Volume 135, Issue 24, 28 December 2011

We present a unified continuumlevel model for bilayer energetics that includes the effects of bending, compression, lipid orientation (tilting relative to the monolayersurface normal), and microscopic noise (protrusions). Expressions for thermal fluctuation amplitudes of several physical quantities are derived. These predictions are shown to be in good agreement with molecular simulations.
 COMMUNICATIONS


Communication: Manipulating the singlettriplet equilibrium in organic biradical materials
View Description Hide DescriptionWe investigated the tunability of the singlettriplet equilibrium population in the organic biradical 1,4phenylenedinitrene via magnetooptical spectroscopy. A rich magnetochromic response occurs because applied field increases the concentration of the triplet state species, which has a unique optical signature by comparison with the singlet biradical and the precursor molecule. A Curielike analysis of the magnetoopticalproperties allows us to extract the spin gap, which is smaller than previously supposed. These measurements establish the value of localprobe photophysical techniques for magnetic property determination in openshell systems such as biradicals where a traditional electron paramagnetic resonance Curie law analysis has intrinsic limitations.

Communication: Spectroscopic phase and lineshapes in highresolution broadband sum frequency vibrational spectroscopy: Resolving interfacial inhomogeneities of “identical” molecular groups
View Description Hide DescriptionThe ability to achieve subwavenumber resolution (0.6 cm^{−1}) and a large signaltonoise ratio in highresolution broadband sumfrequency generation vibrational spectroscopy (HRBBSFGVS) allows for the detailed SFG spectral lineshapes to be used in the unambiguous determination of fine spectral features. Changes in the structuralspectroscopic phase in SFGVS as a function of beam polarization and experimental geometry proved to be instrumental in the identification of an unexpected 2.78 ± 0.07 cm^{−1}spectral splitting for the two methyl groups at the vapor/dimethyl sulfoxide (DMSO, (CH_{3})_{2}SO) liquid interface as well as in the determination of their orientational angles.

Communication: The reason why +c ZnO surface is less stable than −c ZnO surface: Firstprinciples calculation
View Description Hide DescriptionIt has been experimentally shown that an O(−c)polar ZnOsurface is more stable than a Zn(+c)polar surface in H_{2} ambient. We applied firstprinciples calculations to investigating the polarity dependence on the stability at the electronic level. The calculations revealed that the −c surface terminated with H atom was stable maintaining a wurtzite structure, whereas the +c surface was unstable due to the change of coordination numbers of Zn at the topmost surface from four (wurtzite) to six (rock salt). This causes the generation of O_{2} molecules, resulting in instability at the +c surface.
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 ARTICLES

 Theoretical Methods and Algorithms

Localization scheme for relativistic spinors
View Description Hide DescriptionA new method to determine localized complexvalued oneelectron functions in the occupied space is presented. The approach allows the calculation of localized orbitals regardless of their structure and of the entries in the spinor coefficient matrix, i.e., one, two, and fourcomponent Kramersrestricted or unrestricted oneelectron functions with real or complex expansion coefficients. The method is applicable to localization schemes that maximize (or minimize) a functional of the occupied spinors and that use a localization operator for which a matrix representation is available. The approach relies on the approximate joint diagonalization (AJD) of several Hermitian (symmetric) matrices which is utilized in electronic signal processing. The use of AJD in this approach has the advantage that it allows a reformulation of the localization criterion on an iterative 2 × 2 pair rotating basis in an analytical closed form which has not yet been described in the literature for multicomponent (complexvalued) spinors. For the onecomponent case, the approach delivers the same FosterBoys or PipekMezey localized orbitals that one obtains from standard quantum chemical software, whereas in the multicomponent case complexvalued spinors satisfying the selected localization criterion are obtained. These localized spinors allow the formulation of local correlation methods in a multicomponent relativistic framework, which was not yet available. As an example, several heavy and superheavy element systems are calculated using a Kramersrestricted selfconsistent field and relativistic twocomponent pseudopotentials in order to investigate the effect of spinorbit coupling on localization.

