Index of content:
Volume 122, Issue 3, 15 January 2005
- Theoretical Methods and Algorithms
Ground- and excited-state diatomic bond lengths, vibrational levels, and potential-energy curves from conventional and localized Hartree–Fock-based density-functional theory122(2005); http://dx.doi.org/10.1063/1.1824892View Description Hide Description
Ground- and excited-state diatomic bond lengths, vibrational levels, and potential-energy curves are determined using conventional and localized Hartree–Fock (LHF)-based density-functional theory. Exchange only and hybrid functionals (with various fractions of exchange) are considered, together with a standard generalized gradient approximation (GGA). Ground-state bond lengths and vibrational wave numbers are relatively insensitive to whether orbital exchange is treated using the conventional or LHF approach. Excited-state 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 LHF-based approaches, providing an asymptotic correction is present. Excited-state 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 potential-energy curves are compared with near-exact Rydberg–Klein–Rees curves. Agreement is very good for the ground and first excited state, but deteriorates for the higher states.
122(2005); http://dx.doi.org/10.1063/1.1829050View Description Hide Description
This 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 one-determinant wave functions constructed from Hartree-Fock and, in particular, from Kohn-Sham 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 co-workers, 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 atoms-in-molecules projectors. In addition, the physical significance of nonzero values for closed-shell 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 model122(2005); http://dx.doi.org/10.1063/1.1831271View Description Hide Description
A 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 so-called 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, third-harmonic generation (THG), and electric field induced second-harmonic 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.
122(2005); http://dx.doi.org/10.1063/1.1809605View Description Hide Description
From coupled-cluster theory and many-body perturbationtheory we derive the local exchange-correlation potential of density functional theory in an orbital dependent form. We show the relationship between the coupled-cluster approach and density functional theory, and connections and comparisons with our previous second-order correlation potential [OEP-MBPT(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 exchange-correlation functional, potential and orbitals. Specifying initially to second-order 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 infinite-order 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 second-order method [OEP-MBPT(2)-f] and [OEP-MBPT(2)-sc] are often of coupled-cluster accuracy and substantially better than ordinary Hartree–Fock based second-order
122(2005); http://dx.doi.org/10.1063/1.1834562View Description Hide Description
This paper proposes methods for calculating the derivative couplings between adiabatic states in density-functional theory(DFT) and compares them with each other and with multiconfigurational self-consistent field calculations. They are shown to be accurate and, as expected, the costs of their calculation scale more favorably with system size than post-Hartree-Fock calculations. The proposed methods are based on single-particle excitations and the associated Slater transition-state 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 linear-response theory was found to offer the best trade-off between accuracy and efficiency. The algorithms presented here have been implemented for doublet-doublet excitations within a plane-wave-basis and pseudopotential framework but are easily generalizable to other excitations and basis sets. Owing to their fundamental importance in cases where the Born-Oppenheimer separation of motions is not valid, these derivative couplings can facilitate, for example, the treatment of nonadiabaticcharge transfers, of electron-phonon couplings, and of radiationless electronic transitions in DFT.
122(2005); http://dx.doi.org/10.1063/1.1831276View Description Hide Description
The 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 spin-orbit coupling operator and their use in molecular -tensor calculations122(2005); http://dx.doi.org/10.1063/1.1829047View Description Hide Description
Approximations to the Breit-Pauli form of the spin-orbit coupling(SOC) operator are examined. The focus is on approximations that lead to an effective quasi-one-electron operator which leads to efficient property evaluations. In particular, the accurate spin-orbit mean-field (SOMF) method developed by Hess, Marian, Wahlgren, and Gropen is examined in detail. It is compared in detail with the “effective potential” spin-orbit operator commonly used in density functional theory(DFT) and which has been criticized for not including the spin-other orbit (SOO) contribution. Both operators contain identical one-electron 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 spin-same 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 DFT-SOC treatment is to multiply the exchange contribution to the operator by This is verified numerically in calculations of molecular -tensors and one-electron 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 one-center approximation to the Coulomb and one-electron SOC terms leads to errors on the order of Small absolute errors are obtained for the one-center approximation to the exchange term which is consequently the method of choice for large molecules.
122(2005); http://dx.doi.org/10.1063/1.1829253View Description Hide Description
We use projection operators to address the coarse-grained multiscale problem in harmonic systems. Stochastic equations of motion for the coarse-grained 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 system-specific 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 coarse-grained variables is not necessarily Markovian, even though the variables are slow. Our approach is applicable to any system in which the coarse-grained regions are linear. As an example, we apply it to the dynamics of a single mesoscopic particle in the infinite one-dimensional harmonic chain.
122(2005); http://dx.doi.org/10.1063/1.1834911View Description Hide Description
We 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 second-order Møller-Plesset (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 local-correlation calculations.
- Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry
122(2005); http://dx.doi.org/10.1063/1.1828045View Description Hide Description
A double minimum six-dimensional 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 ammonia-like 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 in-plane distortion and the out-of-plane bending modes, the higher overtones and combination levels are difficult to assign unequivocally.
