Volume 140, Issue 20, 28 May 2014

The explicit polarization (XPol) theory is a fragmentbased quantum chemical method that explicitly models the internal electronic polarization and intermolecular interactions of a chemical system. XPol theory provides a framework to construct a quantum mechanical force field, which we have extended to liquid hydrogen fluoride (HF) in this work. The parameterization, called XPHF, is built upon the same formalism introduced for the XP3P model of liquid water, which is based on the polarized molecular orbital (PMO) semiempirical quantum chemistry method and the dipolepreserving polarization consistent point charge model. We introduce a fluorine parameter set for PMO, and find good agreement for various gasphase results of small HF clusters compared to experiments and ab initio calculations at the M062X/MG3S level of theory. In addition, the XPHF model shows reasonable agreement with experiments for a variety of structural and thermodynamic properties in the liquid state, including radial distribution functions, interaction energies, diffusion coefficients, and densities at various state points.
 COMMUNICATIONS


Communication: Systemsize scaling of Boltzmann and alternate Gibbs entropies
View Description Hide DescriptionIt has recurrently been proposed that the Boltzmann textbook definition of entropy S(E) = k ln Ω(E) in terms of the number of microstates Ω(E) with energy E should be replaced by the expression examined by Gibbs. Here, we show that S G either is equivalent to S in the macroscopic limit or becomes independent of the energy exponentially fast as the system size increases. The resulting exponential scaling makes the realistic use of S G unfeasible and leads in general to temperatures that are inconsistent with the notions of hot and cold.

Communication: Oscillating charge migration between lone pairs persists without significant interaction with nuclear motion in the glycine and GlyGlyNHCH_{3} radical cations
View Description Hide DescriptionCoupled electronnuclear dynamics has been studied, using the Ehrenfest method, for four conformations of the glycine molecule and a single conformation of GlyGlyNHCH3. The initial electronic wavepacket was a superposition of eigenstates corresponding to ionization from the σ lone pairs associated with the carbonyl oxygens and the amine nitrogen. For glycine, oscillating charge migration (when the nuclei were frozen) was observed for the 4 conformers studied with periods ranging from 2 to 5 fs, depending on the energy gap between the lone pair cationic states. When coupled nuclear motion was allowed (which was mainly NH2 partial inversion), the oscillations hardly changed. For GlyGlyNHCH3, charge migration between the carbonyl oxygens and the NH2 lone pair can be observed with a period similar to glycine itself, also without interaction with nuclear motion. These simulations suggest that charge migration between lone pairs can occur independently of the nuclear motion.
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 ARTICLES

 Theoretical Methods and Algorithms

Analytic energy gradient for the projected Hartree–Fock method
View Description Hide DescriptionWe derive and implement the analytic energy gradient for the symmetry Projected Hartree–Fock (PHF) method avoiding the solution of coupledperturbed HFlike equations, as in the regular unprojected method. Our formalism therefore has meanfield computational scaling and cost, despite the elaborate multireference character of the PHF wave function. As benchmark examples, we here apply our gradient implementation to the ortho, meta, and parabenzyne biradicals, and discuss their equilibrium geometries and vibrational frequencies.

Estimating the entropy and quantifying the impurity of a swarm of surfacehopping trajectories: A new perspective on decoherence
View Description Hide DescriptionIn this article, we consider the intrinsic entropy of Tully's fewest switches surface hopping (FSSH) algorithm (as estimated by the impurity of the density matrix) [J. Chem. Phys.93, 1061 (1990)]. We show that, even for a closed system, the total impurity of a FSSH calculation increases in time (rather than stays constant). This apparent failure of the FSSH algorithm can be traced back to an incorrect, approximate treatment of the electronic coherence between wavepackets moving along different potential energy surfaces. This incorrect treatment of electronic coherence also prevents the FSSH algorithm from correctly describing wavepacket recoherences (which is a well established limitation of the FSSH method). Nevertheless, despite these limitations, the FSSH algorithm often predicts accurate observables because the electronic coherence density is modulated by a phase factor which varies rapidly in phase space and which often integrates to almost zero. Adding “decoherence” events on top of a FSSH calculation completely destroys the incorrect FSSH electronic coherence and effectively sets the Poincaré recurrence time for wavepacket recoherence to infinity; this modification usually increases FSSH accuracy (assuming there are no recoherences) while also offering longtime stability for trajectories. In practice, we show that introducing “decoherence” events does not change the total FSSH impurity significantly, but does lead to more accurate evaluations of the impurity of the electronic subsystem.

