Volume 136, Issue 8, 28 February 2012

Orbitalfree density functional theory (OFDFT), with its attractive linearly scaling computation cost and low prefactor, is one of the most powerful first principles methods for simulating large systems (∼10^{4}–10^{6} atoms). However, approximating the electron kinetic energy with density functionals limits the accuracy and generality of OFDFT compared to KohnSham density functional theory (KSDFT). In this work, we test whether the HuangCarter (HC) kinetic energydensity functional (KEDF), which contains the physics to properly describe covalently bonded semiconductor materials, can also be used to describe covalent bonds in molecules. In particular, we calculate a variety of homonuclear diatomic molecules with the HC functional within OFDFT. The OFDFT bonddissociation energy, equilibrium bond length, and vibrational frequency of these dimers are in remarkably good agreement with benchmark KSDFT results, given the lack of orbitals in the calculation. We vary the two parameters λ (controlling the reduced density gradient contribution to the nonlocal kernel) and β (the exponent of the density in the nonlocal term) present in the HC KEDF and find that the optimal λ correlates with the magnitude of the highest occupied molecular orbital  lowest unoccupied molecular orbital energy gap. Although the HC KEDF represents a significant improvement over previous KEDFs in describing covalent systems, deficiencies still exist. Despite the similar overall shape of the KSDFT and OFDFT ground state electron densities, the electron density within the bonding region is still quite different. Furthermore, OFDFT is not yet able to give reasonable description of magnetic states. The energy orderings of the triplet and singlet states of Si_{2} and Al family dimers are not consistent with KSDFT or experimental results and the spin polarization distributions also differ widely between the two theories.
 COMMUNICATIONS


Communication: Fundamental measure theory for hard disks: Fluid and solid
View Description Hide DescriptionTwodimensional hardparticle systems are rather easy to simulate but surprisingly difficult to treat by theory. Despite their importance from both theoretical and experimental points of view, theoretical approaches are usually qualitative or at best semiquantitative. Here, we present a density functional theory based on the ideas of fundamental measure theory for twodimensional harddisk mixtures, which allows for the first time an accurate description of the structure of the dense fluid and the equation of state for the solid phase within the framework of density functional theory. The properties of the solid phase are obtained by freely minimizing the functional.

Communication: Identical temperature dependence of the time scales of several linearresponse functions of two glassforming liquids
View Description Hide DescriptionThe frequencydependent dielectric constant, shear and adiabatic bulk moduli, longitudinal thermal expansion coefficient, and longitudinal specific heat have been measured for two van der Waals glassforming liquids, tetramethyltetraphenyltrisiloxane (DC704) and 5polyphenyl4ether. Within the experimental uncertainties the losspeak frequencies of the measured response functions have identical temperature dependence over a range of temperatures, for which the Maxwell relaxation time varies more than nine orders of magnitude. The time scales are ordered from fastest to slowest as follows: Shear modulus, adiabatic bulk modulus,dielectric constant, longitudinal thermal expansion coefficient, and longitudinal specific heat. The ordering is discussed in light of the recent conjecture that van der Waals liquids are strongly correlating, i.e., approximate singleparameter liquids.
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 ARTICLES

 Theoretical Methods and Algorithms

Mapping quantumclassical Liouville equation: Projectors and trajectories
View Description Hide DescriptionThe evolution of a mixed quantumclassical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining projection operators onto the mapping states corresponding to the physical quantum states, it is shown that the mapping quantumclassical Liouville operator commutes with the projection operator so that the dynamics is confined to the physical space. It is also shown that a trajectorybased solution of this equation can be constructed that requires the simulation of an ensemble of entangled trajectories. An approximation to this evolution equation which retains only the Poisson bracket contribution to the evolution operator does admit a solution in an ensemble of independent trajectories but it is shown that this operator does not commute with the projection operators and the dynamics may take the system outside the physical space. The dynamical instabilities, utility, and domain of validity of this approximate dynamics are discussed. The effects are illustrated by simulations on several quantum systems.

