Volume 129, Issue 10, 14 September 2008
Index of content:
- Theoretical Methods and Algorithms
129(2008); http://dx.doi.org/10.1063/1.2956507View Description Hide Description
Density fitting is an important method for speeding up quantum-chemical calculations. Linear-scaling developments in Hartree–Fock and density-functional theories have highlighted the need for linear-scaling density-fitting schemes. In this paper, we present a robust variational density-fitting scheme that allows for solving the fitting equations in local metrics instead of the traditional Coulomb metric, as required for linear scaling. Results of fitting four-center two-electron integrals in the overlap and the attenuated Gaussian damped Coulomb metric are presented, and we conclude that density fitting can be performed in local metrics at little loss of chemical accuracy. We further propose to use this theory in linear-scaling density-fitting developments.
129(2008); http://dx.doi.org/10.1063/1.2975336View Description Hide Description
This paper analyzes the different contributions to the magnetic coupling in systems with more than one unpaired electron per center. While in spin systems the Heisenberg Hamiltonian involving only bilinear exchange interactions is reliable for the description of the magnetic states, biquadratic exchange interactions must be sometimes introduced for (or higher) spin systems to account for isotropic deviations to Heisenberg behavior. The analysis establishes that the excited atomic states, the so-called non-Hund states, are responsible for the main contribution to the deviations. The kinetic exchange contribution and the spin, hole, and particle polarizations increase the magnetic coupling but essentially maintain the Heisenberg pattern. The importance of the different contributions has been studied for a series of compounds with a polarizable double azido bridge. The coupling between two ions in the molecular crystal , which is known experimentally to present large deviations to Heisenberg behavior, has also been investigated.
Benchmarks for electronically excited states: Time-dependent density functional theory and density functional theory based multireference configuration interaction129(2008); http://dx.doi.org/10.1063/1.2973541View Description Hide Description
Time-dependent density functional theory (TD-DFT) and DFT-based multireference configuration interaction (DFT/MRCI) calculations are reported for a recently proposed benchmark set of 28 medium-sized organic molecules. Vertical excitation energies,oscillator strengths, and excited-statedipole moments are computed using the same geometries (MP2/6-) and basis set (TZVP) as in our previous ab initio benchmark study on electronically excited states. The results from TD-DFT (with the functionals BP86, B3LYP, and BHLYP) and from DFT/MRCI are compared against the previous high-level ab initio results, and, in particular, against the proposed best estimates for 104 singlet and 63 triplet vertical excitation energies. The statistical evaluation for the latter reference data gives the lowest mean absolute deviations for DFT/MRCI (0.22 eV for singlets and 0.24 eV for triplets) followed by TD-DFT/B3LYP (0.27 and 0.44 eV, respectively), whereas TD-DFT/BP86 and TD-DFT/BHLYP are significantly less accurate. The energies of singlet states with double excitation character are generally overestimated by TD-DFT, whereas triplet state energies are systematically underestimated by the currently investigated DFT-based methods.
129(2008); http://dx.doi.org/10.1063/1.2970927View Description Hide Description
A good approximation to the one-electron self-energy operator in the calculation of quasiparticle energy spectra including the first ionization potential (IP) and electron affinity (EA) is to expand it as a simple product of a one-particle Green’s function and a dynamically screened Coulomb interaction , namely, approximation. We developed a spin-polarized version of the all-electron approach and applied it to the first-principles calculation of quasiparticle energy spectra of alkali-metal clusters ( and , ). Our all-electron mixed basis approach, in which wave functions are expressed as a linear combination of numerical atomic orbitals and plane waves, enables us to compare the absolute values of the singly (or highest) occupied molecular orbital and the lowest unoccupied molecular orbital levels with available experimental IPs and EAs. The agreements with the corresponding experimental values are fairly good. Comparing with the non-spin-polarized results of and , we discuss the effect of spin polarization as well as the cluster size dependence of IPs or EAs.
Application of magnetically perturbed time-dependent density functional theory to magnetic circular dichroism. III. Temperature-dependent magnetic circular dichroism induced by spin-orbit coupling129(2008); http://dx.doi.org/10.1063/1.2976568View Description Hide Description
A methodology for calculating the temperature-dependent magnetic circular dichroism(MCD) of open-shell molecules with time-dependent density functional theory (TDDFT) is described. The equations for the MCD of an open-shell molecule including spin-orbit coupling in the low- and high-temperature limits are reviewed. Two effects lead to the temperature-dependent MCD: the breaking of degeneracies and the perturbation of transition dipoles by spin-orbit coupling. The equations necessary to evaluate the required terms using TDDFT-derived quantities are presented. The performance of the formalism is demonstrated through application to the MCD of several molecules. The spectra of these molecules have differing properties with respect to bandwidth, temperature dependence of the MCD, and relative magnitude of the temperature-dependent and temperature-independent components of the MCD. The important features of the experimental spectra are reproduced by the calculations.
- Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry
Different equation-of-motion coupled cluster methods with different reference functions: The formyl radical129(2008); http://dx.doi.org/10.1063/1.2975205View Description Hide Description
The doublet and quartet excited states of the formyl radical have been studied by the equation-of-motion (EOM) coupled cluster (CC) method. The spin-conserving singles and doubles (EOM-EE-CCSD) and singles, doubles, and triples (EOM-EE-CCSDT) approaches, as well as the spin-flipped singles and doubles (EOM-SF-CCSD) method have been applied, subject to unrestricted Hartree–Fock (HF), restricted open-shell HF, and quasirestricted HF references. The structural parameters, vertical and adiabatic excitation energies, and harmonic vibrational frequencies have been calculated. The issue of the reference function choice for the spin-flipped (SF) method and its impact on the results has been discussed using the experimental data and theoretical results available. The results show that if the appropriate reference function is chosen so that target states differ from the reference by only single excitations, then EOM-EE-CCSD and EOM-SF-CCSD methods give a very good description of the excited states. For the states that have a non-negligible contribution of the doubly excited configurations one is able to use the SF method with such a reference function, that in most cases the performance of the EOM-SF-CCSD method is better than that of the EOM-EE-CCSD approach.
129(2008); http://dx.doi.org/10.1063/1.2973588View Description Hide Description
The ejection processes of hydrogen molecular ion from 12 kinds of hydrocarbon molecular species, methanol, ethanol, 1-propanol, 2-propanol, acetone, acetaldehyde, methane, ethane, ethylene, allene, 1,3-butadiene, and cyclohexane, induced by intense laser fields have been investigated by time-of-flight mass spectroscopy. The observation of the production with the kinetic energy range of from doubly ionized ethylene, allene, 1,3-butadiene, and cyclohexane, which have no methyl groups, showed the existence of the ultrafast hydrogen migration processes that enables three hydrogen atoms to come together to form within a hydrocarbon molecule.
An excited state ab initio and multidimensional Franck–Condon analysis of the band system of fluorobenzene129(2008); http://dx.doi.org/10.1063/1.2970092View Description Hide Description
This work combines high level ab initio calculations with multidimensional Franck–Condon calculations to refine and augment previous assignments of the lower wavenumber region of the band system of fluorobenzene. The strength of the assignment has been greatly assisted by the use of zero electron kinetic energy spectroscopy in a series of pump-probe experiments where the response of the molecule to selective excitation in specific modes prior to ionization has been studied. The net result of this analysis is the reassignment of 7 of the 12 previously assigned bands in the region below about using a strategy that aims to trace the origins of excited statenormal modes of fluorobenzene to the well-known Wilson modes of benzene by taking full account of the Duschinsky mixing that accompanies electronic excitation. Duschinsky normal modeanalyses of the ground and first excited states of fluorobenzene as well as the electronic ground state of fluorobenzene cation have shown that the common use of the benzene Wilson notation to describe normal modes of this prototypical benzene derivative is highly questionable, particularly following electronic excitation and ionization.
Effects of isotopic substitution on the rotational spectra and potential splitting in the complex: Improved measurements for and , new measurements for the mixed isotopic forms, and ab initio calculations of the energy separation129(2008); http://dx.doi.org/10.1063/1.2973638View Description Hide Description
Rotational spectra have been observed for , , , and with complete resolution of the nuclear magnetic hyperfine structure from the OH and water protons. Transition frequencies have been analyzed for each isotopic form using the model of Marshall and Lester [J. Chem. Phys.121, 3019 (2004)], which accounts for partial quenching of the OH orbital angular momentum and the decoupling of the electronic spin from the OH molecular axis. The analysis accounts for both the ground and first electronically excited states of the system, which correspond roughly to occupancy by the odd electron in the and orbitals, respectively (where is in the mirror plane of the complex and is perpendicular to and the OH bond axis). The spectroscopic measurements yield a parameter, , which is equal to the vibrationally averaged energy separation that would be obtained if spin-orbit coupling and rotation were absent. For the parent species, . substitution on the water increases by , while substitution on the OH decreases by . In the complex, the observed value of implies an energy spacing between the rotationless levels of the and states of . Ab initio calculations have been performed with quadratic configuration interaction with single and double excitations (QCISD), as well as multireference configuration interaction (MRCI), both with and without the inclusion of spin-orbit coupling. The MRCI calculations with spin-orbit coupling perform the best, giving a value of for the energy spacing at the equilibrium geometry. Calculations along the large-amplitude bending coordinates of the OH and moieties within the complex are presented and are shown to be consistent with a vibrational averaging effect as the main cause of the observed isotopic sensitivity of .