Distinguishability and chiral stability in solution: Effects of decoherence and intermolecular interactions
View Description Hide DescriptionWe examine the effect of decoherence and intermolecular interactions (chiral discrimination energies) on the chiral stability and the distinguishability of initially pure versus mixed states in an open chiral system. Under a twolevel approximation for a system, intermolecular interactions are introduced by a meanfield theory, and interaction between a system and an environment is modeled by a continuous measurement of a population difference between the two chiral states. The resultant equations are explored for various parameters, with emphasis on the combined effects of the initial condition of the system, the chiral discrimination energies, and the decoherence in determining: the distinguishability as measured by a population difference between the initially pure and mixed states, and the decoherence process; the chiral stability as measured by the purity decay; and the stationary state of the system at times long relative to the time scales of the system dynamics and of the environmental effects.

Covalent bonds are created by the drive of electron waves to lower their kinetic energy through expansion
View Description Hide DescriptionAn analysis based on the variation principle shows that in the molecules H2 ^{+}, H2, B2, C2, N2, O2, F2, covalent bonding is driven by the attenuation of the kinetic energy that results from the delocalization of the electronic wave function. For molecular geometries around the equilibrium distance, two features of the wave function contribute to this delocalization: (i) Superposition of atomic orbitals extends the electronic wave function from one atom to two or more atoms; (ii) intraatomic contraction of the atomic orbitals further increases the interatomic delocalization. The interatomic kinetic energy lowering that (perhaps counterintuitively) is a consequence of the intraatomic contractions drives these contractions (which per se would increase the energy). Since the contractions necessarily encompass both, the intraatomic kinetic and potential energy changes (which add to a positive total), the fact that the intraatomic potential energy change renders the total potential binding energy negative does not alter the fact that it is the kinetic delocalization energy that drives the bond formation.

Resonant activation in a colored multiplicative thermal noise driven closed system
View Description Hide DescriptionIn this paper, we have demonstrated that resonant activation (RA) is possible even in a thermodynamically closed system where the particle experiences a random force and a spatiotemporal frictional coefficient from the thermal bath. For this stochastic process, we have observed a hallmark of RA phenomena in terms of a turnover behavior of the barriercrossing rate as a function of noise correlation time at a fixed noise variance. Variance can be fixed either by changing temperature or damping strength as a function of noise correlation time. Our another observation is that the barrier crossing rate passes through a maximum with increase in coupling strength of the multiplicative noise. If the damping strength is appreciably large, then the maximum may disappear. Finally, we compare simulation results with the analytical calculation. It shows that there is a good agreement between analytical and numerical results.

Classical mapping for Hubbard operators: Application to the doubleAnderson model
View Description Hide DescriptionA classical Cartesian mapping for Hubbard operators is developed to describe the nonequilibrium transport of an open quantum system with many electrons. The mapping of the Hubbard operators representing the manybody Hamiltonian is derived by using analogies from classical mappings of boson creation and annihilation operators visàvis a coherent state representation. The approach provides qualitative results for a double quantum dot array (double Anderson impurity model) coupled to fermionic leads for a range of bias voltages, Coulomb couplings, and hopping terms. While the width and height of the conduction peaks show deviations from the master equation approach considered to be accurate in the limit of weak systemleads couplings and high temperatures, the Hubbard mapping captures all transport channels involving transition between many electron states, some of which are not captured by approximate nonequilibrium Green function closures.

Generating accurate dipole moment surfaces using modified Shepard interpolation
View Description Hide DescriptionWe outline an approach for building molecular dipole moment surfaces using modified Shepard interpolation. Our approach is highly automated, requires minimal parameterization, and is iteratively improvable. Using the water molecule as a test case, we investigate how different aspects of the interpolation scheme affect the rate of convergence of calculated IR spectral line intensities. It is found that the interpolation scheme is sensitive to coordinate singularities present at linear geometries. Due to the generally monotonic nature of the dipole moment surface, the onepart weight function is found to be more effective than the more complicated twopart variant, with firstorder interpolation also giving betterthanexpected results. Almost all sensible schemes for choosing interpolation reference data points are found to exhibit acceptable convergence behavior.

Modeling delay in genetic networks: From delay birthdeath processes to delay stochastic differential equations
View Description Hide DescriptionDelay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birthdeath processes with delay. Here, we examine the relationship between delay birthdeath processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, crosscorrelations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birthdeath processes with delay.