Can orbitalfree density functional theory simulate molecules?
View Description Hide DescriptionOrbitalfree density functional theory (OFDFT), with its attractive linearly scaling computation cost and low prefactor, is one of the most powerful first principles methods for simulating large systems (∼10^{4}–10^{6} atoms). However, approximating the electron kinetic energy with density functionals limits the accuracy and generality of OFDFT compared to KohnSham density functional theory (KSDFT). In this work, we test whether the HuangCarter (HC) kinetic energydensity functional (KEDF), which contains the physics to properly describe covalently bonded semiconductor materials, can also be used to describe covalent bonds in molecules. In particular, we calculate a variety of homonuclear diatomic molecules with the HC functional within OFDFT. The OFDFT bonddissociation energy, equilibrium bond length, and vibrational frequency of these dimers are in remarkably good agreement with benchmark KSDFT results, given the lack of orbitals in the calculation. We vary the two parameters λ (controlling the reduced density gradient contribution to the nonlocal kernel) and β (the exponent of the density in the nonlocal term) present in the HC KEDF and find that the optimal λ correlates with the magnitude of the highest occupied molecular orbital  lowest unoccupied molecular orbital energy gap. Although the HC KEDF represents a significant improvement over previous KEDFs in describing covalent systems, deficiencies still exist. Despite the similar overall shape of the KSDFT and OFDFT ground state electron densities, the electron density within the bonding region is still quite different. Furthermore, OFDFT is not yet able to give reasonable description of magnetic states. The energy orderings of the triplet and singlet states of Si_{2} and Al family dimers are not consistent with KSDFT or experimental results and the spin polarization distributions also differ widely between the two theories.

NonBornOppenheimer electronic and nuclear densities for a HookeCalogero threeparticle model: Nonuniqueness of densityderived molecular structure
View Description Hide DescriptionWe consider the calculation of nonBornOppenheimer, nBO, oneparticle densities for both electrons and nuclei. We show that the nBO oneparticle densities evaluated in terms of translationally invariant coordinates are independent of the wavefunction describing the motion of center of mass of the whole system. We show that they depend, however, on an arbitrary reference point from which the positions of the vectors labeling the particles are determined. We examine the effect that this arbitrary choice has on the topology of the oneparticle density by selecting the HookeCalogero model of a threebody system for which expressions for the oneparticle densities can be readily obtained in analytic form. We extend this analysis to the oneparticle densities obtained from full Coulomb interaction wavefunctions for threebody systems. We conclude, in view of the fact that there is a close link between the choice of the reference point and the topology of oneparticle densities that the molecular structure inferred from the topology of these densities is not unique. We analyze the behavior of oneparticle densities for the HookeCalogero BornOppenheimer, BO, wavefunction and show that topological transitions are also present in this case for a particular mass value of the light particles even though in the BO regime the nuclear masses are infinite. In this vein, we argue that the change in topology caused by variation of the mass ratio between light and heavy particles does not constitute a true indication in the nBO regime of the emergence of molecular structure.

Reduced density matrix hybrid approach: Application to electronic energy transfer
View Description Hide DescriptionElectronic energy transfer in the condensed phase, such as that occurring in photosynthetic complexes, frequently occurs in regimes where the energy scales of the system and environment are similar. This situation provides a challenge to theoretical investigation since most approaches are accurate only when a certain energetic parameter is small compared to others in the problem. Here we show that in these difficult regimes, the Ehrenfest approach provides a good starting point for a dynamical description of the energy transfer process due to its ability to accurately treat coupling to slow environmental modes. To further improve on the accuracy of the Ehrenfest approach, we use our reduced density matrix hybrid framework to treat the faster environmental modes quantum mechanically, at the level of a perturbative master equation. This combined approach is shown to provide an efficient and quantitative description of electronic energy transfer in a model dimer and the FennaMatthewsOlson complex and is used to investigate the effect of environmental preparation on the resulting dynamics.