Unambiguous optimization of effective potentials in finite basis sets
View Description Hide DescriptionThe optimization of effective potentials is of interest in densityfunctional theory(DFT) in two closely related contexts. First, the evaluation of the functional derivative of orbitaldependent exchangecorrelation functionals requires the application of optimized effective potential methods. Second, the optimization of the effective local potential that yields a given electron density is important both for the development of improved approximate functionals and for the practical application of embedding schemes based on DFT. However, in all cases this optimization turns into an illposed problem if a finite basis set is introduced for the Kohn–Sham orbitals. So far, this problem has not been solved satisfactorily. Here, a new approach to overcome the illposed nature of such finitebasis set methods is presented for the optimization of the effective local potential that yields a given electron density. This new scheme can be applied with orbital basis sets of reasonable size and makes it possible to vary the basis sets for the orbitals and for the potential independently, while providing an unambiguous potential that systematically approaches the numerical reference.

Exact onlattice stochastic reactiondiffusion simulations using partialpropensity methods
View Description Hide DescriptionStochastic reactiondiffusion systems frequently exhibit behavior that is not predicted by deterministic simulation models. Stochastic simulation methods, however, are computationally expensive. We present a more efficient stochastic reactiondiffusion simulation algorithm that samples realizations from the exact solution of the reactiondiffusion master equation. The present algorithm, called partialpropensity stochastic reactiondiffusion (PSRD) method, uses an onlattice discretization of the reactiondiffusion system and relies on partialpropensity methods for computational efficiency. We describe the algorithm in detail, provide a theoretical analysis of its computational cost, and demonstrate its computational performance in benchmarks. We then illustrate the application of PSRD to two and threedimensional patternforming GrayScott systems, highlighting the role of intrinsic noise in these systems.

Analytic second derivatives for the spinfree exact twocomponent theory
View Description Hide DescriptionThe formulation and implementation of the spinfree (SF) exact twocomponent (X2c) theory at the oneelectron level (SFX2c1e) is extended in the present work to the analytic evaluation of second derivatives of the energy. In the X2c1e scheme, the fourcomponent oneelectron Dirac Hamiltonian is block diagonalized in its matrix representation and the resulting “electronsonly” twocomponent Hamiltonian is then used together with untransformed twoelectron interactions. The derivatives of the twocomponent Hamiltonian can thus be obtained by means of simple manipulations of the parent fourcomponent Hamiltonian integrals and derivative integrals. The SF version of X2c1e can furthermore exploit available nonrelativistic quantumchemical codes in a straightforward manner. As a first application of analytic SFX2c1e second derivatives, we report a systematic study of the equilibrium geometry and vibrational frequencies for the bent ground state of the copper hydroxide (CuOH) molecule. Scalarrelativistic, electroncorrelation, and basisset effects on these properties are carefully assessed.

Computing the energy of a water molecule using multideterminants: A simple, efficient algorithm
View Description Hide DescriptionQuantum Monte Carlo (QMC) methods such as variational Monte Carlo and fixed node diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although SlaterJastrow wave functions are the most commonly used variational ansatz in electronic structure, more sophisticated wave functions are critical to ascertaining new physics. One such wave function is the multiSlaterJastrow wave function which consists of a Jastrow function multiplied by the sum of Slater determinants. In this paper we describe a method for working with these wave functions in QMC codes that is easy to implement, efficient both in computational speed as well as memory, and easily parallelized. The computational cost scales quadratically with particle number making this scaling no worse than the single determinant case and linear with the total number of excitations. Additionally, we implement this method and use it to compute the ground state energy of a water molecule.

Rigorous formulation of twoparameter doublehybrid densityfunctionals
View Description Hide DescriptionA twoparameter extension of the densityscaled double hybrid approach of Sharkas et al. [J. Chem. Phys.134, 064113 (2011)] is presented. It is based on the explicit treatment of a fraction of multideterminantal exact exchange. The connection with conventional double hybrids is made when neglecting density scaling in the correlation functional as well as secondorder corrections to the density. In this context, the fraction a _{c} of secondorder MøllerPlesset (MP2) correlationenergy is not necessarily equal to the square of the fraction a _{x} of HartreeFock exchange. More specifically, it is shown that , a condition that conventional semiempirical double hybrids actually fulfill. In addition, a new procedure for calculating the orbitals, which has a better justification than the one routinely used, is proposed. Referred to as λ_{1} variant, the corresponding double hybrid approximation has been tested on a small set consisting of H_{2}, N_{2}, Be_{2}, Mg_{2}, and Ar_{2}. Three conventional double hybrids (B2PLYP, B2GPPLYP, and PBE0DH) have been considered. Potential curves obtained with λ_{1} and regular double hybrids can, in some cases, differ significantly. In particular, for the weakly bound dimers, the λ_{1} variants bind systematically more than the regular ones, which is an improvement in many but not all cases. Including density scaling in the correlation functionals may of course change the results significantly. Moreover, optimized effective potentials based on a partiallyinteracting system could also be used to generate proper orbitals. Work is currently in progress in those directions.