Phase separation in solutions with specific and nonspecific interactions
View Description Hide DescriptionProtein solutions, which tend to be thermodynamically stable under physiological conditions, can demix into proteinenriched and proteindepleted phases when stressed. Using a latticegas model of proteins with both isotropic and specific, directional interactions, we calculate the critical conditions for phase separation for model proteins with up to four patches via Monte Carlo simulations and statistical associating fluid theory. Given a fixed specific interaction strength, the critical value of the isotropic energy, which accounts for dispersion forces and nonspecific interactions, measures the stability of the solution with respect to nonspecific interactions. Phase separation is suppressed by the formation of protein complexes, which effectively passivate the strongly associating sites on the monomers. Nevertheless, we find that protein models with three or more patches can form extended aggregates that phase separate despite the assembly of passivated complexes, even in the absence of nonspecific interactions. We present a unified view of the critical behavior of model fluids with anisotropic interactions, and we discuss the implications of these results for the thermodynamic stability of protein solutions.

Daubechies wavelets for linear scaling density functional theory
View Description Hide DescriptionWe demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the KohnSham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10 000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.

Nonorthogonal molecular orbital method: Singledeterminant theory
View Description Hide DescriptionUsing the variational principle, we have derived a variant of the Adams–Gilbert equation for nonorthogonal orbitals of a singledeterminant wave function, which we name the modified Adams–Gilbert equation. If we divide the molecular system into several subsystems, such as bonds, lone pairs, and residues, we can solve the equations for the subsystems one by one. Thus, this procedure has linear scaling. We have presented a practical procedure for solving the equations that is also applicable to macromolecular calculations. The numerical examples show that the procedure yields, with reasonable effort, results comparable with those of the Hartree–Fock–Roothaan method for orthogonal orbitals. To resolve the convergence difficulty in the selfconsistentfield iterations, we have found that virtual molecularorbital shifts are very effective.

Calculation of exact vibrational spectra for P_{2}O and CH_{2}NH using a phase space wavelet basis
View Description Hide Description‘‘Exact” quantum dynamics calculations of vibrational spectra are performed for two molecular systems of widely varying dimensionality (P2O and CH2NH), using a momentumsymmetrized Gaussian basis. This basis has been previously shown to defeat exponential scaling of computational cost with system dimensionality. The calculations were performed using the new “SWITCHBLADE” blackbox code, which utilizes both dimensionally independent algorithms and massive parallelization to compute very large numbers of eigenstates for any fourthorder force field potential, in a single calculation. For both molecules considered here, many thousands of vibrationally excited states were computed, to at least an “intermediate” level of accuracy (tens of wavenumbers). Future modifications to increase the accuracy to “spectroscopic” levels, along with other potential future improvements of the new code, are also discussed.

When a single hole aligns several spins: Double exchange in organic systems
View Description Hide DescriptionThe double exchange is a wellknown and technically important phenomenon in solid state physics. Ionizing a system composed of two antiferromagnetically coupled highspin units, the ground state of which is a singlet state, may actually produce a highspin ground state. This work illustrates the possible occurrence of such a phenomenon in organic chemistry. The hereconsidered highspin units are triangulenes, the ground state of which is a triplet. Bridging two of them through a benzene ring produces a molecular architecture of singlet ground state. A careful exploitation of a series of unrestricted density functional calculations enables one to avoid spin contamination in the treatment of the doublet states and shows that under ionization the system becomes of quartet multiplicity in its ground state. The possibility to align more than three spins from conjugated hydrocarbon polyradicals is explored, considering partially hydrogenated triangulenes. A dramatic example shows that ionization of a singlet ground state molecule may generate a decuplet.
 Advanced Experimental Techniques

Model free isoconversional procedure for evaluating the effective activation energy values of thermally stimulated processes in dinitroimidazoles
View Description Hide DescriptionThe decomposition kinetics of 1,4dinitroimidazole, 2,4dinitroimidazole, and Nmethyl2,4dinitroimidazole have been investigated using thermogravimetry–differential thermal analysis technique under N2 atmosphere at the flow rate 100 cm^{3}/min. The FlynnWallOzawa method and the Friedman method were used for the estimation of the effective activation energy values. These model free isoconversional kinetic methods showed variation in the calculated values due to the approximation of temperature integral used in the derivations of the kinetic equations. The model compounds were decomposed by multistep kinetics evident from the nonlinear relationship of the effective activation energy values with the conversion rate. Three different reaction pathways namely NO2 elimination, NO elimination, and HONO elimination are expected to play crucial role in the decomposition of nitroimidazoles. The model dinitroimidazoles represent different decomposition kinetics, and the reaction pathways the NO2 elimination, and NO elimination compete with each other for the decomposition mechanism. The present study is certainly helpful in understanding the decomposition kinetics, and dynamics of substituted nitroimidazoles to be used for fuel, and explosive applications.
 Atoms, Molecules, and Clusters

