes in the spectra and from numerical solutions of the spin Hamiltonian for two nonequivalent magnetic nuclei. Thus, the complete set of components of hyperfine and gfactor tensors of were obtained: and and Comparison of the measured hyperfine parameters with those predicted by densityfunctional theory(DFT) calculations indicates, that relativistic DFT gives true electron spin distribution in the groundstate, whereas nonrelativistic theory underestimates dramatically the electronnuclear contact Fermi interaction on the Xe atom. Analysis of the obtained magneticdipole interaction constants shows that fluorine and xenon atomic orbitals make a major contribution to the spin density distribution in Both relativistic and nonrelativistic calculations give close magneticdipole interaction constants, which are in agreement with the measured values. The other relativistic feature is considerable anisotropy of gtensor, which results from spin–orbit interaction. The orbital contribution appears due to mixing of the ionic states with the ground state, and the spin–orbit interaction plays a significant role in the chemical bonding of