Volume 139, Issue 10, 14 September 2013

Computing phase diagrams of model systems is an essential part of computational condensed matter physics. In this paper, we discuss in detail the interface pinning (IP) method for calculation of the Gibbs free energy difference between a solid and a liquid. This is done in a single equilibrium simulation by applying a harmonic field that biases the system towards twophase configurations. The Gibbs free energy difference between the phases is determined from the average force that the applied field exerts on the system. As a test system, we study the LennardJones model. It is shown that the coexistence line can be computed efficiently to a high precision when the IP method is combined with the NewtonRaphson method for finding roots. Statistical and systematic errors are investigated. Advantages and drawbacks of the IP method are discussed. The high pressure part of the temperaturedensity coexistence region is outlined by isomorphs.
 COMMUNICATIONS


Communication: Two measures of isochronal superposition
View Description Hide DescriptionA liquid obeys isochronal superposition if its dynamics is invariant along the isochrones in the thermodynamic phase diagram (the curves of constant relaxation time). This paper introduces two quantitative measures of isochronal superposition. The measures are used to test the following six liquids for isochronal superposition: 1,2,6 hexanetriol, glycerol, polyphenyl ether, diethyl phthalate, tetramethyl tetraphenyl trisiloxane, and dibutyl phthalate. The latter four van der Waals liquids obey isochronal superposition to a higher degree than the two hydrogenbonded liquids. This is a prediction of the isomorph theory, and it confirms findings by other groups.

Communication: Trapping upconverted energy in neat platinum porphyrin films via an unexpected fusion mechanism
View Description Hide DescriptionDirect observation of an unexpected product from excited state fusion of two excited triplet states in platinum octaethylporphyrin is reported. Transient spectroscopy was used to identify the product as a metal centered (d, d) state that decays slowly compared with the rate of fusion. The reaction was demonstrated to be second order with a rate coefficient of k TTF = (5.4 ± 0.4) × 10−10 cm3 · s−1. The results contrast with the common assumption that fusion proceeds directly to annihilation via rapid nonradiative deactivation of the products. Following visible photoexcitation, the fusion process results in energetic upconversion of the incident photons stored in the higher energy (d, d) state at irradiances below the threshold for multiphoton absorption.

Communication: Determination of the molecular structure of the simplest Criegee intermediate CH_{2}OO
View Description Hide DescriptionThe simplest Criegee intermediate CH2OO was detected in a discharged supersonic jet of a CH2Br2 and O2 gas mixture by Fouriertransform microwave spectroscopy. The experimentally determined rotational constants of CH2OO and its isotopologues enabled us to derive the geometrical structure. The determined OO and CO bond lengths, which are relevant to a discussion on its electronic structure, are 1.345(3) and 1.272(3) Å, respectively. The CO bond length is close to that of a typical double bond and is shorter than that of the OO bond by 0.07 Å, indicating that CH2OO has a more zwitterionic character H2C = O⊕–O⊖ than biradical .
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 ARTICLES

 Theoretical Methods and Algorithms

Development of openboundary cluster model approach for electrochemical systems and its application to Ag^{+} adsorption on Au(111) and Ag(111) electrodes
View Description Hide DescriptionWe present a theoretical method to investigate electrochemical processes on the basis of a finitetemperature density functional theory (FTDFT) approach combined with our recently developed openboundary cluster model (OCM). A semiinfinite electrode is well mimicked by a finitesized simple cluster with an open quantum boundary condition rationalized by OCM. An equilibrium state between adsorbates and an electrode is described by the grand canonical formulation of FTDFT. These implements allow us to calculate electronic properties of an adsorbate and electrode system at a constant chemical potential μ, i.e., electrode potential. A solvation effect is approximated by a conductorlike polarized continuum model. The method is applied to the electrochemical processes of Ag+ adsorption on Au(111) and Ag(111). The present constant μ approach has proved essential to electrochemical systems, demonstrating that the method qualitatively reproduces the experimental evidence that Ag+ adsorbs more on the Au electrode than the Ag one, while the conventional quantum chemistry approach with a constant number of electrons incorrectly gives exactly the opposite result.