129(2008); http://dx.doi.org/10.1063/1.2970088View Description Hide Description
The ultrafast charge migration following outer-valence ionization in three different but related molecules, namely, 2-phenylethyl--dimethylamine (PENNA), and its butadiene (MePeNNA) and ethylene (BUNNA) derivates, is studied in detail. The molecules have different chromophore-donor sites, but nearly identical amine-acceptor sites. The results show that the charge migration process depends strongly on the particular donor site, varying from ultrafast migration of the charge from the donor to the acceptor site ( for MePeNNA) to no migration at all (for BUNNA). The influence of the geometrical structure of the molecule on the charge migration is also investigated. It is shown that energetically closely lying conformers may exhibit dramatically different charge migration behaviors. The basic mechanism of the charge migration process in the studied molecules is analyzed in detail and is demonstrated to be due to electron correlation and relaxation effects.
129(2008); http://dx.doi.org/10.1063/1.2976789View Description Hide Description
Vertical ionizationenergies of and fullerenes are calculated with semidirect implementations of electron propagator methods and a triple- plus polarization basis set. These predictions are in close agreement with photoelectron spectra for final states in which the Koopmans description is qualitatively valid. Many correlation states, where the latter description fails, are predicted by methods with nondiagonal self-energies.
129(2008); http://dx.doi.org/10.1063/1.2976761View Description Hide Description
The rotational barriers of (where , OH, , , and H) were investigated with respect to the hyperconjugation and steric effects at the levels of RHF, MP2, and B3LYP using a basis set of . At all levels of theory, the dihedral angle of the minimum energy conformation was found to increase with decreasing electronegativity of the atom bonded to boron. The substituents that possess no lone pairs have greater steric exchange energy, destabilizing the planar conformation relative to the perpendicular. However, the planar conformation of compounds with substituents having lone pairs on the heavy atom is counterstabilized by conjugative delocalization into the “empty” -orbitals associated with boron. For , neither factor dominates and the optimal geometry is skewed at a dihedral angle of 37.62° (MP2).
129(2008); http://dx.doi.org/10.1063/1.2975194View Description Hide Description
The first quantum mechanical investigation of the rotational deactivation of HF induced by collisions with ortho- and para- molecules is reported. Ab initio potential energy calculations are carried out at the coupled cluster level with single and double excitations, using a quadruple-zeta basis set. The global rigid rotor four-dimensional potential energy surface is obtained by fitting ab initio points with a least squares procedure for the angular terms and interpolating the radial coefficients with cubic splines. It is shown that the equilibrium structure of the complex is T-shaped and the well depth is found to be . Close coupling scattering calculations are performed at collision energy ranging from . A comparison of the rotational quenching of HF with para- and is used to validate our potential energy surface. The rotational quenching cross sections of HF by ortho- and para- are also compared and found to be very different. An explanation of these differences based on a resonance mechanism is proposed.
High resolution study of spin-orbit mixing and the singlet-triplet gap in chlorocarbene: Stimulated emission pumping spectroscopy of and129(2008); http://dx.doi.org/10.1063/1.2977686View Description Hide Description
We report on high resolution studies of spin-orbit mixing and the singlet-triplet gap in a prototypical halocarbene, CHCl, using stimulated emission pumping (SEP) spectroscopy from the state. Results are reported for two isotopomers, and . We have obtained rotationally resolved spectra for the majority of levels lying between 0 and above the zero-point level that were previously observed under low resolution in single vibronic level emission studies and several new levels that were previously unobserved or unresolved. In addition, SEP spectra were obtained for six levels in and three levels in . The derived term energies and rovibrational parameters of the and states are in good agreement with theory. The triplet spin-spin parameter is vibrational state dependent, and dominated by a second-order contribution from spin-orbit coupling with nearby levels; it therefore provides a sensitive probe of spin-orbit mixing in this system. An analysis of three pairs of interactions between specific and levels in affords a pure electronic spin-orbit coupling element of , in good agreement with theoretical expectations. The derived singlet-triplet gaps, which are the most precise determined to date for any carbene, are compared with the predictions of high level ab initio theory.