A novel method to describe the interaction pressure between charged plates with application of the weighted correlation approach
View Description Hide DescriptionBased on the Euler–Lagrange equation for ion density distribution in an inhomogeneous, charged, and hardsphere fluid, a novel method is proposed to determine the interaction pressure between charged plates. The resulting expression is a sum of distinct physical contributions to the pressure, which involves different contributions to the singleparticle direct correlation function. It can, therefore, be conveniently used in any density functional approach to facilitate analysis of the pressure components. In this study, the socalled fundamental measure theory (FMT)/weighted correlation approach (WCA) approach is applied to estimate both the hardsphere and the electric residual contributions to the singleparticle direct correlation function, upon the calculation of the ionic density profiles between charged plates. The results, against the Monte Carlo simulations, show that the FMT/WCA approach is superior to the typical FMT/mean spherical approximation approach of the density functional theory in predicting the interaction pressure between charged plates immersed in an electrolyte solution upon various conditions in the primitive model. The FMT/WCA approach can well capture the fine features of the pressureseparation dependence, to reproduce not only the shoulder shape and the weak attractions in monovalent electrolytes but also the strongly oscillatory behavior of pressure in divalent electrolytes where pronounced attractions are observed. In addition, it is found that the FMT/WCA approach even has an advantage over the anisotropic, hypernetted chain approach in that it agrees with the Monte Carlo results to a very good extent with, however, much less computational effort.

Anisotropy effect on global minimum structures of clusters: Twocenter LennardJones model
View Description Hide DescriptionUsing a twocenter LennardJones (2CLJ) model, the simplest anisotropic case, we investigated how anisotropy affects global minimum structures of clusters and obtained some interesting results. The anisotropy parameter, R, is defined as the ratio of the bond length of 2CLJ dimer to the LJ equilibrium pair separation, where a larger R value means higher anisotropy. For low R values, the structures resemble those of the LennardJones atomic clusters. However, as the pairwise interaction becomes more anisotropic, the “magic numbers” change, and several novel cluster patterns emerge as particularly stable structures, and the global minima change from icosahedral, to polyicosahedral and to novel irregular structures. Moreover, increasing the anisotropy effectively softens the 2CLJ potential. Given the general importance of the LJ cluster as a simple model cluster, 2CLJ model can provide a straightforward and useful analysis of the effect of molecular shape on the structures of clusters.

On a relationship between molecular polarizability and partial molar volume in water
View Description Hide DescriptionWe reveal a universal relationship between molecular polarizability (a singlemoleculeproperty) and partial molar volume in water that is an ensembleproperty characterizing solutesolvent systems. Since both of these quantities are of the key importance to describe solvation behavior of dissolved molecular species in aqueous solutions, the obtained relationship should have a high impact in chemistry, pharmaceutical, and life sciences as well as in environments. We demonstrated that the obtained relationship between the partial molar volume in water and the molecular polarizability has in general a nonhomogeneous character. We performed a detailed analysis of this relationship on a set of ∼200 organic molecules from various chemical classes and revealed its fine wellorganized structure. We found that this structure strongly depends on the chemical nature of the solutes and can be rationalized in terms of specific solutesolvent interactions. Efficiency and universality of the proposed approach was demonstrated on an external test set containing several dozens of polyfunctional and druglike molecules.

Quantum entanglement between electronic and vibrational degrees of freedom in molecules
View Description Hide DescriptionWe consider the quantum entanglement of the electronic and vibrational degrees of freedom in molecules with tendencies towards double welled potentials. In these bipartite systems, the von Neumann entropy of the reduced density matrix is used to quantify the electronvibration entanglement for the lowest two vibronic wavefunctions obtained from a model Hamiltonian based on coupled harmonic diabatic potentialenergysurfaces. Significant entanglement is found only in the region in which the ground vibronic state contains a density profile that is bimodal (i.e., contains two separate local maxima). However, in this region two distinct types of density and entanglement profiles are found: one type arises purely from the degeneracy of energy levels in the two potential wells and is destroyed by slight asymmetry, while the other arises through strong interactions between the diabatic levels of each well and is relatively insensitive to asymmetry. These two distinct types are termed fragile degeneracyinducedentanglement and persistententanglement, respectively. Six classic molecular systems describable by two diabatic states are considered: ammonia, benzene, BNB, pyridine excited triplet states, the CreutzTaube ion, and the radical cation of the “special pair” of chlorophylls involved in photosynthesis. These chemically diverse systems are all treated using the same general formalism and the nature of the entanglement that they embody is elucidated.