Direct calculation of the solidliquid Gibbs free energy difference in a single equilibrium simulation
View Description Hide DescriptionComputing phase diagrams of model systems is an essential part of computational condensed matter physics. In this paper, we discuss in detail the interface pinning (IP) method for calculation of the Gibbs free energy difference between a solid and a liquid. This is done in a single equilibrium simulation by applying a harmonic field that biases the system towards twophase configurations. The Gibbs free energy difference between the phases is determined from the average force that the applied field exerts on the system. As a test system, we study the LennardJones model. It is shown that the coexistence line can be computed efficiently to a high precision when the IP method is combined with the NewtonRaphson method for finding roots. Statistical and systematic errors are investigated. Advantages and drawbacks of the IP method are discussed. The high pressure part of the temperaturedensity coexistence region is outlined by isomorphs.

Polaron dynamics in twodimensional photonecho spectroscopy of molecular rings
View Description Hide DescriptionWe have developed a new approach to the computation of thirdorder spectroscopic signals of molecular rings, by incorporating the Davydov soliton theory into the nonlinear response function formalism. The Davydov D1 and Ansätze have been employed to treat the interactions between the excitons and the primary phonons, allowing for a full description of arbitrary excitonphonon coupling strengths. As an illustration, we have simulated a series of optical 2D spectra for two models of molecular rings.

The role of available sites in the activity of lattice gases with geometric constraints
View Description Hide DescriptionThe activity in latticegas systems with geometric constraints is shown to be the ratio of the number of particles to the number of available sites. The key role of sites available for occupation is emphasized. Available sites may be different for different species and are not necessarily just unoccupied sites. Locationspecific or nonlocal constraints are allowed. An analytical expression for the number of available sites is given for the hardhexagon model. The utility of an expression for available sites is illustrated for the nontrivial case of a mixed Langmuir/hardhexagon adsorption system, where the influence of the Langmuir adsorbates on the hardhexagon phase transition is investigated. The dependence on available sites indicates how to extend these results to the kinetic regime and simulations of kinetic voltammograms for the hardhexagon model are given as an example.

Role of sampling in evaluating classical time autocorrelation functions
View Description Hide DescriptionWe analyze how the choice of the sampling weight affects efficiency of the Monte Carlo evaluation of classical time autocorrelation functions. Assuming uncorrelated sampling or sampling with constant correlation length, we propose a sampling weight for which the number of trajectories needed for convergence is independent of the correlated quantity, dimensionality, dynamics, and phasespace density. By contrast, it is shown that the computational cost of the “standard” algorithm sampling from the phasespace density may scale exponentially with the number of degrees of freedom. Yet, for the stationary Gaussian distribution of harmonic systems and for the autocorrelation function of a linear function of phasespace coordinates, the computational cost of this standard algorithm is also independent of dimensionality.

Solvatochromic shifts from coupledcluster theory embedded in density functional theory
View Description Hide DescriptionBuilding on the framework recently reported for determining general response properties for frozendensity embedding [S. Höfener, A. S. P. Gomes, and L. Visscher, J. Chem. Phys.136, 044104 (Year: 2012)]10.1063/1.3675845, in this work we report a first implementation of an embedded coupledcluster in densityfunctional theory (CCinDFT) scheme for electronic excitations, where only the response of the active subsystem is taken into account. The formalism is applied to the calculation of coupledcluster excitation energies of water and uracil in aqueous solution. We find that the CCinDFT results are in good agreement with reference calculations and experimental results. The accuracy of calculations is mainly sensitive to factors influencing the correlation treatment (basis set quality, truncation of the cluster operator) and to the embedding treatment of the groundstate (choice of density functionals). This allows for efficient approximations at the excited state calculation step without compromising the accuracy. This approximate scheme makes it possible to use a first principles approach to investigate environment effects with specific interactions at coupledcluster level of theory at a cost comparable to that of calculations of the individual subsystems in vacuum.