129(2008); http://dx.doi.org/10.1063/1.2976768View Description Hide Description
Making use of the molecular closed-orbit theory and a new model potential for the Rydberg molecule, we calculated the recurrence spectra of molecule ion in a magnetic field for different quantum defects. The Fourier transformed spectra of molecule ion have allowed direct comparison between peaks in the spectra and the scaled action values of closed orbits of the excited electron in the external fields. We find that the spectral modulations can be analyzed in terms of the scattering of the excited electron on the molecular core. Unlike the case of the Rydberg atom where the elasticscattering is predominant, modulations produced by inelastic scattering are also vital to the photoabsorptionspectrum of Rydberg molecule. Our results are in good agreement with the quantum results, which suggest that our method is correct.
129(2008); http://dx.doi.org/10.1063/1.2970936View Description Hide Description
The electronic spectra of 7-azaindole-clusters were measured by mass-selected two-color resonance-enhanced multiphoton ionization spectroscopy. The laser-induced fluorescence spectrum obtained by monitoring the UV fluorescence shows well-structured vibrational bands for the monomer and 7-azaindole-clusters, while no signals appear for the 7-azaindole-cluster. The action spectrum obtained by monitoring visible emission shows no signal for all species, which suggests little reactivity for excited-state proton/hydrogen transfer. From the observed and calculated IR spectra, the geometry of 7-azaindole- was concluded to be a hydrogen-bonded bridge form, which is similar to the photochemically reactive 7-hydroxyquinoline-cluster. The difference in the photochemical reactivity is discussed on the basis of excited-state quantum chemical calculations.
- Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation
Structural and dynamical aspects of the phase transition in the new thiourea thiazolium bromide inclusion compound129(2008); http://dx.doi.org/10.1063/1.2972141View Description Hide Description
A new thiourea thiazolium bromide inclusion compound is presented here. Detailed investigations of its phase transition were performed by differential scanning calorimetry, x-ray diffraction, and dielectric and nuclear magnetic resonance spectroscopy methods, completed by calculation of the steric hindrances for molecular reorientations and simulations of the second moment of the nuclear magnetic resonance line by the Monte Carlo method. A second order ferrielectric structural phase transition has been detected at as thiazolium cations collectively reorient inside channels. The dynamics is discussed in terms of inequivalent energy barriers associated with cation rotation as the symmetry breaking occurs. Oscillations of thiourea molecules and groups have been also observed.
Direct spectral evidence of single-axis rotation and ortho-hydrogen-assisted nuclear spin conversion of in solid para-hydrogen129(2008); http://dx.doi.org/10.1063/1.2975340View Description Hide Description
Observation of two weak absorption lines from the level and one intense feature from for degenerate modes and of provides direct spectral evidence that isolated in rotates about only its symmetry axis, and not about the other two axes. An interaction between and vibrational levels caused by the partially hindered spinning rotation is proposed. Conversion of nuclear spin between and components of is rapid when contains some , but becomes slow when the proportion of is much decreased.
129(2008); http://dx.doi.org/10.1063/1.2970084View Description Hide Description
First principles molecular dynamics simulations are used to characterize dynamic properties of supercooled liquid silicon across the liquid-liquid phase transition. Our results evidence the presence of a boson peak in the terahertz frequency range for the low-density liquid and support the scenario of a fragile-to-strong transition. The analysis of the collective excitations shows that its origin is due to a coupling of the longitudinal and transverse acoustic modes localized on the nanometer scale and can be attributed to collective vibrations of connected tetrahedra.
Calibration of the isomer shift for the 77.34 keV transition in using the full-potential linearized augmented plane-wave method129(2008); http://dx.doi.org/10.1063/1.2973558View Description Hide Description
The isomer shift calibration constant has been calculated for the 77.34 keV Mössbauer transition connecting the ground state of the nucleus with the first excited state of this nucleus. The full-potential linearized augmented plane-wave method was used in the fully relativistic approach, albeit without taking into account the spin-orbit coupling. The final assignment of the calibration constant was based on calculations performed for AuCN, , , , , and metallic gold. It is found that the calibration constant takes on the following value . The error quoted is due to the linear regression fit, and the real error might be as large as 10%. The spectroscopicelectric quadrupole moment for the ground state of the nucleus was calculated as the by-product. It was found that this moment equals in fair agreement with the accepted value based on the muonic hyperfine spectroscopy results. The error quoted is again due to the linear regression fit and the real error might be as large as 10%. The final assignment of the value for the quadrupole moment is based on the calculations for the following compounds: AuCl, AuBr, AuI, AuCN, and . Results for the magnetically ordered were applied to determine the sign of the quadrupole moment.