Basis set convergence of molecular correlation energy differences within the random phase approximation
View Description Hide DescriptionThe basis set convergence of energy differences obtained from the random phase approximation (RPA) to the correlation energy is investigated for a wide range of molecular interactions. For dispersion bound systems the basis set incompleteness error is most pronounced, as shown for the S22 benchmark [P. Jurecka et al., Phys. Chem. Chem. Phys.8, 1985 (2006)10.1039/b600027d]. The use of very large basis sets (> quintuplezeta) or extrapolation to the complete basis set (CBS) limit is necessary to obtain a reliable estimate of the binding energy for these systems. Counterpoise corrected results converge to the same CBS limit, but counterpoise correction without extrapolation is insufficient. Corevalence correlations do not play a significant role. For medium and shortrange correlation, quadruplezeta results are essentially converged, as demonstrated for relative alkane conformer energies, reaction energies dominated by intramolecular dispersion, isomerization energies, and reaction energies of small organic molecules. Except for weakly bound systems, diffuse augmentation almost universally slows down basis set convergence. For most RPA applications, quadruplezeta valence basis sets offer a good balance between accuracy and efficiency.

Temperature inhomogeneities simulated with multiparticlecollision dynamics
View Description Hide DescriptionThe mesoscopic simulation technique known as multiparticle collision dynamics is presented as a very appropriate method to simulate complex systems in the presence of temperature inhomogeneities. Three different methods to impose the temperature gradient are compared and characterized in the parameter landscape. Two methods include the interaction of the system with confining walls. The third method considers open boundary conditions by imposing energy fluxes. The transport of energy characterizing the thermal diffusivity is also investigated. The dependence of this transport coefficient on the method parameters and the accuracy of existing analytical theories is discussed.

Canonical transcorrelated theory with projected Slatertype geminals
View Description Hide DescriptionAn effective Hamiltonian perturbed with explicit interelectronic correlation is derived from similarity transformation of Hamiltonian using a unitary operator with Slatertype geminals. The Slatertype geminal is projected onto the excitation (and deexcitation) component as in the F12 theory. Simplification is made by truncating higherbody operators, resulting in a correlated Hamiltonian which is Hermitian and has exactly the same complexity as the original Hamiltonian in the second quantized form. It can thus be easily combined with arbitrary correlation models proposed to date. The present approach constructs a singularityfree Hamiltonian a priori, similarly to the socalled transcorrelated theory, while the use of the canonical transformation assures that the effective Hamiltonian is twobody and Hermite. Our theory is naturally extensible to multireference calculations on the basis of the generalized normal ordering. The construction of the effective Hamiltonian is noniterative. The numerical assessments demonstrate that the present scheme improves the basis set convergence of the postmeanfield calculations at a similar rate to the explicitly correlated methods proposed by others that couple geminals and conventional excitations.

Dynamic hyperpolarizability calculations of large systems: The linearscaling divideandconquer approach
View Description Hide DescriptionWe report a linearscaling computation method for evaluating the dynamic first hyperpolarizability β based on the divideandconquer (DC) method. In the present scheme, we utilized the quasidensitymatrix expression derived from Wigner's (2n + 1) rule for β, where the quasidensity matrices are constructed from the solution obtained via the DC timedependent selfconsistent field (TDSCF) method [T. Touma, M. Kobayashi, and H. Nakai, Chem. Phys. Lett.485, 247 (2010)10.1016/j.cplett.2009.12.043]. Numerical evaluation of πconjugated and saturated organic chain systems verified that the present scheme considerably reduces the computational time for the β evaluation with a slight loss of accuracy, even around the singular frequency appearing at the electronic excitation energy. This evaluation indicates that the present linearscaling TDSCF scheme can also be used to estimate the molecular excitation energy. Furthermore, we succeeded in accurately evaluating the macroscopic secondharmonic generation coefficient of the polyvinylidene fluoride from the molecular (hyper)polarizabilities.