Path integral density matrix dynamics: A method for calculating timedependent properties in thermal adiabatic and nonadiabatic systems
View Description Hide DescriptionWe introduce a new approach for calculating quantum timecorrelation functions and timedependent expectation values in manybody thermal systems; both electronically adiabatic and nonadiabatic cases can be treated. Our approach uses a path integral simulation to sample an initial thermal density matrix; subsequent evolution of this density matrix is equivalent to solution of the timedependent Schrödinger equation, which we perform using a linear expansion of Gaussian wavepacket basis functions which evolve according to simple classicallike trajectories. Overall, this methodology represents a formally exact approach for calculating timedependent quantum properties; by introducing approximations into both the imaginarytime and realtime propagations, this approach can be adapted for complex manyparticle systems interacting through arbitrary potentials. We demonstrate this method for the spin Boson model, where we find good agreement with numerically exact calculations. We also discuss future directions of improvement for our approach with a view to improving accuracy and efficiency.

Nonequilibrium OrnsteinZernike relation for Brownian manybody dynamics
View Description Hide DescriptionWe derive a dynamic OrnsteinZernike equation for classical fluids undergoing overdamped Brownian motion and driven out of equilibrium. Inhomogeneous twotime correlation functions are obtained from functional differentiation of the onebody density and current with respect to an appropriately chosen external field. Functional calculus leads naturally to nonMarkovian equations of motion for the twotime correlators. Memory functions are identified as functional derivatives of a space and timenonlocal power dissipation functional. We propose an excess (over ideal gas) dissipation functional that both generates modecoupling theory for the twobody correlations and extends dynamical density functional theory for the onebody fields, thus unifying the two approaches.

Natural occupation numbers: When do they vanish?
View Description Hide DescriptionThe nonvanishing of the natural orbital (NO) occupation numbers of the oneparticle density matrix of manybody systems has important consequences for the existence of a density matrixpotential mapping for nonlocal potentials in reduced density matrix functional theory and for the validity of the extended Koopmans' theorem. On the basis of Weyl's theorem we give a connection between the differentiability properties of the ground state wavefunction and the rate at which the natural occupations approach zero when ordered as a descending series. We show, in particular, that the presence of a Coulomb cusp in the wavefunction leads, in general, to a power law decay of the natural occupations, whereas infinitely differentiable wavefunctions typically have natural occupations that decay exponentially. We analyze for a number of explicit examples of twoparticle systems that in case the wavefunction is nonanalytic at its spatial diagonal (for instance, due to the presence of a Coulomb cusp) the natural orbital occupations are nonvanishing. We further derive a more general criterium for the nonvanishing of NO occupations for twoparticle wavefunctions with a certain separability structure. On the basis of this criterium we show that for a twoparticle system of harmonically confined electrons with a Coulombic interaction (the socalled Hookium) the natural orbital occupations never vanish.

Longrange interactions and the sign of natural amplitudes in twoelectron systems
View Description Hide DescriptionIn singlet twoelectron systems, the natural occupation numbers of the oneparticle reduced density matrix are given as squares of the natural amplitudes which are defined as the expansion coefficients of the twoelectron wave function in a natural orbital basis. In this work, we relate the sign of the natural amplitudes to the nature of the twobody interaction. We show that longrange Coulombtype interactions are responsible for the appearance of positive amplitudes and give both analytical and numerical examples that illustrate how the longdistance structure of the wave function affects these amplitudes. We further demonstrate that the amplitudes show an avoided crossing behavior as function of a parameter in the Hamiltonian and use this feature to show that these amplitudes never become zero, except for special interactions in which infinitely many of them can become zero simultaneously when changing the interaction strength. This mechanism of avoided crossings provides an alternative argument for the nonvanishing of the natural occupation numbers in Coulomb systems.

Description of electronic excited states using electron correlation operator
View Description Hide DescriptionThe electron correlation energy in a chemical system is defined as a difference between the energy of an exact energy for a given Hamiltonian, and a meanfield, or single determinant, approximation to it. A promising way to model electron correlation is through the expectation value of a linear twoelectron operator for the KohnSham single determinant wavefunction. For practical reasons, it is desirable for such an operator to be universal, i.e., independent of the positions and types of nuclei in a molecule. The correlation operator models the effect of electron correlation on the interaction energy in a electron pair. We choose an operator expanded in a small number of Gaussians as a model for electron correlation, and test it by computing atomic and molecular adiabatic excited states. The computations are performed within the Δ SelfConsistent Field (ΔSCF) formalism, and are compared to the timedependent density functional theory model with popular density functionals. The simplest form of the correlation operator contains only one parameter derived from the helium atom ground state correlation energy. The correlation operator approach significantly outperforms other methods in computation of atomic excitation energies. The accuracy of molecular excitation energies computed with the correlation operator is limited by the shortcomings of the ΔSCF methodology in describing excited states.