An algebraic operator approach to electronic structure
View Description Hide DescriptionIn this paper, we introduce an algebraic approach to electronic structure calculations. Our approach constructs a Jordan algebra based on the secondquantized electronic Hamiltonian. From the structure factor of this algebra, we show that we can calculate the energy of the ground electronic state of the Hamiltonian operator. We apply our method to several generalized Hubbard models and show that we can usually obtain a significant fraction of the correlation energy for lowtomoderate values of the electronic repulsion parameter while still retaining the O(L ^{3}) scaling of the HartreeFock algorithm. This surprising result, along with several other observations, suggests that our algebraic approach represents a new paradigm for electronic structure calculations which opens up many new directions for research.

Efficient electron dynamics with the planewavebased realtime timedependent density functional theory: Absorption spectra, vibronic electronic spectra, and coupled electronnucleus dynamics
View Description Hide DescriptionThe electron dynamics with complex thirdorder SuzukiTrotter propagator (ST_{3}) has been implemented into a planewave (PW) based density functional theory program, and several applications including linear absorption spectra and coupled electronnucleus dynamics have been calculated. Since the ST_{3} reduces the number of Fourier transforms to less than half compared to the fourthorder SuzukiTrotter propagator (ST_{4}), more than twice faster calculations are possible by exploiting the ST_{3}. We analyzed numerical errors of both the ST_{3} and the ST_{4} in the presence/absence of an external field for several molecules such as Al_{2}, N_{2}, and C_{2}H_{4}. We obtained that the ST_{3} gives the same order of numerical errors (10^{−5} Ry after 100 fs) as the ST_{4}. Also, the time evolution of dipole moments, hence the absorptionspectrum, is equivalent for both ST_{3} and ST_{4}. As applications, the linear absorptionspectrum for an ethylene molecule was studied. From the density difference analysis, we showed that the absorption peaks at 6.10 eV and 7.65 eV correspond to the π → 4a_{g} and π → π* excitation bands, respectively. We also investigated the molecular vibrational effect to the absorption spectra of an ethylene molecule and the dynamics of a hydrogen molecule after the σ → σ* transition by formulating coupled electronnucleus dynamics within the Ehrenfest regime. The trajectory of nuclei follows the excited state potential energy curve exactly.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Highresolution Fouriertransform extreme ultraviolet photoabsorption spectroscopy of ^{14}N^{15}N
View Description Hide DescriptionThe first comprehensive highresolution photoabsorptionspectrum of ^{14}N^{15}N has been recorded using the Fouriertransform spectrometer attached to the Desirs beamline at the Soleil synchrotron. Observations are made in the extreme ultraviolet and span 100 000–109 000 cm^{−1} (100–91.7 nm). The observed absorption lines have been assigned to 25 bands and reduced to a set of transition energies, f values, and linewidths. This analysis has verified the predictions of a theoretical model of N_{2} that simulates its photoabsorption and photodissociation cross section by solution of an isotopomer independent formulation of the coupledchannel Schrödinger equation. The mass dependence of predissociationlinewidths and oscillator strengths is clearly evident and many local perturbations of transition energies, strengths, and widths within individual rotational series have been observed.

Multiphoton dissociative ionization of tertpentyl bromide near 265 nm
View Description Hide DescriptionWe report on the photodissociation dynamics of tertpentyl bromide near 265 nm investigated by timesliced velocity map imaging. The speed and angular distributions have been analyzed for both the groundstate Br(^{2} P _{3/2}) atom (denoted Br) and the spin–orbit excitedstate Br(^{2} P _{1/2}) atom (denoted Br*). The speed distributions of Br and Br* atoms are all found to consist of three Gaussian components, which correlate to three independent dissociation pathways on the excited potential energy surfaces: (1) the high translational energy (E _{T}) component from the prompt dissociation along the C–Br stretching mode, (2) the middle E _{T} component from the repulsive mode along the C–Br stretching coupled with some bending motions, and (3) the low E _{T} component from the repulsive mode along the C–Br stretching coupled with more bending motions. More interestingly, we have also observed the ions in 263–267 nm. The nearzero kinetic energy distributions extracted from the three images near 265 nm show the typical characteristics that are attributable to multiphotondissociativeionization, suggesting the existence of a neutral superexcited state of the parent tertpentyl bromide molecule. The contribution of bromine atoms formed in this dissociativeionization channel adds in the total relative distribution of low E _{T} component in the Br*(Br) formation channel, which reasonably explains the abnormal distributions observed in between the middle and low E _{T} components in the Br*(Br) formation channel.