Excited state dynamics in SO_{2}. I. Bound state relaxation studied by timeresolved photoelectronphotoion coincidence spectroscopy
View Description Hide DescriptionThe excited state dynamics of isolated sulfur dioxide molecules have been investigated using the timeresolved photoelectron spectroscopy and timeresolved photoelectronphotoion coincidence techniques. Excited state wavepackets were prepared in the spectroscopically complex, electronically mixed ( )^{1}B1/(Ã)^{1}A2, Clements manifold following broadband excitation at a range of photon energies between 4.03 eV and 4.28 eV (308 nm and 290 nm, respectively). The resulting wavepacket dynamics were monitored using a multiphoton ionisation probe. The extensive literature associated with the Clements bands has been summarised and a detailed time domain description of the ultrafast relaxation pathways occurring from the optically bright ( )^{1}B1 diabatic state is presented. Signatures of the oscillatory motion on the ( )^{1}B1/(Ã)^{1}A2 lower adiabatic surface responsible for the Clements band structure were observed. The recorded spectra also indicate that a component of the excited state wavepacket undergoes intersystem crossing from the Clements manifold to the underlying triplet states on a subpicosecond time scale. Photoelectron signal growth time constants have been predominantly associated with intersystem crossing to the ( )^{3}B2 state and were measured to vary between 750 and 150 fs over the implemented pump photon energy range. Additionally, pump beam intensity studies were performed. These experiments highlighted parallel relaxation processes that occurred at the one and twopumpphoton levels of excitation on similar time scales, obscuring the Clements band dynamics when high pump beam intensities were implemented. Hence, the Clements band dynamics may be difficult to disentangle from higher order processes when ultrashort laser pulses and lessdifferential probe techniques are implemented.

Nonadiabatic and intersystem crossing dynamics in SO_{2}. II. The role of triplet states in the bound state dynamics studied by surfacehopping simulations
View Description Hide DescriptionThe importance of triplet states in the photorelaxation dynamics of SO2 is studied by mixed quantumclassical dynamics simulations. Using the SHARC method, standing for Surface Hopping including ARbitrary Couplings, intersystem crossing (ISC) processes caused by spinorbit coupling are found occurring on an ultrafast time scale (few 100 fs) and thus competing with internal conversion. While in the singletonly dynamics only oscillatory population transfer between the ^{1} B 1 and ^{1} A 2 states is observed, in the dynamics including singlet and triplet states we find additionally continuous ISC to the ^{3} B 2 state and to a smaller extent to the ^{3} B 1/^{3} A 2 coupled states. The populations obtained from the dynamics are discussed with respect to the overall nuclear motion and in the light of recent TRPEPICO studies [I. Wilkinson, A. E. Boguslavskiy, J. Mikosch, D. M. Villeneuve, H.J. Wörner, M. Spanner, S. Patchkovskii, and A. Stolow, “Excited state dynamics in SO2. I. Bound state relaxation studied by timeresolved photoelectronphotoion coincidence spectroscopy,” J. Chem. Phys.140, 204301 (2014)].

Excited state dynamics in SO_{2}. III. An ab initio quantum study of single and multiphoton ionization
View Description Hide DescriptionWe present an ab initio quantum study of the photoelectron spectra of sulfur dioxide, based on wavepacket propagations on manifolds of ionic, and excited/Rydberg states. We obtain excellent agreement for two different cases. First, the one photon ionization case where we can reproduce all details of the experimental spectrum and demonstrate the influence of the conical intersection between two of the ionic states. Then the multiphoton ionization regime, in which the dynamics of the wave packet on the two lowest singlet states is directly mapped in the spectra via a pumpprobe scheme, as proposed in the experimental companion paper [I. Wilkinson et al. , J. Chem. Phys.140, 204301 (2014)].

Dynamical photoionization observables of the CS molecule: The role of electron correlation
View Description Hide DescriptionHighly correlated calculations are performed on the primary ionic states and the prominent satellite present in the outer valence photoelectron spectrum of carbon monosulfide (CS). Dyson orbitals are coupled to accurate one particle continuum orbitals to provide a correlated description of energy dependent cross sections, asymmetry parameters, branching ratios, and molecular frame photoelectron angular distributions. The comparison with results obtained at the HartreeFock and Density Functional Theory level shows the strong sensitivity of these observables to details of the correlation in the bound states. The behaviour of the well characterized satellite state is analyzed in detail, and shows differences from the relevant primary states, revealing the limitations of a simple intensity borrowing mechanism. The results resolve the intensity disagreement with experiment obtained at the level of the sudden approximation.