Equivalence of particleparticle random phase approximation correlation energy and laddercoupledcluster doubles
View Description Hide DescriptionThe recent proposal to determine the (exact) correlation energy based on pairing matrix fluctuations by van Aggelen et al. [“Exchangecorrelation energy from pairing matrix fluctuation and the particleparticle random phase approximation,” preprint arXiv:1306.4957 (Year: 2013)] revived the interest in the simplest approximation along this path: the particleparticle random phase approximation (ppRPA). In this paper, we present an analytical connection and numerical demonstrations of the equivalence of the correlation energy from ppRPA and laddercoupledcluster doubles. These two theories reduce to identical algebraic matrix equations and correlation energy expressions. The numerical examples illustrate that the correlation energy missed by ppRPA in comparison with coupledcluster singles and doubles is largely canceled out when considering reaction energies. This theoretical connection will be beneficial to design density functionals with strong ties to coupledcluster theories and to study molecular properties at the ppRPA level relying on well established coupled cluster techniques.

Particleparticle and quasiparticle random phase approximations: Connections to coupled cluster theory
View Description Hide DescriptionWe establish a formal connection between the particleparticle (pp) random phase approximation (RPA) and the ladder channel of the coupled cluster doubles (CCD) equations. The relationship between RPA and CCD is best understood within a Bogoliubov quasiparticle (qp) RPA formalism. This work is a followup to our previous formal proof on the connection between particlehole (ph) RPA and ringCCD. Whereas RPA is a quasibosonic approximation, CC theory is a “correct bosonization” in the sense that the wavefunction and Hilbert space are exactly fermionic, yet the amplitude equations can be interpreted as adding different quasibosonic RPA channels together. Coupled cluster theory achieves this goal by interacting the ph (ring) and pp (ladder) diagrams via a third channel that we here call “crossedring” whose presence allows for full fermionic antisymmetry. Additionally, coupled cluster incorporates what we call “mosaic” terms which can be absorbed into defining a new effective onebody Hamiltonian. The inclusion of these mosaic terms seems to be quite important. The ppRPA and qpRPA equations are textbook material in nuclear structure physics but are largely unknown in quantum chemistry, where particle number fluctuations and Bogoliubov determinants are rarely used. We believe that the ideas and connections discussed in this paper may help design improved ways of incorporating RPA correlation into density functionals based on a CC perspective.

Extension of manybody theory and approximate density functionals to fractional charges and fractional spins
View Description Hide DescriptionThe exact conditions for density functionals and density matrix functionals in terms of fractional charges and fractional spins are known, and their violation in commonly used functionals has been shown to be the root of many major failures in practical applications. However, approximate functionals are designed for physical systems with integer charges and spins, not in terms of the fractional variables. Here we develop a general framework for extending approximate density functionals and manyelectron theory to fractionalcharge and fractionalspin systems. Our development allows for the fractional extension of any approximate theory that is a functional of G 0, the oneelectron Green's function of the noninteracting reference system. The extension to fractional charge and fractional spin systems is based on the ensemble average of the basic variable, G 0. We demonstrate the fractional extension for the following theories: (1) any explicit functional of the oneelectron density, such as the local density approximation and generalized gradient approximations; (2) any explicit functional of the oneelectron density matrix of the noninteracting reference system, such as the exact exchange functional (or HartreeFock theory) and hybrid functionals; (3) manybody perturbation theory; and (4) randomphase approximations. A general rule for such an extension has also been derived through scaling the orbitals and should be useful for functionals where the link to the Green's function is not obvious. The development thus enables the examination of approximate theories against known exact conditions on the fractional variables and the analysis of their failures in chemical and physical applications in terms of violations of exact conditions of the energy functionals. The present work should facilitate the calculation of chemical potentials and fundamental bandgaps with approximate functionals and manyelectron theories through the energy derivatives with respect to the fractional charge. It should play an important role in developing accurate approximate density functionals and manybody theory.