Ab initio calculations of the electronic states of AsH_{2} including dissociation characteristics
View Description Hide DescriptionMultireference configuration interaction calculations have been carried out for lowlying electronic states of AsH_{2}. Bending potentials for the ten lowest states of AsH_{2} are obtained in C _{2v } symmetry for As–H distances fixed at the the ground state equilibrium value of 2.845 a _{0}, as well as for the minimum energy path constrained to R _{1} = R _{2}. The calculated equilibrium geometries for the ground state and the excited state agree very well with the previous experimental and theoretical results, whereas the data for the higherlying states are obtained for the first time. Asymmetric potential energy surface (PES) cuts (at R _{1} = 2.845 a _{0}, θ = 90.7°) and twodimensional (2D) PESs for the lowest three states are also new. The calculated ab initio data are used for analysis of possible AsH_{2}photodissociation channels and predissociation effects. It is shown that the transition dipole moment decreases with increasing bending angle, which influences the intensity distribution in the emission spectrum ( bending series), shifting its maximum to smaller quantum numbers.

Rotational and vibrational energy transfer in vibrationally excited acetylene at energies near 6560 cm^{−1}
View Description Hide DescriptionCollisional energy transfer kinetics of vibrationally excited acetylene has been examined for states with internal energies near 6560 cm^{−1}. Total population removal rate constants were determined for selected rotational levels of the (1,0,1,0^{0},0^{0}) and (0,1,1,2^{0},0^{0}) states. Values in the range of (10–18) × 10^{−10} cm^{3} s^{−1} were obtained. Measurements of statetostate rotational energy transfer rate constants were also carried out for these states. The rotational energy transfer kinetics was found to be consistent with simple energy gap models for the transfer probabilities. Vibrational transfer out of the (0,1,1,2^{0},0^{0}) state accounted for no more than 16% of the total removal process. Transfer from (1,0,1,0^{0},0^{0}) to the usymmetry (0,2,0,3^{1},1^{−1}), (0,1,1,2^{0},0^{0}), and (1,1,0,1^{1},1^{−1}) states was observed. Applying the principle of detailed balance to these data indicated that vibrational transfer to (1,0,1,0^{0},0^{0}) accounted for ∼0.1% of the population loss from (0,2,0,3^{1},1^{−1}) or (0,1,1,2^{0},0^{0}), and 3% of the loss from (1,1,0,1^{1},1^{−1}). Relative rotational transfer probabilities were obtained for transfer to the gsymmetry (1,1,0,2^{0},0^{0})/(0,0,2,0^{0},0^{0}) dyad. These results are related to recent studies of optically pumped acetylene lasers.

HNO_{3}−NH_{x}, H_{2}SO_{4}−NH_{x}, CH(O)OH−NH_{x}, and CH_{3}C(O)OH−NH_{x} complexes and their role in the formation of condensation nuclei
View Description Hide DescriptionThe formation of sulfuric acid (H_{2}SO_{4}), nitric acid (HNO_{3}), acetic acid (CH_{3}C(O)OH), and formic acid (HC(O))H) complexes with ammonia (NH_{3}), amidogen radical (NH_{2}), and imidogen radical (NH) was studied using natural bond orbital calculations. The equilibrium structures, binding energies, and harmonic frequencies were calculated for each acidNH_{x} complex using hybrid density functional (B3LYP) and secondorder MøllerPlesset perturbation approximation methods with the 6311++G(3df,3pd) basis set. The results presented here suggest that the effect of NH_{2} on the formation of new condensation nuclei will be similar to that of NH_{3}, but to a lesser degree and confined primarily to complexes with H_{2}SO_{4} and HNO_{3}. The NH radical is not expected to play a significant role in the formation of new atmospheric condensation nuclei.