Natural polarizability and flexibility via explicit valency: The case of water
View Description Hide DescriptionAs the dominant physiological solvent, water drives the folding of biological macromolecules, influences conformational changes, determines the ionization states of surface groups, actively participates in catalytic events, and provides “wires” for longrange proton transfer. Elucidation of all these roles calls for atomistic simulations. However, currently available methods do not lend themselves to efficient simulation of proton transfer events, or even polarizability and flexibility. Here, we report that an explicit account of valency can provide a unified description for the polarizability, flexibility, and dissociability of water in one intuitive and efficient setting. We call this approach LEWIS, after the chemical theory that inspires the use of valence electron pairs. In this paper, we provide details of the method, the choice of the training set, and predictions for the neat ambient liquid, with emphasis on structure, dynamics, and polarization. LEWIS water provides a good description of bulk properties, and dipolar and quadrupolar responses.

Stochastic selfassembly of incommensurate clusters
View Description Hide DescriptionNucleation and molecular aggregation are important processes in numerous physical and biological systems. In many applications, these processes often take place in confined spaces, involving a finite number of particles. Analogous to treatments of stochastic chemical reactions, we examine the classic problem of homogeneous nucleation and selfassembly by deriving and analyzing a fully discrete stochastic master equation. We enumerate the highest probability steady states, and derive exact analytical formulae for quenched and equilibrium mean cluster size distributions. Upon comparison with results obtained from the associated massaction BeckerDöring equations, we find striking differences between the two corresponding equilibrium mean cluster concentrations. These differences depend primarily on the divisibility of the total available mass by the maximum allowed cluster size, and the remainder. When such mass “incommensurability” arises, a single remainder particle can “emulsify” the system by significantly broadening the equilibrium mean cluster size distribution. This discretenessinduced broadening effect is periodic in the total mass of the system but arises even when the system size is asymptotically large, provided the ratio of the total mass to the maximum cluster size is finite. Ironically, classic massaction equations are fairly accurate in the coarsening regime, before equilibrium is reached, despite the presence of large stochastic fluctuations found via kinetic MonteCarlo simulations. Our findings define a new scaling regime in which results from classic massaction theories are qualitatively inaccurate, even in the limit of large total system size.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Electromagnetically induced transparency with quantum interferometry
View Description Hide DescriptionWe have shown that electromagnetically induced transparency can be achieved by controlprobe interferometry using two delayed phaselocked ultrashort pulses. Two vibrational wavepackets on the excited state, excited by two delayed phaselocked ultrashort pulses, interfere constructively or destructively leading to enhancement or suppression of absorption to a selective set of vibrational levels. Depending on the phase difference and the delay between the pulses with same carrier frequency, one can design different transparency windows between absorption peaks at consecutive even(odd) vibrational levels by eliminating absorption at odd(even) vibrational levels. We have shown that by switching the phase difference of two delayed femtosecond pulses, one can switch to complete elimination of absorption from enhanced absorption to a particular set of vibrational levels in the excited state. Thus, switching of transparency through window between odd vibrational levels to that between even vibrational levels is possible. By properly choosing the temporal width and the carrier frequency of the pulses, lossless transmission of complete or bands of frequencies of the pulses can be achieved through these transparency windows. Hence, designing of single or multimode transparency windows in NaH molecule is feasible by controlprobe quantum interferometry.

In search of the next Holy Grail of polyoxide chemistry: Explicitly correlated ab initio full quartic force fields for HOOH, HOOOH, HOOOOH, and their isotopologues
View Description Hide DescriptionExplicitly correlated ab initio methods have been used to compute full quartic force fields for the three chain minima for HOOOOH, which are found to lie within 1 kcal mol^{−1}. The CCSD(T)F12 method with the ccpVTZF12 basis set was used to compute equilibrium structures, anharmonic vibrational frequencies, and rotational constants for HOOH, HOOOH, and three chain isomers of HOOOOH, with the two former force fields being used as benchmarks for the latter three. The full quartic force fields were computed in such a way as to yield fundamental frequencies for all isotopologues at once. The present research confirms the recent experimental identification of HOOOH and provides reliable force fields in support of future experimental work on the enigmatic bonding paradigms involved in the HOOOOH chain.