Hyperfine interactions in a gadoliniumbased MRI contrast agent: Highfrequency modulations from ab initio simulations
View Description Hide DescriptionHyperfine coupling tensors of the water molecule coordinated to the Prohance contrast agent in liquid water were calculated within and beyond the point dipole approximation along an ab initio molecular dynamics trajectory. We observe the nonequivalence at short time scales on structural as well as magnetodynamical properties of inner sphere water protons due to hydrogen bonds formation with the solvent. In addition, the influence of ultrafast internal motions on the anisotropic, dipolar, contribution to hyperfine couplings was probed thanks to a decomposition of its fluctuations in terms of a small set of meaningful collective variables.

Analytic energy gradients for the orbitaloptimized thirdorder Møller–Plesset perturbation theory
View Description Hide DescriptionAnalytic energy gradients for the orbitaloptimized thirdorder Møller–Plesset perturbation theory (OMP3) [U. Bozkaya, J. Chem. Phys.135, 224103 (Year: 2011)]10.1063/1.3665134 are presented. The OMP3 method is applied to problematic chemical systems with challenging electronic structures. The performance of the OMP3 method is compared with those of canonical secondorder MøllerPlesset perturbation theory (MP2), thirdorder MøllerPlesset perturbation theory (MP3), coupledcluster singles and doubles (CCSD), and coupledcluster singles and doubles with perturbative triples [CCSD(T)] for investigating equilibrium geometries, vibrational frequencies, and openshell reaction energies. For bond lengths, the performance of OMP3 is in between those of MP3 and CCSD. For harmonic vibrational frequencies, the OMP3 method significantly eliminates the singularities arising from the abnormal response contributions observed for MP3 in case of symmetrybreaking problems, and provides noticeably improved vibrational frequencies for openshell molecules. For openshell reaction energies, OMP3 exhibits a better performance than MP3 and CCSD as in case of barrier heights and radical stabilization energies. As discussed in previous studies, the OMP3 method is several times faster than CCSD in energy computations. Further, in analytic gradient computations for the CCSD method one needs to solve λamplitude equations, however for OMP3 one does not since and . Additionally, one needs to solve orbital Zvector equations for CCSD, but for OMP3 orbital response contributions are zero owing to the stationary property of OMP3. Overall, for analytic gradient computations the OMP3 method is several times less expensive than CCSD (roughly ∼4–6 times). Considering the balance of computational cost and accuracy we conclude that the OMP3 method emerges as a very useful tool for the study of electronically challenging chemical systems.
 Atoms, Molecules, and Clusters

Slow photoelectron velocitymap imaging spectroscopy of the C_{9}H_{7} (indenyl) and C_{13}H_{9} (fluorenyl) anions
View Description Hide DescriptionHighresolution photoelectron spectra are reported of the cryogenically cooled indenyl and fluorenyl anions, and , obtained with slow electron velocitymap imaging. The spectra show wellresolved transitions to the neutral ground states, giving electron affinities of 1.8019(6) eV for indenyl and 1.8751(3) eV for fluorenyl. Numerous vibrations are observed and assigned for the first time in the radical ground states, including several transitions that are allowed only through vibronic coupling. The fluorenyl spectra can be interpreted with a FranckCondon simulation, but explaining the indenyl spectra requires careful consideration of vibronic coupling and photodetachment threshold effects. Comparison of high and lowresolution spectra along with measurements of photoelectron angular distributions provide further insights into the interplay between vibronic coupling and the photodetachment dynamics. Transitions to the neutral first excited states are also seen, with term energies of 0.95(5) eV and 1.257(4) eV for indenyl and fluorenyl, respectively. Those peaks are much wider than the experimental resolution, suggesting that nearby conical intersections must be considered to fully understand the vibronic structure of the neutral radicals.