122(2005); http://dx.doi.org/10.1063/1.1810513View Description Hide Description
A heterodyned fifth-order infrared pulse sequence has been used to measure a two-dimensional infrared (2D-IR) spectrum of azide in the ionic glass By rephasing a two-quantum coherence, a process not possible with third-order spectroscopy, the 2D-IR 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 fifth-order infrared pulse sequence, possible cascaded contributions to the signal are investigated. No evidence of cascaded signals is found. Compared to third-order spectroscopies, fifth-order 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 complex122(2005); http://dx.doi.org/10.1063/1.1832596View Description Hide Description
The competition between vibrational and electronic predissociations of the van der Waals complex has been studied using several dynamical computational methods: exact quantum wave-packet propagation, time-dependent golden rule, and quasiclassical trajectory with quantum jumpsmodel. Five electronic states are considered using recent three-dimensional coupled surfaces obtained with a perturbative diatoms-in-molecules 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 sparse-intermediate 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 two-photon ionization spectroscopy of jet-cooled 1-hydroxy-9,10-anthraquinone122(2005); http://dx.doi.org/10.1063/1.1829977View Description Hide Description
We carried out laser induced fluorescence and resonance enhanced two-color two-photonionization spectroscopy of jet-cooled 1-hydroxy-9,10-anthraquinone (1-HAQ). The 0-0 band transition to the lowest electronically excited state was found to be at 461.98 nm (21 646 cm−1). A well-resolved vibronic structure was observed up to 1100 cm−1 above the 0-0 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 0-0 band showed Stokes-shifted 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 9,10-quinone and the 1,10-quinone forms, the latter of which, the proton-transferred form of 1-HAQ, 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 9,10-quinone form of 1-HAQ is the lowest energy structure in the ground state, with the 1,10-quinone form lying ∼5000 cm−1 above it. The intramolecular hydrogen bond of the 9,10-quinone was found to be unusually strong, with an estimated bond energy of ∼13 kcal/mol (∼4500 cm−1), probably due to the resonance-assisted nature of the hydrogen bonding involved.
122(2005); http://dx.doi.org/10.1063/1.1829991View Description Hide Description
The structures of hydrated 1-hydroxyanthraquinone complexes (1-HAQ), with intramolecular and intermolecular hydrogen bonding interactions were studied using laser spectroscopic methods such as laser induced fluorescence, fluorescence-detected infrared, infrared-visible hole burning, and visible-visible hole burning spectroscopy. In the 1:1 complex the water binds to the free carbonyl group of 1-HAQ 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 1-HAQ. 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 0-0 band of vibronic transition due to the asymmetry of the two phenyl rings in 1-HAQ. The 0-0 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.
122(2005); http://dx.doi.org/10.1063/1.1830483View Description Hide Description
Structural and electronic properties of S-doped fullerene were calculated systematically via Hartree–Fock self-consistent field (SCF) and density functional B3LYP levels of theory with basis set. The most stable represents an open cage structure with a nine-member 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).
Vibration-rotation interactions between overtone and combination levels of asymmetric-top molecules: Application to the infrared spectroscopy of formaldehyde and ketene122(2005); http://dx.doi.org/10.1063/1.1835263View Description Hide Description
The conventional vibration-rotation Hamiltonian for an asymmetric-top 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 low-frequency vibrational modes are less reliable. Comparisons are made between the calculated values and experimental results.
122(2005); http://dx.doi.org/10.1063/1.1825994View Description Hide Description
The photodissociationdynamics of vinyl bromide and perfluorovinyl bromide have been investigated at 234 nm using a photofragment ion imaging technique coupled with a state-selective [2+1] resonance-enhanced 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. Low-energy 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
122(2005); http://dx.doi.org/10.1063/1.1832599View Description Hide Description
A perturbative approach is employed to solve the Bloch-Torrey equations in the presence of distant-dipole 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 two-dimensional correlation spectroscopy revamped by asymmetric Z-gradient echo detection spectra are shown to be free from some inadequacies resulting from a simplistic application of standard approximations.
122(2005); http://dx.doi.org/10.1063/1.1832593View Description Hide Description
We extend the quantum mode-coupling 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 Lennard-Jones particles. Our treatment may be used to study quantum aging and exotic glass melting scenarios in structural supercooled quantum liquids.
High-resolution 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 atom122(2005); http://dx.doi.org/10.1063/1.1829058View Description Hide Description
Xenon fluoride radicals were generated by solid-state 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 g-factor tensors of were obtained: and and Comparison of the measured hyperfine parameters with those predicted by density-functional theory(DFT) calculations indicates, that relativistic DFT gives true electron spin distribution in the ground-state, whereas nonrelativistic theory underestimates dramatically the electron-nuclear contact Fermi interaction on the Xe atom. Analysis of the obtained magnetic-dipole 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 magnetic-dipole interaction constants, which are in agreement with the measured values. The other relativistic feature is considerable anisotropy of g-tensor, 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