Collisional electron transfer to photoexcited acceptor radical anions
View Description Hide DescriptionIn this article, we show that photoexcitation of radical anions facilitates electron transfer from sodium atoms in femtosecond encounters. Thus, excitation of 7,7,8,8tetracyanopquinodimethane (TCNQ) and fluorinated TCNQ (TCNQF_{4}) anions to the second optically active state at 478 nm led to increases in the yields of dianions of about 20% and 10%, respectively. Photoexcitation with a nanosecondlong laser pulse was done a few microseconds before the ions entered the sodium collision cell so that none of the ions would be in any of the initially reached doubletexcited states. We suggest an explanation for the higher electron capture cross section based on the formation of longlived quartet state anions. Excitation of TCNQ anions within the lowestenergy absorption band, where there are no accessible quartet states, led instead to a lower yield of dianions. There are at least three explanations for the lower dianion yields: (1) Depletion of the monoanion beam due to photodetachment after the absorption of minimum two photons; (2) Formation of shortlived vibrationally excited dianions that decay by electron autodetachment prior to identification; and (3) Lower electron capture cross sections of vibrationally excited monoanions. Similar losses in dianion signal can occur at 478 nm so the actual yield of dianions at this wavelength due to the population of quartet states is therefore greater than that observed. Our methodology devises a more efficient route for the production of molecular dianions, and at the same time it may provide information on longlived electronic states.

Overtoneinduced dissociation and isomerization dynamics of the hydroxymethyl radical (CH_{2}OH and CD_{2}OH). I. A theoretical study
View Description Hide DescriptionThe dissociation of the hydroxymethyl radical, CH_{2}OH, and its isotopolog, CD_{2}OH, following the excitation of high OH stretch overtones is studied by quasiclassical molecular dynamics calculations using a global potential energy surface (PES) fitted to ab initio calculations. The PES includes CH_{2}OH and CH_{3}O minima, dissociation products, and all relevant barriers. Its analysis shows that the transition states for OH bond fission and isomerization are both very close in energy to the excited vibrational levels reached in recent experiments and involve significant geometry changes relative to the CH_{2}OH equilibrium structure. The energies of key stationary points are refined using highlevel electronic structure calculations. Vibrational energies and wavefunctions are computed by coupled anharmonic vibrational calculations. They show that high OHstretch overtones are mixed with other modes. Consequently, trajectory calculations carried out at energies about ∼3000 cm^{−1} above the barriers reveal that despite initial excitation of the OH stretch, the direct OH bond fission is relatively slow (10 ps) and a considerable fraction of the radicals undergoes isomerization to the methoxy radical. The computed dissociation energies are: D _{0}(CH_{2}OH → CH_{2}O + H) = 10 188 cm^{−1}, D _{0}(CD_{2}OH → CD_{2}O + H) = 10 167 cm^{−1}, D _{0}(CD_{2}OH → CHDO + D) = 10 787 cm^{−1}. All are in excellent agreement with the experimental results. For CH_{2}OH, the barriers for the direct OH bond fission and isomerization are: 14 205 and 13 839 cm^{−1}, respectively.

Overtoneinduced dissociation and isomerization dynamics of the hydroxymethyl radical (CH_{2}OH and CD_{2}OH). II. Velocity map imaging studies
View Description Hide DescriptionThe dissociation of the hydroxymethyl radical, CH_{2}OH, and its isotopolog, CD_{2}OH, following excitation in the 4ν_{1} region (OH stretch overtone, near 13 600 cm^{−1}) was studied using sliced velocity map imaging. A new vibrational band near 13 660 cm^{−1} arising from interaction with the antisymmetric CH stretch was discovered for CH_{2}OH. In CD_{2}OH dissociation, D atom products (correlated with CHDO) were detected, providing the first experimental evidence of isomerization in the CH_{2}OH ↔ CH_{3}O (CD_{2}OH ↔ CHD_{2}O) system. Analysis of the H (D) fragment kinetic energy distributions shows that the rovibrational state distributions in the formaldehyde cofragments are different for the OH bond fission and isomerization pathways. Isomerization is responsible for 10%–30% of dissociation events in all studied cases, and its contribution depends on the excited vibrational level of the radical. Accurate dissociation energies were determined: D _{0}(CH_{2}OH → CH_{2}O + H) = 10 160 ± 70 cm^{−1}, D _{0}(CD_{2}OH → CD_{2}O + H) = 10 135 ± 70 cm^{−1}, D _{0}(CD_{2}OH → CHDO + D) = 10 760 ± 60 cm^{−1}.

Surface temperature effect on the scattering of D_{2}(v = 0, j = 0)Cu(111) system
View Description Hide DescriptionWe perform fourdimensional (4D⊗2D) as well as sixdimensional (6D) quantum dynamics on a parametrically time and temperaturedependent effective Hamiltonian for D_{2}(v, j)Cu(111) system, where such effective potential has been derived through a meanfield approach between molecular degrees of freedom and surface modes with BoseEinstein probability factor for their initial state distribution. We present the convergence of the theoretically calculated sticking probabilities employing 4D⊗2D quantum dynamics with increasing number of surface atoms as well as layers for rigid surface and the surface at a particular temperature, where the temperaturedependent sticking probabilities appear exclusively dictated by those surface modes directed along the Zaxis. The sticking and statetostate transition probabilities obtained from 6D quantum dynamics are shown as a function of initial kinetic energy of the diatom at different surface temperature. Theoretically calculated sticking probabilities display the similar trend with the experimentally measured one.

Lowenergy electron collisions with glycine
View Description Hide DescriptionWe report cross sections for elastic electron scattering by gas phase glycine (neutral form), obtained with the Schwinger multichannel method. The present results are the first obtained with a new implementation that combines parallelization with OpenMP directives and pseudopotentials. The position of the well known π* shape resonance ranged from 2.3 eV to 2.8 eV depending on the polarizationmodel and conformer. For the most stable isomer, the present result (2.4 eV) is in fair agreement with electron transmission spectroscopy assignments (1.93 ± 0.05 eV) and available calculations. Our results also point out a shape resonance around 9.5 eV in the A ^{′} symmetry that would be weakly coupled to vibrations of the hydroxyl group. Since electron attachment to a broad and lower lying σ* orbital located on the OH bond has been suggested the underlying mechanism leading to dissociative electron attachment at low energies, we sought for a shape resonance around ∼4 eV. Though we obtained cross sections with the target molecule at the equilibrium geometry and with stretched OH bond lengths, leastsquares fits to the calculated eigenphase sums did not point out signatures of this anion state (though, in principle, it could be hidden in the large background). The low energy (∼1 eV) integral cross section strongly scales as the bond length is stretched, and this could indicate a virtual state pole, since dipole supported bound states are not expected at the geometries addressed here.

Ab initio study of dynamical E × e JahnTeller and spinorbit coupling effects in the transitionmetal trifluorides TiF_{3}, CrF_{3}, and NiF_{3}
View Description Hide DescriptionMulticonfiguration ab initio methods have been employed to study the effects of JahnTeller(JT) and spinorbit (SO) coupling in the transitionmetal trifluorides TiF_{3}, CrF_{3}, and NiF_{3}, which possess spatially doubly degenerate excited states (^{ M } E) of even spin multiplicities (M = 2 or 4). The ground states of TiF_{3}, CrF_{3}, and NiF_{3} are nondegenerate and exhibit minima of D _{3h } symmetry. Potentialenergysurfaces of spatially degenerate excited states have been calculated using the stateaveraged completeactivespace selfconsistentfield method. SO coupling is described by the matrix elements of the BreitPauli operator. Linear and higher order JT coupling constants for the JTactive bending and stretching modes as well as SOcoupling constants have been determined. Vibronic spectra of JTactive excited electronic states have been calculated, using JT Hamiltonians for trigonal systems with inclusion of SO coupling. The effect of higher order (up to sixth order) JT couplings on the vibronic spectra has been investigated for selected electronic states and vibrational modes with particularly strong JT couplings. While the weak SO couplings in TiF_{3} and CrF_{3} are almost completely quenched by the strong JT couplings, the stronger SO coupling in NiF_{3} is only partially quenched by JT coupling.